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Quantitative Analysis of Solid-State Homonuclear Correlation Spectra of Antiparallel #-Sheet Alanine Tetramers Akira Naito, Keiko Okushita, Katsuyuki Nishimura, Gregory Steven Boutis, Akihiro Aoki, and Tetsuo Asakura J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.7b11126 • Publication Date (Web): 08 Feb 2018 Downloaded from http://pubs.acs.org on February 13, 2018

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The Journal of Physical Chemistry

Quantitative Analysis of Solid-State Homonuclear Correlation Spectra of Antiparallel β-Sheet Alanine Tetramers

Akira Naito,1 Keiko Okushita,1,2 Katsuyuki Nishimura,2 Gregory S. Boutis,3,4 Akihiro Aoki,1 and Tetsuo Asakura1 *

1

Department of Biotechnology, Tokyo University of Agriculture and Technology, Koganei,

Tokyo 184-8588, Japan. 2

Institute for Molecular Science, 38 Nishigo-Naka, Myodaiji, Okazaki 444-8585, Japan.

3

Department of Physics, Brooklyn College of The City University of New York, 2900

Bedford Avenue, Brooklyn NY 11210, USA. 4

Department of Physics, The Graduate Center of The City University of New York, 365 5th

Avenue, New York, NY 10016, USA

* To whom correspondence should be addressed (Tel & Fax, 81-42-383-7733) email: [email protected]

Running title: Quantitative analysis of 2D

13

C -13C DARR spectra for structural analysis of

poly-alanine tetramers.

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ABSTRACT: Poly-L-alanine (PLA) sequences are a key element in the structure of the crystalline domains of spider dragline silks, wild silkworm silks, antifreeze proteins and amyloids. To date, no atomic level structures of AP-PLA longer than Ala4 have been reported using single crystal X-ray diffraction analysis. In this work, dipolar assisted rotational resonance (DARR) solid-state NMR spectra were observed to determine the effective inter-nuclear distances of C uniformly labeled alanine tetramer with antiparallel (AP) β-sheet structure, whose atomic

13

co-ordinates are determined from the X-ray crystallographic analysis. Initial build-up rates, Rj,k, were obtained from the build-up curves of cross peaks by considering the inter-nuclear distances arising in the master equation. Subsequently, experimentally obtained effective inter-nuclear distances reffj,k(obs) were compared with the calculated reffj,k(calc) values obtained from X-ray crystallographic data. Fairly good correlation between reffj,k(obs) and reffj,k(calc) was obtained in the range of 1.0 ~ 6.0 Å, with standard deviation of 0.244 Å, without considering zero quantum line shape functions. It was further noted inter-nuclear distances of inter-molecular contributions provide details relating to molecular packing in solid-state samples. Thus, the present data agree well with AP-β-sheet packing, but did not agree with P-β-sheet packing.


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1. INTRODUCTION Spider dragline silks and wild silkworm silks possess excellent mechanical properties by combining high modulus, strength, and extensibility. At present, these silks continue to attract the attention of researchers in biology, biochemistry, biophysics, analytical chemistry, polymer technology, textile technology and tissue engineering.1 Poly-L-alanine (PLA) sequences appear as key elements in the structure of the crystalline domains of these silks.2–5 In addition, PLA also exists in antifreeze proteins6,7 and in amyloids.8–11 Thus, the determination of PLA structure with anti-parallel (AP) β-sheet structure is important for understanding the mechanical properties of diverse polymers. However, there are no atomic level structures of AP-β-PLA larger than Ala4, because it is difficult to prepare large single crystals for use in X-ray diffraction analysis.12 Thus, it is necessary to develop spectroscopic methods to determine the atomic level structures of AP-β-PLA longer than Ala4. Homonuclear correlation NMR is routinely implemented to obtain inter-nuclear distance information, allowing for structural studies of a vast array of spin systems.13 In solution NMR, 1

H two-dimensional (2D) homo-nuclear NOE methods are often used to measure distance

constraints for structural elucidation.14 On the other hand, in solid materials, spectral resolution is usually poor due to strong 1H-1H dipolar interactions which do not allow for separating individual peaks in a 1H magic angle spinning (MAS) spectrum. One robust method for obtaining inter-nuclear distances in a solid sample involves

13

C homo-nuclear

correlation NMR. These experiments often provide sufficient spectral resolution, and thus, combined with selective or uniform 13C labeling methods, structural studies of solids are more readily approachable. Heteronuclear distances in solid state, such as a

13

C-15N nuclear pair, have been

measured by the rotational echo double resonance (REDOR) method.15–17 For example, accurate inter-nuclear distances have been obtained by REDOR to determine the three 3 ACS Paragon Plus Environment


dimensional molecular structure

16

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as well as details relating to the molecular packing

arrrangement.17 Among the currently available

13

C homonuclear correlation NMR methods, theoretical

and simulation studies of proton-driven spin diffusion (PDSD) have been recently improved.18 For example, a combined experimental and theoretical study of PDSD via 2D spectroscopy of a single crystal has been presented by Suter and Ernst in 198519. Additional groups have explored the energy conservation process via spatially separated spins20, or spins with different chemical shifts,21,22 based on experimental results from single molecules. Veshtort and Griffin have considered the non-Markovian kinetic equation instead of the master equation.23 One merit of the PDSD experiment is that any given peak intensity is not influenced by dipolar truncation.24,25 As a result, information through all inter-carbon distances of the sample can be obtained simultaneously.24 Combined with molecular dynamics simulations, the PDSD experiment has been recently utilized to refine the structure of proteins by using NMR determined distance constraints.26 13

C-1H dipolar assisted rotational resonance (DARR)27,28 experiment is a second

solid-state

13

C homonuclear correlation NMR experiment that makes use of proton-driven

spin diffusion. These experiments make use of a 1H radio frequency (rf) field at the amplitude satisfying the rotary resonance recoupling (R3)29 condition. Under the R3 condition, the line width of 13C-1H dipolar recoupled spectra become broadened. As a result of peak broadening, the build-up rate of cross peaks, which reflect spin exchange rate between two correlated 13C nuclei, may be increased. The build-up of the cross peak intensity as a function of the mixing time (termed a build-up curve) provides the rate constant between the correlated 13C nuclear pair. Consequently, inter-nuclear distances of the correlated pairs can be determined. Therefore, DARR experiments are useful for detecting of weak cross peak signals with long inter-molecular distance. Compared with PDSD, DARR’s advantage lies mainly in distance 4 ACS Paragon Plus Environment

