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Water permeability of spider dragline silk by solid state NMR Li, Xiang 2005

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Water Permeability of Spider Dragline Silk Solid State N M R by Xiang Li B.Sc, Nankai University, P.R.China, 2002 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF Master of Science in The Faculty of Graduate Studies (Physics) The University Of British Columbia August 19, 2005 © Xiang Li 2005 11 Abstract The remarkable mechanical properties of spider dragline silk can be radically altered by the addition of water. Unconstrained spider silk fibers contract to about half of their original length when immersed in water, a phenomenon named supercontraction. With an eye to-wards understanding supercontraction and facilitating the study of the permeability of other molecules into silk, we use solid-state N M R to investigate the penetration of deuterium oxide into spider dragline silk. The quadrupolar echo N M R experiments are used to examine the hydrogen-deuterium exchange process in a silk sample that has been soaked in deuterium oxide (D 2 0) and then dried. 1 3 C - D Rotational Echo Double Resonance (REDOR) N M R experiments are performed to quantify water permeability of silk's different structural re-gions. In contrast to the indications from previous studies by X-ray diffraction and NMR, our study reveals that the P-sheet crystalline regions of silk are accessible to water. We also show that the correlation between isotope exchange rate and molecular structure, usu-ally found for proteins in solutions and crystal lattices, also holds true for the insoluble silk proteins; the exchange rate is smaller in the /3-sheet crystalline regions than in the rest of the silk. We further found that in the interphase regions of silk, which connect the /3-sheet with the amorphous regions, water permeation is restricted, a reflection of rigid molecular structure or strong hydrogen-bonding in those regions. iii Contents Abstract ii Contents iii List of Tables I . . . v List of Figures vi 1 Introduction 1 2 Nuclear Magnetic Resonance 3 2.1 Zeeman Interaction 3 2.2 Equation of Motion 4 2.3 Relaxation • 5 2.4 The Density Matrix 6 2.5 Pulsed Nuclear Magnetic Resonance 7 2.6 Spin Echoes 9 2.6.1 Classical Description 10 2.6.2 Quantum Mechanical Description 11 2.7 N M R Interactions 12 2.7.1 Chemical Shift Interaction 12 2.7.2 Dipolar Interaction . 13 2.7.3 Quadrupolar Interaction 14 2.8 High Resolution Solid-State N M R 16 2.8.1 Magic Angle Spinning \ . 16 2.8.2 Decoupling . .' . 17 2.8.3 Cross Polarization 18 2.9 REDOR 19 3 Silk Background 22 3.1 Silk Composition 22 3.2 Primary Structure : • • • 22 3.3 Secondary Structure 24 3.4 Water-induced Protein Dynamics 27 4 Silk Permeability: Hydrogen-Deuterium Exchange 29 4.1 Experimental 29 4.2 Deuterium Spectrum 29 Contents iv 4.3 Hydrogen-Deuterium Exchange in Silk 30 4.3.1 Dynamical Processes and Exchange Model 30 4.3.2 Exchange Rates . K : . : . 33 4.4 Discussion 34 5 1 3 C - D REDOR: Permeability of Different Structural Regions 36 5.1 Experimental . 37 5.2 Initial Analysis 38 5.2.1 Gaussian Description 38 5.2.2 Probability Description 39 5.3 Simulation 42 5.3.1 Approximation 42 5.3.2 Program and Parameters 42 5.3.3 Simulated REDOR Dephasing Curves 42 5.4 Result: Alanine . 43 5.5 Result: Glycine :... . , 45 5.6 Discussion . . 49 5.7 Conclusions 51 6 Summary and Recommendation 53 Bibliography . 55 A SIMPSON Simulation of Three-Coupling REDOR Dephasing Curve . . 58 B Fitting Two-Component REDOR Data to One-Component R E D O R func-tion 61 V List o f Tables 2.1 The magnitudes of internal interactions 12 3.1 Dynamics of different amino acids in wet silk 27 3.2 Fractions of different amino acids in 0-sheet, amorphous and interphase regions. 28 5.1 Seven different kinds of neighboring environment of a C Q in /3-sheets and the probability of being in each of them. . 41 5.2 Chemical shift information for alanine C Q and glycine C a . 42 5.3 Alanine C a : best fit fs values for different soaking times . . . 45 5.4 Glycine Ca: best fit fj + a values for different soaking times 49 5.5 REDOR results for the deuterated silk sample mentioned in Chapter Four. . 51 5 vi List of Figures 2.1 Zeeman interaction 4 2.2 Evolution of a magnetic moment in a magnetic field. . . • 5 2.3 Effective field in the rotating frame 8 2.4 On-resonance excitation. 9 2.5 Spin-echo pulse sequence 10 2.6 Evolution of magnetization under the spin-echo pulse sequence 10 2.7 Dipolar interaction 14 2.8 Effect of quadrupolar interaction for spin-1. . . 16 2.9 Deuterium resonance frequencies 17 2.10 1 3 C spectrum of our silk sample under magic angle spinning 18 2.11 Cross polarization pulse sequence 19 2.12 1 3 C - 1 5 N REDOR pulse sequence 20 2.13 Complications in REDOR 20 3.1 General structure of most amino acids 22 3.2 Side chain structures of the seven most abundant amino acids in silk 23 3.3 Peptide bond formation : 23 3.4 Amino acid sequence of silk 24 3.5 Examples of secondary structures • • • • 25 3.6 Silk structure model 26 3.7 Si-helical structure 26 3.8 Model of the dynamics and phase structure of silk 27 4.1 Quadrupolar Echo pulse sequence. . . : 30 4.2 Deuterium spectrum of our silk sample. 31 4.3 Change of deuterium spectrum with exposure time (1) 32 4.4 Change of deuterium spectrum with exposure time (2) 32 4.5 Hydrogen-deuterium exchange model. 33 4.6 Changes of deuterium content in three pools with exposure time 34 5.1 Part of the 1 3 C C P / M A S chemical shift spectrum of silk 36 5.2 The REDOR pulse sequence 37 5.3 Many types of possible neighboring environment 38 5.4 Amide hydrogen sites in the neighborhood of an alanine C Q present in /3-sheets. 39 5.5 Silk sample soaked in D 2 0 for 16 days: alanine C a REDOR data and the best fit to a Gaussian function 40 5.6 C a and its three nearest deuterium neighbors on an alanine antiparallel B-sheet 41 List of Figures vii 5.7 Examples of the principle axis systems of interaction tensors 43 5.8 Simulated REDOR dephasing curves: (jjf)A, ( | f ) and 44 5.9 Simulated REDOR dephasing curves: {W)AC A N D ( ^ ) B C 4 4 5.10 Simulated REDOR dephasing curve: ( ^ ) 45 5.11 Silk sample soaked in D 2 0 for 16 days: alanine C Q REDOR data and best fits. 46 5.12 Silk samples soaked in D 2 O for 3 hours and 2 minutes: alanine C a REDOR data and best fits 47 5.13 Silk sample soaked in D 2 0 for 16 days: glycine C Q REDOR data and best fits. 48 5.14 Silk sample mentioned in Chapter Four: REDOR data and best fits 51 B . l REDOR data defined by Equation 5.7 and the best fits to Equation 5.8 with (a) f2 equal to 1.0 and (b) f2 equal to 0.1. . 61 B.2 Example One: relationship between f i + 2 and f 62 B.3 Example Two: relationship between f i + 2 and f 62 Chapter 1 i Introduction Nature has been evolving spider silk for millions of years, giving it a simultaneous optimiza-tion of several significant properties. Most remarkably, spider silk has a unique combina-tion of high tensile strength and large elongation to break [1]. The major ampullate gland (dragline) silk of the golden orb-weaving spider Nephila clavipes, for example, is five times stronger by weight than steel, tougher than Kevlar and more resilient than its synthetic ri-vals. Added to those mechanical properties is the non-polluting way spider silk is made. The production of modern man-made super fibres like Kevlar involves petrochemical processing which contributes to pollution. Kevlar is also drawn from concentrated sulphuric acid. In contrast, the production of spider silk is completely environmentally friendly. It is made by spiders at ambient temperature and pressure and is drawn from aqueous solution. In addi-tion, spider silk is completely biodegradable. If the production of spider silk ever becomes industrially viable, it could in many ways replace Kevlar and be used to make a wide range of items such as surgical sutures, bullet-proof vests, artificial tendons and ligaments. Owing to their highly territorial and aggressive nature, spiders cannot be farmed like silkworms. The alternative approach is to learn the design of spider silk and copy spiders' production techniques to make synthetic silk. Investigations into the design of spider silk have included X-ray diffraction, transmission electron microscopy, solid-state N M R and atomic force microscopy [2] with the same goal of unraveling the molecular origin of silk's remarkable mechanical properties. Efforts to artificially manufacture spider dragline silk started with producing recombinant spider silk proteins in bacteria and yeast systems, but with limited success [3, 4, 5, 6, 7]. In 2002, water-soluble recombinant silk proteins were produced in mammalian cells [8]. The resulting silk is comparable to native spider silk in terms of toughness and elasticity, but is only 30% as strong as native silk. Two considerations have motivated us to study the water permeability of spider silk. The first one is to gain a better understanding of spider silk supercontraction. Certain spider silks shrink to about half of their original length when immersed in water, a phenomenon named supercontraction [9]. Supercontraction is accompanied by a large decrease in fiber stiffness, thus is undesirable in most of the cases. If one wishes to eliminate supercontraction from synthetic fibers inspired by spider silk, it is critical to understand the molecular origin of this phenomenon. Since supercontraction is induced by water, one would naturally question where inside silk water can permeate. The second reason for studying the water permeability of spider silk is to facilitate further studies of the effect of other molecules on silk. Those include molecules in various solvents, dyes and salts. Sodium nitrate, for example, when absorbed by silk increases the strength of the fiber.. Other examples are harsh solvents like hexafluoroisopropanol (HFIP) which are used to dissolve silk-like proteins so that fibers can be spun from the solutions. Two kinds of studies can provide information about the water permeability of spider silk. Chapter 1. Introduction 2 When silk gets wet, the change of protein dynamics in certain regions of silk can serve as an indicator of water permeation into those regions. This approach has been pursued elsewhere [10, 11]. A more direct approach, however, is to examine the penetration of isotope-labeled water ( D 2 0 or H 2 1 7 0 ) into silk, namely using isotopes D or 1 7 0 as a tracer of water. The capacities of N M R to probe molecular dynamics and measure local nuclear interactions make it particular suited for such purposes. This thesis begins with an introduction to NMR in Chapter 2 and background material on spider silk in Chapter 3. In Chapter 4, we use the quadrupolar echo NMR technique to investigate the hydrogen-deuterium exchange process in a silk sample that has been soaked in deuterium oxide (D 2 0) and then dried. In Chapter 5, the rotational-echo double resonance (REDOR) NMR technique is employed to quantify water permeability in silk's different structural regions. . . . Chapter 2 Nuclear Magnetic Resonance Nuclear magnetic resonance (NMR) is a phenomenon that occurs when the nuclei of certain atoms are immersed in a static magnetic field (B0) and at the same time exposed to a second oscillating magnetic field (Si). Only nuclei with magnetic moments experience this phenomenon. The magnetic moment /2 of a nucleus is related to its angular momentum by fi = lJ (2.1) where 7 is the gyromagnetic ratio characteristic of the nucleus in question. For example, 7i# = 42.5759 x 1 0 6 H z - T - 1 7 i 3 C = 10.7054 x 106 Hz • T _ 1 7i5jv = —4.3142 x 106 Hz • T " 1 2.1 Zeeman Interaction In the presence of a magnetic field B0, a nucleus ;with a magnetic moment p, has a Zeeman Hamiltonian given by: HQ = -jl-B0 (2.2) Taking the magnetic field direction as the laboratory z-axis, we find: Ho = -lhBQIz (2.3) The eigenenergies of this Hamiltonian are Em = -jhB0m (2.4) where m can take on values: 1,1 — 1,... —I and / is the total angular momentum of the nucleus. For spin-1/2 nuclei (such as *H and 1 3 C ) , Equation 2.4 gives two energy levels (Figure 2.1). In thermal equilibrium, these energy levels are populated according to the Boltzmann distribution: Q — Em/kBT Pm = J— . (2.5) W here m (2-6) Chapter 2. Nuclear Magnetic Resonance 4 — m = - l / 2 AE=yhB0 m = l / 2 Figure 2.1: Zeeman interaction. For a spin-1/2 nucleus, there are two eigenstates. is the partition function for normalization. In a moderate magnetic field BQ and at a tem-perature higher than millikelvin, there is a'small thermal equilibrium population difference between the two energy levels. This population difference results in a net total magnetization M0 = ( ^ ' l f i ) e Q = MQ£Z pointing along the magnetic field B 0 direction. 