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Surfactant surface chemistry and heparin-based anticoagulant drug design studied by molecular dynamics… Mafi, Amirhossein 2018

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SURFACTANT SURFACE CHEMISTRY AND HEPARIN-BASED ANTICOAGULANT DRUG DESIGN STUDIED BY MOLECULAR DYNAMICS SIMULATION by  Amirhossein Mafi  M.Sc., Amirkabir University of Technology, Iran, 2012 B.Sc., Amirkabir University of Technology, Iran, 2010  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  DOCTOR OF PHILOSOPHY  in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (CHEMICAL AND BIOLOGICAL ENGINEERING)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)  February 2018  © Amirhossein Mafi, 2018   ii Abstract  This dissertation uses molecular dynamics (MD) simulations to mainly focus on the study of the interaction between neutral surfactants-water and anionic surfactant-anionic polyelectrolyte on the water surface. Besides, this study devotes to finding the possible routes of improving the design of a drug candidate, polyethylene-glycol-linked cationic binding groups (PEG)n-HBG, to inhibit polyphosphate (polyP) thrombotic activities.  It is found that the behavior of the nonionic polyoxyethylene glycol alkyl ether on the water surface is more anionic-like, even though the surfactant is overall neutral. The non-ionic surfactant increases the depth of the surface anisotropic layer and the average number of hydrogen bonds per water molecule. MD simulation showed that the negatively-charged O atoms have the most impact on the orientation of water as most water molecules arrange with their H atoms pointing toward the surface.   In contrast, the behavior of the zwitterionic surfactant, N-dodecyl-N, N-dimethyl-3-ammonio-1-propanesulfonate, on the water surface is more cationic-like as the positively charged group is more capable of orienting interfacial water. The zwitterionic surfactant orients water molecules with their OHs mostly pointing toward the liquid water.  While the complex formation between highly-charged surfactants and polyelectrolytes of the same charge is generally expected to be prohibited by the electrostatic repulsion, my study shows it is possible to form thermodynamically stable complexes in the presence of excess ions. With excess Na+ ions, the charge screening effect allows anionic polyelectrolyte to weakly interact with anionic surfactant via hydrogen bonds. In the presence of divalent Ca2+ ions, the surfactant and the polymer is strongly coupled by forming Ca2+ ion bridges and hydrogen bonds.   iii The mechanism of complex formation between (PEG)n-HBG and polyP are studied using metadynamics simulations with the all-atom and coarse-grained force fields. It is shown that the PEG length does not have any impact on the interaction between the (PEG)n-HBG and polyP. However, it mostly improves the drug’s hemocompatibility by preventing the cationic drug from binding to other negatively- charged biomolecules. Increasing the number of the positive charges on the headgroup strengthens drug binding to polyP. It is found that the binding of (PEG)n-HBG remains intact against various lengths of polyP.    iv Lay summary  Water is a good solvent, because it is capable of dissolving a wide variety of materials. Besides, it is cheap and abundant. Therefore, it is used in many applications. However, it is often desirable to modify the properties of aqueous solutions. In many practical applications, surfactants /polymers are added into aqueous solutions to modify their properties. Nonetheless, it is necessary to understand how surfactants/polymers affect the properties of water and how water behaves in the presence of surfactants or polymers. This dissertation mainly attempts to provide molecular-level answers for these questions.    Thrombosis is the formation of blood clot in the blood vessels, which can lead to heart attack and stroke. It has been recently known that the polymeric drugs are good candidates to reduce thrombosis. Using the molecular-level information, this dissertation attempts to find an efficient polymeric drug to inhibit the main blood clotting agent in the aqueous solution.    v Preface  A version of Chapter 3 has been published: Amirhossein Mafi, Dan Hu, and Keng C. Chou “Interactions of water with the nonionic surfactant polyoxyethylene glycol alkyl ethers studied by phase-sensitive sum frequency generation and molecular dynamic simulation” Surface Science 2016, 648: 366-370. This project was initiated by Dr. Chou. Dr. Hu conducted the SFG experiment and collected the required spectra. I performed molecular dynamics simulations, and collected data. All authors contributed to writing the manuscript and analyzing the data.  A version of Chapter 4 has been published: Amirhossein Mafi, Dan Hu, and Keng C. Chou “Interactions of sulfobetaine zwitterionic surfactants with water on water surface, Langmuir 2016, 32(42): 10905–10911. This project was initiated by Dr. Chou. Dr. Hu measured surface tensions and conducted the SFG experiment and collected the required spectra. I designed the project, developed the required force field, performed molecular dynamics simulations, and collected data. All authors contributed to writing the manuscript and analyzing the data. A version of Chapter 5 has been published: Amirhossein Mafi, Dan Hu, and Keng C. Chou “Complex formations between surfactants and polyelectrolytes of the same charge on water surface”, Langmuir 2017, 33(32): 7940-7946. This project was initiated by Dr. Chou. Dr. Hu conducted the SFG experiment and collected the required spectra. I designed the project, performed molecular dynamics simulations, metadynamics simulations, and collected data. All authors contributed to writing the manuscript and analyzing the data.    vi A version of Chapter 6 has been submitted: Amirhossein Mafi, Jayachandran N Kizhakkedathu, Jim Pfaendtner, Keng C Chou “Design of Polyphosphate Inhibitors: a Molecular Dynamics Investigation on Polyethylene-glycol-linked Cationic Binding Groups” 2017. Dr. Kizhakkedathu, Dr. Chou and I initiated the project. Dr. Pfaendtner and I designed the required methodologies. Dr. Kizhakkedathu, Dr. Pfaendtner, and Dr. Chou guided the project. I developed the required coarse-grained force field, performed molecular dynamics simulations, metadynamics simulations, and collected data. All authors contributed to writing the manuscript and analyzing the data.    vii Table of contents  Abstract .......................................................................................................................................... ii	Lay summary ................................................................................................................................ iv	Preface .............................................................................................................................................v	Table of contents ......................................................................................................................... vii	List of tables.................................................................................................................................... x	List of figures ............................................................................................................................... xii	List of symbols ............................................................................................................................ xix	List of abbreviations ................................................................................................................. xxii	Acknowledgements .................................................................................................................. xxiv	Dedication ................................................................................................................................. xxvi	Chapter 1: Introduction ............................................................................................................... 1	Chapter 2: Brief description of molecular dynamics simulations ............................................ 8	2.1	Considerations for MD simulations .................................................................................. 9	2.2	Thermodynamics properties ........................................................................................... 13	2.3	Performing MD simulations ........................................................................................... 15	2.4	Well-tempered metadynamics ........................................................................................ 16	2.5	Parallel tempering metadynamics ................................................................................... 19	2.6	Reweighting .................................................................................................................... 20	2.7	Theoretical background of sum frequency generation spectroscopy ............................. 23	  viii Chapter 3: Interactions of water with the nonionic surfactant polyoxyethylene glycol alkyl ethers studied by phase-sensitive sum frequency generation and molecular dynamic simulation ................................................................................................................................ 26	3.1	Introduction ..................................................................................................................... 26	3.2	Material and methods ..................................................................................................... 27	3.3	Results and Discussion ................................................................................................... 30	3.4	Conclusions ..................................................................................................................... 36	Chapter 4: Interactions of sulfobetaine zwitterionic surfactants with water on water surface ...................................................................................................................................... 37	4.1	Introduction ..................................................................................................................... 37	4.2	Material and Methods ..................................................................................................... 39	4.3	Results and Discussion ................................................................................................... 42	4.4	Conclusions ..................................................................................................................... 50	Chapter 5: Complex formations between surfactants and polyelectrolytes of the same charge on water surface .......................................................................................................... 52	5.1	Introduction ..................................................................................................................... 52	5.2	Material and Methods ..................................................................................................... 55	5.3	Results and Discussion ................................................................................................... 59	5.4	Conclusions ..................................................................................................................... 68	Chapter 6: Design of polyphosphate inhibitors: a molecular dynamics investigation on polyethylene-glycol-linked cationic binding groups ............................................................ 69	6.1	Introduction ..................................................................................................................... 69	6.2	Materials and Methods ................................................................................................... 73	  ix 6.3	Results and Discussion ................................................................................................... 79	6.4	Conclusions ..................................................................................................................... 86	Chapter 7: Conclusions and future work ................................................................................. 88	Bibliography .................................................................................................................................92	Appendices ..................................................................................................................................104	       Appendix A Supplementary information- interactions of sulfobetaine zwitterionic surfactants with water on water surface ..................................................................... 104        Appendix B Supplementary information-design of polyphosphate inhibitors: a molecular dynamics investigation on polyethylene-glycol-linked cationic binding groups  ........................................................................................................................ 107	      x List of tables  Table  1.1. Summery of chemical structures and names of molecules used in this thesis. .............. 5	Table  4.1. Measured and simulated surface tension of water in the presence of DDAPS. The standard deviation was determined by dividing the last 30 ns of simulation run into 5 blocks of 6 ns. .................................................................................................................................................. 45	Table  5.1. The number of ion-bridges and hydrogen bond for different systems in terms of the excess ion. ..................................................................................................................................... 66	Table  6.1. The configurations of different (PEG)n-Ri and polyP simulations. ............................. 74	Table  6.2. Configurations of the (PEG)24-R1 and the numbers of polyP monomers used for CG-MD simulations. ............................................................................................................................ 78	Table  6.3. Extracted S number of (PEG)n-Ri around polyP corresponding to the minimum free energy. ........................................................................................................................................... 80	Table A. 1. Bond stretching parameters. ...................................................................................... 105	Table A. 2. Angle bending parameters. ....................................................................................... 105	Table A. 3. The torsion parameters. ............................................................................................. 106	Table A. 4. The Lennard- Jones parameters. ............................................................................... 106	Table  B.1. Calculated partial charges of atoms in polyP in the different groups and segments as indicated in Figure B1. ................................................................................................................ 107	Table  B.2. Calculated partial charges of the PEG atoms in different groups and segments as indicated in Figure B2. ................................................................................................................ 108	Table  B.3. Calculated partial charges of R1 atoms in the different groups and segments as indicated in the Figure B3. .......................................................................................................... 109	  xi Table  B.4. Calculated partial charges of R2 atoms in the different groups and segments as indicated in the Figure B4. .......................................................................................................... 110	Table  B.5. Calculated partial charges of R3 atoms in the different groups and segments as indicated in Figure B5. ................................................................................................................ 111	Table  B.6. The MARTINI CG bonded potentials and parameters for polyP and (PEG)24-R1. .. 119	Table  B.7. The types and charges of MARTINI CG beads for polyP and (PEG)24-R1. ............. 124	   xii List of figures  Figure 2.1. Periodic boundary conditions in two dimensions. The grey circles are in the image cells while the red circles are in the MD simulation cell. The dashed-line circle is the cut-off length for the calculation of the non-bonded interactions. The figure has been redrawn from reference 38. .................................................................................................................................. 11	Figure 2.2. The Flowchart of MD simulation algorithm .............................................................. 17	Figure  2.3. (a) Schematic of experimental geometry for SFG. E1 is the incident beam at 800 nm. E2 is the IR beam, and ESF is the SFG. (b) Energy diagram of SFG. The solid lines are resonant states, and the dash line is a virtual state. The figure has been sketched from References 74-76......................................................................................................................................................... 23	Figure 3.1. Im(χ(2)) spectra of air/water interfaces with 0 M (a) and 7×10-5 M (b) of C12E4 ........ 31	Figure 3.2. (a) The simulation box with a dimension of 3.6 × 3.6 × 32 nm3. (b) The density of water as a function of depth z with (red) and without (blue) C12E4. (c) Orientation factor <cosθ> of water's dipole with (red) and without (blue) C12E4. The insert shows θ  the definition of the orientation angle. The z-axis (θ  = 0) is the surface normal of the water surface. The dot lines are the Gibbs dividing surfaces, in which the density of water is half the density in the bulk. Please note that for representing the simulation box, the effect of periodic boundary is removed. ........ 33	Figure 3.3. (a) The structure and labeling of atoms of C12E4. (b), (c), (d), (e), and (f) are the angle-resolved radial density distributions of H atoms of water (HW) centered at O1, O2, O3, O4, and O5, respectively. (g), (h), (i), (j), and (k) are the angle- resolved radial density distributions of O atoms of water (OW) centered at O1, O2, O3, O4, and O5, respectively. The   xiii radial density distributions were obtained by calculating the time-averaged number density of HW (or OW) and averaged over 60 C12E4 in the simulation box. They do not represent the true densities of atoms as some atoms are counted more than once. ................................................... 35	Figure 3.4.  (a), (b), (c), (d), (i), (j), (k) and (l) are the angle-resolved radial density distributions of HW centered at C13, C14, C15, C16, C17, C18, C19, and C20, respectively. (e), (f), (g), (h), (m), (n), (n) and (p) are the angle-resolved radial density distributions of OW centered at C13, C14, C15, C16, C17, C18, C19, and C20, respectively. ............................................................... 36	Figure  4.1. (a) Surface tension of water with various DDAPS concentrations. Im(χ(2)) spectra of air/water interfaces in the CH (b) and OH (c) regions with DDAPS at 0 M (cyan), 1×10-5 M (magenta), 2.5×10-5 M (orange), 1×10-4 M (blue), and 2.6×10-3 M (red). The Im(χ(2)) spectra have a lower signal-to-noise ratio toward both ends of the spectra because the broadband IR laser has a Gaussian spectral profile. ..................................................................................................... 43	Figure  4.2. (a) Simulation box with a dimension of 3.6 × 3.6 × 32 nm3 filled with 3017 water and 54 DDAPS molecules. Color codes for atom types: white (hydrogen), red (oxygen), cyan (carbon), blue (nitrogen), yellow (sulfur), and magenta (water). (b) Water density as a function of depth z. (c) Orientation factor <cosθ µ> of water's dipole vs. z. The insert shows the definition of the orientation angles of the dipole moment and the OH bond with respect to the surface normal (z axis). (d) Density weighted orientation factor. The statistical error of <cosθ µ> is ~0.06 (standard deviation). Please note that for representing the simulation box, the effect of periodic boundary is removed. .................................................................................................................... 47	Figure  4.3. Orientation distributions of water’s OH bonds in the ‘10-90” layer without (a) and with (b) DDAPS (2.6×10-3 M). The blue curves are OHs forming hydrogen bonds with water, the   xiv red curves are OHs not forming hydrogen bonds, the black curves are the total OHs, and the green curve is OHs forming hydrogen bonds with the sulfonate groups of DDAPS. .................. 48	Figure  4.4. (a) Labeling of atom in DDAPS. (b) Distributions of the titling angle for the tail (NC1) and the head (NS) groups with DDAPS concentration at 1×10-4 M (blue), 3×10-4 M (green), and 2.6×10-3 M (red). NC1 is the vector from the N atom to the C1 atom, and NS is the vector from the N atom to the S atom. .......................................................................................... 50 Figure  5.1. The molecular structure of SDS (a) and HPAM (b) in aqueous solutions. ................ 54	Figure  5.2. Simulation box with dimensions of 5.0 × 5.0 × 10.0 nm3 filled with ~8000 water molecules, 114 SDS, 2 HPAM, and 122 Na+. (a) No excess ions. (b) 30 excess NaCl. (c) 30 excess CaCl2. Color codes for atom types: red (oxygen), green (carbon), blue (nitrogen), yellow (sulfur), white (hydrogen), magenta (Na+), orange (Cl−), black (Ca2+), and cyan (water). ....... 60	Figure  5.3. Calculated binding free as function of distance between the z-component of the center of mass of the four acrylic acid groups in HPAM to the z-component of the center of mass of the S atoms in all SDS for the systems with no excess ions (a), 30 excess NaCl (b), and 30 excess CaCl2 (c). The red and blue curves represent the results from each water surface in the simulation box. The negative distance refers to states in which the position of the center of mass of the acrylic acid groups in HPAM is higher than the center of mass of the S atoms. ............... 61	Figure  5.4. Time-averaged number density profiles of the –SO4- groups in SDS, the H atoms in the NH2 groups of HPAM (HP), the O atoms in the CO2 groups of HPAM (OP), Na+, Cl-, and Ca2+. (a) no excess ions. (b) 30 excess NaCl. (c) 30 excess CaCl2. The values of HP, OP, Na+, Cl-, and Ca2+ are magnified by 5, 20, 5, 10, and 5 times, respectively for a better visibility. ............. 62	  xv Figure  6.1. The molecular structure of polyP (a), PEG-based chain (b), and different HBGs: R1 (c), R2 (d), and R3 (e). P denotes the attachment location of PEG-based chain and the head group in (c), (d), and (e). ......................................................................................................................... 69	Figure  6.2. The reweighted binding free energy between (PEG)n-R1and polyP. The distance is defined between the center of mass of polyP and the center of mass of (PEG)n-R1 headgroups. The binding free energy profile was obtained by calculating the averaged binding free energy of all (PEG)n-HBG molecules in the system. The error bar indicates the standard deviation. ......... 79	Figure  6.3. Radial distribution functions of the unprotonated amine N atoms (N0), the protonated connective amine N atom (N1), the protonated terminal amine N atom (N2), O atoms of PEG-based chain, and the only O atom of hydroxyl group (OH) with respect to the P atoms of polyP. (a) (PEG)8-R1, (b) (PEG)12-R1, (c) (PEG)24-R1. The radial distribution function was obtained from 10 ns of classical MD simulations in the NPT ensemble. P atoms were the reference point of the radial distribution function. ................................................................................................ 