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determination and obtaining correlations among multiply labelled 13C nuclei. In this paper, we discuss the applicability for distance measurements by DARR. In previous PDSD studies, the build-up curves have been simulated and fit to the observed spectra, where peaks are separable.18,30 However, in many samples with iterative sequences such as silks, there are structural heterogeneities and many overlapping peaks, making analysis of the data challenging. As a solution to this problem, we compare the experimental build-up curves with those calculated from candidate structures. Here we introduce an example of how to evaluate the effective inter-nuclear distances from experimental build-up curves of AP-β-Ala4 with that of a known β-sheet structure.31 The

13

C solid-state NMR

spectra of an alanine monomer to alanine trimer often show narrow NMR line widths, and it is relatively easy to obtain single crystals for X-ray diffraction analysis32 In the alanine tetramer, however, there are several peaks that overlap in the 13C NMR data. Additionally, it is difficult to prepare large crystals required for X-ray diffraction analysis. Alanine peptides longer than a hexamer show broaden 13C spectral patterns reminiscent of a large polymer.32. PLA sequence of different lengths have been synthesized and crystallized. Ala3 and Ala4 were crystallized having both parallel- and anti-parallel β-sheet structures. Although we were able to determine the atomic co-ordinates of Ala4 in anti-parallel β-sheet structure using single-crystal X-ray diffraction analysis, the crystal size of Ala4 in parallel β-sheet structure was too small for the single-crystal X-ray diffraction analysis. The longer peptides than Ala5 form only anti-parallel structures as indicated by FTIR and

13

C NMR spectra, however, the

crystal sizes were too small and difficult to determine atomic-coordinates.32 It is also reported that anti-parallel PLAs are more stable than the parallel β-sheet as calculated by ONIOM method programmed in the Gaussian09.33 PLA packs into two different arrangements, depending on the length of the sequence. Short sequences (n=5 or less) pack into rectangular arrangements, in which the packing of the 5 ACS Paragon Plus Environment


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chains in adjacent planes is rectangular, while longer PLAs (n>6) pack in a staggered arrangement, in which the packing of the chains in adjacent planes is staggered. 34 The atomic co-ordinates of PLA sequences in Samia cynthia ricini silk fibroin fiber packed into a staggered arrangement were reported previously.5 In our previous works,5,35 the packing structures of [U-13C] silk fibroin fiber of Samia cynthia

ricini

(a

wild

silkworm)

and

their

GGAGGGYGGDGG(A)12GGAGDGYGAG, with different

13

34-mer

model

peptide,

C labelled positions have been

examined by DARR. The results showed that the silk fibroin fiber and polypeptide is packed in a staggered arrangement with an AP-β-sheet structure. Further, in our previous work, the heavy atom coordinates of the AP-β-Ala4 structure, including the intermolecular structure, have been determined by X-ray diffraction with a small single crystal (100×200×30 µm3).32 Moreover, the 1H coordinates of the AP-β-Ala4 peptide have been determined from 1H chemical shift assignments in a 1H MAS spectrum by ultra-fast MAS and chemical shift calculations with the use of Cambridge Serial Total Energy Package (CASTEP).31 Thus, AP-β-Ala4 is the largest in the polyalanine peptide family with a known structure, and is well suited for the evaluation of effective inter-nuclear distances from the build-up curves observed from polymer-like compounds with iterative sequences. The central aim of this work is to report on the applicability of distance measurements by DARR on a uniformly

13

C-labeled ([U-13C]) AP-β-Ala4, whose structural coordinates have

been completely determined. In the distance measurements by DARR, the rate constant Rj,k values were obtained from the initial slope analysis by taking into account the zero-quantum line shape function obtained from the

13

C-1H dipolar recoupled spectra. Subsequently, we

evaluated the inter 13C-13C distances from the rate constant Rj,k and converted to reffj,k(obs) and these values are compared to the reffj,k(calc) values obtained from x-ray diffraction data. Further, we characterize the standard deviation between experimental and simulated effective 6 ACS Paragon Plus Environment

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inter-nuclear distances to evaluate the accuracy of the distance measurements.

2. EXPERIMENTAL SECTION 2-1. Sample Preparation [U-13C] AP-β-sheet Ala4 was synthesized from an Fmoc [U-13C3] Ala monomer in the solid-phase synthesis. The terminal compound was treated with H2O / EtOH = 1:1 to form an AP β-sheet fine crystal32 and is denoted as the AP-β-Ala4 peptide. The purities of these peptides were checked by 13C solution NMR and IR to be greater than than 95%.

2-2. Solid-state 13C NMR experiments All of solid-state NMR measurements were performed on a Bruker Avance 600 spectrometer at Larmor frequency of 600 and 150 MHz for the 1H and

13

C nuclei, respectively, equipped

with a 2.5 mm O.D.1H-13C-15N triple resonance MAS probe. Sample was packed into 4 mm space at the middle of sample tube using original diflon spacers of 1 mm thickness for maintaining rf homogeneity. Typical rf fields of 1H and

13

C pulses were 100 and 93 kHz,

respectively. Spinning frequency of sample tube was actively controlled to 13.5 kHz ± 5Hz at room temperature. 1H-13C ramped amplitude cross polarization (CP) was employed for sensitivity enhancement with contact time of 1.5 ms at 1H rf field of 80 kHz. 1H decoupling was achieved using the SPINAL6436 sequence at the rf field of 100 kHz. 2D DARR experiments were performed under 1H rf irradiation with MAS, to satisfy R3 condition, during various mixing times shown Figure 1(a) (mixing times from 0.075 to 500 ms). A 2D

13

C

chemical shift resolved 13C-1H local field experiment, shown in Figure 1(b), was carried out to obtain the 13C zero-quantum line shape function during 1H irradiation in DARR experiments for the analysis of build-up curves in DARR. Quadrature detection in the indirect dimension was achieved by States procedure with t1 points of 350 and 500 for DARR and 13C-1H local 7 ACS Paragon Plus Environment


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field experiments, respectively. The number of scans used was 8 and 256 for DARR and 13

C-1H local field experiments, respectively, with repetition times of 3s for [U-13C]AP-β-Ala4.