2.2 Equation of Motion When present in a magnetic field B 0 , a magnetic moment experiences a torque T, given by f = px B 0 (2.7) The effect of this torque is to change the spin angular momentum over time: dJ dt = T Given the definition in equations 2.1 and 2.7, equation 2.8 can be rewritten as dpi dt = p x 7 B 0 (2.8) (2.9) Considering the system quantum mechanically yields an analogous equation for the expec-tation value of p: d < p > dt =< P > X 7 B 0 (2.10) Since the torque is perpendicular to both p and B 0 , the result is a precession of the magnetic moment around the magnetic field direction, as shown in Figure 2.2. The frequency of this Chapter 2. Nuclear Magnetic Resonance 5 Figure 2.2: Evolution of a magnetic moment in a magnetic field. precession u)o = —JBQ is known as the Larmor frequency. A nuclear magnetic moment is often likened to a spinning top because both can precess about an axis other than its own rotation axis. For an ensemble of nuclear spins, if the spins do not interact with one another, one can sum the magnetic moments over a unit volume to obtain the equation of motion for the magnetization: d ^ = 1MxB0, (2.11) at i.e. a magnetization in a magnetic field will precess about the field in the same way as a magnetic moment does. 2.3 Relaxation As with a spinning top, the precession of a magnetization about the magnetic field is not infinite. A spinning top eventually stops precessing due to friction; magnetization will even-tually stop precessing because of a phenomenon known as relaxation. A phenomenological description of relaxation is given by the Bloch equations: dMx Mx D M Y = ^ M ^ B L ( 2 . 1 3 ) dt " J T2 dMz = Mz - M 0 dt Ti (2.14) where Mo is the thermal equilibrium magnetization and Ti , T 2 are known as the longitudinal and transverse relaxation times respectively. Chapter 2. Nuclear Magnetic Resonance 6 Longitudinal Relaxation Longitudinal relaxation arises from the interactions of nuclear spins with their surrounding environment and is often referred to as spin-lattice relaxation. These interactions allow the exchange of energy between the spins and the surroundings so that thermal equilibrium can be obtained. Solving equation 2.14 yields: Mz(t)- Mo = (MM -M0)e-% (2.15) i.e. the difference between the longitudinal magnetization Mz and the thermal equilibrium magnetization M 0 will decay with time, characterized by a time constant Ti . Transverse Relaxation Transverse relaxation arises from the interaction between spins and is often referred to as spin-spin relaxation. As a result of this interaction, the magnetization in the xy-plane will eventually vanish. This process is characterized by a time constant T 2 . Given an initial condition M± — Mx(0)ex, equations 2.12 and 2.13 have the following solutions: Mx(t) = Mx(0)cos(cjQt)e~^ (2.16) My(t) = Mx(0)sm(uot)e~^ (2.17) 2.4 The Density Matrix The Bloch equations are intuitively easy to understand, but are insufficient for describing the interactions in a spin ensemble. The average properties of a spin ensemble are best described by the density matrix: p = Y,Pn\n><n\ (2.18) n where the summation is over a complete set of states and Pn is the probability of being in state | n >. With the density matrix, the expectation value of any observable A is simply given by <A>=Tr(Ap) . (2.19) Using the Schroedinger equation: one can derive the time evolution of the density matrix and the result is the Liouville-von Neumann equation: Chapter 2. Nuclear Magnetic Resonance 7 Equation 2.21 has the following solution: p(t) = U(t,0)p(0)U^t,Q), (2.22) where p(0) is the density operator at time zero and U(t, 0) is a time evolution operator defined as tf(t,0) = f e - * / o (2.23) in which T is the Dyson time-ordering operator. 2.5 Pulsed Nuclear Magnetic Resonance In NMR, we apply radio frequency (rf) pulses to perturb the spin system, tipping the magne-tization away from its thermal equilibrium and observe its evolution with time as it returns back to equilibrium. When an rf pulse is applied, the total magnetic field felt by a nuclear spin is given by Bit) = B0ez + B^t) (2.24) with Bi(t) = 5i(cos(cv r/t)ex + sm(urft)ey) (2.25) The Hamiltonian of the spin now becomes: H = Ho + Uy = -jhB0Iz - -yHB^I* cos(w r /t) + Iy sin(o» r /t)) (2.26) Working with a time-dependent Hamiltonian like this is difficult. We therefore introduce a new frame of reference called the rotating frame in which the magnetic field, hence the Hamiltonian is time-independent. The transformation from the laboratory frame to the rotating frame is performed with the unitary operator R = eluJrftIz. The rotating-frame density matrix is given by: p=R-lpR (2.27) The time evolution of p can be written as: I4P-«I <2-28> where H = R~lHR — hwrfIz (2.29) is the rotating frame Hamiltonian. For the laboratory Hamiltonian of Equation 2.26, we have the rotating frame Hamiltonian: H = miz + Ljxhlx (2.30) Chapter 2. Nuclear Magnetic Resonance 8 where Q = -j(B0 + — ) = UJ0 - u r f 7 is known as the apparent resonance frequency and uj! = --yBi Equation 2.30 can also be written as: n = - 7 f t j • [(So + + 5 i e ; ] 7 i.e. the effective magnetic field in the rotating frame is: Beff = (B0 + ^)ez + Bx£x, 7 (2.31) (2.32) (2.33) (2.34) which is time-independent as well. In the rotating frame, magnetization nutates about 5 e / / as shown in Figure 2.3. Bn rf Beff / • • y B, (a) (b) Figure 2.3: (a) Effective field, (b) Motion of the magnetization in the rotating frame. On-Resonance Excitation If the rf pulse is applied exactly on resonance, i.e. urf = simply given by Beff = B\€x - 7 S 0 = w0, ^ n e effective field is (2.35) Chapter 2. Nuclear Magnetic Resonance 9 z Bx x Figure 2.4: The rf pulse is applied on resonance and the magnetization nutates in the y-z plane. In this case, the magnetization will nutate in the y-z plane of the rotating frame as shown in Figure 2.4. An rf pulse which flips the magnetization from the z-axis to the x-y plane is known as a 90° pulse. In general, the pulse flip angle can be written as: B ^ - i B i T , (2.36) where r is the time duration of the pulse. Off-Resonance Excitation More often than not, the condition of u>rf = u)0 cannot be fulfilled for all spins in the sample simultaneously. As long as the frequency offset Q = u0 — torf < W [ , w e can ignore this offset in the duration of the pulse. Free Induction Decay After the rf pulse is turned off, the system is left to evolve. The magnetization will precess because of the presence of the B0 field, with a frequency of LOQ in the laboratory frame and a frequency of f2 in the rotating frame. This precession induces rf voltages in the coil surrounding the sample, which are the signals we detect in an NMR experiment. The free precession of the magnetization following an rf pulse is referred to as a Free Induction Decay (FID). 2.6 S p i n Echoes Spin-echo pulse sequence (Figure 2.5) is an essential component of many N M R experiments. In this section, we will examine this important pulse sequence in both classical and quantum mechanical languages. Chapter 2. Nuclear Magnetic Resonance 10 Figure 2.5: Spin-echo pulse sequence. 2.6.1 Classical Description The evolution of magnetization under the spin-echo pulse sequence can be understood using the vector diagram shown in Figure 2.6. After having been flipped from the z-axis by a 90° (a) z (b) z Figure 2.6: Evolution of magnetization under the spin-echo pulse sequence. pulse around the -y axis (a), the magnetization starts its precession in the transverse plane. The precession frequency of a nuclear spin in the rotating frame is the apparent resonance frequency fi = u>0 — u>rf, where the Larmor frequency u0 can differ from spin to spin for a variety of reasons, such as B0 field inhomogeneity. The result of this difference in Q. is that over the first delay time r, spins with different fj'' values go through different phase angles fir, i.e. they spread out on the transverse plane (dephase) as shown in (b). (c) A 180° pulse around the x-axis inverts the phase from fir to -fir. This phase inversion is completely compensated by another phase fir acquired during the second delay time r, i.e. at time Chapter 2. Nuclear Magnetic Resonance 11 2T, all spins are back aligned along the x-axis (d) and a maximum in signal intensity (echo maximum) is observed. 2.6.2 Quantum Mechanical Description The above analysis can also be done using the time evolution of the density matrix (Equations 2.22 and 2.23). For a given nuclear spin with apparent resonance frequency Q, the density matrices at representative time points in the pulse sequence (Figure 2.5) are derived as following: A: p(0) = Iz (2.37) B: p(tB) = e-iVvIzeiVv = IX (2.38) C : p(tc) = eiQTl*Ixe-iilTl* = 4 cos(ftr) - Iy sin(fh-) (2.39) D : p(tD) = ei,r/a[/xcos(nr)-/ysin(nr)]e-i,r/-= Ix cos(fir) + Iy sin(ftr) (2.40) At any time t after point D, p{t) = em{t-T)I> [Ix cos(ftr) +Jy s in(Qr)]e- i n ( t - r ) / z = cos(fir)[/x cos(fi(i — r)) — Iysm(Cl(t — r))] + sm(Q,r)[Iy cos(fi(t - T)) + J x sin(f2(t - r))] = / x cos(fi(t - 2r)) - 7y sin(fi(t - 2r)) (2.41) In the above derivation, we have used the property of rotation operators: for any three operators obeying the cyclic commutation rules [A, B] = iC, e~idABei9A = Bcos6 + Csm6 (2.42) The last line of Equation 2.41 shows that at t i m e - = 2r, pits) = Ix- In other words, due to the 180° pulse, the effect of the first delay time r is completely undone by the effect of the second delay time r. Note that such a result is independent of the value of O, i.e. at time ts = 2T, all spins are back aligned along the rc-axis, regardless of their individual fl values. The big advantage of the spin-echo pulse sequence over single-pulse excitation is that signal acquisition can start from the echo maximum so that the adverse effect of the rf coil ringing on the N M R signals can be minimized. In general, the effect of any NMR interaction that is equivalent to a spread in £1 can be eliminated by the spin echo. For example, heterpnuclear dipolar coupling or the effects of chemical shifts, which will be discussed in the following section, can both be eliminated by use of echoes. Chapter 2. Nuclear Magnetic Resonance 12 Table 2.1: The magnitudes of internal interactions compared with that of the ZeemanK inter-action. , , , Interaction Order of Magnitude Zeeman 108 Hz Chemical Shift Scalar Dipolar Quadrupolar 103 Hz 1 ~ 100 Hz , 103 Hz 103 ~ 106 Hz 2.7 N M R Interactions Up to now, we have dealt with two external NMR interactions: the interaction with the static B0 field (the Zeeman interaction) and the interaction with the radio frequency magnetic field Bi (t). In NMR, the interactions of particular interest are the internal interactions as listed in the bottom part of Table 2.1. Al l of these interactions result in small perturbations of the resonance away from the Larmor frequency. In the following, we will go through the internal interactions relevant to our discussion in the later chapters. 