Packing Arrangements and Inter-sheet Interaction of Alanine

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Article

Packing Arrangements and Inter-Sheet Interaction of Alanine Oligopeptides as Revealed by Relaxation Parameters Obtained From High-Resolution C Solid-State NMR 13

Akira Naito, Yugo Tasei, Akio Nishimura, and Tetsuo Asakura J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.7b07068 • Publication Date (Web): 05 Sep 2017 Downloaded from http://pubs.acs.org on September 6, 2017

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The Journal of Physical Chemistry B is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

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The Journal of Physical Chemistry

Packing Arrangements and Inter-sheet Interaction of Alanine Oligopeptides as Revealed by Relaxation Parameters Obtained from High-Resolution 13C solid-state NMR

Akira Naito, Yugo Tasei, Akio Nishimura, Tetsuo Asakura*

Department of Biotechnology, Tokyo University of Agriculture and Technology Koganei, Tokyo 184-8588 JAPAN

*Author to whom correspondence should be addressed ([email protected])

1

ACS Paragon Plus Environment


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Abstract Alanine oligopeptides provide a key structure of the crystalline domains of the silks from spiders and wild silkworm, and also the sequences included in proteins such as antifreeze proteins and amyloids. In this paper, the local dynamics of alanine oligopeptides, (Ala)3, (Ala)4 and (Ala)6 were examined by high-resolution 13C solid-state NMR. The 13C spin-lattice relaxation times (T1’s) for the Cβ4 carbons of antiparallel (AP)-β-sheet (Ala)4 significantly prolonged and the correlation time was estimated as 3.6 x 10-11 sec which was shorter than those of other carbons in the AP-β-sheet (Ala)4 (2.8 x 10-10 sec). The T1 values for the Cβ carbons of (Ala)6 showed significantly longer correlation time (8.8 x 10-9 sec) than those of AP-β-sheet (Ala)4. It is thus revealed that AP-β-sheet (Ala)6 exhibited stronger inter-sheet interaction than those of AP-β-sheet (Ala)4. The 13C spin-spin relaxation times (T2’s) for the Cβ4 carbons showed longer than those of the other Cβ1-3 carbons of AP-β-sheet (Ala)4. T2 values of Cβ carbons reflect the slow time-scale (~70 kHz) backbone motions. The C-terminal forms strong hydrogen bonds with water molecules and thus the backbone motion is slower than ~70 kHz, while the central backbone motions are faster than ~70 kHz in AP-β-sheet (Ala)4.

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Introduction Polyalanine (poly-A) is the simplest polypeptide and has long been the sequence of choice for modeling polypeptide structure, particularly anti-parallel β-sheet structure.1–6 Moreover, poly-A sequences are a key element in the structure of silk fibers and also the sequences included in proteins such as antifreeze proteins7,8 and amyloids.9–12 Recently, the excellent properties such as high strength and high toughness of spider silks and silkworm silks have attracted researchers in wide variety of fields, such as biology, biochemistry, biophysics, analytical chemistry, polymer technology, textile technology and biomaterials.13–15 Especially, the exceptionally high tensile strength and toughness of the major ampullated silk fibers of spiders have been postulated from many structural studies, to attribute greatly to the crystalline β-sheet structures formed by the repeating poly-A sequences of (Ala)4-7 in these proteins.14-21 On the other hand, wild silkworms such as Samia cynthia ricini,22–24 Antheraea pernyi,25-29 Antheraea yamamai30 and Antheraea mylitta31, also produce silk fibroin containing an abundant portion of poly-A sequences, where the lengths of Ala residues are generally (Ala)12,13. In our previous paper,4 we reported two different packing arrangements of poly-A with anti-parallel β-sheet structure depending on the number of Ala residue. Namely, short poly-A sequences ((Ala)n n=6 or less) in anti-parallel β-sheet structure have been reported to pack into a rectangular arrangement, as shown by the X-ray single crystal analysis of the crystal structures of (Ala)3 32 and (Ala)4.4 For example, the (Ala)4 molecules with anti-parallel β-sheet structure are aligned in head-to-tail rows with methyl groups arranged alternately above and below the plane of the β-sheets. Single water molecules bridge between adjacent N and C termini. The strands are packed into a rectangular lattice and form hydrogen bonds both side-to-side as well as end-to-end. 3



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The end-to-end interactions occur through the bridging water molecules.