The 13C transmitter frequency was set at 100 ppm that was the center of sweep width (SW) in both dimensions. 2D FIDs were zero filled to 4 K for both t1 and t2 time domains prior to Fourier transformation without apodization. Data processing was performed using TOPSPIN 2.1 (Bruker Biospin, Japan).

13

C chemical shifts were calibrated indirectly through

adamantane and tetramethylsilane (TMS).

Figure 1. Pulse sequences implemented in this study. (a) DARR, 2D correlation. (b) 2D chemical shift resolved 1

13

13

C homonuclear

C-1H local field experiment modified from (a).

H rf irradiation is applied with the amplitude at R3 condition (13.5 kHz) during t1 with a

fixed mixing time of 3 µs.

2-3. Analysis of DARR spectra A. Deconvolution of peaks in 2D DARR spectra To obtain the observed peak volume in the 2D DARR spectra, the line widths and the chemical shifts were determined in each dimension (ω1, ω2) of the 2D DARR spectra. An 8 ACS Paragon Plus Environment

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average of 14 build-up curve slices at each peak was used, including four of C1-4, Cβ1-4 and Cα1-4 carbon nuclei, and the intensities were fit to evaluate the initial slope. The fitting was performed using a FORTRAN program that assumed a 2D Gaussian line shape. The area obtained was normalized by the sum of the diagonal peaks in the observed peak intensity matrix ࡹ࢕࢈࢙ ሺ0ሻ obtained by the extrapolation of peak intensities from the DARR spectra. B. Calculation of build-up curves though polarization transfer matrix The underlying recoupling mechanism for

13

C-DARR27 includes

1

H-driven and

rotor-driven recoupling. The recoupling for the requisite residual energy for the

13

C-13C

flip-flop transition is provided from the 1H reservoir as well as macroscopic sample rotation through magic angle spinning.28 From the DARR spectra, a build-up curve which correlates with polarization transfer rate for a polarization-transfer rate for a distance of the

13

13

C-13C pair, may be obtained. Moreover, the

C-13C has been shown to correlate with the inter-nuclear

13

C-13C pair.28 In the DARR measurements, small dipolar couplings can be

measured even in the presence of larger couplings, because of the suppression of dipolar truncation.24 Therefore, for the determination of inter-nuclear distances from the uniformly 13

C-labeled 2D DARR spectra, we apply a master equation analysis.21,30 The DARR experiment may be used to determine the inter-nuclear distances of carbon

nuclei as follows. First, spin diffusion among multiply labeled 13C spins can be characterized by a master equation.26,30

M (τm) = [ exp (-Rτm)] M (0)

[1]

where M(τm) represents the cross peak intensities for the labeled

13

C spins at the mixing

time τm. In the above expression, M (0) is the initial peak intensities for the diagonal 9 ACS Paragon Plus Environment


components. The initial build-up rate, R

j, k

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, for the direct polarization transfer from j to k

nuclei under MAS rate of ωr is given by 21

ܴ௝,௞ =  1   r eff  j ,k

ംర ℏమ భ ቌ ೐೑೑ቍ భఱ ೝ ೕೖ

ల

ሺೕ,ೖሻ

భ ሺೕ,ೖሻ మ

ሺೕ,ೖሻ

భ ሺೕ,ೖሻ మ

൬௄ೋೂ ሺఠೃ ሻା௄ೋೂ ሺିఠೃ ሻା ௄ೋೂ ሺଶఠೃ ሻା ௄ೋೂ ሺିଶఠೃ ሻ൰

[2]

6

  Nj Nk 1   = ∑∑    m =1 l =1 r 6  j , k ,l , m   

[3]

( j ,k ) where K ZQ is the zero-quantum (ZQ) line-shape function and r j ,k ,l ,m is the effective

inter-nuclear distance between spin j in group l with Nl equivalent spins, and spin k in group m with Nm equivalent spins. The zero-quantum line-shape function is given by.21

( j ,k ) K ZQ (nω R ) =

1 2π

∫

∞

−∞

Similarly, the initial build up rate R case where the

[4]

F j (ω − nω R ) Fk (ω )dω

13

j, k

for the spin diffusion of the static sample or for the

C-1H dipolar interaction is not averaged out by slow MAS frequency, is

given by

ܴ௝,௞ =

ംర ℏమ భ ቌ ೐೑೑ቍ భఱ ೝ ೕ,ೖ

ల

ሺೕ,ೖሻ

Ｋೋೂ

[5]

The zero-quantum line-shape function is given by37

‫ܭ‬௓ொ ൫∆߱௝,௞ ൯ = ଶగ ‫ି׬‬ஶ ‫ܨ‬௝ ൫߱ − ∆߱௝,௞ ൯‫ܨ‬௞ ሺ߱ሻ݀߱ ሺ௝,௞ሻ

ଵ

ஶ

[6]


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where Fj (ω) is the single-quantum (SQ) dipolar line-shape function of spin j under 13C-1H a 1

H DARR recoupling field (ωR). ∆ωj,k is the peak difference frequency between j and k peaks.

Rj,

k

values are obtained by varying τm values using Eq. [1] in the DARR experiments.

Consequently, the effective inter-nuclear distance rj k eff (DARR distance) can be determined from R j, k values using Eqs. [2] and [4], or Eqs. [5] and [6]. Using the experimental data, SRj,k is initially obtained as the initial build up rate, where S is the phenomenological scaling factor. Second, the value of S value is evaluated by obtaining the best correlation between reffj,k(obs) and reffj,k(calc) values. In the multiply labeled samples, DARR experiments are not strongly influenced by dipolar truncation—polarization transfer may occur across both small and large couplings24 . Therefore, even long inter-nuclear distances can be determined accurately. The effect due to multiple spin labeling such as multiple spin diffusion pathways may be taken into account by a master equation analysis.26,30

3. RESULTS AND DISCUSSION 3-1. Peak assignment of AP-β β -Ala4 in 13C CP MAS NMR spectrum. The assignment of each peak in the 13C CP/MAS spectrum of the [U-13C] AP-β-Ala4 is shown in Figure 2b. Nine peaks were resolved and each peak was assigned to the carbon nuclei shown in Figure 2a as follows; P1(C4; 181 ppm), P2(C2; 173 ppm), P3(C1, C3; 171 ppm), P4(Cα4; 51 ppm), P5(Cα2, Cα3; 50 ppm), P6(Cα1; 48 ppm), P7(Cβ3; 22 ppm), P8(Cβ1, Cβ3; 20 ppm), and P9(Cβ4; 19 ppm). In these spectra, P3 (C1, C3), P5(Cα2, Cα3) and P8(Cβ1, Cβ2) represent overlapping peaks. The build-up curves with overlapping components were analyzed by summing the all components included in a given peak.