2.7.1 Chemical Shift Interaction The chemical shift interaction arises from the interaction of a nuclear spin with its sur-rounding electrons. Under the influence of the B0 field, the electron cloud also generates an additional local field. The local magnetic fields experienced by nuclei at two sites in the same molecule are different if the electronic environments are different. For example, protons located in the -CH2 groups of ethanol molecules have slightly different local fields from protons located in the - C H 3 groups. ; Because the electronic environment of a nuclear spin is often not isotropic, the additional local field also has an orientation dependence. The local field B^ is, to a very good approxi-mation, linearly proportional to the B0 field, Bk = 8 • B0, where 8 is a second-order tensor known as the chemical shift tensor. The chemical shift Hamiltonian can then be written as: Hcs = -lhI-6-B0 (2.43) We denote the principle values (eigenvalues) of 8 as 8n, 822 and 833 ordered according to <5ii > 822 > 833. In a strong magnetic field, where first order perturbation theory accurately predicts the shift in energy levels due to the chemical shift, we need consider only the secular portion 1 of the chemical shift Hamiltonian: Hcs = -lhB0 ^8iso + ^ p [ 3 cos2 6 - 1 I n sin 2 6 + cos 2<f>]^j Iz (2.44) 1The secular portion is that part of the perturbing Hamiltonian that commutes with the Zeeman Hamil-tonian. Chapter 2. Nuclear Magnetic Resonance 13 where 6 and 4> are the polar and azimuthal angles defining the orientation of the principle axis system of 8 with respect to the laboratory frame and for \8U - 6iso\ < \833 - 8i: ^ f t x + fa + fa ( 2 _ 4 5 ) S 3 3 - 8 l s o , (2.46) 822 — S-n 8aniso (2.47) for \8n - 5iso\ > \833 - 61 fianiso ~ $U — Siso (2.48) r, = % ^ (2.49) c-isoi fianiso and rj are known as the isotropic chemical shift, the anisotropy parameter and the asymmetry parameter respectively. To facilitate our discussion in Chapter Five, here we show the calculation of the c5jSO, Saniso and n values for the chemical shift tensor of the a carbon 2 in L-alanine [12]. For the a carbon in L-alanine, (<5n, 622,533)=(65.3, 56.7, 31.5) ppm with respect to tetramethylsilane (TMS) 3 . Therefore, 8n + 822 + 833 , . 8iso = — = 51.2 ppm (2.50) Saniso = 533 - 8iso = -19.7 ppm (2.51) % ^ I = 0.437 (2.52) $amso 2.7.2 Dipolar Interaction Each nuclear spin with a magnetic moment generates a magnetic field, looping around in the surrounding space. A second nuclear spin interacts with this magnetic field (Figure 2.7 (a)). The dipolar Hamiltonian follows from the classical interaction energy between two magnetic moments and is given by: ; ' • ; ' : HD = 7i72ft 2 h • h 3 ( / i • f)(I2 • f) (2.53) where f is the internuclear vector as depicted in Figure 2.7 (b). In high magnetic fields, we again take the secular form of the dipolar Hamiltonian: HHomo = fti_L3IuJ2z _ fx . J 2 ) ( 1 _ 3 c o s 2 0) (2 .54) 2The definition of a carbon is given in Chapter Three. 3Chemical shifts are usually labeled in parts-per-million (ppm), with respect to a reference compound. Chapter 2. Nuclear Magnetic Resonance 14 Z Figure 2.7: Dipolar interaction. for homonuclear coupling and H%eter° = 2L7|_/ l z/ 2 z(i _ 3 c o s 2 0)) ( 2 5 5 ) for heteronuclear coupling. The constant term in front of Equations 2.54 and 2.55 are the homonuclear and heteronu-clear dipolar coupling constants respectively, which are often used to specify the strength of the dipolar coupling: D = ^ (Hz) (2.56) Some typical dipolar coupling strengths are listed here: DHH-r* = 120000 H z - A 3 (2.57) Dcc-r3 = 7500 H z - A 3 (2.58) DHC-r3 = 30000 H z - A 3 (2.59) As an example, we show the calculation ofithe dipolar coupling constant for a 1 3 C - 2 D spin pair. The calculation uses an internuclear distance; of 2.1lA and is performed in cgs units: _ (4.107 x 103rad/s • G)(6.728 x 103rad/s • G)(6.626 x !Q- 2 7erg • sec/2?r) ~ 2TT(2.11 x 10- 8cm) 3 = 493.4 Hz (2.60) 2.7.3 Quadrupolar Interaction The quadrupolar interaction exists for a nuclear spin with spin quantum number I > 1. It is an interaction of the nuclear quadrupolar moment with the electric field gradient (EFG) Chapter 2. Nuclear Magnetic Resonance 15 surrounding it. The quadrupolar Hamiltonian can be written as [13]: H q = 4 / f f - l ) [ ( 3 / - 2 " / 2 ) + ^ + ! y 2 ) ] ( 2 ' 6 1 ) where e is the electron charge, eq = Vzz is the largest principle value of the EFG tensor, Q is the quadrupolar moment, -q = \Vyy — Vxx\/Vzzis the asymmetry parameter of the E F G and Ix, Iy and Iz are spin operators with respect to the EFG principle axis system. In high magnetic fields, we can take the secular form of the quadrupolar Hamiltonian: nQ = lhujQ(3 cos2 e - l + nsmH cos 2cl))(I^\l2) = hnQ(I^-\l2) (2.62) in which and U Q = 41(21-m ( 2 - 6 3 ) c}Q = IO;Q(3COS20 - 1 + 77sin20cos2</>) (2.64) This Hamiltonian gives rise to a shift in the resonance frequency: um = ^h(2m-l) (2.65) Air for an m to m — 1 transition. For a spin-1 nucleus like deuterium, the frequency shifts due to the quadrupolar interaction are illustrated in Figure 2.8. To understand the line shape of a deuterium spectrum, let's now consider a powder sample, in which every molecule has an equal probability of taking any spacial orientation (#,</>)• According to Equation 2.64, each orientation (6, (j)) corresponds to an individual value and thus gives an individual doublet as shown in Figure 2.8 (b). The result is a powder spectrum which is the superposition of all the doublets given by all orientations. Figure 2.9 illustrates the deuterium resonance frequencies for the simple case of TJ = 0. Only m = 1 to m = 0 transition frequencies are plotted for clarity. The relative intensity of a peak depends on the number of orientations that correspond to the peak frequency. The real powder spectrum is the spectrum in Figure 2.9 plus its mirror image about uQ. The powder spectrum has two singularities at frequencies ±I/Q/2, where the quantity VQ = LUQ/2TT, i.e. the separation of the two singularities, is often used to characterize the size of the quadrupolar interaction. The quadrupolar coupling constant (QCC) one often sees in the literature is defined as: QCC=^- (2.66) which for deuterium is related with VQ by VQ — ^QCC. Chapter 2. Nuclear Magnetic Resonance 16 m— — \ PlOOr m=0 hcoQ—hQ,Q h(x>Q+hQQ 2TT v o+TZ v0 v 0 -fh 2n m— 1 * Frequency (Hz) (a) (b) Figure 2.8: (a) Energy level shifts due to quadrupolar interaction for spin-1. (b) The effect of quadrupolar interaction on N M R spectrum for spin-1: one resonance peak splits into a doublet centered about the resonance frequency v0 = 2.8 High Resolution Solid-State NMR In this section, we shall give phenomenological descriptions of several techniques often used in solid-state N M R to enhance spectral resolution and signal intensity. 2,8.1 Magic Angle Spinning For powder samples, anisotropic interactions result in broadened spectra and resonances from different chemical environments tend to overlap. Averaging of the anisotropies, occurring naturally in liquids by rapid molecular reorientation, can also be achieved in solid-state NMR by macroscopic sample rotation. Magic angle spinning (MAS) of the sample is performed about an axis that makes the "magic angle" of 54.74° with respect to the B0 field. MAS averages out all anisotropic interactions that can be described by second-rank tensors. Below we summarize the effects of MAS on the chemical shift and dipolar interactions. Effect on Chemical Shift Anisotropy If the spinning frequency is less than the magnitude of the chemical shift anisotropy (CSA), the powder spectrum will break up into a centerband at the isotropic frequency SiSO, with a series of sidebands separated by the spinning frequency. The amplitudes of the sidebands roughly follow the envelope of the powder pattern line shape. If the spinning frequency exceeds the magnitude of the CSA, sidebands can appear outside the powder pattern enve-lope, but with severely reduced amplitudes so that only the centerband is generally observed. Shown in Figure 2.10 is the 1 3 C spectrum of our silk.sample under magic angle spinning. The spinning frequency is 5000 Hz. For carbonyl C, one can see both the centerband and Chapter 2. Nuclear Magnetic Resonance 17 6=90° e=o° 0 V e 2 Frequency (Hz) Figure 2.9: Deuterium resonance frequencies for the case of r\ — 0. Only m=l to m=0 transition frequencies are plotted for clarity. /<> is taken as the reference frequency (i.e. VQ — 0) and VQ = CUQ/2TT. the sidebands separated by 5 kHz. For alanine C Q , glycine C Q and alanine Cp, only the centerbands can be observed. Effect on Dipolar Interaction For a pair of isolated spins, the effect of MAS on the dipolar interaction is similar to that on the chemical shift interaction. For a strong coupling to a spin in a bath of strongly coupled spins, as for a 1 3 C nucleus with a directly attached proton in a proton-rich solids (Equations 2.57 and 2.59), no significant spectral narrowing can be achieved by MAS because of the hardship to obtain a spinning frequency close to the 1 H - 1 H coupling strength, which can be as large as 50 or 60 kHz. 2.8.2 Decoupling Large heteronuclear dipolar couplings, unable to be averaged by MAS, can be removed by another technique called decoupling. Continuous high-power irradiation on one spin species can eliminate the heteronuclear couplings to the other spin species, regardless of the states of the magnetization. For example, a high-power rf irradiation is applied at the proton resonance frequency, which flips the proton spin operators 1^ rapidly between ± i f . If this can be performed faster than the dipolar coupling frequencies, then the dipolar interaction Hamiltonian 4 HD = — (2.67) All the angular factors of Equations 2.54 and 2.55 are incorporated into the Q.oi and floij-Chapter 2. Nuclear Magnetic Resonance 18 400 Chemica l Shif t (ppm) Figure 2.10: 1 3 C spectrum of our silk sample under magic angle spinning, in which S means sideband. may be averaged away, considerably sharpening the 1 3 C spectrum. Examples of effective heteronuclear dipolar decoupling methods include Two Pulse Phase Modulation (TPPM) [14] and Direct Spectral Optimization (eDroopy) [15]. 