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In contrast,

for (Ala)7 and higher, both the 13C solid state NMR spectra and X-ray powder pattern data are markedly different from those for short poly-A sequences although the conformation is still anti-parallel β-sheet. The main difference is the packing structure where the packing of the chains in adjacent planes is staggered for longer poly-A rather than rectangular for shorter poly-A mentioned above.4 Most recently, we found out that change in the packing form occurred from the rectangular arrangement of (Ala)6 to staggered arrangement after keeping the (Ala)6 sample at 200 o C for 4 hr.33 The change could be monitored by the shape of the Ala Cβ peak in the 13C CP/MAS NMR spectrum and could reproduce by the MD simulation after removal of the bound water molecules. The MD simulation indicates that the steric repulsion occurs, especially among Ala Cβ carbons in adjacent layers of the (Ala)6 molecules in the rectangular arrangement, but the stabilization of the inter-molecular hydrogen bonding with bound water molecules occurs at the end groups of the terminal residues which contributes significantly to the stabilization of the rectangular arrangement in the system. Degree of hydration effects for the Australian spider silks have been investigated by using solid state NMR relaxation analysis.34 Thus, it seems important to clarify the inter-sheet interaction produced by Ala Cβ carbons from view points of the relaxation experiments. Site specific molecular dynamics can be obtained from the various relaxation measurements in the solid state. 13C and 2H spin lattice relaxation times (T1’s) provide the segments or sidechain motions in the motional frequency of 107 ~ 109 s-1 in the solid state.35–37 13C spin spin relaxation time (T2) under proton decoupling provides the backbone motions in the motional frequencies of 104 ~ 105 s-1 in the solid state.36–38 In 4


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case of poly-A compounds in the solid-state NMR, hopping motion about the C3 axis in Cβ carbon is the main source of the T1 processes. Thus, T1’s of the Cβ in various location reflect the local motion or local inter-strand and inter-sheet interactions of poly-A compounds. The major advantage to use 13C NMR as a diagnostic tool is that 13C chemical shifts of the Ala Cβ, as well as those of Cα and C=O carbons in polypeptides and proteins vary with their local conformation defined by the torsion angle (φ,ψ) of local peptide units as well as the manner of hydrogen bonds as generally characterized as the conformation-dependent displacement of 13C chemical shift.39,40 Moreover, only the Ala Cβ peak is also sensitive to the packing structure as reported previously41-49 and many useful information has been obtained by the detailed analyses of the line shape. In this paper, we recorded solid-state 13C NMR spectra of a series of alanine oligopeptides, (Ala)3, (Ala)4 and (Ala)6 with anti-parallel β-sheet structure, in order to clarify the molecular dynamics in relation to possible packing arrangements in the presence of the bound water. It is stressed that T1 values of Cβ carbons in alanine oligopeptides reflect the hopping motion of the methyl groups and lead to correlation times of the methyl hopping motion together with temperature variation of T1 values and equation expressing T1 values of methyl carbons by taking into account of anisotropic hopping motions in solid state. Another stress point in this paper is to measure T2 values of Cβ carbons, which reflect the slow local backbone motion rather than the hopping motion. It is not well established to reveal dynamic properties of poly-alanine solids by using both T1 and T2 data in relation to molecular structures and packing arrangements. We, therefore, analyzed different manner of packing in molecular chains as viewed from dynamic features of side chains and backbones as 5



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viewed from 13C T1 and T2 values, respectively. Because poly-A region forms β-sheet structure in the fibril form, hydrophobic interaction among methyl groups of other inter strand and those in inter-sheet interaction may play important role for the property of fibril.

Materials and Methods Alanine oligopeptides A series of poly-As, (Ala)3, (Ala)4 and (Ala)6 with anti-parallel β-sheet structure were purchased from Bachen AG (Bundendorf, Switzerland), and used without further purification. In order to assign the Cβ peaks of AP-β-sheet (Ala)4 clearly, three kinds of 13

C,15N labeled AP-β-sheet (Ala)4 samples, that is, [U-13C,15N]Ala (Ala)3,

(Ala)2[U-13C,15N]AlaAla and (Ala)3[U-13C,15N]Ala were synthesized in our laboratory.50 In short, these peptides were synthesized using solid-phase methods with Fmoc-chemistry. The crude peptide samples were purified by high-performance liquid chromatography. The purities of the peptides were checked by 13C solution NMR and IR to be more than 95%. The samples were lyophilized from aqueous solution to measure NMR signals.

Solid-state 13C NMR measurements All 13C CP/MAS NMR spectra were recorded on a Bruker Avance 400 NMR spectrometer using double resonance MAS probe for the rotor with 4 mm outer diameter and the MAS frequency was set to 10 kHz. Typical experimental parameters for the 13C CP/MAS NMR experiments included 3.5 µsec 1H 90° pulse, 1 msec ramped CP pulse with 71.4 kHz rf field strength, TPPM 1H decoupling during acquisition, 2048 6


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data points, 512 scans, and 4 sec recycle delay. The chemical shifts were referenced to TMS, using adamantine as an external standard (13CH peak at 28.8 ppm). 13C T1’s were determined by the method of Torchia,51 after peak-intensities of individual components were evaluated by deconvoluted spectra based on Lorentzian lineshape. The delay times were varied in a range of 0.01~ 2 sec for the measurement on Ala Cβ carbons in a number of poly-As, AP-β-sheet (Ala)3, AP-β-sheet (Ala)4 and AP-β-sheet (Ala)6. The temperatures were varied from 20, 40, 60 ºC using temperature control unit of the spectrometer. 13C T2 values were determined for the same samples using Hahn echo pulse sequence by setting the rotor synchronized delay time with multiple of rotor period to be varied in a range of 2 ~ 200 msec.38 The temperatures were also varied from 20, 40 and 60 ºC.

