General Applicable Frequency Map for the Amide-I Mode in Î²

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General Applicable Frequency Map for the Amide-I Mode in #-peptides Kaicong Cai, Fenfen Du, Xuan Zheng, Jia Liu, Renhui Zheng, Juan Zhao, and Jianping Wang J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.5b11643 • Publication Date (Web): 29 Jan 2016 Downloaded from http://pubs.acs.org on February 1, 2016

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The Journal of Physical Chemistry

General Applicable Frequency Map for the Amide-I Mode in β -Peptides

Kaicong Cai,a,b* Fenfen Du,a,b Xuan Zheng,a,b Jia Liu,a,b Renhui Zheng,c Juan Zhao,d and Jianping Wangd*

a

College of Chemistry and Chemical Engineering, Fujian Normal University, Fuzhou,

Fujian 350007, P. R. China b

Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry,

Xiamen, Fujian 361005, P. R. China c

Beijing National Laboratory for Molecular Sciences, Structural Chemistry of

Unstable and Stable Species Laboratory, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, P. R. China d

Beijing National Laboratory for Molecular Sciences, Molecular Reaction Dynamics

Laboratory, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, P. R. China

* Corresponding author: E-mail: (K. Cai) [email protected]; (J. Wang) [email protected]

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Abstract: In this work, a general applicable amide-I vibrational frequency map (GA map) for β-peptides in a number of common solvents was constructed, based on a peptide derivative, N-ethylpropionamide (NEPA). The map utilizes force fields at the ab initio computational level to accurately describe molecular structure and solute-solvent interactions, and also force fields at the molecular mechanics level to take into account long-range solute-solvent interactions. The results indicate that the GA map works reasonably for mapping the vibrational frequencies of the amide-I local-modes for β-peptides, holding promises for understanding the complicated infrared spectra of the amide-I mode in β-polypeptides.

Keywords β-peptide; amide-I mode; vibrational spectroscopy; electrostatic interaction; ab initio computations.


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1. INTRODUCTION One of the well-known unnatural peptides, β-peptide that is composed of β-amino acids, can be used as building blocks for molecular design and pharmaceutical applications since it can form various secondary and tertiary structures.1,2 The conformation ensemble of β-peptides is greatly expanded in the energetically accessible conformational space because more torsional freedom is allowed, in comparison to naturally occurred α−peptides. The conformational possibility of β-peptides is largely enhanced also because the amide unit (CONH) in β-peptides is capable of forming differently sized intramolecular hydrogen-bonding structures.3 It remains a challenge to predict the three-dimensional structure from sequence for natural α-peptides and proteins, not to mention unnatural β-peptides. The amide unit of the peptide backbone has several structurally sensitive and strong infrared (IR)-active vibrations. One of them is the amide-I mode, which is mainly composed of C=O stretching motion, with its vibrational frequency appearing in the mid-IR region (1600-1700 cm-1). Interpretation of the amide-I spectra of peptides has drawn much attention in recent years. Advanced vibrational experimental and computational techniques have been used to shed light on the structural and the functional aspects of peptides. The amide-I mode has been known as effective probe for peptide structure as well as its solvation environment.4-6 The amide-I vibrational frequency is quite helpful for the assignment of the secondary structure of peptides since different conformations give rise to distinctively different IR absorption peaks.7-9 For example, α-helix has a single broad band peaked at ca. 1650 cm-1. As for β-sheet, there are two peaks located at ca. 1630 cm-1 and 1680 cm-1 respectively, and the low-frequency peak has stronger absorption than the high-frequency counterpart.5,6,10-13 Femtosecond two-dimensional infrared

(2D IR) spectroscopy developed in recent years has

greatly enhanced the knowledge of the amide-I vibration of α-peptides, by, for example, being able to structurally decipher a network of vibrational coupling between different amide-I vibrators.14-26 On the other hand, increasing interests have been seen in recent years for establishing a relationship between the spectral and 3 ACS Paragon Plus Environment


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structural features of β-peptides.27,28 Femtosecond 2D IR spectroscopy has been used to reveal the structural dynamics of a 12/10-helical β-peptide,29 and a β-peptide model compound N-ethylpropionamide (NEPA) that has a single amide unit.28 Nanosecond time-resolved IR with temperature-jump has been used to study the folding mechanism of a helical β-peptide.30 Single-conformation IR and UV spectra of different synthetic β-peptide foldamers have been reported.31-34 The structural basis of the amide-I vibration for several helical β-peptides has been examined very recently. 35