2.8.3 Cross Polarization In solid-state NMR, cross polarization (CP), i.e. transferring magnetization from spins with larger 7 (high sensitivity) to spins with lower 7 (low sensitivity), is a standard building block of many pulse sequences. Figure 2.11 illustrates a } H - 1 3 C CP pulse sequence. At the beginning, the 1 H magnetization is nutated to the x-axis by a 90Z.y pulse. Then the phase of the 1 H irradiation is shifted by 90° so as to align the 1 H magnetization with the B\H field. Magnetization aligned along a strong B\ field is spin-locked: it does not dephase, neither by chemical shifts nor by dipolar couplings. It only relaxes with a time constant T l p for 1 H . If now continuous irradiation is applied simultaneously at the 1 3 C resonance frequency with the B i field strengths satisfying -1HB1H = 1 C B 1 C , (2.68) magnetization will be transferred from J H to 1 3 C . Equation 2.68 is known as the Hahn-Hartmann condition. In a simplistic picture, this magnetization transfer can be explained as a matching of energy-level huiin = h<±>ic m the doubly rotating frame. For dilute 1 3 C nuclei Chapter 2. Nuclear Magnetic Resonance 19 90° CP -y x CP 3 C Figure 2.11: Cross polarization pulse sequence. in a proton-rich solid, the enhancement in the 1 3 C magnetization that one can expect from using C P is where M 9 0 ° is the magnetization after a single 90° pulse. In addition to signal enhancement, the advantage of CP also includes a considerable decrease in measurement time, since the Tj relaxation of 1 H is often much faster than 1 3 C . 2.9 R E D O R In solid-state NMR, MAS is often used to enhance spectral resolution, but at the same time, MAS averages out weak dipolar interactions which can provide distance and orientation information. The rotational-echo double resonance (REDOR) experiments [16] are specially designed to reintroduce weak dipolar couplings under MAS, thus allowing us to measure them. Shown in Figure 2.12 is the REDOR pulse sequence for measuring the dipolar interaction of an isolated 1 5 N - 1 3 C spin pair. The 1 5 N TT pulses part way through a rotor cycle serve to invert the sign of the heteronuclear dipolar Hamiltonian: IZNIZC ~* —IZNIZC, a n d interrupt the averaging. To measure the dipolar coupling, one employs the pulse sequence, then performs the same experiment again without the 1 5 N 7r pulses. Evaluating the time evolution of the density matrix shows that the ratio of the acquired signals of the two experiments S/SQ, after crystal averaging for powder samples, depends only on the dipolar coupling constant D of the spin pair: I- = ^!Lj^V2N-)J^(V2N^-) (2.70) So 4 < v uR' vR' Chapter 2. Nuclear Magnetic Resonance 20 7t/2 13, CP CP decouple Acquire 15 N rotor 7 C 7 C J C 7 C 7 C % % % % % ± _L X 0 6T r Figure 2.12: 1 3 C - 1 5 N REDOR pulse sequence. where J ± i are Bessel functions of order ± | , VR is the MAS spinning frequency and N is the number of rotor cycles. By measuring S/S0 at several values of N and fitting to Equation 2.70, one can obtain the dipolar coupling constant, hence the internuclear distance. In practise, the following REDOR dephasing function is often used: AS So = 1 = 1 y/2ir Ji(V2tD)J_i(V2W) (2.71) where t = N/UR is known as the dipolar evolution time. If only a fraction p of all 1 3 C spins in the sample have an 1 5 N neighbor, then the measured Pi P 2 1 5 N 1 l - P f P 2 4 / 1 3 C / 1 3 C 1 3c (a) (b) Figure 2.13: (a) Two possible neighboring environments of a 1 3 C spin, (b) One 1 3 C spin coupled to three neighbors simultaneously. Chapter 2. Nuclear Magnetic Resonance 21 R E D O R signal is scaled by a factor p: (—) ~P — (2 72) V So J m So If two possible neighboring environments exist (Figure 2.13 (a)) with probabilities p x and P 2 respectively, the measured REDOR signal is: : •. AS\ / A S \ / A . S \ OO / m \ <->0 / 1 \ Oo / 2 where (^f) a n d ( ^ ) 2 a r e the REDOR dephasing curves corresponding to the two indi-vidual neighboring environments. If every 1 3 C spin in the sample is coupled to more than one 1 5 N neighbor (Figure: 2.13(b)), no universal dephasing curve like Equation 2.70 exists. In this case, numerical evaluation can be done to simulate the REDOR dephasing curves (see Chapter Five). 22 Chapter 3 Silk Background 3.1 Silk Composition The spider silk under investigation is the major ampullate gland (dragline) silk of the golden orb-weaving spider Nephila clavipes 1. Although past studies have indicated small amounts of phosphorus compounds [17] and calcium [18] in silk, it is believed that the silk consists of almost entirely of proteins [19]. The building blocks of all proteins are amino acids. Of the 20 amino acids usually found in proteins, 19 have the general structure shown in Figure 3.1 and differ only in the chemical structure of the side chain R. The central carbon atom of an amino acid is denoted as a. The carbon atoms of the side chains are commonly designated fl, j, 5, e and (, in the order away from the a carbon atom. The carbon atom on the carboxyl end is known as the carbonyl carbon. Seven amino acids account for over 90% of the silk [20, 21, 22]: glycine (42%), alanine (25%), glutamine (10%), leucine (4%), arginine (4%), tyrosine (3%) and serine (3%). Figure 3.2 gives the side chain structures of these seven amino acids. carboxyl end C O O amino end alpha carbon chain Figure 3.1: General structure of most amino acids. 3.2 Primary Structure Amino acids are linked into proteins by the peptide bond through a dehydration synthesis reaction between the carboxyl end of the first amino acid and the amino end of the second amino acid (Figure 3.3). Generally, between 50 and 3000 such amino acids are linked in this way to form a typical linear polypeptide chain. The backbone of the polypeptide chain 1Unless specially specified, the silk mentioned throughout the rest of the thesis refers to the major ampullate gland (dragline) silk of the golden orb-weaving spider Nephila clavipes. Chapter 3. Silk Background 23 C H I H glycine Gly G I C H C H C H I 2 N H N H + N H arginine Arg R I C H 3 alanine Ala A C H I O H tyrosine Tyr Y C H H N 2 o glutamine Gin Q H - O H serine Ser S C H C H H 3 C C H leucine Leu L Figure 3.2: Side chain structures of the seven most abundant amino acids in silk. Figure 3.3: Peptide bond formation. Chapter 3. Silk Background 24 consists of a repeated sequence of three atoms of each amino acid residue 2 in the chain: the amide N , the C a , and the carbonyl C. The linear sequence of amino acids is known as the primary structure of a protein. The primary structures of the silk have been examined by partial sequencing of the corresponding cDNA [19, 23] (Figure 3.4); It can be seen that the silk proteins consist of repeating units in which a polyalanine run of five to seven residues is followed by a glycine-rich sequence containing residues with bulky side chains. QGAGAAAAAA-GGAGQGGYGGLGGQG AGQGGYGGLGGQG AGQGAGAAAAAAAGGAGQGGYGGLGSQG AGR GGQGAGAAAAAA-GGAGQGGYGGLGSQG AGRGGLGGQGAGAAAAAAAGGAGQGGYGGLGNQG AGR GGQ—GAAAAAA-GGAGQGGYGGLGSQG AGRGGLGGQ-AGAAAAAA-GGAGQGGYGGLGGQG _ AGQGGYGGLGSQG AGRGGLGGQGAGAAAAAAAGGAGQ GGLGGQG AGQGAGASAAAA-GGAGQGGYGGLGSQG AGR GGEGAGAAAAAA-GGAGQGGYGGLGGQG --AGQGGYGGLGSQG AGRGGLGGQGAGAAAA GGAGQ—GGLGGQG AGQGAGAAAAAA-GGAGQGGYGGLGSQG AGRGGLGGQGAGAVAAAAAGGAGQGGYGGLGSQG AGR GGQGAGAAAAAA-GGAGQRGYGGLGNQG AGRGGLGGQGAGAAAAAAAGGAGQGGYGGLGNQG AGR GGQ—GAAAAA—GGAGQGGYGGLGSQG AGR--GGQGAGAAAAAAA-VGAGQEGIR GQG . -AGQGGYGGLGSQG SGRGGLGGQGAGAAAAAA-GGAGQ GGLGGQG AGQGAGAAAAAA-GGVRQGGYGGLGSQG AGR GGQGAGAAAAAA-GGAGQGGYGGLGGQG VGRGGLGGQGAGAAAA—GGAGQGGYGGV-GSG Figure 3.4: Amino acid sequence of silk obtained by Xu and Lewis [19]. 3.3 Secondary Structure One level above the primary structure is the secondary structure which describes the local conformation of the polypeptide backbone. One example of secondary structure is the right-handed a-helix (Figure 3.5 (a)). It has 3.6 amino acids per turn of the helix, which places the C = 0 group of amino acid i exactly in line with the H-N group of amino acid i + 4. Another commonly observed secondary structure is the antiparallel /3-sheet (Figure 3.5 (b) 2The polypeptide backbone is a repetition of tlie basic unit common to all amino acids. When the side chain is included, this unit is described as an amino acid residue. Residue mass is equal to the mass of the nonionized amino acid minus that of water. Chapter 3. Silk Background 25 (a) (b) Figure 3.5: Examples of secondary structures (from [24]): (a) right-handed a-helix (b) left: antiparallel /3-sheet; right: parallel /3-sheet. left). In this structure, antiparallel extended strands form stabilizing inter-strand hydrogen bonds. Parallel /3-sheets may also form, but are less stable because the hydrogen bonds are not well aligned (Figure 3.5 (b) right). The secondary structures of the silk were initially studied using X-ray diffraction [25] and Fourier transform infrared measurements [26]. The silk was found to be a semicrystalline polymer and its crystalline regions are composed of antiparallel pleated sheets. The intersheet spacing determined by X-ray diffraction matches that of /3-sheets comprised of polyalanine. A silk structure model in which the polyalanine regions form /3-sheets which stack and form crystals in an amorphous glycine-rich matrix was proposed [27] (Figure 3.6). Further evidence of alanine-rich segments being present as /3-sheets was provided by solid-state NMR [29]; the carbon chemical shifts for alanine in the silk match that for alanine residues known to be present in a /3-sheet conformation. Deuterium N M R further showed that the crystalline fraction of the silk consists of two types of alanine-rich regions. One is highly oriented and the other is poorly oriented and less densely packed [10]. A model for the folding of silk polypeptide chain into alanine-rich /3-sheets and glycine-rich amorphous regions was proposed [10]. In this model, the molecular chain direction reverses at the points in the sequence where L G X Q occurs (where X is S, G or N). This was later supported by 1 3 C - 1 5 N REDOR [30]. The secondary structures of the Nephila edulis dragline silk were also studied by solid-state NMR [31] and the glycine-rich regions were found to form a 3i-helical structure (Figure 3.7), which we assume describe equally well the same regions in our silk sample. Chapter 3. Silk Background 20 Figure 3.6: An illustration of the silk structure model: polyalanine regions form /^-sheets which stack and form crystals in an amorphous glycine-rich matrix (from [27, 28]). (a) (b) Figure 3.7: Side (a) and top (b) projections of the 3i-helical structure (from [31]). Chapter 3. Silk Background 27 Table 3.1: Dynamics of different amino acids in wet silk (from [10, 11]). *Group here refers to Gin, Leu, Ser, Tyr, Arg as a group. ., . Gly (40±5) % (35±10) % -25 % static highly mobile (T x of C a < 1 sec) reorient faster than 20 kHz, but T i of Ca > 1 sec Ala nearly all static Leu Population 1 Population 2 reorient nearly isotropically dynamics are not very different whether wet or dry Group* more than half highly mobile (Ti of C a < 1 sec) 3.4 Water-induced Protein Dynamics Unconstrained silk fibers contract to about half of their original length when immersed in water, a