Figure 2. (a) X-ray crystallographic structure and (b) the

13

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C CP/MAS spectrum of [U-13C]

AP-β-Ala4. The bold numbers in (b) correspond to the numbers of the following matrix element numbers.

3-2. Assignments of the cross peaks in the DARR spectra. Figure 3 shows the DARR spectra of [U-13C] AP-β-Ala4 for the mixing times τm = 0, 100, and 200 ms. As expected, the higher enhancement of the cross peak intensities was detected for C-Cα, Cα-Cβ, and C-Cβ bonds when τm = 20 ms. It is noted that even in the cross peak with large chemical shift difference (e.g. the C4-Cβ4 cross peak) showed a significantly large intensities. The enhancement was significant at longer mixing times (Figure 3, 150 ms) and all 81 peaks were resolvable in the DARR spectrum at τm = 150 ms. It was thus possible to observe the build-up curves for all 81 diagonal and cross peaks as shown in Figure 4.


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Figure 3. (a) 2D 13C-13C DARR spectra of [U-13C] AP-β-Ala4 observed at the mixing times (τm) of 0,100 and 200 ms.

3-3. Determination of inter-nuclear distances from the initial slopes of DARR spectra The observed build-up curves of each peak in the DARR spectra are shown in Figure 4 and Figure S1. The experimental data are plotted on a normalized scale. In these graphs the maximum intensities were evaluated from their 2D peak volume in individually observed build-up curves. The diagonal elements of the DARR matrix decreased, while the off-diagonal elements of DARR matrix increased and subsequently decreased with increasing mixing time. In 2D homonuclear experiments, there are two pathways for spin diffusion; spatial spin diffusion and spectral spin diffusion.19 In the case of spatial spin diffusion, the nuclei are identical, the energy level differences are equivalent and the nuclear spin system is isolated from other lattice interactions (e.g. phonons). On the other hand, in the case of spectral diffusion, the energy level differences for dipolar coupled spins are not equivalent, and an additional energy reservoir is required for coherence transport to occur. In these experiments, the contribution from the atomic coordinates (spatial spin diffusion) are the same, so that the difference in the build-up curve rate in Figure 4 arises from spectral spin diffusion. For example, in the cross peaks corresponding to the most spectrally separated spins along the 13C 13 ACS Paragon Plus Environment


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chemical shift, such as the (row, column) = (1, 9) showed a fast build-up curve as shown in Figure 4. In general, to overcome the inefficient spectral spin diffusion between peaks with large chemical shift differences, the DARR experiments (Figure 1(a)) were performed using a 1

H-13C recoupling pulse27,28 shown in Figure 1(b). Then, as expected, such an effective

build-up rate by DARR was clearly observed (see Figure 4) even for spectrally separated spins.

Figure 4. Build-up curves of AP-β-Ala4 observed with DARR. The numbers shown for the peaks observed and labeled in Figure 2.


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Figure 5. Initial build-up curves for peaks P9-P4, P1-P2 and P1-P5. (a) Rapid initial build-up curve for peak P9-P4 (Cβ4-Cα4). (b) Slow initial build-up curve for peak P1-P7 (C4-Cβ3). (c) Initial build-up curve with poor fitting for peak P1-P5 (C4-Cα2).

Figure 5 shows the build-up curves for P9-P4, P1-P2 and P1-P5 cross peaks. Figure 5(a) shows a fast build-up curve, indicating a short inter-nuclear distance for the Cβ4-Cα4 direct bond. Figure 5(b) shows long build-up curve, indicating a long inter-nuclear distance for the C4-Cβ3 bond. Figure 5(c) shows build up curves arising from a long inter-nuclear distance, with poor fitting. The discrepancy between the fitted line and the experimental data may arise from the overlap of neighboring peaks, and these data were neglected in the initial slope analysis.



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In Figure 6, 13C chemical shift peaks resolved 13C-1H dipolar recoupled spectra under 1H rf irradiation at R3 conditions are shown. In addition, the cross-section along each

13

C

chemical shift in the direct ω2 dimension is shown in Figure 6 under 1H rf irradiation at R3 conditions. The 1H irradiation power for R3 (Figure 6a) is the same as that of 2D DARR experiments for obtaining the build-up intensities in Figure 5.

13

C-13C

The detected spectral

region in the DARR condition and the peak intensity is smaller, because of the active recoupling of 13C-1H dipolar interaction under 1H irradiation at R3 condition. Thus, the 13C-1H dipolar coupled spectrum was broadened and did not show side band patterns, except for carbonyl and carboxyl carbons.

Figure 6.

The cross section of 13C chemical shift resolved 13C-1H local field spectra under

R3 conditions. The cross-sections at each chemical shift are displayed.