MD Simulations MD simulation was performed using the Discover program of the Accelrys software, Inc. with the polymer consistent force field (pcff). In the calculation, initial coordinates determined by X-ray diffraction analyses for AP-β-sheet (Ala)332 and AP-β-sheet (Ala)44 were used. Finally, energy minimization was performed using Material Studio Visualizer Material Studio Discover (Accelrys Inc.).

Results 13

C chemical shifts of Ala Cβ β carbons of (Ala)3, (Ala)4 and (Ala)6 with anti-parallel

β-sheet structures The expanded Ala Cβ peaks of AP-β-sheet (Ala)3, AP-β-sheet (Ala)4 and AP-β-sheet (Ala)6 observed at 20°C were shown in Fig.1(a), (b) and (c) together with the packing 7



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structures of these two (Ala)3 and (Ala)4 polypeptides reported previously from the X-ray single crystal diffraction methods.4,32 The (Ala)3 molecules had two types of molecules labeled A and B per unit cell (Fig. 1(d)), while (Ala)4 exhibited only one type of molecule in the unit cell (Fig. 1(e)). Thus, the packing structure of (Ala)3 is a heterogeneous mixture, but that of (Ala)4 is uniform in composition. As shown in our previous reports,41,42 the peaks of AP-β-sheet (Ala)3 could be assigned to the carbons, Cβ1A(19.0ppm), Cβ1B(19.7ppm), Cβ2A(20.6ppm), Cβ2B(20.1ppm), Cβ3A(19.9ppm) and Cβ3B(19.2ppm) using 13C selectively labeled (Ala)3 samples to distinguish overlapped signals.42 Thus, we tried the assignment of AP-β-sheet (Ala)4 using three kinds of AP-β-sheet [13C,15N]labeled (Ala)4 samples as shown in Fig.2. The peaks could be assigned to the carbons, Cβ1(19.9ppm), Cβ2(19.9ppm), Cβ3(21.1ppm) and Cβ4(18.9ppm). On the other hand, the spectral pattern changes remarkably for AP-β-sheet (Ala)6. Namely, a single peak centered at 20.6 ppm with broad tail around 19.0 ppm toward higher field, and with shoulder at lower field at 21.1 ppm together with tail to lower field (Fig. 1(c)).

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Fig. 1. Expanded Ala Cβ peaks in the 13C CP/MAS NMR spectra at 20 ºC of AP-β-sheet (Ala)3 (a), AP-β-sheet (Ala)4 (b) and AP-β-sheet (Ala)6 (c) together with the packing models of AP-β-sheet (Ala)3 with A and B-types (d), and AP-β-sheet (Ala)4 (e).

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Fig.2. Assignment of Ala Cβ peaks of AP-β-sheet (Ala)4 at 20 ºC. The Ala Cβ peaks of non-labeled AP-β-sheet (Ala)4 (a), AP-β-sheet [U-13C,15N]Ala (Ala)3 (b), AP-β-sheet (Ala)2[U-13C,15N]AlaAla (c) and AP-β-sheet (Ala)3[U-13C,15N]Ala (d) are shown for the assignment. 13

C spin-lattice relaxation times (T1’s) of Cβ β carbons as probes for hopping

motions of methyl groups. A series of partly relaxed spectra of Ala Cβ peaks of AP-β-sheet (Ala)4 for 13C T1 value determination were shown in Fig. 3(a). The 13C T1 values were determined by a plot of the peak area intensities vs. delay times as proposed by Torchia51 and summarized in Table 1. Significantly long T1 value (0.51 sec) at 20 ºC was observed for the peak at18.9 ppm of AP-β-sheet (Ala)4, although the other peaks exhibited relatively 10


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shorter values in the order of ~ 0.09 sec. This peak is assigned to Cβ4 carbon which is located at the C-terminal. The reason for such exceptionally long T1 value for the C-terminal Cβ4 carbon for AP-β-sheet (Ala)4 is not fully understood yet, but will be discussed in the later section.

On the other hand, the Cβ carbons in AP-β-sheet (Ala)3

exhibited slightly longer T1 values in the range of 0.10 ~ 0.20 sec at 20 ºC than those of AP-β-sheet (Ala)4, including the C-terminal Cβ3A and Cβ3B carbons (Table 1). The T1 value of the center peak of AP-β-sheet (Ala)6 exhibited 0.19 sec, as shown in Fig. 4(a) and Table 1, which was longer than those for AP-β-sheet (Ala)3 and AP-β-sheet (Ala)4 except for the value of the Cβ4 carbon of AP-β-sheet (Ala)4.

Fig. 3. 13C spin lattice relaxation decays of Cβ carbons for AP-β-sheet (Ala)4 at 20 ºC (a). Plots of T1 values against reciprocal temperatures (b).