phenomenon named supercontraction [9]. In recent years, a great deal has been done to probe the protein dynamics in wet silk with the goal of understanding the mechanism of supercontraction. Spin-lattice relaxation measurements were used to study fast backbone dynamics in wet silk and line-shape analysis of 1 3 C chemical shift anisotropy provided information about slower backbone motion [11]. Deuterium N M R was applied to probe side chain dynamics [10, 11]. Table 3.1 summarizes the results of those studies. Based on those results, a model of the dynamics and phase structure of silk was proposed, dividing the silk amino acid sequence into three kinds of regions [11] (Figure 3.8): the j3-sheet region, static in wet silk, is depicted as white characters on a black background; the amorphous region, fast moving in wet silk, is shown as italic characters; and the interphase, having increased dynamics in wet silk, is in dark characters. Fractions of different amino acids in the three regions are summarized in Table 3.2. G Q N Figure 3.8: Model of the dynamics and phase structure of silk (from [11]). Chapter 3. Silk Background 28 Table 3.2: Fractions of different amino acids in /3-sheet, amorphous and interphase regions /3-sheet region amorphous region interphase region Gly 32 % 25 % 43 % Ala 90 % 10 % 0 Leu 0 45 % 52 % Glu 50 % 50 % 0 Tyr, Ser, Asn 0 ~ 100 % 0 and Arg Judging from the above information, one would estimate the water permeability of silk as follows: • amorphous regions are easily accessible to water, • interphase regions have access to water, '• • /3-sheet regions are inaccessible to water. Chapter 4 29 Silk Permeability: Hydrogen-Deuterium Exchange Solvent-exposed amide hydrogens 1 of the polypeptide backbone can exchange with deu-terium in deuterium oxide (D 2 0) rapidly [32]. If silk is soaked in deuterium oxide and then dried, the detection of deuterium in certain regions of the silk can serve as a marker of water permeation into those regions, considering the low natural abundance of deuterium (0.015%). In this chapter, we use quadrupolar echo [33, 34] NMR to investigate the overall hydrogen-deuterium exchange in silk. 4.1 Experimental Silk Sample The major ampullate gland (dragline) silk from adult female Nephila clavipes spiders was used. 30 mg silk fibers were collected and made into an unoriented sample. The sample was soaked in deuterium oxide (Cambridge Isotope Labs, Andover, MA) for 3 hours and then dried in a vacuum oven at room temperature for 3 hours. N M R Spectroscopy Deuterium quadrupolar echo NMR experiments were performed on a home-built N M R spec-trometer [35] based upon an 8.4 T magnet (Oxford Instruments, Oxford, U.K.) providing a deuterium resonance frequency of 55 MHz. The pulse sequence is shown in Figure 4.1. The dephasing of magnetization during the first echo delay r under the quadrupolar interaction is completely refocused at the end of the second delay r. We used 2-/is 90° pulses, a 25-ms echo delay and a 7-s recycle delay. 4.2 Deuterium Spectrum Figure 4.2 shows the deuterium spectrum of the prepared silk sample. The spectrum has two components. The isotropic component centered at zero frequency reflects residual mo-bile D 2 0 in the silk 2 . The static component (broad powder pattern), corresponding to a 1In proteins, amide hydrogens refer to the hydrogen atoms attached to the nitrogen atoms on the protein backbone. 2 A component of static (frozen) D 2 O , which corresponds to a quadrupolar coupling constant of 308 kHz and an asymmetry parameter of 0.135 [36], is not seen in our deuterium spectrum. Chapter 4. Silk Permeability: Hydrogen-Deuterium Exchange 30 quadrupole coupling constant (QCC) of 201.741 kHz and an asymmetry parameter of 0.192, is representative of the powder spectrum of amide deuterium [37] 3 . 4.3 Hydrogen-Deuterium Exchange in Silk 4.3.1 Dynamical Processes and Exchange Model The above prepared silk sample was placed in a NMR tube. The rest of the tube was filled with teflon tape. A deuterium spectrum was collected right after the sample preparation (taken as time zero). The same experiment was then repeated 13 times. Spectra at some representative time points are shown in Figures 4.3 and 4.4. It can be seen that as time went on, the isotropic component of the spectrum first increased and then decreased. After about 200 hours, the isotropic component went to almost zero. The static component of the spectrum, on the other hand, continued to decrease. The overall spectral intensity dropped with time. From 189 hours to 235 hours, the spectrum had almost no change. When deuterium remains in the silk sample, it is either attached to protein backbone as amide deuterium or present in mobile water. The fprmer contributes to the static component of the spectrum while the latter produces the isotropic component of the spectrum. The changes in spectral intensities of the two components, therefore, are results of the movement of deuterium in three pools: the proteins, the residual water in silk and the air. In other words, the following processes account for the change in the deuterium spectrum: • evaporation of the residual D 2 0 from the sample into the air, • entry of H 2 0 from the air into the sample, • hydrogen-deuterium exchange between silk proteins and residual water ( D 2 0 , H 2 0 , DHO) in the sample. 3In reference [37], the quadrupole coupling constant and asymmetry parameter for the N-D group in the crystalline model dipeptide glycylglycine monohydrochloride monohydrate were found to be 198.26 kHz and 0.2138 respectively. Chapter 4. Silk Permeability: Hydrogen-Deuterium Exchange 31 7000 -100 l(200 150 100 50 0 -50 -100 -150 -200 Frequency (kHz) Figure 4.2: Deuterium spectrum of a silk sample soaked in D 2 0 for three hours, then dried. Here, we propose an exchange model 4 to describe the movement of deuterium in the three pools (Figure 4.5). In Figure 4.5, Ni and N 2 denote the amount of deuterium represented by the static and isotropic components of the spectrum respectively. N 3 is the amount of deuterium missing from the sample. K i 2 , K 2 1 , K 2 3 and K 3 2 * are exchange rates between different pools. Considering the fact that the spectrum showed almost no change from 189 hours to 235 hours, we divide N i into two parts: an exchangeable part (Ni x ) and a nonexchangeable part (Ni n ) . Considering the low natural abundance of deuterium (0.015 %), we assume K 3 2 *=0. The exchange processes can then be expressed by the following differential equations: dNln dt dNlx dt dN2 dt dN3 dt = 0 -Kl2Nlx + K21N2 - ( K 2 i + K23)N2 + K12NU K23N2 (4.1) (4.2) (4.3) (4.4) Assuming K i 2 = K 2 i , this equation group has the following solutions AT rrrt t - A r ^ , - [ 2 ^ ^ 2 ( 0 ) + J r M ^ 1 J ( 0 ) ] s i n h ( ^ ) Nix{0) cosh(-tK ) H — 4 *Philip T. Eles is acknowledged for his contributions to the exchange model. Chapter 4. Silk Permeability: Hydrogen-Deuterium Exchange 32 0 hours 200 150 100 50 0 -50 -100 -150 -200 Frequency (kHz) Figure 4.3: Change of spectrum with time: spectra collected at 0 hour, 2 hours and 28 hours. 1 1 I i i i 28 hours 800 70 hours . 189 hours 235 hours 600 -400 fl 11 / 1 J t 1 A A J'i 200 0 Jit"'"' i i i 200 150 100 50 0 -50 -100 -150 -200 Frequency (kHz) Figure 4.4: Change of spectrum with time: spectra collected at 28 hours, 70 hours, 189 hours and 235 hours. Chapter 4. Silk Permeability: Hydrogen-Deuterium Exchange 33 N j tatic 1 poncnt N 2 \£- ft->.-***.-rs-",i-*«i..,i"'-: ' ' c o m p o n e n t K 23 T N 3 Air (missing) I K • • • • K *=0 II 21 [. 'r^* '^*— '^""4 32 ! ^ 1 n Figure 4.5: Model of the hydrogen-deuterium exchange processes in the prepared silk sample. + iV l n(0) N2(t) = e-\(^+K23)t N2(0) cosh^iT") + m M - K M m s m ^ K ' ) ,i N3(t) = e - ^ 2 ^ 2 + ^ 2 3 ) t [ - [ i V 1 : c ( 0 ) - l - i V 2 ( 0 ) ] c o s h ( - ^ ' ) + e 2 (2Ki2+K23)t \(2Kl2 + K23)Nlx(0) + (2K12 - Ar2 3)JV2(0)] sinh(itX') + Nlx(Q) + N2(Q) + N3(0) where (4.5) (4.6) By fitting our experimental data of Ni(t) , N 2 (t) and N 3 (t) to Equation 4.5, we can extract the exchange rates K i 2 and K 2 3 . 4.3.2 Exchange Rates We obtain N x(t), N 2(t) and N 3(t) by calibrating the integrated intensities of our deuterium spectra relative to the spectral intensity of a deuterium standard: a fully deuterated poly methyl methacrylate (PMMA) sample. The isotropic and static components are separated based on the line shape of the powder pattern 5 . The data 6 are shown in Figure 4:6 together with the best fit to Equation 4.5. It can be seen that the three-pool exchange model describes our experimental data extremely well. The fit yields the following exchange rates: Ki2 = 0.031 per hour K23 = 0.055 per hour (4.7) 5Deuterium spectra at all time points were printed out. Based on the line shape of the powder pattern, the isotropic components were manually separated from the static components. We then weighed the two components to find their ratios. 6When calculating deuterium content in the three pools, we neglected the T2 effect during the first echo delay and the effect of finite deuterium pulse power, because according to Equation 4.5 only relative deuterium content matters. Chapter 4. Silk Permeability: Hydrogen-Deuterium Exchange 34 0.45 0.4 0.35 0.3 £ 0.25 o U £ •a 0.2 0 .15 0.1 3 Q 0.05 0 -0.05. 1 1 static N , x " \ isotropic N 2 + - \ missing N * ---1 1 1 0 50 100 150 Time (hour) 200 250 Figure 4.6: Changes of deuterium content with time: Ni(t), N 2(t) and N 3(t) and the best fit to Equation 4.5. While K 23 reflects how well our sample container was sealed, K i 2 depends on both the rate of the exchange reaction and the time of water permeation. We consider the time of water permeation to be the leading factor here because the rate of the exchange reaction for the N-H group in model protein compounds was found to be about 1000 per minute at pH=7 [32], 107 times faster than Ki2. We collected a deuterium spectrum on the silk sample four months later and found that the spectral intensity (of the static component) decreased by 28 % relative to that at 235 hours, i.e. the "nonexchangeable part" in the model was exchangeable, but exchanged at a very slow rate of 0.01% per hour during four months' time. We should therefore rename this part of the silk as a "slow-exchanging part". 4.4 Discussion We propose that the slow-exchanging part of the silk corresponds to its /3-sheet crystalline regions. Studies of proteins in solutions and crystal lattices have shown that amide hydrogen atoms in the interior of a folded protein molecule and involved in hydrogen bonding in B-sheets can participate in hydrogen-deuterium exchange process [32]. Whether we can extend those findings to our silk sample needs to be tested because the silk is insoluble and the slow-exchanging process was happening when the silk was nearly dry 1 . Since the /3-sheet 7The silk was not completely dry because of the residual water in the silk and the small amount of water coming into the silk from the air. It is also interesting to notice that study of the Nephila edulis dragline Chapter 4. Silk Permeability: Hydrogen-Deuterium Exchange 35 regions mainly consist of alanine and the rest of silk are rich in glycine, measuring deuterium content in silk's different amino acid segments at representative time points in Figure 4.6 holds promise for solving this mystery. The vigorous exchange between our sample and its surroundings also poses a technical challenge for any experiment on the deuterated silk sample prepared this way. To guarantee a consistent sample during an experiment, the sample container needs to be very well sealed and the measurement time should be minimized. silk showed evidence of mobile water confined in native silk at temperatures far below the freezing point of water [38]. 