On the basis of the

13

C-1H dipolar coupled spectra in Figure 6, the zero-quantum

line-shape functions Kj,kZQ(nωr) in Eq. [4] and Kj,kZQ(∆ωj,k) in Eq. [6] for the individual peaks were calculated. The simulated build-up curves and experimental build-up intensities from the DARR experiments are displayed in Figures 4 and 5 respectively. In the DARR build-up curves, the rapid build-up was well simulated even when correlations arise from peaks with 16 ACS Paragon Plus Environment

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large chemical shift differences (e.g. the P4-P9 build-up curve shown in Figure 5a). In the P9-P4 build-up curves, the intensities of experimental build-up curves increased exponentially and reached a maximum intensity at τm = 10 ms and then decreased gradually. In these simulations, we used the experimental 13C-1H recoupled spectra as shown in Figure 6 for evaluating the zero-quantum line shape function (see Eqs [4] and [6]). SReffj,k (obs) was evaluated using Eq. [1] with initial slope approximation. In the first step, the sum of zero-quantum line shape functions are assumed to be unity for the total of Kj,kZQ(ω) values, and differences of spectral diffusion components were not considered. Consequently, SRj,k. values were evaluated for the individual build-up element of a master equation (Eq. [1]). Using Eq. [2] with the sum of KZQ(ωr) components to be unity, the terms reffj,k (obs) were evaluated from the Rj,k using Eq. [3] by considering the S value. These reffj,k (obs) components were compared with the reffj,k (calc) based on the atomic coordinates obtained from X-ray crystallographic analysis,29 and the best fitted S value was evaluated. The correlation of reffj,k (calc) with reffj,k (obs) is plotted in Figure 7, and the standard deviation of 0.244 Å was obtained. Second, the zero-quantum line shape function under the MAS frequency ωr was considered to evaluate KZQ(ωr). Consequently, reffj,k (obs) was estimated using Eq. [3] with the best fitted S value. The correlation of reffj,k (calc) with reffj,k (obs) is shown in Figure 8. The standard deviation from the known values increased to 0.577 Å which is not as good as the first case. Furthermore, the term reffj,k (obs) for P1-P2, P1-P2, P2-P3 appeared beyond the vertical axis. Third, the K(j,k)ZQ(∆ωj,k) component was calculated using the zero-quantum line shape function in Eq. [6]. This is used because the 1H rf irradiation at R3 conditions recouples the 13

C-1H dipolar interaction and generates the K(j,k)ZQ(obs) component as described in the static

sample.19,22 The correlation of reffj,k(calc) with reffj,k(obs) using the best fitted S value is plotted 17 ACS Paragon Plus Environment


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in Fig. S2. The correlations of P1-P2, P1-P3 and P2-P3 cross peaks appear better and the correlation parameter achieved was 0.296 Å. We note that this correlation is as good as that for the first case (zero-quantum correlation functions are unity).

Fig. 7 Correlation between reffj,k(obs) and reffj,k(calc). Zero-quantum line shape functions are not included. The standard deviation across the data was 0.244 Å.


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Fig. 8 Correlation between reffj,k(obs) and reffj,k(calc). Zero-quantum line shape functions of Eq. [2] are included. Peaks P1-P2, P2-P3 and P1-P3 showed very long distances and were not within the displayed range. The standard deviation across the data was 0.577 Å.

The results indicate that the best fit for reffj,k(obs) were obtained without considering any zero-quantum line shape functions. This may observation may arise from the fact that that 13

C-1H dipolar interaction was significantly recoupled or that spectral components were

improved significantly, which is similar to the case of static samples. Thus, inter atomic distances obtained using the first method are summarized in Table 1. Thirty two reffj,k(obs) values were evaluated out of 36 cross peaks. Four of them (P1-P5, P4-P5, P4-P5, P5-P1) showed quite poor fitting, as shown in Figure 5c, and were removed from the Table 1 and Figure 7.

Table 1. Effective inter-nuclear distances reffj,k(obs) obtained from 2D DARR experiments, and reffj,k(calc) of obtained from X-ray diffraction data a AP-β-sheet A4 arrangement.29 Minimum inter-nuclear distances of inter- and intra-strand pairs for AP-β-sheet Ala4 crystals are provided.

Cross peak reffj,k(obs) (Å)

reffj,k(Calc) (Å)

Inter atomic pair

Minimum distance of Intra-strand pair (Å)

P1-P4 P2-P5

1.775 1.689

1.532 1.490

P3-P5

1.644

1.502

P3-P6

1.665

1.494

C4-Cα4 C2-Cα2, C2-Cα3 C1-Cα2 C1-Cα3 C3-Cα2 C3-Cα3 C1-Cα1

1.53 1.51 2.42 1.52 2.43 4.81 5.92 1.50

Minimum distance of Inter strand pair (Å) 4.46 4.22 5.02 4.45 4.91 4.96 5.04 4.35 19

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P4-P9 P5-P7

1.681 1.668

1.534 1.529

P5-P8

1.668

1.516

P6-P8

1.696

1.525

P1-P9 P2-P8

2.243 2.268

2.445 2.408

P3-P4

2.910

2.443

P3-P7

2.243

2.413

P3-P8

2.181

2.313

P1-P3

3.419

3.396

P2-P3

3.040

3.104

P2-P7 P3-P9

3.083 2.962

2.980 3.018

P4-P5

3.239

3.586

P5-P6

3.206

3.500

P2-P6 P4-P7 P5-P9

3.879 3.731 3.406

4.357 3.929 3.872

P1-P7 P7-P8

4.411 3.323

4.524 3.189

P7-P9 P1-P2 P2-P9 P6-P7 P1-P8

3.781 5.656 4.861 4.367 4.032

3.881 5.415 5.077 4.504 3.767

P4-P6

3.942

3.831

C3-Cα1 Cα4-Cβ4 Cα2-Cβ3 Cα3-Cβ3 Cα2-Cβ1 Cα2-Cβ2 Cα3-Cβ1 Cα3-Cβ2 Cα1-Cβ1 Cα1-Cβ2 C4-Cβ4 C2-Cβ1 C2-Cβ2 C1-Cα4 C3-Cα4 C1-Cβ3 C3-Cβ3 C1-Cβ1 C1-Cβ2 C3-Cβ1 C3-Cβ2 C4-C1 C4-C3 C2-C1 C2-C3 C2-Cβ3 C1-Cβ4 C3-Cβ4 Cα4-Cα2 Cα4-Cα3 Cα2-Cα1 Cα3-Cα1 C2-Cα1 Cα4-Cβ3 Cα2-Cβ4 Cα3-Cβ4 C4-Cβ3 Cβ3-Cβ1 Cβ3-Cβ2 Cβ3-Cb4 C4-C2 C2-Cβ4 Cα1-Cβ3 C4-Cβ1 C4-Cβ2 Cα4-Cα1

8.31 1.54 1.53 4.52 1.52 4.49 4.49 7.16 1.53 4.55 2.51 2.49 5.16 2.47 9.50 2.48 6.25 2.49 3.25 5.22 8.51 3.69 10.62 3.62 3.65 3.21 3.22 9.81 3.79 7.17 3.78 7.03 4.76 4.42 4.54 7.39 5.09 5.56 7.00 5.52 7.04 6.39 7.20 8.59 11.86 10.72