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Table 1. 13C spin lattice relaxation times (T1’s sec) and 13C chemical shifts (δ’s ppm) of Ala Cβ signals of AP-β-sheet (Ala)3, AP-β-sheet (Ala)4 and AP-β-sheet (Ala)6. T1 (sec), [δ (ppm)]

(Ala)3

20 ºC

40 ºC

60 ºC

(Ala)4

Cβ2

Cβ2B

Cβ3A

Cβ1B

Cβ3B

Cβ1A

[20.6]

[20.1]

[19.9]

[19.7]

[19.2]

[19.0]

0.197

0.133

0.140

0.174

0.142

0.104

±0.004

±0.003

±0.007

±0.003

±0.001

±0.003

0.218

0.150

0.171

0.162

0.162

0.096

±0.003

±0.002

±0.004

±0.011

±0.005

±0.004

0.238

0.158

0.200

0.166

0.194

0.087

±0.003

±0.003

±0.003

±0.003

±0.003

±0.003

Cβ3

Cβ1, Cβ2

Cβ4

[21.1]

[19.9]

[18.9]

20 ºC

0.087 ±0.006

0.091 ±0.001

0.505 ±0.048

40 ºC

0.095 ±0.005

0.100 ±0.002

0.581 ±0.071

60 ºC

0.130 ±0.004

0.103 ±0.003

0.711 ±0.117

Cβ [20.6] (Ala)6

20 ºC

0.191 ±0.014

40 ºC

0.175 ±0.004

60 ºC

0.094 ±0.005

Temperature variations of T1 values for Cβ carbons of AP-β-sheet (Ala)3, AP-β-sheet (Ala)4 (Fig. 3(b)) and AP-β-sheet (Ala)6 (Fig. 4(c)) were performed as shown in Table 1. It was found that T1 values for Cβ2 and Cβ3 carbons in AP-β-sheet (Ala)3 and all Cβ carbons in AP-β-sheet (Ala)4 were elongated when the temperature increased as shown in Fig. 3(b). These results indicate that the time scale of the motion belong to a higher motion domain with respect to the T1 minimum which corresponds to ~126 MHz of motional frequency. On the other hand, T1 values for Cβ1Α and Cβ1B

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carbons in AP-β-sheet (Ala)3 and Cβ carbons in AP-β-sheet (Ala)6 decreased when the temperature increased as shown in Fig. 4 (c). This result indicates that the motional frequency belongs to slower motion domain with respect to the T1 minimum value of ~ 126 MHz.

Fig. 4. 13C spin lattice relaxation (a) and spin spin relaxation (b) decays of Cβ carbons for AP-β-sheet (Ala)6 at 20 ºC. Plots of T1 (c) and T2 (d) values against reciprocal temperatures.

13

C T1 values for methyl carbon with hopping motion under the solid-state MAS

condition can be expressed as 35,43

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ଶ

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where, 13


(1)


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

଺

‫ܬ‬ሺ଴ሻ ሺ߱ሻ ൌ ሺ‫݊݅ݏ‬ଶ 2∆ ൅ ‫݊݅ݏ‬ସ ∆ሻ ቂ

ఛ೎

ହ

ଵାఠమ ఛ೎మ

ଵ

ఛ

ቃ

‫ܬ‬ሺଵሻ ሺ߱ሻ ൌ ሺ‫݊݅ݏ‬ଶ 2∆ ൅ ‫݊݅ݏ‬ସ ∆ሻ ቂଵାఠ೎మ ఛమ ቃ ହ ସ

೎

‫ܬ‬ሺଶሻ ሺ߱ሻ ൌ ହ ሺ‫݊݅ݏ‬ଶ 2∆ ൅ ‫݊݅ݏ‬ସ ∆ሻ ቂ

ఛ೎

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ቃ,

where, I is the spin quantum number of proton which is 1/2, ωC and ωH are Larmor frequencies of carbon and proton nuclei, respectively. ∆ is the angle between the C-H internuclear vector and the C3 axis. τc is the correlation time of the hopping motion of methyl groups about the C3 axis. Using this equation and parameters of the anisotropic motion of methyl group (∆=69.8º, rCH=1.098 Å in L-alanine crystal52) plot of T1 values against correlation times was calculated as shown in Fig. S1. This diagram provides the T1 minimum value of 0.0602 sec with the correlation time of 1.26 x 10-9 sec and frequency of 126 MHz in the magnetic field of 9.4 T (Larmor frequencies of carbon and proton nuclei are 100 MHz and 400 MHz, respectively). It is stressed that the relaxation mechanism for Ala Cβ carbon in the solid-state is well characterized. Namely, hopping motion of C-H vector about C3 axis of methyl group is the main source of spin lattice relaxation process. Thus, this diagram can be used to determine the correlation times of Ala Cβ carbons accurately. The correlation time is a good parameter to discuss the hopping motion of the methyl group, because it is independent of the static magnetic field strength. Thus, it is possible to compare the parameters with the data from other types of experiments. Using this diagram together with the temperature variation data, correlation times of the methyl hopping motions were calculated as summarized in Table 2. It is thus 14