36 Chapter 5 13C-D REDOR: Permeability of Different Structural Regions The availability of the assigned 1 3 C spectrum of silk [29] makes it possible to quantify water permeability of silk's different structural regions. Shown in Figure 5.1 is part of the 1 3 C C P / M A S chemical shift spectrum of a native silk sample 1 . Of particular interest are the alanine C Q and glycine Ca resonance peaks because they are relatively well separated and can provide information about the permeability of silk's polyalamne and glycine-rich regions. Our initial attempt of 1 H - D - 1 3 C polarization transfer was unsuccessful. 1 3 C - D REDOR proved to be an appropriate approach. ,. CZ3 i n C chemical shift (ppm) Figure 5.1: Part of the 1 3 C C P / M A S chemical shift spectrum of silk. The area between the two dashed lines is chosen as the alanine C a resonance peak; the area between the two solid lines is chosen as the glycine Ca resonance peak. LFor a full 1 3 C CP/MAS chemical shift spectrum, see Section 2.8.1 of Chapter Two. Chapter 5. 1 3 C - D REDOR: Permeability of Different Structural Regions 37 5.1 Experimental Silk Samples The major ampullate gland (dragline) silk from adult female Nephila clavipes spiders was used. The samples are unoriented and each contains 30 mg silk. Each sample was soaked in deuterium oxide (Cambridge Isotope Labs, Andover, MA) for a controlled amount of time and then dried. Our sample container, the MAS rotor, was well sealed 2 . N M R Spectroscopy The 1 3 C - D REDOR experiments were performed on a Varian Inova 400 spectrometer, using a Varian 3-channel 4 mm MAS probe. The 1 3 C and D resonance frequencies are 100.5 and 61.4 MHz respectively. The REDOR pulse sequence used here was introduced by T. Gullion [39, 40] and is reproduced in Figure 5.2. The pulse sequence is shown with a six rotor cycle dipolar evolution period. The deuterium pulse has a flip angle of 6 = TT/2. A l l 1 3 C pulses after the CP pulse are IT pulses following the xy — 4 phase cycle, except for the two pulses specifically marked with the CP phase cf>. We used rf field amplitudes of 83.3 kHz for 1 H - 1 3 C CP, 100 kHz for *H decoupling, and 96 kHz for the deuterium pulse. The spinning rate was set to 5000 Hz. l H 13 c CP CP* decouple x y - 4 <|» x y - 4 (j> acquire nil rotor 0 6T r Figure 5.2: The REDOR pulse sequence. For the above pulse sequence, the universal REDOR dephasing curve for a powder sample 2The narrow hole in the spacer at one end of the rotor was sealed with a specially made teflon screw to minimize escaping of deuterium. Chapter 5. 13C-D REDOR: Permeability of Different Structural Regions 38 is given by [41] AS 1 5o~ ~ 6 1 + A^Ji(V2tD)J_l_(V2tD) + ^-Ji(2y/2tD)J_i(2y/2tD) (5.1) where J±i are Bessel functions of order ±\, D is the dipolar coupling constant and t is the dipolar evolution time. 5.2 Initial Analysis As shown in Chapter Two and the preceding section, in an ideal sample where every spin pair is identical and all pairs are well isolated from each other, the interpretation of REDOR data is straightforward. Complication arises when there are couplings to multiple spins (e.g. a 1 3 C nucleus coupled to three 2 D nuclei simultaneously) and many types of neighboring envi-ronment are possible (Figure 5.3). Our deuterated silk sample exemplifies such complicated 2D \ 13/"! 2D \ 1 3 C I 2D etc. Figure 5.3: Many types of possible neighboring environment. Each type is different from the other types only in terms of available deuterium neighbors. cases and several strategies have been employed to interpret our REDOR data. 5.2.1 Gaussian Description A consequence of the central limit theorem is that a 1 3 C spin having a large number of independent heteronuclear dipolar interactions will have a dipolar evolution described by a Gaussian function [42]. Figure 5.4 illustrates the amide hydrogen sites in the neighborhood of an alanine C a present in a polyalanine /3-sheet crystal. If a large fraction of those amide sites are occupied by deuterium, the alanine C a REDOR data could be described by a Gaussian function: (5.2) Chapter 5. 1 3 C - D REDOR: Permeability of Different Structural Regions 39 (a) (b) Figure 5.4: Amide hydrogen sites in the neighborhood of an alanine C Q present in a /3-sheet conformation: (a) amide hydrogen sites on the same /3-sheet with the C a (b) amide hydrogen sites on the neighboring /3-sheets of the C a . Distances to the seven nearest amide hydrogen sites are labeled. The figure was generated by the molecular visualization software RasMol using the atomic coordinate data provided by X-ray diffraction [43]. i.e. the data would reach a limiting value of a, representing the fraction of all alanine C Q s sufficiently close to deuterium atoms to undergo extensive dipolar dephasing. We could then use this a value to quantify water permeability in silk. For a silk sample soaked in D 2 0 for 16 days, our alanine Ca REDOR data and the best fit to Equation 5.2 are shown in Figure 5.5. Since 90 % of all alanine residues are present as /3-sheets, the data itself clearly demonstrates that hydrogen-deuterium exchange has happened in the /3-sheet regions. The Gaussian function, however, doesn't appear to be the most appropriate description in this case. Our data do not show a plateau as described by a Gaussian function. This is not too surprising if one considers the maximum dipolar evolution time of 10 ms in our REDOR experiments. The contributions from far away deuterium neighbors with dipolar coupling constants much less than 100 Hz are negligibly small. 5.2.2 Probability Description The above analysis suggests that we should consider only the nearest deuterium neighbors. Figure 5.6 shows the three nearest of all possible deuterium neighbors of an alanine C Q in Chapter 5. 1 3 C~D REDOR: Permeability of Different Structural Regions 40 0.8 S£ 0.6 < 0.4 0.2 16 d a y s : A l a C « a=0 .64±0 .01 4 6 T ime (ms) 10 Figure 5.5: Silk sample soaked in D 2 0 for 16 days: REDOR experimental data for alanine CL resonance with the best fit to Gaussian function 5.2. a polyalanine /3-sheet crystal. As indicated in the figure, we denote these three nearest neighbors as deuterium A, B and C, corresponding to 1 3 C - D distances of 2.11 A , 2.53 A and 3.71 A or dipolar coupling constants of 493 H z , 286 H z and 91 H z respectively. To quantify water permeability, we introduce the symbol f, which stands for the probability for an amide hydrogen to be replaced by deuterium. According to the phase structure model of silk (Figure 3.8 and Table 3.2), a careful analysis of water permeability would involve at least three f values: fs, f a and fj for the /?-sheet, amorphous and interphase regions respectively. We can however use fs alone to describe alanine because 90 % of all alanine residues in silk are present as /3-sheets. Listed in Table 5.1 are the seven different types of neighboring environment a C Q can have and the probabilities of being in each of them. The REDOR dephasing curve for a Ca in /3-sheets can then be written as: AS So +fs •/,-(!- /,) ( f ) + (¥) + (f) \ On / A \ ° 0 / B \ <J0 / C . ( — ) AB V S0 J AC BC ~^~fs fs ' fi /AS (5.3) ABC where, for example, (^f) A B i s the REDOR dephasing curve for the case of having deuterium neighbors A and B only. To fit our experimental data to Equation 5.3, we need to first simulate (4^) etc. \ So J AB Chapter 5. 13C-D REDOR: Permeability of Different Structural Regions 41 alpha carbon amide deuterium Table 5.1: Seven different kinds of neighboring environment of a C Q in /3-sheets and the probability of being in each of them. neighboring environment probability A only B only fs • (l-f s) • (l-f s) C only AB only AC only f, • f. • O f . ) BC only A B C Chapter 5. 1 3 C - D REDOR: Permeability of Different Structural Regions 42 Table 5.2: Chemical shift information for alanine C a [12] and glycine Ca [45]. Ca On, 622, S33)ppm relative to TMS fiiso (pP m ) relative to transmitter frequency Saniso (PPm) V Ala Ca (65, 57, 32) -39.35 -19.7 0.437 Gly Ca (66, 46, 27) -45.15 19.7 0.96 5.3 S imula t ion 5.3.1 Approximation In a /3-sheet conformation, the polypeptide chains are almost fully extended. We shall thus approximate the /3-sheet in Figure 5.6 by three polypeptide chains of trans conformation, i.e. with torsion angles (</), ip, w)=(180D, 180°, 180°). With all atoms coplanar, it is not hard to work out the Euler angles for transforming from the principle axis system (PAS) of an interaction tensor to the crystal frame ( X 0 - , Y"", Z"") which we will choose as the PAS of the CQ-deuterium A dipolar interaction tensor. 5.3.2 Program and Parameters Our simulations of the REDOR dephasing curves for ) A etc. were performed using the SIMPSON program [44], which is essentially a numerical evaluation of the Liouville-von Neumann equation 2.21 mentioned in Chapter Two. The SIMPSON program for simulating (^r) A B C is given in Appendix A as an example. The parameters used in the simulations are explained as below: a-Carbon Chemical Shift Tensors The chemical shift information for alanine C Q and glycine C Q are listed in Table 5.2. The Euler angles of chemical shift PAS in the crystal frame are irrelevant for our R E D O R simu-lation and are picked arbitrarily. Amide Deuterium Quadrupolar Interaction Tensor For the amide deuterium, we use a quadrupolar coupling constant (QCC) of 201.741 Hz and an asymmetry parameter of 0.192 as derived from birr quadrupolar echo deuterium spectrum (see Chapter Four). According to reference [37], the largest component of the quadrupolar tensor V 2 2 lies nearly along the N-D bond; the second largest component V x x lies, to a good approximation, along the normal to the molecular plane (Figure 5.7). 5.3.3 Simulated R E D O R Dephasing Curves Figures 5.8, 5.9 and 5.10 show the simulated REDOR dephasing curves for ( ^ ) etc. Chapter 5. 1 3 C - D REDOR: Permeability of'Different Structural Regions 43 HH alpha carbon • amide deuterium Figure 5.7: Principle axis systems of deuterium B quadrupolar interaction tensor Vs and CQ—deuterium B dipolar interaction tensor DB. Y c r and are the Y and Z axes of the crystal frame. 5.4 Resul t : A l a n i n e For the silk sample soaked in D 2 0 for 16 days, our REDOR experimental data for alanine C Q resonance and the best fit to Equation 5.3 are shown in Figure 5.11 (a). It can be seen that our model describes the experimental data extremely well. We obtain an fs value of 0.51, which means, after a long soaking time, about 50 % of the amide hydrogens in the /3-sheet regions are replaced by deuterium. Apparently, adding a fourth nearest deuterium neighbor to the analysis won't improve the quality of the fit very much. But one may question whether including only the two nearest neighbors A and B would be sufficient, since the coupling strength to deuterium C is significantly smaller than A and B. Figure 5.11 (b) shows the same data as in Figure 5.11 (a), but with the best fit to the following equation: The worse quality of the fit shows that deuterium C has a measurable contribution to the Chapter 5. 