82	Figure  6.4. Binding free energy between the (PEG)12-Ri and the polyP. The distance is defined between the center of mass of the polyP and the center of mass of (PEG)12-Ri headgroups. The binding free energy profile was obtained by calculating the averaged binding free energy of (PEG)12-Ri molecules in the system. The error bar is the standard deviation. ............................. 83	Figure  6.5. Radial distribution functions of the unprotonated amine N atoms (N0), the protonated connective amine N atom  (N1), the protonated terminal amine N atom  (N2), O atoms of PEG-based chain, and the only O atom of hydroxide group (OH) with respect to the P atoms of polyP. (a) (PEG)12-R2, (b) (PEG)12-R3. The radial distribution function was obtained from 10 ns of classical MD simulations in the NPT ensemble. The P atom is the reference point of the radial distribution function. ..................................................................................................................... 84	  xvi Figure  6.6. Final snapshot of a microsecond CGMD simulation for polyPs with 28 (a), 61 (b), 115 (c), and 133 (d) phosphate monomers. Details of the system are listed in Table 6.2. Color codes for the beads: MARTINI polarizable water (green), PEG monomer (red), protonated connective and terminal amine groups (dark blue), unprotonated amine group (light blue), phosphate group (BP) (yellow), Na+ (magenta), and Cl- (black). The visualization was made by VMD computer program100. .......................................................................................................... 85	Figure  6.7. Calculated fraction of protonated amine beads involved in the complex formation with polyPs with 28 (a), 61 (b), 115 (c), and 133 (d) phosphate monomers. The details of the systems are described in Table 6.2. Np(t) is the calculated number of protonated amine beads interacting with the phosphate beads. N is the total number of protonated amine beads in each system. .......................................................................................................................................... 86	Figure A.1. Calculated partial charges of DDPAS head group. ................................................. 104	Figure B.1. Molecular structure of polyphosphate (polyP). PolyP is divided into several identical groups on the basis of their structural symmetricity shown by different colors (red, blue, and orange), as described in Table B.1. Each functional group is also divided into segments labeled with numbers. .............................................................................................................................. 107 Figure B.2. Molecular structure of the PEG-based tail. PEG is divided into three groups shown by red, blue, and green color as described in Table B.2. Each group is then divided into segments labeled with numbers .................................................................................................................. 108 Figure B.3. Molecular structure of the HBG R1. R1 is divided into the several identical groups on the basis of their structural symmetricity and shown in red, blue, and green as described in Table B.3. Each group is then divided into segments labeled with numbers ....................................... 109   xvii Figure B.4. Molecular structure of the HBG R2. R2 is divided into the several identical groups on the basis of their structural symmetricity and shown in red, blue, and green as described in Table B.4. Each group is then divided into segments labeled with numbers ....................................... 110 Figure B.5. Molecular structure of the HBG R3. R3 is divided into the several identical groups on the basis of their structural symmetricity and shown in red, blue, and green as described in Table B.5. Each group is then divided into segments labeled with numbers ....................................... 111 Figure B.6. Definition of the coarse grained (CG) sites on (a) polyP, (b) R1, (c) R2, and (d) R3 structure to calculate the Debye-Huckle (DH) energy based on eq. (6.1) .................................. 112 Figure B.7. Free energy as a function of DH energy for the systems I to V .............................. 112 Figure B.8. Free energy as a function of stoichiometry (S) number for the systems I to V ....... 113 Figure B.9. Figure B.9. The MARTINI CG sites and their labeling for (a) PEG and (b) R1. The P denotes the attachment location of PEG-based tail and the headgroup. (c) The CG structure of (PEG)24-R1 .................................................................................................................................. 117 Figure B.10. (a) The MARTINI CG sites and their labeling for (a) polyP and (b) the CG structure of polyP ....................................................................................................................................... 118 Figure B.11. Bond stretching probability profiles for AA and CG for (a) 𝐵𝐶𝐸 − 𝐵𝐻!, (b)𝐵𝐻! −𝐵𝐻!, and (C) 𝐵𝐻! − 𝐵𝐻! ........................................................................................................... 120 Figure B.12. Angular bending probability profiles for AA and CG for (a) 𝐵𝐶 − 𝐵𝐶𝐸 − 𝐵𝐻!, (b) 𝐵𝐶𝐸 − 𝐵𝐻! − 𝐵𝐻!, and (C) 𝐵𝐻! − 𝐵𝐻! − 𝐵𝐻!, and (d) 𝐵𝐻! − 𝐵𝐻! − 𝐵𝐻! ......................... 121 Figure B.13. Torsional angle probability profiles for AA and CG for (a) 𝐵𝐶 − 𝐵𝐶 − 𝐵𝐶𝐸 −𝐵𝐻!, (b) 𝐵𝐶 − 𝐵𝐶𝐸 − 𝐵𝐻! − 𝐵𝐻!, and (C) 𝐵𝐶𝐸 − 𝐵𝐻! − 𝐵𝐻! − 𝐵𝐻! .................................. 122 Figure B.14. Bond stretching probability profiles for AA and CG for (a) 𝐵𝑃 − 𝐵𝑃 (𝑆𝐵𝑃) ...... 122   xviii Figure B.15. Angular bending probability profiles for AA and CG for (a) 𝐵𝑃 − 𝐵𝑃 𝑆𝐵𝑃 −𝐵𝑃(𝑆𝐵𝑃) ..................................................................................................................................... 123 Figure B.16. Torsional angle probability profiles for AA and CG for (a) 𝐵𝑃 − 𝐵𝑃 − 𝐵𝑃(𝑆𝐵𝑃)−𝐵𝑃(𝑆𝐵𝑃) ..................................................................................................................................... 123 Figure B.17. Free energy as a function of the DH energy for the CG systems 1 to 4 ................ 124 Figure B.18. Free energy as a function of stoichiometry (S) number for the CG systems 1 to 4 ..................................................................................................................................................... 125 Figure B.19. Binding free energy between the (PEG)24-R1 and polyP. The distance is defined between the polyP center of mass and the center of mass of drug headgroups .......................... 125 Figure B.20. Radial distribution functions between BP (SBP) and (a) BH1, (b) BH2, (c) BH3, and (d) BC (BCE). BP beads were the reference points in all calculations ................................ 126      xix List of symbols  c   Speed of light !E   Electric field   Mass of the particle i   Cartesian atomic coordinates of the particle i   Acceleration of the particle i   Net force exerted on the particle i   Total potential energy   Kinetic energy   Partial charge of the particle i   Bond stretching force constant   Angular bending force constant   Torsional force constant   Equilibrium bond length   Multiplicity   Time   Velocity of the particle i   Temperature   Boltzmann constant   Number of degrees of freedom mi!ri!ai!FiUKqikrkθknr0nt!viTk,kBNdf  xx   Number of constraints NV (S,t)  Normalized histogram in a biased simulation   Wiener process   Pressure P(S)   Probability distribution in an unbiased simulation PB (S)   Probability distribution in a biased simulation !PS   Polarization   Volume of the simulation box   Probability distribution of velocity   Metadynamics biased potential   Initial Gaussian amplitude   Collective variable function   Free energy surface   Surface tension   Length of the box in z direction   Surfactant concentration   Avogadro’s number   Surface coverage   Upper-wall potential energy   Position of the wall    Debye-Huckel energy NcdWPVp(vi )V (S, t)W0Si (R)f (S)sLzcNAAVκaDH  xxi   Stoichiometry number β   Inverse temperature   Lennard-Jones potential well depth    Lennard-Jones diameter   Equilibrium angle between two bonds    Dipole moment   Wall energy constant   Density   Phase angle for the torsional potential   Thermostat time constant   Width of the Gaussian potential    Surface excess concentration   Debye-Huckel screening length   Water dielectric constant   Permittivity of free space   Time step between bias depositions ω   Angular frequency )2(χ!   Second-order nonlinear susceptibility   Sεijσ ijθ0µκργτTσ iΓ1κεwε0τ  xxii List of abbreviations  AA   All-atom CCD   charge-couple device CmEn   Polyoxyethylene glycol alkyl ethers CG    Coarse-grained  CMC   Critical micelle concentration CV   Collective variable DDAPS  N-dodecyl-N, N-dimethyl-3-ammonio-1-propanesulfonate GAFF   Generalized AMBER force field GDS   Gibbs dividing surface HB   Hydrogen bond HBG   Heparin based group HF   Hartree-Fock HPAM   Partially hydrolyzed polyacrylamide MD   Molecular dynamics MetaD   Metadynamics OPLS-AA  All-atom optimized potential for liquid simulation PAA   Polyacrylic acid PAM   Polyacrylamide PAMAM  Polyamidoamine PEG   Poly ethylene glycol (PEG)n-HBG  Polyethylene glycol linked cationic bind group   xxiii PEI    Polyethylenimine PME   Particle mesh Ewald polyP   Polyphosphate PTMetaD  Parallel tempering metadynamics REMD   Replica exchange molecular dynamics RESP   Restrained electrostatic potential SDS   Sodium dodecyl sulfate SFG   Phase sensitive sum frequency generation spectroscopy SPC/E   extended simple point charge TEAM   Transferable, extensible, accurate and modular UHRA   Universal heparin reversal agents WTE   Well-tempered ensemble       xxiv Acknowledgements  I would like to express my deep gratitude to my supervisor, Prof. Keng C. Chou for his continuous guidance, encouragement, advice, and massive support that he has provided throughout my PhD studies. He helped me to be an independent researcher by giving me the freedom to choose and do the projects on my own ways that I really enjoyed. I have been extremely fortunate to have a supervisor who is my role model because of his great enthusiasm and dedication to the science. Besides, I would like to thank Prof. Madjid Mohseni for his great support during my PhD studies. Undoubtedly, this dissertation could not be finished without his help. I am grateful to Prof. Jim Pfaendtner and his group members at University of Washington for allowing me to join their friendly and goal-oriented research group to learn necessary techniques and carry out my research project. Also, I would like to acknowledge Prof. Jayachandran N Kizhakkedathu for sharing a really interesting research topic with us and giving me the opportunity to work on a challenging problem.   I also wish to thank my research colleagues, Dr. Dan Hu, Dr. Reza Tafteh, and Kaitlin Levering who have been helpful and friendly to me. I have enjoyed every moment of working with them.   I would like to acknowledge the University of British Columbia for providing the financial support for my PhD studies through the Four Year Doctoral Fellowship Program. I also would like to thank Compute/Calcul Canada for providing the computational facility through the   xxv Westgrid cluster.  I wish to deeply thank my parents and my lovely sister for enduring love and their unconditional supports in my entire life. The last but not the least, I also thank with love to my wife who has been my best friend and companion during this journey. Her love, patience, and immense support always encourage me to pursue my dreams.   xxvi Dedication  To my Parents, Sousan and Valiollah  To my lovely sister Elham  To my beloved wife Samaneh    1 Chapter 1: Introduction Water is a nonlinear and polar molecule with an electrical dipole moment where the oxygen atom is slightly negative and its hydrogen atoms are slightly positive. This polarity allows every water molecule to form up to 4 hydrogen bonds with its neighboring water molecules in the bulk liquid, leading to the creation of hydrogen bonding networks. The strong hydrogen bonding network is the main cause that water has the relatively high melting, boiling point, and surface tension among common liquids.1 A water molecule, on average, experiences no net forces in the bulk liquid, as it is surrounded by the other water molecules, which exert attractive intermolecular forces from all directions. In contrast, a molecule at an interface experiences a net inward force due to truncation in hydrogen bonding network. Hence, the properties of water at an interface essentially differ from those in the bulk. The mentioned inward force tends to minimize the surface area of the liquid, which regulates water orientation2 and consequently the interfacial properties. Therefore, the balance of the forces at the interface determines the interfacial properties. The balance of the forces is altered if a molecule such as a surfactant occupies a place at the water.  Surfactants are amphiphilic compounds usually containing hydrophobic carbon tails and hydrophilic headgroups. They have been used in a broad range of applications and commercial products such as detergents3, cosmetics3, membrane protein purification and crystallization4, drug delivery5, pharmaceutical sciences3, and oil recovery6. Surfactants in terms of their headgroups are classified into ionic, non-ionic, and zwitterionic surfactants, which determine their functionalities and applications. The presence of surfactants at water surface significantly affects the surface properties of water. Once surfactants settle on the water surface, the net inward force originating from the bulk water decreases since the surfactant-water and surfactant-  2 surfactant interactions are weaker than the water-water interactions. Therefore, the surfactants lower the surface tension as a result of disrupting the balance of the force at the surface. Undoubtedly, to choose a suitable surfactant for a specific application, it is necessary to find out how the mutual interaction between surfactant and water affects the interfacial properties, the structure of both water and surfactant at the surface.  Among different types of surfactants, the ionic surfactants have the most pronounced influence on the interface structure as the charged headgroup has more affinity to penetrate the water layer and disturb the water structure. For example, sodium dodecyl sulfate (SDS) is one of the most common anionic surfactants used in industry and science. The headgroup imposes a negative electrostatic charge, which induces water molecules to orient with their H atoms pointing toward the water surface.7-8 The surface tension analysis revealed that the presence of the SDS at the water surface results in decreasing the surface entropy compared to the bulk.8 Also, it was found that9 the reduction in surface entropy is associated with the escalation of surfactant-induced ordering of water and the enhancement in hydrogen bonds formation at the water surface. In contrast to the ionic surfactants, non-ionic and zwitterionic surfactants carry no net charges on their headgroup. Therefore, it is expected that their impacts on water should be much less than those of ionic ones. However, microscopic information to characterize the interface of either nonionic or zwitterionic water surface remains mostly unknown because it is technically challenging to probe water surfaces.  Regardless of the technical challenges, various approaches have been utilized to acquire information about both water and surfactant roles at the interface. Measuring surface tension of the water surface is the simplest and widely used technique to study the surface of water.10 It, however, is limited to provide macroscopic-level information. It is sometimes difficult to   3 interpret the complex behavior of the surface tension8. Neutron reflectometry measurement11 has been used to characterize the surfactant thin film on the water surface by measuring the thickness and the surface number density of surfactants. Nonetheless, it is not able to describe the behavior of water molecules near the surfactants. Furthermore, phase-sensitive sum frequency generation (SFG) vibrational spectroscopy has been shown to be a promising method to study water surfaces owing to its high surface specificity for studying the interaction between surfactant monolayers and water.12-15 SFG vibrational spectroscopy measures the surface's vibrational resonances and the averaged orientation of the functional groups.16-17 Although SFG vibrational spectroscopy has made significant contributions to surface science, the technique has its own drawback. For example, SFG can observe only ordered molecules. Therefore, SFG alone is not capable of providing complete structural information. One approach, which provides molecular-level information about the water surface in the presence of surfactants, is molecular dynamics (MD) simulation. MD simulation is a numerical solution of equations of motions based on Newtonian classical mechanics. Since MD simulation considers electrostatic, van der Waals, and valance types of interactions, it is also well suited to unravel the more complicated behaviors resulting from the interplay of surfactant, polyelectrolyte, and water at the surface. The interaction between surfactants and polyelectrolytes at the water surface may significantly modify the interfacial properties as a result of complex formations. Many applications in pharmaceuticals, personal care products, and oil recovery contain a mixture of surfactants and polymers.18-23 Therefore, investigating the behavior of surfactants and polymers at the water surface is of great interest. The interaction between polymer and surfactants are categorized into two main groups24, i) relatively weak: interaction between neutral polymer chains and charged surfactant headgroups, and ii) strong: electrostatic attractive interaction   4 between oppositely charged polymer chains and surfactant headgroups. Generally, surfactants and polyelectrolytes of the same charge do not form complexes because of the long-range electrostatic repulsion. Therefore, the formation of surfactant-polymer complexes of the same charge on water surface has never been reported. Nevertheless, mediating the repulsive forces can facilitate the complex formation. The ionic salts with their charge screening effects are potential candidates to counteract the strong electrostatic repulsion. As a result, surfactants-polyelectrolytes complex formations via ion-bridged mechanism become possible. The study of complex formation between oppositely charged polyelectrolytes in aqueous media is also important because of its impacts on diverse applications, in particular, drug design for thrombosis treatment. Thrombosis is a blood clotting disorder in the vein or artery of the circulatory system and is one of the compounding causes for heart attack or stroke. It was recently discovered that highly negatively charged polyphosphate (polyP) released from platelets increase the thrombosis risk by activating the contact pathway of blood coagulation.25-29Therefore, polyP is a potential therapeutic target for the design of novel antithrombotic drugs. Several cationic polyelectrolytes have been applied to couple with the polyP to block the adverse effects.30-33 Interestingly, the proposed cationic polyP inhibitors have been effective to reduce thrombus formations.30-33 However, to increase the efficiency, it is desirable to strengthen the binding and specificity of the inhibitors to polyP. For this purpose, understanding the mechanism of complex formation between the cationic inhibitor and polyP is essential to find potential routes for the drugs improvement.   This dissertation employs MD simulations to study interactions between surfactant-water, surfactant-polyelectrolyte, and polyelectrolyte- polyelectrolyte in aqueous media. Chapter 2 is devoted to a brief theoretical background of MD simulations. Chapter 3 focuses on the study of    5 Table 1.1. Summery of chemical structures and abbreviations of molecules used in this thesis.   Name Represented  Structure Sodium dodecyl sulfate SDS  N-dodecyl-N, N-dimethyl-3-ammonio-1-propanesulfonate DDAPS   Polyoxyethylene glycol alkyl ether C12E4  Hydrolyzed polyacrylamide HPAM  Polyethylene glycol-based chain PEG  Polyphosphates polyP  Heparin binding groups (R1) HBG (R1)   Heparin binding groups (R2) HBG (R2)  Heparin binding groups (R3) HBG (R3)       Recent Progress (last 6 months)•To study the factors determining the ability of a surfactant to decrease surface tension.SDS(anionic)DTAB(cationic)DDAPS(zwitterionic)PEO (C12E 4) (non-ionic) 9ONaSOOONBrNSO OOOOH4Recent Progress (last 6 months)•To study the factors determining the ability of a surfactant to decrease surface tension.SDS(anionic)DTAB(cationic)DDAPS(zwitterionic)PEO (C12E 4) (non-ionic)9ONaSOOONBrNSO OOOOH4      6  the interaction between water and non-ionic polyoxyethylene glycol alkyl ethers (Table1.1) surfactants on the water surface. Chapter 4 discusses the interaction between zwitterionic sulfobetaine and water at the water/air interface. In these two chapters, we investigate how neutral surfactants adsorb on the water surface and how interfacial water molecules structure around the surfactant headgroups. We found that the behavior of the polyoxyethylene glycol alkyl ether is more anionic-like (imposing a negative electric field), even though the surfactant is overall neutral. On the contrary, the sulfobetaine (Table1.1) was found to be more cationic-like (imposing a positive electric field) because the positively charged group is more capable of orienting the interfacial water. In chapter 5, we study the complex formation between an anionic surfactant (Table 1.1) with an anionic polyelectrolyte (Table 1.1) on the water surface via a different mechanism: ion-bridged ionic/ionic interactions and hydrogen bonds. Our study showed that it is possible to form thermodynamically stable complexes between surfactant and polyelectrolyte of the same charge provided that excess ions are present in the solution. Finally, in chapter 6, we attempt to find the possible routes of improving the design of polyethylene-glycol-linked cationic binding groups, namely (PEG)n-HBG32 (Table 1.1) for polyP inhibition. For this purpose, the effects of the PEG chain length, the charge densities of the heparin based group (HBG), and the polyP chain length are investigated to obtain a structure that could potentially increase polyP binding and inhibition efficiency. We found that the length of the PEG-based tail does not have any impact on the interaction between the (PEG)n-HBG and polyP. Therefore, the PEG tail is not directly involved in interacting with polyP, and its function is mostly to improve the drug’s hemocompatibility by preventing the cationic drug from binding to other negatively charged biomolecules. On the other hand, increasing the number of the charged   7 tertiary amine groups in the headgroup strengthens its binding to polyP. Finally, MD simulations revealed that the binding of (PEG)n-HBG remains intact against various lengths of polyP.           8 Chapter 2: Brief description of molecular dynamics simulations  MD simulation is developed using the classical Newtonian mechanics. For an N-particle system, the step-by-step numerical solution of the equations of motion as represented by eq. 2.1.      (2.1) here, is the Cartesian atomic coordinates for the particle , denotes the mass of the particle , refers to the acceleration of the particle , and is the net force exerted by the other particles on the particle . The force  acting on particle i, is obtained from the negative gradient of the total potential energy ,        (2.2) The total potential energy of the system is grouped into non-bonded and bonded potential energies. The non-bonded potential energy describes the van der Waals and electrostatic interactions between the particles, which are not bonded to each other. The Lennard-Jones and the coulomb potentials are expressed with the following functional forms:34   (2.3) Here, σ is the diameter, ε refers to the well depth, q denotes the partial charge, is the distance between particles i and j, and ε0 is the permittivity of free space. On the other hand, the bonded potential energy considers the bond stretching, angle bending, and dihedral torsions of the atoms bonded in a molecule, and it is calculated using the following AMBER functional forms34:  (2.4) mi!!"ri=mia"i=F#"i;i =1,2,...,Nr!i i mii a!i i F!"i N −1i F!"iU (!r N )F!"i=-∇r"iU(r"1, r"2,..., r"N )U(rij)non-bonded = 4εij  (σ ijrij)12 -(σ ijrij)6⎡⎣⎢⎢⎤⎦⎥⎥⎛⎝⎜⎜⎞⎠⎟⎟  +qiq j4πε0rij⎛⎝⎜⎜⎞⎠⎟⎟⎛⎝⎜⎜⎞⎠⎟⎟atomsi< j∑r!ijU(rij)bonded = kr (r-r0  )2( )bonds∑  + kθ (θ-θ0  )2( )angles∑  + kn  (1+cos(nφ+γ ))( )torsions∑    9 where , , and  are force constants,  stands for the equilibrium bond length,  is the equilibrium angle between two bonds, n is the multiplicity, and  refers to a phase angle for the torsional potential.  The set of potential functions and their required parameters is called force field, which is used to describe the behavior of the particles during simulations. To find the position and velocity of each particle, one needs to numerically solve the N set of second order differential equations (eq. 2.1) at discrete time steps provided that the total energy of the system is conserved during the calculations. If the position, velocity, and acceleration can be approximated by a Taylor series expansion, the velocity Verlet algorithm35 can be used for integrating the coupled differential equations. Given , , and  at time , one evaluates the new position of the particle  at  by:35    (2.5) where  is the order of truncation error. Also, the velocity can be explicitly evaluated by35   (2.6) Although the truncation error in calculating displacements and velocities are on the order of , eventually the global error increases as , which is similar to the global errors of other variations of the Verlet algorithm36-37.  2.1  Considerations for MD simulations Periodic boundary conditions. With the current computational capacity, MD simulations can handle just a small number of particles up to ~1,000,000 atoms, which is really relatively small compared to the number of atoms present in a macroscopic system with ~ 1023 kr kθ kn r0 θ0γ!ri!vi!ai ti t +δt!ri (t +δt) =!ri (t)+!vi (t)δt +12!ai (t)δt2 +O(δt3)O(δt3)!vi (t +δt) =!vi (t)+δt2!ai (t)+!ai (t +δt)⎡⎣ ⎤⎦+O(δt3)δt3δt2  10 particles.  Dealing with finite system size involves two potential problems. First, if a particle leaves the simulation box, it never comes back to the system. Therefore, as MD simulation proceeds, the size of the system becomes even smaller, causing inaccuracy in estimating the properties of materials. Second, in a real macroscopic system, a tiny fraction of atoms reside in the vicinity of the boundaries, as a result, the surface atoms contributions on the bulk properties is negligible.  On the contrary, the ratio of surface to the bulk atoms is significant in the small system size. Therefore, surface atoms have great contributions on the behavior of the system. To avoid artifacts caused by the unwanted edge effects and losing particles during the simulations, the periodic boundary conditions are applied. Figure 2.138illustrates how the periodic boundary conditions are enforced. The simulation cell is infinitely replicated into image cells in all three Cartesian directions. Once a particle leaves the cell, instantaneously it is replaced with an identical particle entering from the opposite side of the cell. Therefore, the total number of particles during simulation is always conserved. However, using the periodic boundary conditions vastly increases the calculation workload on the non-bonded interactions as each particle is subject to interact with the all other particles in the simulation and image cells. By defining a reasonable cut-off length, each particle in the simulation cell is allowed to interact with a given particle just once, which reduces the required computations remarkably.          11            Long-range electrostatic interactions. Calculating the non-bonded interactions for an N-particle system takes most part of the computations since different pairwise interactions need to be evaluated for every single step. As mentioned above, to speed up the process, the cut-off radius is usually applied to significantly decrease the number of required calculations. However, using a cut-off radius for the non-bonded interactions implies that the main contribution to the net force stems from the interactions among the neighboring particles. This is acceptable for the short-range interactions such as van der Waals. The van der Waals interaction is mostly described by the Lennard-Jones potential. The Lennard-Jones potential decays relatively fast with the distance as the repulsive and attractive contributions are proportional to  and , respectively. In contrast, the electrostatic interaction falls off N(N −1)2∝1r6 ∝1r12                                              Figure 2.1. Periodic boundary conditions in two dimensions. The grey circles are in the image cells while the red circles are in the MD simulation cell. The dashed-line circle is the cut-off length for the calculation of the non-bonded interactions. The figure has been redrawn from reference 38.   12 slowly, as it is proportional to . Therefore, the Coulomb potential describes long-range interactions between the atoms. If the net charge of a molecule is not zero, the truncation of the Coulombic interaction might result in spurious effects. To avoid the artifacts, some algorithms such as the Ewald summation39 and its variants40-43 as well as the Coulomb reaction field44-45 have been proposed to treat the long-range electrostatic interactions. The Particle Mesh Ewald40-41 (PME) algorithm is the fastest method among the Ewald summation methods39-43. PME40-41 divides the total electrostatic interaction into short-range and long-range interactions. Within the cut-off radius, the Coulomb potential is directly calculated between particles in the Cartesian space. However, the charges of particles outside the cut-off length, whether in the simulation or image cells, are distributed on grids using interpolation. Afterwards, the grids are Fourier transformed, and all calculations are done in that space to increase the pace of computation. Its computational performance scales with NlogN. Similarly, the coulomb reaction field44-45 method also considers the short-range and long-range contributions separately. The short-range electrostatic contribution results from the direct interactions between the charged particles within the cut-off radius. However, outside of the cut-off radius, it is assumed that there is a medium with a uniform dielectric constant. The indirect interaction between each molecule and the surrounding medium induces polarization in the surrounding medium, which creates a reaction field, affecting the particles.  Time step for integration. To integrate the set of equations of motions (eq. 2.1), it is vital to choose a time step as large as possible to speed up the sampling of different states without losing significant accuracy. Therefore, to achieve accurate dynamics, the fastest vibration frequency in the system controls the size of the time step. In the most cases, C-H with ∝1r  13 the bond stretching frequency of  and a vibration period of 11 fs has the fastest motion. Generally, the time step of 1 fs (1/10 of the fastest motion) has been accepted as an appropriate value for performing MD simulations.46 The vibration of covalent bonds is not the interesting part of the simulation studies. Hence, the covalent bonds are handled with various constraints algorithms47-50 so as to fix their stretching during the simulations. Vanishing the high vibrational motions from the system allows enlarging the time step even more. 2.2 Thermodynamics properties Temperature. The absolute temperature of the system T is related to the total kinetic energy      (2.7) where,  is the Boltzmann constant, and stands for the number of degrees of freedom, which can be obtained by:     (2.8) Here, is the number of constraints applied to fix the covalent bonds or angles. Sometimes we would like to calculate the physical property of interest at a constant temperature. For this purpose, the system temperature is regulated in the MD simulation by coupling it with a heat bath or the so-called thermostat, which gains or loses the necessary heat to ensure that the system temperature is near the desired value. Several methods51-55 have been introduced to control the temperature in MD simulations. A case in point, the Berendsen thermostat56 slowly corrects the 9×1013s−1T =mivi2i=1N∑Ndf kk NdfNdf = 3N − Nc −3Nc  14 temperature with a first-order kinetics equation when the temperature deviates from the desired value (T0):      (2.9) The temperature deviation from the set point decays exponentially with a time constant . The Berendsen thermostat surpasses the fluctuation of the kinetic energy of the system; hence it cannot provide accurate kinetic energy distribution in accord with the canonical ensemble. To solve this problem, Bussi et al.55 extended the Berendsen thermostat in which a random fluctuation based on the Brownian motion is added to the velocity of the particles to ensure that the kinetic energy distribution is correctly assigned for the canonical ensemble. In contrast to the Berendsen thermostat, the kinetic energy is controlled during the simulation via following equation:    (2.10) where, K is the kinetic energy, K0 denotes the average kinetic energy corresponding to the desirable temperature T0. dW refers to a Wiener process which is used to construct the random force properly during the simulation. Once the true kinetic energy distribution is attained, the average temperature is estimated from Eq (2.7). Without the stochastic term, Eq (2.10) is essentially simplified to Eq (2.9).   Pressure. If the interactions are described with the pairwise additive potentials, one can use the virial equation57 to obtain the pressure for an N-particle system. dTdt =T0 −TτTτTdK = (K0 −K )dtτT+ 2 KK0NdfdWτT  15     (2.11) where is the volume of the simulation box. Similar to the temperature, we would like to estimate a property at a constant pressure. Several algorithms51, 58-60 have been proposed for controlling the pressure in MD simulations. These methods readjust the simulation box in every computation step to guarantee that the average value of the pressure is near to the desired value.  2.3 Performing MD simulations  The flowchart shown in Figure 2.2 describes how MD simulation is performed. To initiate the process, one needs to specify the initial coordinates and velocities of the atoms. All atoms can be arranged in a crystalline lattice or placed randomly in the volume of the system. Besides one can even obtain the initial configuration from the experiment. No matter how the initial structure is obtained but it is important that the atoms must not overlap on each other. To avoid any probable core overlaps, an energy-minimization algorithm such as steepest descent or conjugate gradient is performed to relax the structure before starting the dynamics. If the leap-frog37 or velocity Verlet algorithm35 is used to integrate Eq. (2.1), one needs to specify the initial velocities too.  Using the Maxwell-Boltzmann distribution, the velocity components are randomly picked for the ith particle:     (2.12) where is the probability distribution. However, randomly assigning the velocity might lead to inaccurate kinetic energy for the required temperature (T). Therefore, all velocities are typically P = NkTV +13V F!"(rij!"i< j∑i∑ ) ⋅ r"ijVp(vi ) =mi2πkT exp −mivi22kT⎛⎝⎜⎞⎠⎟p  16 shifted using the net momentum value obtained from eq. (2.1) to ensure that the kinetic energy corresponds to the desired temperature. In this thesis, all the required calculations to proceed with the flowchart represented in Figure 2.2 have been done using GROMACS software package61-63. 2.4 Well-tempered metadynamics  The time-step for integrating the equations of motion is in the range of 1.0-2.0 femtosecond in typical MD simulations. However, some physical behavior of interest takes place on the order of the millisecond or even longer time scale, which is not accessible by the current computer power. Limited accessible simulation time prevents complete sampling of the conformational phase space. Usually, high-energy barriers separate a system’s metastable states. Overcoming energy-barriers larger than thermal energy rarely happens in a time period of the nanosecond or even microsecond. To tackle the poor sampling of the phase space, several enhanced sampling methods have been proposed.64-67 In these methods, one or a few relevant collective variables (CVs), describing the system in reduced dimensions, are biased, encouraging exploration of large regions of phase space. Using well-tempered metadynamics (metaD)68,    17                  Set initial positions and velocities ( ) Calculate forces ( ) using eq. (2.2) to eq. (2.4)               Solve equations of motions over  to find ( ) using Eq. (2.5) and Eq. (2.6) Update ,  Calculate desired physical properties  Yes No Print out positions, velocities, forces, and … Figure 2.2. The Flowchart of MD simulation algorithm   18  an external Gaussian potential favorably biases the CVs to release the system from the local minima and explore all possible states during the simulations. Generally, the well-tempered bias potential is constructed as the sum of the Gaussians in the CV space to discourage the system from exploring the previous visited conformations. The bias potential at time  is deposited with following functional form    (2.13)  where  refers to the initial Gaussian amplitude, k is the Boltzmann constant, and  is the time step between bias deposition. The first exponential factor on the right-hand side of Eq. (2.13) scales the amplitude to prevent overfilling the energy landscape. is the virtual temperature difference which controls the hill height decay rate in the CVs space. The virtual temperature difference is scaled by the bias factor , where T is the temperature at which the bias is imposed. In the second exponential term, is the width of the Gaussian, which is centered at the i-th CV coordinate at time . Si(R) represents the i-th CV function. Eventually, the bias potential smoothly converges after visiting all possible metastable states:    (2.14) where C is the constant and f refers to the free energy surface. By comparing the free energy differences between various metastable states, one can simply identify the system configuration corresponding to the global minimum or the so-called equilibration state. In this thesis, metadynamics simulations have been performed using PLUMED2 software package69. tV (S, t) = W0τe−V (S,T )kΔT( )τ=1τ f∑ e−Si (R)−Si (R(t )( )22σ i2i=1d∑⎛⎝⎜⎜⎞⎠⎟⎟W0 τΔTγ = T +ΔT( ) Tσ itV (S, t→∞) = − ΔTT +ΔT f (S)+C  19 2.5 Parallel tempering metadynamics  Identifying the slow degree of freedom in a system to bias is not an easy task. Even with careful considerations, it is likely that some of the relevant collective variables remain hidden during the simulation run which hinder the exploration of the whole conformational phase space quickly and accurately. As a result, it causes a serious problem such that the final results could be greatly dependent on the choice of the CVs. A possible way to explore some or all degrees of freedom is to sample at a higher temperature in accord with the parallel tempering method65 (PT). In the PT algorithm, M identical replicas of a system with an increasing temperature () are simulated independently in the canonical ensemble. Here, the system with the lowest temperature ( ) is the system of interest in which the sampling is difficult. In contrast, sampling at a higher temperature is much easier. Periodically, an exchange of configuration is allowed between each two adjacent replicas based on the Metropolis criterion. The acceptance probability of an exchange between replica  and  can be determined as65     (2.15) where    (2.16) where the inverse temperature  is defined as ,  and  are the atomic coordinates at temperature  and , respectively.   T1 <T2 < ...<TMT1i jΡ(i→ j) =min 1,eΔi , j }{Δi , j = βi −β j( ) U (Ri )−U (Rj )( )β β =1kTRi RjTi Tj  20  To enhance the sampling efficiency, the metadynamics simulation can be combined with the PT method70 (PTmetaD) such that one performs metadynamics simulation with the same CVs in all replicas with different temperatures. Given the bias potential acting on the i-th replica ( ), the acceptance probability in Eq. (2.15) is calculated by70  (2.17) 2.6 Reweighting  Performing the metaD significantly alters the Boltzmann equilibrium distribution for a given CVs.  Therefore, recovering the unbiased probability distribution is needed to evaluate any property of interest within the equilibrium distribution and estimate the unbiased free energy difference. In this section, the reweighting formulism is presented. To do this, one first consider the unbiased probability distribution for a given CV ( S(R) ) as71-72 P(S) =δ(S − S(R))e −βU (R)( ) dR∫e −βU (R)( ) dR∫   (2.18) With Eq. (2.18), the unbiased free energy surface can also be defined as71 f (S) = − 1βlogP(S)+ const.     (2.19) On the other hand, when the system is under the action of the internal potential (U (R) ) and the bias potential (V (S(R)) ) on the relevant CV, one can experess the new instant equilibrium distribution as73 ViΔi , j = βi −β j( ) U (Ri )−U (Rj )( )+βi Vi (S(Ri ),t)−Vi (S(Rj ),t)⎡⎣ ⎤⎦+β j Vj (S(Rj ),t)−Vj (S(Ri ),t)⎡⎣ ⎤⎦  21 PB (S) =δ S − S(R)( )e−β U (R)+V (S (R)( ) dR∫e−β U (R)+V (S (R)( ) dR∫   (2.20)  Mathematically the enumerator integration is carrid out over all degrees of freedom except S . Since the bias potential is just a function of S , one can simplify Eq. (2.20) to72 PB (S) = e−βV (S ) ⋅δ S − S(R)( )e−β U (R)( ) dR∫e−β U (R)+V (S (R)( ) dR∫   (2.21) Inserting Eq. (2.19) into Eq. (2.21), and rearranging the new equation gives P(S) = PB (S) ⋅eβV (S ) e−β U (R)+V (S (R))( ) dR∫e−βU (R) dR∫    (2.22) where e−β U (R)+V (S (R))( ) dR∫e−βU (R) dR∫=1eβV (S )   (2.23) Inserting Eq. (2.23) into Eq. (2.22) gives P(S) = PB (S) ⋅eβV (S )eβV (S )     (2.24) where the right hand side of Eq. (2.24) is computed from the biased ensemble. Using a similar relation P(R)∝ PB (R) ⋅eβV (S (R)) , other R-dependent properties O(R)  of the unbiased ensemble can be recovered from the biased ensemble by weighting each biased trajectory as71   22 O(R) =O(R).eβV (S (R))eβV (S (R))    (2.25) This reweighting procedure is valid as long as the bias potential is static. In other words, the bias potential must be converged already. Using Eq. (2.24), one can calculate the unbiased free energy surface using f (S) = − 1βlogPB (S)−V (S)+C    (2.26) where C = − 1βlog e−βV (S )( )  is independent of S . In practice, the free energy surface is calculated using71 f (S) = − 1βlimt→∞logNV (S,t)( )−V (S)    (2.27) Here the additive constant is ignored because the constant will be canceled when calculating the free energy difference. NV (S,t)  is a normalized histogram accumulated in the biased simulation and is computed by71 NV (S,t) =δ S − S(R( ʹt ))( )d ʹt0t∫d ʹt0t∫   (2.28) Therefore, the free energy surface is calculated by counting.   23  2.7 Theoretical background of sum frequency generation spectroscopy  In chapter 3 - 5, phase-sensitive sum frequency generation (SFG) spectroscopy has been used to verify the accuracy of the MD simulations. The following is a brief theoretical background describing the SFG spectroscopy.74-76          Given an interface of interest is placed between Medium I and Medium II, as depicted in Figure 2.3a, two beams in the range of 800 nm and IR with the frequency of  and  incident to the interface at angles of  and , respectively. The beams, interacting with molecules at the interface, generate a nonlinear polarization with the sum frequency ( ), which appears in both the transmitted and reflected directions. The induced polarization (!PS(2) ) is ω1 ω2θ1 θ2ωSF =ω1 +ω2𝜽𝑺𝑭 𝜽𝑻 𝑬𝑺𝑭 𝑬𝑺𝑭 𝑬𝟏 𝑬𝟐 𝜽𝟏  Medium I Medium II    Interface 𝝎𝟏 𝝎𝟐 𝝎𝑺𝑭 Figure 2. 3. (a) Schematic diagram describing the SFG process to characterize an  re 2.3. (a) Schematic of experim ntal geometry for SFG. E1 is t e incident beam at 800 nm. E2 is the IR beam, and ESF is the SFG. (b) Energy diagram of SFG. The solid lines are resonant states, and the dash line is a virtual state. The figure has been sketched from References 74-76. (a) (b) 𝜽𝟐   24 proportional to the electrical field strength of the incoming waves and the nonlinear susceptibility ( !χ S(2) ). The polarization can be expressed as75  !PS(2) =!χ S(2) :!E1!E2      (2.29) Here the electric fields in Medium I are specified by !Ei (ω) =!Fi (ω) :!Ei (ω)  where !Fi (ω) refers the transmission Fresnel coefficient at ω . The input electrical fields can be written as75  !E1 = eˆ1ε1 exp i!k1 ⋅!r − iω1t⎡⎣ ⎤⎦!E2 = eˆ2ε2 exp i!k2 ⋅!r − iω2t⎡⎣ ⎤⎦     (2.30)  where  is the wave vector of the incident incoming fields, denotes the unit vector of the light field, and  refers to the dielectric constant. Under the electric-dipole (ED) approximation, SFG is forbidden in a centrosymmetric media such as bulk. A non-zero in a noncentrosymmetry media such as an interface, consists of non-resonant and resonant contributions. The resonant part considers the molecular vibration of the nonlinear susceptibility. When a molecular vibration mode is resonant with the IR frequency ( ), an enhanced SFG signal can be detected as illustrated in Figure 2.3b. can be express as75      (2.31) !ki eˆiεi!χ S ,eff(2)ω2!χ S ,eff(2)!χ S ,eff(2) =!χNR(2) +!χR(2)!χR(2) =Aq (ωq )ω2 −ωq + iΓqq∑Im !χ S ,eff(2) =ΓqAq (ωq )(ω2 −ωq )2 +Γq2q∑  25 where  is the non-resonant background. , , and denote the amplitude, damping constant and frequency of qth vibrational resonance, respectively. The absorption term reveals both the ordering (the amplitude of a peak) and orientations (the sign of a peak) of surface molecules.  !χNR(2) Aq Γq ωqIm !