With the development of advanced experimental IR methods, the interpretation on the increasing amount of experimental data of amide vibrations of peptides needs to be improved on the theoretical front. Recently, several spectroscopic maps were proposed on the basis of the peptide "building block" models, especially the simplest analogue for α-peptide, N-methylacetamide (NMA), to gain insight into the relationship between the structural features of peptide to corresponding spectral parameters in the solution phase. In these maps, the solvent induced frequency shift of the amide-I vibration is treated mainly based on the electrostatic potential, field, and field gradient, thus the amide-I vibrational frequency shift from the gas phase to solution phase can be expressed by the map as a function of the electrostatic effect projected

onto

amide

units.8,13,15,36-57

The

dispersion

force,

polarization,

exchange-repulsion, and charge-transfer effects were also included for the amide-I mode especially when model compound was in non-polar solvent.58-60 The frequency maps built on the basis of NMA are capable of obtaining the essential vibrational feature of the amide-I, -II, -III, and -A modes at the same time.45,49,61 The application of a simple amide-I frequency map for β-peptides has also been reported very recently based on NEPA, which is an analog of NMA for β-peptides, in D2O solution under molecular mechanics force field scheme.28,40 Vibrational frequency maps were also parameterized for other molecular systems, for example, liquid water.38,48,62-67 These frequency maps have advantages and disadvantages in terms of their construction procedure and accuracy. Here, the maps built by performing ab initio 4 ACS Paragon Plus Environment

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calculations on the solute-solvent clusters that were selected from molecular dynamics (MD) snapshots or artificially constructed are referred to as "ab initio based maps", while the maps built on the basis of structural sampling and normal-mode frequency calculations using the MD snapshots are referred as the "molecular mechanics force field based maps". The ab initio based maps have advantages of being accurate in computing

vibrational

frequencies,

and

also

in

describing

short-distance

intermolecular interactions. However, it either requires a careful selection of a series of solute-solvent clusters,42,43,48 or needs sophisticated modeling on the electrostatic effects.49,68 In particular for the former, because of limited computational power, one can neither have unlimited sample size for solute-solvent clusters, nor use sufficiently high-level theory and basis sets for electronic structure and vibrational frequency calculations.44 Thus the bulk solvent effect is not fully taken into account. It is known that long-distance solvent-solute interactions can still affect the electronic structure of the solute to some extent. To include such effects, one may use polarizable continuum model (PCM) of solvent,69-71 or use external field49,50 for charged solvent environment, all at a reasonable computational cost. Moreover, it would be more computationally demanding for sampling solute-solvent clusters for β-peptides, because of even larger molecular size is involved in comparison to the case of α-peptides. Additionally, it has been shown that density functional method may lead to an incorrect anharmonic amide-I potential energy in α-peptides.72 The pure molecular mechanics force field based maps, on the other hand, have the advantage of being simple in scheme and efficient in construction. No quantum mechanical frequency computations on the solute-solvent clusters are needed and the outer solvation shell effect on vibrational frequency can be taken into account by sampling a sizable MD-ensemble that explicitly contains both solute and solvent species.28,37,40,41 However, this protocol lacks accuracy in assessing short-distance intermolecular interactions. Of course the force fields used in the MD simulations is also important for the map construction.73 Nevertheless, from the discussion above one sees that the advantages of the ab initio based maps and that of the molecular 5 ACS Paragon Plus Environment


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mechanics based maps are complementary to each other. These considerations inspire the construction of a new map that can take the advantages of the merits of both. In this work, we aimed to establish a generally applicable amide-I frequency map (named as GA map) for β-peptides. To this end, the model molecule for β-peptide NEPA was used. Sample space was composed of a sub ensemble of NEPA-solvent trajectories from MD simulations in several typical solvents, and a series of hydrogen-bonded NEPA-solvent clusters extracted from the MD trajectories. The GA map treated the intermolecular interactions between NEPA and surrounding solvent molecules in terms of ab initio calculations by which electronic structural feature and vibrational parameters can be evaluated at a more accurate level. At the same time, the long range electrostatic effect from the bulk was taken into account at molecular mechanics level. In this way, the sampling size actually spans from the first solvation shell to the entire MD system. We examined the obtained amide-I frequencies and their distributions for NEPA and a β-dipeptide in different solvents, followed by linear IR spectral simulations. Factors influencing the amide-I vibrational properties of β-peptides were discussed.

2. COMPUTATIONAL AND EXPERIMENTAL DETAILS A. MD simulations MD simulations were performed to sample the structure and dynamics of NEPA in solvents with different polarities (D2O, DMSO, and CHCl3) by using NAMD program.74 The side length of each cubic box of solvent was set to 36 Å with periodic boundary condition applied. NEPA was placed in the geometrical center of 1421 D2O molecules, 345 DMSO molecules, and 289 CHCl3 molecules, respectively. The non-bonded cutoff was set to 12 Å to avoid the interaction with the self-images. The Particle-Mesh Ewald (PME) summation was employed for long-range coulomb interactions.