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noted that hopping motion of Cβ carbons in the AP-β-sheet (Ala)3 and AP-β-sheet (Ala)4 becomes faster than ~126 MHz because T1 values become longer at higher temperature. Namely, the correlation time of methyl hopping of Cβ carbons is shorter than 1.26 x 10-9 sec. In case of T1’s of Cβ carbons in AP-β-sheet (Ala)3, all Cβ carbon nuclei show the similar values in the range of 0.10 ~ 0.20 sec which correspond to 0.96 x 10-10~ 2.2 x 10-10 sec in correlation times. It is noted that T1’s of Cβ carbons in AP-β-sheet (Ala)4 exhibit the correlation times of 2.8 x 10-10 ~ 3.0 x 10-10 sec for most of the Cβ carbons except Cβ4 carbons which show significantly shorter correlation times of 3.6 x 10-11 sec. It is noted that the correlation times of the Cβ carbons in AP-β-sheet (Ala)6 are the longest among those of AP-β-sheet (Ala)3 and (Ala)4. Quite long correlation time of 8.8 x 10-9 sec was determined and obtained for Cβ carbon in AP-β-sheet (Ala)6. This indicates that hopping motion of the Cβ carbon in AP-β-sheet (Ala)6 is more restricted than those in AP-β-sheet (Ala)3 and AP-β-sheet (Ala)4. Table 2. Correlation times (τc’s) of Ala Cβ carbons of AP-β-sheet (Ala)3, AP-β-sheet (Ala)4.and AP-β-sheet (Ala)6. τc / ×10-11 sec Cβ2A

Cβ2B

Cβ3A

Cβ1B

Cβ3B

Cβ1A

(Ala)3 20℃

9.59±0.22

15.3±0.5

14.4±0.9

11.0±0.2

14.1±0.1

21.8±1.0

40℃

8.58±0.13

13.2±0.2

11.3±0.3

12.0±1.0

12.0±0.4

24.9±1.9

60℃

7.80±0.11

12.4±0.3

9.43±0.16

11.7±0.3

9.76±0.17 30.1±2.2

Cβ3

Cβ1, Cβ2

Cβ4

(Ala)4 20℃

30.1±4.5

27.5±0.6

3.57±0.35

40℃

25.4±2.5

23.2±0.8

3.09±0.39

60℃

15.8±0.6

22.1±1.1

2.52±0.43

Cβ (Ala)6 20℃

881±69

40℃

803±20

15



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60℃

13

389±28

C spin spin relaxation times (T2’s) as a probe for backbone dynamics 13

C T2’s for Ala Cβ peaks of AP-β-sheet (Ala)3, AP-β-sheet (Ala)4 (Fig. 5(a)) and

AP-β-sheet (Ala)6 (Fig. 4(b)) were evaluated from a series of partially relaxed spectra using Hahn spin echo pulse sequence. Echo interval should be adjusted to be the multiple of rotor period, which compensates the sampling at the top of rotational echo.38 The 13C T2 values thus obtained were summarized in Table 3. T2 values for individual peaks were also evaluated from the plot of echo intensity against the echo intervals. It is noted that T2 value of Cβ4 (75.6 msec) in AP-β-sheet (Ala)4 was significantly longer than those of Cβ1-3 (25.5 ~ 28.9 msec). T2 values of Cβ1A (29.0 msec) and Cβ1B (46.2 msec) in AP-β-sheet (Ala)3 were shorter than Cβ2-3 (56.4 ~ 70.1 msec). T2 value of Cβ (39.2 msec) is similar to those of Cβ1-3 in AP-β-sheet (Ala)4.

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Fig. 5. 13C spin spin relaxation decays of Cβ carbons for AP-β-sheet (Ala)4 (a) at 20 ºC. Plots of T2 values against reciprocal temperatures (b).

Table 3. 13C spin spin relaxation times (T2’s sec) and 13C chemical shifts (δ’s ppm) of Ala Cβ signals of AP-β-sheet (Ala)3, AP-β-sheet (Ala)4 and AP-β-sheet (Ala)6. T2 (msec), [δ (ppm)] (Ala)3

Cβ2A

Cβ2B

Cβ3A

Cβ1B

Cβ3B

Cβ1A

[20.6]

[20.1]

[19.9]

[19.7]

[19.2]

[19.0]

20 ºC

66.5 ±2.9

56.4 ±2.3

67.3 ±3.7

46.2 ±3.4

70.1 ±7.5

29.0 ±7.4

40 ºC

69.9 ±3.4

63.8 ±4.2

68.4 ±2.3

45.5 ±3.9

75.2 ±3.0

33.9 ±2.2

60 ºC

67.7 ±3.4

59.2 ±2.4

72.8 ±4.3

52.4 ±1.9

86.0 ±3.3

31.5 ±1.7

Cβ3

Cβ1, Cβ2

Cβ4

[21.1]

[19.9]

[18.9]