χ S ,eff(2)  26 Chapter 3: Interactions of water with the nonionic surfactant polyoxyethylene glycol alkyl ethers studied by phase-sensitive sum frequency generation and molecular dynamic simulation   3.1 Introduction Nonionic polyoxyethylene glycol alkyl ethers are widely used in detergents3, cosmetics3, drug delivery5, membrane proteins purification and crystallization77,  and pharmacy3 because of their detergency, wetting, and foaming properties. Polyoxyethylene glycol alkyl ethers with the chemical structure of CmH2m+1–(OCH2CH2)n–OH are generally referred as CmEn with m denoting the number of carbon in hydrophobic carbon chain and n being the number the ethylene oxide units. Much work has been carried out to study the properties of surfactant aggregates in the solution phase.78-80 However, a good understanding of an adsorbed layer on water surface is still lacking because it is technically challenging to probe water interfaces. Neutron reflection has been used to determine the structure of a monolayer of C12E8 adsorbed on water surface at its critical micelle concentration (CMC). It was found that there was a large average tilt of the surfactant molecules away from the surface normal.81 In a later study Lu et al. showed that the hydrocarbon chain in the C12Em series where m ≤ 6 tilted at ~40º away from the surface normal.82  Kuhn et al. used molecular dynamics (MD) simulations to study a C12E5 monolayer (0.55 nm2/molecule) at the water surface and found the monododecyl chains had an average tilt angle of 43º at the CMC 83, which agrees with the neutron reflection measurement.82 A more recent MD simulation of C12E2 adsorbed at the air/water interface (0.34 nm2/molecule at the CMC)   27 showed that the water molecules have a strong tendency to form hydrogen-bonded bridged structures with the oxygen atoms of the same surfactant chain.84 Chanda et al. carried out a MD simulation for a monolayer of C12E6 (0.55 nm2/molecule), showing that the surfactant monolayer strongly influences the translational and rotational mobility of interfacial water molecules.85 Currently a good understanding of the structural changes of water in the presence of polyoxyethylene glycol alkyl ethers is still lacking, and it is important to obtain a further microscopic understanding of the interaction between the surfactants and the interfacial water. The current study uses phase-sensitive sum frequency generation (SFG) vibrational spectroscopy and MD simulation to study the interaction of water molecules with polyoxyethylene glycol alkyl ethers. SFG is known for its high surface sensitivity.86 Recent developments in phase-sensitive SFG have allowed direct measurements of both the surface’s vibrational resonances and the averaged orientation of the functional groups.87-88 This new technique provides an opportunity to gain further molecular-level information at the water surface. In addition, MD simulation was used to obtain a detailed structure of water at the interface.   3.2 Material and methods Material and Sample Preparation. Tetraethylene glycol monododecyl ether (>98%) was purchased from Sigma-Aldrich. Water (resistivity > 18.2 M MΩ·cm) used in the experiments was obtained from Millipore system. The 7×10-5 M surfactant solution was obtained by diluting the stock solution with water. The solutions were freshly prepared before measurements. All experiments were performed at 20 ± 0.5 °C and under 1 atmosphere pressure.     28 Phase-sensitive SFG setup. A femtosecond Ti-sapphire laser (120 fs, 800 nm, 1 kHz and 2 mJ/pulse) was used to pump an optical parametric amplifier in order to generate a broad-band femtosecond IR beam. The IR beam and a narrow-band picosecond 800 nm beam were aligned collinearly with an incident angle of 60°.89-90 A reference SFG was obtained by focusing the IR and picosecond 800 nm beams into a quartz crystal (thickness ~50 µm). The IR, 800 nm, and reference SFG beams were then focused again on the sample. The reference SFG and the SFG generated at the sample went through a time-delay, a polarizer, a band pass filter, a lens, and a monochromator, and then the interference pattern was recorded by a charge-couple device (CCD) camera. The polarization combination used in this study was SSP (s-polarized SFG, s-polarized 800 nm and p-polarized IR). The energy of the 800 nm and IR beam were ~10 µJ/pulse and ~3 µJ/pulse, respectively. Spectra presented in the paper were acquired over a period of 20 min.  MD Simulation. MD simulations were performed using GROMACS 5.0.2 61-63 in the canonical ensemble. The all-atom force field proposed by Shen and Sun for polyoxyethylene glycol alkyl ethers was used for C12E4.91 The flexible extended simple point charge (SPC/E) model was used for water molecules92 as it results to better prediction of interfacial water properties.93 The dimension of the simulation box was 3.6 × 3.6 × 32 nm3. A slab of 3.6 × 3.6× 7 nm3 was filled with 3017 water molecules. This slab of water was placed at the center of the simulation box, and a vacuum of approximately 12.5 nm exists on both sides of the water slab. Thirty C12E4 were randomly placed on each side of the water interface using the PACKMOL package.94 The surface coverage was ~0.44 nm2/molecule, which corresponds to the surface coverage of C12E4 with a CMC of 7×10-5 M.95 The steepest descent energy minimization was conducted to prepare the system for the simulation. The temperature was maintained at 293 K using the V-rescale   29 thermostat with the temperature constant, 𝜏! = 0.1 ps.96 All bonds were constrained by the SHAKE algorithm with a tolerance of 10-4.48 The Lennard-Jones interactions were truncated with a cut-off radius of 1.2 nm. Unlike-atom interactions were computed using the standard Lorentz-Berthelot combination rules.97-98 Periodic boundary conditions were applied to all three directions. The particle-mesh Ewald (PME) algorithm with a cut-off radius of 1.2 nm and a grid spacing of 0.12 nm was used for the long-range columbic interactions.99 The simulation was executed for 40 ns with a step of 2 fs for integrating the equations of motion. The system took 10 ns to reach equilibrium, and the following 30 ns were used to produce the results presented in the current study. The visualizations were made by VMD 1.9.1.100   The accuracy of the MD simulation was verified using the value of the surface tension. The surface tension was calculated by the indirect method developed by Kirkwood- Buff:101      (3.1) where Lz is the total length of the system, Pxx and Pyy are the parallel components of pressure tensor with respect to the surface, and Pzz is the perpendicular component. The energy and pressure tensor were recorded every 2 fs to integrate eq. (3.1). We performed the simulation with 10 different initial configurations built by PACKMOL94 and obtained a surface tension of 33.1±1.40 𝑚𝑁/𝑚, which was in reasonable agreement with our experimentally measured value of 29.6 ±0.2 𝑚𝑁/𝑚. Also, the surface tension of 64.0 ±1.5 𝑚𝑁/𝑚 was attained for pure water which is fairly in agreement with the experimental value of 72.7 ±1.5 𝑚𝑁/𝑚.102 To determine hydrogen bonding, we used positional order based on the distance between O of acceptors with H of donors in the system.103 Two molecules are assumed to be hydrogen bonded if they satisfy the following condition:  s = 12 Pzz − 0.5 Pxx +Pyy( )( )0Lz∫ dz  30      (3.2) The cutoff distance  was derived from the radii of the first hydrogen atom shell. The cutoff distance between the O atoms of the surfactant and the H atoms of water was 0.20 nm for O1-O4 (defined in Figure 3.3a) and 0.25 nm for O5 (defined in Figure 3.3a). The cutoff distance between water's O atoms and water's H atoms was 0.22 nm. The terminal H in C12E4 were also allowed to form hydrogen bond (HB) with water's O with a cutoff distance of 0.22 nm.   3.3 Results and Discussion Figure 3.1a shows the SFG spectrum of pure air/water interface. The spectrum has two major distinguishable OH bands: a positive OH band near 3100 cm-1 and a negative OH band near 3450 cm-1. For the OH symmetric stretch, the Im(χ(2)) can be positive or negative, depending on the sign of the OH projection with respect to the surface normal: a positive peak indicates water molecules with the hydrogen pointing toward the air (up), and a negative peak indicates the OHs pointing toward the bulk (down).88, 90, 104 It has been proposed that the low-frequency band is the result of a strongly hydrogen-bonded water structure while the high-frequency band is the result of a weakly hydrogen-bonded water structure.105-106 However, the origin of the low-frequency peak has been controversial.107-109 Tian et al. proposed that “ice-like” tetrahedrally bonded water molecules have a dominating contribution to the positive band at 3100 cm-1.106 Nevertheless, Nihonyanagi et al. attributed the positive peak to water dimers at the surface, which generates a vertical induced dipole pointing toward the air,110 rather than tetrahedrally coordinated water molecules. Experimentally, it was clearly demonstrated that the low-frequency peak has a negative sign when the water surface was occupied by cationic CutoffHOHO RR −− <CutoffHOR −  31 surfactants and a positive sign when the water surface was occupied by anionic surfactants.111-113 It is generally accepted that the negative 3450 cm-1 peak is water molecules with their OHs pointing down. Nihonyanagi et al., using phase-sensitive SFG along with MD simulation, showed that the H-bonded OH groups near the surface, on average, point down toward the bulk, causing the negative OH band to be at a frequency similar to that of bulk water (3410 cm-1).110 Figure 3.1b shows the SFG spectrum of air/water interface in the presence of the nonionic surfactant C12E4 near its CMC. The enhancement of the lower frequency peak and the reduction of the higher frequency peak suggest that C12E4 may have increased the interaction strength of water molecules at the surface. Since the positive peak was enhanced, the spectrum suggests that the effect of C12E4 on the orientation of water is more anionic-like,111-113 even though the surfactant is overall neutral.             MD simulations were carried out to obtain a more detailed structure of water at the interface. The simulation box is shown in Figure 3.2a. The density profiles of the water with and Figure 3.1. Im(χ(2)) spectra of air/water interfaces with 0 M (a) and 7×10-5 M (b) of C12E4    32 without the surfactant are shown in Figure 3.2b. An error function can be used to fit the density profile93    (3.3) where, is liquid density,  is vapor density,  is Gibbs dividing surface (GDS), and d is the thickness parameter. The so called "10-90" thickness (te) is defined as the distance along the interface over which the density changes from 10% to 90% of the bulk water density. On the basis of eq. (3.3), it can be shown that te = 2.56d. Our simulations showed that te is 0.31 nm without the surfactants and increases to 1.82 nm with the surfactant. For pure water, a thickness of 0.31 nm is in good agreement with previous values reported using the SPC/E water    model.93, 114 Figure 3.2c shows the averaged orientation factor <cosθ> of water's dipole as a function of depth, where θ is the angle between surface normal (θ = 0) and water's dipole moment, and the triangular brackets denote an average over time. Beside the aforementioned increase in the "10-90" thickness, Figure 3.2c shows that the adsorbed C12E4 flips the orientation of water compared to that of the pure air/water interface. An analysis of the HB in the "10-90" regions indicated that the averaged number of HB per water molecules is 2.7 for the neat water surface and 3.1 with the absorbed C12E4. The increased number of HB is a possible origin for the enhancement of the lower frequency peak in Figure 3.1b. To better understand the local structure of water near the O atoms of the surfactant, angle-resolved radial density distributions of water's H (HW) and O (OW) atoms were presented in Figure 3.3. The labeling of atoms in C12E4 is shown in Figure 3.3a. Each radial density   ⎟⎠⎞⎜⎝⎛ −−−+=dzzerfz VLVL222)( 0ρρρρρLρ Vρ 0z  33                            distribution was obtained by calculating the time-averaged number density of HW (or OW) around an O atom in C12E4 and averaged over all 60 C12E4. For example, Figure 3.3b is the number density of HW around O1 in the C12E4. The number density was calculated based on a polar coordinate system with r being the distance between the HW and O1, and θ being the angle Figure 3.2. (a) The simulation box with a dimension of 3.6 × 3.6 × 32 nm3. (b) The density of water as a function of depth z with (red) and without (blue) C12E4. (c) Orientation factor <cosθ> of water's dipole with (red) and without (blue) C12E4. The insert shows θ the definition of the orientation angle. The z-axis (θ = 0) is the surface normal of the water surface. The dot lines are the Gibbs dividing surfaces, in which the density of water is half the density in the bulk. Please note that for representing the simulation box, the effect of periodic boundary is removed.     34 between 𝑂1𝐻! (the vector connecting O1 and HW) and the surface normal of the water surface (θ = 0). Figure 3.3b-3k show that both HW and OW are confined in well-separated shells near all O atoms in the head group. Since the oxygen of the surfactant is negatively charged (-0.55e for O1-O4 and -0.69e for O5),91 the water molecules are rearranged such that the HW are closer to the surfactant's oxygen no matter if the water is located above or below the surfactant. As a result, the water molecules above the O atoms of C12E4 have their OH pointing down, and the water molecules below the O atoms of C12E4 have their OH pointing up. Figure 3.3b and 3.3g show that the water density above the O1 atom (θ < 90°) is small, indicating that O1 is located near the top of the surface. For the other O atoms in C12E4, the HW and OW are distributed more evenly, indicating they are submerged in water. A special OW layer was indentified above the O2 and O3 atoms. As shown in Figure 3.3h and 3.3i, for θ > 90º the first layer of OW is located at r = 0.22 nm, and the second layer is located at r = 0.47 nm. On the other hand, for θ < 90º, there is a special OW layer located at r ~ 0.37 nm. This special surface layer disappears for O4 and O5 atoms (Figure 3.3j and 3.3k) as they reach the end of the head group.  Figure 3.4 shows the angle-resolved radial density distributions of HW and OW near the C atoms of C12E4. Although the C atoms in the head group are positively charged (+0.32e), the HW atoms are still located in the inner layer for all C atoms indicating the neighboring O atoms have more influence on water than the C atoms. This is consistent with the SFG spectra shown in Figure 3.1 showing that C12E4 is more anionic-like. Overall, the distributions of HW and OW near the C atoms are not as well-structured as those near the O atoms. The H atoms bonded to the C atoms have a relatively small charge of -0.02e, which does not play a significant role in determining the orientation of water.   35                       Figure 3.3. (a) The structure and labeling of atoms of C12E4. (b), (c), (d), (e), and (f) are the angle-resolved radial density distributions of H atoms of water (HW) centered at O1, O2, O3, O4, and O5, respectively. (g), (h), (i), (j), and (k) are the angle- resolved radial density distributions of O atoms of water (OW) centered at O1, O2, O3, O4, and O5, respectively. The radial density distributions were obtained by calculating the time-averaged number density of HW (or OW) and averaged over 60 C12E4 in the simulation box. They do not represent the true densities of atoms as some atoms are counted more than once.   36                      3.4 Conclusions  We carried out phase-sensitive SFG vibrational spectroscopy and MD simulation to characterize the interfacial properties of C12E4 adsorbed on water surface. The effect of C12E4 was found to be more anionic-like. MD simulations showed that the presence of C12E4 increases the thickness of water's surface layer and the average number of HB per water molecule. For water near the surfactant, the H and O atoms of water are confined in well-separated shells. Both the O and C atoms in the head group of C12E4 are surrounded by the H atoms of water indicating that the O atoms in C12E4 have more influence on the orientation of water. The simulation also confirmed that the orientation of surface water molecules is flipped in the presence of the surfactant, which is consistent with the observed SFG spectra. Figure 3.4.  (a), (b), (c), (d), (i), (j), (k) and (l) are the angle-resolved radial density distributions of HW centered at C13, C14, C15, C16, C17, C18, C19, and C20, respectively. (e), (f), (g), (h), (m), (n), (n) and (p) are the angle-resolved radial density distributions of OW centered at C13, C14, C15, C16, C17, C18, C19, and C20, respectively.   37 Chapter 4: Interactions of sulfobetaine zwitterionic surfactants with water on water surface   4.1 Introduction Zwitterionic (or amphoteric) surfactants, which have two distinct and opposite charges in their head groups, are of great interest because of many unique properties, such as their water solubility, biodegradability, biosafety, and temperature stability.115-118 They have been widely used in a variety of consumer and industrial products, which underlie many aspects of our daily lives. A range of methods has been developed for producing zwitterionic surfactants, many of which contain a positively-charged quaternary ammonium ion and a negatively-charged group, such as sulfonate (R-SO3-). The interaction between zwitterionic surfactants and water is particularly interesting because the surfactants, carrying both positive and negative charges, induce a complex behavior of water molecules.  The structures of water surfaces in the presence of ziwitterionic surfactants are not fully understood. It was observed that zwitterionic molecules enhanced the ordering of surface water molecules.102, 119-120 Many previous studies on the interaction between water and ziwitterionic surfactants were focused on phospholipids. Sovago et al. studied the ziwitterionic lipids dipalmitoyl phosphatidylethanolamine (DPPE) and   dipalmitoyl phosphatidylcholine (DPPC) on water surface using sum frequency generation (SFG) vibrational spectroscopy.121 With a numerical maximum entropy phase retrieval algorithm,122-123 Sovago et al. concluded that the averaged orientation of water dipoles pointed toward the bulk.121 Sovago et al. proposed that water in contact with the net neutral zwitterionic lipids DPPC and DPPE were oriented in the   38 same fashion as those in contact with the anionic surfactants because there was a layer of water situated above the phosphate group with their OHs pointing down, which had more contribution to the SFG signal than those underneath the head group. A contradictory result was reported by Chen et al. using phase-sensitive SFG showing that the imaginary second-order nonlinear susceptibility Im(χ(2)) was positive over the entire OH stretch region indicating that the water molecules were oriented with their OHs pointing up in the presence of DPPE and DPPC.13 Another SFG study by Mondal et al. on zwitterionic phospholipid, palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC), at air/water interface also showed a positive Im(χ(2)) spectrum over the entire OH stretch region.112 Mondal et al. also concluded that the negatively charged phosphate group was more capable of orienting interfacial water than the positively charged choline group, i.e., the zwitterionic phospholipids were anionic-like. Relatively fewer studies have been carried out on industrially-relevant zwitterionic surfactants, such as sulfobetaine, which has some fundamental structural differences compared to phospholipids. Surface tension has been the most widely used measurement to study the properties of sulfobetaine on water interfaces.124-126 However, surface tension provides little molecular-level information on their interaction with water molecules. Previously the micelle formation and aggregation of sulfobetaine have been studied by molecular dynamics (MD) simulation.127-128 However, MD simulation of sulfobetaine on water surface that has a correct surface tension prediction has not been reported.129-130  To gain a better insight into the interaction between water and sulfobetaine zwitterionic surfactants, we carried out a combined study using surface tension, phase-sensitive SFG, and MD simulations on N-dodecyl-N, N-dimethyl-3-ammonio-1-propanesulfonate (DDAPS) at air/water surface. Here we also report a new force field which correctly simulates the surface   39 tension of DDAPS on water surface. We found that the Im(χ(2)) spectrum of DDAPS/water interface exhibited both positive and negative peaks, which is significantly different from those of ziwitterionic phospholipids. In contract to the anionic-like phospholipids, we found that the sulfobetaine zwitterionic surfactant was more cationic-like because the positively charged group was more capable of orienting interfacial water.  4.2 Material and Methods Material and Sample Preparation. DDAPS (> 99.5%) was purchased from Sigma-Aldrich. Water with a resistivity > 18.2 MΩ·cm was obtained from a Millipore system. DDPAS solutions were freshly prepared before experiments. All experiments were performed at 20 ± 0.5 °C and 1 atmosphere pressure.   