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The force field parameters of NEPA were obtained from Cui and co-workers75. Heavy water (D2O) was described by using TIP3P model,76 DMSO were parameterized by Feller and co-workers,77 and the parameters for CHCl3 were transferred from OPLS-AA force field.78 These force fields have been utilized in the MD studies of biomolecules.13,37,40 Each of the MD simulations was initiated by an energy minimization process to remove possible spatial overlap with high energy and to reconcile their structures with the force field by using conjugate gradient minimization method at T=0 K. A heating process was then carried out to raise the temperature from 0 K to 298 K. MD simulations were performed by using Langevin-piston Nosé-Hoover method at 298 K for 10 ns at the time step of 1 fs under NPT ensemble. The MD trajectory was saved every 50 fs for evaluation of the structural feature and the amide-I vibrational frequency. Radial distribution functions (RDF) were computed using VMD,79 and spatial distribution functions (SDF) were examined by using Gromacs program80 and visualized in VMD. B. Ab initio calculations Ab initio calculations were performed for NEPA-solvent clusters, which were sampled from the MD trajectories (10 clusters for each NEPA-n-solvent system, n=1-5, total 150 clusters for three kinds of solvents). These clusters were first undergone structure optimization, then followed by normal-mode analysis to obtain the vibrational parameters of the amide-I mode. All the computations were performed at B3LYP/6-311++G** level of theory, unless otherwise stated, by using Gaussian 09.81 C. General applicable map (GA map) construction A general applicable amide-I vibrational frequency map (the GA map), which is an extension of our previous work for α-peptide,37,41 was constructed based on NEPA in different solvation environments. To construct the map, a sample space was selected first. For each solvent (D2O, DMSO, and CHCl3), 200 MD snapshots were randomly extracted from 10-ns MD trajectories, and 50 structure-optimized NEPA-solvent clusters at the ab initio level were originally selected from the 200 MD snapshots. 7 ACS Paragon Plus Environment


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Thus 600 MD snapshots (200 for NEPA in each solvent) and 150 NEPA-solvent clusters (50 for each NEPA-solvent system) were gathered together as a complete sample for the map parameterization. The red shift of the amide-I vibrational frequency of NEPA from the gas phase to the solution phase was evaluated by the electrostatic potential originated from the micro-environment of the solvated NEPA, including solvent and NEPA backbone on the atomic sites of the amide unit through following equation, 4

vs = v0 + ∑ fiϕi .

(1)

i =1

vs is the amide-I frequency obtained from the samples, and treated in two ways. For

the MD snapshots, vs is calculated through instantaneous normal mode analysis82 (INM) and assigned by the potential energy distribution (PED) analysis by using the VIBRAN module of CHARMM.83 However, the INM frequencies are not well described and could not directly be used for map parameterization since the force fields were designed to mimic the structure dynamics other than vibrational frequency. So a constant (C) is introduced to shift the INM results to a lower frequency region where the amide-I frequencies refined by the GA map would have the same frequency center with the experimental data in solution phase (C = vinm - vs, and a typical value of C is 77 cm-1 for the case of D2O). For the structural optimized solute-solvent clusters, vs is calculated at B3LYP/6-311++G** level of theory, and the obtained amide-I vibrational frequencies were scaled (by a factor of 0.976),48 based on the ratio of experimental gas-phase amide-I frequency (v0=1696 cm-1, from a recent IR measurement of Ac-β-HAla-NHMe in the Kr matrix84) and the calculated gas-phase frequency (1738 cm-1). fi is the coefficient of the map that needs to be parameterized, and the ϕi is electrostatic potential on the four selected atomic sites. Therefore, the frequency shift from gas phase to solution phase induced by the electrostatic potential 4

from solvent and peptide can be denoted as

∑ fϕ i

i

. The electrostatic potentials from

i =1


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solvents and peptide backbone projected onto four sites of the amide unit (namely on the C, O, N, H atoms) were calculated using the following expression, qk

1

ϕi =

4πε 0

∑r k

i ,k

.

(2)

Here, qk is the atomic partial charge of solvent and ethyl groups of NEPA; ri,k is the distance between the ith site of NEPA and the kth atom of solvent or ethyl groups. The ethyl groups of NEPA were considered as united atoms, whose center of mass was set at the middle of the C-C bond of ethyl groups. The total partial charges of each ethyl group were therefore summed to its center of mass. The atomic partial charges for the solvents and the NEPA were assigned according to the molecular mechanics force field parameters. Since the NEPA-solvent clusters were all in the charge neutrality condition, i.e.,

∑q

k

= 0 , so the parameters at the four atomic sites are not independent, but are

constrained by

∑f

i

= 0 .42 Then Eq. (1) can be rewritten as:

3

vs = v0 + ∑ f i (ϕi −ϕ4 ) .

(3)

i =1

The multivariate least square fitting method was used to obtain the map parameters (Table 1). The four parameters have the same sign as those in our recent amide-I vibrational frequency map built for NMA,37 and the parameters on C and N atoms have the relatively larger magnitude, similar to those found in the amide-I map for α-peptide.37,47,48 A comparison of recent amide-I vibrational frequency maps for the

simplest analogue of α-peptides is given in Table S1 of the Supporting Information (SI). It is clear that the sign of each parameter is model dependent. For four-site models, the sign of the parameter at the H site can be either positive or negative. Our map here is more or less like a three-site map (C,O, and N), provided that C, O, N, and H are the most important sites. However, we find that four-site GA map shown in Table 1 works more reasonably, even though the parameter on the H site present an insignificant value in comparison to those of the C, O, and N sites. In addition, the



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obtained parameters are different from the pure MM maps built for NEPA sorely in D2O (shown in Table S1) or CHCl3,40 because the present map contains ab initio computational contributions, and the treatments of vs, v0, and the electrostatic potential from peptide backbone are different from the previous map.40

Table 1. Map parameters (in cm-1V-1) for the amide-I frequency of NEPA in different solvents. NEPA

C

O

N

H

GA

156.350

-70.528

-92.102

6.281

The distributed amide-I vibrational frequencies can be obtained after applying the fitting coefficients to the electrostatic potentials on the amide unit throughout the 10 ns MD trajectory of each NEPA-solvent system for a better performance of simulating amide-I spectra in the form of 4

v = v0 + ∑ f iϕi .