20 ºC

28.9 ±2.0

25.5 ±1.0

75.6 ±8.4

40 ºC

30.9 ±2.5

26.0 ±0.9

73.9 ±5.4

60 ºC

34.7 ±3.4

28.0 ±1.7

72.3 ±5.2

(Ala)4

(Ala)6

Cβ [20.6] 20 ºC

39.2 ±3.3

40 ºC

32.8 ±1.2

60 ºC

27.3 ±2.0

The 13C T2 value under strong proton decoupling field can be expressed as 44,45

ଵ

்మ಴

ൌ

ସఊ಺మ ఊೄమ ԰మ ଵହ௥ల

‫ܫ‬ሺ‫ ܫ‬൅ 1ሻ

ఛ಴

మ ଵାఠ಺మ ఛ಴

,

(2)

where, ωI is the proton decoupling frequency. According to Eq. (2), T2 value provides minimum value when the motional frequency is ~70 kHz which is the same as proton 17



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

decoupling frequency. To evaluate motional frequency, temperature variation of the T2 values was performed. It is noted that T2 values for Cβ4 in AP-β-sheet (Ala)4 decreased when the temperature increased as shown in Fig. 5(b). This result indicates that motional frequency of Cβ4 should be slower than ~70 kHz according to Eq. (2). On the other hand, T2 values of Cβ1-3 increased a little when the temperature increased, which indicates that motional frequency is slightly higher than ~70 kHz corresponding to the correlation time of 2.3 x 10-6 sec. Because hopping motion of Cβ methyl group is higher than 126 MHz as observed from T1 value, motional frequency which is sensitive to the T2 value must be backbone chain motion rather than the hopping motion of the methyl carbons. Thus, backbone motional frequency of the Cβ carbon is almost 70 kHz. It is of interest to point out that hopping motion of Cβ4 is faster than those of Cβ1-3, and frequency order is about 126 MHz, while backbone motion of Cβ4 is slower than those of Cβ1-3. It is also noted that T2 values of Cβ carbons decreased when the temperature increased as shown in Fig. 4(d), indicating that motional frequency is slower than ~70 kHz.

Discussion Molecular packing arrangements for elucidating dynamic properties of AP-β β-sheet (Ala)3, (Ala)4 and (Ala)6 Fig. 6 shows the crystal structure of AP-β-sheet (Ala)4.4 The molecules are aligned in head-to-tail rows with methyl groups arranged alternately above and below the plane of the sheets (Figs. 6 A and B). Single water molecules bridge between adjacent N and C termini. The stacks are packed into a rectangular lattice and form hydrogen bonds both side-to-side as well as end-to-end (Fig. 6 C). The end-to-end 18


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interaction occurs through the bridging water molecule. Poly-A chains form anti parallel β-sheet structure stabilized by inter-strand hydrogen bonds (Fig. 6 C). Methyl groups of Ala Cβ face out from the β-sheet plane and cross together to form hydrophobic inter-sheet interaction between the methyl groups of Ala Cβ (Fig. 6 A). These hydrophobic inter-sheet interactions largely stabilized inter sheet packing arrangement. It is therefore stressed that hopping frequency may reflect not only the hydrophobic inter-strand interaction (Fig. 6 B) but also the hydrophobic inter-sheet interaction (Fig. 6 A).

Fig. 6. Packing arrangement of AP-β-sheet (Ala)4 molecules which are projected to a-b (A) and b-c (B, C) planes. The Cβ-Cβ distances (Å) inter-sheet (A) and inter-strand (B) and. hydrogen bonding networks (C) are shown.4

19



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It is noted that 13C T1’s of Ala Cβ reflect fast C3 hopping motion about the C3 axis in the crystalline state in the order of 0.09 sec as found for Cβ1, Cβ2, and Cβ3 carbons in AP-β-sheet (Ala)4 (Table 1), which indicates that the correlation times are 2.8 x 10-10 ~ 3.0 x 10-10 sec (Table 2). It is of interest to note that C-terminal Ala Cβ4 carbon showed 6 times longer T1 value (0.51 sec) of other Cβ1, Cβ2 and Cβ3 carbons for AP-β-sheet (Ala)4. Furthermore, increasing the temperature causes the elongation of the T1 values for the C-terminal Cβ4. This result indicates that the methyl hopping frequency of the C-terminal Cβ4 is much higher than the T1 minimum frequency and the correlation time was evaluated to be 3.6 x 10-11 sec. It is, therefore, revealed that restriction of the motion of the methyl group for the C-terminal Ala Cβ4 should be smaller than those of the other methyl Cβ1, Cβ2 and Cβ3 groups in AP-β-sheet (Ala)4 which show the correlation times of 2.8 x 10-10 ~ 3.0 x 10-10 sec. To estimate the origin of the restrictions for the methyl dynamics, inter-atomic distances between methyl groups were evaluated as summarized in Table 4 and Fig. 6. The results indicate that the C-terminal Cβ4 has two closely located (3.82, 4.05 Å) methyl groups, while other Cβ1, Cβ2 and Cβ3 carbons have three closely located methyl groups. These results clearly indicate that the C-terminal Cβ4 group in AP-β-sheet (Ala)4 exhibits less restriction and thus has faster methyl hopping frequency. In case of AP-β-sheet (Ala)3, Cβ1 and Cβ3 have two closely located counter Cβ carbons with inter-strand and inter-sheet connections and Cβ2 carbon has two closely located counter Cβ carbons and one relatively longer Cβ-Cβ distance (see Table 4 and Fig.7). It is consistent with that all the T1's for Cβ carbons show the similar values in the case of AP-β-sheet (Ala)3. In case of AP-β-sheet (Ala)6, much longer correlation times of 8.8 x 10-9 sec for the hopping motions of Cβ carbons were obtained. This value is significantly longer 20


