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Detection and analysis of nucleic acids using nanometer-scale pores Nakane, Jonathan Jamie 2006

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DETECTION AND ANALYSIS OF NUCLEIC ACIDS USING NANOMETER-SCALE PORES By JONATHAN JAMIE N A K A N E B.A.Sc, The University of British Columbia, 2000 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY In THE FACULTY OF GRADUATE STUDIES (Physics) THE UNIVERSITY OF BRITSH COLUMBIA June 2006 © Jonathan Jamie Nakane, 2006 11 Abstract A d v a n c e s i n genomics and i n its appl icat ion to personal ized med ic ine have increased the demand for faster and cheaper methods o f nuc le ic ac id analysis techniques. Nanopore -based s ing le -molecu le detect ion schemes are except ional ly good candidates for n o v e l technologies to address this demand. Th is thesis presents the in i t ia l attempts and character izat ion o f two implementat ions o f the a lpha -h e m o l y s i n ( a H L ) protein nanopore as a nanosensor for the detection and analysis o f s ingle nuc le ic ac id molecu les . The two detection schemes address shortcomings i n present analysis techniques, and are dist inguished b y the mode o f molecu le capture and ident i f icat ion and b y the proposed appl icat ion. In the first method , s ingle-stranded D N A fragments are captured f r o m the b u l k solut ion on the cis-side o f the pore membrane, w i t h the resul t ing rate o f capture used as an electronic means o f measur ing l o c a l nuc le ic ac id concentrations, obv iat ing the need for optics or f luorescent mo lecu la r tags used dur ing convent ional D N A detection. E x p e r i m e n t a l results o f s ingle-stranded D N A fragment capture at h igh transmembrane potentials and an i m p r o v e d m o d e l o f molecu le capture from the b u l k so lut ion show that nanopore capture rates m a y be a v iab le method o f est imat ing nuc le ic ac id concentrations. In the second method, the a H L pore is used i n conjunct ion w i t h a synthetic probe mo lecu le to capture ind i v idua l s ingle stranded D N A molecu les on the trans-side o f the membrane to per fo rm s ing le -mo lecu le hybr id i za t ion and force -d issoc iat ion experiments. Exper imenta l results demonstrate that ensemble measurements can be used to measure the kinet ics o f hybr id i za t ion and dissociat ion o f single molecu les o f nuc le ic acids h y b r i d i z i n g to the probe molecu le , w i t h s ing le -molecu le sensi t iv i ty and s ingle -nucleot ide speci f ic i ty . The detection o f molecu les across a membrane us ing force -d issoc iat ion techniques shows potent ial i n use for the next generation o f instrumentation for genomics and potent ia l ly for in vivo, rea l - t ime detection o f b iomolecu les . C o n t e n t s A B S T R A C T II C O N T E N T S I l l L I S T O F T A B L E S V I L I S T O F F I G U R E S VII A C K N O W L E D G E M E N T S X C H A P T E R 1 I N T R O D U C T I O N 1 1.1 THE NEED FOR IMPROVED NUCLEIC ACID ANALYSIS TOOLS 2 1.2 SINGLE-MOLECULE TECHNIQUES 3 1.3 NANOPORES FOR SINGLE-MOLECULE NUCLEIC ACID DETECTION 4 1.4 THESIS OUTLINE 9 C H A P T E R 2 O S - S I D E M O L E C U L E C A P T U R E A N D A N A L Y S I S 11 2.1 INTRODUCTION ; 1 2 2.1.1 Conventional nucleic acid detection for sequence analysis 12 2.1.2 Nanopores for estimating nucleic acid concentration 13 2 . 2 EXPERIMENTAL PROTOCOL 1 4 2 .3 EXPERIMENTAL RESULTS 1 6 2.3.1 Capture time distribution 16 2.3.2 Concentration dependence 18 2.3.3 Length dependence 19 2.3.4 Dependence on applied potential 22 2 . 4 A MODEL FOR POLYMER CAPTURE 2 3 2.4.1 Shortcomings in existing models 23 2.4.2 A Hybrid Model of Polymer Capture 25 C o l l i s i o n Rate 2 6 S c a l i n g o f N u m e r i c a l S imu la t ion 2 7 N u m e r i c a l S i m u l a t i o n 3 0 2 .5 MODEL RESULTS AND DISCUSSION 3 3 2.5.1 Simulation results with varying ratio of capture radius to escape radius 33 2.5.2 Comparison with experimental results 35 2.5.3 Crossover potential 38 2.5.4 Concentration Measurement Performance 40 2.5.5 Further issues 42 IV 2.6 C H A P T E R S U M M A R Y 45 C H A P T E R 3 TRANS-SIDE M O L E C U L E C A P T U R E A N D A N A L Y S I S 47 3.1 INTRODUCTION 48 3.1.1 Shortcomings in existing genotyping detection methods 48 3.1.2 Shortcomings in existing in vivo detection methods 50 3.1.3 A trans-membrane nanosensor 57 3.2 E X P E R I M E N T A L M E T H O D 5 4 3.3 ESTIMATION OF EFFECTIVE C H A R G E A N D A P P L I E D F O R C E 57 3.3.1 Nanosensor probe effective charge 57 3.3.2 Applied forces 61 3.4 S I N G L E - M O L E C U L E HYBRIDIZATION KINETICS 6 2 3.5 S L N G L E - M O L E C U L E DISSOCIATION KINETICS 66 3.5.1 Dissociation models 66 Two-state Trans i t ion M o d e l 66 P a r a l l e l Two -Sta te Transi t ions, Same Init ial State 71 Para l le l Two -Sta te Transi t ions, Di f ferent Ini t ial States 72 Three-State Transi t ion 73 3.5.2 Experimental Results 76 Presence o f mul t ip le t imescales 76 Ident i f icat ion o f D o m i n a n t T imescales 78 C o m p a r i s o n o f Di f ferent M o l e c u l e s 82 Ion Current B l o c k a g e L e v e l 84 E n e r g y Bar r ie r Est imates 85 3.5.3 Effective barrier length scale 87 3.6 DISCUSSION 89 3.6.1 Physical modifications to nanosensor 89 3.6.2 Modifications to nanosensor protocol 91 3.6.3 Biologically relevant interactions 92 3.6.4 In vivo applications : 92 3.6.5 Further issues 94 3.7 C H A P T E R S U M M A R Y 96 C H A P T E R 4 C O N C L U S I O N S 97 B I B L I O G R A P H Y 101 A P P E N D I X A E X P E R I M E N T A L M A T E R I A L S , I N S T R U M E N T A T I O N , A N D D A T A A C Q U I S I T I O N 117 A . 1 A L P H A - H E M O L YSIN PROTEIN 117 A . 2 PHOSPHOLIPID B I L A Y E R 120 A . 3 SUPPORTING EQUIPMENT 122 A P P E N D I X B A H L F O R N U C L E I C A C I D D E T E C T I O N 125 B. 1 S E M I N A L EXPERIMENTS 125 B . 2 SEQUENCE DETERMINATION FROM CURRENT SIGNATURE 127 B . 3 N A N O P O R E UNZIPPING 128 B . 4 H A I R P I N STRUCTURES 129 V B . 5 MODIFIED A H L 130 B . 6 O T H E R N O T A B L E A H L EXPERIMENTS 131 A P P E N D I X C S Y N T H E T I C N A N O P O R E S 132 C . 1 T R A C K - E T C H E D M E M B R A N E S 132 C . 2 N A N O P O R E S FROM SEMICONDUCTOR FABRICATION TECHNIQUES 133 A P P E N D I X D I N V A L I D I T Y O F C O N T I N U U M A P P R O A C H E S F O R N U C L E I C A C I D C A P T U R E 136 A P P E N D I X E E F F E C T I V E C H A R G E O F S I N G L E - S T R A N D E D D N A T R A P P E D I N S I D E N A N O P O R E S 141 A P P E N D I X F R E G I M E O F V A L I D I T Y F O R C O L L E C T E D D A T A 145 F . l C A P T U R E R A T E LIMITATIONS DUE TO LOWPASS FILTERING 145 F . 2 E X A M I N A T I O N OF R E L E V A N T TIMESCALES 147 F .3 PORE GATING 148 A P P E N D I X G T I M E - V A R Y I N G A P P L I E D P O T E N T I A L S F O R D U P L E X D I S S O C I A T I O N 151 VI List of Tables T A B L E 2-1 - P A R A M E T E R S USED FOR COMPUTER SIMULATION 32 T A B L E 3-1 - SEQUENCES A N D BINDING ENERGIES OF MOLECULES USED IN THIS STUDY. BINDING ENERGIES WERE C A L C U L A T E D USING THE M F O L D DNA HYBRIDIZATION SERVER. N U C L E O T I D E VARIATIONS FROM THE PERFECTLY C O M P L E M E N T A R Y SEQUENCE A R E HIGHLIGHTED. C A L C U L A T I O N S WERE CARRIED AT 20 °C ASSUMING 1 M N A C L 55 T A B L E 3-2 - V A L U E S USED TO ESTIMATE REACTION BARRIER WIDTH 87 T A B L E 0-1 - P A R A M E T E R S FOR TYPICAL TEST CONDITIONS FOR C/S-SIDE M O L E C U L E CAPTURE 138 Vll List of Figures FIGURE 1.1 - S C H E M A T I C OF N ANOPORE CAPTURE OF M O L E C U L E S IN THE B U L K SOLUTION (LEFT). G E N E R A L I Z E D T R A N S M E M B R A N E IONIC CURRENT AS MOLECULES TRANSLOCATE THROUGH THE NANOPORE A T CONSTANT APPLIED POTENTIAL (RIGHT) 5 FIGURE 1.2 - (A) T H E A H L PROTEIN PORE, AS INFERRED FROM CRYSTALLOGRAPHIC ANALYSIS (B) THE A H L PORE, IN CROSS-SECTION. FIGURES EXCERPTED FROM SONG ETAL. [42] COPYRIGHT 1996 A A A S . . . . . 7 FIGURE 1.3 - G E N E R A L EXPERIMENTAL APPARATUS WITH A H L INSERTED INTO A LIPID BILAYER M E M B R A N E FOR IONIC CURRENT DETECTION .. 7 FIGURE 2.1 - SCHEMATIC OF TRADITIONAL LASER-INDUCED FLUORESCENCE DETECTION (LEFT) A N D NANOPORE-BASED CONCENTRATION DETECTION (RIGHT) DURING C A P I L L A R Y ELECTROPHORESIS 14 FIGURE 2.2 - SCHEMATIC DEPICTING TCAPTURE A N D TBLOCK DURING B L O C K A G E EVENTS 16 FIGURE 2.3 - L O G - L I N E A R PLOT OF HISTOGRAMS OF TCAPTURE FOR P O L Y ( D A ) 5 0 A T 1 2 0 M V A N D 3 4 0 M V , BOTH A T 2 u M CONCENTRATION 17 FIGURE 2.4 - CONCENTRATION VERSUS NORMALIZED CAPTURE RATE FOR P O L Y ( D A ) 5 0 M O L E C U L E S FOR APPLIED POTENTIALS F R O M IOOMV (BOTTOM) TO 3 4 0 M V ( T O P ) , IN 2 0 M V STEPS 18 FIGURE 2.5 - N O R M A L I Z E D CAPTURE RATE VERSUS APPLIED POTENTIAL FOR P O L Y ( D A ) 5 0 MOLECULES 19 FIGURE 2.6 - CAPTURE RATE FOR P O L Y ( D A ) 5 0 A N D P O L Y ( D A ) 1 0 MOLECULES A T 0.4 u M 20 FIGURE 2.7 - M E A S U R E D CAPTURE RATE OF 0.4 u M P O L Y ( D A ) 1 0 AT V A R Y I N G FILTERING / SAMPLING RATES (10 K H Z FILTER / 50 K H Z S A M P L E , 100 K H Z FILTER / 333 K H Z SAMPLE) 21 FIGURE 2.8 - M E A S U R E D CAPTURE RATE OF 0.4 \xM P O L Y ( D A ) 5 0 A T V A R Y I N G FILTERING / SAMPLING RATES (10 I<HZ FILTER / 50 K H Z S A M P L E , 100 K H Z FILTER / 333 K H Z SAMPLE) 21 FIGURE 2.9 - T H E O V E R A L L CAPTURE RATE RTOT(V) CONSISTS OF THE COLLISION RATE OF MOLECULES DIFFUSING IN FREE SOLUTION WITH A CAPTURE HEMISPHERE OF RADIUS A, RCOLUSION(A) (LEFT), MULTIPLIED B Y THE PROBABILITY OF CAPTURE A T A GIVEN APPLIED POTENTIAL V A N D DISTANCE A, PTOT(V, A) (RIGHT) 26 FIGURE 2.10 - G R A P H I C A L REPRESENTATION OF RELATION B E T W E E N PTOT A N D PSIMFOR A GIVEN ESCAPE A N D CAPTURE RADII A, B 29 FIGURE 2 . 1 1 - R A T E OF CAPTURE FROM DIFFERENT START RADII WITH THE ESCAPE RADIUS A N D T R A N S M E M B R A N E POTENTIAL HELD CONSTANT (5=1 5 N M , F = 3 4 0 M V ) . D A S H E D LINE INDICATES EXPERIMENTAL CAPTURE RATE OF 20.5 H z / u M 34 Vll l FIGURE 2 . 1 2 - R A T E OF CAPTURE FROM DIFFERENT START RADII WITH THE ESCAPE RADIUS A N D T R A N S M E M B R A N E POTENTIAL HELD CONSTANT (5=1 5 N M , F = 9 0 0 M V ) 35 FIGURE 2.13 - M O D E L PREDICTION VERSUS EXPERIMENTAL D A T A FOR THE PROBABILITY OF CAPTURE OF P O L Y ( D A ) 5 0 36 FIGURE 2 . 1 4 - M O D E L PREDICTION FOR P O L Y ( D A ) 5 0 AT POTENTIALS GREATER T H A N THOSE ACHIEVED DURING EXPERIMENTS WITH THE A H L PORE 37 FIGURE 2.15 - S IMULATION RESULTS VERSUS EXPERIMENTAL RESULTS FOR P O L Y ( D A ) 1 0 38 FIGURE 3.1 - S C H E M A T I C OF THE MAJOR COMPONENTS OF THE T R A N S M E M B R A N E NANOSENSOR 52 FIGURE 3.2 - I O N I C CURRENT A N D APPLIED T R A N S M E M B R A N E POTENTIAL DURING PROBE CAPTURE, A N A L Y T E CAPTURE A N D DISSOCIATION ... 56 FIGURE 3.3 - M E A N PROBE ESCAPE TIME VERSUS APPLIED T R A N S M E M B R A N E POTENTIAL. A CLOSE-UP OF THE LOW-POTENTIAL DATA IS SHOWN IN THE INSET 58 FIGURE 3 . 4 - I L L U S T R A T I O N OF THE REGIONS OF NUCLEOTIDES ON THE TRANS-SIDE OF THE PORE 60 FIGURE 3.5 - SCHEMATIC OF THE APPLIED T R A N S M E M B R A N E POTENTIAL A N D RESULTING IONIC CURRENT DURING SINGLE-MOLECULE HYBRIDIZATION RATE EXPERIMENTS, HIGHLIGHTING THE EXPOSURE TIME OF THE PROBE M O L E C U L E TO THE TRANS-S\DE, TH0LD 63 FIGURE 3.6 - P R O B A B I L I T Y OF BINDING FOR SINGLE-MOLECULE HYBRIDIZATION OF 14PM M O L E C U L E AT 0.5 MM. T H E LINE INDICATES THE EXPONENTIAL FIT TO THE EXPERIMENTAL DATA 64 FIGURE 3.7 - S C H E M A T I C ILLUSTRATION OF THE BARRIER A N D REACTION COORDINATE DURING PROBE-TARGET DISSOCIATION 69 FIGURE 3.8 - S C H E M A T I C ILLUSTRATION OF THE DUPLEX A N D TWO POSSIBLE STATES AT THE P E A K OF THE ENERGY BARRIER 69 FIGURE 3.9 - PROBABILITY DISTRIBUTION OF DISSOCIATION TIMES B(T) FOR 14PM M O L E C U L E A T - 7 0 M V 77 FIGURE 3 .10 - N O R M A L I Z E D HISTOGRAM OF DISSOCIATION TIMES B(T) FOR 14PM M O L E C U L E AT - 7 0 M V 77 FIGURE 3.11 - H I S T O G R A M OF RANDOMNESS PARAMETER V A L U E S ACROSS A L L FOUR TARGET M O L E C U L E S A T A L L APPLIED POTENTIALS (LEFT). E X P A N D E D VIEW OF HISTOGRAM FOR RANDOMNESS PARAMETERS BELOW 4 INDICATES O N L Y 4 DATA POINTS OUT OF 42 ( - 1 0 % ) HAD R < 1 78 FIGURE 3 . 1 2 - T I M E SCALES AJ FOR 7C AT - 5 5 M V (A) A N D 14PM A T - 5 5 M V (B) 80 F IGURE 3.13 - C O M P L E T E DISSOCIATION TIME SCALES AJ FOR 10C M O L E C U L E A T VARIOUS APPLIED POTENTIALS. T H E DIAMETER OF E A C H SPOT INDICATES THE RELATIVE MAGNITUDE OF THE TIMESCALE. POINTS BELOW THE DOTTED LINE WERE CONSIDERED SPURIOUS A N D IX WERE NOT INCLUDED IN THE WEIGHTED AVERAGING TO GENERATE T off 81 FIGURE 3 .14 - AVERAGE MEASURED EVENT LIFETIMES EXTRACTED FROM NON-NEGATIVE LEAST SQUARE ERROR FITS TO PESC(T) FOR ALL FOUR FIGURE 3.15 -AVERAGELOCKAGE CURRENT VERSUS DISSOCIATION TIME FIGURE 3 .16 -CORRELATION BETWEEN MFOLD ENERGIES AND D N A BINDING INTERCEPT. INCLUDED ARE THE SLOPES AND INTERCEPTS FROM THE FORCE-DISSOCIATION CURVES SHOWN IN FIGURE 3.14.... 86 FIGURE A . l - GENERAL EXPERIMENTAL APPARATUS WITH A H L INSERTED INTO A LIPID BILAYER MEMBRANE FOR IONIC CURRENT DETECTION FIGURE A . 2 -CALCULATED CONCENTRATION OF AN ABSORBING PORE ALONG THE PORE AXIS USING CONSTANTS LISTED IN TABLE 2-1.. . . 139 FIGURE A . 3 - TIME BETWEEN INDUCED GATING EVENTS VERSUS APPLIED NEGATIVE TRANSMEMBRANE POTENTIAL FOR THE A H L PORE IN 1 M MOLECULES 83 FOR IOC MOLECULE AT - 5 5 M V 85 123 K C L 150 X Acknowledgements M a n y thanks to m y graduate research supervisor A n d r e M a r z i a l i for h is t ime and guidance throughout m y late undergraduate and graduate years at U B C . M a y other students invo l ved in research at the univers i ty be as fortunate as I have been to w o r k alongside a supervisor w i t h the k i n d o f insight, intel lectual s t imulat ion, creativity and endless support that he has p rov ided both i n his lab and n o w i n his ro le as D i rec tor for the Eng ineer ing Phys ics program. It has been m y pleasure, and I a m eternal ly grateful . Thanks to M a r k A k e s o n , D a v i d Dearner, W e n o n a h Vercoutere , and V e r o n i c a d e G u z m a n at U C Santa C r u z for f ru i t fu l d iscussions o n nuc le ic ac id interactions w i t h nanopores, and for their guidance dur ing our in i t ia l exper imental w o r k w i t h the a lpha -hemolys in pore. Thanks to M a t t h e w W i g g i n for our shared successes and fut i l i t y dur ing nanopore - format ion , exper imental gathering, data analysis sessions, and discussions on nuc le ic ac id -pore interactions. Thanks to those that have contr ibuted to nanopore exper imental and computat ional approaches over the years i n the M a r z i a l i lab: C a r l Hansen , M i r i a m T o r c h i n s k i , Tudor Cos t in , D a n Green , A v i v Keshet , S i b y l Dr iss ler , N i c k F a m e l i , Dhtrut i T r i ved i , N a h i d Jetha and C a r o l i n a T r o p i n i have a l l made thoughtful contr ibutions to our efforts to probe the w o r l d o f the very s m a l l . Thanks to the m a n y other students and researchers that have passed through the M a r z i a l i lab and w i t h w h o m I have shared i n the experience: Steve C h o w , A z i e n Safarpour, D a v e B r o e m e l i n g , P h i l Dext ras , K u r t i s Guggenheimer , Jason T h o m p s o n , N e h a Shah , Joe l P e l , T revor P u g h , K e d d i e B r o w n , and the m a n y others that have passed through the lab. x i Thanks to Robin Coope for enlightening discussions, friendship, and five years in one shared office. Thanks to the undergraduate students of the U B C Engineering Physics program - 1 have had the great fortune of supervising five years of students through Physics 253, and look forward to my continued involvement with the students and program through the Engineering Physics Project Lab. Their efforts serve as a constant reminder to me of how much a small group of people with the right balance of talent, motivation, and resources can accomplish. Thanks to my thesis committee members for their time and guidance throughout this intellectual pursuit: Jeff Young, Steve Plotkin, and John Hobbs have all been valuable guides in my academic and research endeavours. Thanks to my family - Arlene and Mits Nakane, Marcia and Wayne Tamagi, K y r a and Avery, my aunts, uncles and cousins - I love you all very much. Jon Nakane June 2006 Chapter 1: Introduction 1 Chapter 1 Introduction Chapter 1: Introduction 2 1.1 The Need for Improved Nucleic Acid Analysis Tools The large amount o f nuc le ic ac id sequence in format ion resul t ing from the H u m a n G e n o m e Project [ 1 , 2 ] has generated great demand for further development o f rap id and inexpensive nuc le ic ac id detect ion and sequencing methods. F o r example , developments i n the funct ional analysis o f the h u m a n genome and its under l y ing genetic regulatory network w o u l d be greatly accelerated b y the ava i lab i l i t y o f D N A sequence in fo rmat ion f r o m organisms o f va ry ing evolut ionary p r o x i m i t y to humans [3]. A t present, the f inancia l cost o f sequencing a m a m m a l i a n genome de novo (~3 b i l l i o n nucleot ide pairs) us ing standard Sanger sequencing methods [4] is at least $10 m i l l i o n [5]. M u c h o f the cost for b i o m o l e c u l a r analysis is expended i n sample preparation pr io r to analysis : ampl i f i ca t ion , pur i f i cat ion and fluorescent labe l ing is requi red to prov ide suff ic ient reagent to achieve acceptable s ignal - to -no ise and spec i f ic i ty for the major i ty o f c o m m o n b iomolecu le detection schemes [4]. W i t h this i n m i n d , any D N A analysis method w h i c h can detect un label led molecu les or w h i c h is capable o f detecting trace quantit ies w i t h h igh spec i f ic i ty is h i g h l y compe l l i ng . Improvements i n D N A analysis methods w i l l also a id i n a l l o w i n g c l in ic ians to use sequence and genotype data assessed f r o m i n d i v i d u a l patients to design and prescribe speci f ic treatment protocols [6]. A t present, personal i zed genomic analyses and treatments for spec i f ic disease markers are not w i d e l y used due to the lack o f appropriate technology for t i m e l y and cost -effect ive testing. F o r c l in ic ians to ga in da i l y and rap id access to genome analysis tools , the cost o f instrumentat ion, disposables and labour for genetic analysis must be greatly reduced. Chapter 1: Introduction 3 A t a more fundamental leve l , there is an unmet demand for technologies that w i l l a l l o w ce l l b io logists to elucidate the internal mechanisms o f l i v i n g cel ls . M o s t exist ing b i o m o l e c u l e techniques require sample harvested f r o m large numbers (10,000+) o f lysed ce l ls i n order to achieve reasonable signals. Th is obscures both the inherent popu lat ion heterogeneity as w e l l as the real - t ime dynamics o f ce l lu lar s ignal propagat ion pathways and regulatory networks. In vivo measurement techniques are avai lable us ing f luorescent probes either genet ical ly or external ly introduced into ind i v idua l cel ls [7-10] for t rack ing the concentrat ion o f molecules i n various internal regions. H o w e v e r , these are h igh l y perturbative methods where the probe molecu les m a y unintent ional ly b i n d to funct ional regions o f the proteins o f interest and m a y miss more subtle conformat ion or c h e m i c a l changes such as phosphory lat ion that dr ive ce l l mechanisms and s ignal propagat ion pathways. Techniques able to detect shor t - l i ved changes i n spec i f ic b iomolecu le concentrations without the use o f f luorescent labe l ing or genetic m o d i f i c a t i o n w o u l d be o f great ut i l i t y to researchers p rob ing the dynamics o f single l i v i n g cel ls . 1.2 Single-Molecule Techniques The demands for reduced b iomolecu le detection costs, h igher sensit iv i ty , increased temporal resolut ion, and the poss ib i l i t y o f in vivo detect ion are d r i v ing forces behind research i n s ing le -molecu le analysis methods [11]. M a n y s ing le -molecu le methods do not require labe l ing target molecu les w i t h fluorescent or radioact ive tags w h i c h m a y both s i m p l i f y analysis protocols and reduce reagent costs. S ing le mo lecu le techniques w i t h adequate sensit iv i ty m a y a l l o w for detection o f trace amounts o f speci f ic b iomolecu les i n the presence o f other molecu les , w h i c h m a y reduce preparation and pur i f icat ion costs w h i l e uncover ing molecu la r properties t yp ica l l y h idden b y ensemble averaging i n convent ional measurements. Informat ion can be obtained o n b i n d i n g and d issoc iat ion kinet ics between ind iv idua l nuc le ic acids, proteins and other b iomolecu les [12], w h i c h can i n turn be used to give insight to the funct ional and structural interactions w h i c h occur in vivo, and lead to Chapter 1: Introduction 4 i m p r o v e d instrumentation i n genomics and c l i n i c a l appl icat ions w h i c h explo i t these interactions. M a n y s ing le -molecu le analysis techniques are current ly under research: opt ical tweezers and traps [13-17] , a tomic - force m i c r o s c o p y [18 -20] , magnet ic tweezers [21-23] , b iomembrane force probes [24], steady shear f l o w [25], osc i l la t ing n o n - u n i f o r m electr ic f ie lds [26], s ing le -molecu le f luorescence detection [27 -30] , Forster resonance energy-transfer ( F R E T ) probes [31], capi l la ry electrophoresis separation w i t h single molecu le detection [32, 33] , and combinat ions o f opt ica l t rapping and mechan ica l actuators [34] have a l l been used to detect and manipulate i n d i v i d u a l molecules to elucidate interactions i n v o l v i n g D N A [12], R N A [34], and proteins [35]. The techniques used i n this invest igat ion are based o n nanopore detection o f single molecu les [36], w h i c h have a number o f d is t inguish ing characteristics m a k i n g them excel lent candidates for instrumentation in high-throughput genomics w o r k , non- f luorescent nuc le ic ac id detection, and in vivo s ingle c e l l work . 1.3 Nanopores for Single-Molecule Nucleic Acid Detection The general term "nanopore" refers to pores o f nanometer -scale diameter i n th in membranes. S u c h pores are either t ransmembrane protein channels found i n ce l l and nuclear membranes, or synthet ical ly fabricated pores fo rmed i n t h i n - f i l m dielectr ic materials . In the m i d -1990s it was demonstrated that ind i v idua l charged nuc le ic ac id molecu les i n free solut ion cou ld be isolated and loca l i zed i n a b i o l o g i c a l nanopore under an external ly -appl ied transmembrane potent ia l , result ing i n eventual translocation through the nanopore f r o m one side o f the membrane to the other [37]. D u r i n g this translocation event, measurements o f the appl ied potential , ion ic current, and durat ion o f the Chapter 1: Introduction 5 blockage can be used to infer structural or chemica l details o f the translocat ing molecu le , as shown schematical ly i n F igure 1.1. I -1 + I - fM&*htoiMfa - f t * * W « * Open-channel current Blocked-channel current time Figure 1.1 -Schematic of nanopore capture of molecules in the bulk solution (left). Generalized transmembrane ionic current as molecules translocate through the nanopore at constant applied potential (right). Several characteristics make proteinaceous nanopores very attractive for use i n s ing le -molecu le detect ion exper iments. Proteinaceous nanopores produced through genetic expression i n b i o l o g i c a l cel ls have a f idel i ty and reproducib i l i ty on the sub-nanometer scale far beyond any present synthetic fabr icat ion techniques. The charge and chemica l groups l i n i n g the inside o f the pore m a y interact strongly w i t h organic molecules such as nucle ic ac ids , s l o w i n g d o w n translocat ion ve loc i ty enough to a l l o w ind iv idua l molecu les to be ident i f ied i n the ion ic current signature over the measurement noise. Some classes o f b i o l o g i c a l nanopores can also self - insert into l i p i d b i layers , a property explo i ted by researchers to per form s ing le -molecu le detect ion experiments [36, 3 8 - 4 1 ] . In such experiments, b i o l o g i c a l pores have been chosen w i t h inner diameters comparable to m o n o m e r units o f l inear b i o l o g i c a l po lymers such as nuc le ic acids or proteins; i n this w a y , i n d i v i d u a l po l ymer molecules are forced to travel i n s ing le - f i le fash ion through the pore under an appl ied transmembrane potent ial , as shown i n F igure 1.1. Chapter 1: Introduction 6 Ef for ts i n nanopore-based nuc le ic ac id sensors have p r i m a r i l y used the a - h e m o l y s i n ( a H L ) channel , a heptameric protein channel produced b y the bacter ia Staphylococcus aureus. The structure o f a H L has been revealed b y crystal lography to 1.9 A resolut ion as s h o w n i n F igure 1.2 [42]. The aqueous channel contained i n the pore extends across the 1 0 - n m long protein and is composed o f a 2.6 n m diameter entrance, a 4.6 n m m a x i m u m diameter vest ibule, a 1.4 n m diameter l i m i t i n g aperture, f o l l o w e d b y a 5 n m long beta-barrel stem approx imate ly 2 run i n diameter. The exper imental setup for the pore inserted into an art i f ic ia l l i p i d b i layer membrane is s h o w n i n F igure 1.3. A p p e n d i x A gives a more detai led overv iew o f the a H L pore, the support ing l i p i d b i layer , and the exper imental apparatus used to f o r m single nanometer -scale channels for nuc le ic ac id analysis . E a r l y exper imental w o r k w i t h a H L [37] demonstrated that w i t h this pore inserted i n an art i f ic ia l ly fo rmed l i p i d b i layer , s ingle-stranded nuc le ic acids i n free solut ion on either the cis or trans-sides o f the pore 1 c o u l d be made to translocate across the channel under a constant appl ied transmembrane electr ic potential , as shown i n the exper imental setup i n F igure 1.3. D u r i n g translocation, i nd i v idua l s ingle-stranded nuc le ic ac id fragments b l o c k the passage o f electrolyte ions, resul t ing i n a measurable change i n the channel current (>80% reduction). E v e n more impress ive is that the size o f the beta-barrel stem o f the pore can be used to dist inguish single-stranded and double-st randed nuc le ic acids. The beta barrel and l i m i t i n g aperture o f the pore ster ical ly prevents double-stranded nuc le ic acids f r o m pass ing through, as the doub le -he l i x has a diameter ~ 2.0 n m . O n the other hand, s ing le -stranded nuc le ic acids w i t h a diameter ~ 1 . 2 n m are smal l enough to translocate through the pore i n a l inear fashion. Th i s sub-nanometer di f ference i n size between the single and double-stranded diameters o f the nuc le ic acids can be used to select ively f i l ter s ingle-stranded nuc le ic 1 cis and trans refer to the side of the membrane which the proteinaceous aHL pore self-inserts into the membrane. By convention, the as-side is the side of die membrane into which the protein was inserted, and which has the larger vestibule opening. Chapter 1: Introduction 7 acids from a mix of single and double-stranded fragments in solution under an applied transmembrane potential [37]. B c/s-side entrance vestibule limiting aperture beta-barrel frans-side entrance Figure 1.2 - (a) The a H L protein pore, as inferred from crystallographic analysis (b) the a H L pore, in cross-section. Figures excerpted from Song et al. [42] Copyright 1996 A A A S . Figure 1.3 - General experimental apparatus with a H L inserted into a lipid bilayer membrane for ionic current detection Limited information about the sequence composition of single-stranded nucleic acids can be obtained from ensemble measurements of the average blockage duration and blockage current over a population of identical molecules [44, 45]. For example, two populations of long (~50 bases) homopolymer strands composed of different nucleotides can be Chapter 1: Introduction 8 dist inguished f r o m one another (e.g. s ingle-stranded R N A fragments poly(A)5o versus poly(C)5o), though stochastic spread i n the average values o f b lockage duration and channel current prevent def in i t i ve c lass i f icat ion o f any ind i v idua l molecu le f r o m a single i o n current signature. Observat ion o f the b lockage current dur ing a s ingle b lockage can be used to detect the transit ion o f b l o c k h o m o p o l y m e r sequences at least ~30bp l o n g w i t h i n longer strands. Other characterist ics, such as nuc le ic ac id degradation due to phosphory lat ion, incomplete synthesis, or other chemica l hand l ing and storage issues have also been detected us ing i o n current measurement [46]. A p p e n d i x B contains further d iscussions o n seminal experiments for nuc le ic ac id analysis w i t h the a H L pore. A l t h o u g h the results o f studies o f nuc le ic ac id analysis us ing nanopores have i n the past raised prospects for D N A sequencing d i rect ly f r o m the i o n current b lockage signatures [47], accurate determinat ion o f i n d i v i d u a l bases based on i o n current measurements alone either w i t h a b i o l o g i c a l nanopore or w i t h synthetic membranes is u n l i k e l y to be feasible. A l t h o u g h the transitions between different h o m o p o l y m e r regions have been detected [44], the modulat ion for the change o f a single nucleot ides w i t h i n a sequence is swamped b y the k n o w n noise levels us ing contemporary i o n current measur ing techniques. A l s o , the thermal m o t i o n o f a D N A molecu le passing through a c y l i n d r i c a l pore under an appl ied electr ic potential as investigated b y computer s imulat ions indicate that D N A translocat ion invo lves frequent " b a c k w a r d " m o t i o n o f D N A i n the pore, even w i t h an appl ied electr ic potent ial [48]. Th is reverse mot ion can be mit igated w i t h h igher transmembrane potentials, w h i c h then results i n m u c h higher t ranslocat ion rates, exacerbating the d i f f i cu l ty o f measur ing base -spec i f ic f luctuations i n the ion ic current dur ing translocation. T h o u g h direct sequence measurement or nucleot ide count ing us ing nanopores m a y one day be poss ib le , it must occur either b y opt ica l l y or e lect r ica l ly m o n i t o r i n g some aspect o f the translocation process other than the i o n current signature, by int roducing a m e c h a n i s m for cont ro l lab ly decreasing the translocation rate by several orders o f magnitude under Chapter 1: Introduction 9 h igh electr ic f i e ld , or by some other means o f ef fect ive ly c o m b i n i n g ensemble measurements o f the i o n current s ignal . W i t h these properties and shortcomings i n m i n d , nanopores can be used i n the near - term in a variety o f conf igurat ions for gathering usefu l in format ion about ind iv idua l b iomolecu les , such as: Cou l te r counters for enumerating the number o f molecu les passing through a pore [38, 4 0 , 4 9 ] ; selective size f i l t rat ion [50, 51] ; a means o f a f f in i ty -based select ion [52] ; as a conduit for sensitive s ingle mo lecu le pos i t ion and conformat ion detection [53, 54] ; a means o f mo lecu le loca l i za t ion w i t h i n a 2 - d plane for s ing le -molecu le f luorescence or other detect ion scheme [55, 56] ; and i n combinat ion w i t h f luorescence or other detect ion schemes for serial l inear process ing o f po l ymer molecu les [47]. A l l o f these techniques a l l o w for rea l - t ime d isc r iminat ion o f molecu les or mo l ecu l e populat ions, and i l lustrate the poss ib i l i t y o f us ing nanopores as the basis o f s ing le -molecu le instrumentation development. 