(4)

i =1

The fluctuating amide-I vibrational frequencies were then refined for NEPA in D2O, DMSO and CHCl3 throughout the MD trajectories by using the GA map. However, the obtained frequency distributions are not the actual IR spectra since it neglects the motional narrowing effect.85,86 It is well known that the IR fundamental absorption spectrum can be written in terms of the Fourier transform of the transition dipole time correlation function: ∞ t I (v) ~ ∫ e − iν t × µ (0) ⋅ µ (t ) exp i ∫ dτν (τ )  dt ,  0  −∞

(5)

in the semi-classical limit. Here, µ is the dipole operator, ν is the time-dependent amide-I transition frequency. Neglecting the orientational dynamics, formula (5) can be rewritten as:


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∞

I (v ) ~ ∫ e

− i (ν − ν ) t

−∞

t × µ (0) ⋅ µ (t ) exp i ∫ dτδν (τ )  dt ,  0 

(6)

where δν (t ) = ν (t ) − ν . ν is the average of amide-I frequency, and µ=|µ|. The Condon approximation44,87,88 is achieved by assuming that the transition dipole is independent of the nuclear coordinates of the solvents, therefore, µ can be treated as a constant, leading to a Condon line shape function, ∞

I (v ) ~ ∫ e −∞

− i (ν − ν ) t

t × exp i ∫ dτδν (τ )   0 

{e } dt . − t / T1

(7)

Here, the lifetime broadening is also taken into account (T1 = 0.5 ps was used), which is a typical vibrational lifetime for the amide-I excited state in α-peptides.40,89

D. IR experiment The IR spectra of NEPA dissolved in different solvents (D2O, DMSO, and CHCl3) at same concentration (75 mM) were measured using a Thermo-Fisher Nicolet 6700 FTIR spectrometer equipped with a liquid nitrogen cooled mercury-cadmium-telluride (MCT) detector. The samples were placed in a homemade demountable IR cell composed of two 2-mm thick CaF2 windows with a 50-µm polyester spacer (Du Pont Teijin Films). Nitrogen gas was used to purge the FTIR spectrometer and its sample chamber during IR spectral measurements. The IR spectra were measured by averaging 64 scans with 2-cm-1 spectral resolution.

3. RESULTS AND DISCUSSION A. FTIR spectra of NEPA in different solvents The experimental linear FTIR spectra of NEPA in D2O, DMSO, and CHCl3 are shown in Figure 1. In aqueous solution, the amide-I mode only exhibits a Gaussian type absorption band that is peaked at 1612.3 cm-1. Curve fitting shows that its full width half maximum (FWHM) is about 25.9 cm-1. The amide-I peak position in DMSO is blue shifted to 1661.5 cm-1 with slightly narrowed Gaussian profile (FWHM = 24.4 cm-1). In CHCl3, the amide-I frequency is peaked at 1654.4 cm-1 11 ACS Paragon Plus Environment


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(FWHM = 32.1 cm-1) with a low-frequency shoulder that might be due to the co-existence of two species with and without the weak hydrogen bonding between carbonyl group and the hydrogen of CHCl3. In addition, it is interesting to see that the amide-I peak position might closely correlated with the solute-solvent interaction.

Figure 1. FTIR spectra of amide-I mode of NEPA in D2O, DMSO, and CHCl3.

B. Structural dynamics of solvated NEPA To examine the structural dynamics of NEPA in the three solvents and the distribution of solvent molecules in the vicinity of NEPA, statistical tools were applied on the MD trajectories. First, the spatial distribution functions (SDFs) were computed in order to get insight into a view of three-dimensional probability distributions of solvent species. The results are given in Figure 2, in which the isosurfaces in blue, red, and green colors represent the probable distributions of the H, O, and Cl atoms of solvent molecules, respectively. It is found that the probability distributions of solvents around NEPA vary with the solute-solvent interaction.


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Figure 2. Spatial distribution functions of NEPA in different solvents (panel a/b/c; blue, red and green isosurfaces present water hydrogen, water oxygen and Cl of chloroform, respectively), and the radial distribution functions between the selected atoms of NEPA and different solvent molecules (panel e/d/f).