Phase-sensitive SFG setup. A femtosecond Ti-sapphire laser (120 fs, 800 nm, 1 kHz, and 2 mJ/pulse) was used to pump an optical parametric amplifier for generating a femtosecond IR beam. The broad-band IR beam and a narrow-band picosecond 800 nm beam were aligned collinearly.8, 12, 131 The incident angle was 60°. A reference SFG was generated by focusing the IR and the picosecond 800 nm beams into a 50-µm thick quartz crystal. The IR, 800 nm, and reference SFG beams were then focused again on the sample. The reference SFG and the SFG generated at the sample went through a time-delay, a polarizer, a band pass filter, a lens, and a monochromator, and then the interference pattern was recorded by a camera. The polarization combination used in this study was SSP (s-polarized SFG, s-polarized 800 nm and p-polarized IR). The energy of the 800 nm and IR beam were ~10 µJ/pulse and ~3 µJ/pulse, respectively. Each spectrum presented in the paper was acquired over a period of 20 min.    40 MD simulation. Molecular dynamics simulations were carried out using GROMACS 5.1.2 61, 63, 132 in the canonical ensemble. We built an all-atom type force field by combining the TEAM (Transferable, Extensible, Accurate, and Modular) force field91 with the Generalized Amber Force Fields (GAFF)133 to describe the behavior of DDAPS on water. The tail and the sulfonate atoms were parameterized using the TEAM force field, which has been designed in a way that the parameters can be transferred to the other molecules with the same functional groups. Some intra-molecular and inter-molecular interactions in DDAPS, which were not defined by the TEAM force field (i.e. N-C), were obtained from the GAFF force field using ACPYPE134. The TEAM and GAFF force fields are compatible as they both are designed for the same potential energies:  (4.1) where kr, kq, and kn are constants, r0 is the equilibrium length of bond, 𝜃! is the equilibrium angle between two bonds, 𝜙! is the dihedral angle, σ is the van der Waals diameter, ε is the well depth, εo is the permittivity of the free space, and q is the partial charge. The partial charges of atoms in the head group were obtained by using Gaussian 09135 B3LYP136-137/6-31g(d) with the Mullikan atomic charge method. The partial charges of the other atoms were given by the TEAM force field. The parameters are presented in the Appendix A. The flexible SPC/E model was used to describe the water molecules92 as it results to better prediction of interfacial water properties.93 The simulation box dimensions were 3.6 × 3.6 × 32 nm3. As shown in Figure 4.2a, a slab with thickness of 7 nm was filled with 3017 water molecules with vacuum at the both ends of the box. Various number of surfactants, as shown in Table 4.1, were randomly distributed using  4qq+ )r(-)r( 4))-cos(n+(1 2k+ ) -(2k+ ) r-(r2k=U0ji6ijij12ijijij0n2020r∑∑∑ ∑∑∑≠⎟⎟⎠⎞⎜⎜⎝⎛⎟⎟⎠⎞⎜⎜⎝⎛⎟⎟⎠⎞⎜⎜⎝⎛⎥⎥⎦⎤⎢⎢⎣⎡+⎟⎠⎞⎜⎝⎛⎟⎠⎞⎜⎝⎛⎟⎠⎞⎜⎝⎛i ij ijtorsions nanglesbondsrπεσσεφφθθθ  41 PACKMOL94 on each side of the water surface with their head groups pointing toward the water. The steepest descent energy minimization was conducted to prepare the system for the MD simulation. The system temperature was maintained at 293 K using the V-rescale thermostat138 with the temperature constant 𝜏! equal to 0.1 ps. All bonds including water’s OH bonds were constrained by the P-LINCS139 algorithm with a LINCS order of 8. The Lennard-Jones interaction was truncated with a cut-off radius of 1.6 nm. Unlike-atom interactions were computed using the standard Lorentz-Berthelot combination rules.140-141 Periodic boundary conditions were applied to all three directions. The particle mesh Ewald (PME) algorithm99 with a real cut-off radius of 1.6 nm and a grid spacing of 0.16 nm was used to calculate the long-range columbic interactions. Each simulation was carried out for a time period of 40 ns with a step of 2 fs when integrating the equations of motion. The system required 10 ns to reach an equilibrium state. Therefore, data in the first 10 ns were discarded, and all results presented in the current study were based on the later 30 ns. The visualizations were produced using VMD 1.9.1 computer program.100  To correlate the measured surface tension with the MD simulation, the surface coverage of the surfactant for each concentration of DDAPS in Table 4.1 was determined by the Gibbs adsorption equation       (4.2)       (4.3) where c is the surfactant concentration, R is the gas constant, T is the absolute temperature, s is the surface tension,  is the surface excess concentration, NA is the Avogadro’s number, and Γ= −1RTdsd lnc⎛⎝⎜⎞⎠⎟TΓ=ANA 1Γ A  42 is the area occupied by one surfactant molecule. Eq. (4.2) was solved numerically by the forward difference method which requires a known value to find the next data point. When the slope         ( ) in Eq. (4.2) approaches 0, Eq. (4.2) fails to predict the surface coverage ( ). Therefore, the Gibbs adsorption equation is applicable only in the range of ~2.5×10-5 - 2.5×10-3 M where the slope is significantly larger than 0 in Figure 4.1a. We started with a concentration of 2.5×10-5 M and a surface tension of 71.85 mN/m to estimate the surface coverage of DDPAS at a higher concentration. The calculated surface coverage is presented in Table 4.1. The surface tension in the simulated system was calculated by the Kirkwood-Buff method101 using Eq. (3.1). To calculate the hydrogen bonds, geometric criteria were used based on 1) the distance between the O atom of acceptor and the O atoms of donors and 2) alignment of H between both O of donors and acceptors.142 Two molecules were assumed to be hydrogen bonded if the following conditions were satisfied      (4.4) where the cutoff distance ( ) was derived from the first minimum of radial distribution function. The cutoff distance ( ) was 0.32 nm between a surfactant O atom and water O atom (OW) and 0.33 nm between two OWs. The cutoff angle ( ) for a OW − HW ---O hydrogen bond was 140 degrees.142   4.3 Results and Discussion Figure 4.1a shows the surface tension of water vs. the concentration of DDAPS with the corresponding SFG spectra in the CH and OH regions shown in Figure 4.1b and 4.1c, dsd lnc ∞→AcutoffOHOcutoffOOOOWWWWRRθθ ><−−−...cutoffRcutoffRcutoffθ  43 respectively. When the DDAPS concentration is less than 10-5 M, the surface tension of water has a relatively small change. At 10-5 M, no significant CH peaks were observed (magenta curve in Figure 4.1b), and the OH spectrum of water (magenta curve in Figure 4.1c) was very similar to that of pure water (cyan curve in Figure 4.1c) indicating DDAPS had little surface activity at 10-5 M. Above 2.5×10-5 M, the surface tension decreased when the DDPAS concentration increased. Once the concentration reached the critical micelle concentration (CMC), ~2×10-3 M, micelles formed in the bulk water, and further increase in the surfactant concentration did not further decrease the surface tension of water.   Figure 4.1. (a) Surface tension of water with various DDAPS concentrations. Im(χ(2)) spectra of air/water interfaces in the CH (b) and OH (c) regions with DDAPS at 0 M (cyan), 1×10-5 M (magenta), 2.5×10-5 M (orange), 1×10-4 M (blue), and 2.6×10-3 M (red). The Im(χ(2)) spectra have a lower signal-to-noise ratio toward both ends of the spectra because the broadband IR laser has a Gaussian spectral profile.  The interpretation of the SFG spectrum of pure water surface (cyan curve in Figure 4.1c) has been controversial. The spectrum shows a smaller positive OH band near 3100 cm-1 and a   44 larger negative OH band near 3450 cm-1. For the OH symmetric stretch, the Im(χ(2)) can be positive or negative depending on the sign of the OH projection with respect to the surface normal: a positive peak indicates water molecules with the hydrogen pointing toward the air (up), and a negative peak indicates the OHs pointing toward the liquid water (down).8, 143-144 The OH stretch mode of water in the gas phase is around 3756 cm−1. The frequency is red-shifted in the liquid phase because of hydrogen bonds. The SFG band near 3450 cm-1 is generally accepted as the OH stretch mode from water molecules which are weakly hydrogen-bonded, but the origin of the low-frequency peak near 3100 cm-1 has been controversial. Tian et al. proposed that “ice-like” tetrahedrally bonded water molecules had the dominating contribution to the 3100 cm-1 band.106 On the other hand, Nihonyanagi et al. reported that the 3100 cm-1 band came from surface water dimers, which generated a vertical induced dipole pointing toward the air,110 rather than tetrahedrally coordinated water molecules. Nevertheless, the MD simulations carried out by Pieniazek et al. using a three-body-interaction model showed that the positive peak at the lower frequency was a result of cancellation between the positive contributions from four-hydrogen-bonded molecules and the negative contribution from those molecules with one or two broken hydrogen bonds.145 Despite the uncertainty in the origin of the 3100 cm-1 band, it is theoretically correct that a larger SFG peak indicate a better ordering of water. Figure 4.1c suggests that the organization of water molecules near the sulfobetaine  zwitterionic surfactants is fundamentally different from those near zwitterionic phospholipids. While zwitterionic phospholipids, such as DPPE and DPPC, are anionic-like and produce positive Im(χ(2)) over the entire OH stretch region,13, 112 the presence of DDAPS only moderately enhances both the positive OH peaks. The SFG spectra suggest that, in contrast to anionic-like   45 zwitterionic phospholipids, which flip the orientation of water molecules, DDAPS enhances the ordering of water without significantly flipping the orientation of water.   MD simulations were carried out to obtain a more detailed structure of water at the interface. A snapshot of the equilibrium state in the simulation is shown in Figure 4.2a. Since a new force field was used (details described in the Appendix A), the accuracy of the force field was verified by comparing the calculated surface tension to the measured surface tension at various concentrations of DDAPS. The results are summarized in Table 4.1. A reasonably good agreement between the measured and simulated surface tension values was achieved in the range of 1×10-4 - 2.6×10-3 M, in which the Gibbs adsorption equation (eq. 4.2 and 4.3) could be applied as described in the Material and Methods Section,   Table 4.1. Measured and simulated surface tension of water in the presence of DDAPS. The standard deviation was determined by dividing the last 30 ns of simulation run into 5 blocks of 6 ns.  DDAPS concentration  (M) 1×10-4 3×10-4 2.6×10-3 Calculated surface coverage (nm2/molecules) 0.85 0.63 0.48 Number of surfactants in the simulation (both surfaces) 30 41 54 Measured surface tension (mN/m) 66.3 ± 0.2 59.2 ± 0.2 41.7 ± 0.2 Simulated surface tension (mN/m) 65.3 ± 0.9 61.6 ± 1.3 47.0 ± 4.6    46 Figure 4.2b shows the density profiles of water with various concentrations of DDAPS. The density profiles can be fitted with Eq. (3.3)93 Using Eq. (3.3), it can be shown that te = 2.56d. Our simulations show that the "10-90" thickness for pure water is 0.35 nm, which is in good agreement with the values reported previously using the SPC/E water model.93, 114 The presence of surfactants significantly perturbs the structure of surface water as the thickness of the "10-90" layer increases by ~3 times from 0.35 nm (pure water) to a value between 0.95 nm and 1.10 nm.  To demonstrate the effect of DDAPS on the orientation of water molecules, Figure 4.2c shows the averaged orientation factor <cosθµ> of water's dipole as a function of depth, where θµ is the angle between the dipole moment of water and the surface normal (z-axis), as shown in the inset of Figure 4.2c. The triangular bracket denotes an average over time and all water molecules located at the same depth within a layer with a thickness of 0.2 nm. On the pure water surface (cyan curve in Figure 4.2c), water molecules have their averaged dipole pointing up in the low density region and pointing down in the higher density region. The density-weighted plot in Figure 4.2d is a better description of the depth dependent orientation factor with their relative population. For pure water in Figure 4.2d (cyan), water with their dipole pointing down dominates, which is consistent with previous studies showing water molecules at the surface have their OH pointing down to maximize the number of hydrogen bonds.110 Overall, in the presence of the zwitterionic surfactant, the thickness of the non-isotropic layer (<cosθµ> ≠ 0) increases compared to that of pure water. It is interesting that in Figure 4.2d the maximum value of the density-weighted orientation factor ρ<cosθµ> occurs at a DDAPS concentration below the CMC. This is qualitatively consistent with the SFG spectra in Figure 4.1c showing the OH spectrum with the highest DDAPS concentration does not have the highest SFG peak intensity,   47 which suggests that a larger number of DDAPS on the surface will disturb the ordering of water molecules.   Figure 4.2. (a) Simulation box with a dimension of 3.6 × 3.6 × 32 nm3 filled with 3017 water and 54 DDAPS molecules. Color codes for atom types: white (hydrogen), red (oxygen), cyan (carbon), blue (nitrogen), yellow (sulfur), and magenta (water). (b) Water density as a function of depth z. (c) Orientation factor <cosθµ> of water's dipole vs. z. The insert shows the definition of the orientation angles of the dipole moment and the OH bond with respect to the surface normal (z axis). (d) Density weighted orientation factor. The statistical error of <cosθµ> is ~0.06 (standard deviation). Please note that for representing the simulation box, the effect of periodic boundary is removed.    48 Our studies also suggests that DDAPS is cationic-like in contrast to DDAO zwitterionic surfactant112 or zwitterionic lipids which show anioinic-like behaviors.13, 112, 146 As explained below, the positively-charged cationic group of DDPAS has a higher impact on the orientation of water molecules because the positive charge of the head group is distributed on a larger number of atoms, in comparison to the negative charge. Therefore, a larger number of water molecules can interact with the positively charged atoms in the head group.    Figure 4.3. Orientation distributions of water’s OH bonds in the ‘10-90” layer without (a) and with (b) DDAPS (2.6×10-3 M). The blue curves are OHs forming hydrogen bonds with water, the red curves are OHs not forming hydrogen bonds, the black curves are the total OHs, and the green curve is OHs forming hydrogen bonds with the sulfonate groups of DDAPS.  Figure 4.3a-b show the angle distribution of water’s OH bonds in the ‘10-90’ layer with and without DDAPS. Figure 4.3a indicates that the non-hydrogen-bonded OHs (red curve) in the   49 pure water peak at  θOH ~ 10° and 170° suggesting that the non-hydrogen-bonded OHs are more likely to align normal to the surface. On the other hand, the hydrogen-bonded OHs (blue curve in Figure 4.3a) show a peak at θOH ~ 85° indicating that hydrogen-bonded OHs tend to orient parallel to the water surface. Figure 4.3b shows that DDAPS significantly reduces the number of OHs parallel to the water surface. The water OHs forming hydrogen bonds with the sulfonate groups are mostly pointing upward (green curve in Figure 4.3b). This is consistent with the SFG spectra in Figure 4.1c showing DDAPS also enhances the positive OH peak. Overall, the presence of DDPAS on water surface reduces the number of OHs parallel to the surface; hence it enhances both the positive and negative peaks in Figure 4.1.  The orientation of DDPAS on water surface was investigated by plotting the angle distribution of the vectors defined from the N atom to the C atom in the methyl group (NC1) and from the N atom to the S atom (NS). The labeling of atoms is shown in Figure 4.4a. Figure 4.4b shows the angle distribution of NC1 and NS with respect to the surface normal (𝜃 = 0°). The tails (NC1) on average point toward the air (𝜃 < 90°), and the tilting angle decreases when the surface coverage of DDPAS increases. Interestingly, the majority of the head groups (NS) are nearly parallel to the water surface, and an increase in the surface coverage of DDPAS has little effect on the orientation of the head group. In this geometry, both the positive segment (from C12 to CT2) and the negative segment (from CT3 to SO3) of the head group (detailed partial charges given in the Supporting Information) have nearly equal chance of interacting with water molecules. However, because the size of the positive segment is significantly larger than that of the negative segment, a larger number of water molecules can interact with the positively charged atoms in the head group, which makes DDPAS appear more cationic.   50   Figure 4.4. (a) Labeling of atom in DDAPS. (b) Distributions of the titling angle for the tail (NC1) and the head (NS) groups with DDAPS concentration at 1×10-4 M (blue), 3×10-4 M (green), and 2.6×10-3 M (red). NC1 is the vector from the N atom to the C1 atom, and NS is the vector from the N atom to the S atom.  4.4 Conclusions We carried out a combined study using surface tension, phase-sensitive SFG, and MD simulations to investigate DDAPS on water surface. The Im(χ(2)) spectra showed that the presence of DDAPS enhanced the ordering of surface water molecules. We built a new force field for the MD simulation and produced the correct surface tension of water with various DDPAS coverages. MD simulations showed the head groups of DDPAS were nearly parallel to the water surface, and an increase in the surface coverage had little effect on the orientation of   51 the head group. The sulfobetaine zwitterionic surfactant was cationic-like because the positively charged group was more capable of orienting interfacial water.                52 Chapter 5: Complex formations between surfactants and polyelectrolytes of the same charge on water surface   5.1 Introduction The interaction between surfactants and polyelectrolytes has been extensively studied because of their broad applications in pharmaceuticals, personal care products, and many industrial processes.18-24 The interaction leads to the formation of surfactant-polymer complexes, which modify the interfacial properties. Investigations of surfactant-polyelectrolyte interactions are motivated in part by seeking new types of surfactant-polymer complexes with novel interfacial or dispersion properties. In the past several decades, the interactions between oppositely-charged surfactants and polyelectrolytes have been thoroughly studied.147 On the other hand, few studies have been reported on the interaction between surfactants and polyelectrolytes of the same charge. Generally, surfactants and polyelectrolytes of the same charge do not form complexes because of the long-range electrostatic repulsion force. It has been reported that amphiphilic polyelectrolytes in bulk solutions may form complexes with surfactants of the same charge via hydrophobic interactions.148-153 In these cases, the hydrophobic interaction may overcome the electrostatic repulsion and distort the polymer backbone such that the polymers form complexes with surfactants of the same charge.  On a water surface, the hydrophobic interaction between surfactants and polyelectrolytes of the same charge diminishes because surfactants are known to have their hydrophilic groups pointing toward the liquid water. Therefore, complex formation via the aforementioned hydrophobic interaction becomes difficult on water surface. It has been reported that cationic   53 polyehtylenimine (PEI) and cationic alkyltrimethylammonium bromide (CTAB) form ordered mesostructured films on water surface.154 However, the films were not thermodynamically stable as they showed a loss of structure from their neutron reflectometry profiles with time. The authors concluded that the dominant interaction between the polymer and surfactant is a neutral/cationic interaction, where the dipole on the amine groups of PEI interacts with the charged CTAB ammonium groups.   Here we study the interaction between surfactants and polymers of the same charge on water surface via a different mechanism: ion-bridged ionic/ionic interactions and hydrogen bonds. Divalent cations, such as Ca2+, may lead to a charge reversal of a charged surface.155-156 It has been reported that the addition of Ca2+ results in binding of an anionic surfactant onto an anionic surface. On the other hand, monovalent ions (Na+) do not show any evidence of such adsorption.157 The current study investigates whether excess ions, such as Na+ or Ca2+, present in the solution can neutralize the charge of surfactants and allow polymers of the same charge to approach the surface and form complex with the surfactant on water surface. We used the anionic surfactant sodium dodecyl sulfate (SDS), as shown in Figure 5.1a, and the anionic polymer partially hydrolyzed polyacrylamide (HPAM), as shown in Figure 5.1b, to explore this cation-bridged anionic/anionic interactions. SDS is an anionic surfactant used in many industrial processes and consumer products. Anionic HPAM, a copolymer of poly(acrylamide) (PAM) and poly(acrylic acid) (PAA)158, is widely used for enhanced oil recovery159 and water treatments160-161. HPAM and SDS are also commonly being used as chemical flooding agents to reduce the mobility of the aqueous phase and interfacial tension between water and oil.159, 162 It has been reported that the addition of SDS decreases the viscosity of HPAM solutions.163 However, the mechanism for the decrease in viscosity is not fully understood. Samanta et al.164 suggested that   54 SDS affects the viscosity of HPAM solutions through a charge-shielding mechanism but no details of the mechanism were described. Previous studies have shown that HPAM do not form complexes with SDS.150, 163 Only anionic polymers with a very pronounced hydrophobic nature, such as poly-(1-decene-co-maleic acid) and poly(l-octadecene-co-maleic acid), are able to form complexes with SDS in the bulk solution.148           To gain a molecular-level understanding of how ions affect the interaction between the anionic surfactant and the anionic polymer, we carried out a combined study using molecular dynamics (MD) simulation and phase-sensitive sum-frequency generation (SFG) vibrational spectroscopy. As expected, the MD simulation shows that the presence of SDS on the water surface pushes HPAM into the bulk liquid. However, in the presence of excess Na+ ions, the charge screening effect allows HPAM to approach the water surface and weakly interact with the SDS via hydrogen bonding. The addition of divalent cation Ca2+ induces a much stronger interaction between SDS and HPAM by forming ion-bridges and hydrogen bonds. The results of the MD simulation were confirmed by the SFG spectra of the water surface. We observed that Figure 5.1. The molecular structure of SDS (a) and HPAM (b) in aqueous solutions.   55 introducing excess Na+ ions produced only a small change in the SFG spectrum of the water surface, indicating a minor change in the ordering of surface water molecules. On the other hand, Ca2+ ions significantly decreased the SFG intensity and disturbed the ordering of surface water molecules.   5.2 Material and Methods MD Simulations. We employed full atomistic MD simulations to study the interaction between SDS and HPAM in the presence of NaCl and CaCl2. The all-atom optimized potentials for liquid simulation (OPLS-AA)165 were used for SDS and HPAM. The parameters reported by Li et al.166 were used to describe the intramolecular and intermolecular interactions of SDS molecules. HPAM molecules consisting of 20 monomers with an amine-to-carboxylate functional groups ratio of 4:1 was used in the simulation. The HPAM was parameterized using the OPLS-AA force field,165, 167 which was provided in the GROMACS 5.1.263, 132, 168 database. The parameters provided by Aqvist169 were used for NaCl and CaCl2. The behavior of water molecules was described by the extended single point charge (SPC/E) model92. Although the OPLS-AA was originally designed to work with the TIP3P water model, the combination of SPC/E water model with the OPLS-AA force field has been applied successfully to study aqueous interfaces.166, 170-171 Because SDS on the water surface orients interfacial water molecules102, a minimum thickness of 5 nm is required to obtain a bulk-like water region. Therefore, a simulation box of 5 nm × 5 nm × 10 nm with two water surfaces was created. Two oligomers of HPAM were initially placed within 2 nm from the water surface on each side. The simulation box was filled with 8067 water molecules. The surface coverage of SDS was fixed at its critical micelle concentration with a surface coverage of 0.44 nm2/molecule172, which was equivalent to 57 SDS   56 molecules on each side of the water surface. The SDS were randomly distributed on water surface using the PACKMOL package94 such that the hydrophilic head groups were pointing toward the liquid water. To maintain the electrical neutrality of the system, 122 water molecules were randomly substituted by 122 Na+ ions (114 from SDS and 8 from HPAM). Two vapor regions with a thickness of 25 nm were created on each side of the simulation box. To examine the effect of excess salts, 60 and 90 water molecules were randomly replaced by 30 NaCl and 30 CaCl2, respectively. The steep-descent energy minimization (10000 steps) was used to correct the position of each atom before the simulation.  