1.4 Thesis Outline Th is dissertation presents the invest igat ion o f two nanopore-based detection schemes for nuc le ic acids w h i c h take advantage o f the unique characteristics o f nanopores to address speci f ic shortcomings i n present nuc le ic ac id analysis techniques. The rationale and mot i va t ion for pursu ing each scheme w i l l be discussed, a long w i t h descr ipt ions o f the exper imental method , results, and a theoretical analysis o f the mechan isms and l imitat ions o f each part icular scheme. Chapter 2 describes a method o f us ing nanopores for measur ing the l o c a l concentrat ion o f nuc le ic acids based on the rate o f capture f r o m the b u l k so lut ion on the cis-side o f the pore. Th is method is intended to be a h i g h l y sensit ive replacement for opt ica l exc i tat ion or absorbance detection methods c o m m o n l y used i n D N A analysis and sequencing. Th i s appl icat ion w o u l d a l l o w for the replacement o f opt ica l laser induced f luorescence or absorbance equipment w i t h nanopore-based detect ion schemes. Feas ib i l i t y o f this scheme depends o n ach iev ing suf f ic ient ly h igh molecu le capture rates us ing appl ied potentials larger than those Chapter 1: Introduction 10 documented in the existing literature. Results from experimental work with the a H L pore and single-stranded D N A molecules at the highest transmembrane potentials supported by biological pores w i l l be presented. A n improved model of molecule capture from bulk solution combining analytic estimates with a computational model w i l l also be discussed. Chapter 3 describes a novel nanosensor used for sequence-specific detection of short nucleic acid fragments across a l ipid membrane, with single-molecule sensitivity. This method can achieve high levels of specificity between the probe and target molecules and allows for the discrimination of different types of target molecules based on dissociation kinetics. Though the transmembrane nature of the nanosensor offers the possibility of in vivo applications, it can also be used to directly measure the kinetics of single molecules of nucleic acids hybridizing to the probe molecule, with sensitivity and specificity not found in any conventional single-molecule technique but which have only recently been achieved by nanofabricated resonators [57]. Results from experimental work with the transmembrane nanosensor and various target molecules w i l l be presented, as well as the theoretical analysis for hybridization and dissociation measurements, and a discussion of practical applications. Chapter 2: Cis-side molecule capture and analysis 11 Chapter 2 Cis-side Molecule Capture and Analysis Chapter 2: Cis-side molecule capture and analysis 12 2 . 1 Introduction Th is chapter examines the feasib i l i ty o f est imating the concentrat ion o f nuc le ic acids b y measur ing the rate o f i o n conductance b lockages under an appl ied transmembrane potential . Th i s method is intended to be a h igh l y sensit ive and spatial ly loca l i zed analog to the laser induced f luorescence detection methods c o m m o n l y used i n D N A analysis and sequencing. The mot ivat ion and rationale for this method , exper imental results and analysis , a hybr id m o d e l for est imating the rate o f capture o f po lymers f r o m the b u l k solut ion, and a b r ie f descr ipt ion o f pract ica l appl icat ions are discussed. 2.1.1 Conventional nucleic acid detection for sequence analysis C a p i l l a r y E lectrophoresis ( C E ) is a wel l -es tab l ished technique for separation o f nuc le ic acids based on fragment s ize, and is w i d e l y used for D N A sequencing and f ingerpr int ing [4]. Widespread implementat ion o f C E devices for areas such as sequencing o f organisms o f b i o l o g i c a l and env i ronmental interest and c l in i ca l screening o f m e d i c a l patients is h indered b y the capital cost o f detection equipment. E f for ts to reduce instrumentat ion s ize, complex i t y and cost are negated i n part b y the laser induced f luorescence (L IF ) optics required for analyte detect ion, as w e l l as requi r ing analyte molecules to be f luorescent ly tagged. Increased para l le l i sm and data throughput through the use o f min ia tur i zed and poss ib l y d isposable C E devices w i l l require size and cost reduct ion o f both the C E separation and detection system. T h o u g h progress has been made i n on -ch ip integration o f f luorescence detection [58], alternative detection techniques m a y be one avenue for pursu ing the product ion o f inexpensive , d isposable, and h igh l y paral le l ch ip -based electrophoresis systems. Chapter 2: Cis-side molecule capture and analysis 13 2.1.2 Nanopores for estimating nucleic acid concentration Nanopores can conce ivab ly be used i n place o f L I F as a pure ly electronic means o f detecting and quant i fy ing nuc le ic acids or other b iomolecu les . A nanopore can be employed as a part icle counter b y measur ing the rate o f capture o f charged b iomolecu les under an appl ied transmembrane potent ial in a conf igurat ion s imi la r to the Cou l ter p r inc ip le [49] prev ious ly used for moni to r ing cel ls and other larger objects. In addi t ion to requi r ing no opt ical detection, laser exc i tat ion, or f luorescent labe l ing o f the b iomolecu les , the method becomes more eff ic ient overa l l as the sampled v o l u m e decreases, since o n l y analytes i n the v i c i n i t y o f the pore are sampled and contribute to the s ignal . In contrast, convent ional opt ical exci tat ion and f luorescence systems require a m i n i m u m number o f labeled molecules for detection above background noise and therefore require higher analyte concentrations to main ta in acceptable s ignal - to -no ise w i t h decreasing v o l u m e . A l t h o u g h h igh -per formance f luorescence detection systems can reach s ingle mo l e cu l e sensit iv i ty b y us ing evanescent wave techniques or other conf igurat ions to decrease the i m a g i n g v o l u m e [59], such techniques are impract ica l i n c o m m e r c i a l C E systems because o f the cost, complex i t y , l i m i t e d robustness o f such systems, and the d i f f i cu l t y i n para l le l i z ing such systems. A schematic o f a f luorescence detection system and a proposed nanopore-based detection scheme for C E is s h o w n i n F igure 2 .1 . N o t e that nanopore detection w o u l d not be expected to improve the resolut ion o f D N A sequencing over current techniques but w o u l d instead e l iminate components associated w i t h laser exci tat ion and opt ica l f luorescence detection w h i l e requi r ing comparable quantit ies o f nuc le ic acids. The w o r k presented herein describes the exper imental p rotoco l us ing the a H L protein channel and short s s D N A fragments as a m o d e l system for e x a m i n i n g the relat ionship between b lockage rate and exper imental condi t ions, and extrapolat ing those results to condi t ions amenable to future instrumentation us ing a synthetic pore w i t h s imi la r per formance characteristics. Chapter 2: Cis-side molecule capture and analysis 14 V D N A V D N A Photomultiplier Tube Figure 2.1 - Schematic of traditional laser-induced fluorescence detection {left) and nanopore-based concentration detection (right) during capillary electrophoresis 2.2 Experimental Protocol A l l experimental work presented here used the a H L protein channel reconstituted into a phosphatydylcholine lipid bilayer membrane; the experimental apparatus and protocol for incorporating aHL has been described in detail previously [36] and is included in Appendix A . Briefly, a lipid bilayer is formed across a -50 p. m hole in a Teflon tube which connects two reservoirs containing electrolyte buffer solution as the conducting medium. Each reservoir contains a silver chloride-coated electrode connected to a patch-clamp amplifier (Axopatch 200B, Axon Instruments, Foster City, C A ) . The pore is formed by addition of monomeric aHL to the electrolyte solution on one side of the bilayer, which defines the cw-side of the membrane; pore formation is detected by applying a lOOmV electric potential across the bilayer with the anode (positive electrode) on the trans-side of the membrane, and waiting for a stepwise increase in the measured current from OpA to ~100pA. The cis-side chamber is then quickly rinsed with fresh buffer solution to prevent formation of more than one pore. The ion current and applied transmembrane potentials are sampled by the data acquisition system (NI-DAQ card and L a b V I E W software, National Chapter 2: Cis-side molecule capture and analysis 15 Instruments, A u s t i n T X ) and stored to the hard dr ive o f a dedicated P C for later analysis . The cw -s ide capture experiments used s ingle-stranded h o m o p o l y m e r s o f deoxyadeny l ic ac id 50 bases and 10 bases l o n g (po l y (dA )50 and p o l y ( d A ) 1 0 , "respectively) . A l l samples were synthesized and ammonia -butano l pur i f ied w i t h no further pur i f i ca t ion steps ( M W G B i o t e c h , H i g h Po int N C ) . A n y w h e r e f r o m 2 to 10// L o f a 40 // M stock solut ion o f either o l igonucleot ide was added to the 200 // L cw -s ide chamber, m i x e d b y ref lux , and a l lowed to di f fuse for 5 minutes. Un less otherwise noted, a l l experiments were carr ied out at 20 .0 ± 0.5 °C i n 1 M K C l buffered w i t h l O m M H E P E S free ac id and l m M E D T A , then titrated w i t h 2 M K O H to p H 8.0. Constant transmembrane potentials ranging f r o m 60 to 340 m V were appl ied across the membrane to faci l i tate s s D N A capture and translocation. O n average - 5 0 0 unique translocat ion events were recorded at each transmembrane potential and concentrat ion. The chamber was a l lowed to sit for 10 m i n after each change i n po l ymer concentrat ion to reach equ i l i b r ium, and a pseudo-random order o f appl ied transmembrane potentials was used to mit igate any t ime-dependent effects. The ion ic current data was either low -pass f i l tered i n hardware b y the patch -c lamp ampl i f ie r at 10 k H z and sampled b y the data acquis i t ion system at 50 k H z , or low-pass f i l tered at 100 k H z and sampled at 333 k H z . A d iscuss ion on the effect o f low-pass f i l ter ing on the col lected data is inc luded i n A p p e n d i x F . l A n a l y s i s o f the i o n current and transmembrane potential was per formed us ing an automated event -ca l l ing a lgor i thm wri t ten i n the L a b V I E W p r o g r a m m i n g language to generate statistics f r o m al l b lockage events. B l o c k a g e events i n the ion ic current s ignal are s h o w n schemat ica l l y i n F igure 2.2. F o r each detected event, the durat ion o f the b lockage (t b l o c k) and the t ime f r o m the end o f one event to the beg inn ing o f the next event (t re) were recorded. The start o f an event was def ined as a reduct ion o f the ion ic current to b e l o w 80 percent o f the open-channel current (i.e. a 20 percent reduct ion i n current), and the end o f a b lockage event def ined as return o f the ion ic current to the mean open -channel value. The use o f two thresholds precludes i o n current Chapter 2: Cis-side molecule capture and analysis 16 noise dur ing a single event to be counted as several i nd i v idua l events. The use o f a threshold proport ional to the open-channel current has been used i n other exper imental setups [45, 60] , and a l lows the same protoco l to be appl ied irrespective o f the magnitude o f the transmembrane potent ial . current * capture tblock t ime Figure 2.2 - Schematic depicting tcaplare and tMock during blockage events 2.3 Experimental Results 2.3.1 C a p t u r e t i m e d i s t r i b u t i o n His tog ram analysis o f the capture t ime t l u r c d ist r ibut ion for both the 10 and 5 0 - m e r molecules y ie lds an exponential d ist r ibut ion, as shown i n F igure 2.3 for two representative potentials for the p o l y ( d A ) 5 0 molecu le . A n exponential d istr ibut ion is expected for a P o i s s o n process, p rov ided that the probabi l i ty o f interaction between ind i v idua l molecu les s imultaneously at the pore mouth is negl ig ib le . A l l subsequent analysis considers capture t ime distr ibutions as single exponentials , where the mean t imes to capture, tcaplure, is the inverse o f the b lockage rate. Chapter 2: Cis-side molecule capture and analysis 17 F o r the representative curves shown i n F igure 2 .3 , the mean t imes to capture were 380 ± 50ms at 120 m V and 25 ± 5ms at 3 4 0 m V , both at 2 p M . In compar ison , the mean molecu le translocat ion t ime ttram for the p o l y ( d A ) 5 0 molecu le is a m a x i m u m o f - 4 . 0 ± 0.5 m s at a l l appl ied potentials used for molecu le capture, i n agreement w i t h a theoret ical estimate o f - 0 . 1 5 Angstroms/ JLIS or ~ 1.3 ms for the 50-base molecu le at 120 m V [60]. A s the translocation t imes are never more than 4 percent o f t t u r e even at the highest transmembrane potentials and highest mo lecu le concentrations, the translocation t imes thlock were exc luded f r o m further analys is , and the rate o f capture R def ined as the inverse o f the mean t ime to capture, R = 1 /1 l u r e . 1 0.1 Normal i zed f r e q u e n c y 0 .01 0 . 0 0 1 2 0 0 4 0 0 6 0 0 time (ms) o 3 4 0 m V • 1 2 0 m V 8 0 0 1 0 0 0 Figure 2.3 - Log-linear plot of histograms ottcaplim for poly(dA)50 at 120mV and 340mV, both at 2uM concentration. Chapter 2: Cis-side molecule capture and analysis 18 2.3.2 Concentration dependence E m p i r i c a l data suggests that the capture rate is l inear ly dependent o n the nuc le ic ac id concentrat ion, as demonstrated b y the plots o f capture rate versus concentrat ion for various potentials shown i n F igure 2.4. L i n e a r regression analysis gave R 2 values greater than 0.95 for a l l appl ied potentials except at 100 m V ( R 2 = 0.87) , where it is be l ieved that a lower capture rate resulted in fewer samples and less re l iable statistics. F igure 2.5 shows the capture rate versus appl ied potential curves for a l l concentrations for the p o l y ( d A ) 5 0 molecu le n o r m a l i z e d b y a concentrat ion o f 1 // M ; a l l capture rate data co l lapsed onto the l e n g t h -s p e c i f i c c h a r a c t e r i s t i c curves for both the p o l y ( d A ) 5 0 and p o l y ( d A ) 1 0 molecu les . Concentration (mM) Figure 2.4 - Concentration versus normalized capture rate for poly(dA)50 molecules for applied potentials from lOOmV (bottom) to 340mV(top), in 20mV steps. Chapter 2: Cis-side molecule capture and analysis 19 100 10 Normalized Capture Rate 1 (Hz/nM) 0.1 0.01 * I I I rt 100 200 300 Applied Potential (mV) 400 Figure 2.5 - Normalized capture rate versus applied potential for poly(dA)50 molecules. 2.3.3 Length dependence The capture rate versus appl ied potential curves for the 5 0 - m e r and 10-mer molecu les , shown i n F igure 2.6, indicate that p o l y ( d A ) 1 0 exhibi ts a higher capture rate than p o l y ( d A ) 5 0 at a g iven concentrat ion and transmembrane potential . F o r example , at 300 m V and 0.4 p M the measured capture rate for p o l y ( d A ) 5 0 was 8.2 ± 0.4 H z , w h i l e the measured capture rate for p o l y ( d A ) 1 0 in the same condit ions was 21.5 ± 0.6 H z . Th is result agrees qual i tat ively w i t h results presented b y some researchers [37], but stands i n contrast to one observat ion that the capture rates for samples were independent o f length (R = 5.8 events sec" 1 p M " 1 at 120 m V for 6, 20 and 40-nt s s D N A ) [61], as compared to 5.4 ± 0.3 events s e c " ' / / M " 1 for p o l y ( d A ) 1 0 , and 0.63 ± 0.1 events sec"1 p M " 1 for p o l y ( d A ) 5 0 found dur ing this investigation). Chapter 2: Cis-side molecule capture and analysis 20 100 10 Capture Rate (Hz) 0.1 o 10-mer ° 50-mer 0 <j> at 100 200 300 Applied Potential (mV) 400 Figure 2.6 - Capture rate for poly(dA)50 and poly(dA)10 molecules at 0.4 uM The low-pass cutof f f requency chosen for f i l ter ing o f b lockage events had a substantial effect on the measured rate o f capture for the shorter p o l y ( d A ) 1 0 molecu les , but very l itt le effect o n the longer p o l y ( d A ) 5 0 molecu le . Measured capture rates f r o m data f i l tered at 10 k H z and at 100 k H z for the 10-mer molecules are shown i n F igure 2 .7 , w i t h the capture rates f r o m data f i l tered at 100 k H z consistent ly h igher than f r o m data f i l tered at 10 k H z . In compar ison , the capture rates for the 5 0 - m e r molecu le shown i n F igure 2.8 shows that the almost ident ica l results for 10 k H z and 100 k H z f i l ter ing. H o w e v e r , at a l l f i l ter settings the rate o f capture o f the shorter 10-mer was greater than the longer 5 0 -mer molecu le . Further d iscuss ion on the topic o f s ignal f i l ter ing is inc luded i n A p p e n d i x F. 1. Chapter 2: Cis-side molecule capture and analysis 21 3 5 30 2 5 Capture 2 0 Rate (Hz) 1 g 10 5 0 I • 100 kHz filtering ° 10 kHz filtering I T ( i a E m 100 2 0 0 3 0 0 Applied Potential (mV) 4 0 0 Figure 2.7 - Measured capture rate of 0.4 u M poly(dA)10 at varying filtering / sampling rates (10 kHz filter / 50 kHz sample, 100 kHz filter / 333 kHz sample) Capture Rate (Hz) 20 18 16 14 12 10 8 6 4 2 0 » 1 n n-j z filtering Hz filtering ^ I • i u t\n • 100 k : r ffi 3 I I I c s r $ s ffi I < 100 2 0 0 3 0 0 Applied Potential (mV) 4 0 0 Figure 2.8 - Measured capture rate of 0.4 u M poly(dA)50 at varying filtering / sampling rates (10 kHz filter / 50 kHz sample, 100 kHz filter / 333 kHz sample) Chapter 2: Cis-side molecule capture and analysis 22 2.3.4 Dependence on applied potential The rate o f capture has a crossover i n behaviour at - 1 5 0 m V , as seen i n F igure 2.6. The dependence o f R on V exhibits two regimes: for V b e l o w the crossover potent ial , R d isplays an exponent ia l dependence on V. A n exponent ia l fit to the energy bar r ie r - l imi ted reg ion at l o w transmembrane potentials for the p o l y ( d A ) 5 0 molecu les takes the f o r m : R = 0.0037 e ( 0 0 4 8 5 v ) events/sec • u M ( 2 _ 1 ) Here , V is the appl ied transmembrane potential i n m V . H o w e v e r , the capture rate deviates f r o m this s imple re lat ion for V above the crossover potent ial , as seen most c lear ly on the log - l inear p lot i n F igure 2.6. A t the higher appl ied potentials, the relat ion appears to f o l l o w one o f three dependencies: an exponential dependence w i t h an exponent ia l constant o f - 0 . 0 0 7 2 m V " 1 , a reduct ion o f ~ 7 x f r o m the l o w transmembrane potentials [61]; a power law fit w i t h an exponent 1.2 ± 0 . 1 ; or a l inear dependence o n the appl ied potential . P r io r to the invest igat ion described herein , o n l y a l i m i t e d amount o f exper imental w o r k had examined the process o f captur ing i n d i v i d u a l s s D N A molecu les f r o m the bu lk solut ion. H e n r i c k s o n et al. [62] used an Ar rhen ius relat ionship to m o d e l the capture rate dependence o n transmembrane potential up to 1 2 0 m V , far be low the m a x i m u m potent ial o f 3 0 0 - 4 0 0 m V at w h i c h point the l i p i d b i layer becomes unstable. A p p l y i n g this group's m o d e l at higher potentials results i n predicted capture rates that exceed the d i f fus ive f lux o f molecules to the pore [48]. In another study, M e l l e r and Branton ]noted the presence o f a crossover potential at - 1 5 0 m V , and determined that at potentials above the crossover potential the exponential dependence o n the appl ied potent ial reduced b y a factor o f - 5 t imes the exponential dependence at l o w potentials [61]. However , the m o d e l d id not address the issue o f any upper bounds o n the overa l l capture rate. In order to use the exper imental capture rate data at h igh transmembrane potentials to forecast capture rates at potentials achievable us ing synthet ical ly Chapter 2: Cis-side molecule capture and analysis 23 fabricated nanopores, a m o d e l o f molecu le capture was developed to complement and extend models i n the ex ist ing literature. 2.4 A model for polymer capture 2.4.1 Shortcomings in existing models The major i ty o f previous analyt ic w o r k e x a m i n i n g po lymers m o v i n g f r o m the b u l k solut ion into a membrane -bound pore examined the process starting f r o m an in i t ia l l y restricted state, de Gennes [63] der ived an expression for the t ime taken for a single end o f a p o l y m e r to enter into the pore due to concentrat ion gradients i n the absence o f an appl ied potent ia l , but the analysis began w i t h one end o f the cha in already w i t h i n one radius from the mouth o f the pore. M u t h u k u m a r [64] descr ibed the d i f fus ive escape o f po lymers conf ined w i t h i n a sphere through a hole i n the w a l l o f the sphere: the t ime required for the end o f a p o l y m e r trapped inside a sphere to f ind a hole in the sphere scaled w i t h the length o f the po l ymer as N 1 3 ' . K o n g and M u t h u k u m a r [65] descr ibed the energy barrier for end-capture o f a conf ined molecu le and its dependence o n the free-energy difference o f a molecu le conf ined w i t h i n the pore, w i t h a decreasing barrier as the molecu le increased i n length. A l t h o u g h usefu l for analyt ic evaluat ion o f i n i t i a l l y - c o n f i n e d molecu les , these models are insuff ic ient to estimate the rate o f capture o f po lymers f r o m the b u l k so lut ion under the present exper imental condi t ions. A m b j o r n s s o n et al. presented a more fo rmal analyt ic m o d e l o f p o l y m e r end-capture i n a pore and the result ing rate o f capture [66]. P o l y m e r capture was descr ibed i n two parts: first, a 3 - d i m e n s i o n a l r a n d o m - w a l k m o d e l o f molecules i n free solut ion to determine the probabi l i t y o f finding an end segment o f the po l ymer near the pore m o u t h ; and second, a 1 -d imensional dr iven d i f fus ion m o d e l for t ranslocat ion o f the po l ymer to estimate the l i k e l i h o o d that a p o l y m e r w o u l d pass through the pore. The dr iven d i f fus ion o f the p o l y m e r was subject to a d r i v ing electric field, as w e l l as a free-energy barr ier due to Chapter 2: Cis-side molecule capture and analysis 24 po lymer -pore f r ic t ion and to the entropic cost o f conf in ing the mo lecu le i n the pore. The m o d e l b y A m b j o r n s s o n et al. was able to fit exper imental results for transmembrane potentials up to ~ 1 5 0 m V [67], i n c l u d i n g the presence o f a crossover potential Vp separating an exponent ia l dependence at l o w potentials and a l inear dependence at h igher appl ied potentials. The m o d e l contained a number o f shortcomings and unphys ica l overs impl i f i cat ions . The 3 - D r a n d o m - w a l k used to m o d e l p o l y m e r end capture c o u l d not account for pores w i t h entrances f lush w i t h the surface o f the membrane and w h i c h d i d not protrude into the so lut ion , such as for synthetic nanopores w h i c h have already been successfu l ly used for capture and translocation o f nuc le ic acids [68 -70] . Th i s cond i t ion also introduced phys ica l l y incorrect boundary condi t ions , such as a l l o w i n g molecules to pass through the wa l l s o f the membrane and the pore dur ing the in i t ia l end-capture, and not account ing for the electr ic f ie ld dur ing in i t ia l end-capture, found anecdotal ly i n prev ious computer s imulat ion results to affect the d w e l l - t i m e and l i k e l i h o o d o f capture at higher appl ied fields [48, 7 1 , 72]. The parameter f i t t ing as presented b y A m b j o r n s s o n et al. was done w i t h exper imental results b e l o w 1 2 0 m V ; fits to experimental data i n c l u d i n g higher transmembrane potentials [67] y ie ld good fits to data at l o w appl ied potentials , but predict a crossover voltage Vf = 320 m V , about two t imes greater than the exper imental crossover value o f ~ 1 5 0 m V . A s w i t h analyt ical approaches, computer s imulat ions o f p o l y m e r -pore interactions have focused on the translocation k inet ics o f po l ymers after in i t ia l capture [36], w h i l e observations about transit ion f r o m the b u l k so lut ion pr ior to translocation have general ly been qual i tat ive i n nature. A l l - a t o m simulat ions o f nucle ic acids translocating through a synthetic nanopore per formed by H e n g et al. [68, 71] suggest that the ra te - l imi t ing step for translocation is not the actual translocation t ime but rather the search for an in i t ia l conformat ion that faci l i tates the translocation. S imulat ions o f this nature have not been the basis for quantitative in format ion relat ing the probabi l i ty o f capture o f the mo l ecu l e f r o m the b u l k solut ion, nor do they relate the appl ied transmembrane potentials w i t h any further capture rate in format ion . Chapter 2: Cis-side molecule capture and analysis 25 2.4.2 A Hybrid Model of Polymer Capture Analytic estimates of the diffusive flux of ssDNA molecules in free solution to a hemispherical region within one pore radius from the pore without an applied potential are far higher than the observed blockage rate. This indicates that that either a large fraction of molecules coming into such close proximity to the pore entrance do not result in blockages or that analytic estimates for diffusive flux cannot be applied to this case. A discussion on the invalidity of using diffusive flux calculations alone to estimate capture rates is included in Appendix D. Here is presented a model with two components: first, an analytic estimate of molecule flux into a well-defined hemisphere around the pore; and second, a numerical estimate of the potential-dependent probability of translocation for molecules starting at the surface of such a hemisphere. These two parts are used to estimate the rate of capture as shown schematically in Figure 2.9. An expression for the potential-dependent overall rate of capture Rlol(V) is: KXn = Kollisiol,(a)Ptor(V,a) (2-2) Here, Rcomsio„(a) is the rate at which molecules from the bulk solution collide with a hemisphere of radial distance a from the pore, while Ptol(V,a) is the probability that a molecule initially a radial distance a from the pore will eventually translocate through the pore at a given transmembrane potential V before diffusing away from the pore. The expression RcoIUsiolXa) is derived analytically, while Ptot{V,a) is obtained through computer simulations. Note that the final expression Rlol(V) should be independent of the choice of the radius of collision a, though choices of large a will lead to long computation times. This point is examined using results from the model in Section 2.5.1. Chapter 2: Cis-side molecule capture and analysis 26 R c o l l i s i o n ( a ) / I P e s c (V,a)= / l - P t o t ( V , a ) / \ P t o t f V , a) Figure 2.9 - The overall capture rate R«„(V) consists of the collision rate of molecules diffusing in free solution with a capture hemisphere of radius a, RcoiiisionW ifcft), multiplied by the probability of capture at a given applied potential ^and distance a, P„„(V, a) (right) Collision Rate A n analytic expression for the flux of diffusive molecules in bulk solution to the surface of a perfectly adsorbing hemisphere with radius a on the surface of a non-adsorbing membrane was derived by Berg [73]: Rcolllxl-M-2nCDa. (2-3) Here, C is the concentration of ssDNA with bulk diffusion constant D. Equation (2-3) cannot be used to directly estimate the capture rate of nucleic acids in a nanopore because it assumes the pore is a perfect adsorber, and does not model the probability of capture of the nucleic acid and the entropy loss associated with such capture. However, the expression is still appropriate for estimating the collision rate of particles into a well-defined hemispherical region around the pore where the polymeric nature of individual molecules does not interfere with the bulk diffusive properties of the polymer. Chapter 2: Cis-side molecule capture and analysis 27 Appendix D contains a discussion on the invalidity of using Equation (2-3) alone to estimate the flux of polymeric molecules across the pore, as the radius of gyration of an individual molecule is greater than both the size of the pore and the length scale of the concentration gradient required to produce the diffusive flux. However, the expression is still valid for estimating the diffusive flux of molecules which approach the pore and collide with the surface of a well-defined hemisphere defined by the collision radius, provided that every molecule which collides with that surface can be unambiguously accounted for in the expression Ptot(V,a). Once a molecule has made contact with the hemisphere defined by the capture radius a, the subsequent path of the molecule will result in it being labeled as either a captured or escaped molecule. Regardless of this, crossing the capture radius removes the molecule from the bulk, as the numerical calculation tracks the rest of its path to either an eventual capture or escape to infinity. This explicit accounting for each molecule results in an effective molecule concentration gradient consisting of molecules which have not yet passed into the capture hemisphere, and is exactly equivalent to the concentration gradient established by a perfect adsorbing hemispherical surface. This argument holds true provided that individual molecules do not interact with one another. Note that Equation (2-3) applies only in regions where the molecule drift from electric fields is small compared to diffusive motion. Due to the small scale of the pore, this will generally be true for any capture radius a outside the pore at most applied potentials, though it is likely that at higher potentials and small values of a, this approximation wil l lead to some error. This error will need to be accepted in favor of short computational times, and is quantified in Section 2.5.1. S c a l i n g o f N u m e r i c a l S i m u l a t i o n In order to use Equation (2-2), the expression we must explicitly account for every molecule which enters into the hemisphere defined by the capture radius a and unambiguously determine one of two final conditions for the molecule: (a) the molecule is eventually captured and translocates across the pore; or (b) or whether eventually escapes and Chapter 2: Cis-side molecule capture and analysis 28 does not pass through the pore. In this way we can define a probability of capture Ptot(V,a) for each molecule at a defined capture radius. To simulate polymer capture in finite time, a computer simulation was written to estimate Psu„(V, a, b), the probability that a polymer starting at a distance a from the centre of the pore is captured by the transmembrane potential V and translocates through the pore before diffusing as far as an arbitrary escape radius b. In order to convert the simulation result PSi,„(V, a, b) to the overall probability of capture Ptot(V, a) required in Equation (2-2), the dependence on the fixed escape radius b must be removed from the expression. The probability that a polymer released at a radial distance b from an absorber will diffuse to a capture radius a before escaping and no longer interacting with the absorber was analytically derived by Berg [73] as: p = alb (2-4) The total capture probability, Ptot(V, a), defined as the probability that a molecule starting at a will be captured in the limit that the escape distance is infinite, can therefore be expressed as a geometric series based on the simulation capture rate, PSi,n(V, a, b) = PSi„, combined with the analytic expressionp = a/b as: P,oXV,a) = Psim+(\-Ps;m)pPsim+(l-Psim)2p2Psim +... (2-5) = Y ( i - p . )"p"P-/ i \ sim / r sim 11=0 where (l-PSi„,)"pn is the probability that the molecule will make n trips from b to a without being captured or drifting away to infinity. Figure 2.10 is a schematic of Equation (2-5). Chapter 2: Cis-side molecule capture and analysis 29 > \ Figure 2.10 - Graphical representation of relation between P„„ and Psim for a given escape and capture radii a, b. Th is geometr ic series can be reduced i n the inf in i te l imi t to: Pl„XV,a) = - (2 -6) C o m b i n i n g the expressions for the capture rate from E q u a t i o n (2-4) and the probabi l i ty o f capture f r o m Equat ion (2-6) into the or ig ina l express ion f r o m Equat ion (2-3) , the f ina l expression for the capture rate is : Chapter 2: Cis-side molecule capture and analysis 30 R,otyV) = RcomsioM) Psim(V,a,b) \--y\-Psim{V,a,b) b (2-7) = (2nCDa) Psim(V,a,b) !