More specifically, for NEPA in D2O, there are distinct blue areas around the oxygen of carbonyl group in very short distance with red areas in relative longer distances, showing that the carbonyl group tends to form hydrogen bonds; and the N-H group is surrounded by the oxygen of water which is indicated as red area, showing it is also hydrogen bonded. It is shown that the C=O and N-H groups of NEPA are both hydrophilic in heavy water. The interaction between NEPA and DMSO, on the other hand, is not as intense as that in D2O, and the carbonyl group is relatively isolated while the N-H group is surrounded by a bunch of red area, indicating that oxygen atoms of DMSO prefer to move around the N-H group. As for NEPA in CHCl3, the C=O group is covered with blue area at a relative long distance, showing the interactions between solute and solvent are less intense. Moreover, the N-H group is covered with green regions which presented as a ring cycle all around NEPA but only not at the amide proton site, showing that the H atom interacts weakly with bulk chloride atoms. Further, the radial distribution functions (RDFs) were calculated for a more quantitative description of the microstructure of solvated NEPA in different solvents (Figure 2). The RDFs for C=O and N-H groups of NEPA show that there are interactions between amide group and solvent molecules, and the hydrogen-bonding interactions between NEPA and solvent molecules are quite intense in polar solvents. For NEPA in D2O, the RDFs present distinctive peaks that appear within short distances, indicating there are clear hydrogen bonding preference between amide unit and D2O. The RDF curve of O(C=O) ~ D(D2O) pair shows a sharp peak at 1.75 Å with the g(r) value close to 1.4, while the pair of H(N-H) ~ O(D2O) shows its first maximum at 2.15 Å with the g(r) value around 0.4. The coordination number of the 13 ACS Paragon Plus Environment


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solvents in the first solvation shell is calculated by integrating g(r) to the first minimum of RDF curve, and the results show that there are approximately two deuterium atoms and one oxygen atom of heavy water moving around the NEPA, confirming the presence of roughly one heavy water molecule in the neighborhood of the C=O group of NEPA in the first hydration shell. For NEPA in DMSO, the solvent molecules tend to gather around the N-H group of NEPA rather than the C=O group. The g(r) maximum (equals to 4.9) located at the distance of 1.85 Å indicates a strong interaction between the H(H-N) ~ O(O=S) pair. The coordination number of the first peak area is found to be around one, showing that there is about one DMSO bound to the H(H-N) group in the first solvation shell. As for NEPA in nearly nonpolar solvent (CHCl3), the locations of the first RDF peaks are much further than those observed in D2O and DMSO. The RDF peak of O(O=C) ~ H(CHCl3) pair is located at about 2.8 Å, due to a weak hydrogen bond. The first RDF peak of H(H-N) ~ Cl(CHCl3) pair is difficult to define. These MD results suggest that NEPA is well solvated in the three solvents with CO and NH groups interacting with solvent reasonably. Thus the MD trajectories can be used for sampling the typical NEPA solution structures for electronic structure calculation, and also for constructing the electrostatic frequency map of amide-I mode.

C. Ab initio samplings on the representative MD Structures To examine the correlation between the structure feature and the amide-I frequency of NEPA, representative NEPA-solvent clusters were sampled from MD simulations with only 1 to 5 solvent molecules around NEPA were chosen. Vibrational frequencies of these NEPA-solvent clusters were obtained specifically for the amide-I mode of NEPA, and are shown in Figure 3 for the three solvent cases. Linear correlations are found between the amide-I frequencies and the C=O bond length.42 Hydrogen bond between solvent molecule and carbonyl group of NEPA lowers the frequency of C=O stretching vibration. Relatively larger frequency red shift is observed in NEPA-D2O 14 ACS Paragon Plus Environment

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clusters (frequency ranging from 1715.7 to 1651.7 cm-1), where strong hydrogen bonds are formed between the oxygen of carbonyl group and the deuterium of heavy water molecules. As for NEPA in CHCl3, the solvent induced frequency red shifts are smaller due to the weak hydrogen bonding effect (frequency ranging from 1718.6 to 1669.1 cm-1). The smallest degree of frequency red shifts are found for NEPA in DMSO (frequency ranging from 1719.6 to 1680.4 cm-1), since the interaction between oxygen of amide group and the DMSO is negligible. The number of surrounding solvents is important to the solvated structure of the NEPA and greatly affects the degree of amide-I frequency red shift. For NEPA-1-D2O, the hydrogen bond between carbonyl group and D2O makes amide-I vibrational frequency average red shift to 1706.3 cm-1, while the increasing number of D2O molecule enlargers the degree of frequency red shift to an average of 1662.6 cm-1 (5-D2O). The average frequency of the amide-I mode of the NEPA-1-CHCl3 is about 1712.8 cm-1, and red shifts to 1689.8 cm-1 (2-CHCl3), 1679.2 cm-1 (3-CHCl3), 1676.2 cm-1 (4-CHCl3), and 1676.2 cm-1 (5-CHCl3) for NEPA in CHCl3. The degree of frequency red shift becomes smaller with the addition of solvent molecules around NEPA, and the average amide-I frequencies are the same for the solvated NEPA with 4- and 5-CHCl3. The average amide-I frequency of NEPA in DMSO shifts from 1717.4 cm-1 (1-DMSO) to 1692.0 cm-1 (5-DMSO), and exhibits similar trend like NEPA in CHCl3 only with smaller degree of frequency red shift.