All simulations were performed using GROMACS 5.1.2 GPU computation algorithm63, 132, 168 in the canonical ensemble. The temperature of water and the non-water groups were maintained at 293 K independently using the V-rescale138 thermostat with a temperature constant of 0.1 ps. The OH bonds of water were constrained by the SETTLE which is an analytical constraint algorithm 173 to enable a simulation time step of 2 fs. The rest of bonds were constrained using the parallel LINCS (P-LINCS) algorithm174 with the LINCS order of 4. The Lennard-Jones interactions were truncated with a cutoff radius of 2.1 nm. Unlike-atom interactions were computed using the geometric combination rule, which the OPLS-AA was designed for. Periodic boundary conditions were applied to all three directions. The cutoff radius for the Coulomb potential was 2.1 nm. The long-range Coulomb interaction was treated with the particle mesh Ewald (PME)99 algorithm with a grid spacing of 0.16 nm. The simulations were carried out for 40 ns, but 30 ns was needed to reach equilibrium. Therefore, the trajectories of the final 10 ns were used for the analysis presented in the current study. The visualization was prepared using VMD 1.9.2 computer program.100     57 Enhanced Sampling Methods. Typical MD simulations suffer from the lack of sampling all possible metastable states, which a system may have. The transition between metastable states often requires overcoming high energy barriers which rarely happens in a typical nanosecond or even microsecond simulation. To overcome this limitation, we carried out well-tempered metadynamics simulations175 in which an external Gaussian potential favorably biases the collective variables (CV) to release the system from the local minima and explore all possible states during the simulations. The CV considered in our simulations is the distance between the z-component of the center of mass of the four acrylic acid groups in HPAM to the z-component of the center of mass of all S atoms of SDS. This distance was biased separately for each interface. A bias factor of 20 was used. The bias was deposited with a Gaussian width of 0.05 nm, an initial Gaussian amplitude of 2.0 KJ/mol, and a deposition period of 0.4 ps. The well-tempered metadynamics simulations were carried out using the PLUMED 269computer program. To expedite the metadynamics convergence, we put two harmonic potentials with the following form for the distance between the HPAM and the SDS to limit the region of the phase space accessible during the run:           (5.1) where  is the wall energy constant and 1500 KJ.mol-1.nm-1 was used, z is the z-component of Cartesian coordinates, and a is the position of the wall. In this study, we set the wall at the distance of 6 nm between the center of mass of the four acrylic acid groups in HPAM to the z-component of the center of mass of all S atoms of SDS for each surface. To start the well-tempered metadynamics, the last trajectory of the typical MD simulation was used as the initial configuration for each system. The temperature of water and non-water groups were maintained Vκ =κ (z− a)2κ  58 at 293 K independently using the V-rescale138 thermostat with a temperature constant of 0.1 ps. The OH bonds of water were constrained by the SETTLE algorithm173 to enable a simulation time step of 2 fs. The rest of bonds were constrained using the P-LINCS algorithm174 with the LINCS order of 4. The Lennard-Jones cutoff radius was 1.0 nm where the interaction was smoothly reduced to 0 after 0.9 nm. The unlike-atom interactions were computed using the geometric combination rule. Periodic boundary conditions were applied to all three directions. The cutoff radius for the Coulomb potential was 1.0 nm. The long-range Coulomb interaction was treated with the particle mesh Ewald (PME)99 algorithm with a grid spacing of 0.16 nm. The simulations were carried out for 100 ns, where the convergence was attained. Finally, to calculate the binding free energy between the HPAM and the SDS, the reweighting algorithm176 developed by Tiwary and Parrinello was used.  Materials and Sample Preparation. HPAM (average molecular weight ~520,000 g/mol with 80 wt % acrylamide), NaCl (> 99%), CaCl2 (> 99%), and SDS (> 99%) were purchased from Sigma-Aldrich. Water with resistivity > 18.2 MΩ·cm was obtained from a Millipore system. A 0.008M SDS solution was made by dissolving SDS into pure water. A solution with 0.008 M SDS and 10-8 M HPAM was made by adding 0.016 M SDS solution to an equal volume of 2×10-8 M HPAM solution under vigorous stirring. Mixtures of SDS, HPAM, and the salts were made by mixing an equal volume of the SDS/salt solution and the HPAM solution. All solutions were freshly prepared right before spectroscopic measurement. All experiments were performed at 20°C and 1 atm.  Phase-sensitive SFG setup. A femtosecond Ti-sapphire laser (120 fs, 800 nm, 1 kHz, and 1 mJ/pulse) was used to pump an optical parametric amplifier for generating a femtosecond IR   59 beam. The broad-band IR beam and a narrow-band picosecond 800 nm beam were aligned collinearly.8, 12 The incident angle was 60°. A reference SFG was obtained by focusing the IR and picosecond 800 nm beams into a 50 µm thick quartz crystal. The IR, 800 nm, and reference SFG beams were then focused again on the sample. The reference SFG and the SFG generated at the sample went through a time-delay, a polarizer, a band pass filter, a lens, and a monochromator, and then the interference pattern was recorded by a camera. The polarization combination used in this study was SSP (s-polarized SFG, s-polarized 800 nm and p-polarized IR). The energy of the 800 nm and IR beam were ~10 µJ/pulse and ~3 µJ/pulse, respectively. Spectra presented in the paper were acquired over a period of 20 min.  5.3 Results and Discussion The snapshots of the MD simulation without excess ion, with excess Na+, and with excess Ca2+ are shown in Figure 5.2. Without excess ions (Figure 5.2a), HPAM are not able to overcome the repulsive forces from the surfactants and stay in the bulk water. Excess Na+ ions in the solution led to a weak association between SDS and one of the HPAM polymers (Figure5.2b). In the presence of Ca2+ (Figure 5.2c), both HPAM polymers approach the surface and interact with the SDS layer on water surface.          60              reduces the repulsive force and creates a small and gradual attractive potential for HPAM.  The relatively weak potential explains why it is rare to have both HPAM polymers attached to the surfaces. In contrast, Figure 5.3c shows that the presence of Ca2+ creates a steep potential well of ~ 30 KJ/mol, which is higher than typical hydrogen bonds. Therefore, the Ca2+ bridged HPAM-SDS complex, shown in Figure 5.2c, is thermodynamically stable.      (a) (b) (c) Figure 5.2. Simulation box with dimensions of 5.0 × 5.0 × 10.0 nm3 filled with ~8000 water molecules, 114 SDS, 2 HPAM, and 122 Na+. (a) No excess ions. (b) 30 excess NaCl. (c) 30 excess CaCl2. Color codes for atom types: red (oxygen), green (carbon), blue (nitrogen), yellow (sulfur), white (hydrogen), magenta (Na+), orange (Cl−), black (Ca2+), and cyan (water).    61                         140120100806040200-20Binding free energy (KJ/mol)6543210-1Distance (nm)(a) (b) (c) 140120100806040200-20Binding free energy (KJ/mol)6543210-1Distance (nm)140120100806040200-20Binding free energy (KJ/mol)6543210-1Distance (nm)Figure 5.3. Calculated binding free as function of distance between the z-component of the center of mass of the four acrylic acid groups in HPAM to the z-component of the center of mass of the S atoms in all SDS for the systems with no excess ions (a), 30 excess NaCl (b), and 30 excess CaCl2 (c). The red and blue curves represent the results from each water surface in the simulation box. The negative distance refers to states in which the position of the center of mass of the acrylic acid groups in HPAM is higher than the center of mass of the S atoms.    62                                         Figure 5.4. Time-averaged number density profiles of the –SO4- groups in SDS, the H atoms in the NH2 groups of HPAM (HP), the O atoms in the CO2 groups of HPAM (OP), Na+, Cl-, and Ca2+. (a) no excess ions. (b) 30 excess NaCl. (c) 30 excess CaCl2. The values of HP, OP, Na+, Cl-, and Ca2+ are magnified by 5, 20, 5, 10, and 5 times, respectively for a better visibility.  To better understand the nature of the surfactant-polymer interaction, Figure 5.4 shows the time-averaged number density profiles of the –SO4 groups in SDS, the H atoms in the NH2 groups of HPAM (HP), the O atoms in the CO2 groups of HPAM (OP), and the intrinsic Na+ ions, 181614121086420Number density (nm-3)-6 -4 -2 0 2 4 6z (nm) SO4-  HP  OP Na+  (a)181614121086420Number density (nm-3)-6 -4 -2 0 2 4 6z (nm) SO4- HP OP Na+ Cl- (b)181614121086420Number density (nm-3)-6 -4 -2 0 2 4 6z (nm)SO4- HP OP Na+ Cl- Ca2+(c)  63 which come with the SDS and HPAM. Even without excess ions (Figure 5.4a), a significant number of the intrinsic Na+ ions accumulate near the surface, but they do not allow HPAM to overcome the strong electrostatic repulsion force. This result is consistent with the previous experimental observation that HPAM and SDS do not associate with each other in pure water.163 Figure 5.4b shows that the addition of NaCl in the solution results in more Na+ ions accumulating at the surface. The charge screening produced by the additional Na+ ions allows the polymers to approach the surface. In the presence of excess Ca2+ (Figure 5.4c), nearly all Ca2+ ions are located near the surface, and the distributions of the surfactant and the polymers become overlapped near the surface.    A detailed analysis of the simulation data reveals that the complex formation between the surfactants and the polymers in the presence of Ca2+ ions is dominated by the Ca2+ bridged interaction between the OP in HPAM and the ionic O atoms (Oi) of SDS. Figure 5.5a shows the radial distribution function of Oi with respect to OP in the presence of excess Na+ and Ca2+ ions.  It is clear that Ca2+ ions induce a distinguishable layered structure between OP and Oi, (red curve in Figure 5.5a) while Na+ ions only allow OP and Oi to approach each other (blue curve in Figure 5.4a). Figure 5.5b shows that the ester O atoms of SDS (Oe) are not directly involved in the interaction with the polymer as Oe mostly resides in the second layer.             64                  Our simulation indicates that the hydrogen bond formation plays an important role in the interaction between HPAM and SDS. Hydrogen bonds may form between the O atoms of SDS (both Oi and Oe) and the H atoms in the NH2 group of HPAM (HP). Figure 5.6 illustrates the radial distribution functions of the Oi and Oe with respect to HP in the presence of Ca2+ and Na+. Overall, Ca2+ promotes the hydrogen bond formation more than Na+ does. In Figure 5.6, narrower peaks within 1 nm originate from the neighboring H atoms of the polymer (NH2 groups), and the broad peak above 1 nm originate from the O atoms in the neighboring SDS. 35302520151050Radial distribution funct ion2.52.01.51.00.50.0r (nm) OP-Oi (Ca2+) OP-Oi (Na+)(a)35302520151050Radial distribution funct ion2.52.01.51.00.50.0r (nm) OP-Oe(Ca2+) OP-Oe(Na+)(b)Figure 5.5. Radial distribution functions between the O atoms in the CO2 groups of HPAM (OP) and the O atoms in SDS: (a) ionic O atoms (Oi); (b) ester O atoms (Oe). OP is the reference point of the radial distribution functions.   65                       To quantitatively study the mechanism for the complex formation between SDS and HPAM, the number of ion-bridges were calculated. It was assumed that an ion bridge (OP-ion-Oi or OP-ion-Oe) is established if an ion (either Na+ or Ca2+) resides within a cutoff distance from the C atom in the CO2 groups of HPAM ( ) and from the S atom of SDS head groups    ( ). The cutoff distances were determined by the first minimum in the radial distribution function: , , , , and . The numbers of various types of ion-Rcutoff (ion−C )Rcutoff (ion−S )Rcutoff Ca−C( ) = 0.45nm Rcutoff Na−C( ) = 0.40nm Rcutoff Ca− S( ) = 0.44nmRcutoff Na−C( ) = 0.40nm Rcutoff Na− S( ) = 0.43nm2520151050Radial distribution function2.52.01.51.00.50.0r (nm) HP-Oe(Ca2+) HP-Oe(Na+)(b)403020100Radial distribution function2.52.01.51.00.50.0r (nm) HP-Oi (Ca2+) HP-Oi (Na+)(a)Figure 5.6. Radial distribution functions between the H atoms in the NH2 group of HPAM (HP) and (a) the ionic O atoms (Oi) and (b) the ester O atoms (Oe) of SDS. HP is the reference point of the radial distribution functions.   66 bridges are presented in Table 1. Without salts in the solution, the intrinsic Na+ ions from SDS and HPAM do not produce any ion bridges between SDS and HPAM. The addition of NaCl to the system allows a small amount of Na+ ions to participate in the formation of ion bridges between SDS and HPAM. On the other hand, the presence of Ca2+ significantly facilitates the complex formations between SDS and HPAM. When Ca2+ ion bridges are formed between SDS and HPAM, Na+ ions further stabilized the SDS-HPAM complex as the number of Na+ ion bridges increases significantly. Table 5.1. The number of ion-bridges and hydrogen bond for different systems in terms of the excess ion. Mediate Ions Ion bridges (per ns) Hydrogen bonds (per ns) Na+ (no salts) 0 0 Na+ (with NaCl) 7 2568 Na+ (with CaCl2) 364  3239 Ca2+ (with CaCl2) 193  To quantitatively study the hydrogen bond formation between SDS and HPAM, the number of hydrogen bonds was calculated using geometric criteria. A hydrogen bond is formed between HP and Oi (or Oe) if the distance between the N atom of NH2 groups of HPAM and Oi (or Oe) is less than the cutoff distance ( ; ), which was derived from the first minimum in the radial distribution function. Additionally, the angle  should be less than , which is commonly used to identify hydrogen bonding.177 The number of hydrogen bonds between SDS and HPAM is presented in Table 5.1. With the Rcutoff (N −Oi ) = 0.46nm Rcutoff (N −Oe ) = 0.60nm∠H...N...O 30°  67 addition of NaCl, a significant number of hydrogen bonds are formed although very few Na+ bridges are present indicating that hydrogen bonds are the dominating interaction between SDS and HPAM with the addition of NaCl. While a greater number of hydrogen bonds are formed in the presence of Ca2+, the stronger electrostatic interaction of Ca2+ ions play a more important role in linking SDS and HAPM. Phase-sensitive SFG vibrational spectra were collected at air/water interfaces to verify the MD simulation results. SFG has been known for its high surface sensitivity because under the electric-dipole approximation the second-order optical process is forbidden in a centrosymmetric medium, such as bulk water. While the traditional SFG vibrational spectroscopy measures only the amplitude of the 2nd-order nonlinear optical susceptibility |χ(2)|, phase-sensitive SFG also measures the phase of  χ(2).17, 178-180 For the OH symmetric stretch of water surface, the imaginary part of χ(2), Im(χ(2)), can be positive or negative, depending on the sign of the OH projection with respect to the surface normal: a positive peak indicates water molecules with the hydrogen pointing toward the air (up), and a negative peak indicates the OHs pointing toward the bulk (down).7 Figure 5.7 illustrates the Im(χ(2)) of water surface with (a) SDS only, (b) SDS + HPAM, (c) SDS + HPAM + excess Na+, (d) SDS + HPAM + Ca2+, and (e) SDS + Ca2+. As shown in Figure 5.7, because of the negative charge of SDS, SDS (magenta curve) produces an ordered water structure with the water’s OHs pointing up (a positive SFG peak). This observation is in agreement with previous studies revealing that anionic surfactants lead to flipping of water molecules at the surface.7-8 Adding HPAM with or without excess Na+ does not significantly alter the SFG spectrum. However, the presence of Ca2+ dramatically changes the SFG spectrum of water. The decrease in SFG intensity suggests that the ordering of water is significantly disturbed in the presence of Ca2+. Although Ca2+ ions alone perturb the hydrogen network of   68 surface water molecule (black curve), addition of HPAM further disrupts the ordering of water molecules, which is consistent with the MD simulations suggesting that SDS and HPAM form stable complexes at the surface via ion bridges and hydrogen bonds.           5.4 Conclusions    We investigated the interaction between surfactants and polymers of the same charge at air/water interfaces using MD simulation and SFG. The results indicated that excess Na+ in the system allowed the polymer to approach the surface and interact with the surfactant via hydrogen bonding. In the presence of Ca2+ ions, HPAM and SDS interact via forming Ca2+ ion bridges and hydrogen bonds. These results are consistent with the observed SFG spectra showing excess Na+ ions induce only a minor change in the ordering of surface water molecules while Ca2+ ions significantly alter the ordering of interfacial water.  0.80.60.40.20.0Im(χ(2) ) (arb. u.)350034003300320031003000Wavenumber (cm-1) SDS SDS+HPAM SDS+HPAM+Na+ SDS+HPAM+Ca2+ SDS+Ca2+Figure 5.7. Im(χ (2)) spectra of air/water interfaces in the OH regions for various aqueous solutions of 0.008M SDS (magenta), 0.008M SDS + 1× 10-8 M HPAM (green), 0.008M SDS + 1× 10-8 M HPAM + 0.1 M excess NaCl (blue), 0.008 M SDS + 1× 10-8 M HPAM + 0.1 M excess CaCl2  (red), and 0.008M SDS + 0.1 M excess CaCl2  (black).   69 Chapter 6: Design of polyphosphate inhibitors: a molecular dynamics investigation on polyethylene-glycol-linked cationic binding groups  6.1 Introduction Thrombosis, the formation of clots within the blood vessels, blocks blood flow and can cause serious health complications. It can be fatal if the clot moves to a crucial part of the circulatory system, such as the brain or the lungs.181 Recently it has been identified that highly-anionic polyphosphates (polyP), ranging from a few to hundreds of orthophosphate units (Figure 6.1a), activates blood coagulation via multiple pathways25-29. The process is not fully understood, but it has been proposed that polyP may accelerate the activation of factor V by factor XIa182, enhance resistive fibrin clot structures to fibrinolysis183, promote the activation of factor XI by thrombin184, and trigger the activation of the contact pathway of blood clotting26, 185. Therefore, polyP has been proposed as a therapeutic target to inhibit thrombosis.  Figure 6.1. The molecular structure of polyP (a), PEG-based chain (b), and different HBGs: R1 (c), R2 (d), and R3 (e). P denotes the attachment location of PEG-based chain and the head group in (c), (d), and (e).    70  Electrostatic attraction between cationic macromolecules and negatively charged polyP has been used to design antithrombotic agents that counteract the prothrombotic activity of polyP. Two cationic polymers, polyethylenimine (PEI) and polyamidoamine (PAMAM), have been investigated as inhibitors of polyP.30-31 Both PEI and PAMAM bind to polyP with high affinity and consequently attenuate blood clotting.30-31 Despite the effectiveness of these polycations, a major limitation is that they are not biocompatible. The PEI and PAMAM carry a large number of unshielded positive charges at the physiological pH as a result of the protonation of the amine groups. An undesirable effect of such a highly-charged state is that these polymers also bind to other proteins and cell membrane, leading to toxicity.186-188 Recently a new class of dendritic polymer-based universal heparin reversal agents (UHRA) has been synthesized by our group to address this limitation32. UHRA has a protective short-chain polyethylene glycol (PEG) and several cationic heparin binding groups (HBGs) containing tertiary amines. The protective PEG shield generates excellent biocompatibility, selectivity and non-toxicity.33, 189However, modifications are still required to strengthen the binding and specificity to polyP in order to increase the drug efficiency. To optimize the HBG structure for an enhanced drug efficacy, we utilized linear model compounds with various HBGs (Figure 6.1c-e) and PEG tail length (Figure 6.1b). An atomic-level understanding on how the HBG structure, charge density, and PEG length affect their polyP binding efficiency may provide guidance for the future drug development.  Molecular dynamics (MD) simulation, which has been increasingly used to assist drug discovery during the past several years190-192, has significantly increased the pace of drug development by providing atomic-level information and high-throughput initial screening. A great challenge in carrying out MD simulations for large pharmaceutical molecules is the limited   71 time scale accessible by current computer power. Limited simulation time prevents complete sampling of the conformational phase space, usually because a system’s metastable states are separated by high energy barriers. Overcoming energy-barriers larger than thermal energy rarely happens in a time period of nanosecond or even microsecond. To overcome the insufficient sampling of the phase space, several enhanced sampling methods have been applied.64-67 In these methods, one or a few relevant collective variables (CVs), describing the system in reduced dimensions, are biased, encouraging exploration of large regions of phase space.64-67 Among enhanced sampling methods, metadynamics67 (MetaD) and its variant forms70, 175, 193 have been successfully applied to study the mechanism of drug binding to bio-macromolecules.194 In this study, the parallel tempering metadynamics70 (PTMetaD) is employed to study the interaction between the (PEG)n-Ri and the polyP. PTMetaD takes advantages of the enhanced sampling at different temperatures in accord with the replica exchange molecular dynamics65 (REMD) while one or two CVs are actively biased by implementing well-tempered MetaD175 during the simulation. Hence, the choice of CVs, which is a common difficulty, associated with the MetaD, no longer affects the final results. To increase the overall efficiency, PTMetaD is sometimes employed in the well-tempered ensemble195-196 (WTE) where the energy overlap and the exchange acceptance probability are increased by enlarging the potential energy fluctuations through using the potential energy as a system CV. This study implements PTMetaD-WTE to speed up the transition of the binding between polyP and (PEG)n-Ri from one metastable state to another. Besides the enhanced sampling methods, another way to accelerate the MD simulation is to exploit coarse-grained (CG) MD simulations, in which lumping groups of atoms into several CG beads reduces the number of degrees of freedom. Subsequently, applying softer potentials   72 and larger time steps lifts the time scale limitation and extends the simulation to a larger length scale. For these reasons, CG-MD simulation has become a necessary tool to study many large biomolecular197-199 systems. The MARTINI force field200 is one of the most well-known CG force fields with which a variety of biomolecules, such as peptides/proteins201-203, lipids204-207, carbohydrates208-209, and polymers210-213, have been parameterized to study a wide range of applications.200 Based on the MARTINI force field200, every three or four heavy atoms along with their H atoms are mapped to CG beads. Then, the beads in terms of the chemical nature are categorized into four major types of interaction sites: polar, non-polar, apolar, and charged. To represent an accurate chemical nature of the underlying atomic structure, each particle type is divided into subtypes according to their hydrogen-bonding capability and degree of polarity. To the best of our knowledge, neither polyP nor (PEG)n-Ri has been parameterized in accord with the MARTINI force field. In this study, we will develop the required parameters to study the interaction between (PEG)n-Ri and polyP. In this paper, we use MD simulations to find the possible routes of improving the design of PEG-HBGs for polyP inhibition. The effects of the PEG chain length, the charge densities of the HBG, and the polyP chain length are investigated to obtain a PEG-HBG structure that could potentially increase polyP binding and inhibition efficiency. We found that the PEG length did not have any impact on the interaction between the PEG-HBG and polyP. Most likely, the main function of the PEG was to provide a shield and prevent the cationic drugs from binding to other biomolecules. On the other hand, increasing the charge density on the HBGs strengthens the PEG-HBG avidity of binding to polyP, indicating that the columbic interaction is the main driving force for counteracting the polyP’s prothrombotic effects. Additionally, we found that the binding of PEG-HBGs to polyP was not affected by the chain length of the polyP.   