--(!-PsiJV,a,b) V b It is expected that the Rtoi(V) values estimated us ing E q u a t i o n (2-7) w i l l be independent o f the arbitrary escape radius b for any g i ven capture radius a. Sect ion 2.5.1 examines the var iat ion i n Rtol(V) w h i l e va ry ing the ratio o f capture radius to escape radius a/b. Numerica l Simulation A s imulat ion o f D N A translocation through a c y l i n d r i c a l pore under an appl ied transmembrane potential was performed to estimate PSim(V, a, b). S ingle -st randed nuc le ic ac id molecules were m o d e l e d as chains o f hard-sphere beads l inked by semi -extensib le springs, f o l l o w i n g i n the same v e i n as other nanopore -po lymer s imulat ions [72, 74 , 75] . E a c h bead represented one K u h n length o f the s s D N A molecu le , or h a l f the persistence length o f s s D N A , in s imi lar salt condit ions (3 nucleot ides = 1.5 n m between beads) [21]. D u r i n g each t ime step r o f the s imulat ion , each bead was disp laced due to the stochastic thermal force, electrophoretic and electrostatic forces dr i ven b y the loca l electric field, and a constraint to fix the bead- to -bead distance: drnT.=d„ ..+dFri,.+d • • (2"8) TOT,i thermal,! Efield ,j spring,i The magnitude o f the stochastic thermal d isplacement dlhermal scales w i t h the square root o f the number o f K u h n lengths i n the p o l y m e r Chapter 2: Cis-side molecule capture and analysis 31 /V and the overall diffusion constant of the polymer D, and points in the direction of a random unit vector n : d M J = JN6DT n (2-9) The displacement of the bead is due to the local electric field: Here, p is the electric mobility of the bead, and Ei is the electric field vector at the bead's position due to the applied transmembrane potential and the screened bead-to-bead coulombic repulsion. E=E r,.+E A . (2" 1 1 ) ( applied ,i screenea,i The electric field due to the applied transmembrane potential, as derived in Appendix D , is: E applied ,i V L + 2a 1- r. (2-12) r\ Here, V/(L+2a) represents the magnitude of the electric field due to the applied transmembrane potential V over both the pore length L as well as the access resistance to a pore of radius a, with the bead position ri relative to the origin at the centre of the pore mouth. The screened bead-to-bead coulombic repulsion is given by: w ^ z exp(- | r , . - r | / / r ) r _ , E• screened,/ = L ~A _ ~~1 Vj ~ T \ ( ' j*i ^ n s s 0 r, - r Here, K is the Debye length due to counter-ions present in the electrolyte solution. The displacement on the rth bead from the bead-to-bead exponential constraint from the /+ith bead and the /-7th bead separated by a distance d was given by: Chapter 2: Cis-side molecule capture and analysis 32 d . .=(1/2) springs \ J (1/2) d \ri-x-ri\JJ (2-14) \rM~ ri\J The simulation used a hard-wall potential for the membrane and pore walls, and modeled the pore as a straight-walled cylinder, ignoring finer details such as static electrostatic charges on the pore walls and complex pore geometry. Table 2-1 contains the value of parameters used during the simulation. Note that the simulations for the 10-mer and 50-mer molecules differed in two parameters: the number of beads in the simulation (N = 3 for the 10-mer, =17 for the 50-mer), as well as the bulk diffusion constants D obtained from experiments measuring the 11 2 free-solution diffusion, constants of ssDNA fragments (6 xlO" m /s for the 50-mer, and -1.0 x 10"10m2/s for a 10 -mer fragment). n electrical mobility 2 x 10"* m 2/Vs [76] D diffusion constant 6x10"" m2/s (50-mer), 1.0 x 10"'°m 2/s (10-mer) [76] L pore length 5 nm a pore radius 0.7nm N number of beads 17 (50-mer) 3 (10-mer) CT monomer radius 0.5 nm d monomer-to-monomer distance 1.5nm K Debye length 0.3 nm Z unit charge per monomer 1 T time step 25ps T 1 max maximum simulation time 0.25 ms a capture radius 0.5 nm b escape radius 15 nm Table 2-1 -Parameters used for computer simulation Chapter 2: Cis-side molecule capture and analysis 33 The s imulat ion was init iated w i t h the center o f mass o f a thermal ly -equi l ib rated p o l y m e r m o v i n g a long the central axis o f the pore f r o m the b u l k so lut ion unt i l the nearest m o n o m e r unit was i n contact w i t h the c o l l i s i o n radius a. F r o m this point , the s imulat ion r a n ' u n t i l either: (a) the center o f mass o f the po l ymer emerged f r o m the trans-side, o f the pore, representing a capture event; (b) the center o f mass d i f fused outside the escape radius b\ or (c) the po l ymer became trapped i n some loca l m i n i m u m and was not able to either translocate or escape i n a m a x i m u m amount o f t ime Tmax; such rare events were exc luded f r o m the f ina l ca lcu lat ion . Ensemble measurements were taken at transmembrane potentials f r o m 0 to 1 V for both the 5 0 - m e r and the 10-mer fragments for compar i son w i t h avai lable exper imental data and forecast to h igher potentials. 2.5 Model Results and Discussion 2.5.1 Simulation results with varying ratio of capture radius to escape radius In order to val idate the c l a i m o f independence o f the m o d e l predict ions over va ry ing capture and escape radi i a and b, the s imula t ion for the p o l y ( d A ) 5 0 molecu le was run w i t h a range o f values for the ratio a/b at two appl ied potentials: at 3 4 0 m V , comparable to the m a x i m u m appl ied potential obtained w i t h the a H L pore, and at 9 0 0 m V , substantial ly h igher than can be obtained w i t h the present exper imental b i layer arrangement. The s imulat ions were run w i t h the start radius a vary ing f r o m 0.5 n m to 10 n m , w i t h a f i xed capture radius b o f 15 n m . The results o f each s imulat ion PSim(V, a, b) were used i n conjunct ion w i t h Equat ion (2-7) to calculate the estimated capture rate Rm(V), w i t h the n o r m a l i z e d concentrat ion o f 1 p M and a d i f fus ion constant Dexpt = 4 x 1 0 " " m 2 /sec 2 2 Selection of diffusion constant 4 x IO 1 1 m 2/s described in Section 2.5.2 Chapter 2: Cis-side molecule capture and analysis 34 The m o d e l predict ion o f the capture rate Rm(V) showed reasonable consistency over vary ing ratios o f a/b, and agreement w i t h exper imental capture rates w i t h the p o l y ( d A ) 5 0 molecu le . F igure 2.11 shows that at 340 m V the capture rate is centered around the exper imental capture rate o f 20.6 Hz/ p M for a/b ranging f r o m 0.03 to 0 .66 ; the var iance about the expected capture rate ( ± 1.6 H z ) is due i n large part to the l imi ted number o f s imulat ion runs at each data point ( - 8 0 0 ) . F igure 2.12 shows that the capture rate at 900 m V ( - 1 2 0 0 s imulat ion runs) has a distinct negative trend as the ratio a/b approaches 1; this is an ind icat ion o f the extent that electrophoretic effects m a y inf luence the capture rate at higher potentials g iven the capture and end rad i i examined here. Th is trend w i l l serve as an estimate o f the var iab i l i t y o f the f ina l ca lcu lat ion at these potentials, o n the order o f ±10 percent o f the in i t ia l ca lcu lat ion . In order to estimate the upper l i m i t o f the capture rate i n reasonable computat ional t ime, the s imulat ion was ini t iated w i t h a capture radius a o f 0.5 n m , equal to the shortest capture radius used i n this invest igat ion. 25.00 20.00 15.00 R.ot(340mV) (Hz/mM) 10.00 5.00 0.00 • • • • • • 0.2 0.4 a/b 0.6 0.8 Figure 2.11 - Rate of capture from different start radii with the escape radius and transmembrane potential held constant (b=\5nm, V= 340mV). Dashed line indicates experimental capture rate of 20.5 Hz/(j.M Chapter 2: Cis-side molecule capture and analysis 35 120.00 100.00 80.00 R,o,(900mV) (Hz/mM) 60.00 40.00 20.00 0.00 -I i 1 ; I i : 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 a/b Figure 2.12 - Rate of capture from different start radii with the escape radius and transmembrane potential held constant (£=15nm, V= 900mV). 2.5.2 Comparison with experimental results F o r compar ison w i t h the computer s imulat ion , the exper imental rates o f capture Rexpt(V) were converted to exper imental capture probabi l i t y Pexpt(V, a) by d i v i d i n g the measured rate o f capture b y the analyt ic c o l l i s i o n rate w i t h a capture radius a: P e x p t ( V > a ) = = (2 -15) In Equat ion (2 -15) , the d i f fus ion coeff ic ient Dexp, was kept as a free parameter to f ind the o p t i m u m fit between Pexpt(V, a) and Ptot(V, a). N o t e that since exper imental ly determined values o f D for both the . p o l y ( d A ) 5 0 and p o l y ( d A ) 1 0 molecules are used direct ly i n the m o d e l , Dgxpt is not a truly free parameter and large variat ions i n its value for Equat ion (2-15) w o u l d render the fit inva l id . The estimated capture probabi l i t ies generated f r o m the m o d e l for both the 10-mer and the 50 -mer molecules showed the same general Chapter 2: Cis-side molecule capture and analysis 36 trends as the empi r i ca l data. The predicted and exper imental capture rates for the longer p o l y ( d A ) 5 0 molecules are shown i n F igure 2 .13 , w h i l e predicted capture rates at potentials that cannot be achieved exper imental ly us ing l i p i d b i layer membranes are s h o w n i n F igure 2 .14. The best- f i t o f the m o d e l w i t h the exper imental data for p o l y ( d A ) 5 0 results in a d i f fus ion coeff ic ient Dexpt = 4 x 1 0 " " m 2 /sec, in somewhat reasonable agreement w i t h the bu lk solut ion value D used i n the m o d e l s imula t ion (6 x 1 0 " " m 2/sec [76]). 0.4 0.35 0.3 0.25 Ptot(V) 0.2 0.15 0.1 0.05 0 I * Exp Data poly(A)50 * Model Prediction poly(A)50 I : I II X 1 * I 5 : * 0.1 0.2 Applied Potential (V) 0.3 0.4 Figure 2.13 -Mode l prediction versus experimental data for the probability of capture of poly(dA)50 Chapter 2: Cis-side molecule capture and analysis 37 1 0.9 0.8 0.7 0.6 Ptot(V) 0.5 0.4 0.3 0.2 0.1 0 * x * * * X I i 7 ft 4 i * Exp Data poly(A)50 » Model Prediction poly(A)50 i « ^ X D 0 2 0 4 0.6 0 8 1 Applied Potential (V) Figure 2.14 - Model prediction for poly(dA)50 at potentials greater than those achieved during experiments with the a H L pore The m o d e l d isplays a crossover behaviour s imi la r to that noted i n the exper imental data, w h i c h separates an exponential dependence o n the potent ia l at l o w potentials and the near ly - l inear dependence at higher potentials . The presence o f the crossover potential i n the m o d e l indicates that the crossover is at least part ia l ly a result o f entropic considerat ions w i t h the p o l y m e r trapped inside the pore and not entirely f r o m other exper imental parameters such as internal charge groups, c o m p l e x geometry o f the pore, or po lymer -sur face interactions. The m o d e l predicts that at the g iven potential the capture rate w o u l d reach a probabi l i t y o f capture greater than 9 5 % at approx imate ly I V . W i t h the parameters used i n the s imulat ion , this translates to - 1 3 0 H z / / / M as a m a x i m u m capture rate. Th is estimate o f the m a x i m u m capture rate can be used to estimate the sensit iv i ty o f the system i n measur ing loca l concentrations. The m o d e l d i d not f o l l o w the exper imental data as c lose ly for the shorter p o l y ( d A ) 1 0 molecu le , and cou ld not be made to fit the exper imental data w e l l even w h i l e vary ing the free parameter value Dexpt over a reasonable range o f d i f fus ion constants. S h o w n i n F igure 2.15 are the m o d e l predict ions and the exper imental Ptot(V) w i t h a free parameter value Dexpl = 0.5 x 1 0 " 1 0 m 2 /s. A better fit to the data requires a d i f f u s i o n Chapter 2: Cis-side molecule capture and analysis 38 constant w h i c h deviates b y more than 5 0 % f r o m the value used i n s imula t ion for the p o l y ( d A ) 1 0 molecu le o f D = 1.0 x 1 0 " 1 0 m 2 /s, and becomes substantial ly different f r o m the d i f fus ion values found exper imental ly for short D N A fragments [76]. Part o f this disagreement for the shorter p o l y m e r m a y be the missed events as a result o f the lowpass f i l ter ing as descr ibed i n Sect ion 2 .2 , even w i t h f i l ter ing set at 100 k H z . The translocation t ime o f a 10-base s s D N A molecu le is very near the threshold o f this detection technique discussed i n A p p e n d i x F . l , beyond w h i c h a p o l y m e r m a y translocate through the pore undetected due to bandwidth l imitat ions. 1 0.9 0.8 0.7 0.6 Ptot(V) 0.5 0.4 0.3 0.2 0.1 0 • # » * i • Model Prediction poly(A)10 — * Exp Data polv(A)10 * 0.5 1 Applied Potential (V) 1.5 Figure 2.15 - Simulation results versus experimental results for poly(dA)10 2.5.3 Crossover potential The capture rate dependence on appl ied potential undergoes a change i n behavior at a crossover potential independent o f mo lecu le concentrat ion [48, 61] . The results generated b y the hyb r id m o d e l suggest that the conf inement o f the p o l y m e r strand w i t h i n the pore contributes to the presence o f the crossover potential . E m p i r i c a l results can be used to make an estimate o f the energy barrier for molecules to translocate through the pore. F r o m F igure 2 .6 , an exponent ia l fit to the energy bar r ie r - l imi ted reg ion at l o w transmembrane potentials for the p o l y ( d A ) 5 0 molecu les takes the f o r m : Chapter 2: Cis-side molecule capture and analysis 39 R = 0.0037 e ( 0 0 m v ) events/sec • u M ( 2 " 1 6 ) Here , V is the appl ied transmembrane potential i n m V . A s descr ibed b y H e n r i c k s o n et al. [62], a f irst -order Ar rhen ius relat ion at l o w potentials for p o l y m e r translocation takes the fo rm: R = R g e ( - E 0 ( V ) l k l l T ) (2 -17) Here , R0 is the rate constant, kBT the thermal energy scale factor, and E0(V) the act ivat ion energy term for the capture and translocat ion process to proceed. EQ(V) can be expressed as the sum o f the contr ibut ions f r o m the transmembrane potential Epoten,u,i(V) w i t h the other contr ibut ions contr ibut ing to the overa l l barrier EBAIRIER(V): I f it is assumed that EBARRIER(V) ~ EBWRIER is independent o f potent ia l , a straightforward estimate can be made for the potent ial energy required to overcome EBAIRIER. A n expression for Epo,enti„i(V) w h i c h assumes that the appl ied potential is u n i f o r m across a l l nucleot ides i n the probe strand is : (2 -19) E potential (^ 0 — Zporentraits^ w i t h z the effective charge per nucleot ide, ntrnns the number o f nucleot ides w h i c h have translocated across the pore, and e the unit charge. H o w e v e r , it was apparent dur ing s imulat ion runs that there are several instances w h e n one end o f the po l ymer w o u l d enter into the pore then return to the cz's-side without result ing i n complete translocat ion. It is poss ib le that there is an effective threshold distance to w h i c h the molecu le m a y have to enter into the pore pr ior to translocat ion and obtain an in i t ia l conformat ion , ref lected i n the gain i n electrostatic energy b y the p o l y m e r inside o f the pore. A better approx imat ion o f the distance the target mo lecu le enters into the pore can be made by assuming a l inear drop i n potent ial across the length o f the beta-barrel o f the pore. In this case, the expression for the potential energy can be restated f r o m Equat ion (2-19) as: Chapter 2: Cis-side molecule capture and analysis 40 E ' potential (V) = Z p o r e e a V ^ 2 (2"20) kBT 21 kBT Here , m is the number o f nucleotides inside o f the pore, a is the p h y s i c a l length per nucleot ide and / the length o f the beta-barrel sect ion. U s i n g lengths o f a = 0.5 n m and 1 = 6 n m and a charge per nucleot ide o f zpore ~ 0.4 w i t h i n the h i g h - f i e l d beta-barrel o f the pore 3 , substitution o f E q u a t i o n (2 -20) into the exponential port ion o f Equat ion (2-16) results i n an estimate o f m ~ 9 as the number o f bases required for entry into the h i g h -f i e ld reg ion pr ior to translocation. Th is translates to ~ 4 . 5 n m into a 6 n m l o n g h i g h - f i e l d region. A l t h o u g h Equat ion (2-20) m a y prov ide a basis for ca lcu lat ing the order o f magnitude for E b a r r i e r , it cannot be used exact ly , as the prefactor i n Equat ion (2-16) cannot be further d i v ided into the contr ibut ion f r o m RQ and the contr ibut ion f r o m e E b " ' n e r / k J \ 2.5.4 Concentration Measurement Performance The exper imental and theoretical analysis o f the capture rates can be used to predict the performance o f nanopore-based methods for est imating loca l nuc le ic ac id concentrations. The f o l l o w i n g d iscuss ion describes an estimate for the l o w e r - l i m i t o f concentrat ion to establ ish a min ima l l y -acceptab le s ignal - to -no ise ratio. A fa lse -posi t ive event occurs w h e n there is a reduct ion i n the measured ion ic current that is not caused by the capture o f the target mo lecu le , but w h i c h m a y be mistaken as a capture event. Th is m a y occur i f contaminants i n the buffer solut ion interact w i t h the pore, or as a result o f a stochastic reduct ion o f the pore conduct iv i ty resul t ing f r o m interactions o f divalent ions w i t h the pore k n o w n as pore gating. I f the reduct ion is large enough, there is no w a y to d is t inguish between a fa lse -pos i t i ve event and an actual b lockage event due to nuc le ic acids i n the b u l k solut ion. B a c k g r o u n d event rates i n the absence o f s s D N A o n the czs-side are measured to be less than 0.2 events/sec i n the present system; this value can be used as the sensit iv i ty l imi t on the system. Pore gat ing A n estimate of the charge per nucleotide inside the pore is made in Section 3.3.1. Chapter 2: Cis-side molecule capture and analysis 41 is not a p r imary issue w i t h the present exper imental condi t ions , as the salt concentrat ion and p H o f the buffer used (buffered 1 M K C l , p H 8.0), and the exc lus ion o f divalent cations f r o m the buffer , precludes gat ing events f r o m occur r ing ; this m a y not ho ld true as solutions w i t h more phys io log ica l l y - re levant composi t ions are used. Other characteristics o f the i o n current b lockage signature might be used to d is t inguish between translocat ion and fa lse -posi t ive signals [44, 45] . A d iscuss ion o f experiments e x a m i n i n g pore gating is inc luded i n A p p e n d i x F .3 . P o i s s o n statistics can be used to determine the m i n i m u m concentrat ion required to pos i t i ve ly c o n f i r m the presence o f nuc le ic acids i n the presence o f background fa lse-posi t ive events. P o i s s o n statistics state that g iven an expected number o f events / lover a speci f ied t ime interval , the probabi l i ty that there are exact ly k events w h i c h occur is g iven by : P(x = k,X) = ^ (2-2D k\ W e can estimate the m i n i m u m value o f X required so that there is a 95 percent probabi l i ty that the actual number o f events measured over any g i ven interval exceeds a lower event threshold value t: ( 1 - 0 . 9 5 ) = 0.05 > = M ) *=° (2-22) 0.05 > X ^ e'lXk Equat ion (2-22) can be solved i terat ively for A g i ven a lower event threshold value t. I f t = 2.0 events/sec is the m a x i m u m a l lowab le background noise for a synthet ical ly - fabr icated nanopore ( l O x that o f a H L ) , so l v ing Equat ion (2-22) shows that a m i n i m u m event rate X = 8 events/sec is required to ensure a 95 percent probabi l i t y o f pos i t i ve conf i rmat ion o f nuc le ic acids. A m i n i m u m nuc le ic acid concentration can be calculated us ing this sensit iv i ty estimate. U s i n g 8 events/sec as the m i n i m u m required Chapter 2: Cis-side molecule capture and analysis 42 capture rate, and assuming that the capture rate is l inear ly dependent o n the s s D N A concentrat ion, the a H L pore can detect a m i n i m u m concentrat ion o f 0 . 5 p M at 3 0 0 m V . Ext rapolat ing to I V , where a m a x i m u m capture rate o f - 1 3 0 H z / / / M m a y be achieved us ing a synthetic nanopore, the loca l concentrat ion can be as l o w as (8 H z / 130 Hz/ // M ) ~ 6 0 n M to achieve the m i n i m u m event rate. These concentrations alone do not compare favourably w i t h c o m m e r c i a l LTP detect ion schemes at typ ica l capi l la ry diameters, w h i c h at present can reach sensit iv it ies o f 1-10 p M i n 75 pm capi l lar ies . F o r example , a t yp ica l " b a n d " o f nuc le ic acids t ravel ing electrophoret ical ly d o w n a cap i l la ry m a y have a band length o f 1 m m , translating to - 5 x l 0 3 to 5 x l 0 4 total molecu les . Some h igh -per formance L I F systems not coup led to C E systems can reach single molecu le sensit iv i ty b y further decreasing the i m a g i n g v o l u m e or coup l ing to evanescent wave techniques [59]. Y e t as nanopore-based estimates o f concentration depend o n l y o n loca l mo lecu le concentrat ion and are independent o f both v o l u m e and the total number o f molecu les present i n the region, the total number o f molecu les used becomes comparable to L I F systems as the cap i l la ry diameter decreases. F o r example , at a diameter o f 5 p m , a size w h i c h is amenable for fabr icat ion o f m i c r o f l u i d i c analysis tools for c l i n i c a l and research use, and assuming nuc le ic acids m o v i n g through a standard electrophoretic separation f ie ld (// = 2x10" 8 m 2 / V s , E = 500 V / c m , v = 10 um/sec), and w i t h a band - 1 0 0 pm long result ing i n lOsec o f s a m p l i n g t ime, at the m i n i m u m concentration o f 6 0 n M this translates to - 7 x 1 0 4 total molecu les for detection, on the same range as the m i n i m u m required for f luorescence detection. 2.5.5 Further issues The m o d e l presented here can be used as the basis for general trends on capture rates for synthetic pores; further details can be inc luded i n future iterations o f the m o d e l to improve the level o f detai l i n the representation o f actual exper imental condit ions. Features such as po l ymer -pore interactions, inc lus ion o f pore geometry s imi la r to the a H L pore or synthetic pores, m o d e l i n g o f charge groups l i n i n g the inner w a l l s Chapter 2: Cis-side molecule capture and analysis 43 o f the pore, and a more detai led m o d e l o f the nuc le ic ac id strand account ing for the phosphate backbone and nitrogenous bases have been used i n other nanopore s imulat ions examin ing details o f the t ranslocat ion process [77-80] and m a y serve to extend the m o d e l to improve estimates o f mo lecu le capture at higher potentials. Sequence and or ientat ion o f the nuc le ic ac id fragment m a y also p lay a role i n the mo lecu le capture process. E a c h nuc le ic ac id strand has a polar i ty w i t h the ends k n o w n as the 5' and 3' end o f the molecu le , such that the 5 ' -hydroxy l group o f the first nucleot ide is at one end o f the strand and the 3 ' -hydroxy l group o f the f ina l nucleot ide is at the other end o f the strand. Th is or ientat ion i n the m o lecu le leads to differences i n h o w the po l ymer interacts w i t h the pore and result in two distinct translocation t ime populat ions for a g iven p o l y m e r [45] and i n subtle differences i n the ion ic current signature o f fragments o f d i f fe r ing compos i t ion and different t ranslocat ion or ientat ion [81]. It is possible that these or other sequence- and orientation-dependent biases m a y not o n l y affect t ranslocat ion dynamics and i o n conductance measurements, but m a y also result i n differences i n the rate o f capture o f molecu les f r o m the b u l k solut ion. Recent w o r k us ing synthetic nanopores has raised the issue o f whether the non- l inear crossover potential found empi r i ca l l y for the a H L channel w i l l also h o l d true for synthetic membranes. F o r example , synthetic pores i n Si3N4 m o d i f i e d b y atomic layer deposi t ion o f AI2O3 have pores larger than a H L (~15nm) but w h i c h can st i l l d iscr iminate i n d i v i d u a l part icles b y count ing b lockage events [84]. In these exper iments, the capture rate o f molecules f r o m the b u l k so lut ion was l inear w i t h the appl ied transmembrane potential . W h i l e the repeatabi l i ty o f such synthetic pores has not been established, there remains the poss ib i l i t y that the sensit iv i ty o f the results m a y depend non - t r i v ia l l y o n structural and charge properties o f the pore and h o w c lose l y they are related i n size or c h e m i c a l interaction to the molecu le o f interest. I f s m a l l var iat ions i n the structure, compos i t ion or contaminants l i n i n g the w a l l lead to h igh levels o f var iat ion i n translocation and capture dynamics , it m a y be d i f f icu l t to construct pores w i t h the consistency required to obtain quantitative in format ion based o n the rate o f capture and translocat ion across the pore. Chapter 2: Cis-side molecule capture and analysis 4 4 Experimental conditions can also be varied to identify the ideal conditions for nanopore-based detection schemes: variation in the pH, temperature, electrolyte concentration and buffer constituents may either improve or worsen the overall sensitivity of the method for nucleic acid detection. Other groups have examined the effects of these parameters on interactions during translocation and double-stranded nucleic acid dissociation either in the aHL pore [45, 82] or in synthetic membranes [83]; the dependence of such parameters on molecule capture and translocation have yet to be investigated. There are certainly experimental and fabrication issues in attempting to combine nanopore detection with conventional separation techniques. In the embodiment shown in Figure 2.1, nanopores used for analyte detection are placed perpendicular to the direction of separation during capillary electrophoresis. Experimentally, there will be numerous issues which make such a setup problematic: electro-osmotic flow along the walls of the capillary; the difficulty of establishing a well-defined electrical potential across the pore and in accurately measuring the ionic current through the pore; fabrication issues regarding synthetic pore formation in the wall of a separation tube; and selection of separation media to minimize interference with nanopore detection sensitivity. Any of these issues may negate the use of nanopores for detection and quantification of analytes as a replacement for conventional detection schemes; future work is required to investigate and ameliorate each of these issues before such an application is a possibility. Chapter 2: Cis-side molecule capture and analysis 45 2.6 Chapter Summary Nanopore detection shows promise as a non-fluorescent means of measuring single-stranded nucleic acid concentrations in small volumes. Empirical results using the aHL protein channel show that the capture rate of single-stranded nucleic acids is linear with molecule concentration, while exhibiting a non-trivial dependence on the applied potential. As existing theoretical approaches either could not account for the experimental results at higher potentials or had shortcomings in accounting for some experimental details, a hybrid model of the capture rate combining analytic estimates and computational simulations was formed. The model demonstrated that one source of the non-linearity and presence of the crossover potential was the polymer nature of the nucleic acids and the resulting entropic cost of confining the polymer prior to translocation. The model formed the basis for predicting performance of synthetic nanopores which could approach transmembrane potentials higher than is possible with pores embedded in lipid bilayer membranes. Experimentally there are several issues to be addressed before nanopore detection can be used as a viable method for estimating nucleic acid concentration for common analysis techniques. As the method is sensitive to the length of the nucleic acid molecules under investigation, there may be a limited length regime of operation for analyte molecules. Nanopores have been used to capture molecules ranging from as low as four [60] to as long as hundreds [37] of nucleotides long, and it is clear that longer fragments have lower capture rates. The method will require calibration for each type of target molecule and buffer solution. It is also not clear how the method can be used to distinguish between populations of multiple types of analytes present in one solution: although the method may be used to detect the presence of nucleic acids within mixtures of other different biomolecules, it will be difficult to detect the Chapter 2: Cis-side molecule capture and analysis 46 presence of different types of nucleic acids based on the duration or the depth of the ion current blockage signatures except for fragments with substantial length differences. A s the molecules to be detected increase in length, the probability of the molecule translocating through a channel of fixed size at a fixed voltage decreases. The practical implication of this is that an analyte detection system based on nanopore capture for detecting various lengths of nucleotides may need to incorporate multiple, electrically independent pores of different sizes to efficiently capture a large range of molecule lengths; in such cases, the process of molecule capture and translocation from the bulk solution may alter substantially from those described for the a H L pore. With a method of measuring local concentrations that is label-free and requires no optical detection, and a straightforward method for applying across multiple samples running in parallel, nanopore methods may be candidates for low-cost measurement of nucleic acid concentration. A s device size continues to decrease toward 1 pm, and as synthetic pore manufacturing methods improve, nanopore detectors may become a practical alternative to optical detection. Chapter 3: Trans-side molecule capture and analysis 47 \ Chapter 3 Trans-side molecule capture and analysis Chapter 3: Trans-side molecule capture and analysis 48 3.1 Introduction Th is chapter presents the development o f a prototype nanopore -based sensor for the sequence-speci f ic detect ion o f short nuc le ic ac id fragments across a l i p i d membrane, w i t h s ing le -molecu le sensit iv i ty and the poss ib i l i t y o f use for in vivo detection o f b iomolecu les . The sensor achieves h igh levels o f spec i f ic i ty between the probe and target molecu les and a l lows for the d iscr iminat ion o f different types o f target molecu les based on d issociat ion kinet ics o f hyb r id i zed base-complementary nuc le ic ac id fragments. The mot i va t ion and rationale for the development o f the nanosensor, results and analysis o f exper imental evaluat ion w i t h different target molecu les , and pract ical appl icat ions w i l l be d iscussed. 