Figure 3. Correlation between amide-I vibrational frequencies and the C=O bond length of NEPA-solvent clusters obtained from ab initio calculations. Insert shows the mean values of clusters with different number of solvents to the same scale. 15 ACS Paragon Plus Environment


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These ab initio calculations on the solute-solvent clusters provide us an insight into the solvated peptide structure and its chemical environment of the first solvation shell. This is critical to the construction of the GA map since the solute-solvent interactions such as hydrogen bonding and electrostatic interactions take place when NEPA and the solvent molecules are in close contact. It is obvious that the surrounding solvent molecules can also induce structural distortion of the solvated NEPA, which results in peak-position shift and spectral width change in the amide-I spectra. However, the structure optimization performed on theses clusters would change the initial structural feature to some extent especially for the solvent which form strong intermolecular hydrogen bond with NEPA. However, regardless of the location of the surrounding solvent molecules, the amide-I frequency red-shift is found to be linearly correlated with the C=O bond length, and more shift occurs if more solvent molecules are included.

D. Amide-I frequency distributions and simulated IR spectra of solvated NEPA After applying the GA map parameters (Table 1) to the MD trajectory, the refined amide-I frequency distributions can be obtained and the corresponding simulated IR spectra can also be calculated by using Eq. (7). The density of states (DOS) of the obtained amide-I vibrator of different NEPA-solvent systems are shown in Figure 4a, indicating different profiles of vibrational frequency shift and frequency distributions.


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Figure 4. Computed vibrational frequency distributions (a) and simulated IR spectra of amide-I bands (b) for NEPA in different solvents with experimental IR spectra for comparison.

For NEPA in D2O, the most probable transition frequency of amide-I vibrator is located at 1629.4 cm-1, which is about 17.1 cm-1 blue shifted from the experimental observed data with a broad distribution profile (FWHM = 47.4 cm-1). For NEPA in DMSO, the amide-I transition frequency is mainly located at 1660.3 cm-1 (FWHM = 28.2 cm-1), which perfectly agrees with the experimental value (1661.5 cm-1). The amide-I mode of NEPA in CHCl3 is at 1657.4 cm-1 (FWHM = 11.3 cm-1), only blue shifted by 3.0 cm-1 with respect to the experimental value.

Table 2. Comparison of the line shape parameters (in cm-1) for amide-I vibration of NEPA in different solvents obtained from the GA map. D2 O

GA Exp

DMSO

RMSd

CHCl3

Freq

FWHMc

Freq

FWHM

Freq

FWHM

DOSa

1629.4

47.4

1660.3

28.2

1657.4

11.3

IRb

1629.0

24.3

1660.0

17.0

1657.2

11.2

IRa

1612.3

25.9

1661.5

24.4

1654.4

32.1

a

Gaussian fitting.

b

Lorentzian fitting.

c

FWHM: full width at half maximum.

d

RMS: root mean square.

Freq

FWHM

9.8

12.8

In order to examine the performance of our GA map, linear IR spectra of the amide-I mode of NEPA were simulated (Figure 4b), with experimental results are also given for a direct comparison. The line shape parameters are listed in Table 2. The simulated IR peaks are almost identical to the DOS, and band width is narrower than



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the corresponding frequency distribution because of the motional narrowing effect.89 The relative peak positions in three solvents observed experimentally are reasonably reproduced by the GA map. The absolute deviations from the peak values with Lorentzian fitting to the experimental data are 16.7 cm-1 for NEPA in D2O, 1.5 cm-1 in DMSO, and 2.8 cm-1 in CHCl3, respectively. Besides, it is very interesting that the map can differentiate the subtle frequency difference between NEPA in DMSO and CHCl3 as experimentally observed. However, the line widths of the simulated IR spectra are somewhat different from the experimental observed ones since the quality of the simulated IR is strongly depending on the map method. For NEPA-D2O system, the FWHM of amide-I mode is 24.3 cm-1, which is only 1.6 cm-1 narrower than the experimental data. The predicted line width of amide-I spectrum in D2O seems as good as the one obtained from the map built for NEPA sorely in D2O.28 The FWHM of the amide-I mode of NEPA-DMSO system is 7.4 cm-1 narrower than the experimental observed data. Small deviation arises since the GA map simultaneously takes three different solvation environments into account, but its transferability does save much time for individual map construction and even suitable for the IR prediction of peptide in mix-solvent environments.37 As for NEPA-CHCl3 system, the FWHM (11.2 cm-1) of amide-I mode is much narrower than the experimental data. Here, the FWHM is not well predicted for NEPA in CHCl3 because of the dispersion force, which is much stronger than the coulomb interaction in this case, is not taken into consideration in the GA map construction. To take into account the dispersion correction, we also performed ab initio calculations on NEPA-n-CHCl3 clusters using the Grimme's DFT-D3 method.90 The computed amide-I frequencies and the electrostatic potentials on the amide unit were used to construct a new frequency map (GA_GD3), as listed in Table S1 of the SI. As can be seen that the map parameters in GA_GD3 are almost identical to those in the GA map, suggesting the addition of dispersion effect in such a fashion introduces negligible influences on the GA map. Further, we compared the amide-I local-mode 18 ACS Paragon Plus Environment

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frequency distribution of NEPA by using the two maps. The results are shown in Figure S1 of the SI. As can be seen that also only a marginal difference is seen in the amide-I local-mode frequency distribution. Thus one can conclude that the dispersion effect embedded in the Grimme's DFT-D3 method does not improve much the GA map constructed in the present work. In fact, the dispersion force may be introduced using different ways, for example, by introducing a varying v0 value instead of the gas-phase constant to represent the non-polar environment,39 or by considering the polarizability, multipole effects and the van de Waals forces.8,13,38 These approaches may also be considered in our GA map in future. In practice it is feasible because in recent studies the electrostatic, exchange-repulsion, polarization, dispersion, and charge-transfer interactions have been considered in examining vibrational solvatochromism of peptides. 58-60 However, in this work, we only focus on seeking a simple way to better describe the electrostatic effect on amide-I vibration by combining the ab initio calculation and the molecular mechanics force fields.