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than the correlation times of 1.0 x 10-10 ~ 1.5 x 10-10 sec for Cβ2 carbons in AP-β-sheet (Ala)3 and 3.0 x 10-10 sec for Cβ2 and Cβ3 carbons in AP-β-sheet (Ala)4. This result indicates that the hopping motion of Cβ carbon in AP-β-sheet (Ala)6 exhibits stronger restriction as compared to those of AP-β-sheet (Ala)4 and AP-β-sheet (Ala)3. Inter nuclear distances between Cβ carbons shown in Table S1 are similar to the case of AP-β-sheet (Ala)4 and (Ala)3 and significant differences of packing restrictions were not observed. Nevertheless, much shorter Cβ-Cβ distances were obtained for Cβ1-Cβ2 (3.69 Å) and Cβ1-Cβ6 (3.54 Å), which may show stronger inter-sheet interaction in the N-terminus and inter-strand interaction in the C-terminus. In addition, longer β-sheet strand in AP-β-sheet (Ala)6 may induce stronger inter-sheet interaction as compared to those of AP-β-sheet (Ala)4 and (Ala)3. It is of interest to note that T2 data indicate that slow frequency motion which is due to backbone motion, is much slower than ~70 kHz for C-terminal Cβ carbon for AP-β-sheet (Ala)4. To evaluate the slow motional nature, hydrogen bonding networks were considered. Based on the X-ray crystal data, hydrogen bonding distances for individual residues are determined and summarized in Fig. 6C and Table 5. These results indicate that hydrogen bonding distances of AP-β-sheet (Ala)4 are entirely shorter than those of AP-β-sheet (Ala)3 as shown in Figs. 6C and 7C, respectively, and Table 5. In particular, hydrogen bonding distance of the C-terminal carbonyl carbon of (Ala)4 and water is much shorter than those of (Ala)3. This indicates that Cβ4 should be very rigid and can exhibit very slow backbone motion than the other position of the backbone.

21



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Page 22 of 33

Table 4. Inter atomic distances less than 4.2 Å among Cβ carbons, and counter Cβ carbons or amino nitrogens of AP-β-sheet (Ala)44 and AP-β-sheet (Ala)3.32 These distances were calculated using X-ray structure data of the peptides. Carbon

Counter Cβ carbon

Distance (Å)

Connection

or amino nitrogen AP-β-sheet (Ala)4 Cβ1

Cβ2

3.80

Inter sheet

Cβ1

Cβ4

3.82

Inter strand

Cβ1

N1

2.46

Intra strand

Cβ1

N1

3.63

Inter sheet

Cβ2

Cβ1

3.80

Inter sheet

Cβ2

Cβ3

3.76

Inter strand

Cβ2

Cβ3

3.79

Inter sheet

Cβ3

Cβ2

3.76

Inter sheet

Cβ3

Cβ2

3.79

Inter strand

Cβ3

Cβ4

4.05

Inter sheet

Cβ4

Cβ1

3.82

Inter sheet

Cβ4

Cβ3

4.05

Inter sheet

Cβ1

Cβ2

3.90

Inter strand

Cβ1

Cβ3

3.81

Inter sheet

Cβ2

Cβ1

3.90

Inter sheet

Cβ2

Cβ2

4.03

Inter strand

Cβ2

Cβ3

4.03

Inter sheet

Cβ3

Cβ1

3.84

Inter strand

Cβ3

Cβ2

4.03

Inter sheet

Cβ1

Cβ2

3.93

Inter strand

Cβ1

Cβ3

3.84

Inter sheet

Cβ2

Cβ1

3.93

Inter sheet

Cβ2

Cβ3

3.79

Inter sheet

Cβ2

Cβ2

4.03

Inter strand

Cβ3

Cβ2

3.79

Inter sheet

Cβ3

Cβ1

3.81

Inter strand

AP-β-sheet (Ala)3 (A-type)

AP-β-sheet(Ala)3 (B-type)

22


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Fig. 7. Packing arrangement of AP-β-sheet (Ala)3 molecules which are projected to a-b (A) and b-c (B, C) planes. The Cβ-Cβ distances (Å) of inter-sheet (A) and inter-strand (B) and hydrogen bonding networks (C) are shown.32

Table 5. Hydrogen bonding networks for AP-β-sheet (Ala)4 4 and AP-β-sheet (Ala)3 32 crystals. AP-β-sheet (Ala)4

Da·····Ab (Å)

H·····A (Å)

D˗˗H····A (degree)