3.1.1 Shortcomings in existing genotyping detection methods H u m a n genome sequencing and analysis prov ides a p la t fo rm for researchers and c l in ic ians to beg in uncover ing the relat ionship between speci f ic genetic sequences and predisposit ions for certain diseases. In part icular , c lass i f icat ion o f patients accord ing to genetic markers , a process k n o w n as genotyping, is expected to a l l o w c l in ic ians to prov ide personal ized m e d i c a l treatment protocols [6]. Researchers and c l in ic ians are also concerned w i t h measurement o f the expression o f genetic products such as messenger R N A or proteins i n tissue samples as a means to accurately prof i le var iable diseases such as cancer. Consequent ly , there exists a strong and c o m p e l l i n g need for rap id c l i n i c a l genotyping technologies. A number o f enzymat ic , electrophoretic, and chromatographic methods are presently used for b iomolecu le analysis o f target molecu les [85]. One technique w i d e l y used for genotyping and gene expression analysis is so l id -phase hybr id i zat ion , w h i c h rel ies on sequence-speci f ic hybr id i za t ion o f nuc le ic acids [86]. In a typ ica l embodiment , probe nuc le ic ac id fragments w h i c h are base -complementary to the targeted Chapter 3: Trans-side molecule capture and analysis 49 nuc le ic ac id sequences are tethered to a glass sl ide or s imi la r s o l i d surface, w h i l e the f luorescent ly - tagged target sequences are kept i n free solut ion. U V absorbance or f luorescence detection is used to moni to r the presence or absence o f target molecules on the surface [87-90] . A l t h o u g h sol id -phase hybr id i za t ion can be used i n a para l le l i zed , h igh throughput format i n commerc ia l l y -ava i lab le o l igonucleot ide microarrays , the technique has a number o f shortcomings w h e n used to measure gene expression or make quantitative measurements. E n z y m a t i c ampl i f i ca t ion and pur i f icat ion o f the or ig ina l sample is required to generate suff ic ient D N A for detection, w h i c h m a y induce sequence-speci f ic ampl i f i ca t ion bias as w e l l as l imi t the detection o f gene sequences present i n l o w copy numbers [91]. H i g h spec i f i c i t y for microarrays also requires long anneal ing t imes: as hybr id i za t ion rates for short ( - 1 5 - 3 0 nucleot ide bases) complementary strands w i t h a s ing le -base m i s m a t c h are very s imi la r to those w i th f u l l y complementary sequences [92], anneal ing t imes on the order o f hours (often 16 hrs or greater) at elevated temperatures are required to obtain adequate hybr id i za t ion speci f ic i ty . A l t h o u g h some c o m m e r c i a l instruments improve spec i f ic i ty b y electrophoret ical ly d r i v ing molecu les toward or away f r o m the tethered complementary strands [93], these disposable chips are expensive and the technique st i l l requires several hours for sample preparation and surface hybr id izat ion . M i c r o a r r a y s are also k n o w n to have prob lems ach iev ing base-speci f ic d isc r iminat ion i n cases where sequences d i f fe r ing b y o n l y a few nucleot ides are present i n very different quantit ies. D N A microarrays and other genetic analysis techniques w h i c h require c e l l lys is to isolate target b iomolecu les are not appropriate tools for pe r fo rming t ime-dependent gene expression studies or rea l - t ime analysis o f s ingle cel ls . Other techniques must be used for in vivo genotyp ing suitable for real - t ime determinat ion o f genetic expression wi thout the need for ce l l lys is or nuc le ic acid ampl i f i ca t ion . Chapter 3: Trans-side molecule capture and analysis 50 3.1.2 Shortcomings in existing in vivo detection methods A t present, f luorescent probes w h i c h b i n d to target molecu les are introduced into l i v i n g cel ls to uncover spatial and temporal in fo rmat ion about the under l y ing c e l l regulatory networks and mechanisms [7]. F o r example , molecu la r beacons are synthesized dual - labe led f luorescent ly -tagged nuc le ic ac id strands w h i c h use Forster resonance energy transfer ( F R E T ) to f luoresce on ly w h e n the beacon is hybr id i zed to a target strand; such molecu les can be introduced into l i v i n g cel ls to detect the presence o f speci f ic nuc le ic ac id fragments [8 -10] . Another technique is the genetic introduct ion o f Green Fluorescent Prote in ( G F P ) : the D N A cod ing sequence for G F P is added to the end o f the cod ing sequence for the protein o f interest, mean ing that every protein mo lecu le synthesized in vivo has a G F P protein attached v i a a protein chain . Th i s a l lows for proteins produced in l i v i n g cel ls to be tracked opt ica l l y us ing the G F P tethered to the protein o f interest [94]. F luorescence in vivo detection methods have several shortcomings w h i c h l imi t their overal l ut i l i ty . F luorescence detect ion requires a m i n i m u m amount o f f luorescent mater ia l to achieve adequate sensit iv i ty , w h i c h l imi ts the overa l l sensit iv i ty o f the method. Probes such as G F P are large macromolecu les w i t h potent ia l ly l o n g . t i m e -constants for fo ld ing and degradation, t yp ica l l y 30 minutes or longer [95, 96] , w h i c h make them good choices for d i f fus ion measurements l ike F luorescence R e c o v e r y A f t e r Photob leach ing ( F R A P ) and F luorescence Cor re la t ion Spectroscopy ( F C S ) , but poor for fast t ime resolut ion o f synthesis and degradation. F luorescent probes introduced into the c e l l can also perturb the cel lu lar regulatory network b y h y b r i d i z i n g to structures that w i l l then no longer be able to participate i n the dynamics o f the network. Techniques that re ly on base-spec i f ic nuc le ic ac id hybr id i za t ion have l im i ted control on the degree o f non -spec i f i c b i n d i n g w i t h i n the c e l l and m a y not have suff ic ient spec i f ic i ty to d is t inguish fragments d i f fe r ing b y single base mismatches. These shortcomings m a k e it d i f f icu l t for contemporary techniques to measure s ing le - ce l l gene express ion i n real t ime. It is desirable to pursue development o f techniques w h i c h m a y lead to less perturbative techniques for mo lecu le detect ion i n single l i v i n g cel ls . Chapter 3: Trans-side molecule capture and analysis 51 3.1.3 A traws-membrane nanosensor A prototype nanopore-based sensor has been deve loped w h i c h m a y f o r m the basis for new tools i n c l i n i c a l genotyping and in vivo molecu la r studies o f single cel ls . The nanosensor, shown schemat ica l l y i n F igure 3 . 1 , is composed o f an a H L protein channel hous ing a synthesized s s D N A - b a s e d probe molecu le , and can be used for sequence-speci f ic detection o f single nuc le ic ac id molecu les across a l i p i d b i layer . The probe molecu le has an av id in protein anchor at one end and a short nucleot ide b ind ing reg ion sequence at the other end designed to hybr id i ze spec i f i ca l l y to the targeted strand i n solut ion. The operat ion o f the nanosensor is as fo l l ows : w h e n the nuc le ic ac id fragment o f the probe molecu le is electrophoret ical ly inserted into the pore f r o m the m - s i d e , the av id in anchor, too large to fit i n the pore, b l o c k s the probe molecu le f r o m translocating and posi t ions the probe such that the speci f ic hybr id i zat ion sequence protrudes f r o m the trans-side o f the pore. I f this sequence hybr id izes to a base -complementary target m o lecu le on the trans-side, the probe is ef fect ive ly l o c k e d i n p lace unt i l a transmembrane potential is appl ied to p u l l the probe mo lecu le towards the cis-side. S ince the probe-target duplex is too large to fit through the pore, this results i n a d issociat ion force o n the probe-target duplex . The t ime required for d issociat ion o f the probe-target duplex and subsequent escape o f the probe f rom the pore under an appl ied transmembrane potential y ie lds ident i fy ing characteristics o f the target m o l e c u l e ' s interaction w i t h the probe. The nanosensor is thus capable o f transmembrane detection and d isc r iminat ion o f i n d i v i d u a l o l igonucleot ides d i f fe r ing b y a single nucleot ide, and prov ides a means for exp lo r ing s ing le -molecu le hybr id i zat ion and d issociat ion k inet ics . Chapter 3: Trans-side molecule capture and analysis 52 avidin/biotin anchor aHL pore linker target molecule binding region Figure 3.1 -Schematic of the major components of the transmembrane nanosensor The transmembrane nanosensor has a combination of properties not found in any existing methods for analysis of individual nucleic acid duplex structures. Its operation requires no fluorescent tags or sensitive detection optics, and leaves the target molecules being examined unaltered by the detection process. As the assembly and operation of the nanosensor is directed by the applied potential (~100mV) and monitored by ionic current measurement (~10-100pA), the instrumentation required is relatively simple and inexpensive. The system achieves high signal-to-noise ratios of the ionic current (~40) for detection of single-molecule hybridization at room temperature. Unlike many force-dissociation techniques for nucleic acid analysis, the method can also be used to estimate the on-rates of single-molecule hybridization by changing the time allowed for a target molecule to hybridize and monitoring the frequency of binding. The proposed nanosensor lends itself to at least three areas of present interest. First, the scale of the nanosensor and its ability to sample single molecules make it a useful model for an eventual array of synthetic nanopores for rapid clinical genotyping as an alternative to solid-phase hybridization and oligonucleotide microarrays. Second, this Chapter 3: Trans-side molecule capture and analysis 53 nanosensor can also be used to elucidate parameters important for nucleic acid duplex hybridization, which may be used to optimize the design of nucleic acids for in vivo experiments [97], polymerase chain reaction [98], D N A microarrays [99], molecular computations [100, 101], and the construction of nucleic acid-based structural crystals [102]. And third, the organic nature of the pore makes the sensor ideal for incorporation in single living cells and for monitoring and control by means of established patch-clamp techniques; this opens the possibly of in vivo detection of biomolecules in single cells. This chapter describes the testing of the prototype sensor for sequence-specific detection of short nucleic acid fragments for both hybridization and dissociation experiments. The work described includes details on the calibration procedure for estimating the effective charge and force on the confined probe strand, and for distinguishing different populations of molecules based on the time to dissociation under an applied transmembrane potential. Chapter 3: Trans-side molecule capture and analysis 54 3.2 Experimental Method A l l o f the exper imental prototype nanosensor w o r k uses the a H L protein channel reconstituted into a phosphat idy lchol ine l i p i d b i layer membrane ; the protocol for f o r m i n g a H L pores is descr ibed i n detai l i n a prev ious pub l icat ion [36], in A p p e n d i x A , and in Sect ion 2 .2 . A l l nuc le ic ac id fragments and sequences for both the probe and target molecu les i n this study were deoxyr ibose nuc le ic acids. The backbone o f the synthesized probe mo lecu le is a 6 5 -nucleot ide l o n g s s D N A fragment ( M W G B i o t e c h , H i g h Po in t N C ) . The s s D N A fragment consists o f a 51 -base long l inker section cons is t ing o f deoxyadeny l i c ac id (poly(dA) 5 |) w i t h a section o f 14 speci f ic nucleot ides f o r m i n g a hybr id i za t ion region that is complementary to the target mo l ecu l e at the 3' end. The sequence used i n the probe mo lecu le , 3 ' -C C A C C A A C C A A A C C ( d A 5 , ) - 5 ' was chosen to m i n i m i z e both self -hybr id i zat ion and the potential for misa l ignment between the target and probe molecu le dur ing hybr id i zat ion A b iot in group is attached at the 5' end o f the probe molecu le . A 6 nm-d iameter av id in protein is hybr id i zed to the b io t in group, f o r m i n g a molecu lar anchor w h i c h ster ical ly prevents the probe molecu le f r o m complete translocation through the pore. S i n c e each av id in protein molecu le has 4 b i n d i n g sites for b io t in molecu les , the probe molecu les are fabricated b y adding an excess o f a v i d i n i n a 2:1 ratio to lower the l i k e l i h o o d o f mul t ip le s s D N A fragments o n a s ingle a v i d i n protein molecu le . The f a m i l y o f target molecules used in the study consists o f 14 -base long s s D N A fragments either fu l l y complementary to the hybr id i za t ion site o n the probe molecu le or w i t h single nucleot ide mismatches , as shown i n Tab le 3 - 1 . A l s o inc luded i n Tab le 3 -1 is an estimate o f the free energy o f b i n d i n g to the probe molecu le . The free energy estimates were calculated us ing the M f o l d server [103] , an appl icat ion avai lable through the Internet for the predic t ion o f secondary structure and thermodynamic properties o f nuc le ic ac id structures. Chapter 3: Trans-side molecule capture and analysis 55 Molecule Sequence Free energy of binding to probe molecule Probe 3 'CC A C C A A C C A A A C C ( A 5 , ) 5 biotin 14-pc 14-7C 14-10C 14-1A 5 ' -GGTGGTTGGTTTGG -3' 5 ' -GGTGGTT|GTTTGG -3' 5 ' - G G T G I T T G G T T T G G -3' 5 ' -GGTGGTTGGTTTGl l -3' •23.2 kcal/mole •17.3 kcal/mole •17 kcal/mole •21.5 kcal/mole •39.8 k b T •29.7 k b T •29.2 kbT •36.9 k b T Table 3-1 - Sequences and binding energies of molecules used in this study. Binding energies were calculated using the Mfold D N A hybridization server. Nucleotide variations from the perfectly complementary sequence are highlighted. Calculations were carried at 20 °C assuming 1 M NaCl . In a typ ica l experiment, the probe molecules are added to the cis-side o f the pore at ~ 0.5 to 1.0 pM, and target molecu les added to the trans-side o f the pore at 0 . 5 p M . Operat ion o f the nanosensor is contro l led b y vary ing the appl ied transmembrane potential i n response to the measured ion current, as shown i n F igure 3 .2 . The appl ied transmembrane potential is contro l led i n response to the measured i o n current v i a the data acquis i t ion hardware and patch -c lamp ampl i f ie r . The ramp rate for a l l transit ions in the appl ied transmembrane potent ial was 5 V/sec unless otherwise stated. A p p l i c a t i o n o f a + 2 0 0 m V forward potential (anode o n trans-side) across the b i layer induces the free end o f a probe molecu le i n the b u l k solut ion on the cw-s ide to enter the pore and translocate through the pore far enough to be held i n place b y the av id in anchor (F igure 3 . 2 A , B ) . The probe molecu le restricts the f l o w o f charge -car ry ing ions across the pore, result ing i n an increase i n pore impedance f r o m ~ 1 G Q to ~ 4 G Q . The probe molecu le is held i n this pos i t ion under appl ied potential to a l l o w t ime for a target molecu le in bu lk so lut ion o n the trans-side o f the membrane to hybr id i ze to the probe (Figure 3 .2B) . T o determine whether or not a hybr id i za t ion event has occurred, the appl ied potent ial across the membrane is lowered to + 1 0 m V at the end o f this b i n d i n g interval (F igure 3 .2C) . A t this l o w potential , unbound probe molecu les rap id ly exit the pore, result ing i n a return to the open-channel l o w -Chapter 3: Trans-side molecule capture and analysis 56 impedance state. Probe molecules that have hybr id i zed to target molecules remain trapped in the pore, as the probe-target dup lex is too large to enter the pore. Once a persistent b lockage has been detected, the appl ied potent ial is then reversed (anode on cw-s ide) to ~ - 3 0 m V to - 1 0 0 m V , w h i c h results i n a force tending to dissociate the probe-target dup lex (F igure 3 .2D) . The probe-target duplex eventual ly dissociates, at w h i c h point the probe molecu le escapes back to the cz's-side and the pore returns to its l o w - i m p e d a n c e open-channel state (F igure 3 .2E ) . T h e l i fet ime o f the duplex bonds under force can be extracted f r o m the measured ion ic current data. The magnitude o f the d issoc iat ion force (control led by the reverse transmembrane potential) , the t ime a l l o w e d for the probe mo lecu le to hybr id ize to a target strand on the trans-side, and the ramp rate o f the transmembrane potential can a l l be var ied for a g i ven combinat ion o f probe and target molecules i n order to examine the nature o f the bonds w i th in the probe-target duplex . Figure 3.2 -Ionic current and applied transmembrane potential during probe capture, analyte capture and dissociation Chapter 3: Trans-side molecule capture and analysis 57 R e a l - t i m e control o f the appl ied transmembrane potent ial i n response to the measured ion ic current is p rov ided b y a P C - b a s e d feedback-contro l a lgor i thm written i n L a b V I E W software (Nat ional Instruments, A u s t i n T X ) . The measured current is lowpass - f i l te red b y the patch c lamp ampl i f ie r at 10 k H z and sampled at 50 k H z b y the data acquis i t ion system for o f f - l i ne analysis. The t ime resolut ion o f the dissoc iat ion t imes is l imi ted b y the lowpass filtering o f the data acquis i t ion s ignal : w i t h a 4 -po le lowpass B e s s e l f i l ter at 10 k H z , the 10 -9 0 % rise t ime for a step-input is l imi ted to a rise t ime 7}~ 0.33 I fc [104] , w i t h fc the corner f requency o f the lowpass filter. In-the case o f these exper iments, fc= 10 k H z , and Tf~ 33 microseconds . The s ignal is also l i m i t e d b y the ramp-rate o f the appl ied transmembrane voltage due to the capacitance o f the phospho l ip id bi layer , w i t h a step-response t ime constant o f ~ 5 ms . 3.3 Estimation of Effective Charge and Applied Force 3.3.1 Nanosensor probe effective charge Exper iments were conducted to estimate the characteristic charge o f the probe molecu le w i t h i n the pore. Probe molecules were captured f r o m the c/s-side i n the absence o f target molecules on the trans-side. Once the capture o f a probe molecu le was detected, the appl ied potent ial was decreased f r o m + 2 0 0 m V to a smal l pre-set forward potential i n the range o f +7 to +20 m V . The t ime required for the probe molecu les to escape to the cw-s ide , tescape, was recorded. The measurements were repeated to obtain ensemble measurements o f the probe escape t ime, as s h o w n i n F igure 3 .3 . Chapter 3: Trans-side molecule capture and analysis 58 Mean escape time (ms) 9000 8000 7000 ^ 6000 5000 4000 3000 2000 1000 0 300 -, / 200 100 -i t — U 7 8 9 10 11 12 13 14 15 9 11 13 15 Applied Potential (mV) 17 19 Figure 3.3 - Mean probe escape time versus applied transmembrane potential. A close-up of the low-potential data is shown in the inset. A n exponential f it to the probe escape t ime curve i n F igure 3.3 takes the f o r m W = f * W e f t S / 5 / * K (3-D Here , K i s the appl ied potential in m V . Th is relat ion can be used to m a k e an estimate o f the effect ive charge o f the probe molecu le w i t h i n the pore. A f i rst -order m o d e l for probe molecu le escape is an Ar rhen ius re lat ion, w h i c h takes into account the energy barrier associated w i t h the free energy o f conf inement o f the probe molecu le and the appl ied d issoc iat ion force due to the transmembrane potential [105] : R = R gC-'WWO (3 -2) Here , R is the rate o f escape o f probe molecules f r o m the pore, RQ the process-dependent rate constant, Eprobe(V) the force-dependent energy barrier, and kgT the thermal energy scale factor. Eprobe(V) can be expressed as the sum o f the contr ibutions f r o m the transmembrane potential Epotentiai(V), and a l l o f the other contr ibut ions due to the conf inement o f the molecu le such as entropy and p robe -po l ymer interactions Econfmement(V): Chapter 3: Trans-side molecule capture and analysis 59 Eprobe (V) Econj-memml (V) Epotential (V) ^ ^) In the f o l l o w i n g d iscuss ion , Eco„fmement (V) ~ E c o n f i n e m e n t is assumed to be independent o f the appl ied potential . In a previous pub l i shed argument, empi r i ca l data col lected to that point suggested the presence o f a crossover potential at V ~ 10 m V w h i c h separated a d i f f u s i o n -l i m i t e d l inear regime for F l e s s than l O m V , and an energy bar r ie r - l imi ted exponent ia l regime for V greater than l O m V [106]. H o w e v e r , recent invest igat ions at lower appl ied potentials indicates that the transit ion is exponent ia l d o w n to zero appl ied potential [107]. A s s u m i n g a s ingle-barr ier for probe escape 4 , the off - rate R is the inverse o f the escape t ime constant, R = r (3 -4) escape Equat ions (3-2) , (3 -3) , and (3-4) can be c o m b i n e d as: escape D (3-5) = K exp Here , the prefactor K combines both the d i f fus ive re lat ion t ime rD and the exponent ia l contr ibut ion o f the conf inement energy ^V(Ecmf_,lkBT) [105]. A n estimate o f the potential energy term due to the probe mo l ecu l e contained i n the pore is : Epo,en,,al(V) = Zpore(n,rans + * pore ''^V (3"6) In the above expression, zpore is the effective charge per nucleot ide, n,rans the number o f nucleot ides on the trans-side o f the membrane, npore the number o f nucleot ides inside o f the pore, and e the unit charge. The V2 probe (V)/k„T) _ --TDe f _ E potential V kBT J 4 A discussion on models widi multiple barriers and metastable intermediate states can be found in Section 3.5.1 Chapter 3: Trans-side molecule capture and analysis 60 factor for the npore term results f rom the approx imat ion that the drop i n the appl ied potential a long the h igh - f ie ld region o f the pore is approx imately l inear. C o m p a r i n g the crystal lography data o f a H L [42] and the length per nucleot ide i n a single-stranded fragment o f nuc le ic acids results i n an estimate o f ntrans ~ 40 o f the nucleotides on the trans-side o f the membrane, w h i l e npore - 12 w i l l be located in the h i g h - f i e l d reg ion o f the pore, across w h i c h the major i ty o f the electric potential fa l l s , as s h o w n schemat ical ly i n Figure 3.4. Substituting these values into E q u a t i o n (3-6) and match ing the empi r ica l curve f r o m E q u a t i o n (3 -1) y ie lds an estimate zpore - 0 . 4 . -12 i 40 Figure 3.4 -Illustration of the regions of nucleotides on the trans-side of the pore Th is estimate on the fractional charge per nucleot ide zpore - 0.4 is substantial ly h igher than estimates made by M a t h e et al and Sauer -B u d g e et al. f r o m force -d issoc iat ion o f double-st randed nuc le ic ac id ha i rp in structures w i t h i n the vestibule o f the nanopore (0.094 [108] and 0.1 [82]). One recent computer s imulat ion demonstrated that there is substantial counter - ion condensation on nucle ic ac id strands trapped ins ide a nanopore w i t h comparable d imensions to the a H L pore , w h i l e also exc lud ing the c o - i o n i c species f rom the pore [109]. Chapter 3: Trans-side molecule capture and analysis 61 A t least one o f the publ ished methods used to estimate the effect ive charge per nucleot ide us ing d issociat ion experiments appears to be prob lemat ic , as assumptions about the number o f charges w h i c h pass through the appl ied potent ial m a y not apply to the descr ibed d issoc iat ion experiment. A detai led d iscuss ion o f the prev ious exper iment and the result ing ca lcu lat ion o f zpore are inc luded i n A p p e n d i x E . In this l ight , the estimate zpore ~ 0.4 der ived dur ing these experiments w i l l be used i n the next section to estimate the d issociat ion force appl ied to the probe-target duplex . 3.3.2 Applied forces A n estimate o f the appl ied force dur ing forced d issoc iat ion can be made b y assuming a l inear potential prof i le inside the beta-barrel o f the a H L pore [72, 74] , meaning that a l l nucleotides w i t h i n the pore have the same force due to the appl ied potential . The appl ied force is independent o f the number o f nucleotides w h i c h have passed through the pore and o f the number o f nucleot ide base pairs w h i c h have been separated i n the duplex [110], s ince the number o f nucleotides i n the h igh - f i e ld reg ion o f the pore is translat ional ly invariant pr ior to actual escape o f the probe. The s implest estimate o f the force appl ied is on the order: Here , zpore is the effect ive charge per nucleot ide inside the pore, npore the number o f nucleot ides i n the h igh - f i e ld beta barre l , e the unit charge, V the appl ied transmembrane potential , and A/ the length o f the h i g h - f i e l d region. U s i n g the estimate zpore ~ 0.4 inside the pore f r o m the prev ious sect ion, a pore length A/ ~ 6 n m (the approximate length o f the beta-barrel) , and w i t h npore - 1 2 nucleotides inside the h i g h - f i e l d reg ion , an appl ied transmembrane potential o f l O O m V generates a d issoc iat ion f o r c e / - 1 2 p N . Th i s estimate o f the d issociat ion force is i n the range o f forces estimated i n previous s ing le -molecu le d issoc iat ion experiments us ing atomic force m i c r o s c o p y or opt ical tweezers, where bond-breakage due to u n z i p p i n g requires ~ 9 - 2 0 p N o f force [17, 111], w h i l e remain ing Z H i pore pore AT (3-7) Chapter 3: Trans-side molecule capture and analysis 62 w e l l b e l o w the ~ 6 5 p N required to force structural changes i n D N A strands f r o m its t radit ional b e t a - D N A f o r m to stretched S - D N A [112]. 3.4 Single-Molecule Hybridization Kinetics Measurements o f hybr id i zat ion on-rates o f nuc le ic acids are t yp ica l l y conducted w i t h ensembles o f molecules either i n f ree -so lut ion or w i t h probe molecu les tethered to so l id surfaces. Improved methods such as s ing le -molecu le f luorescence cross -corre lat ion spectroscopy [101] have been used to obtain base-speci f ic b i n d i n g in fo rmat ion i n v o l u m e s as l o w as 0.5 femtoliters at l O n M concentrat ion. Surface p l a s m o n resonance techniques, where changes i n the opt ica l refractive indices o f surfaces due to hybr id i zed nuc le ic acids o n surfaces can be detected [87], have led to improvements i n detecting rates o f hybr id i za t ion onto surfaces. E v e n w i t h these improvements , experimental ists have noted d i f f icu l t ies in extracting in fo rmat ion due to background noise f r o m mul t ip le species present i n the sample, the addi t ion o f other reagents to increase hybr id i zat ion str ingency condi t ions to the buffer so lut ion to increase b i n d i n g speci f ic i ty , and the lack o f active contro l o f hybr id i zat ion parameters- other than temperature to improve the spec i f ic i ty o f the reaction. The nanosensor can be used to generate statistical in fo rmat ion about the on-rates o f ind i v idua l molecules . H y b r i d i z a t i o n on-rates can be estimated b y va ry ing the t ime that probe molecu les are exposed to target molecules on the trans-side o f the membrane, thouu as s h o w n schemat ica l l y i n F igure 3 .5 . Th is technique a l lows for m i l l i s e c o n d accuracy and prec is ion i n cont ro l l ing the exposure t ime o f the probe molecu le to the analyte so lut ion not possible w i t h convent ional f l o w - c e l l technologies for f ree -so lut ion or sur face-hybr id izat ion analysis . H y b r i d i z a t i o n on-rates can be estimated without re l y ing on compl i ca ted m i c r o f l u i d i c s to regulate and vary exposure t imes. The nanosensor can also prov ide an increased leve l o f b ind ing str ingency, as s ing le -molecu le hybr id i za t ion events can be combined w i t h the d issoc iat ion event Chapter 3: Trans-side molecule capture and analysis 63 discrimination described in Section 3.5, a function that cannot be duplicated by any other conventional means of measuring hybridization on-rates. 2 0 0 < Q. - 1 0 0 > E - 1 0 0 .4,,, . ^ W W . i ^ hold 0 . 0 5 0 . 1 0 0 . 1 5 : | J [ _ ! 0 . 2 5 t(8) 0 . 3 0 Figure 3.5 - Schematic of the applied transmembrane potential and resulting ionic current during single-molecule hybridization rate experiments, highlighting the exposure time of the probe molecule to the trans-side, thlM To verify the operation of the nanosensor for measurement of hybridization on-rates, experiments were conducted with the perfectly-complementary target molecule 14PM at a concentration C = 0.5 pMon the trans-side of the membrane. In order to estimate a hybridization on-rate for the probe-target interaction, the probability that a target molecule had hybridized to the probe molecule was calculated for a range of thoid values shown in Figure 3.6. For the perfectly-complementary target molecule at the given concentration, the hybridization probability versus thoid saturates exponentially with a time-constant of 280ms to a steady-state value for -80 percent of the population of attempts. The remaining -20 percent are believed to be attempts resulting in no hybridization, even after an extended wait. Hybridization experiments on solid surfaces show analogous behavior, with 4 to 15 percent of events believed to result in no hybridization [87], presumably as a result of non-specific interactions between the probe and surface, hindering probe-target binding. The experimental time-constant and the target molecule concentration can be combined to estimate the hybridization on-rate, as follows: Chapter 3: Trans-side molecule capture and analysis 64 C*ko„=-3.6s~' ->kon= 7 . 2 x ^ A r V ' (3"8) Th is is a m u c h faster on-rate than those found for surface-tethered molecu les (kolh s u r f „ c e ~ 1.2 x 1 0 4 M ' V [87]), but is i n reasonable agreement w i t h the hybr id i zat ion on-rates measured b y H o w o r k a et al. for nuc le ic ac id fragments h y b r i d i z i n g to complementary strands tethered w i t h i n the pore entrance o f a genet ical ly m o d i f i e d a H L pores (kon_ inner pore - 1 - 2 x l O 7 Ivf's"1 [113]). It is somewhat surpr is ing to get better agreement w i t h the strand tethered to the vest ibule o f the a H L channel : internal ly - tethered strands m a y benefit f r o m a more favourable geometry f r o m the l inear izat ion o f translocating target molecu les , but are i n a reg ion o f h igh electr ic f ie ld w h i c h m a y tend to separate the probe and target molecu les before fu l l b ind ing . Analyte Capture Probability 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 100 1000 Hold Time (ms) 10000 Figure 3.6 -Probability of binding for single-molecule hybridization of 14PM molecule at 0.5 u M . The line indicates the exponential fit to the experimental data. The exper imental hybr id i zat ion on-rates can be used to estimate the lower l i m i t o f target concentrat ion est imation. The concentrat ion required i n order to result i n the detection o f one event g i v e n a mean capture t ime for the probe molecu le to hybr id i ze to a target mo lecu le w i t h a 75 percent probabi l i t y is : Chapter 3: Trans-side molecule capture and analysis 65 In 1 -0 . 