E. Contributions to the amide-I frequency shifts The electrostatic potentials on the atomic sites contribute differently to the amide-I frequency shifts. To identify these contributions, the frequency shifts were evaluated at each atomic site (Figure 5). It is shown that the amide-I frequency red shift is mainly originated from the O and N atomic sites, while frequency blue shift is observed on the C site. The net change of frequency shift correlates nicely with the signs of the map parameters given in Table 1. It is observed that the frequency shifts are mainly attributed to the electrostatic potential on the C, O, and N sites. The contribution to the amide-I frequency shift from H site is the smallest, so is the magnitude of the map parameter on H site, which is due to the fact that the H atom is far away from the amide carbonyl group. This phenomenon is consistent with previous maps presented by Bour's and Cho's groups,47,91 although the H atom seems not that important, it is indispensable for the amide unit that composed peptides and protein. The four site map can also be directly applied on the peptide groups in a given polypeptide.91 However, the map built on 19 ACS Paragon Plus Environment


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only two sites was also proposed by Skinner and coworkers since the electric-field coefficients are particularly large on the C and N sites.44

Figure 5. Contributions to the amide-I frequency shifts of NEPA in three solvents at different atomic sites.

The electrostatic potential from the solvent molecules for NEPA-solvent systems has the largest impact on the O site, which is positive; while that from the peptide backbone has the strongest impact on the N site, which is also positive. Engaging with the map parameters (the parameters on O and N sites are negative), the amide-I frequency red shifts are mainly contributed by O and N sites, where the O site is a little stronger for NEPA in D2O, almost equal for NEPA in DMSO and weaker for NEPA in CHCl3 than the N site due to the solute-solvent interactions. Since the map parameters at the four atomic sites are constrained by

∑f

i

=0

, the parameter on C

site is positive, plus the electrostatic potential on this site (also positive), then its contribution to the amide-I frequency shift is towards high-frequency region. Inter- and intramolecular interactions are assumed to be independent during the map parameterization process, the amide-I frequency red shifts are accounted for the contributions from peptide and solvent in separate calculations, 20 ACS Paragon Plus Environment

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v = v0 + ∑ f iϕisolvent + ∑ f iϕipeptide . i

(8)

i

Here, the map parameters (fi) are already listed in Table 1, ϕisolvent and ϕipeptide are the electrostatic potential on the four atomic sites originated from solvent molecules and the peptide backbone for NEPA in different solvation environments. The contributions to the frequency red shifts from solvent and peptide for different NEPA-solvent systems are shown in Figure 6.

Figure 6. Frequency red shift due to peptide backbone and solvent molecules for the amide-I mode of NEPA in three solvents obtained from GA map.

It is shown that for NEPA in D2O the amide-I frequency red shift caused by solvent molecules is at the same magnitude as that caused by peptide backbone (namely the ethyl group), while the frequency red shifts for NEPA in DMSO and CHCl3 are mainly originated from the electrostatic potential of peptide backbone. It is shown that the amide-I frequency red shift is mainly determined by the peptide itself, which is consistent with the recent study of amide-I mode for the NMA and the helical β-peptides.37,40 However, the solvent effect has been incorporated into the structural feature of solvated peptide to some extent.41 The frequency red shift is related to the electrostatic potential on the amide unit, so the frequency red shift can be a direct reflection of the interaction between the solute and solvent molecule. The electrostatic potential would be much stronger since the polar solvent molecules and the carbonyl group are in a relatively short distance, so the electronic structure calculations for the first hydration shell during the GA map construction can guarantee the precise 21 ACS Paragon Plus Environment


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description of the intermolecular interactions of solvated NEPA and the amide-I frequency prediction. In short, it is shown that peptide itself contributes uniformly 36 cm-1 regardless of the solvent. The physical implication of this result is that the solvated peptide has structure different from the gas-phase case. As for the solvent contribution, the RDF and SDF have shown that the carbonyl group of NEPA tends to form strong hydrogen bond with D2O molecules, while the solute-solvent interactions are much weaker in DMSO and CHCl3. A very weak hydrogen bond between carbonyl group and CHCl3 can be found, and the carbonyl group is in a relatively isolated situation in DMSO. Therefore, the solvent induced frequency red shifts in DMSO and CHCl3 are much smaller than the one observed in D2O. These results explain the subtle difference between the computed IR spectra for NEPA in DMSO and CHCl3.