1 3 C - D REDOR: Permeability of Different Structural Regions 44 0.8 55 0.6 0.4 0.2 A only B only Conly O Q • + + + • •B Q • 4 6 Time (ms) 10 Figure 5.8: Simulated REDOR dephasing curves: (^ ) , (ff)B a n d (If),. 0.8 GO 0.61-<3 0.4 0.2 AB only AC only BC only + • Q • • B • + + + + + + + + + + + « * 1 * g i S S § 1 • f • • • Q * X 10 Time (ms) Figure 5.9: Simulated REDOR dephasing curves: (^ f) , (ff) c and (ff) BC Chapter 5. 13C-D REDOR: Permeability of Different Structural Regions 45 4 6 Time (ms) 10 Figure 5.10: Simulated REDOR dephasing curve: (AS) ABC Table 5.3: Alanine C Q : best fit fs values for different soaking times. soaking time fs x 2 16 days 0.51 0.002 3 hours 0.35 0.006 2 minutes 0.24 0.04 REDOR dephasing within 10 ms. The effect of this additional small coupling manifests itself as a slightly shallower rise and less oscillation. For samples with shorter soaking times: 3 hours and 2 minutes, R E D O R data and the best fits to Equation 5.3 are shown in Figure 5.12 and the results are listed in Table 5.3 in comparison with that of 16 days. It can be seen that f s doesn't change linearly with soaking time. Instead it increases dramatically at the beginning of the soaking, but increments very slowly over a long time. Analysis of the glycine REDOR data in the next section gives us some insights into this result. 5.5 Resul t : G lyc ine As mentioned in Chapter Three, glycine-rich regions (including both the interphase and the amorphous regions) of the Nephila edulis dragline silk were found to form a 3i-helical structure [31], which we assume describe equally well the same regions in our silk sample. Chapter 5. 13C-D REDOR: Permeability of Different Structural Regions 46 0.8 16 days: Ala C a fs=0.51 %2= 0.002 1 0.8 16 days: Ala C« fs= 0.58 0.02 Ca 2 4 6 8 10 Time (ms) (a) 2 4 6 8 Time (ms) (b) 10 Figure 5.11: Silk sample soaked in D20 for 16 days: REDOR experimental data for alanine C a resonance with the least-squares fits to (a) Equation 5.3, which considers deuterium neighbors A, B and C and to (b) Equation 5.4, which considers only deuterium neighbors A and B and neglects of effect of deuterium C. %2 values are the least-squares values defined by x2 = z~2i [Vi — y(xi)]2 f ° r a data set (XJ, fitted to a function y(x). Like the /3-sheet structure, the 3i-helical structure is stabilized by inter-chain hydrogen-bonding and is well extended [46]. We shall hence continue to use the approximation in Section 5.3.1 for the glycine-rich regions of silk. For the sample soaked for 16 days, assuming f a = l 3 and using the fs value of 0.51 we obtained above, we can fit our glycine experimental data to the following equation to extract f i-AS ~So~ = 0.32 • \fs • (1 - f„) • (1 - /,) + fs 'Is -(l-fs) \ i~>0 ' AB (AS\ + Js'fs'Js\ C I V O f ) ' ABC + 0 .25 , ( f ) \ J O / ABC + 0.43 • \fi • (1 - fi) • (1 - fi) + \ S 0 J B V SQ ) AC \ SQ J BC \SoJc + (f) + (^) + ( f ) \ DO / A s Do ' B \ DQ / T 3Since the amorphous regions were found to be highly mobile in wet silk, we assume the amorphous regions are easily accessible to water. This assumption is removed in the later discussion. Chapter 5. 1 3 C - D REDOR: Permeability of Different Structural Regions 47 0.8 3 hours: Ala C a fs= 0.35 X = 0.006 0.8 ^ 0.6 < 0.4 10 2 minutes: Ala C a fs= 0.24 X2= 0.04 4 6 8 Time (ms) (b) 10 Figure 5.12: (a) Alanine C a REDOR data for a silk sample with 3 hours' soaking time, (b) Alanine C Q REDOR data for a silk sample with 2 minutes' soaking time. The best fits are to Equation 5.3. + fi-fi'(l-fi) ( ¥ ) + (x) V OQ / AB V OQ 'AC V O 0 / BC + fi-fi-fi(^) ) (5-5) V 00 / ABC J in which 0.32, 0.25 and 0.43 are the fractions of glycine in the three regions as listed in Table 3.2. Figure 5.13 (a) shows our REDOR experimental data for the glycine Ca resonance and the best fit to Equation 5.5. The quality of the fit for glycine is not as good as that for alanine, indicating that the approximation we made in Section 5.3.1, although describing very well the /3-sheet conformation, is insufficient to represent the molecular structure in the glycine-rich regions 4 . For the 16 days' soaking time, we obtain a fj value of 0.67, in between fs and fa, showing that the permeation of water into the interphase regions is restricted. It is interesting to notice that the REDOR data in Figure 5.13 (a) can be equally well 4 T h i s is possibly due to • the trans comformation can't approximate the 3i-helical structure very well, • the 3i-hel ical structure alone is insufficient to describe the irregularity in the glycine-rich regions, • when silk is wetted and then dried, the molecular structures of the glycine-rich regions are altered considerably and can no longer be described by 3i-helices. Chapter 5. 1 3 C-D REDOR: Permeability of Different Structural Regions 48 2 4 6 8 10 2 4 6 8 10 Time (ms) Time (ms) (a) (b) Figure 5.13: Silk sample soaked in D 2 0 for 16 days: REDOR experimental data for glycine C Q resonance with the least-squares fit to (a) Equation 5.5 and (b) Equation 5.6. fitted to the following equation (Figure 5.13 (b)): AS ~So~ = 0 . 3 2 - j / s - ( l - / s ) . ( l - / 5 ) + fs-f,-(i-fs)\(^r) \ Do / AB "V fs'fs'fsi ~7T ) V O O / ABC V O O / B \ o n / C SoJ AC S0 J 0 / BC + 0.68 • fi+a • (1 - fi+a) • (1 - fi+a) "F / i + a ' fi+a ' (1 fi+a) / A 5 \ ~t~ /t+a ' / i + a ' fi i+a fAS\ \ '.AB • \ o n / AC ABC ( f ) + ( x ) + (f) ' V O O / A Voo/fi Voo/c A S \ .CM) So / B C (5.6) where we have assumed that the permeability of the glycine-rich regions (including both the interphase and the amorphous regions) can be described by a single f value: f; + a . The fit yields fi+a=0.74, approaching the weighted average of the fj and fa values above, which is 0.77. In principle, if the REDOR data defined by a function with two components: 2 AS (T) + ( f ) + ( £ ) ' \ OQ / A • \ OQ / B V O Q / C Chapter 5. 1 3 C-D REDOR: Permeability of Different Structural Regions 49 Table 5.4: Glycine C Q : best fit f i + a values for different soaking times using Equation 5.6. soaking time fs from section 5.4 fi+a x1 16 days 0.51 0.74 0.04 3 hours 0.35 0.49 0.06 2 minutes 0.24 0.41 0.07 + fj-frfj(^r) V J0 ''ABC is fitted to a function with one component: AS ( ¥ ) + ( ¥ ) + ( ¥ ) \ / AB \ &0 / AC s. On / BC (5.7) S0 f1+2 • (1 - / 1 + 2 ) • (1 - / 1 + 2 ) (AS + + fl+2 + fl+2 • (1 - /l+2) /AS\ V So J B \ So / c V So ^) AB ^ So )yic V So J BC '0 s ABC (5.8) /1+2 • fi+2 • fi+2 ^-^r the resultant fx+2 is not equal to the average of f i and {2, because in general, / • ( l - / ) - ( l - / ) ^ / - ( l - / ) - ( l - / ) (5.9) in which the top bar means weighted average. In practice, by making different choices of (ai, a2, f i , f2) and fitting the REDOR data defined by Equation 5.7 to Equation 5.8, we found that the quality of fit is excellent in most of the cases and the resultant f i + 2 approaches f very well when fx and f2 are close and deviates from f by no more than 0.1 even if f i and ^ are very different. Examples of this analysis are given in Appendix B. Although this is not a rigorous deduction, it holds for all the choices of (ai,.a2, f i , f2) we have sampled and we believe the situation in silk is no exception. This finding is important, because if the assumption of f a = l is not valid, especially for shorter soaking times: 3 hours and 2 minutes, we can still use Equation 5.6 to obtain f i + a , which approximates the average f of the interphase and amorphous regions. The best fit f i + a values for shorter soaking times are listed in Table 5.4 in comparison with that of 16 days. Similar to the change of fs with soaking time, f j + a also increases dramatically at the beginning of the soaking, but increments very slowly over a long time. For the same soaking times, however, the fractions of amide hydrogen atoms being replaced by deuterium are smaller in the /3-sheets than in the interphase and amorphous regions, i.e. the exchange rate in the /3-sheets is smaller. 5.6 Discuss ion In the above analysis, we use three f values (fs, fj, fa) to describe the water permeability of silk's three different kinds of structural regions. One certainly wouldn't expect an abrupt Chapter 5. 1 3 C-D REDOR: Permeability of Different Structural Regions 50 change in f at the interface of any two regions. A gradual change in f is probably closer to the truth. As an extension of the argument we make in Appendix B, we explain fs, fj, fa as approximated averages over each kind of structural regions. Take the /3-sheet regions for example. One possible explanation for the change of fs with soaking time is that at the beginning of soaking, the distribution of deuterium in a /9-sheet crystal is highly nonuniform, i.e. exchange happens a great deal at the surfaces of a /3-sheet crystal but very little within the crystal. Water then permeates slowly into the crystal interior over a long soaking time. In this case, there must be a gradient of fs from the surface to the interior of a crystal even when the soaking time is long. The fs values we obtained above are then the approximated average of all the fs values in the /3-sheet regions. Similarly, the change of f j + a with soaking time reflects domains in the glycine-rich regions, most likely the interphase regions, where water permeation is restricted and isotope exchange is slow. One complication associated with 1 3 C - D REDOR is the effect of deuterium on cross polarization dynamics [39]. This effect manifests itself as a scaling factor e relating the measured REDOR data with the theoretical ones : AS ~So~ AS ' So (5.10) Therefore, strictly speaking, Equation 5.3 should be written as AS So f s - ( l ~ fs) • (1 - fs) +fs •/,•(!- fs) +fs • fs • f £ ( A S ) I C ( A S ) + £ ( A S ) V So ) A \ So J B \ So / C /AS\ ,' /AS\ (AS\ £AB + € A C [ - ^ - J +eBc[-z-) V on J AB \ on / AC \ Oo / BC (AS\ £ A B C [ j \ OQ J ABC (5.11) in which each term is scaled by a different factor, because the effect of deuterium on CP dynamics may be slightly different for different types of neighboring environment. Since the amide deuterium is not directly bonded to C a , we estimate this effect to be small and neglected it for simplification. Another complication often met in 1 3 C - D REDOR is the effect of finite deuterium pulse power. For REDOR data described by the universal dephasing functions, this often leads to underestimation if REDOR is used to quantify isotope content (see Equation 2.72). Our data analysis circumvents the need for correcting this effect, because the SIMPSON simulation is done with the same deuterium pulse power as used in our REDOR experiments. In Chapter Four, we posed a question about the "slow-exchanging part" of the silk: can we relate it to silk's specific structural regions? To address this problem, the REDOR experiment was performed on the silk sample mentioned in Chapter Four, which had been slowly exchanging with the air for four months. Figures 5.14 (a) and (b) show the REDOR data and results of the best fits. The results are also listed in Table 5.5 in comparison with the results from the sample which was soaked for the same amount of time (3 hours), dried and well sealed, because the latter represents exactly the situation at time zero in Figure 4.6. It is very clear that in a nearly dry silk sample, the /3-sheet crystalline regions can exchange isotope with water from the air. During four months' exposure, the change of Chapter 5. 