7 5 ^ ,(-Ckml V o.8o; (3-9) 0.75 = 0.80(1 -e ) c = -W i t h kon = 7.2 x 1 0 6 M~'s~l, and a n o m i n a l upper mean capture t ime o f 10 seconds, the m i n i m u m concentrat ion for operat ion is C ~ 30 n M . Th i s corresponds extremely w e l l to w o r k b y M o v i l e a n u et al. for est imating streptavidin concentrations in so lut ion (—50 n M ) us ing b iot iny lated polyethy lene g l y c o l molecules tethered inside a H L channels Investigations o f hybr id i zat ion on-rates o f target o l igonucleot ides that do not have per fect ly -matched sequences to surface-tethered probe molecu les have had m i x e d results: both faster [87] and s lower [89] kon rates have been observed for fu l l y complementary strands compared to those w i t h single base-pai r mismatches. S u c h conf l i c t ing results m a y be the result o f several different condit ions: surface preparation, total number o f bases in the strand (15 vs. 60) , pos i t ion o f the m i s m a t c h , or length and nature o f the l inker ho ld ing the tethered o l igonucleot ide to the surface [88] are a l l areas w h i c h can be investigated w i t h thoughtful select ion o f probe and target molecules . In a l l l i k e l i h o o d , it w i l l not be pract ical to d iscr iminate populat ions based str ict ly on hybr id i za t ion rates, but rather to use the measurements discussed i n this sect ion a long w i t h the d issoc iat ion kinet ics discussed in Sect ion 3.5 to more comple te l y quant i fy target molecu les i n solut ion. [114]. Chapter 3: Trans-side molecule capture and analysis 66 3.5 Single-Molecule Dissociation Kinetics D i s s o c i a t i o n experiments us ing the nanosensor have been used to d ist inguish between populat ions o f s ingle-stranded nuc le ic acids d i f fe r ing b y o n l y a single nucleotide. P r io r to e x a m i n i n g the exper imental d issoc iat ion data, it is useful to first discuss the poss ib le mode ls for d issoc iat ion as a basis for understanding the col lected data. Th i s sect ion describes the construct ion o f an appropriate d issoc iat ion m o d e l for the nanosensor experiments, and an analysis o f exper imental data f r o m four target molecu le populat ions d i f fe r ing b y a s ingle nucleot ide. 3.5.1 Dissociation models D i s s o c i a t i o n k inet ics o f nucle ic ac id duplexes can be investigated b y statistical analysis o f the d issociat ion t imes o f an ensemble o f s ingle d issoc iat ion events. External force as appl ied b y the transmembrane potent ial restricts the phys ica l m o t i o n o f the probe molecu le to the d i rect ion o f the appl ied force [105], i n this case a long the central nanopore axis . Th is assumes that both mic roscop ic f luctuations o f i n d i v i d u a l base pairs d issoc iat ing and re forming as w e l l as the thermal re laxat ion o f nuc le ic ac id sections not i n the duplex structure are m u c h faster than the overa l l rate o f d issociat ion. I f this is true, then the system can be reduced to a 1 -D m o d e l a long a single react ion coordinate and an appropriate transit ion m o d e l can be ident i f ied i n con junct ion w i t h empi r i ca l data. T w o - s t a t e T r a n s i t i o n M o d e l A two-state transit ion m o d e l for d issociat ion is a f i rst -order k inet ic m o d e l , starting w i t h the probe-target duplex , here ca l led state A, and proceeding to the f inal d issociat ion o f the probe and target molecu les , here ca l led state B, w i t h no stable intermediaries a long the react ion path [115]. A s the events detected by the nanosensor are s ing le -Chapter 3: Trans-side molecule capture and analysis 67 molecule interactions, the functions Aft) and Bft) below represent the probability that the system is fully bound as a duplex in state A or with the two strands completely dissociated in state B at time t, with Aft) + Bft) = J for all t, and with initial conditions A(0) =1, BfO) = 0. In all of these discussions, once state B is achieved there is no possibility of returning to state A; the dissociation of the probe and target molecule is permanent and is not a reversible process. In this case, the first-order transition has the form: A ^ ^ B (3-10) dA _ dB _ M dt dt This system has the solution A(t) = A0e~l" and B(t) = 4,(1-ef*'). The observable dissociation time in this case is Bft), in this case a simple exponential approach to 1 with time constant 1/k. A two-state model for the dissociation kinetics of the probe-target duplex can be examined in further detail by applying an Arrhenius relation, also referred to as Kramer's relation for overdamped kinetics [105]: R = R e(-Eo(V)lkHT) (3-11) Here R is the off-rate or escape rate, R0 the process-dependent off-rate constant, E0fV) the force-dependent energy barrier, and kBT the thermal energy scale factor. E0(V) can be expressed as the sum of the contributions from the transmembrane potential Ep0,enliai(V), and all o f the other contributions due to entropy and probe-polymer interactions Eb(V): E0(V) = Eb(V)-Epotenlial(V) (3-12) For a single-barrier model, the off-rate R is the inverse of the escape time constant, (3-13) Chapter 3: Trans-side molecule capture and analysis 68 Equat ions (3 -11) , (3 -12) , and (3-13) can be c o m b i n e d to f o r m : _ - T „(E„(V)im ((Eh{V)-EIMmM(V))lk„T) (3 -14) escape D D In this expression, zD is the duplex re laxat ion t ime, w h i c h can be though o f as the inverse o f the attempt rate o f duplex d issociat ion. A n approx imat ion for the energy o f the appl ied potential can be expressed as: E P " ( V ) =F(F)Ax (3 -15) Here , F(V) is the force appl ied to the mo lecu le and Ax the p h y s i c a l barr ier w i d t h a long the react ion coordinate. In a nanopore-d issoc iat ion experiment, the appl ied force F(V) due to an appl ied transmembrane potential does not depend on the pos i t ion o f the p o l y m e r w i t h i n the pore, o n l y that the force remain translat ional ly invar iant as the strand moves through the pore. Th is w i l l be true as the probe strand goes from the duplex state to d issociat ion. The distance value Ax represents the phys i ca l distance a long w h i c h that force acts in go ing f r o m the f u l l y b o u n d state to a transit ion state i n w h i c h the two fragments have reached the peak o f the d issoc iat ion energy barrier; i n this state, the probe and target molecu les m a y be part ly or fu l l y dissociated, as the peak o f the barrier does • not necessari ly represent fu l l d issoc iat ion o f the duplex sect ion. W i t h the d issociat ion measurements taken i n these exper iments, w e can on ly infer what these d issoc iat ion distances are, g i ven exper imental estimates o f A x . F igure 3.7 schemat ica l ly i l lustrates the relat ionship between the barrier and the react ion coordinate distance, w h i l e F igure 3.8 i l lustrates possib le conf igurat ions o f the duplex and transit ion states. Chapter 3: Trans-side molecule capture and analysis 69 A x Transition state Figure 3.7 -Schematic illustration of the barrier and reaction coordinate during probe-target dissociation. duplex a ^^ ^^ ^^ ^ Full dissociation Partial dissociation Figure 3.8 -Schematic illustration of the duplex and two possible states at the peak of the energy barrier. Chapter 3: Trans-side molecule capture and analysis 70 A n estimate for the translat ional ly - invar iant appl ied force ins ide o f a nanopore is g iven by : F(V) = ZP o r e n e V Al (3 -16) Here , zpore and AI are the effect ive charge and length per nucleot ide, n the number o f nucleotides in the h i g h - f i e l d region o f the pore, and e the elementary charge. A s s u m i n g Ey(V) ~ E0 is constant under va ry ing potent ia l , c o m b i n i n g Equat ions (3-14) and (3 -15) , w e get: T off ~ T D e X P f E ^ kBT exp - Z p o r e n e V v Ax^ Al (3 -17) The expression takes into account the energy barrier associated w i t h the sequence-dependent free energy o f the duplex and the appl ied d issoc iat ion force due to the transmembrane potential . T a k i n g the logar i thm o f both sides o f Equat ion (3-17) results i n : l n r 0 # =(lnr 0 )-\ k B T J jieVY Ax A Al (3 -18) It is possib le to dist inguish the target molecu le populat ions based on differences i n the energy barrier Ea, and the phys ica l distance to the energy barrier A x b y m a k i n g ensemble measurements o f d issoc iat ion t imes Toff for a part icular probe-target duplex at var ious appl ied potentials. There is phys i ca l just i f i cat ion for the use o f a two-state system w i t h a single-barr ier potential to m o d e l the dissociat ion o f the 14-base l o n g probe-target duplex . The probe-target mo lecu le forms a double -he l i x w h i c h contains h igh l y cooperative bonds due to base -s tack ing and nearest -neighbor interactions, meaning that it m a y be imposs ib le to break a s ingle nucleot ide base-pai r without break ing them a l l s imultaneously . D u p l e x d issoc iat ion is often v iewed as a two-state transit ion, a l though at Chapter 3: Trans-side molecule capture and analysis 71 higher salt concentrations (>1M) the transitions become less cooperat ive due to sh ie ld ing o f electrostatic interactions o f the backbone [116]. A l t h o u g h intermediates m a y be found dur ing the d issoc iat ion o f m u c h longer molecu les such as A - D N A (~ 48 ,000 bp) [117] and others [82], the stiffness and short length o f the 14 nucleot ide double-stranded h e l i c a l reg ion , w i t h a persistence length o f - 5 0 n m at h igh salt concentrations [118], and the cooperative interactions a long the duplex a l l m a k e it l i k e l y that a two-state m o d e l is appropriate for this part icular system. The two-state m o d e l fai ls w h e n the results f r o m force -d issoc iat ion t ime experiments do not f o l l o w a s imple exponent ia l d ist r ibut ion, as is the case required to a l l o w Equat ion (3 -13) to be used. In the case where the d issociat ion is not a s imple exponent ia l re lat ion and therefore not a true two-state interaction, several other poss ib i l i t ies m a y occur , o f w h i c h three are examined here. F i rst , para l le l react ion paths m a y exist between the in i t ia l duplex state and the f ina l d issoc iat ion state and act s imultaneously ; second, mul t ip le in i t ia l duplex states m a y exist , each o f w h i c h has a unique path to the same f ina l d issoc iat ion state; and th i rd , the react ion coordinate m a y have one or more intermediate states pr ior to reaching the d issoc iat ion state. P a r a l l e l T w o - S t a t e T r a n s i t i o n s , S a m e I n i t i a l State Processes w i t h two or more reaction paths operating i n para l le l between the in i t ia l duplex state A and the f ina l d issoc iat ion state B can be mode led as [115]: A ^ ^ B (3 -19) A k" >B — = -— = -(&, +k2 +... + kN)A = -kA, k = 'Yki dt dt /=1 Chapter 3: Trans-side molecule capture and analysis 72 Th i s system has a so lut ion o f the same f o r m as the s ing le -path f i rst -order t ransit ion A(t) = A0e'k' and B(t) = A^(l -e~kl), w h i c h combines the rate constant f r o m a l l o f the paths into a single effect ive rate constant k. It is clear that a system w i t h paral le l paths between states A and B h a v i n g mul t ip le rate constants k is observat ional ly ident ical to a system w i t h o n l y one react ion pathway and rate constant k. A n Ar rhen ius analysis as per Equat ion (3-17) impl ies that the relative we ight ing o f each d issoc iat ion pathway is necessari ly : Exper imenta l l y it is not possib le to dist inguish the react ion paths f r o m one another i f o n l y the in i t ia l and final states are observable. Parallel Two-State Transitions, Different Initial States It is possib le that there are N different in i t ia l states, labeled A/ through AN, w h i c h f o l l o w independent d issociat ion pathways to reach the same final dissociated state B. Th is w o u l d be the case i f target molecu les w o u l d b i n d to the probe molecu le i n different conf igurat ions, poss ib l y offset f r o m the perfect al ignment, or i f there are in i t ia l states w i t h the probe molecu le interacting w i t h the surface or pore prevent ing b i n d i n g w i t h the target molecu le . Th is react ion can be mode led as [113]: (3 -20) A N 'N_ >B (3 -21) dA: = -KA, clB — ^ i v 4 j k-jA*) ... dt dt N 2> , (o )= i Chapter 3: Trans-side molecule capture and analysis 73 Th i s di f ferent ial equation has a solut ion o f the f o r m : 4(0 = 4 (OK* ' (3 -22) 5(0 = i -X4 ( 0 K * ' ' -In this case, the observable d issociat ion t ime Bft) is the s u m o f a series o f s imple exponentials , the sum o f w h i c h approaches 1 as t increases. N o t e that the weight o f each o f the t ime constants is on ly dependent o n the in i t ia l we ight ing o f the states AfO), and not on the rate constants kt as was the case for paral le l f i rst -order transitions w i t h the same in i t ia l state. Therefore the different states should be dist inguishable f r o m one another b y observ ing the presence o f different t imescales i n the col lected data, p rov ided that the we ight ing o f the or ig ina l states is not g i ven b y E q u a t i o n (3 -20) , i n w h i c h case the solut ion appears ident ical to a s ingle exponent ia l . F o r example , i n one study per formed b y H o w o r k a et al. [113] , ident i f icat ion o f mul t ip le starting conf igurat ions was conf i rmed b y ident i f y ing that the we ight ing o f the or ig ina l states d i d not f o l l o w E q u a t i o n (3-20) . T h r e e - S t a t e T r a n s i t i o n A three-state transit ion introduces an intermediate state I between the in i t ia l duplex state A and the f ina l d issociat ion state B. h i the present system, this w o u l d be case i f there was a case where the duplex entered into a metastable conf igurat ion where the duplex was o n l y par t ia l l y d issociated. Th i s react ion has the f o l l o w i n g format [115] : —*-»./<-^—k-^B ( 3 " 2 3 ) I f the bias due to the appl ied potential is h igh enough so that the backwards reactions k./ and k.? are both essential ly neg l ig ib le , the react ion can be s i m p l i f i e d to: (3 -24) Chapter 3: Trans-side molecule capture and analysis 74 dl_ dt = klA-k2I dB_ dt = k2I Solut ions o f these coupled di f ferent ial equations, w i t h the in i t ia l cond i t ion A(0) = A0, have the f o r m : A(t) = A0e -k.i I(t) = Aa (e -* ' ' -e -* J ' ) k2 - kx = Ar B{t) = A0-A(t)-I(t) f k A l_g-*. ' l l_( e -*. '_ e -*2 ') k2 - kx (3 -25) A l /C-y fat \kxe-kl' -k2e-k'') The distr ibut ion o f d issociat ion t imes to state B(t) has a characterist ic p rof i le more c o m p l e x than found i n the prev ious examples . A h is togram o f the d issoc iat ion t ime distr ibut ion can be used i n order to exper imenta l ly infer the presence o f an intermediate state, as a h is togram is analogous to the derivat ive o f the probabi l i t y d ist r ibut ion o f the observable l i fe t ime B(t): dt k^ (3 -26) N o t e that the derivat ive o f the probabi l i ty d istr ibut ion is zero at t imes t = 0 and t -> oo , and w i l l reach a m a x i m u m value at t ime t = ln(A:, Ik2) k^ (3 -27) Chapter 3: Trans-side molecule capture and analysis 75 A l s o note that the sign o f the expression i n Equat ion (3-27) remains greater than zero regardless o f whether k/ > k2 or kj < k2. Another too l used to infer the presence and number o f intermediate states is the randomness parameter, def ined as [119]: 2 r = (3 -28) 2 Toff Here <x, is the standard dev iat ion o f the mean t ime to d issoc iat ion . F o r a single two-state process, the d issoc iat ion t imes are exponent ia l l y distr ibuted, and roff = cr, , w i t h the result ing randomness parameter r = 1. In the case where there are Af intermediate states, each o f w h i c h can be m o d e l e d as a two-state process w i t h ident ical mean t ime and standard deviat ions roff and a respect ively , the numerator o f the randomness parameter r scales as a]otal = Naf w h i l e the denominator o f r scales as Toff = Nroff. Therefore, the randomness parameter r scales as 1/N. T h e inverse o f the parameter, 1/r, can therefore be used as an estimate o f the lower l i m i t o f the number o f intermediates that are i n the process [119, 120] 5 . A s the number o f intermediates introduced i n the process increases, r decreases, and the overa l l process becomes more determinist ic as the relat ive value o f the standard dev iat ion versus the mean value decreases. Th is mechan ism o f adding intermediate states to reduce the stochastic character o f a process is important for regulat ion o f enzymat ic processes [119]. In cases w i t h r > 1, the d ist r ibut ion has a standard dev iat ion larger than an exponential d ist r ibut ion, and m a y reflect the presence o f mul t ip le d issociat ion pathways w h i c h contr ibute to the increased standard deviat ion. 5 This expression only estimates the lower bound, since faster intermediate states will be dominated in the expressions in Equation (3-28) by the slower states and will not have the same effect on the randomness parameter value. Chapter 3: Trans-side molecule capture and analysis 76 3.5.2 Experimental Results Presence of multiple timescales The d issociat ion t ime t0ff for each o f the four different target molecu les l isted i n Table 3-1 on page 55 were measured at a var iety o f appl ied potentials. 60 to 500 successful d issoc iat ion events were recorded for each target molecu le at each appl ied potential and used to generate statistical in format ion at each data point . F o r each data point , the col lected exper imental d issoc iat ion t imes t0jf are converted to probabi l i t y d ist r ibut ion B(t) by p lac ing the N d issoc iat ion t imes t0ff i n rank order and creating the distr ibut ion: B(<oA0) = j;> i = W,-,N (3"29) N o t e that this distr ibut ion is analogous to a probabi l i ty d ist r ibut ion funct ion w i t h unequal t ime spacing for the d issociat ion t imes Bft). A representative example o f Bft) is shown i n F igure 3.9 for the 1 4 p m mo l e cu l e at - 7 0 m V . A typ ica l h is togram o f d issoc iat ion t imes, again for the 1 4 p m target molecu le at - 7 0 m V , is shown i n F igure 3 .10. The lack o f a dist inct peak i n the histogram shown and those for the vast major i t y o f a l l other molecules and appl ied potentials indicate that intermediate states are not l i k e l y i n the d issociat ion. The randomness parameter value r for each o f the four target molecu les at each appl ied potential was calculated. The exper imental randomness parameters ranged f rom 0.75 to 15, w i t h the vast major i t y o f parameters greater than 1, g i v i n g no conc lus ive ind icat ion that any intermediate states were present i n the d issociat ion. F igure 3.11 shows a his togram o f the distr ibut ion o f the four molecules across a l l potentials. There was no discernable trend in the informat ion w h e n l o o k i n g at data co l lected for speci f ic molecu les , at specif ic potentials, or i n data sets w i t h a larger number o f col lected events. Chapter 3: Trans-side molecule capture and analysis 11 B(t) 0.1 0.01 • • • • • 10 100 1000 10000 100000 time (ms) Figure 3.9 - Probability distribution of dissociation times B(t) for 14pm molecule at -70mV normalized count # 0.3 0.25 0.2 0.15 0.1 0.05 0 10 32 100 316 1000 3162 10000 31623 100000 dissociation time (ms) Figure 3.10 -Normalized histogram of dissociation times B(t) for 14pm molecule at -70mV Chapter 3: Trans-side molecule capture and analysis 78 2 4 6 8 10 12 14 More all randomness parameter values count, i n 0.5 1 1.5 2 2.5 3 3.5 ' randomness parameter below 4 Figure 3.11 -Histogram of randomness parameter values across all four target molecules at all applied potentials (left). Expanded view of histogram for randomness parameters below 4 indicates only 4 data points out of 42 (-10%) had r< 1. It is possible that intermediate states m a y be present i n mul t ip le pathways, but more data is necessary to draw evidence in the d issoc iat ion mechanisms and to d ist inguish between d issoc iat ion events and other issues w i t h probe escape [107]. G i v e n these observat ions, a l l o f the f o l l o w i n g analyses assume no intermediate states dur ing d issoc iat ion . The lack o f intermediate states is i n agreement w i t h other exper imental w o r k w i t h nanopore -unz ipp ing us ing duplex structures o f s imi la r lengths [108], but is different f r o m models used to examine longer strands (~50 bases) where it is expected that the process proceeds by a s t i ck -and -s l ip method w h i c h inherently introduces intermediate states a long the d issoc iat ion pathway [82, 113]. I d e n t i f i c a t i o n o f D o m i n a n t T i m e s c a l e s A s imple exponential fit cou ld not be consistently used to f it the co l lected data sets for d issoc iat ion t imes at a g i ven appl ied potent ia l . The probabi l i ty d istr ibut ion B(t) presented i n F igure 3.9 is indicat ive o f this issue, i n part icular because o f s k e w i n g at both short and l o n g t imes. In order to ident i fy the t ime scales o f relevance present i n the analysis o f the t imescales rnff for each target molecu le at each appl ied potent ia l , an approach us ing non-negat ive least squares ( N N L S ) f i t t ing w i t h regular izat ion [121, 122] was appl ied to the col lected data. Th i s Chapter 3: Trans-side molecule capture and analysis 79 approach is used i n nuclear magnetic resonance spectroscopy for ident i f y ing dominant t imescales i n T I and T 2 re laxat ion t imes, and a l lows for the e luc idat ion o f the number and relat ive we ight ing o f the t imescales present w h i l e m i n i m i z i n g the coeff ic ients o f t imescales already c lose to zero. The N N L S procedure at each appl ied potential for each target mo lecu le and appl ied potential begins by f i t t ing the probabi l i t y d ist r ibut ion B(t) to an expression containing exponent ia l terms distr ibuted equal ly o n a logar i thmic scale w i t h u n k n o w n coeff ic ients , tak ing the f o r m : B(toff(i)) = 1 - f>, .e~" r y , / = 1,2,.. . , TV •'=' (3 -30) T . = ( l 0 0 1 2 5 / ' / 5 0 , 0 0 0 ) s e c ; j = 0,1,.. . ,48 In this analys is , the a l lowed t imescales ranged f r o m 20 ps to 20 s, w i t h 48 values chosen to g ive adequate coverage across the spectrum o f poss ib le t imescales i n this rage. F o r each target m o l e c u l e , the coeff ic ients aj were free parameters fit to the exper imental d ist r ibut ion i n E q u a t i o n (3 -27) us ing a N N L S w i t h regular izat ion a lgor i thm c o m p o s e d i n Mathemat ica . The expression to be m i n i m i z e d i n the N N L S w i t h regular izat ion is : K{ax,a1,...,aj) = ^ 1=1 l - 5 ( * o j r ( 0 ) - J > ; e 4 8 7 = 1 4 8 + 1" ' 7=1 0. F igure 3.12 shows the result o f this analysis o n two different target molecu les at - 5 5 m V : F igure 3 . 1 2 A shows the best fit for the weight ings aj to B(t) for the 7c molecu le , wh i le F igure 3 . 1 2 B shows the best fit for the 14pc molecu le . In both these cases, the t imescales for B(t) are dominated b y one or two t ime-scales , a situation w h i c h ho lds true for a l l co l lected data. F o r the 7c molecu le at - 5 5 m V , the dominant t i m e -scales are 2.7 ms (wi th the we ight ing coeff ic ient a, = 0.58) and 8.4 m s (a, = 0.24), w h i l e for the 1 4 P M molecu le at - 5 5 m V , the dominant t ime (3 -31) Chapter 3: Trans-side molecule capture and analysis 80 scales were 100 ms (a, = 0.39) and 1300 ms (a, = 0.34), w i t h a th i rd peak at 27ms (a, = 0.10). CO 0.6 0.4 0.2 0 jl A 0.4 0.2 0 B JL 0.01 0.1 1 10 100 1000 ms 0.01 0.1 1 10 100 1000 ms Figure 3.12 - Time scales aj for 7c at -55mV (A) and 14pm at -55mV (B) Figure 3.13 shows the t ime scales for the 10C target mo lecu le at appl ied potentials ranging f r o m - 3 5 to - 8 0 m V . E a c h point i n this p lot represents one o f the t ime scales ident i f ied i n the non-negat ive least squares f it , w i t h the diameter o f the c i rc le ind icat ing the relat ive magnitude o f the coeff ic ient a,-. The dotted l ine on the f igure separates the dominant t ime scales inc luded in the calculat ion o f the average t ime scale at each potent ial , and the short - l i ved t ime scales considered to be spurious and not used i n the calculat ion. N o t e that f r o m F igure 3.13 it appears that two distinct processes may be part o f probe-target d issoc iat ion , w i t h a different process b e c o m i n g more dominant at higher appl ied potentials. Th is effect m a y be a result o f access to different probe-target d issociat ion pathways at higher potentials, or m a y be a secondary effect o f the N N L S a lgor i thm w h i c h m i n i m i z e s coeff ic ients already close to zero rather than a l l o w i n g a range o f smal l -ampl i tude coeff ic ients . T o date, there has been no invest igat ion or conf i rmat ion as to w h i c h o f these two mechanisms is the most l i k e l y cause o f this effect. Chapter 3: Trans-side molecule capture and analysis 81 10000n ms 0.1 "I 1 , 1 T 1 • 1 1 1 20 30 40 50 60 70 80 90 100 mV Figure 3.13 - Complete dissociation time scales iij for 10c molecule at various applied potentials. The diameter of each spot indicates the relative magnitude of the timescale. Points below the dotted line were considered spurious and were not included in the weighted averaging to generate T f ) / . The analyses descr ibed above assume that the dominant t imescales o f Bft) ident i f ied i n F igure 3.13 are the direct result o f the d issoc iat ion o f the probe-target duplex , though poor ly def ined shorter and longer t ime scales do appear i n most o f the data. Short t ime scale events m a y result f r o m analyte molecules incorrect ly hyb r id i zed to the probe, an event w h i c h also occurs in surface hybr id i za t ion experiments [87], as do the occasional delayed escape o f unbound probe molecu les noted i n Sect ion 3 .3 . Occas iona l l o n g - l i v e d events m a y result f r o m the probe or probe-analyte duplex becoming lodged i n the pore leading to b lockages last ing seconds to minutes, as prev ious ly observed i n studies o f s s D N A translocat ion through the a H L pore [37, 4 4 , 48] . Prev ious investigations o f se l f -complementary nuc le ic ac id fragments w h i c h f o r m hai rp in structures d id not make note o f mul t ip le Chapter 3: Trans-side molecule capture and analysis 82 t imescales present i n the col lected data [82, 108]. It is not entirely clear whether this effect is caused by the constituents o f the probe mo lecu le , the select ion o f av id in as the anchor to ho ld the probe mo lecu le w i t h i n the pore, any possib le interactions between the probe mo lecu le and the membrane surface, or a result o f the reversal i n the appl ied potent ial w h i c h might alter the structure or funct ion o f the pore or support ing membrane. Further invest igat ion is necessary to loca l i ze and address these effects [107]. C o m p a r i s o n o f D i f f e r e n t M o l e c u l e s The average t imescales for the four target molecu les were obtained b y averaging the weight ings obtained f r o m the non-negat ive least squares fit exc lud ing the spurious t imescales: V = e x p [ ' ] (3 -32) i where j is the set o f coeff ic ients pertaining to dominant t ime scales. The average t imescales are plotted as functions o f the appl ied potential i n F igure 3.14. Errors bars for each data point i n F igure 3.14 were calculated b y app ly ing a bootstrap a lgor i thm to the generation o f the coeff ic ients [123]. In br ief , the bootstrap a lgor i thm consists o f f irst select ing w i t h replacement a subset o f N elements f r o m the exper imental t0ff t imes, then us ing the subset to generate we ight ing coeff ic ients a(. T h i s process was repeated K t imes to generate K sets o f we ight ing coeff ic ients w h i c h were then used to calculate the mean and standard error for each coeff ic ient a y by f i t t ing to a sum o f Gauss ian curves. T h e composi te error bars at each appl ied potential were then calculated b y add ing the errors f r o m each o f the dominant a, coeff ic ients i n quadrature. Chapter 3: Trans-side molecule capture and analysis 83 10000 -1000 100 Average Event Lifetime (ms) 10 1 0.1 -15 -25 -35 -45 -55 -65 -75 Applied Potential (mV) Figure 3.14 - Average measured event lifetimes extracted from non-negative least square error fits to Pesc(t) for all four molecules Exper imenta l evidence presented i n F igure 3.14 g ives strong support that the average t imescales t0ff depends exponent ia l ly o n the appl ied potent ia l , as expected f r o m the Ar rhen ius relat ionship and t w o -state m o d e l . In addi t ion, it is clear that target molecu les d i f fe r ing i n sequence b y a single nucleot ide y i e l d measurably different dominant t imescales at the same appl ied potential . A l l three target molecu les w i t h s ingle -point mismatches and correspondingly lower free energy o f b i n d i n g had lower dominant t imescales than the per fect ly -matched 14PC target molecu le . T y p i c a l average dissociat ion t imes measured in these experiments were o n the order ~ l m s to ~ l s ; shorter average d issoc iat ion t imes at higher transmembrane potentials cou ld not be resolved due to the capaci t ive effect o f the membrane, w h i l e longer average d issoc iat ion t imes cou ld not be resolved w e l l due to the lower number o f measured d issociat ion events at t imes > 10 s contr ibut ing to the overa l l statistics w h i c h were not w e l l represented i n the col lected data as dist inguishable f r o m permanent b lockages [44]. Chapter 3: Trans-side molecule capture and analysis 84 The dominant t imescales described here were comparable to other exper imental w o r k for d issociat ion o f nuc le ic ac id duplexes b y Sauer -Budge et al. and M a t h e et al.; i n these experiments, d issoc iat ion occurred on a s ingle-stranded nuc le ic ac id overhang on one o f the duplex ends extending into the h i g h - f i e l d beta barrel reg ion o f the pore w h e n d issoc iat ing on the cz's-side o f the pore (0.01 - 1 sec) [82, 108], yet were ~2 orders o f magnitude shorter than w o r k b y Vercoutere et al. o n the d issoc iat ion o f b lunt -ended hai rp in structures on the czs-side o f the pore [54]. I o n C u r r e n t B l o c k a g e L e v e l A s prev ious ly noted i n Sect ion 3 . 5 . 