73  6.2 Materials and Methods All-atom MD simulations. Studies on the interaction between (PEG)n-Ri and polyP in aqueous solutions with NaCl concentration of 0.1 M were carried out using the  GROMACS-5.1.4 software package63, 168. The force field parameters describing the behaviors of PolyP, (PEG)n-Ri, and NaCl were originated from the Generalized Amber force field (GAFF)133. All bonded and non-bonded interaction parameterizations for (PEG)n-Ri and polyP except the partial charges were carried out using the ACPYPE134. To assign the partial charges for the polyP and (PEG)n-Ri atoms, quantum mechanical calculations with the Hartree-Fock (HF) method using the 6-31G(d) basis set were used to obtain the optimized geometry and energy. All required calculations were done using the Gaussian 09 program135. The restrained electrostatic potential (RESP)214 approach was used to assign the electrostatic point charges for the polyP and (PEG)n-Ri using antechamber-14215. The obtained partial charges are presented in Table B1-5 in the Appendix B. The TIP3P216 model was used to describe the behaviors of water molecules since AMBER force field34 was designed to work properly with it. The details of the studied systems are shown in Table 6.1. In the all-atom-MD simulations, we studied the interaction between one polyP with 28 phosphate monomers and the corresponding number of (PEG)n-Ri, which satisfies the total charge ratio of 1:1. To set up the initial configuration, the (PEG)n-Ri along with the polyP were randomly placed into the simulation box. Before starting the MD simulations, 10000 steps of the steep-descent energy minimization were performed to correct the position of each atom.        74   Table 6.1. The configurations of different (PEG)n-Ri and polyP simulations. System Ligand NPEGa Ndrugb Qdrugc NNaCld Nwatere Box size  (nm3) I R1 24 10 +3 21 11000 7 × 7 × 7 II R1 12 10 +3 11 6000 4.5 × 6 × 7 III R1 8 10 +3 11 6000 4.5 × 6 × 7 IV R2 12 10 +3 11 6000 4.5 × 6 × 7 V R3 12 5 +6 11 6000 4.5 × 6 × 7 a) the total length of PEG-based chain b) number of (PEG)n-R in the simulations c) the total charge for each molecule of (PEG)n-Ri d) the number NaCl corresponding to 0.1 M e) the approximate number of water molecules in the simulation box  After setting up the initial configuration, a 2 ns MD simulation in the canonical ensemble (NVT) was performed while the positions of the heavy atoms in polyP and (PEG)n-Ri were fixed to relax the water molecules. Then, a 10-ns MD simulation in the NVT ensemble without any position restraints was performed to equilibrate the system. The temperature of the polyP/(PEG)n-Ri/ions and water molecules was maintained at 310 K separately using a stochastic global thermostat193 with a coupling constant of 0.1 ps. The OH-bonds of water were constrained by the SETTLE algorithm173. The rest of the bonds were constrained using the P-LINCS algorithm174 with a LINCS order of 4. A simulation time step of 2 fs was used for integrating the equation of motions. The Lennard-Jones cutoff radius was 1.0 nm, where the interaction was smoothly shifted to 0 after 0.9 nm. Periodic boundary conditions were applied to all three directions. The particle mesh Ewald (PME) algorithm with a real cutoff radius of 1.0 nm and a grid spacing of 0.16 nm was used to calculate the long-range columbic interactions.99 To prepare   75 the system for the PTMetaD-WTE simulations, a 4-ns MD simulation was performed isothermally and isobarically (NPT) at 1 bar with water compressibility of 4.48 × 10-5 bar-1 to relax the box volume. The pressure was maintained at 1 bar using the Parrinello-Rahman barostat58 with a pressure constant of 2.0 ps. Subsequently, by fixing the box volume, the PTMetaD-WTE simulations were carried out in the NVT ensemble.  To start the PTMetaD-WTE simulation, the last trajectory of the NPT simulation was chosen as initial atomic coordinates of replicas at different temperatures, which were distributed exponentially217 in the range of 310-460 K to achieve an efficient exchange rate between the replicas. A 4-ns NVT-MD simulation was performed so that each replica reached the specified temperature with some relaxation of the polymer structures. Except system I where 12 identical replicas were used, 8 identical replicas were simulated for all other systems (shown in Table 6.1). Afterwards, a 15-ns WTE simulation was carried out195-196, allowing us to achieve an optimum exchange rate of 30-35% between the replicas. The theoretical background of how the metadynamics simulation is implemented, has been thoroughly reviewed elsewhere.71 Here we briefly represent the parameters for performing our PTMetaD-WTE simulations. The bias factor of 50 was used for all systems except for the system I, where a bias factor of 40 was used because of its smaller system size. The bias was deposited with a Gaussian width of 250 KJ/mol, an initial Gaussian amplitude of 4.18 KJ/mol, and a deposition period of 0.5 ps. The well-tempered metadynamics simulations were implemented using the PLUMED 269. In a typical PTMetaD-WTE simulation, the bias potential acts statically on the potential energy of different replicas, allowing biasing other CVs duuring the production runs. However, the obtained static bias potential during the initial setup has to be smooth, or it may affect the final results. To overcome this problem, Sprenger and Pfaendtner have suggested a new protocol in which   76 potential energy and CVs are biased on two separate bias potentials in the same time during the production run.218 The bias potential from the initial step is carried over and the frequency of Gaussian depositions is significantly reduced to one hill every 60 ps. The driving force of interaction between the polyP and (PEG)n-Ri is dominated by the electrostatic attraction, therefore the Debye-Huckel energy219 between the polyP and (PEG)n-Ri (R) was actively biased during the production run using a NaCl ionic strength of 0.1 M with the following functional form:      (6.1) where is the Boltzmann constant,  is the water dielectric constant,  is the electrostatic point charge of atom i,  is the distance between the center of mass of the coarse-grained sites, i, on polyP to the center of mass of the coarse-grained sites, j, on the cationic headgroups (R), which are defined in Figure B.6. is the screening length which is a function of the ionic strength.219 In addition, the (PEG)n-Ri binding stoichiometry (S) number around polyP is one of the main factors which determines the efficiency of binding, and it was estimated by the following switching function:      (6.2)  where S varies between 0 to Ndrug (shown in Table 6.1). For instance, when all headgroups of (PEG)12-R1 are associated with the polyP, S is 10. n, m, and r0 are the tuning parameters which were adjusted using 200 ns simulation run of system I in an NVT ensemble so that a smooth DH = 1kBTεwqiqjj∈R∑ e−κ rijriji∈polyP∑kB εw qirij1κS =1− rijr0⎛⎝⎜⎞⎠⎟n1− rijr0⎛⎝⎜⎞⎠⎟m⎛⎝⎜⎜⎜⎜⎜⎞⎠⎟⎟⎟⎟⎟j∈R∑i∈polyP∑  77 switching curve for each drug molecule was obtained. The parameters n, m, and r0 are 12, 24, and 1.5 nm, respectively. The same values were used for all systems.  is the distance from the center of mass of the HBG (Ri) to the center of mass of the polyP. The S number was monitored for all the systems shown in Table 6.1 except for the system I where it was biased alongside the Debye-Huckel energy. The bias factor for the all systems was 20. The Gaussian bias was deposited every 0.4 ps with an initial amplitude of 2 KJ/mol and a width of 0.2 KJ/mol. All PTMetaD-WTE simulations were performed for 150 ns using the PLUMED 269. At the end of each simulation, the reweighting176 algorithm developed by Tiwary and Parrinello was used to find the unbiased probability distributions of any desirable properties, such as the binding free energies from the production runs. In the last step, we recorded the trajectory corresponding to the minimum free energy as a function of DH energy for system I-V, and then equilibrated for 15 ns using classical MD simulations in the NPT ensemble with the details that have been described earlier in the all-atom MD simulations section. We used the last 10 ns for the analysis presented in the current study.  CG-MD. To study the performance of (PEG)24-R1 on polyP with various chain length, the force field parameters based on the MARTINI200 CG force field were developed for both the polyP and (PEG)24-R1 (details given in Appendix B). The details of the studied systems including 1 molecule of polyP are presented in Table 6.2. The MARTINI polarizable water model (PW)220 was used to describe the water behaviors. Before initiating the dynamics, the positions of the beads were corrected by performing the steep-descent energy minimization for 30,000 steps. Simulations were performed using the GROMACS 5.1.4 GPU computation algorithm63, 168, 221 in the NPT ensemble. The input options to implement the simulations were mainly adapted from the “martini_v2.x_new.mdp”222 with the slight modifications: the neighbor list was updated rij  78 every 40 steps to compute with the GPUs more efficiently. The temperature of the  polyP/(PEG)n-Ri/ions and water was maintained at 310 K separately using the V-rescale thermostat with a temperature constant of 0.3 ps.193 The isotropic pressure coupling using the Parrinello-Rahman barostat58 with a pressure constant of 12.0 ps was used to maintain the system pressure at 1 bar with a compressibility of 3.0×10-4 bar-1 . The Lennard-Jones interactions were truncated at a cutoff radius of 1.1 nm. However, to better conserve energy, the potentials were modified by the potential-shift-Verlet. Periodic boundary conditions were applied to all three directions. The electrostatic interactions were treated by the reaction-field approach with a cutoff radius of 1.1 nm. The MARTINI polarizable water bonds were constrained using the P-LINCS algorithm174 with a LINCS order of 4. A 4-ns NPT simulation with a time step of 2 fs was run to relax the particles in the system. Subsequently, a NPT simulation of 1 µs was carried out for each system in Table 6.2 with a time step of 8 fs to study the interaction between the polyP and (PEG)24-R1.   Table 6.2. Configurations of the (PEG)24-R1 and the numbers of polyP monomers used for CG-MD simulations. System npolyPa Ndrugb Qdrugc QpolyPd NNaCl Nwatere Box  (nm3) 1 28 10 +30 -30 21 2600 7 × 7 × 7 2 61 21 +63 -63 60 7600 10 × 10 × 10 3 115 39 +117 -117 165 21000 14 × 14 × 14 4 133 45 +135 -135 203 26000 15 × 15 × 15 a number of polyP beads b number of (PEG)24-R1 in the simulations c the total charge for each molecule of (PEG)24-R1 d the total charge of 1 polyP molecule with 28 phosphate monomers e the approximate number of the MARTINI polarizable water in the simulation box      79  6.3 Results and Discussion PEG length effect. Our simulations show that the length of the PEG chain has little impact on the interaction between the (PEG)n-Ri and the polyP. To investigate the effect of the PEG length on the binding efficacy, the binding free energy along with the S number were calculated with various PEG tail length. Figure 6.2 shows the binding free energy reaches its minimum at a distance of around 1 nm, measured from the center of mass of the polyP to the center of mass of the (PEG)n-R1 headgroup. There are no significant differences in the binding free energy for (PEG)n-R1 with n = 8 - 24. In all cases, the binding free energy between (PEG)n-R1 and polyP is ~ -7 KJ/mol.   Figure 6.2. The reweighted binding free energy between (PEG)n-R1and polyP. The distance is defined between the center of mass of polyP and the center of mass of (PEG)n-R1 headgroups. The binding free energy profile was obtained by calculating the averaged binding free energy of all (PEG)n-HBG molecules in the system. The error bar indicates the standard deviation.    80 The binding free energy as a function of the S number was calculated from the PTMetaD-WTE simulations. The S number at the minimum free energy indicates how many (PEG)n-Ri participate in inhibiting the polyP. The results are summarized in System I - III in Table 6.3. The energy profiles of the (PEG)n-R1 with various PEG lengths are presented in Figure B.8 in the Supporting Information. The S number for the (PEG)n-R1 remains in the range of 7 to 8 with n = 8, 12, and 24, suggesting that the PEG tail length has little effect on the value of S.    Table 6.3. Extracted S number of (PEG)n-Ri around polyP corresponding to the minimum free energy.    System Candidates S I (PEG)24-R1 ~7 out of 10 II (PEG)12-R1 ~8 out of 10 III (PEG)8-R1 ~7 out of 10 IV (PEG)12-R2 ~8 out of 10 V (PEG)12-R3 ~4 out of 5  Further analysis of the simulation results confirms that the electrostatic attraction is the main driving force that inhibits the polyP activity. Figure 6.3 (a-c) illustrates the radial distribution function between the P atoms of polyP and the unprotonated amine N atoms (N0), the protonated connective amine N atoms (N1), the protonated terminal amine N atoms (N2), the O atoms of PEG-based chain, and the only O atom of hydroxide group (OH) in the PEG-based chain. It is clear that the electrostatic attraction induces a layered structure of the N1 and N2 atoms near the P atoms (red and blue curves in Figure 6.3a-3c) but N0 does not interact directly with the polyP and mostly resides in the second layer.    81 The hydrogen bonding between the H atoms on the protonated amine groups and O atoms on the phosphate groups also promotes the binding interaction between the (PEG)n-R1 and the polyP. Interestingly, the polyP has no significant interaction with the O atoms in PEG-based chain as no layered structure of O atoms formed around the polyP (magenta curve), suggesting that this hydrophilic interaction is not strong enough to promote the association of the (PEG)n-R1 to the polyP. However, the hydroxyl O atom (OH) strongly interact with the polyP as they can be easily found in the first solving shell of the P atoms. The strong interaction between the P atoms and the hydroxyl O atom of the (PEG)n-R1 mainly stems from the hydrogen bonding between hydroxide H atoms and the O atoms of the phosphate groups in the polyP. Therefore, hydrogen bonding facilitates thwarting of the prothrombotic activity of polyP.  Headgroup effect. Our simulations indicate that increasing the number of the charged tertiary amine groups in the headgroup strengthens the binding to polyP. Figure 6.4 shows the binding free energies of (PEG)12-Ri with three different headgroups R1, R2, and R3, as shown in Figure 6.1c, 6.1d, and 6.1e, respectively. Both R1 and R2 have a net charge of +3 but the unprotonated amine group is removed form R2. Therefore, R2 has slightly higher charge density than R1. On the other hand, R3 has a net charge of +6. Figure 6.4 shows that the binding free energy is almost the same (~ -7 KJ/mol) for (PEG)12-R1 and (PEG)12-R2. (PEG)12-R2 has a slightly greater binding affinity to the polyP because of its higher charge density in the headgroup. On the other hand, R3 has a much higher affinity to the polyP (~-50 KJ/mol) because of its significantly higher net charge. The equilibrium S number presented in Table 6.3 shows that there is no meaningful difference between (PEG)12-R1 and (PEG)12-R2 as both S numbers are around 8. Although the ratio of the number of (PEG)12-Ri participating in the polyP inhibition to the total number of (PEG)12-Ri in the system is around 0.8, the higher binding affinity of (PEG)12-R3 results in a   82 higher residence time and stability in the (PEG)n-R3/polyP complex; therefore it is more effective towards inhibiting the polyP.                                    Figure 6.3. Radial distribution functions of the unprotonated amine N atoms (N0), the protonated connective amine N atom (N1), the protonated terminal amine N atom (N2), O atoms of PEG-based chain, and the only O atom of hydroxyl group (OH) with respect to the P atoms of polyP. (a) (PEG)8-R1, (b) (PEG)12-R1, (c) (PEG)24-R1. The radial distribution function was obtained from 10 ns of classical MD simulations in the NPT ensemble. P atoms were the reference point of the radial distribution function.   83   Figure 6.4. Binding free energy between the (PEG)12-Ri and the polyP. The distance is defined between the center of mass of the polyP and the center of mass of (PEG)12-Ri headgroups. The binding free energy profile was obtained by calculating the averaged binding free energy of (PEG)12-Ri molecules in the system. The error bar is the standard deviation.   The simulations also show that a higher charge density in the headgroup leads to more domination of columbic attraction over the hydrogen bonding and hydrophilic interactions. Figure 6.5a and 6.5b demonstrate the radial distribution functions of N0, N1, N2, O, and the O atom of OH for (PEG)12-R2 and (PEG)12-R3 with respect to the P atoms of polyP. Similar to previous cases, while N1 and N2 atoms form layered structure around the P atoms because of the electrostatic affinity, N0 atoms on the (PEG)12-R3 (Figure 6.5b, green band) are not directly involved in the interaction with the polyP as it mostly settles in the second solvation shell. In contrast to the previous cases in Figure 6.3, the higher charge density in the headgroups of (PEG)12-R3 disturbs the hydrogen bond formations between the OH group and the P atoms as less number of hydroxyl H atoms approach to the P atoms  (black curve in Figure 6.5 a-b). The radial distribution function also indicates that changing in the ligand charge density does not   84 promote the hydrophilic interaction between O atoms of PEG-based chain and P atoms, confirming that the PEG tail length play a little role in inhibiting the polyP. The key role of the PEG tail is likely to reduce the drug toxicity rather than inhibiting the polyP.  Figure 6.5. Radial distribution functions of the unprotonated amine N atoms (N0), the protonated connective amine N atom  (N1), the protonated terminal amine N atom  (N2), O atoms of PEG-based chain, and the only O atom of hydroxide group (OH) with respect to the P atoms of polyP. (a) (PEG)12-R2, (b) (PEG)12-R3. The radial distribution function was obtained from 10 ns of classical MD simulations in the NPT ensemble. The P atom is the reference point of the radial distribution function.  We have also carried out microsecond-scale CG-MD simulations to show the process of the polyP inhibition for the systems listed in Table 6.2. Initially the (PEG)24-R1 form aggregates mostly with the PEG in the core and the hydrophilic R1 groups pointing toward water. Then the aggregates approach the polyP and sandwich the polyP to form a complex, as shown in Figure 6.6. In this complex, the PEG tails are in the outer layer, which may provide a shield preventing the complex from binding to other proteins or membranes as PEG is known for its antifouling properties. Therefore, the PEG tails most likely make the drug more hemocompatible.   85  Figure 6.6. Final snapshot of a microsecond CGMD simulation for polyPs with 28 (a), 61 (b), 115 (c), and 133 (d) phosphate monomers. Details of the system are listed in Table 6.2. Color codes for the beads: MARTINI polarizable water (green), PEG monomer (red), protonated connective and terminal amine groups (dark blue), unprotonated amine group (light blue), phosphate group (BP) (yellow), Na+ (magenta), and Cl- (black). The visualization was made by VMD computer program100.  Effect of PolyP chain length. Our simulations indicate that the chain length of polyP does not significantly affect the binding efficiency. To test if the chain length of the polyP affects the efficiency of the (PEG)n-Ri, we calculated the number of protonated amine groups approaching the polyP to form the complex. We assumed that the CG protonated amine form complexes with the CG phosphate, if the amine beads reside within a cutoff distance from phosphate beads. The cutoff distance for each system was determined by the first minimum of the radial distribution   86 function shown in Figure B.20a and B.20c. Figure 6.7 shows the fraction of protonated amine groups coupled to the polyP with various chain length as a function of time. For all cases, the portion of (PEG)24-R1 involved in inactivating the polyP is around 0.8. It indicates that the polyP chain length does not affect the (PEG)n-Ri binding efficiency. In addition, further analysis of the radial distribution function (Figure B.20) of phosphate particles with unprotonated amine and PEG beads of (PEG)24-R1 confirms that the length of polyP chain does not alter the nature of interactions between the (PEG)n-Ri and polyP.  Figure 6.7. Calculated fraction of protonated amine beads involved in the complex formation with polyPs with 28 (a), 61 (b), 115 (c), and 133 (d) phosphate monomers. The details of the systems are described in Table 6.2. Np(t) is the calculated number of protonated amine beads interacting with the phosphate beads. N is the total number of protonated amine beads in each system.  6.4 Conclusions To provide a molecular-level understanding on the design of cationic inhibitor for polyP, we used MD simulations to investigate the interaction between polyP and (PEG)n-Ri, a model compound containing a PEG-based tail attached to various cationic headgroups.  The binding free energy analysis indicated that PEG length does not have any impact on the interaction   87 between the (PEG)n-R1 and polyP.  Similarly, CG-MD simulations revealed that the binding efficiency of the (PEG)24-R1 remained intact against the various chain lengths of polyP. However, higher charge density on the headgroup strengthens the (PEG)12-Ri avidity of polyP binding, suggesting that the columbic interaction is the main driving force for polyP inhibition.                      88 Chapter 7: Conclusions and future work  In this dissertation, two major subjects have been investigated using MD simulations. The first subject included interactions between water/non-ionic surfactant, water/zwitterionic surfactant, and water/anionic surfactant/anionic polyelectrolytes on the water surface. The second subject devoted to studying the complex formation between oppositely charged macromolecules in the bulk liquid of water.  MD simulations and SFG vibrational spectroscopy were applied to study the interaction between water and non-ionic C12E4 surfactant on the water surface. It was revealed that the behavior of C12E4 at its CMC was more anionic-like, even though the surfactant was overall neutral. MD simulations showed that the surfactant increased the depth of the surface anisotropic layer from 0.31 to 1.82 nm. Additionally, the average number of hydrogen bonds per water molecule increased from 2.7 to 3.1. It was found that the H and O atoms of water molecules near the surfactant headgroup were confined in well-separated shells. On the other hand, the O and C atoms in the head group of the surfactant are surrounded by the water H atoms instead of the O atoms, indicating that the negatively charged O atoms of the surfactant play a more important role than the C atoms in determining the orientation of water. The simulation also showed that the orientation of surface water molecules was flipped in the presence of the surfactant, which was consistent with the observed SFG spectra. A combined study using surface tension, SFG vibrational spectroscopy, and MD simulations were also carried out to investigate the interaction between a zwitterionic surfactant, DDAPS, and water on the water surface. The SFG Im(χ(2)) spectra showed that the interaction between DDAPS and water was different from those between biologically-relevant zwitterionic   89 phospholipids and water. While zwitterionic phospholipids were found to be anionic-like and flipped water molecules with their OHs pointing toward the air, DDAPS oriented water molecules with their OHs mostly pointing toward the liquid water. The MD simulation showed that the head groups of DDPAS were nearly parallel to the water surface. When the surface coverage of DDPAS was increased, the averaged tilting angle of DDPAS’s tails decreased, but it had little effect on the orientation of the head group. The sulfobetaine zwitterionic surfactant was found to be more cationic-like because the positively charged group was more capable of orienting interfacial water.  