N2˗˗H8···O3

2.88

1.90

149.4

N3˗˗H13···O2

2.25

2.01

157.0

N4˗˗H18···O1

2.95

2.01

148.9

WH···O4 AP-β-sheet (Ala)3

1.30 D·····A (Å)

H·····A (Å) 23


D˗˗H·····A (degree)


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Page 24 of 33

N(2A)˗˗H···O(2B)

2.92

2.16

158.0

N(2B)˗˗H···O(2A)

2.92

2.14

158.0

N(3A)˗˗H···O(1B)

2.99

2.17

160.0

N(3B)˗˗H···O(1A)

3.07

2.21

162.0

WH···O3

1.70

a

Donner (D): amino and amido nitrogens and water oxygen

b

Acceptor (A): carbonyl and carboxyl oxygens

Motional analysis by molecular dynamics (MD) simulation Fig.8 indicates the results of MD simulations for comparison of changes in the hopping angles of Cβ carbons in AP-β-sheet (Ala)3 and (Ala)4 at 373 K. It is clearly shown that hopping frequency of Cβ4 is much faster than the other 3 Cβ1-3 carbons for AP-β-sheet (Ala)4 (Fig. 8(c)). It is also shown that the type of motion is stochastic hopping motion rather than a rotational motion. These results consistent with the results of spin lattice relaxation time measurements. On the other hand, hopping frequencies of Cβ3 carbons in AP-β-sheet (Ala)3 are about the same order of frequency as observed in the T1’s for Cβ carbons of AP-β-sheet (Ala)3. These results are also consistent with the facts that number of short inter methyl distances is two for Cβ1 and Cβ3 carbons and Cβ2 carbon has two short Cβ-Cβ distances and one relatively long Cβ-Cβ distance for the case of AP-β-sheet (Ala)3.

24


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Fig. 8. Hopping frequencies of Cβ groups for AP-β-sheet (Ala)3 (A-type) (a) and (B-type) (b), and (Ala)4 (c) by MD simulation. MD simulations were performed at 373 K (100 ºC).

Conclusion Molecular motion of alanine oligopeptides as a model of crystalline domain of silk fiber was investigated based on the 13C T1 and T2 values of Cβ carbons of AP-β-sheet (Ala)3, (Ala)4 and (Ala)6. It is found that T1 values of Cβ carbons reflect the hopping motion of the methyl groups. This motion is significantly changed by the restrictions from other methyl groups of poly-A chains either from inter-strand and inter-sheet connections. Evaluation of these interactions could be important parameters for understanding of the physical properties of silk fiber. Particularly methyl groups of central β-sheet chains play significant role for inter-sheet hydrophobic interaction. It is 25



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demonstrated that the correlation time of the Cβ carbons of AP-β-sheet (Ala)6 (8.8 x 10-9 sec) is the longest and that of AP-β-sheet (Ala)4 (2.8 x 10-10 sec) is longer than that of AP-β-sheet (Ala)3 (1.5 x 10-10 sec). These results, thus indicate that the order of the strength of inter-sheet interaction is AP-β-sheet (Ala)6, AP-β-sheet (Ala)4 and AP-β-sheet (Ala)3. In contrast, methyl group of the C-terminal Cβ4 showed very short correlation time (3.6 x 10-11 sec) as compared with the other Ala Cβs in the case of AP-β-sheet (Ala)4. This behavior could be explained by the facts that the closely located counter methyl groups for Cβ4 are two, while other Cβ groups which have three short distanced counter methyl groups. It is found that T2 values reflect the motional frequencies of local backbones in the order about 70 kHz. Backbone motion of the C-terminus was restricted by strong hydrogen bonding with water molecules. Under this condition, backbone motional frequency of the C-terminus is slower than ~70 kHz, while those of the central Cβ carbons exhibit faster than ~70 kHz in AP-β-sheet (Ala)3 and AP-β-sheet (Ala)4. It is further found that backbone frequency of Cβ carbon in AP-β-sheet (Ala)6 is slower than ~70 kHz.

Supporting Information Fig.S1: Plot of 13C T1 values for Cβ carbons of alanine against correlation times (10-7 – 10-11 sec). Table S1: Inter atomic distances less than 4.2 Å among Cβ carbons, and counter Cβ carbons or amino nitrogens of AP-β-sheet (Ala)6.

Acknowledgement T.A. acknowledges support by a JSPS KAKENHI, Grant-in-Aid for Scientific Research (A), Grant Number JP26248050 and Impulsing Paradigm Change through Disruptive 26


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Technologies Program (ImPACT). A. N. has been supported by MEXT KAKENHI, Grant-in-Aid for Scientific Research in an Innovative Area, Grant Number JP16H00756, and JSPS KAKENHI, Grant-in-Aid for Scientific Research (C), Grant Number JP15K06963.

27



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Table of Contents

Diagram of 13C T1 values for Cβ carbons of alanine against correlation times (10-7–10-11 sec). Correlation times (τc) of Ala Cβ carbons of AP-β-sheet (Ala)4 and AP-β-sheet (Ala)6.

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Packing Arrangements and Inter-sheet Interaction of Alanine

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