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4.87 3.61 3.59 4.39 3.60 3.95 4.34 5.44 3.60 4.39 3.52 3.46 5.49 5.02 5.22 3.52 4.63 3.50 3.72 4.45 5.17 4.83 6.25 5.06 5.55 3.74 4.02 5.19 5.59 6.34 5.32 5.68 6.44 4.57 4.70 6.67 5.65 3.76 5.29 4.05 7.99 7.00 5.60 4.64 6.59 4.24 20

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P1-P6 P6-P9

4.383 3.821

3.769 3.691

C4-Cα1 Cα1-Cβ4

11.75 11.10

4.30 3.96

3-4. Molecular packing arrangements revealed by the inter-nuclear distances. For distances between 1.5 ~ 2.5 Å, minimum inter-nuclear distances of inter-molecular pairs are in good agreement with reffj,k(obs) as shown in Table 1 and Figure 7. On the other hand, for longer distances between 3.0 ~ 5.5 Å, reffj,k(obs) are mostly shorter than the minimum inter-nuclear distances of inter-molecular pairs as shown in Table 1 and Figure 9. These results may arise from longer distances obscuring the contribution of coupled distances. Thus, in uniformly isotopically labelled solid state samples, distance contributions not only arise from intra molecular pairs, but also from inter-molecular pairs. Therefore, these inter-molecular contributions may contain important information on molecular packing arrangements. In the present AP-β-sheet Ala4 system, significant inter-molecular contributions were observed as shown in Table 1 and Figure 9. Most of the minimum inter-nuclear distances of intra- molecular pairs rj,k(intra) are longer than the reffj,k(obs) which contain the characteristics of anti-parallel β-sheet packing of AP-β-sheet-Ala4 crystals. The minimum inter-nuclear distances of intra-molecular pairs were estimated for the case of parallel(P)- β-sheet packing of Ala4, which are based on the X-ray diffraction and solid-state NMR analyses12 (Table S1). The minimum inter-nuclear distance of inter-molecular pairs were plotted as a function of reffj,k(obs) in Figure S3. It was observed that the minimum inter-nuclear distances of peak P2-P9 (C2-Cβ4, 3.71 Å) are significantly shorter than the reffj,k(obs) (4.86 Å). Particularly, inter-molecular minimum distance of 7.00 Å for C2-Cβ4 in AP-β-sheet packing is much longer than that of 3.71 Å for that in P-β-sheet packing (Tables 1 and 2, and Figures 9 and S3). The minimum inter-nuclear distances should not be shorter than reffj,k(obs),

because the

reffj,k(obs) for C2-Cβ4 is influenced by the C2-Cβ4 inter-nuclear distance as well as other 21 ACS Paragon Plus Environment


Page 22 of 31

inter-nuclear distances. Thus, the P-β-sheet packing model is not fit with the presently obtained reffj,k(obs) values for AP-Ala4 system.

Figures 9 and S3 demonstrate that the

C2-Cβ4 (P29) inter-nuclear distances of AP-β-sheet packing are actually significantly larger than those of P-β-sheet packing. The minimum inter-nuclear distances of intra- and inter-nuclear pairs for C2-Cβ4 are shown in Figure 10. Figure 10(a) shows the molecular packing for AP-β-sheet Ala4 crystals which is determined by X-ray diffraction study.29 The inter-nuclear distance of 6.30 Å contributes to reffj,k(obs), which shows good agreement. Figure 10(b) shows the molecular packing for P-β-sheet Ala4 crystals which is evaluated by X-ray diffraction, solid-state NMR data, and MD simulation.12 The inter-molecular pair of 3.71 Å contributes to reffj,k(obs) of 4.80 Å, which does not agree with the experimentally obtained data. It is thus demonstrated that P2-P9 (C2-Cβ4) cross peak is the finger print peak for distinction of AP-β-sheet from P-β-sheet packing arrangements.


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Fig.9 Correlation between reffj,k(obs) and rj,k (minimum) for AP-β-sheet packing arrangement.

Fig. 10. (a) Packing arrangement of AP-β-sheet Ala4 based on X-ray crystallographic analysis.32 Minimum inter-nuclear distances of inter- and intra-strand pairs for P2-P9 (C2-Cβ4) are shown. (b) Packing arrangement of P-β-sheet Ala4 based on X-ray diffraction and solid-state NMR analyses.12 Minimum inter-nuclear distances of inter- and intra-strand pairs for P2-P9 (C2-Cβ4) are shown.

CONCLUSIONS DARR is an experimental method useful to effectively observe the dipolar driven

13

C

spin diffusion rate, which is similar to proton-driven spin diffusion (PDSD) experiment. A key 23 ACS Paragon Plus Environment


feature of DARR is the recoupling of the

13

Page 24 of 31

C-1H dipolar interaction by applying proton

decoupling with a rotary resonance recoupling (P3) condition. Thus, DARR allows for observing larger spin diffusion rates compared with PDSD experiments. This enable us to detect cross peaks with large inter-nuclear distances. In addition, because dipolar truncation is significantly reduced, weak dipolar interactions may also be obtained in the presence of strong dipolar interactions. We have analyzed the cross peak build-up curves of DARR spectra of [U-13C] AP-β-Ala4 and determined effective inter-nuclear distances. The obtained distances were compared with a known structure, and we have discussed the applicability of DARR experiments for quantitative structural evaluation for use in similar model systems. The best standard deviations (0.244 Å) were obtained for the DARR data obtained without considering zero-quantum line shape functions in the range of 1.0 - 6.0 Å. Thus, DARR experiments appear better suited for structural evaluation using multiply labelling samples. It is noted that effective inter-nuclear distances contain not only intra-strand distances but may also contain information relating to inter-strand distances. In the present case, inter-nuclear distances fitted very well for AP-β-sheet packing arrangements, but not for P-β-sheet packing arrangements. As a result, in case of solid-state samples, inter-molecular inter-nuclear distances provide rich information relating to molecular structures as well as molecular packings.

ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the ACS Publications website at DOI: Table S1. Effective inter-nuclear distances reffj,k(obs) obtained from 2D DARR experiments and reffj,k(calc) of AP-β-sheet A4 arrangement obtained from X-ray diffraction data. 24 ACS Paragon Plus Environment

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Minimum inter-nuclear distances of inter- and intra-strand pairs for P-β-sheet Ala4 crystals Figure S1(a), (b) and (c). Build-up curves of (P1-3, P1-9) cross peaks in AP-β-Ala4 crystals obtained from 2D DARR experiments. Figure S2. Correlation between reffj,k(obs) and reff j,k(calc). Zero-quantum line shape functions of Eqs. (5) and (6) in the text are included. Standard deviation is 0.296. Figure S3. Correlation between reffj,k(obs) and rj,k(minimum) for P-β-sheet Ala4 packing arrangement.

AUTHOR INFORMATION Corresponding Author E-mail: [email protected].

Tel: +81-42-383-7733. Fax: +81-42-388-7025.

Notes The authors declare no competing financial interest.

ACKNOWLEDGEMENTS T.A. acknowledges support from Grant-in-Aid for Scientific Research from Ministry of Education, Science, Culture and Supports of Japan (23245045), and Impulsing Paradigm Change through Disruptive Technologies Program (ImPACT), and the Nanotechnology Platform Program of MEXT.



Page 26 of 31

REFERENCES (1)

Asakura, T.; Miller, T. Biotechnology of Silk; Asakura, T., Miller, T., Eds.; Biologically-Inspired Systems; Springer Netherlands: Dordrecht, 2014; Vol. 5.

(2)

Tokareva, O.; Jacobsen, M.; Buehler, M.; Wong, J.; Kaplan, D. L. Structure–Function– Property–Design Interplay in Biopolymers: Spider Silk. Acta Biomater. 2014, 10, 1612–1626.

(3)

Sezutsu, H.; Yukuhiro, K. The Complete Nucleotide Sequence of the Eri-Silkworm(Samia Cynthia Ricini) Fibroin Gene. J. Insect Biotechnol. Sericology 2014, 83, 59–70.

(4)

Numata, K.; Sato, R.; Yazawa, K.; Hikima, T.; Masunaga, H. Crystal Structure and Physical Properties of Antheraea Yamamai Silk Fibers: Long Poly(Alanine) Sequences Are Partially in the Crystalline Region. Polymer (Guildf). 2015, 77, 87–94.

(5)

Asakura, T.; Nishimura, A.; Kametani, S.; Kawanishi, S.; Aoki, A.; Suzuki, F.; Kaji, H.; Naito, A. Refined Crystal Structure of Samia Cynthia Ricini Silk Fibroin Revealed by Solid-State NMR Investigations. Biomacromolecules 2017, 18, 1965–1974.

(6)

Cardoso, M. H.; Ribeiro, S. M.; Nolasco, D. O.; de la Fuente-Núñez, C.; Felício, M. R.; Gonçalves, S.; Matos, C. O.; Liao, L. M.; Santos, N. C.; Hancock, R. E. W.; et al. A Polyalanine Peptide Derived from Polar Fish with Anti-Infectious Activities. Sci. Rep. 2016, 6, 21385.

(7)

Migliolo, L.; Felício, M. R.; Cardoso, M. H.; Silva, O. N.; Xavier, M.-A. E.; Nolasco, D. O.; de Oliveira, A. S.; Roca-Subira, I.; Vila Estape, J.; Teixeira, L. D.; et al. Structural and Functional Evaluation of the Palindromic Alanine-Rich Antimicrobial Peptide Pa-MAP2. Biochim. Biophys. Acta - Biomembr. 2016, 1858, 1488–1498.

(8)

Colletier, J.-P.; Laganowsky, A.; Landau, M.; Zhao, M.; Soriaga, A. B.; Goldschmidt, L.; Flot, D.; Cascio, D.; Sawaya, M. R.; Eisenberg, D. Molecular Basis for Amyloid-β 26 ACS Paragon Plus Environment

Page 27 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Polymorphism. Proc. Natl. Acad. Sci. U. S. A. 2011, 108, 16938–16943. (9)

Nelson, R.; Sawaya, M. R.; Balbirnie, M.; Madsen, A. Ø.; Riekel, C.; Grothe, R.; Eisenberg, D. Structure of the Cross-β Spine of Amyloid-like Fibrils. Nature 2005, 435, 773–778.

(10)

Greenwald, J.; Friedmann, M. P.; Riek, R. Amyloid Aggregates Arise from Amino Acid Condensations under Prebiotic Conditions. Angew. Chemie 2016, 128, 11781– 11785.

(11)

Polling, S.; Ormsby, A. R.; Wood, R. J.; Lee, K.; Shoubridge, C.; Hughes, J. N.; Thomas, P. Q.; Griffin, M. D. W.; Hill, A. F.; Bowden, Q.; et al. Polyalanine Expansions Drive a Shift into α-Helical Clusters without Amyloid-Fibril Formation. Nat. Struct. Mol. Biol. 2015, 22, 1008–1015.

(12)

Asakura, T.; Horiguchi, K.; Aoki, A.; Tasei, Y.; Naito, A. Parallel β-Sheet Structure of Alanine Tetrapeptide in the Solid State As Studied by Solid-State NMR Spectroscopy. J. Phys. Chem. B 2016, 120, 8932–8941.

(13)

Ernst, R. R.; Bodenhausen, G.; Wokaun, A. Principles of Nuclear Magnetic Resonance in One and Two Dimensions; Oxford University Press: New York, 1987.

(14)

Wüthrich, K.; Wider, G.; Wagner, G.; Braun, W. Sequential Resonance Assignments as a Basis for Determination of Spatial Protein Structures by High Resolution Proton Nuclear Magnetic Resonance. J. Mol. Biol. 1982, 155, 311–319.

(15)

Gullion, T.; Schaefer, J. Rotational-Echo Double-Resonance NMR. J. Magn. Reson. 1989, 81, 196–200.