The mechanism of complex formation between surfactants and polyelectrolytes of the same charge on water surface was studied using MD simulations and SFG vibrational spectroscopy. It was shown that in the presence of the excess cations, stable complex formation between the anionic HPAM and anionic SDS become feasible on the water surface, while without any excess cations, SDS pushed HPAM into the bulk regions as a result of electrostatic repulsion. Excess Na+ ions in the solution created the charge screening effect, which allowed HPAM to weakly interact with SDS via hydrogen bonds. In the presence of divalent Ca2+ ions, the surfactant and the polymer is strongly coupled by forming Ca2+ ion bridges and hydrogen bonds. The simulations revealed that the presence of Ca2+ ions creates a steep binding energy of ~30 KJ/mol near the water surface. These results were qualitatively verified using SFG vibrational spectroscopy.  The possible routes of improvement in the design of (PEG)n-HBG were investigated using MD simulations to achieve an effective structure, which decreases the thrombosis by increasing the polyP binding and inhibition efficiency. For this purpose, the effects of the PEG chain length,   90 the charge densities of the HBG, and the polyP chain length were examined. While molecular dynamics (MD) simulation can provide molecule-level information, the time scale required to simulate these large biomacromolecules makes classical MD simulation impractical. To overcome this challenge, we employed metadynamics simulations with both the all-atom and coarse-grained force fields. The force field parameters for polyethylene glycol (PEG) conjugated HBGs and polyP were developed to carry out coarse-grained MD simulations, which enabled simulations of these large biomacromolecules in a reasonable time scale. It was found that PEG length does not have any impact on the interaction between the (PEG)n-HBG and polyP except that it made the drug hemocompatible by producing a shield, which prevents the cationic drugs from binding to other negatively charged biomolecules. On the other hand, increasing the number of the charged tertiary amine groups in HBG strengthens the (PEG)n-HBG binding to polyP, suggesting that the columbic energetic is the main driving force to attenuate thrombosis. Finally, coarse-grained MD simulations revealed that the antithrombotic efficiency of the drug remains intact against the various chain lengths of polyP. • Recommendations for the future work: 1. The results of MD simulations and SFG observations were indirectly linked to each other in order to provide the molecular level information for studying the water surface chemistry. In the other word, the experimental observations were qualitatively described with MD simulations. Therefore, for the future studies on the water surface, it is worth simulating and calculating the SFG spectra directly with MD simulations to gain more detailed and accurate information. However, quantitative analysis of SFG spectra that directly compares to the MD simulation is very challenging, as it requires correct calculation of the dipole moments, polarizabilities, and vibrational frequencies. An accurate simulation of the SFG spectra will   91 require polarizable force fields allowing variations of the partial charges for molecules during the simulation. 2. The binding free energy of (PEG)n-HBG to polyP is yet required to experimentally obtained to validate the MD simulations. An alternative way to validate the MD results is to use different force fields for simulations and comparing the outcomes. However, this is challenging, as the current well-known force fields might not have all the required parameters for all molecules. Therefore, one needs to develop the required non-bonded and bonded parameters for polyP and (PEG)n-HBG for the full-atomistic simulations.  3. 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(Retrieval date: 01/08/2016)   103 224. Bulacu, M.; Goga, N.; Zhao, W.; Rossi, G.; Monticelli, L.; Periole, X.; Tieleman, D. P.; Marrink, S. J., Improved Angle Potentials for Coarse-Grained Molecular Dynamics Simulations. J Chem Theory Comput 2013, 9, 3282-92.        104 Appendices  Appendix A  Supplementary information- interactions of sulfobetaine zwitterionic surfactants with water on water surface Based on the previous work by Shen et al.,91 the partial charges for atoms in the tail of DDPAS were 0.06 for H atoms, -0.18 for the C atom in the CH3 group, and -0.12 for C atoms in CH2 groups. The partial charges for atoms in the head group are shown in Figure A.1.   Figure A.1. Calculated partial charges of DDPAS head group.       105 Table A.1. Bond stretching parameters. Bond Kstr (Kj mol-1nm-2) b0 (nm) C-C91 178619.10 0.15333 C-H91 301481.97 0.10967 C-N134 245680.00 0.14990 C-S134 212550.00 0.17740 S-O91 447625.07 0.14861   Table A.2. Angle bending parameters. Angle Kbend(Kj mol-1 rad-2) 𝜃!  (deg) O-S-O91 692.33 116.44 O-S-C134 557.23 108.32 S-C-H134 367.02 108.11 H-C-H91 298.29 106.68 H-C-C91 381.08 110.13 C-C-C91 521.06 114.18 C-C-N134 539.32 114.32 H-C-N134 410.20 107.91 C-N-C134 525.85 110.64      106  Table A.3. The torsion parameters. Torsions ϕ!"#$ deg ,K!"#$ Kj mol!! ,multiplicity O-S-C-C134 0.00 0.60436 3 O-S-C-H134 0.00 0.60436 3 C-C-C-N134 0.00 0.65084 3 C-N-C-H134 0.00 0.65084 3 H-C-C-N134 0.00 0.65084 3 C-N-C-C134 0.00 0.65084 3 H-C-C-H91 3.40 1.22 -2.14 -2.49 0.00 0.00 H-C-C-C91 1.22 3.42 -1.49 -3.14 0.00 0.00 C-C-C-C91 0.12 3.88 -0.97 -3.02 0.00 0.00  Table A.4. The Lennard- Jones parameters. L-J parameters  (nm) (Kj/mol) N134 0.3250 0.71128 S91 0.3546 1.04600 O91 0.2850 0.87864 C (CH2)91 0.3523 0.27614 C (CH3)91 0.3523 0.26359 H91 0.2434 0.12510 OW-C (CH2)91 0.3341 0.45324 OW-C (CH3)91 0.3344 0.44282 σ ε  107  Appendix B  Supplementary information-design of polyphosphate inhibitors: a molecular dynamics investigation on polyethylene-glycol-linked cationic binding groups             Table B.1. Calculated partial charges of atoms in polyP in the different groups and segments as indicated in Figure B.1.     Atom Charge Segment Atom Charge Segment Atom Charge Segment O- -0.8892 1 O- -0.8860 1 O- -0.8860 1 P 1.2033 2 P 1.44350 1 P 1.4435 1 O -0.8892 2 O -0.8860 1 O -0.8860 1 O- -0.8892 2 O -0.6984 2 O -0.6974 2 O -0.5357 3 - - - - - - 1 2 3 1 2 1 2 Figure B.1. Molecular structure of polyphosphate (polyP). PolyP is divided into several identical groups on the basis of their structural symmetricity shown by different colors (red, blue, and orange), as described in Table B.1. Each functional group is also divided into segments labeled with numbers.   108  Figure B.2. Molecular structure of the PEG-based tail. PEG is divided into three groups shown by red, blue, and green color as described in Table B.2. Each group is then divided into segments labeled with numbers.    Table B.2. Calculated partial charges of the PEG atoms in different groups and segments as indicated in Figure B.2. Atom Charge Segment Atom Charge Segment Atom Charge Segment H 0.0303 1 O -0.6213 1 O -0.6202 1 H 0.0303 1 C 0.3524 2 C 0.3871 2 H 0.0303 1 H -0.0175 2 H -0.0107 2 C 0.1277 1 H -0.0175 2 H -0.0107 2 O -0.4540 2 C 0.3295 3 C 0.2685 3 C 0.1912 3 H -0.0128 3 H -0.0078 3 H 0.0120 3 H -0.0120 3 O -0.7525 4 H 0.0120 3 - - - H 0.4531 4 C 0.3610 4 - - - - - - H -0.0238 4 - - - - - - H -0.0238 4 - - - - - -        1 2 3 4 1 2 3 1 2 3 4   109  Figure B.3. Molecular structure of the HBG R1. R1 is divided into the several identical groups on the basis of their structural symmetricity and shown in red, blue, and green as described in Table B.3. Each group is then divided into segments labeled with numbers.   Table B.3. Calculated partial charges of R1 atoms in the different groups and segments as indicated in the Figure B.3. Atom Charge Segment Atom Charge Segment Atom Charge Segment C -0.3123 1 C -0.1232 1 C 0.2203 1 H 0.1891 1 H 0.1891 1 H 0.0497 1 H 0.1891 1 H 0.1891 1 H 0.0497 1 H 0.1891 1 N+ -0.0250 2 N -0.5148 2 N+ -0.0250 2 H 0.3592 2 C 0.2203 3 H 0.3593 2 C -0.4310 3 H 0.0497 3 C -0.4319 3 H 0.2197 3 H 0.0497 3 H 0.2197 3 H 0.2197 3 C 0.2203 4 H 0.2197 3 C -0.3123 4 H 0.0497 4 C -0.3123 4 H 0.1891 4 H 0.0497 4 H 0.1891 4 H 0.1891 4 - - - H 0.1891 4 H 0.1891 4 - - - H 0.1891 4 - - - - - -  4 1 2 3 1 2 3 4 1 2 3 4   110  Figure B.4. Molecular structure of the HBG R2. R2 is divided into the several identical groups on the basis of their structural symmetricity and shown in red, blue, and green as described in Table B.4. Each group is then divided into segments labeled with numbers.  Table B.4. Calculated partial charges of R2 atoms in the different groups and segments as indicated in the Figure B.4. Atom Charge Segment Atom Charge Segment C -0.004104 1 C -0.316573 1 H 0.123293 1 H 0.202375 1 H 0.123293 1 H 0.202375 1 N+ -0.060385 2 H 0.202375 1 H 0.318753 2 C -0.316573 2 C -0.181838 3 H 0.202375 2 H 0.155073 3 H 0.202375 2 H 0.155073 3 H 0.202375 2 C 0.010109 4 N+ -0.056462 3 H 0.067558 4 H 0.378825 3 H 0.067558 4 C -0.397737 4 C -0.156478 5 H 0.222334 4 H 0.119408 5 H 0.222334 4 H 0.119408 5 - - - C -0.004104 6 - - - H 0.123293 6 - - - H 0.123293 6 - - - 1	2	3	4	1	2	3	4	 5	6	  111   Figure B.5. Molecular structure of the HBG R3. R3 is divided into the several identical groups on the basis of their structural symmetricity and shown in red, blue, and green as described in Table B.5. Each group is then divided into segments labeled with numbers.   Table B.5. Calculated partial charges of R3 atoms in the different groups and segments as indicated in Figure B.5. Atom Charge Segment Atom Charge Segment Atom Charge Segment C -0.160925 1 C -0.058773 1 C -0.299274 1 H 0.103121 1 H 0.136969 1 H 0.203994 1 H 0.103121 1 H 0.136969 1 H 0.203994 1 C 0.051782 2 N+ 0.011677 2 H 0.203994 1 H 0.027503 2 H 0.338113 2 C -0.299274 2 H 0.027503 2 C -0.274243 3 H 0.203994 2 C -0.216138 3 H 0.181743 3 H 0.203994 2 H 0.107176 3 H 0.181743 3 H 0.203994 2 H 0.107176 3 C -0.058773 4 N+ -0.062337 3 C 0.100094 4 H 0.136969 4 H 0.377527 3 H 0.060587 4 H 0.136969 4 C -0.376338 4 H 0.060587 4 - - - H 0.209086 4 C 0.100094 5 - - - H 0.209086 4 H 0.060587 5 - - - - - - H 0.060587 5 - - - - - - N -0.261342 6 - - - - - -   1	2	3	4	 1	2	3	4	1	2	3	4	5	6	  112   Figure B.6. Definition of the coarse grained (CG) sites on (a) polyP, (b) R1, (c) R2, and (d) R3 structure to calculate the Debye-Huckle (DH) energy based on eq. (6.1).    Figure B.7. Free energy as a function of DH energy for the systems I to V. 180160140120100806040200Free energy (KJ/mol)-800 -600 -400 -200 0DH (KJ/mol) (PEG)8  -R1 (PEG)12-R1 (PEG)24-R1 (PEG)12-R2 (PEG)12-R3	 	 	 	 	 	 	 	 	 	 	 	 	 (a) (b) (c) (d) 	 	 	 	 	 	 	      113    Figure B.8. Free energy as a function of stoichiometry (S) number for the systems I to V.   B.1 Coarse grained force field development To develop the coarse grained (CG) force fields for (PEG)24-R1 and PolyP, we followed the MARTINI200 strategy, where every three or four heavy atoms are mapped into one bead. The all-atom (AA) to CG mapping of (PEG)24-R1 and PolyP are illustrated in Figure B9 and Figure B10, respectively. The coarse graining of the headgroup (R1) and PolyP was done in a way that the symmetricity of the structures will not be disturbed. For this purpose, we had to choose 5:1 bead mapping in the initial and terminal phosphate (PO4-) groups and 3:1 bead mapping for the middle (PO2-) for the polyP.  150100500Free energy (KJ/mol)1086420S number (PEG)8  -R1 (PEG)12-R1 (PEG)24-R1 (PEG)12-R2 (PEG)12-R31086420-2-4Free energy (KJ/mol)1086420S number  114 The interactions between the beads are described using a combination of bonded potentials including bond stretching, angle bending, and torsions with different functional forms as presented in Table B6. To parameterize the bonded interactions, we performed a 200 ns MD simulation using the Generalized Amber force field (GAFF)133 for the system I, in an NVT ensemble at the 310 K with the same procedure and conditions presented in the paper and Table B1. By coarse graining the (PEG)24-R1 and polyP in different trajectories in accord with the Figure B9-10, the bond, angle, and dihedral distributions were determined as illustrated in Figures B11-16. The same type of distributions can be obtained for the interactions between the CG particles by performing a 50 ns CG-MD simulation at 310K with the same procedure and conditions represented in the paper and Table B.2. The parameters for the CG potentials were obtained by matching the bond, angle, and dihedral distributions resulted from the CG-MD simulation to the corresponding distributions from the AA-MD simulations. Table B6 represents the obtained parameters for describing the behavior of the drug and polyP, respectively. Note that, the CG parameters describing the interactions in the PEG tail were borrowed from the Lee’s work210 with which they are able to predict the radius of gyration of PEG polymer accurately. The non-bonded interactions are described using the Lennard-Jonnes and the Columbic potentials. The parameters of the non-bonded interactions are determined based on the chemical nature of the beads. Each bead in terms of the chemical nature are categorized into four major types of interaction sites: polar (P), non-polar (N), apolar (C), and charged (Q). To represent an accurate chemical nature of the underlying atomic structure, each particle type is divided into several subtypes in terms of capability of hydrogen bonding, and the degree of polarity.200 The non-bonded parameters for each CG particle were adapted from “martini_v2.2P.itp” 223. The adapted non-bonded parameters were designed to interact with the MARTINI polarized water   115 model.220 Table B7 represents the types of CG particles along with their charges used in this study. To validate the developed CG force field, we calculated the binding free energy between (PEG)24-R1 and polyP and compared it to the one obtained from AA-MD simulation. The parallel tempering metadynamics in a well-tempered ensemble (PTMetaD-WTE)65, 70, 175, 195 was used to calculate the binding free energy. One polyP with 28 beads along with 10 CG (PEG)24-R1 were randomly inserted into the simulation box. The MARTINI polarizable water model (PW)220 was used to describe the water behavior. In addition, 0.1 M of NaCl was also randomly placed into the solution. Before starting the dynamics, 30000 steps of the steep-descent energy minimization were performed to correct the positions of the beads. Then, a short 4-ns NPT simulation with a time step of 2 fs was performed to relax the CG particles. The dynamics were followed by running a 20 ns NPT simulation with a time step of 8 fs such that the temperature and pressure reached 310 K and 1 bar, respectively.  All dynamics were performed using the GROMACS 5.1.4 GPU computation algorithm63, 168, 221. The input options for implementing the simulations were mainly adapted from the “martini_v2.x_new.mdp”222, with the following modifications. The neighbor list was updated every 40 steps. The temperature of the polyP/drugs/ions and water was separately maintained at 310 K using the V-rescale thermostat with a temperature constant of 0.3 ps.138 The isotropic pressure coupling using Parrinello-Rahman barostat58 with a pressure constant of 12.0 ps was used to maintain the system pressure at 1 bar with the compressibility of 3.0 × 10-4 bar-1. The Lennard-Jones interactions were truncated at a cutoff radius of 1.1 nm. The potentials were modified by the potential-shift-Verlet. Periodic boundary conditions were applied to all three directions. The electrostatic interactions were treated by the reaction-field approach with a cutoff radius of 1.1 nm. The MARTINI   116 polarizable water bonds were constrained using the P-LINCS algorithm174 with a LINCS order of 4.  To start the PTMetad-WTE simulations, the last trajectory of the NPT simulation was chosen as an initial configuration of 6 different replicas at various temperatures, which were distributed exponentially217 in the range of 310-460 K to achieve an efficient exchange rate between replicas. We performed a 10-ns MD simulation in the NVT ensemble so that each replica reached its specified temperature. Afterwards, a 20-ns well-tempered metadynamics simulation was carried out in a well-tempered ensemble195-196 to achieve an optimum exchange rate of 30-35% between the replicas. The bias factor of 60 was deposited with a Gaussian width of 250 KJ/mol, an initial Gaussian amplitude of 4.18 KJ/mol, and a deposition rate of 2 ps. The well-tempered metadynamics simulations were implemented using the PLUMED 269. However, during the PTMetaD-WTE simulations, the Gaussian was deposited every 240 ps. The Debye-Huckel (DH) energy219 (eq. (6.1)) between the phosphate beads of polyP and the charged beads of R1 was actively biased during the production run with a salt ionic strength of 0.1 M and water relative dielectric constant of 75 in order to compare with the DH energy obtained from the AA-MD simulations.  In addition, the drug binding stoichiometry (S) (see eq. (6.2)) number around polyP was also biased during the PTMetaD-WTE with the tuning parameters of n, m, and r0 equal to 12, 24, and 1.5 nm, respectively. The bias factor for all systems was 20. The Gaussian bias was deposited every 1.6 ps with an initial amplitude of 2 KJ/mol, and a width of 0.2 KJ/mol. The PTMetaD-WTE simulation was performed for 4 s using the PLUMED 269. At the end, since the DH energy profile was less informative about the binding free energy, we implemented the reweighting176 algorithm on the resulted PTMetaD-WTE trajectories to calculate the binding free µ  117 energy of the drug to the polyP. Figure B.17 and Figure B.18 show that variation of the free energy with the DH energy and the S number are fairly comparable to those calculated from the AA-MD simulation. The reweighted binding free energies between (PEG)24-R1 and polyP obtained from the GAFF and MARTINI force field are in good agreement with each other, as indicated in Figure B.19.     Figure B.9. The MARTINI CG sites and their labeling for (a) PEG and (b) R1. The P denotes the attachment location of PEG-based tail and the headgroup. (c) The CG structure of (PEG)24-R1.     	 	 	 	 (a) 	 	 	 	 BC BH1 BH3 BH3 BCE BC BH2 (b) (c) BCE BH2 BH3 BH3 BH1 BC BC BC   118                       BP BP BP BP BP BP SBP BP BP 	 	 	 	 	 	 BP BP SBP BP BP BP (a) (b) Figure B.10. (a) The MARTINI CG sites and their labeling for (a) polyP and (b) the CG structure of polyP.   119   Table 7.6. The MARTINI CG bonded potentials and parameters for polyP and (PEG)24-R1. Bead Type Functional form Parameters 𝐵𝐶𝐸 − 𝐵𝐻! Bond   𝐵𝐻! − 𝐵𝐻! Bond   𝐵𝐻! − 𝐵𝐻! Bond   𝐵𝑃 − 𝐵𝑃 (𝑆𝐵𝑃) Bond   𝐵𝐶 − 𝐵𝐶𝐸 − 𝐵𝐻! Angle   𝐵𝐶𝐸 − 𝐵𝐻! − 𝐵𝐻! Angle   𝐵𝐻! − 𝐵𝐻! − 𝐵𝐻! Angle  *  𝐵𝐻! − 𝐵𝐻! − 𝐵𝐻! Angle   𝐵𝑃 − 𝐵𝑃(𝑆𝐵𝑃) − 𝐵𝑃(𝑆𝐵𝑃) Angle   𝐵𝐶 − 𝐵𝐶 − 𝐵𝐶𝐸 − 𝐵𝐻! Dihedral   𝐵𝐶 − 𝐵𝐶𝐸 − 𝐵𝐻! − 𝐵𝐻! Dihedral   𝐵𝐶𝐸 − 𝐵𝐻! − 𝐵𝐻! − 𝐵𝐻! Dihedral   𝐵𝑃 − 𝐵𝑃 − 𝐵𝑃(𝑆𝐵𝑃) −𝐵𝑃(𝑆𝐵𝑃)** Dihedral   * Ref 224  ** The initial and terminal phosphate beads were not considered for the dihedral interactions.      Vb(rij ) =12 kb(rij − b)2 kb = 22000Kjmol.nm2 ;b = 0.27nmVb(rij ) =12 kb(rij − b)2 kb = 8000Kjmol.nm2 ;b = 0.35nmVb(rij ) =12 kb(rij − b)2 kb =17000Kjmol.nm2 ;b = 0.39nmVb(rij ) =12 kb(rij − b)2 kb =17000Kjmol.nm2 ;b = 0.27nmVa (θ ) =12 kθ(cosθ − cosθ0 )2sin2θ kθ = 20Kjmol ;θ0 =130°Va (θ ) =12 kθ(cosθ − cosθ0 )2sin2θ kθ = 5Kjmol ;θ0 = 45°Va (θ ) =12 kθ(cosθ − cosθ0 )2sin2θ kθ =10Kjmol ;θ0 = 86°Va (θ ) =12 kθ (cosθ − cosθ0 )2 kθ = 65Kjmol ;θ0 =112°Va (θ ) =12 kθ (θ −θ0 )2 kθ = 500Kjmol.rad 2 ;θ0 = 99°Vd (φ) = kφ (1+ cos(φ −φs )) kφ = 3 Kjmol ;φs = −100°Vd (φ) = kφ (1+ cos(φ −φs )) kφ = 6 Kjmol ;φs = 60°Vd (φ) = kφ (1+ cos(φ −φs )) kφ = 3 Kjmol ;φs = 50°Vd (φ) = kφ (1+ cos(φ −φs )) kφ = 4.5 Kjmol ;φs = 0°  120     Figure B.11. Bond stretching probability profiles for AA and CG for (a) 𝐵𝐶𝐸 − 𝐵𝐻!, (b) 𝐵𝐻! − 𝐵𝐻!, and (C) 𝐵𝐻! − 𝐵𝐻!.        302520151050Normalized probability0.50.40.30.20.1Bond (nm) AA CG403020100Normalized probability0.50.40.30.20.1Bond (nm) AA CG6050403020100Normalized probability0.50.40.30.20.1Bond (nm) AA CG(a) (c) (b)   121    Figure B.12. Angular bending probability profiles for AA and CG for (a) 𝐵𝐶 − 𝐵𝐶𝐸 − 𝐵𝐻!, (b) 𝐵𝐶𝐸 − 𝐵𝐻! −𝐵𝐻!, and (C) 𝐵𝐻! − 𝐵𝐻! − 𝐵𝐻!, and (d) 𝐵𝐻! − 𝐵𝐻! − 𝐵𝐻!.      0.140.120.100.080.060.040.020.00Normalized probability150140130120110Angle (degree) AA CG0.160.140.120.100.080.060.040.020.00Normalized probability14012010080Angle (degree) AA CG0.250.200.150.100.050.00Normalized probability13012011010090Angle (degree) AA CG0.160.140.120.100.080.060.040.020.00Normalized probability13012011010090Angle (degree) AA CG(a) (b) (c) (d)   122  Figure B.13. Torsional angle probability profiles for AA and CG for (a) 𝐵𝐶 − 𝐵𝐶 − 𝐵𝐶𝐸 − 𝐵𝐻!, (b) 𝐵𝐶 − 𝐵𝐶𝐸 −𝐵𝐻! − 𝐵𝐻!, and (C) 𝐵𝐶𝐸 − 𝐵𝐻! − 𝐵𝐻! − 𝐵𝐻!.         0.200.150.100.050Normalized probability100500-50Dihedral (degree) AA CG0.030.0250.020.0150.010.0050Normalized probabi li ty-150 -100 -50 0 50Dihedral (degree) AA CG(a) (b) (c) 0.030.0250.020.0150.010.0050Normalized probability-150 -100 -50 0 50Dihedral (degree) AA CG403020100Normalized probability0.50.40.30.20.1Bond (nm) AA CGFigure B.14. Bond stretching probability profiles for AA and CG for (a) 𝐵𝑃 − 𝐵𝑃 (𝑆𝐵𝑃).   123  Figure B.15. Angular bending probability profiles for AA and CG for (a) 𝐵𝑃 − 𝐵𝑃 𝑆𝐵𝑃 − 𝐵𝑃(𝑆𝐵𝑃).   Figure B.16. Torsional angle probability profiles for AA and CG for (a) 𝐵𝑃 − 𝐵𝑃 − 𝐵𝑃(𝑆𝐵𝑃) − 𝐵𝑃(𝑆𝐵𝑃).       0.60.50.40.30.20.10.0Normalized probabil ity1301201101009080Angle (degree) AA CG0.200.150.100.050Normalized probability6040200-20-40Dihedral (degree) AA CG  124   Table B.7. The types and charges of MARTINI CG beads for polyP and (PEG)24-R1. Bead Type Charge BC SN0 0 BCE SP2 0 BH1 SQd +1 BH2 N0 0 BH3 Qd +1 BP Qa -1 (-2)* SBP SQa -1 * The charge of initial and terminal BP (PO4- ) is -2. The charge of the rest BP (PO3-) is -1.  Figure B.17. Free energy as a function of the DH energy.  120100806040200Free energy (KJ/mol)-600 -500 -400 -300 -200 -100DH (KJ/ml) (PEG)24-R1 (CG) (PEG)24-R1 (AA)  125  Figure B.18. Free energy as a function of stoichiometry (S) number.    Figure B.19. Binding free energy between the (PEG)24-R1 and polyP. The distance is defined between the polyP center of mass and the center of mass of drug headgroups.      140120100806040200Free energy (KJ/mol)1086420S number (PEG)24-R1(CG) (PEG)24-R1(AA)80706050403020100-10Binding free energy (KJ/mol)543210Distance (nm) (PEG)24-R1 (CG) (PEG)24-R1 (AA)  126    Figure B.20. Radial distribution functions between BP (SBP) and (a) BH1, (b) BH2, (c) BH3, and (d) BC (BCE). BP beads were the reference points in all calculations.       120100806040200Radial distribution function2.01.51.00.50.0Distance (nm) 28   BP 61   BP 115 BP 133 BP400350300250200150100500Radial distribuiton function2.01.51.00.50.0Distance (nm) 28   BP 61   BP 115 BP 133 BP350300250200150100500Radial distribution function2.01.51.00.50.0Distance (nm) 28   BP 61   BP 115 BP  133 BP1086420Radial distribution function2.01.51.00.50.0Distance (nm) 28   BP 61   BP 115 BP 133 BP(a) (b) (c) 	 	 (d) 	 

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