F. Application of the GA map on β-dipeptide MD simulations were also performed for Ac-β-Gly-NHMe solvated in a cubic box with 45 Å side-length filled with solvent molecules (D2O, or DMSO, or CHCl3). The details of the MD simulations are the same as discussed in section 2. The GA map was applied onto the β-dipeptide and the obtained frequency distributions of the amide-I modes of Ac-β-Gly-NHMe in different solvents are shown in Figure 7. It is shown that the local-mode frequencies of the amide-Ia (acetyl end) and -Ib (amino end) modes are separately distributed. In D2O, the amide-Ia mode is centered at 1535 cm-1 while the amide-Ib mode is presented at relatively higher frequency region at 1675 cm-1. The amide-Ia and -Ib modes are more isolated in the 1500 ~ 1800 cm-1 frequency region for Ac-β-Gly-NHMe in DMSO and CHCl3. However, the predicted amide-I spectra are not satisfactory since their frequencies are off the range of typical amide-I band (1600~1700 cm-1). The results show that the GA map constructed based on an isolated β-peptide unit requires more input in order to be applicable for β-peptide oligomers.

These

include

side-chain

correction,

vibrational

coupling,

and

conformational dependent local-mode frequency correction. Currently we are working along these lines. 22 ACS Paragon Plus Environment

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Figure 7. Static distributions of the amide-I frequencies of Ac-β-Gly-NHMe in different solvents. The molecular structure of Ac-β-Gly-NHMe is shown in panel (b).

On the other hand, the contributions from peptide and solvent to the amide-I frequency shift were calculated for Ac-β-Gly-NHMe by using Eq. (8). The results show that the amide-Ia frequency red shift is mainly caused by the peptide backbone, while the frequency blue shift is observed for amide-Ib mode from peptide backbone and red shift is observed from solvent molecules (Figure 8). The magnitude of the frequency shift caused by the peptide backbone is larger than the one originated from solvent molecules for amide-Ia and -Ib mode except for the amide-Ib mode of NEPA in D2O. The result is consistent with the picture established earlier that the local-mode frequencies were primarily determined by peptide and side chain, rather than solvent.40



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Figure 8. Local-mode frequency-shift distribution of the two amide-I modes in Ac-β-Gly-NHMe coming from peptide backbone (solid line) and from solvent molecules (dashed lines). (a and d) in D2O; (b and e) in DMSO, and (c and f) in CHCl3.

Note that in this work no efforts have been made to simulate the linear IR spectra of β-dipeptides, because in the current map the treatment of side-chain needs further improvement. However, a previous frequency map for the amide-I mode in α-peptides 92

has been simply applied on the Ac-β-Gly-NHMe system and the two simulated IR

peaks are separated in frequency. At the moment, there are no experimental IR spectra available for this dipeptide system to compare yet. Nevertheless, the covalent effect on the local-mode frequency, vibrational coupling, and the repeating unit of the “amide” group, all require a further refinement, which is particularly important for short peptides. Similar works on the α-peptides have been reported previously.39,92,93 Such a work is undergoing in our laboratory.

4. CONCLUSION In this work, using N-ethylpropionamide (NEPA), a β-peptide analogue with a single amide unit, a general applicable amide-I vibrational frequency map (GA map) for β-peptides was constructed on the basis of molecular mechanics force fields and electronic structure method. MD simulations, performed for NEPA in different 24 ACS Paragon Plus Environment

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explicit solvents, were used to obtain representative NEPA-solvent clusters, and also used to evaluate long-distance electrostatic interactions. Solute-solvent structural dynamics were evaluated using both radial and spatial distribution functions. The constructed GA map is superior to previous ab initio-based maps because the sampling size is no longer limited to the first solvation shell, instead, the electrostatic effect from the bulk is taken into account with the aid of MD trajectories. The GA map’s advantage over pure molecular mechanics force fields based maps is also significant because of the inclusion of electronic structural feature by ab initio computations over NEPA-solvent clusters. More importantly, the GA map can be used to evaluate the amide-I local-mode frequencies simultaneously in several solvents. Applications of the GA map on β-peptides were given in this work. Density of states and local-mode frequency distributions and linear IR spectra for amide-I mode of NEPA were examined and satisfactory results were obtained. In particular, simulated linear IR spectra of NEPA in several solvents were found to be in reasonable agreement with experimental IR results. The results suggested that the carbonyl group of amide unit whose stretching motion is the main component of amide-I vibration, forms strong hydrogen bond with D2O, but forms weak hydrogen bond with CHCl3, and is relatively isolated in DMSO. The results also suggested that the amide-I frequency shift with respect to gas-phase value is largely determined by the electrostatic potential projected on the C, O and N sites. The electrostatic interaction from the solvent molecules is as strong as the peptide backbone for NEPA in D2O, while larger electrostatic interaction is due to the peptide backbone of NEPA in DMSO and CHCl3.

ACKNOWLEDGEMENT This work was supported by the Super Computing Center of Chinese Academy of Sciences for the ScGrid computational resources and financially supported by the National Natural Science Foundation of China (21103021 to K.C. and 21173231 to J.W.), and the Education Department of Fujian Province of China (JA13063 to K.C.). 25 ACS Paragon Plus Environment


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TOC figure:


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General Applicable Frequency Map for the Amide-I Mode in Î²

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