(16)

Naito, A.; Nishimura, K.; Kimura, S.; Tuzi, S.; Aida, M.; Yasuoka, N.; Saitô, H. Determination of the Three-Dimensional Structure of a New Crystalline Form of N-Acetyl-Pro-Gly-Phe As Revealed by 13C REDOR, X-Ray Diffraction, and Molecular Dynamics Calculation. J. Phys. Chem. 1996, 100, 14995–15004. 27 ACS Paragon Plus Environment


(17)

Page 28 of 31

Nishimura, K.; Naito, A.; Tuzi, S.; Saitô, H.; Hashimoto, C.; Aida, M. Determination of the Three-Dimensional Structure of Crystalline Leu-Enkephalin Dihydrate Based on Six Sets of Accurately Determined Interatomic Distances from 13C-REDOR NMR and the Conformation-Dependent 13C Chemical Shifts. J. Phys. Chem. B 1998, 102, 7476– 7483.

(18)

Dumez, J.-N.; Halse, M. E.; Butler, M. C.; Emsley, L. A First-Principles Description of Proton-Driven Spin Diffusion. Phys. Chem. Chem. Phys. 2012, 14, 86–89.

(19) Suter, D.; Ernst, R. R. Spin Diffusion in Resolved Solid-State NMR Spectra. Phys. Rev. B Cover. ondensed matter Mater. Phys. 1985, 32, 5608–5627. (20)

Henrichs, P. M.; Linder, M.; Hewitt, J. M. Dynamics of the 13C Spin‐exchange Process in Solids: A Theoretical and Experimental Study. J. Chem. Phys. 1986, 85, 7077–7086.

(21)

Kubo, A.; McDowell, C. A. Spectral Spin Diffusion in Polycrystalline Solids under Magic-Angle Spinning. J. Chem. Soc. Faraday Trans. 1 Phys. Chem. Condens. Phases 1988, 84, 3713–3730.

(22)

Kubo, A.; McDowell, C. A. 31P Spectral Spin Diffusion in Crystalline Solids. J. Chem. Phys. 1988, 89, 63–70.

(23)

Veshtort, M.; Griffin, R. G. Proton-Driven Spin Diffusion in Rotating Solids via Reversible and Irreversible Quantum Dynamics. J. Chem. Phys. 2011, 135, 134509.

(24)

Grommek, A.; Meier, B. H.; Ernst, M. Distance Information from Proton-Driven Spin Diffusion under MAS. Chem. Phys. Lett. 2006, 427, 404–409.

(25)

Bayro, M. J.; Huber, M.; Ramachandran, R.; Davenport, T. C.; Meier, B. H.; Ernst, M.; Griffin, R. G. Dipolar Truncation in Magic-Angle Spinning NMR Recoupling Experiments. J. Chem. Phys. 2009, 130, 114506.

(26)

Egawa, A.; Fujiwara, T.; Mizoguchi, T.; Kakitani, Y.; Koyama, Y.; Akutsu, H. 28 ACS Paragon Plus Environment

Page 29 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Structure of the Light-Harvesting Bacteriochlorophyll c Assembly in Chlorosomes from Chlorobium Limicola Determined by Solid-State NMR. Proc. Natl. Acad. Sci. 2007, 104, 790–795. (27)

Takegoshi, K.; Nakamura, S.; Terao, T. 13C–1H Dipolar-Assisted Rotational Resonance in Magic-Angle Spinning NMR. Chem. Phys. Lett. 2001, 344, 631–637.

(28)

Takegoshi, K.; Nakamura, S.; Terao, T. 13C–1H Dipolar-Driven 13C–13C Recoupling without 13C Rf Irradiation in Nuclear Magnetic Resonance of Rotating Solids. J. Chem. Phys. 2003, 118, 2325–2341.

(29)

Oas, T. G.; Griffin, R. G.; Levitt, M. H. Rotary Resonance Recoupling of Dipolar Interactions in Solid‐state Nuclear Magnetic Resonance Spectroscopy. J. Chem. Phys. 1988, 89, 692–695.

(30)

Dumez, J.-N.; Emsley, L. A Master-Equation Approach to the Description of Proton-Driven Spin Diffusion from Crystal Geometry Using Simulated Zero-Quantum Lineshapes. Phys. Chem. Chem. Phys. 2011, 13, 7363–7370.

(31)

Asakura, T.; Yazawa, K.; Horiguchi, K.; Suzuki, F.; Nishiyama, Y.; Nishimura, K.; Kaji, H. Difference in the Structures of Alanine Tri- and Tetra-Peptides with Antiparallel β-Sheet Assessed by X-Ray Diffraction, Solid-State NMR and Chemical Shift Calculations by GIPAW. Biopolymers 2014, 101, 13–20.

(32)

Asakura, T.; Okonogi, M.; Horiguchi, K.; Aoki, A.; Saito, H.; Knight, D. P.; Williamson, M. P. Two Different Packing Arrangements of Antiparallel Polyalanine. Angew. Chem. Int. Ed. Engl. 2012, 51, 1212–1215.

(33) Plumley, J. A.; Dannenberg, J. J. Comparison of b-Sheets of Capped Polyalanine with Those of the Tau-Amyloid Structures VQIVYK and VQIINK. A Density Functional Theory Study. J. Phys. Chem. B 2011, 115, 10560-10566. (34) Arnott, S.; Dover, S. D.; Elliot, A. Refined Atomic Co-ordinates for an Antiparallel 29 ACS Paragon Plus Environment


Page 30 of 31

Beta-Pleated Sheet. J. Mol. Biol. 1967, 30, 201-208. (35) Asakura, T.; Miyazawa, K.; Tasei, Y.; Kametani, S.; Nakazawa, Y.; Aoki, A.; Naito, A. Packing Arrangement of 13C Selectively Labeled Sequence Model Peptides of Samia Cynthia Ricini Silk Fibroin Fibers Studied by Solid-State NMR. Phys. Chem. Chem. Phys. 2017, 19, 13379–13386. (36)

Fung, B. M.; Khitrin, A. K.; Ermolaev, K. An Improved Broadband Decoupling Sequence for Liquid Crystals and Solids. J. Magn. Reson. 2000, 142, 97–101.

(37)

Luo, W.; Hong, M. Determination of the Oligomeric Number and Intermolecular Distances of Membrane Protein Assemblies by Anisotropic 1H-Driven Spin Diffusion NMR Spectroscopy. J. Am. Chem. Soc. 2006, 128, 7242–7251.


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