1 3 C - D REDOR: Permeability of Different Structural Regions 51 c/3 < 1 0.8 0.6 0.4 4 months'exposure: Ala C a fs= 0.22 X2= 0.02 0.8 £ 0.6 GO < 0.4 4 months'exposure: Gly Ca fi«= 0.07 X = 0.08 10 4 6 8 10 Time (ms) (a) Figure 5.14: Silk sample mentioned in Chapter Four, which has been slowing exchanging with the air for four months: (a) alanine C a REDOR data with the least-squares fit to Equation 5.3, (b) glycine C Q REDOR data with the least-squares fit to Equation 5.6. Table 5.5: REDOR results for the deuterated silk sample which has been slowly exchanging with the air for four months. The results are in comparison with that for the sample with 3 hours' soaking time. sample fs f i + a soaked for 3 hrs 0.35 0.5 soaked for 3 hrs and exposed for 4 mons 0.22 0.07 f s is significantly smaller than the change of f j + a , showing unambiguously once again that the exchange rate is considerably smaller in the /3-sheet regions than in the interphase and amorphous regions. We should therefore relate the slow-exchanging part of the silk mainly to the /3-sheet regions, especially the interior of /3-sheet crystals. The interphase regions, however, could also participate in slow exchange since water permeation into the interphase regions is also shown to be restricted. 5.7 Conclusions Firstly, our REDOR data clearly demonstrate that the /3-sheet crystalline regions of silk are accessible to water. This result is surprising at first glance, because X-ray diffration showed that the inter-Chapter 5. 13C-D. REDOR: Permeability of Different Structural Regions 52 sheet spacings in the crystalline regions remain unchanged on supercontraction [9] and studies of water-induced protein dynamics using NMR reveal no change in the dynamics of alanine residues when silk is wet (see Chapter Three). We believe, however, that our results support those earlier findings instead of conflicting with them because the SIMPSON simulations for alanine REDOR dephasing curves by themselves were based on a /?-sheet structure. The good quality of fit is evidence that this structure remains the same in supercontracted silk. For proteins in solutions and crystal lattices, studies of hydrogen-deuterium exchange have found that amide hydrogen atoms in the interior of proteins do exchange at a finite rate with isotope-labeled water [32]. There is no consensus on how this occurs and what dynamical fluctuations are responsible for exchange of interior atoms involved in hydrogen bonding. Two popular hypotheses are (1) breathing mechanism, or transient local unfolding of proteins and (2) permeation mechanism, i.e. rare instances of diffusion of water molecules to various sites in the protein interior. Although for proteins in solution, evidence can be found for both mechanisms, local unfolding would be expected to be greatly diminished if the proteins are in crystal lattice [32]. We therefore attribute the unexpected permeability in silk's /3-sheet crystalline regions to the permeation mechanism and explain the exchange happening in the /3-sheet regions of the nearly dry silk sample as due to diffusion of water from the air into those regions. Secondly, for proteins in solutions, it has been found that in general the atoms that exchange least readily from folded proteins are those that are in the interior of the molecule and involved in hydrogen bonding in /3-sheets.: Crystallographic measurements, however, are not very amenable to exchange rate measurements. A few studies for proteins in crystal lattices generally confirm the findings of solution studies [32]. Our REDOR results is a further support for this correlation between exchange rate and structure, because for the same soaking time and exposure time, we found that the fractions of amide isotopes being exchanged (f values) are ordered as fs < f j + a , in accordance with the molecular structure of silk. We further notice that for the longest soaking time (16 days), fj is only 67 %. This is an indication of rigid protein structure or strong hydrogen bonding in the interphase regions. 53 Chapter 6 Summary and Recommendation The work presented in this thesis has two major goals. The first was to probe the water permeability of silk's different structural regions so as to gain a better understanding of silk supercontraction. The second was to develop techniques for similar types of studies, for example, the study of the effect of other molecules on silk and the study of the permeability of other complex biopolymers. Use of isotope-labeled water in our study provides new information about the hydrogen-deuterium exchange processes and the water permeability of silk. Firstly, deuterium N M R clearly demonstrated the vigorous exchange between silk proteins and the surrounding envi-ronments and fact that even in a nearly dry silk sample, silk proteins can exchange isotopes with water from the air. It also suggests that a part of the silk, tentatively assigned as the /3-sheet crystalline regions, has a much slower rate of exchange relative to the rest of the silk. Secondly, in contrast to the indications from previous studies by X-ray diffraction [9] and NMR [10, 11], our 1 3 C - D REDOR NMR study provides direct evidence that the /3-sheet Crystalline regions of silk are accessible to water. Comparing this result with the findings of those earlier experiments, we conclude that one should take caution when correlating structural change and change of protein dynamics with water permeability. In the case of dragline silk, water can permeate slowly into the crystalline regions, but doesn't change the molecular structure and protein dynamics in those regions, and therefore the crystalline regions are not responsible for the supercontraction process. We also show that the corre-lation between isotope exchange rate and molecular structure, usually found for proteins in solutions or crystal lattices, also holds true for the insoluble silk proteins. The exchange rate is smaller in the /3-sheet crystalline regions than in the rest of the silk; for the longest soaking time (16 days), the fraction of amide hydrogens being exchanged by deuterium is 51 % in the /3-sheet regions versus 74 % in the rest,of the silk. We further found that water permeation into the interphase regions is restricted, a reflection of rigid molecular structure or strong hydrogen-bonding in those regions. Lastly, our REDOR study confirmed that the slow-exchanging part of the silk suggested by deuterium N M R is composed mainly of the /3-sheet regions, especially the interior of the /3-sheet crystals but may also include a portion of the interphase regions having rigid molecular structure, hence buried groups. Our study represents a successful case of using REDOR N M R to quantify isotope content in a complicated biopolymer where multiple couplings and multiple neighboring environ-ments exist. Similar techniques can be employed to study the effect of other molecules on silk. For example, sodium nitrate (NaNOa), when absorbed by silk, increases the strength of the fiber. 1 3 C - 1 5 N REDOR can be used to study the penetration of 15N-labeled sodium nitrate into silk's different structural regions so as to elucidate their roles in this change of fiber strength. Similar types of studies should, however, benefit from using selectively 13C-labeled silk sample. For example, labelling of .the alanine C Q site better separates the Chapter 6. Summary and Recommendation 54 alanine C a resonance peak from other resonances and better reflects the situation of the /3-sheet regions. In addition, good labelling results in enhanced single-to-noise ratio which allows measurement of REDOR data at longer dipolar evolution time, and hence allows mea-surement of long-distance interactions, which are often encountered if the isotope of interest is not directly bonded to the protein backbones. 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Nature, 176:780, 1955. 58 Appendix A SIMPSON Simulation of Three-Coupling REDOR Dephasing Curve As an example of the REDOR simulations we did in Section 5.3, the SIMPSON program for simulating REDOR dephasing curve { ^ ) A B C i s shown here. spinsys { channels 13C 2H nuclei 13C 2H 2H 2H dipole 1 2 -493.4 0 0 0 dipole 1 3 -286.2 0 138.9 90 dipole 1 4 -90.77 0 46.7 90 ; quadrupole 2 1 201741 0.192 270 37.3 90 quadrupole 3 1 201741 0.192 90 150.3 -90 quadrupole 4 1 201741 0.192 90 150.2 -90 shift 1 -39.35p -19.7p 0.437 50 20 10 } par { proton_frequency 400e6 spin_rate sw np crystal_file gamma_angles start_operator detect_operator verbose variable r f l variable rf2 5000 spin_rate/2.0 32 replOO 18 Ilx Hp 1101 86207 96154 proc pulseq {}- { global par maxdt 1.0 Appendix A. SIMPSON Simulation of Three-Coupling REDOR Dephasing Curve 59 set t90 [expr 0.25e6/$par(rf2)] set tr4 [expr 0.125e6/$par(rf2)] set tl80 [expr 0.5e6/$par(rf1)] set tr5 [expr 0.25e6/$par(rf1)] set tr2 [expr 0.5e6/$par(spin_rate)-$tl80] set tr3 [expr 0.5e6/$par(spin_rate)-$tr4-$tr5] set tr6 [expr $tr3-$tr2] reset $tr5 delay $tr2 pulse $tl80 $par(rfl) x 0 x delay $tr2 pulse $tl80 $par(rfl) y 0 x store 1 reset $tr5 delay $tr2 pulse $tl80 $par(rfl) x 0 x delay $tr3 pulse $t90 0 x $par(rf2) x delay $tr6 store 2 reset $tr5 delay $tr2 pulse $tl80 $par(rfl) x 0 x delay $tr2 store 3 reset acq for {set j 0} {$j < $par(np)-l} {incr j} { reset delay $tr5 prop 1 $j prop 2 prop 1 $j prop 3 acq } Appendix A. SIMPSON Simulation of Three-Coupling REDOR Dephasing Curve 60 proc main -Q { global par set f [fsimpson] fsave $f $par(name).fid > 61 Appendix B Fitting Two-Component REDOR Data to One-Component REDOR function Here we give two examples of fitting REDOR data defined by Equation 5.7 to Equation 5.8. They show clearly that the quality of the fit is excellent and the resultant f i + 2 approaches f very well when fi and f2 are close and deviates from f by no more than 0.1 even when fi and f2 are very different. Example One Here we choose (alt a 2 , fi, / 2 ) = ( | , §, 0.8, / 2 ) and vary f2 to test the quality of the fit and the relationship between f i + 2 and f. Figures B . l (a) and (b) show the REDOR data defined by Equation 5.7 and the best fits L i / f = 0.33 fi + 2 =0.26 2 4 6 8 10 Time (ms) (b) Figure B . l : REDOR data defined by Equation 5.7 and the best fits to Equation 5.8 with (a) f2 equal to LO and (b) f2 equal to 0.1. to Equation 5.8 with f2 equal to 1.0 and 0.1 respectively. Figure B.2 (a) is a plot of f - f 1 + 2 as a function of f2 and Figure B.2 (b) is a plot of f i + 2 as a function of f. Appendix B. Fitting Two-Component REDOR Data to One-Component REDOR function 62 fl f ( a ) (b) Figure B.2: (a) f - f i + 2 as a function of f 2 , (b) f i + 2 as a function of f Example Two In this example, we choose^ , o 2 , / i , /2)=(0-5, 0.5, 0.5, / 2 ) and vary f 2 to test the rela-tionship between f i + 2 and f. The results are shown in Figures B.3 (a) and (b). f2 f ( a ) (b) Figure B.3: (a) f - f i + 2 as a function of f 2 , (b) f 1 + 2 as a function of f. 

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