1 , shorter and longer t imescales considered spurious i n this invest igat ion m a y be the result o f different d issoc iat ion pathways. One independent means o f invest igat ing the presence o f mul t ip le d issociat ion mechanisms is observat ion o f patterns i n a scatterplot o f the mean b lockage current versus d issoc iat ion t imes. S u c h f luctuations are a sensitive means o f detecting subtle differences for b i o l o g i c a l po lymers interacting w i t h the pore, such as d is t inguish ing between D N A or non -nuc le ic ac id based sections i n the beta-barrel o f the pore [124], and determining the end-phosphory lat ion state o f s s D N A on both the 5' and 3' ends o f the mo lecu le t ranslocat ing across the pore [46]. A representative scatterplot o f the mean b lockage current versus d issoc iat ion t ime is shown i n F igure 3.15 for the 10c mo lecu le at - 5 5 m V . N o t e that the exponential decay o f the b lockage current at t imes shorter than ~ 5 m s is a result o f the t ime required for capaci t ive re laxat ion due to the l i p i d b i layer , ref lected i n scatterplots for i n d i v i d u a l channels. T h e effect o f the l i p i d b i layer capacitance can be corrected i n future experiments through compensat ion electronics bui l t into the patch c l a m p ampl i f ie r to obtain data f r o m shorter d issociat ion t imes [107]. The scatterplot shown i n F igure 3.15 shows that d issoc iat ion t imes longer than ~ l s e c m a y have a lower mean b lockage current, ind icat ing that l o n g - l i v e d blockages m a y result f r o m a different m e c h a n i s m than the short - l i ved b lockages. F o r example , l o n g - l i v e d Chapter 3: Trans-side molecule capture and analysis 85 blockages m a y result f r o m the duplex structure actual ly entering into and b i n d i n g w i t h i n part o f the h i g h - f i e l d beta barrel on the trans-side o f the pore, result ing i n lower ion ic current dur ing the b lockage . Further w o r k is required to elucidate this mechan ism [107], as the data co l lected dur ing this invest igat ion is not suff ic ient to draw any conc lus ions about the relat ionship between b lockage current and d issoc iat ion m e c h a n i s m or the result ing d issociat ion t imes. 20 18 16 14 12 blockage current 10 (PA) 8 6 4 2 0 10 100 1000 dissociation time (msec) 10000 Figure 3.15-Averagelockage current versus dissociation time for 10c molecule at • 55mV E n e r g y B a r r i e r E s t i m a t e s A c c o r d i n g to the Ar rhen ius relat ion under an appl ied d issoc iat ion force descr ibed i n E q u a t i o n (3-18), the Y - in te rcept o f the d issoc iat ion t ime versus appl ied potential curves i n F igure 3.14 is : Yint= ( l n r 0 ) + kT (3-33) Chapter 3: Trans-side molecule capture and analysis 86 Th i s term contains the energy barrier for the d issoc iat ion react ion Eb, w h i c h is expected to be related to the free energy o f b i n d i n g o f the probe-target duplexes shown in Tab le 3 - 1 . The relat ion between the measured intercept values described in Equat ion (3-33) and the f ree-energy M f o l d estimates are shown in F igure 3 .16. I f the energy barrier Eb and the free energy o f b ind ing f r o m the M f o l d server are ident ica l , the relat ionship between these intercept values and b ind ing energies i n units o f kBT at 20°C should y i e l d a slope o f 1 w i t h an intercept o f ln(tD). A s s h o w n i n F igure 3 .16, the actual slope obtained f r o m this re lat ion is - 0 . 6 +/- 0 .2 , w i t h the uncertainty i n the intercept prec lud ing any usefu l estimate o n TD ( ~ l m s to Ins). Figure 3.16 -Correlation between Mfold energies and D N A binding intercept. Included are the slopes and intercepts from the force-dissociation curves shown in Figure 3.14. A number o f factors lead to a difference between the free energy predicted by M f o l d and Eb calculated empi r i ca l l y us ing the nanosensor data. The M f o l d a lgor i thm generates a G i b b s free energy o f d issoc iat ion based o n d issoc iat ion and hybr id i zat ion experiments for nuc le ic acids i n Chapter 3: Trans-side molecule capture and analysis 87 free so lut ion [103]. The nanosensor environment is far f r o m a free so lut ion envi ronment , and includes interactions w i t h tethered molecu les , po lymers and membranes , order ing o f the mismatch bases relat ive to the entrance o f the nanopore, and the direct appl icat ion o f an external d issoc iat ion force o n the nuc le ic ac id duplex f r o m the appl ied potent ia l . In this l ight, the empi r i ca l measurements o f E0 should not be ident ica l to the predicted free energy values, although it is expected that there w o u l d be some posi t ive corre lat ion between the two, as was found here. Th i s pos i t i ve corre lat ion is consistent w i t h previous experiments per formed b y Vercoutere et al. w h i c h looked at the d issociat ion t imes o f b lunt -ended nuc le ic ac id ha i rp in structures trapped i n the vest ibule o n the cis-side o f the pore [54]. 3.5.3 Effective barrier length scale F r o m Equat ion (3-18) the slope o f the average d issoc iat ion t ime versus appl ied potent ial curve shown i n F igure 3.14 is : Slope z ne pore Al Ax \ k B T J (3 -34) Th i s expression is proport ional to A x , the phys ica l barrier w i d t h for the d issoc iat ion pathway projected a long the react ion coordinate from the energy m i n i m u m and the state representing the energy barrier. N o m i n a l values from phys ica l parameters us ing the prototype nanosensor are l is ted i n Tab le 3 - 2 . Zpore 0.4 Charge per nucleot ide (Sect ion 3.3.1) n/Al (0.5nm)"' L inear density o f bases i n h i g h - f i e l d reg ion kBT/e 2 5 m V Ax P h y s i c a l distance to energy barrier Table 3-2 -Values used to estimate reaction barrier width Chapter 3: Trans-side molecule capture and analysis 88 Using these parameters, the physical distance to the energy barrier for the perfectly complementary target molecule (14pc) and the target molecule with one mismatch at the position closest to the pore entrance ( l a ) i s z k ~ 4 - 6 nm. For the two target molecules with mismatches in the middle of the probe-target duplex (10c and 7c), Ax - 1 . 5 - 3 nm. The calculated Ax values for all four target molecules correspond reasonably well with the lengths of the longest contiguous series of fully-complementary bases in the probe-target duplex. As each double-stranded base pair in the duplex measures - 0.3 nm along the helical axis, 14 contiguous bases will be on the order -4.2 nm. The 14pc and l a target molecules each have a single contiguous region of complementary sequence of almost the same length, while the 7c and 1 Oc target molecules contain two shorter regions of fully-complementary sequences approximately half that length. Previous experimental work has been somewhat mixed as to the interpretation of the true physical distance required to generate dissociation for nucleic acid duplexes. Using an atomic-force microscope-based pulling experiment for nucleic acids duplexes 10, 20, and 30-bases long, Strunz et al. found an upper limit on the barrier length scale for dissociation of: Ax = (7±3) + (0.7±0.3)rc Angstroms O 3 5 ) where n is the number of nucleotides in the duplex structure [20], or approximately 1/5 the length of the duplex fragment (3.6 Angstroms/base). For the 14-base long duplex sections used in this study, this corresponds to - 1.7 ± 0.5 nm, far shorter than the estimates from pore dissociation. Calculations of the effective charge within the pore during duplex dissociation experiments by Mathe et al. suggest that the physical barrier width during nanopore dissociation of nucleic acids corresponds to the length of the pore rather than the length of the probe-target duplex in their experiments [108]; a counter-argument to this point is discussed in Appendix E. Throughout these discussions, it is important to note that the physical distance to the energy barrier may be force-dependent, and the Chapter 3: Trans-side molecule capture and analysis 89 mechanism of the reaction may be different for forces approaching zero, revealing different parts of the energy landscape at different forces [125, 126]. Other techniques such as applying time-varying dissociation forces may allow empirical measurement of these features in the energy landscape; this approach is discussed in Section 3.6.2. A number of issues concerning the physical arrangement of the prototype nanosensor ultimately affect the resolution and performance characteristics for detection and discrimination of target molecules through dissociation kinetics. The upper and lower limits on the measured dissociation times, the range of probe-target duplexes which can be discriminated and the presence of pore gating are discussed in further detail in Appendix F. 3.6 Discussion 3.6.1 Physical modifications to nanosensor Modifications can be introduced to the physical arrangement of the nanosensor to both improve performance and address shortcomings in existing nucleic acid detection techniques. In order to mitigate the presence of multiple timescales in the dissociation time constants, the probe molecule can be altered to minimize areas which may contribute to binding. For example, changing the avidin-biotin anchor on the cw-side of the pore to an anchor made from a self-complementary nucleic acid hairpin strand crosslinked with psoralen, a chemical compound which can be used to increase the binding energy between complementary nucleic acid fragments. The elimination of the avidin-biotin anchor may minimize the effect of possible protein-protein interactions between the probe strand and the aHL pore. Additionally, the nucleic acid sequence used within the linker section of the pore may be altered to reduce any possible interactions with the protein residues lining the inside of the pore and to mitigate the effect of secondary structure formation which may hinder translocation Chapter 3: Trans-side molecule capture and analysis 90 of the polymer. For example, the acid dissociation constant pK„ for the adenine within the deoxyadenylic acid (dA) used in the linker section of the probe molecule is 3.5, while for the thymine within deoxythymidylic acid (dT), the pK„ is 9.9. With the experimental conditions held at a p H 8, the nitrogenous bases of the poly(dA) w i l l be deprotonated and may interact strongly with charged groups within the pore, while the exposed thymine in poly(dT) w i l l still be protonated and may be partially shielded from charged residues lining the pore, such as the ring of positively charged lysines at the limiting aperture of the pore. The orientation of the nucleic acids in the probe strand may also have an effect on probe-pore interactions. Recent work by Mathe et al. examined the escape time of long s s D N A fragments with hairpin structures preventing complete translocation through the aHL pore, similar to the probe escape experiments described in Section 3.3; fragments which had the 3' end of the fragment enter into the pore first had longer escape times than those which had the 5' end enter first [127]. These differences due to polymer orientation are believed to be the result of the difference in tilt angle of the bases as s s D N A fragments passes through the pore, resulting in greater effective friction and forced reorientation of the molecule in the 3' configuration and therefore longer escape times. Future iterations of probe design can incorporate information regarding these and other probe-pore interactions to minimize interactions which may interfere with probe-target dissociation. Modifications to the probe molecule may allow for more specific measurements during dissociation. Molecular spacers such as the carbon-backbone C-3 or C-18 spacers (~0.5 nm and -2.3 nm, respectively) [128] may be inserted into the probe molecule structure to allow different sections of the probe strand to freely rotate about one another. This would eliminate the effect of base-stacking interactions along the strand at specified points and may allow multiple target regions to be placed on same probe molecule. Synthesis of probe molecules composed primarily of nucleic acids allows for ease of synthesis, a high degree of control on the quality and consistency of probe molecule fabrication, and an extremely high linear charge density relative to other polymeric structures, resulting in a high dissociation force in the high-Chapter 3: Trans-side molecule capture and analysis 91 f ie ld reg ion. The synthesis o f probe molecules w i t h exot ic constituents should be treated w i t h caut ion, as contro l l ing and quant i fy ing the qual i ty o f probe molecu les synthesized w i t h nucle ic acids is m u c h easier to contro l . 3.6.2 Modifications to nanosensor protocol The dissociat ion experiments presented herein are under constant appl ied force; i n future d issociat ion studies, constant rate o f change i n the force can be used to observe different characteristics o f probe-target duplex d issociat ion and obtain in format ion further about the energy barriers a long the d issoc iat ion pathway [24]. Th is f o r m o f d y n a m i c force spectroscopy has already been used to estimate the magnitude o f the most probable d issoc iat ion force for nuc le ic ac id ha i rp in structures o n the cis-side o f the pore [108]. M a t h e et al. [108] derive an expression for the most l i k e l y d issoc iat ion potent ia l , V(/issoc under a constant rate o f change in the appl ied potential as: Vllissoc=kBT\n kBT (3 -36) Here , V is the constant rate o f change in the appl ied potential and rD is the inverse o f the off - rate descr ibed i n Equat ion (3-4) . Exper imenta l l y , i f the most l i k e l y potential V,iiSsoc is found, then it m a y be possib le to determine rD w i t h m u c h greater accuracy than can be accompl i shed through estimates under constant appl ied potential . A der ivat ion o f the expression found b y M a t h e et al. is inc luded i n A p p e n d i x G . U s i n g the ramp method m a y increase the d y n a m i c range o f the d issoc iat ion forces appl ied to the probe-target duplex , access to f iner estimates o f the energy barriers associated w i t h d issoc iat ion , and poss ib l y greater d isc r iminat ion between target populat ions d i f fe r ing b y s ingle base mismatches. Chapter 3: Trans-side molecule capture and analysis 92 3.6.3 Biologically relevant interactions In its present state, the prototype nanosensor is used to interact w i t h s ingle-stranded nuc le ic acids w i t h a speci f ic base-sequence present i n f ree-solut ion. A l t h o u g h this certainly has appl icat ions for in vivo detect ion and gene expression p ro f i l i ng , the nanosensor can be tai lored to suit interactions w i t h other b i o l o g i c a l l y relevant materials such as proteins and m R N A structures. The nanosensor can be used to investigate interactions between nuc le ic acids and proteins such as R N A polymerases , sequence-speci f ic endonucleases and methy l transferases [129] as observed us ing other techniques w i t h s ing le -mo lecu le resolut ion. F o r example , opt ical t rapping techniques have been used w i t h var ious i n d i v i d u a l endonuclease and polymerase proteins o n nuc le ic ac id strands to mechan ica l l y inf luence their funct ion b y app ly ing forces [130 -132] . C o m p l e x e s such as R e c A bacterial protein used for recombinat ion and repair o f D N A , E.coli R N A polymerase, and T 7 D N A polymerases have been examined w i t h forces appl ied to s ing le -molecu le interactions o n nuc le ic ac id us ing opt ical t rapping o f polystyrene beads [17]. One such f a m i l y o f proteins w h i c h binds spec i f i ca l l y to doub le -stranded fragments o f D N A are transcript ion factors, used to init iate the gene transcr ipt ion process [133] w h i c h the nanosensor m a y be able to observe. M e a s u r i n g the kinet ics o f such interactions us ing the nanosensor m a y prov ide further in format ion about the m e c h a n i s m o f b i n d i n g and dissociat ion o f molecules undergoing passive or directed d i f f u s i o n base -spec i f ic regions on d s D N A [134]. The fact that the nanosensor is designed to detect hybr id i zat ion events across a membrane means that the nanosensor m a y be suitable for in vivo detection o f prote in -nuc le ic ac id interactions and to poss ib ly elucidate and d is t inguish different mechan isms i n l i v i n g cel ls . 3.6.4 In vivo applications One c o m p e l l i n g aspect o f the nanosensor is the poss ib i l i t y o f in vivo detect ion o f sequence-speci f ic nuc le ic ac id fragments. The types o f Chapter 3: Trans-side molecule capture and analysis 93 cel ls w h i c h are potential candidates for in vivo detection, however , are l imi ted b y several cr i ter ia. The cel ls themselves must have exterior membranes w h i c h can be penetrated w i t h an appropriate i o n channel such as a H L . Th is m a y el iminate plant cel ls w i t h ce l l wa l l s conta in ing f ibr i l s o f cel lu lose w h i c h prevent penetration o f external i o n channels. T o c i rcumvent this l imi ta t ion , techniques exist for remova l o f the c e l l wa l l s o f plant ce l ls w h i l e leav ing the c e l l i n a v iab le state, either as spheroplasts (wi th part ial wal ls ) or protoplasts (no c e l l wa l l s at al l ) . A d d i t i o n a l l y , the target molecules w i t h i n the cel ls must be somewhat de loca l i zed throughout the interior o f the c e l l , or at the very least capable o f d i f fus ing c lose to the inner w a l l o f the ce l l membrane to a l l o w for hybr id i za t ion to the probe molecu le . The target molecu les must also be i n suff ic ient c o p y number as to be detected b y r a n d o m sampl ing us ing trans-side mo lecu le detection. These restrictions w i l l exclude the detection o f b iomolecu les loca l i zed around speci f ic organel les w i t h i n the c e l l , and m a y preclude the method f rom being used o n eukaryot ic ce l ls w i t h inherent internal structure. Prokaryot ic cel ls or eukaryotes w i t h very l i tt le structure such as protozoa m a y be the first v iab le candidates for in i t ia l testing o f the in vivo method. It should be noted that a l l o f the tools and handl ing procedures necessary for in vivo use o f the prototype nanosensor can be based o n already-establ ished techniques. H a n d l i n g and loca l i za t ion o f single ce l ls can f o l l o w w i t h m a n y o f the same protocols as for wel l -es tab l i shed patch -c lamp techniques used to probe i o n channels in l i v i n g cel ls [135]. It should be possib le to loca l i ze a spot on the membrane into w h i c h a single or mul t ip le a H L pores have been incorporated, at w h i c h point a patch -c lamp seal w i t h a seal resistance o n the order o f 10 G Q or greater can be establ ished, as is the case w i t h patch -c lamp techniques. A s w i t h convent ional patch -c lamp methods, no addit ional electrode needs to be inserted d i rect ly into the c e l l , as the potential w i t h i n the c e l l w i l l come to electr ical e q u i l i b r i u m w i t h the ce l l bath due to a l l o f the natural ly -occur r ing membrane channels w h i c h are present i n the c e l l membrane at a l l t imes. Chapter 3: Trans-side molecule capture and analysis 94 3.6.5 F u r t h e r issues There remain a number of experimental issues which need to be more completely addressed before trans-side dissociation experiments can be used as a means for generating sequence-specific information about target analytes. Preliminary results with a controlled ratio of different target molecule families present on the /raws-side of the pore have yielded unexpected results [136]. A 50:50 mix of two different target molecules with different dissociation curves did not yield a 50:50 population split between the two characteristic dissociation time curves upon analysis with the N N L S approach. It is not clear whether this result was due to poor quantification of the original oligonucleotide target molecules by the company which synthesized the target molecules, or due to differences in hybridization rates for target molecules with differing sequences. Further investigation is required to ensure that oligonucleotide quantification prior to mixing samples is accurate before any conclusions can be made about the rates of hybridization of different target molecules. At shorter time scales, probe-pore interactions may become significant when compared to dissociation time scales; efforts must be made to minimize these effects to improve the sensitivity and resolution of dissociation experiments. Unpublished work indicates that different nucleic acid sequences in the probe strand result in different escape times for the molecules [137], as expected from investigations of escape time of unanchored ssDNA molecules within the pore using simulations and actual experimental work [65, 138]. Characterizing the interaction between the probe molecule and pore is required to allow for greater levels of discrimination between different target molecules on the trans-side of the pore. The fabrication of appropriately-sized pores in synthetic materials is of great importance to the use of trans-side molecule capture. Pores must be consistently fabricated with a pore geometry Chapter 3: Trans-side molecule capture and analysis 95 which restricts probe-target duplex structures from passing through the pore. At this point, although individual pores have been made and characterized for nucleic acid translocation experiments, all fabrication methods to date result in differences in structure, pore profile, local charge concentration, or contaminants within the pore which result in different conductance characteristics for each pore; this may lead to pore-to-pore variation during probe-target dissociation. There is also an issue with the axial length of the pore: probe molecules which reach from the cis to trans-side of the pore must be at least as long as the thickness of the synthetic material, which in typical nanopore fabrication schemes is in the range of tens of nanometers, much longer than the probe molecule used with the aHL pore. It is entirely likely that the increased probe molecule length leads to an increased level of probe-pore interactions which may lead to a limitation on the sensitivity of force-dissociation measurements. Chapter 3: Trans-side molecule capture and analysis 3.7 Chapter Summary 96 A prototype nanosensor has been demonstrated that has several characteristics which make it unique among single-molecule techniques for probing biomolecules. Based on the aHL pore and nucleic acid duplex structures, the prototype sensor has been used to estimate the hybridization and dissociation rates of single-stranded nucleic acid fragments in free solution across a lipid bilayer membrane. During hybridization studies, the prototype nanosensor was used to measure the on-rate of 14-mer oligonucleotides with single-molecule sensitivity and with greater temporal control and resolution than is possible using conventional microarray technologies. For dissociation studies, the prototype nanosensor was used to distinguish between four 14-mer oligonucleotide structures differing by a single nucleotide when observing ensemble measurements of the dissociation time versus the applied force. Future work with the nanosensor w i l l l ikely involve investigating the relationship of other experimental control factors with the overall sensitivity of the system, including biochemical makeup of the probe molecule, type of target molecule, and buffer conditions. The functionality of the present nanosensor can be extended to observe interactions with other biologically relevant molecules. The absence of fluorescent tags and detection optics, ease of control and detection of individual molecules, and a means of detecting molecules across a biological membrane position the prototype nanosensor to be a very promising basis for future instrumentation. With a method o f measuring local concentrations across a lipid membrane that is label-free and requires no optical detection, and a method for discriminating between different short nucleic acid sequences with a single nucleotide mismatch, the prototype transmembrane nanosensor is the basis for a number of very intriguing investigations for nucleic acid analysis. Chapter 4: Conclusions 97 Chapter 4 Conclusions Chapter 4: Conclusions 98. The two methods for nuc le ic acid analysis presented i n this w o r k demonstrate the v iab i l i t y o f us ing the properties o f nanopores to address spec i f ic shortcomings i n present analysis techniques for nuc le ic acids. Nanopores show promise as a non- f luorescent means o f est imating single-stranded nucle ic ac id concentrations. E m p i r i c a l measurement o f the capture rate o f s ingle stranded nuc le ic acids shows the expected l inear dependence o n concentrat ion, w i t h a non - l inear dependence o f the capture rate on the appl ied transmembrane potent ial . E x i s t i n g theoretical approaches either cou ld not account for the exper imental results at higher potentials or had shortcomings i n m o d e l i n g exper imental details at transmembrane potentials suitable for synthetic pores. In this l ight , a theoretical m o d e l o f the capture rate was constructed c o m b i n i n g analytic estimations and computat ional s imulat ions . Es t imated sensit iv i ty at the h igh appl ied potentials avai lable us ing synthetic nanopores indicate that nanopore detection for detect ion i n s m a l l vo lumes m a y require a comparable number o f molecu les to convent ional f luorescence detection, without the need for opt ica l detect ion equipment or f luorescent tags. The a H L channel was also used to create a prototype transmembrane nanosensor w h i c h has several characteristics unique a m o n g s ing le -molecu le probe methods. The nanosensor was used to investigate hybr id i zat ion and d issociat ion o f s ingle molecules o f nuc le ic ac id duplex structures. F o r hybr id i zat ion studies, the nanosensor was used to estimate the on-rate o f 14-mer o l igonucleot ides us ing s ing le -m o l e c u l e events and w i t h far greater control over the exposure t ime o f the probe molecu les than is poss ib le us ing more convent ional mic roar ray technologies. F o r d issociat ion studies, the nanosensor was used to d is t inguish between four 14-mer o l igonucleot ide structures w h e n observ ing ensemble measurements o f the d issociat ion t ime versus the appl ied force. Further w o r k w i t h the nanosensor invo lves invest igat ing the relat ionship o f other exper imental control factors w i t h the overa l l sensi t iv i ty o f the system, i n c l u d i n g temperature, b i o c h e m i c a l m a k e u p o f the probe molecu le , type o f target molecu le , and a host o f other poss ib le Chapter 4: Conclusions 99 factors. W i t h a method o f measur ing loca l concentrations across a l i p i d membrane that is label - f ree and requires no opt ica l detection, and a method for d isc r iminat ing between different short nuc le ic ac id sequences w i t h a s ingle nucleot ide mismatch , the prototype transmembrane nanosensor is the basis for a number o f very int r igu ing invest igat ions for nuc le ic ac id analysis . Future iterations o f the trans-membrane nanosensor can be extended to observe interactions w i t h other b i o l o g i c a l l y relevant molecu les , a l l o w i n g for invest igat ion o f proteins and other b ioce l lu la r constituents. The absence o f f luorescent tags and detection opt ics , ease o f contro l and detection o f ind i v idua l molecu les , and a means o f detect ing for molecu les across a b i o l o g i c a l membrane pos i t ion the prototype nanosensor to be a very p romis ing basis for future instrumentation. Present -day genomics studies and in vivo measurement a l ike m a y benefit from w o r k done us ing this technique. There are a number o f challenges w h i c h need to be addressed pr ior to the widespread appl icat ion o f either technique for nuc le ic ac id analysis for genotyping or c l i n i c a l endeavours. O f p r imary concern is the issue o f fabr icat ing pores i n synthetic materials w h i c h are robust and consistent; a l though ind i v idua l pores have been made and character ized for nuc le ic ac id translocat ion experiments, there continues to be w i d e var iat ion i n performance for different pores due to dif ferences i n structure, pore prof i le , loca l charge concentrat ion, or contaminants w i t h i n the pore. A t the present t ime, consistency i n fabr icat ion and character izat ion o f nanometer -scale pores remains an e lus ive goal . Nanopore methods m a y one day be used i n pract ical s ing le -mo l e cu l e detection schemes for b iomolecu les analysis . O n g o i n g w o r k b y several groups for the fabricat ion o f synthetic pores on the scale o f b i o l o g i c a l molecu les w i l l one day lead to the abi l i ty to run m a n y o f these reactions i n para l le l i n ways that on ly require measurement o f i on ic current wi thout optics or f luorescent tags. N o t e that as other proposed analysis techniques e x a m i n i n g the compos i t ion o f the t ranslocat ing strands re ly o n sensit ive measurements o f the ion ic current signature, subtle changes i n the structure o f a synthetic pore m a y disrupt i o n current Chapter 4: Conclusions 100 signatures. The two modes for nanopore detection descr ibed i n this w o r k obtain relevant in format ion about the nuc le ic acids f r o m temporal measurements, either the t ime between translocat ion events or the t ime taken for d issoc iat ion to occur ; this m a y a l l o w a w ider tolerance i n the synthetic pores w h i c h are amenable for use i n the two techniques. 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A.l Alpha-hemolysin Protein A l p h a - h e m o l y s i n ( a H L ) is a 293- res idue water soluble protein m o n o m e r that sel f -assembles as a heptamer in ce l l membranes and synthetic l i p i d b i layers , fo rming an aqueous channel through the membrane [42]. The protein is secreted by the h u m a n pathogen Staphylococcus aureus and is intended to b i n d to and lyse h u m a n platelets b y m a k i n g their membranes permeable to water, ions , and l o w molecu lar weight molecu les , e l iminat ing concentrat ion gradients across c e l l membranes for smal l b iomolecu les less than 1000 Dal tons [139]. P h y s i o l o g i c a l l y , the outf lux o f K + and the in f lux o f N a + resul ts . i n Appendix A: Experimental Materials, Instrumentation, and Data 118' A c q u i s i t i o n t r igger ing cytochrome c release f rom cel lu lar mi tochondr ia , lead ing to apoptosis (ce l l death) [140]. A . l . l Structure The structure o f a H L has been revealed b y crystal lography to 1.9 A resolut ion [42]. The pore is a 10 n m long m u s h r o o m shaped heptamer. The pore entrance to the vestibule contains a r ing o f threonine residues, and the exit has a r ing o f alternating lys ine and aspartate residues. The trans-membrane d o m a i n o f the channel is compr ised o f a 14-strand beta barrel w i t h a hydroph i l i c interior and hydrophob ic exterior. F o l l o w i n g the channel or ientation adopted i n most exper iments, the mushroom-shaped " h e a d " o f the mo lecu le is general ly referred to as the cw-s ide , and the stem end as the trans-side. The aqueous channel contained i n the pore is composed o f a 2.6 n m diameter " m o u t h " , a 4.6 n m m a x i m u m diameter "ves t ibu le" , a 1.4 n m diameter " l i m i t i n g aperture", f o l l o w e d b y a 5 n m l o n g stem approx imate ly 2 n m i n diameter. There are m a n y charged residues i n the pore at neutral p H , most notably a r ing o f pos i t i ve ly charged lys ines interposed w i t h a r ing o f negat ively charged glutamates at the l i m i t i n g aperture; the pos i t ion o f these residues m a y a l l o w for tuning the translocat ion properties o f the pore by adjusting the p H . A lack o f cysteine residues l i n i n g the inner wa l l s o f the pore a l lows researchers to genet ica l ly m o d i f y the pore 's cod ing sequence and covalent ly attach tethered molecu les to the pore [141]. W h e n p laced i n free so lut ion , cooperat ive hydrophob ic and hydroph i l i c self - interact ions [142, 143] lead to the format ion o f a beta-barrel structure capable o f se l f - inser t ing into a b i layer l i p i d membrane. Ev idence also indicates that mul t ip le pore insert ions m a y interact w i t h one another and act cooperat ive ly dur ing insert ion and i o n conduct ion [144] A.l.2 Ionic and Small-Molecule Conduction Appendix A: Experimental Materials, Instrumentation, and Data 119 A c q u i s i t i o n E lec t r i ca l behavior o f the channel i n electrolyte solut ions shows ohrnic characteristics w i t h conduct iv i ty l inear ly proport ional to electrolyte i o n concentrat ion, and current l inear ly proport ional to the appl ied transmembrane potent ial , though w i t h some rect i f icat ion such that the channel is more conduct ive w h e n the potential is appl ied trans to cis (posit ive trans-side) [61]. In 1 M K C l so lut ion , l O O m V potential from trans to cis results i n a current o f 100 p A , w h i l e the same potent ial appl ied cis to trans gives approx imately 80 p A . The asymmetry o f the ion ic current f l o w through the pore is p r i m a r i l y electrostatic f r o m the f i xed charges on the ins ide o f the pore entrances, as demonstrated b y 1-D N e r n s t - P l a n k analysis , w h i c h leads to asymmetry i n overa l l conduct ion and for anion select iv i ty [145]. These changes are further re inforced b y experiments s h o w i n g the p H sensi t iv i ty o f certain regions o f the pore [146]. These charge groups co l lec t i ve l y m a k e the channel m i l d l y selective for anions [42]. Th i s asymmetry does not extend to water molecu les , w h i c h w h e n inside the pore appears to behave s imi la r l y to water i n bu lk , due to l o w act ivat ion energy for water transport [147]. V a r y i n g the p H o f the buffer solut ion changes both charged and uncharged groups l i n ing the pore. In experiments us ing the p o l y m e r polyethy lene g l y c o l , increases i n p H f r o m i n the range f r o m 7.0 to 9.0 results i n a decrease o f the characteristic m a x i m u m p o l y m e r s ize that can enter the pore b y - 2 5 % , w h i l e the measured ion ic current increases. Th i s di f ference is l i k e l y due to water hydrat ion shells around charge groups l i n i n g the pore [148]. Because the dielectr ic constant o f the p o l y m e r is lower than that o f water, the p o l y m e r is exc luded from surrounding the ions at the expense o f water. F r o m the l imi ted amount o f voltage-dependence in fo rmat ion about the a H L pore [149], the pore appears to be robust and does not d isp lay the same leve l o f gating as w i t h other proteinaceous channels. A pore gat ing event is one i n w h i c h the ion ic conduct ion inside o f the pore decreases substantial ly , t yp ica l l y from 4 0 - 9 0 % , i n response to vo l tage -induced or thermal l y - induced changes i n the structure o f the pore or interactions w i t h spec i f ic divalent or trivalent cations i n solut ion [139, Appendix A: Experimental Materials, Instrumentation, and Data 120 A c q u i s i t i o n 146, 149, 150]. a H L gating is sensitive to the presence o f both hepar in (a negat ive ly -charged subunit) [146] and divalent cations [139], both o f w h i c h appear to b i n d to sites on the outside o f the pore. The gat ing effect m a y o n l y be an electrostatic effect and not a steric one: dur ing gat ing events, the phys ica l s ize inside the pore changes o n l y b y a factor o f 2 despite a lOx decrease i n the conductance o f the pore, as demonstrated i n experiments w i t h polyethy lene g l y c o l [151]. The w o r k presented i n A p p e n d i x F.3 discusses some o f the gat ing k inet ics o f the pore versus appl ied negative potential , a topic not discussed i n the literature to date and o f relative importance to the trans-side d issoc iat ion experiments descr ibed in Chapter 3 . A.2 Phospholipid Bilayer Nanopore translocation experiments us ing the a H L protein channel are per formed w i t h the pore inserted into a l i p i d b i layer membrane. The phospho l ip id used i n the experiments descr ibed here and i n m a n y a H L studies is ( l , 2 - D i p h y t a n o y l - s n - G l y c e r o - 3 -Phosphocho l ine , A v a n t i Po la r L ip ids ) . Th is phospho l ip id is able to f o r m stable membranes at r o o m temperature and contains phosphat idy lchol ines s imi la r to those ident i f ied i n m a n y b i o l o g i c a l membranes [152]. Structural ly the membrane forms a 5 n m th ick l i p i d b i layer w i t h a s l ight ly cat ionic head group. U n d e r t yp ica l fabr icat ion techniques out l ined b e l o w , the l i p i d is spread across a 5 0 - 1 0 0 p m or i f ice formed i n T e f l o n ® that has been pre -treated w i t h a hexane - l ip id mixture . The result ing b i layer can wi thstand a m a x i m u m appl ied transmembrane potential - 4 0 0 m V at w h i c h point the l i fe t ime o f the b i layer is substantial ly reduced, al though there is ev idence that the b reakdown voltage is dependent on the rate vol tage load ing rate [153] ; i n practice, l i p i d layers w h i c h support h igher potentials have l i k e l y not formed true b i layer structures and are too th ick for a H L pore insert ion. F o r a 5 - n m th ick bi layer , this corresponds to an appl ied electr ic f ie ld o f - 1 0 6 V / m , on the order o f the b reakdown voltage o f the l i p i d used dur ing electroporation o f cel ls [154]. The mechan ica l Appendix A: Experimental Materials, Instrumentation, and Data 121 A c q u i s i t i o n tension o f the l i p i d b i layer is ~ 2 x l 0 " 3 N/m [155]. A l t h o u g h the lateral d i f f u s i o n constant o f the a H L channel inserted i n a l i p i d b i layer membrane is not k n o w n , the lateral d i f fus ion constant for a m u c h smal ler 12 2 membrane channel , a lamethic in , is o n the order - 4 x 1 0 " m / s [156] ; as the a H L pore is several t imes larger than a lamethic in ( - 2 0 0 0 residues versus - 2 0 ) , it is expected that the d i f fus ion constant for a H L i n a l i p i d b i layer is m u c h lower . In theory, one can estimate the size o f the b i layer membrane based o n observ ing the capacit ive spike result ing f r o m an appl ied transmembrane step potent ial [36]. H o w e v e r , several factors prevent this technique f r o m be ing used i n this exper imental setup. The var iance o f the capaci t ive spike for different T e f l o n ® chambers is as great as the -var iance o f the measured capacit ive spike f r o m one part icular T e f l o n ® chamber on different days. The l i p i d is also d isso lved i n hexadecene and hexane w h i c h then act to smooth out the transit ion between the T e f l o n surface and the l i p i d structure, m a k i n g the actual b i layer size somewhat i l l - d e f i n e d . The low-pass f i l ter ing o f the s ignal (nomina l l y 10 k H z ) further makes deconvo lut ion o f the or ig ina l capacit ive spike leve l exceeding ly d i f f i cu l t ; attempts at measur ing the size o f the capaci t ive spike at a bandwidth o f 1 0 0 k H z result i n capacit ive spikes w e l l b e y o n d the range o f the patch c lamp ampl i f ie r used i n the experiments. M o d i f i c a t i o n s to the ex ist ing apparatus m a y improve the robustness o f the l i p i d b i layer membrane. One method is the use o f smal ler support or i f ices (1 pm or less). Another method is the format ion o f b i layers o n molecu lar scaffolds w h i c h l ie underneath the l i p i d b i layer i n order to prov ide mechanica l stabi l i ty to the membrane. There has been some success us ing bacterial surface layer (S - layer ) proteins der ived f r o m the outermost ce l l envelope component i n w a l l e d bacter ia and archaea to support art i f ic ia l l i p i d b i layers ; the insert ion o f a H L into these supported membranes result i n conduct i v i t y measurements s imi la r to those w i t h unsupported membranes [157-159] . The hydroph i l i c headgroups o f the l i p i d m a y have some inf luence on the translocat ion properties o f both ions i n so lut ion and nuc le ic acids Appendix A: Experimental Materials, Instrumentation, and Data 122 A c q u i s i t i o n dur ing experiments. U s i n g a negat ively -charged 1:1 m i x o f P C : P S (PS = bov ine bra in phosphatidylser ine) for the headgroups, M e n e s t r i n a p roduced a 3 0 - f o l d increase i n the concentrat ion o f K + ions at the surface, w h i l e alter ing the i o n current and select iv i ty o f the pore b y less than 10 percent. It was conc luded that the entrance to the pore o n the a s - s i d e is far enough away f rom the surface to not have an inf luence on i o n conduct ion [139]. A s nuc le ic acids are negat ively charged and m a y be electrostat ical ly attracted to the bi layer surface, Chandler et al. used negat ive ly -charged dipthytanoyl phosphat idy lg lycero l ( 5 % added) i n place o f the convent ional l i p i d in order to prevent s s D N A f r o m b i n d i n g to the l i p i d surface [160]. H o w e v e r , it was noted that contro l groups for those experiments, w h i c h were nuc le ic acids w i t h f luorescent ly - tagged streptavidin headgroups, m a y have interacted w i t h the b i layer surface due to the tags and not the nuc le ic ac id . A.3 Supporting Equipment Ion channel experiments require l o w electr ical noise to accurately detect p i c o a m p - l e v e l currents, and extreme cleanl iness i n the wetted parts o f the apparatus to a l l o w rel iable fo rming o f bi layers and organic pores. A schematic o f the components o f the system are shown i n F igure A . l . T w o smal l reservoirs mach ined f rom a single T e f l o n ® b l o c k are connected b y T e f l o n ® heat shr inkable tubing ( D o u b l e - w a l l e d P T F E tub ing , E W - 9 5 8 1 0 - 0 0 , Co le -Parmer ) . One end o f the tubing serves as the support for the l i p i d b i layer and protrudes into the cis-side chamber. The other end o f the tubing is connected to the bot tom o f the trans chamber. The tubing is typ ica l l y 0 . 0 6 5 " ID but can shr ink w i t h heat to complete ly constrict. Heat shr ink ing and internal me l t ing o f the T e f l o n ® is re l ied o n to shr ink the I D o f the tub ing to approx imate ly 25 p m b y us ing th in steel w i re as a mandre l . Ca re fu l remova l o f the wi re and t r i m m i n g o f the shrunk tube results i n a 25 p m opening i n a th in membrane that n o w separates the two f l u i d reservoirs. The membrane is located at the end o f the tube i n the cis-side chamber and is easi ly accessible f r o m above for both manua l and microscope access. Appendix A: Experimental Materials, Instrumentation, and Data 123 A c q u i s i t i o n cis side trans side Figure A . l - General experimental apparatus with a H L inserted into a lipid bilayer membrane for ionic current detection Preparat ion for l i p i d bi layer format ion is init iated by b o i l i n g the b l o c k and tube i n 1 0 % nit r ic ac id for 5 minutes. A f t e r thorough r ins ing w i t h de ion ized water and ethanol and v a c u u m - d r y i n g , the 25 u m or i f i ce is coated w i t h a th in layer o f phosphol ip id i n hexane. T h e T e f l o n ® reservoirs and tubes are then f i l l ed w i th electrolyte, t yp ica l l y buf fered 1 M K C l ( l O m M H E P E S free ac id , I m M E D T A , p H 8.0), and conduct ion between the baths is conf i rmed to check for the presence o f air bubbles . The temperature for the experimental setup is contro l led w i t h a Pel t ier cool ing/heating b l o c k and maintained at 20.0+/-0.5 for a l l exper imenta l work . The appl ied transmembrane potential and ion ic current are measured us ing an A x o p a t c h 2 0 0 B patch c l a m p ampl i f ie r ( A x o n Instruments, Foster C i t y , C A ) normal ly used for measur ing e lectr ical conduct ion across c e l l membranes in vivo. S i l ve r chlor ide electrodes are inserted i n both reservoirs and are connected to the patch c l a m p ampl i f ie r . R M S noise i n the current is typ ica l l y ~ 1 p A rms at D C us ing a 10 k H z bandwidth f i l ter , w i t h the entire apparatus ( inc lud ing the ampl i f ie r headstage) housed in an electromagnetic sh ie ld ing enclosure. Appendix A: Experimental Materials, Instrumentation, and Data 124 A c q u i s i t i o n A p p l i e d potentials up to ± 3 0 0 m V can be appl ied across the b i layer for long - te rm exper imentat ion; potentials greater than ~ 3 0 0 m V result i n an increased l i k e l i h o o d o f l i p i d b i layer rupture. Once a potent ial is set-up across the b i layer , a H L (Ca lb iochem) is added to the cw -s ide reservoir . Incorporat ion o f a single a H L channel is detected as a stepwise increase i n the ion ic current, w i t h each proper ly incorporated channel resul t ing i n approx imate ly 100 p A per 100 m V o f appl ied potential . F l u s h i n g the cis-side chamber w i t h fresh electrolyte solut ion immediate ly after the first increase i n current prevents incorporat ion o f addit ional channels. T h o u g h f lawed channels do occas ional l y incorporate, y i e l d i n g currents w i t h a lower conductance and l a c k i n g the proper i o n conductance asymmetry , the proper heptamer channels can be dist inguished b y the rect i f y ing characteristics in the ion ic current as stated above. D a t a acquis i t ion and real - t ime control o f the appl ied transmembrane voltage is completed w i t h a P C - b a s e d data acquis i t ion board ( N I - M I O - 1 6 E - 4 , N a t i o n a l Instruments, A u s t i n T X ) and the L a b v i e w graphical development p lat form. The data co l lected is n o m i n a l l y lowpass - f i l te red at 10 k H z through a four -po le B e s s e l f i l ter through the patch -c lamp ampl i f ie r , and sampled at 50 k H z . A l l data was streamed di rect ly to the hard dr ive to a l low for post -process ing us ing a var iety o f formats. A n a l y s i s o f the col lected data was per formed i n a var iety o f software packages, inc lud ing L a b v i e w , M a t h e m a t i c a , and M a t l a b . Appendix B: AHL for Nucleic Acid Detection 125 Appendix B AHL for Nucleic Acid Detection Th is section presents a b r ie f retrospective o f some o f the semina l experiments i n the use o f the a H L channel for detection and analysis o f nuc le ic acids. B . l Seminal Experiments The idea o f us ing b i o l o g i c a l nanopores as the basis for ana lyz ing i n d i v i d u a l p o l y m e r molecu les has been around for some t ime. Research i n the area began to accelerate in the m i d - 1 9 9 0 s w i t h the detection o f D N A translocat ion through an ion channel per formed independent ly b y C h u r c h [161] and K a s i a n o w i c z et al. [37]. The first s ingle mo lecu le detect ion o f nuc le ic acids us ing a H L channels [37] used R N A and D N A fragments 100 to 500 nucleot ides long. B l o c k a g e durat ion t imes appear to fa l l into three dist inct events for the same p o l y m e r type. V e r y short - l i ved events result f r o m co l l i s ions between the p o l y m e r and the mouth o f the a H L pore without subsequent t ranslocat ion, w h i l e the two Gauss ian populat ions are the result o f two modes o f translocation o f nuc le ic acids, hypothes ized to be the Appendix B: AHL for Nucleic Acid Detection 126 t ranslocat ion ini t iated f r o m either the 3' or the 5' ends o f the nuc le ic ac ids , a theory re inforced b y more recent exper imental w o r k [46]. T w o methods were used to c o n f i r m translocat ion o f s ing le -stranded nuc le ic acids and exc lus ion o f double-stranded nuc le ic acids. Th i s was conf i rmed b y compet i t ive P C R b y extracting and a m p l i f y i n g the electrolyte sample f r o m the trans chamber and size separating the result ing fragments. T w o Gauss ian populat ions i n the b lockage t imes were d i rect ly related to the quantity o f s ingle-stranded nuc le ic acids detected b y P C R , w h i l e double-stranded nuc le ic acids were not detected o n the opposite side o f the pore [37, 82]. Secondly , the mean t imes o f the Gauss ian populat ions were l inear ly related to the length o f the s ing le -stranded nuc le ic acids translocating through the pore, w h i l e the short-l i v e d b lockages were not, ind icat ing length-dependent translocat ion for the Gauss ian populat ion . A number o f other properties o f nuc le ic acids have been uncovered w i t h the use o f the a H L channel . The lower l i m i t o f detect ion for an i n d i v i d u a l p o l y m e r is ~ 4 nucleotides [60], and m a y be due to the number o f bases that extend a long the beta barrel c o m p l e x at one t ime; i n this l ight, the 12-base lower l imi t o n constant ve loc i t y for D N A translocat ion [60] corresponds w e l l w i t h crystal lography data for the length o f the a H L channel [42]. A n analysis o f the ve loc i t y o f s ing le -stranded nuc le ic acids through the pore [60] showed that the translocat ion ve loc i t y scales w i t h the square o f the appl ied transmembrane voltage, and that fragments shorter than ~12-base had higher ve loc i t ies than those in the long -po l ymer l imi t w h i l e fragments longer than 12 bases had velocit ies that d i d not vary greatly w i t h p o l y m e r length. A n e c d o t a l evidence has also been presented that shorter nuc le ic ac id fragments produce more frequent b lockage events than an equal concentrat ion o f longer fragments [37, 162]. Appendix B: AHL for Nucleic Acid Detection 127 B.2 Sequence determination from current signature Prev ious experiments have shown that one can d is t inguish between nuc le ic ac id populat ions w i t h w i d e l y va ry ing nucleot ide compos i t i on based on the i o n current b lockage leve l and relat ive durations dur ing translocation. Ion current b lockages i n a H L caused b y R N A homopo lymers 100 bases long w i t h different base composi t ions result i n dist inct b lockage levels [37, 45] . There is also ev idence that current b lockage signatures can be used to detect the transit ion between l o n g stretches o f consecutive bases within a s ingle molecu le (e.g. A ( 3 0 ) C ( 7 0 ) G p [44]), and to d ist inguish between molecu les w i t h the same compos i t i on but different sequence order (e.g. p o l y ( d A d C ) 5 0 versus p o l y ( d A 5 0 ) ( d C 5 0 ) [45]). These differences m a y be due to base-spec i f ic interactions between the pore and different species o f nucleot ides, or because o f the phys i ca l properties o f nuc le ic ac id strands i n f ree-solut ion. F o r example , i n the typ ica l sal in i ty and temperatures used i n nuc le ic ac id t ranslocat ion exper iments, an R N A p o l y m e r composed entirely o f po l y (C ) nuc le ic ac id m a y main ta in a single stranded he l i ca l structure 1.3 n m i n diameter as it passes through the pore [44] w h i l e an R N A po lymer composed o f p o l y ( A ) mo lecu le m a y be forced to unravel f r o m its 2 . 1 n m s ing le -stranded he l i x pr ior to t ranslocat ion; this difference m a y account for the longer but shal lower translocation current b lockages for the p o l y ( A ) molecu le . A l t h o u g h some sequence in format ion can be garnered u s i n g this method , the base-sequence resolut ion is u l t imately l im i ted b y the length o f the h i g h - f i e l d region inside the pore, ~ 1 2 nucleot ides long , unless mon i to r ing the ion ic current is coupled w i t h ensemble averaging or some method o f contro l lab ly s l o w i n g d o w n the translocat ion speed o f the po lymer . Other characteristics o f translocating nuc le ic acids can also be elucidated b y mon i to r ing the b lockage t ime and depth over an ensemble o f t ranslocat ing molecu les , such as the phosphory lat ion state o f the nuc le ic ac id [46]. M o n i t o r i n g the distr ibut ion o f b lockage t imes and depths m a y be one w a y o f mon i to r ing sample pur i ty after storage, Appendix B: AHL for Nucleic Acid Detection 128 phosphorylat ion/ dephosphory lat ion, D E P C treatment, and pheno l extractions. U s i n g compar isons o f the b lockages and translocat ion t imes o n m i x e s o f molecules also a l lows for enhanced detect ion o f contaminants i n samples - the technique can detect the presence o f 3 % quantity o f p C l O O i n p A l O O , a sensit iv i ty w h i c h cannot be achieved w i t h any convent ional f luorescence or rad io label ing techniques [46]. B .3 Nanopore Unzipping The a H L pore has been used to dissociate or " u n z i p " nuc le ic acids b y app ly ing a force to separate double-stranded hybr id i zed sections w h i c h are too large to pass through the a H L pore. U s i n g this technique, it is poss ib le to per form experiments on the kinet ics o f nuc le ic ac id duplex d issociat ion. In the most straightforward implementat ion , hyb r id i zed strands o f nuc le ic acids are electrophoret ical ly captured, resul t ing i n persistent reductions i n the i o n i c current. T h e durat ion o f the b lockage depends on the nature o f the complementary bases as w e l l as the appl ied force o f d issociat ion due to the transmembrane force. Exper imenta l work b y Sauer -Budge et al. w i t h 5 0 - m e r complementary segments w i t h 5 0 - m e r singlerstranded overhangs c o n f i r m e d the d issoc iat ion o f the molecu le us ing P C R analysis o f the trans-side product [82]. The placement o f W a t s o n - C r i c k mismatches a long the complementary sections resulted in dist inct differences i n the d issoc iat ion kinet ics o f the duplex , hypothesized to be due to the presence o f intermediates dur ing the d issociat ion process as a result o f the " b u b b l e " w h i c h they inserted into their strands. S i m i l a r w o r k b y Sutherland et al. w i t h shorter 10-mer complementary regions w i t h 2 0 -mer overhangs [163] resulted i n a distinct ion ic current levels for s s D N A alone versus s s D N A w i t h a 10-mer dup lex - reg ion w i t h i n the pore, w i t h -8 1 p A for a s s D N A to on ly a - 7 3 p A drop for the duplex strands at 100 m V . D y n a m i c Fo rce Spectroscopy [105] is a technique o f app ly ing a t i m e - v a r y i n g potential force to the duplex to uncover further detai l about the react ion pathway and energy barrier landscape. Th i s technique has been used b y M a t h e et al. to examine the d issociat ion o f 10-mer D N A ha i rp in structures w i t h 50 -mer long overhangs [108], whereby constant Appendix B: AHL for Nucleic Acid Detection 129 transmembrane vol tage r a m p i n g rates have been appl ied to dissociate the molecu les once they have been captured i n the pore. B.4 H a i r p i n S t r u c t u r e s D N A hairpins w i t h speci f ic hybr id izat ions have been used to increase the d w e l l t imes o f the molecu les and to locate a s ing le nucleot ide pair f r o m the c is -s ide near the a H L l i m i t i n g aperture for a suff ic ient t ime to a l l o w a dist inguishable b lockage signature to be recorded [53, 54] . Th is detection scheme employs synthesized strands o f D N A designed to f o r m speci f ic secondary structures b y f o r m i n g a 4 d T loop f o l l o w e d b y a double-stranded region ranging f r o m 3 to 9 nucleot ides i n length. The ha i rp in loop i n these molecu les prevents the molecu les f r o m translocating through the a l p h a - H L channels, lead ing to very l o n g - l i v e d b lockage states (up to 300sec.) unt i l the mo lecu le dissociates and passes through the l i m i t i n g aperture as a s ingle stranded po l ymer , leading to the deep b lockage expected for s s D N A translocat ing through the pore. The l o n g duration o f the b lockages caused b y these ha i rp in molecu les a l l o w d isc r iminat ion between b lockage ampl i tudes for molecu les d i f fe r ing i n length b y a single base pair . Fur thermore, the durat ion o f the b lockage event correlated strongly w i t h the standard free energy o f the ha i rp in format ion. In this w a y , a 6bp stem molecu le (5' -C G A A C G T T T T C G T T C G - 3 ' ) cou ld be easi ly d ist inguished f r o m the same mo lecu le w i t h a single nucleot ide difference. The compos i t i on and or ientat ion o f the terminal base pair in the stem o f ha i rp in D N A molecu les can also be ident i f ied by observ ing the rate w i t h w h i c h the terminal base pair varies between mul t ip le metastable b lockage levels and characterist ic " s p i k i n g " i n the i o n current [53]. The characteristic d w e l l t ime o f the molecu le in these metastable states prov ides a means o f d isc r iminat ing not o n l y among the four possible combinat ions for the terminal base pair , but also among different combinat ions o f the penult imate base pair . Appendix B: AHL for Nucleic Acid Detection 130 B . 5 Modified a H L The inner l u m e n o f the native a H L protein can be m o d i f i e d to produce pores w i t h speci f ic i ty for a part icular b i o m o l e c u l e o f interest v i a steric, c h e m i c a l or electrostatic interactions. In this w a y , steric interactions and the d isc r iminat ion o f different b i n d i n g sites w i t h i n the pore based on event l i fet imes and frequencies can be elucidated [164]. W o r k b y the B a y l e y lab has had a great deal o f success i n incorporat ing genetic modi f icat ions to the a H L pore and a l l o w i n g short s s D N A fragments to be tethered direct ly into the vestibule o n the cw -s ide o f the pore. These ol igonucleot ides are tethered to genet ical ly m o d i f i e d a H L pores w i t h cysteine residues added i n speci f ic areas i n the vest ibule o f the pore. These tethered D N A fragments alter the translocat ion k inet ics o f s ingle-stranded nuc le ic acids complementary to the tethered strand v i a speci f ic hybr id i zat ion [113, 165]. These strands a l l o w for d i sc r iminat ion o f D N A fragments w h i c h are f u l l y complementary to the strand versus strands w i t h single base mismatches a long the strand based o n b lockage durat ion o f the D N A i n the pore moni tored b y observ ing the ion ic current. There is evidence f r o m the ha i rp in experiments and w i t h strands tethered ins ide the pore that b lunt -ended molecules do not experience a l inear increase i n the d issociat ion force as the transmembrane potent ial increases [166]. T o ameliorate this effect, s ingle-stranded overhangs w h i c h lengthen the translocating molecu le past the tethered s s D N A fragment and into the h igh electric field region o f the pore improve the l inear i ty o f the transmembrane voltage to the force appl ied to dissociate the molecu le [113], and result i n decreasing l i fet imes w i t h increas ing potent ial . Counter - in tu i t i ve ly , it has been noted that w i t h tethered s s D N A molecu les inside the pore terminat ing i n a b lunt -ended structure had an increase i n l i fet ime w i t h an increase in appl ied transmembrane potentials (2x longer for change f r o m 8 0 - 1 7 0 m V ) , ind icat ing that these molecu les m a y have become ster ical ly prevented f r o m be ing able to translocate through, a substantial ly different result than w i t h s ing le -stranded overhangs or w i t h ha i rp in structures noted i n A p p e n d i x B . 4 . Appendix B: AHL for Nucleic Acid Detection 131 B.6 Other Notable aHL Experiments The a H L pore has been used as the basis for numerous other detection schemes and nanosensor-type implementat ions, inc lud ing : • Detect ing protein sequences w h i c h f o r m st i f f rod l ike or f lex ib le p o l y m e r - l i k e chains [163], a technique w h i c h cou ld not o n l y d ist inguish molecu le types but also the presence o f intermediate conformat ions undetected us ing convent ional c i rcu lar d i c h r o i s m measurements. • A s part o f an overa l l sensor for detecting molecu les b y d isc r iminat ing the capture k inet ics o f short and l o n g nuc le ic ac id fragments tethered to av id in proteins [162] • C o m b i n i n g the pore w i t h a synthesized D N A - P E G probe molecu le w h i c h cou ld be used to measured changes in impedance and anion/cation select iv i ty w i t h the probe i n p lace [124]. • Tether ing a P E G / b io t in molecu le to the inside o f the pore and us ing the system for s ing le -molecu le av id in hybr id i zat ion . Ion channel readings f rom the system cou ld be used to detect and dis t inguish the capture o f ind i v idua l a v i d i n molecu les o n the cis and trans-sides o f the pore to detect in concentrations i n the tens o f n M [114]. Appendix C: Synthetic Nanopores 132 Appendix C Synthetic Nanopores T h o u g h a H L protein channels have almost ideal properties for detect ion and l im i ted ident i f icat ion o f ind i v idua l nuc le ic ac id strands, the amount o f t ime and expertise required to f o r m a single channel , and the l im i ted l i fe t ime (5 m i n - 24 hrs) and great f ragi l i ty o f these channels i n the convent ional ar t i f ic ia l l i p i d b i layer system make it essential ly imposs ib le to incorporate a H L i n c o m m e r c i a l instrumentation. In addi t ion , experiments that w o u l d not be feasible for appl icat ion w i t h b i o l o g i c a l l i p i d bi layers m a y be possib le w i t h more robust synthetic nanopores, such as c o m b i n i n g opt ical laser tweezers w i t h nanopores to locate and pos i t ion the fragment i n the planar structure and apply forces to nuc le ic ac id fragments inside the pore [167]. Synthetic channels w i t h d imens ions s imi la r to a H L are one method to apply the detect ion sensit iv i ty and select iv i ty o f the proof -o f - concept appl icat ions for a H L pores for c o m m e r c i a l instrumentation. C l Track-Etched Membranes Track -e tched polycarbonate membranes w i t h pore diameters on the order o f tens o f nanometers are readi ly avai lable f r o m c o m m e r c i a l sources ( W h a t m a n Nuc lepore , N e w t o n , Massachusetts) and have been used successfu l ly for size d isc r iminat ion and f i l ter ing o f proteins and other analytes v i a hydrostatic pressure and electrophoresis through the Appendix C: Synthetic Nanopores 133 pores [168, 169]. The track-etch process invo lves i r radiat ing a s o l i d membrane mater ia l , w i t h a beam o f h igh -energy nuclear fragments to create tracks o f imperfect ions that pass through the mater ia l , then c h e m i c a l l y etching a long the tracks w i t h a h igh degree o f contro l over the pore size and ax ia l un i fo rmi ty based on the concentrat ion and exposure t ime o f the etchant. The length o f the i n d i v i d u a l pores is l i m i t e d b y the thickness o f the polycarbonate membrane, w h i c h hinders their use for measur ing ind i v idua l molecules by the Coul ter counter effect, as the change i n electr ical impedance due to a part ic le o f nanometer -scale i n a tube o f m i c r o n length is d i f f i cu l t to d is t inguish above the basel ine s ignal . In order to reach even smal ler pore diameters and lengths, t rack-etched polycarbonate membranes have been used as the template for g o l d nanotubules, fo rmed us ing electrodeless p lat ing i n A u + so lut ion [169]. The size and prof i le o f the go ld nanotubules formed are h i g h l y dependent on the p H o f the A u + plat ing solut ion, w i t h l o w p lat ing rates leading to pores o f u n i f o r m diameter w h i l e higher p la t ing rates deposit more go ld at the two ends than on the inner w a l l s , resul t ing i n z e p p e l i n -shaped pores. Nanotubules w i t h molecu lar d imensions ( < l n m ) have been obtained us ing this technique [168], but have not been successful i n detect ion o f nuc le ic acids dur ing translocations. C.2 Nanopores from Semiconductor Fabrication Techniques Present state-of-the-art large-scale semiconductor fabr icat ion techniques us ing photol i thography are l imi ted to feature sizes o n the order o f ~ 3 0 - 5 0 n m , over ten t imes larger than w o u l d be desirable for fabr icat ion o f pores s imi lar to a H L . In order to achieve features sizes on the scale required for detection o f b iomolecu les us ing nanopores, other spec ia l i zed fabr icat ion techniques must be appl ied . U s i n g a synthet ical ly - fabr icated pore opens the poss ib i l i t y o f c o u p l i n g the l inear process ing o f the nanopore w i t h other methods o f detect ion for f i e l d -effect t ransistor - l ike structures w i t h charge-sensit ive regions close to the Appendix C: Synthetic Nanopores 134 pore. M o s t techniques w h i c h have fabricated nanopores i n membranes have used convent ional exposure and etching methods for f o r m i n g a th in ( s ing le -mic ron to tens o f nanometer) membrane o f insulat ing mater ia l , then i r radiat ing the surface w i t h h igh -energy electrons or s m a l l ions , re l y ing o n surface d i f fus ion o f atoms to generate mass f l o w into the pore and eventual pore shr inkage over t ime. A group led b y G o l o v c h e n k o and Branton have fabricated synthetic pores o n the scale o f 5 n m i n a S i3N 4 membrane us ing an A r + i o n b e a m incident o n a pre- th inned sample membrane, w h i l e an i o n -focus ing E i n z e l lens and def lect ion system is used to detect A r + ions pass ing through the pore i n the membrane, a l l o w i n g for an extremely sensit ive method o f simultaneous pore fabr icat ion and detect ion [70]. 5 n m holes fabricated us ing this technique are used to detect the presence o f 500bp double-stranded D N A passing through the pore b y observ ing intermittent current b lockades. M o r e recent developments w i t h these pores us ing atomic layer deposit ion o f AI2O3 on the surface o f the pore to mit igate var iable surface charges on the inside o f the pore and the resul t ing effect on both i o n current noise and the probabi l i t y o f capture o f nuc le ic acids f r o m the bu lk so lut ion [84]. Other groups have used s imi la r techniques to produce pores w h i c h were used for nuc le ic ac id detection. T i m p and coworkers [68, 71] have used a 2 0 0 k V transmission electron microscope to fabricate holes i n meta l ox ide semiconductor -compat ib le membranes to f o r m pores as s m a l l as 0.5 n m i n diameter, sma l l enough to successfu l ly separate s s D N A f r o m d s D N A 50-mers through translocat ion [83]. S to rm et al. [170] have also manufactured 4 n m pores i n S i 0 2 layers u s i n g T ransmiss ion E lec t ron M i c r o s c o p y ( T E M ) beams at approx imate ly 3 0 0 k V , detecting d s D N A o f strands less than l k b p long. A s l ight ly different technique us ing thermal ox ide growth to f i l l i n the pore size has been used to fabricate 5 0 - 6 0 n m long and 4 - 5 n m diameter pores i n s i l i con membranes [171]. E - b e a m l i thography was used to define a 100 n m starting pore that was then subject to thermal ox ide growth to the pore to less than 50 n m . Th is results i n pores w h i c h can pass 200-nuc leot ide long d s D N A fragments i n 0 . 1 M K C l . In Appendix C: Synthetic Nanopores 135 contrast to prev ious measurements, the current increases rather than decreases as D N A passes through the pore ( 1 1 . 4 p A , 4ms long at 2 0 0 m V ) . Th i s anomalous observat ion cou ld be a result o f the negat ive-charges o n the wa l l s where the D N A and synthetic pore i n combinat ion act as a f ie ld -ef fect transistor. It is also possib le that the nuc le ic ac id br ings i n a higher concentrat ion o f charge-carr iers as it passes through the pore, and that the decreased speed o f the nuc le ic ac id fragment through the pore ( - 1 . 6 x 1 0 - 5 m/s, m u c h s lower than Si3Mt pores) m a y cause this effect. A l ternat ive techniques have also been used to f o r m pores s m a l l enough to detect b iomolecu les . Sa l eh and S o h n [172] have manufactured 2 0 0 - n m diameter pores i n po ly (d imethy ls i loxane) ( P D M S ) us ing m i c r o m o l d i n g techniques. Interactions between these nanopores and X-phage D N A molecu les (48,500 bp) can be detected as b lockages o f o n the tens o f p A are measured i n an open-channel current o f approx imate ly 15 n A . A l ternat ive materials have also been used for direct fabr icat ion o f nanopores, such as the transparent plast ic p o l y m e t h y l methacrylate ( P M M A ) [173], where a focused i o n b e a m w i t h a 1 p A b e a m current at 300 k V produces pore diameters between 75 and 119 n m , m i l l e d through i n 3sec. Appendix D: Invalidity of Continuum Approaches For Nucleic Acid 136 Capture: Appendix D Invalidity of Continuum Approaches For Nucleic Acid Capture C o n t i n u u m analyt ic arguments have been used to estimate the f lux o f ions through membrane -bound nanopores [135]. These cont inuum approaches assume that the molecules are o f a s m a l l enough s ize scale relative to a l l relevant length scales, and that the l o c a l concentrat ion o f molecu les can be used to quant i fy the molecu les wi thout considerat ion o f the discrete particulate nature o f molecu les i n so lut ion. The f o l l o w i n g argument makes it is clear that such an approach for est imating nuc le ic ac id capture rates f r o m the b u l k so lut ion w i l l lead to a p h y s i c a l l y inaccurate m o d e l o f the system. F i rst , consider the D N A as a part icle f o l l o w i n g d i f fus ion under an appl ied electr ic f ie ld b y app ly ing F i c k ' s second law o f d i f fus ion w i t h drift [174] : D V 2 C + V.Uc)=^ ( D - D v ; dt The first term is due to B r o w n i a n d i f fus ion o f a charged mo lecu le populat ion w i t h concentrat ion C and d i f fus ion constant D, w h i l e the second term describes drift o f the charged molecu les g iven a m o b i l i t y p and an electr ic f i e ld E (such that in the absence o f d i f fus ion , vdrift = Appendix D: Invalidity of Continuum Approaches For Nucleic Acid 137 Capture: pE). In spherical coordinates and assuming azimuthal symmetry this can be re-expressed as: r dr dC_ dr r" dr dC_ dt (D -2) With the pore surface of radius r = a modeled as a perfect absorber in the plane of a nonabsorbing membrane, and with Co the bulk molecule concentration, the physical system can be described with the following boundary conditions: C(<*) = Co C(r<a) = 0 d C ( e = -de (a) (b) (D-3) = 0 (c) Solving Equation (D-2) requires an expression for the non-zero electric field in the vicinity of the pore E, associated with a net ionic current through the pore. In contrast to the electrostatic case, E is not affected by Debye screening. A n approximation for E can be generated by first examining the ionic current density in the buffer solution. The ion current density can be expressed in differential form as: Here, J is the current density and a the charge-carrier density. It is assumed that there is uniform current density across the entire mouth of the pore and zero current across the membrane. From (D-4), the vector field for the electric field E w i l l have the same magnitude and direction at all points as J, assuming cr is constant at all points in the electrolyte solution. Appendix D: Invalidity of Continuum Approaches For Nucleic Acid 138 Capture: Note that the boundary conditions for E are identical to the electric field from a flat disc of uniform charge, and will therefore also have the same magnitude and direction as the electric field from such a disc. A n approximation for the electric field at all points away from the pore mouth is the on-axis electric field generated by a disc of uniform charge, given by: E(r) = f - p - W ( l - r )f- (D-5) \4ns) yjr2+a2 \r\ Here, A is the area charge density on the disc and s the dielectric constant. In the case of the membrane-bound pore, the prefactor in Equation (D-5) is changed to: E{r)^E0(X--TJ~){- (D-6) Jr2+a2 \r\ with E0=V IL is the applied electric field directly at the mouth of the pore, L is the length of the channel, and r is the distance from the center of the pore. A numerical solution of the system formed for by Equation (D-2), (D-3) and (D-6) using typical experimental parameters for single-stranded nucleic acids and synthetic pores as listed in Table 0-1 yields C(r) along the pore axis as shown in Figure A.2. V 200mV a 1 nm Pore radius L 5 nm Pore length C 1 u M Polymer concentration P 2 x 10"" m"/Vs ssDNA D 5 x 10""nr7s [76] ssDNA Table 0-1 - Parameters for typical test conditions for ci's-side molecule capture Appendix D: Invalidity of Continuum Approaches For Nucleic Acid 139 Capture: 1.2 -= 1 -g ra £ 0.8 -c Q) O § 0.6 -o •% 0.4 -Q) * 0.2-0 -0 1 2 3 4 5 Radial distance from pore (nm) Figure A.2 -Calculated concentration of an absorbing pore along the pore axis using constants listed in Table 2-1. U n d e r t yp ica l exper imental condi t ions, the length scale over w h i c h the nuc le ic ac id concentrat ion decreases f r o m the b u l k to the absorbing pore, is on the same size scale as the p o l y m e r itself. A s ingle mo l e cu l e o f p o l y ( d A ) 5 0 i n h igh ion ic strength solut ion has a K u h n length b ~ 1.5 n m (~ 3 nucleotides) [76] and a radius o f gyrat ion Rg ~ bNV5 ~ 8 n m , where N ~ 17 is the number o f K u h n segments i n the molecu le . Th i s imp l ies that it is phys ica l l y imposs ib le to establ ish the part ic le d ist r ibut ion shown i n F igure A . 2 for nuc le ic acids. One useful result o f this exercise is the expectat ion that, o n the length scale o f the po lymer , the molecu le concentrat ion is u n i f o r m everywhere - the presence o f the absorbing pore does not produce s igni f icant l o c a l m o le cu le deplet ion. Therefore, one can consider the upper l i m i t o f the capture rate o f the nanopore b y treating it as a per fect ly -absorb ing hemisphere and calcu lat ing the number o f co l l i s ions o f molecu les i n free so lut ion w i t h the hemisphere us ing the w e l l k n o w n result o f the d i f fus ion equation i n spherical coordinates as der ived b y B e r g [174]: R =2nCDa (D -7) Appendix D: Invalidity of Continuum Approaches For Nucleic Acid 140 Capture: Here , C and D are the concentration and bu lk d i f fus ion constants o f the molecu le , and a the pore radius. U s i n g this expression and the test condi t ions descr ibed in Table 0 - 1 , the theoretical upper l imi t o f the capture rate for the nanopore w i t h radius a ~ 0 .5nm is - 1 5 0 events/sec at 1 pM , far i n excess o f the m a x i m u m rate o f ~ 2 5 events/sec achieved exper imenta l ly at the m a x i m u m transmembrane potentials. I f the po lymers do enter into the hemispher ica l reg ion surrounding the pore at the rate descr ibed b y Equat ion (D -7 ) they do not a l l result i n measurable translocations. The m o d e l for nucle ic ac id - nanopore interactions must inc lude in format ion on the po l ymer ic nature o f the nuc le ic ac id fragments and the dynamics o f their interaction w i t h the electric f ie ld at the m o u t h o f the pore. Appendix E: Effective Charge of Single-stranded DNA Trapped 141 Inside Nanopores Appendix E Effective Charge of Single-stranded DNA Trapped Inside Nanopores Th is section examines the effective internal charge per nucleot ide o f s ingle-stranded nuc le ic acids w i t h i n the a H L protein pore, and the source o f the d iscrepancy between previous publ ished estimates o f - 0 . 1 e per nucleot ide and the estimate o f ~0 .4e per nucleot ide made i n Sect ion 3.3 i n this body o f work . The d iscuss ion be low w i l l demonstrate that the p r i m a r y source o f this d iscrepancy comes f r o m different assumptions about the interpretation o f the energy barrier pos i t ion and the number o f nucleot ides w h i c h are subject to the appl ied transmembrane potent ial dur ing d issoc iat ion . M a t h e et al. [108] examined the force -d issoc iat ion o f nuc le ic ac id duplex segments w i t h single-stranded overhangs f r o m the cz's-side o f the pore. In these experiments, each s s D N A fragment contains a self -h y b r i d i z i n g ha i rp in loop structure at the 5' end o f the - 6 5 nucleot ide l o n g fragment. T h e nuc le ic ac id enters into the pore w i t h the 3' end lead ing the w a y into the pore, and the duplex section entering the vest ibule o n the cw -s ide o f the membrane up to the l i m i t i n g aperture, at w h i c h point it is restricted f r o m passing complete ly through. U n d e r an appl ied transmembrane force, the hai rp in duplex dissociates, leav ing the strand as a s ingle-stranded fragment capable o f t ranslocat ing complete ly through the pore. Est imates for the effect ive charge per nucleot ide zpore were based on force -d issoc iat ion t ime curves at constant appl ied potent ial s imi la r to the w o r k described in Sect ion 3 .5 . Appendix E: Effective Charge of Single-stranded DNA Trapped 142 Inside Nanopores The force -d issoc iat ion experiments were per formed us ing three ha i rp in structures w i t h vary ing duplex lengths: a duplex 10 bases long , duplex 10 bases long w i t h one m i s m a t c h w i t h i n the strand, and a duplex 7 bases long. The result ing force -d issoc iat ion curves show an exponent ia l decrease o f the d issociat ion t imescales w i t h increas ing potent ia l , a l l o f w h i c h had the same slope o f - 2 2 ± 2 m V o n a l inear - log plot . The analysis used b y M a t h e et al was a m o d i f i e d vers ion o f the s ingle-barr ier Ar rhen ius act ivat ion energy relat ion: zv = T0 exp kBT T0 exp kBT V J J (E-8) Here , TV is the d issociat ion t ime o f the duplex sect ion, r0 the t ime constant, and Qe/f the effective charge subject to the appl ied transmembrane potent ial . Qef/ was further b roken into the charge per nucleot ide ze/f, the number o f nucleotides n, and the unit charge e. In a p p l y i n g Equat ion (E-8) to estimate zeff, M a t h e et al. assume that the energy change associated w i t h m o v i n g a long the react ion coordinate f r o m the bound state to the transit ion state at the top o f the energy barr ier results f r o m a displacement o f n charges across the transmembrane potent ial V, stating that n " . . . is associated w i t h -12 nucleot ides that span the a H L c h a n n e l . " Th is associat ion o f n w i t h the number o f nucleot ides spanning the channel is problemat ic i n that it is unrelated to the actual number o f charges that must cross the potential V as the strand moves a long the react ion coordinate between the bound state and the peak o f the energy barrier. It is more l i k e l y that n is related to the f ract ion o f the stem duplex that must dissociate before translocat ion under appl ied f i e ld is energet ical ly favorable ; this m a y be fu l l d issoc iat ion or part ia l d issoc iat ion , as was descr ibed i n F igure 3.8. A n addit ional issue is that E q u a t i o n (E-8) has no means o f account ing for differences i n the slope values on the force -d issoc iat ion curves except b y va ry ing zejj-; it is d i f f i cu l t to env is ion a mechan ism b y w h i c h the charge per nucleot ide Appendix E: Effective Charge of Single-stranded DNA Trapped Inside Nanopores 143 w i t h i n the pore w i l l change i n response to a different duplex sequence outside the pore. F o r these reasons, Equat ion (E -8) alone m a y not prov ide the best estimate o f the true charge per nucleot ide w i t h i n the pore zejj unless other phys ica l parameters can be accounted for i n the m o d e l . The der ivat ion and appl icat ion o f zpore used i n this w o r k rel ies o n a more appropriate phys i ca l interpretation o f the interact ion w i t h i n the pore. A value for zpore was der ived f r o m the probe escape experiments descr ibed i n Sect ion 3 . 3 . 1 . The result ing charge per nucleot ide zpore ~ 0.4 is used to interpret the results o f force -d issoc iat ion experiments between the probe and target fragments us ing E q u a t i o n (3 -17) : Toff = T D e X P r E A b \ k B T J r r -z neV^ ^ exp : r exp: V V A l kBTJ J W A l J \ \ V Ax (E -9 ) Here , the expression combines the prefactor into TP = Td exp(Eb lkBT) to more c lose ly resemble Equat ion (E -8 ) . T h e p r i m a r y dif ference i n this expression as compared to the der ivat ion b y M a t h e et al. is the expansion o f the npore term i n Equat ion (E -8) to inc lude the number o f nucleotides per unit length ratio nl Al and the phys ica l distance to the energy barrier A x , discussed i n Sect ions 3.5.1 and 3 . 5 . 3 . The combinat ion o f the exper imental estimate o f the charge per nucleot ide zpore generated by probe escape experiments descr ibed i n Sect ion 3.3 w i t h the addit ional parameters found i n Equat ion (E -9 ) m a y g ive greater phys i ca l insight into the d issociat ion experiment. The charge per nucleot ide zpore ~ 0.4 can be used i n conjunct ion w i t h the data col lected by M a t h e et al. to estimate A x for that part icular system. The cz's-side d issociat ion experiments resulted i n a slope o f (22 ± 2 m V ) " 1 . U s i n g the same phys ica l parameters as i n the present w o r k ( A / ~ 6 n m , npore ~ 12, kBT/e = 25 m V ) , the estimate for the react ion distance A x ~ 1.4 ± 0.2 m n . A t 0.35 n m / base pair , this is equivalent to ~ 4 bases i n the duplex strand w h i c h are required to dissociate to reach Appendix E: Effective Charge of Single-stranded DNA Trapped 144 Inside Nanopores the maximum of the energy barrier prior to full dissociation and translocation. This value is reasonable given the length of the full duplex region of the hairpin (10 base pairs and 7 base pairs). Appendix F: Regime of Validity for Collected Data 145 Appendix F Regime of Validity for Collected Data Th is sect ion col lects several issues related to aspects o f the exper imental condit ions for molecu le capture and detection for both the cis and trans methods o f nuc le ic ac id analysis descr ibed i n this work . F.l Capture Rate Limitations due to Lowpass Filtering The shortest unambiguous ly detectable nuc le ic ac id capture events are inherently dependent on the degree o f low-pass f i l te r ing appl ied b y the patch -c lamp ampl i f ier . D u r i n g the czs-side molecu le capture studies (Chapter 2) , a typ ica l b lockage for the translocat ion o f a l o n g p o l y ( d A ) molecu le reduces the i o n current b y 85 percent (i.e. to 15 percent o f the open-channel current) [44]. A low-pass f i l ter on a short b lockage event acts to both broaden the event t ime w h i l e decreasing the magnitude o f the b lockage. A s the event c a l l i n g software has a tr igger leve l set to 2 0 % decrease i n ion ic current for the start o f an event, the 8 5 -percent b lockage ampl i tude can be reduced b y a factor o f 85/20 ~ 4.25 due to the low-pass f i l ter ing and st i l l be detected. N u m e r i c a l analysis o f a 10 k H z 4 -po le Besse l f i l ter (not shown) shows that an 15//s pulse pass ing through the f i l ter decreases in ampl i tude b y a factor o f 4.0 and broadens the f u l l - w i d t h h a l f - m a x i m u m o f the pulse to 50 p s. Th i s i m p l i e s that a s ingle b lockage event as short as 15 p s w i l l s t i l l be detected as an event after passing through the 10 k H z f i l ter and w i l l not be missed dur ing 50 k H z d ig i ta l sampl ing f o l l o w i n g the 10 k H z f i l ter (50 k H z = 20 p s per sample) . A s imi la r analysis shows that the 100 k H z Appendix F: Regime of Validity for Collected Data 146 l ow -pass f i l ter requires a pulse durat ion o f at least - 1 . 5 // s to reduce the ampl i tude o f the pulse to the 20 percent threshold leve l . H i s t o g r a m data o f translocation t imes o f s s D N A can be used to estimate the f ract ion o f molecu les that m a y pass through faster than the 15 ps l i m i t on the 1 0 k H z l o w pass filter at h igh transmembrane potentials. The b lockage durat ion h istogram for the D N A strand poly(dA) ioo at 120 m V described by M e l l e r et a l . [45] showed a characteristic h is togram w i t h a mean t ime - 3 3 0 // s. A s s u m i n g that the h is togram prof i le scales w i t h the mean translocat ion t ime, and g iven that b lockage durations depend l inear ly on po l ymer length and o n the square o f the appl ied potential [60], the most frequently occur r ing value o f b lockage durations result ing f r o m po ly (dA) 5 o at 240 m V is - 4 0 p s, and less than 1 % o f p o l y ( d A ) 5 0 molecu le events w i l l be shorter than - 1 5 p s; the vast major i ty o f the 5 0 - m e r molecules should be detected b y the event c a l l i n g software at a sampl ing rate o f 10 k H z . A s imi la r estimate for the shorter po ly (dA) io molecu le shows that m a n y o f the translocations m a y pass through the filter at 10 k H z and at 100 k H z . A l inear relat ion between the translocat ion t ime w i t h the length o f the molecu le (wh ich w o u l d reduce the translocat ion t ime b y a factor o f 5 compared to the 50-mer) o n l y extends d o w n to lengths o f approx imate ly 12 nucleot ides [60]; w o r k by M e l l e r et al shows that for a 10 -mer molecu le there is an addit ional ~2x increase i n the ve loc i t y o f the mo lecu le , as shorter fragments do not have to overcome the same entropic effects due to the po l ymer nature o f s s D N A dur ing translocat ion [60]. Therefore, the overa l l reduct ion i n the translocation t ime w i l l be o n the order (40 ps I (5 x 2)) - 4 ps, shorter than the 15 ps l im i t set b y the 10 k H z filter. A s s u m i n g the translocation t ime prof i le as descr ibed b y M e l l e r et al [45], more than 5 0 % o f the p o l y ( d A ) i 0 t ranslocat ion t imes w i l l be shorter than - 1 5 // s, mean ing that the 10 k H z filter m a y not detect a l l o f the translocations for the 10-mer fragment. Appendix F: Regime of Validity for Collected Data 147 F.2 Examination of relevant timescales D u r i n g d issoc iat ion analysis o f probe-target duplexes us ing the transmembrane nanosensor, d issoc iat ion t imes are on the order o f tens o f mi l l i seconds to tens o f seconds. The other t imescales related to the probe molecu le translocat ion and relaxat ion w i l l be s h o w n to be far shorter than these t imes and should not skew the results o f d issoc iat ion t ime analysis . Once the probe molecu le has in i t ia l l y passed through the pore and extends to the trans-si&e o f the membrane, the re laxat ion t ime for the probe molecu le have a m a x i m u m t ime set by the R o u s e t ime o f the p o l y m e r [175]: T - r relax rouse ~ 2 5n ' & ) J L (E-l) kT ) 37T2 Here , C, is the f l u i d f r ic t ion , b the length o f one K u l i n segment, and TV the total number o f K u h n segments. F o r the port ion o f the probe mo lecu le 12 extending into the trans-side so lut ion (<£" ~ 8 x 10" kg/s, b ~ 1 . 5 n m , N - 2 2 ) , the re laxat ion t ime is - 7 0 ns, far shorter than any o f the d issoc iat ion or hybr id i zat ion t imes measured us ing the nanosensor. G i v e n this , it is assumed that the molecu le w i l l be thermal ly re laxed at a l l t imes dur ing hybr id i zat ion and d issociat ion experiments. D u r i n g probe-target d issociat ion, the t ime required for the probe mo l ecu l e to escape the pore and to result i n an unb locked pore state w i l l be on the same order as the t ime o f translocation for a s s D N A strand under and appl ied potent ia l ; as translocation t imes for a 5 0 - m e r mo lecu le under l O O m V appl ied potential is on the order - l m s (Sect ion 2.3.1) . Th i s indicates that that escape t ime o f the probe molecu le m a y be one l i m i t i n g factor w h e n record ing short d issoc iat ion t imes at h igh appl ied potentials or for weak bonds. T o accommodate for this lower l im i t , the appl ied potent ial can be iteratively set higher or lower dur ing test protocols to ensure that a requisite f ract ion o f capture events and dissoc iat ion t imes occur w i t h i n a g iven range. Appendix F: Regime of Validity for Collected Data 148 F . 3 P o r e g a t i n g A pore gat ing event is one i n w h i c h the ion ic conduct ion ins ide o f the pore decreases substantial ly , t yp ica l l y f r o m 4 0 - 9 0 % , i n response to vo l tage - induced or thermal l y - induced changes i n the structure o f the pore or interactions w i t h speci f ic divalent or tr ivalent cations i n so lut ion [139, 146, 149, 150]. The t ime intervals dur ing and between gat ing events are stochast ical ly distr ibuted, and m a y cause one o f two prob lems dur ing analysis o f the probe-target d issociat ions: f irst, a gat ing event m a y occur so rap id ly after a transit ion f r o m the duplex to d issociated state that the event detection a lgor i thm m a y not be able to d iscern the d issoc iat ion t ime, b ias ing the results to longer d issociat ion t imes; and second, the mechanisms w h i c h cause the gating events m a y occur w h i l e the probe molecu le is s t i l l inside the pore, result ing i n a non-constant force appl ied to the probe-target duplex f rom the appl ied potent ial . F o r the a H L protein pore dur ing cw-side mo lecu le capture exper iments, the rate o f gating is m i n i m a l and not voltage dependent, contr ibut ing ~ 0 . 2 b lockage events per second i n standard 1 M K C l buffer so lut ion . A l t h o u g h the a H L pore i n the absence o f divalent cations is noted as hav ing far less gat ing than typ ica l b i o l o g i c a l nanopores [149], it was recognized dur ing experiments w i t h the prototype nanosensor that gat ing events occurred under the appl icat ion o f negative potentials as is the case dur ing trans-side d issoc iat ion experiments. A l t h o u g h other studies us ing the a H L channel have examined the relat ionship between the m e a n current and the appl ied potential dur ing gating, as w e l l as the t ime-dependence and k inet ics o f gating at one part icular appl ied potent ia l [139, 151] , no prev ious study i n the literature to date has noted the relat ionship between gating kinet ics and the appl ied potent ial . Measurements us ing a H L under standard electrolyte buffer condi t ions and a negative potential demonstrate that the mean t ime f r o m Appendix F: Regime of Validity for Collected Data 149 the end of one gating event and the beginning of the next gating event, tgate, exponentially decreases with increasing applied potential, as shown in Figure A . 3. The tgate times measured at the highest applied potentials used in the dissociation experiments (-lOOmV) were greater than ~0.3 sec between gating events, much longer than the sampling time used by the data acquisition system (20 p s). It is therefore extremely unlikely for the system to miss detecting the time between a probe-target dissociation event followed by a rapid gating event. As the length of the probe-target duplex region grows from 14-bp to 20-bp and longer, comparable to lengths used for R N A primer design, and as the electrolyte buffer solution becomes closer to physiological conditions, it may become necessary to monitor tgate times to ensure that at all applied negative potentials the gating times remain long compared to the dissociation times of the molecules. This discussion does not address the second issue of non-constant dissociation force applied to the probe-target duplex due to the gating of the pore the probe molecule inside the pore. This issue may not cause a problem during dissociation experiments, as studies by Korchev et al. indicate that during pore gating the aHL pore conductance changes by a factor of -10 but the physical size of the channel changes by less than a factor of 2 [151], shown during tests with different sizes of polyethylene glycol. Possible genetic modifications to the pore to decrease the level of voltage-induced gating may be one method of addressing this uncertainty in the prototype nanosensor. Appendix F: Regime of Validity for Collected Data 150 average time between gating events (ms) applied potential (mV) Figure A.3 - Time between induced gating events versus applied negative transmembrane potential for the aHL pore in 1M K C l Appendix G: Time-varying applied potentials for duplex dissociation 151 Appendix G Time-Varying Applied Potentials for Duplex Dissociation M a t h e et al. [108] der ived an expression for the most l i k e l y d issoc iat ion potential for d issoc iat ion o f nucle ic acid duplex structures under a constant rate o f change i n the appl ied transmembrane potent ial . B e l o w is a reproduct ion o f the der ivat ion, w h i c h also notes ver i f i cat ion w i t h a constant appl ied potential where the load ing rate is zero. The der ivat ion begins w i t h an Ar rhen ius relat ion from Equat ion (3-2) , restated to g ive an exponential dependence on the appl ied potential V, and us ing the inverse o f the off -rate descr ibed i n Equat ion (3-4) to express the t ime constant for d issociat ion as a funct ion o f the appl ied potent ia l : (-viv„) ( F -10) T(V) = rDe where Vt, = kBT is the thermal scal ing factor and TD is the is the inverse o f the off - rate t ime constant described i n Equat ion (3-2) . The probabi l i t y d istr ibut ion funct ion for d issoc iat ion at a g i ven t ime t can be estimated f r o m the t ime-dependent t ime constant for d issoc iat ion as: e J o r ( 0 (F-ll) P W = — T T " T{t) In this expression, the numerator is the l i k e l i h o o d o f not undergo ing a d issoc iat ion f r o m t ime 0 to t [176]. Appendix G: Time-varying applied potentials for duplex dissociation 152 For a constant potential V(t) = V0, Equation (F-l 1) reduces to: " (-VnJo"' _ , / r P(0 = (F-12) This is the expected probability distribution for dissociation under a constant applied force. Making the applied potential ramp rate a constant, V(t) = V t, results in a time-dependent time constant for dissociation: Substituting Equation (F-13) into (F-l 1) gives: Jo * p T l > e P(t) = -(F-13) (F-14) r 0 e Solving the expression and making P a function of the applied potential F with dV = V dt gives a final solution of the form: P(V) = ( \ r ( \ 1 exp V e U J _ i • • \ T D V ) V J (F-15) Note that the final expression P(V) should be in units V1, true for Equation (F-15). The most likely applied potential for dissociation n dP'V) occurs with 0 = , occurring when: dV Appendix G: Time-varying applied potentials for duplex dissociation 153 dP(V) clV ( \ 1 ( \ yb ( ( r» • T V ( \ 1 f \ 1 [M v J • • T Dv vh ( ( F -16) This gives an analytic expression for the most likely applied potential for dissociation given a constant rate of increase for the potential. Experimentally, it is possible to test out different ramp rates V and measure the resulting most likely potentials V in order to experimentally determine rD far more accurately than could be done under constant applied potentials. 

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