Examination of Trifluoroethanol Interactions with Trp-Cage in

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Examination of Trifluoroethanol Interactions with TrpCage in Trifluoroethanol-Water at 298 K through MD Simulations and Intermolecular Nuclear Overhauser Effects John T. Gerig J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.9b01171 • Publication Date (Web): 27 Mar 2019 Downloaded from http://pubs.acs.org on March 30, 2019

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The Journal of Physical Chemistry

Examination of Trifluoroethanol Interactions with Trp-Cage in Trifluoroethanol-Water at 298 K through MD Simulations and Intermolecular Nuclear Overhauser Effects J. T. Gerig*

Department of Chemistry & Biochemistry

University of California, Santa Barbara

Santa Barbara, CA 93106 U.S.A.

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ABSTRACT. MD simulations of the protein model Trp-cage in 42% trifluoroethanolwater at 298 K have been carried out with the goal of exploring peptide hydrogensolvent fluorine nuclear spin cross- relaxation. The TFE5 model of trifluoroethanol developed in previous work was used with the TIP5P-Ew model of water. System densities and component translational diffusion coefficients predicted by the simulations were within 20% of the experimental values. Consideration of the calculated relative amounts of TFE and water surrounding hydrogens of Trp-cage indicated that the composition of the solvent mixture beyond ~1.5 nm from the van der Waals surface of the peptide is close to the composition of the bulk solvent but, as observed by others, TFE accumulates preferentially near the peptide surface. In the simulations, both TFE and water molecules make contacts with the peptide surface; water molecules predominate in contacts with the peptide backbone atoms and TFE molecules generally preferentially interact with sidechains. Translational diffusion of solvent molecules appears to be slowed near the surface of the peptide. Depending on location in the structure, TFE molecules form complexes with the peptide that may persist for up to ~7 ns. Many of the peptide spin-solvent fluorine cross-relaxation parameters (  HF ) for which experimental values are available are reasonably well-predicted from the simulations. However, calculated  HF were too small for some hydrogens of the 6Trp -2ACS Paragon Plus Environment

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indole ring and amino acid hydrogens near this residue in the native structure, while

 HF for hydrogens on the sidechains of 1Asn, 4Ile and 7Leu are too large. In 42% TFEwater, persistent conformations of Trp-cage are found that differ from the conformation found in water by the orientation of the 3Tyr ring.



INTRODUCTION Interactions with solvent water molecules are critical to defining three-dimensional structures and structural dynamics of a protein.1 In turn, proteins perturb both the organization and dynamics of water molecules that surround them, although these influences are usually limited to the first few shells of solvent molecules.2-5 Using a mixture of water and a small, water-soluble organic molecule as a solvent for a protein system provides an avenue for altering the structure of the protein and dynamics associated with it. Thus, phenomena such as protein folding or enzyme activity can be regulated by the nature and amount of organic co-solvent present.6 There is much evidence that organic co-solvents can interact preferentially with proteins in a sitespecific manner;7-8 identification of the sites of interaction can provide valuable leads to interaction sites for drugs.9 Fluorinated alcohol co-solvents such as 2,2,2-trifluoroethanol (TFE) or hexafluoroisopropanol are particularly potent in altering the dominant conformations of a protein or peptide in a mixed solvent. Peptides dissolved in solvents containing TFE in water have been widely studied and many mechanisms have been proposed to explain how the presence of TFE alters peptide conformation.10-14 These ideas have been extensively explored by experiment and by molecular dynamics simulations.15-17 Trp-cage is a widely studied, 20-residue peptide that folds to a compact tertiary structure in about 4 s at 296 K.18 The folding process in water has been extensively -4ACS Paragon Plus Environment

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studied.10, 19-22 At low temperatures in water, >90% of Trp-cage molecules are represented by the conformation shown in Figure 1.19 The conformation of Trp-cage in water appears to be retained when the solvent is changed to 42% TFE-water.23 Intermolecular nuclear Overhauser effects (NOEs) can be used to probe the interactions of solvent molecules with dissolved species24-25 and have been used to study interactions of trifluoroethanol with peptides.23, 26-27 An intermolecular NOE is characterized by a cross- relaxation parameter  XY which arises from magnetic interactions between spin X of the solute and spin Y of the solvent. When the molecules bearing spin X and spin Y are modeled as rotating spheres, theory such as that due to Ayant, et al. 28 shows that  XY depends on the gyromagnetic ratios of spins X and Y, the concentration of solvent spins, the distance of closest approach of the molecular entities holding spins X and Y, and the mutual translational diffusion coefficient of solvent and solute.

We have explored solvation of Trp-cage in 42% TFE-water by determination of intermolecular NOEs that arise from peptide hydrogen-solvent fluorine spin dipolar interactions23 and have attempted to elucidate the effects observed at 318 K by means of all-atom molecular dynamics simulation.29 At this temperature in 42% TFE-water, the conformation of Trp-cage shown in Figure 1 is retained and many of the observed intermolecular 1H{19F} NOEs are correctly predicted by simulations. Disagreements



between experimental and predicted NOEs at 318 K were ascribed to conformational motions of the peptide and/or peptide-solvent interactions that were not correctly modeled during the simulations. These considerations presumably have different temperature dependences. In the present work, we attempt to bolster these conclusions by simulations of the peptide-TFE-water system at 298 K. About half of the available experimental 1H{19F} NOEs at the lower temperature are fairly well-predicted by the simulations but others are seriously in error. Possible reasons for these disagreements are discussed. ============== Insert Figure 1. ============== In what follows, we have used the symbol  HF rather than the conventional symbol (

 HF ) to represent the cross-relaxation rate produced by the interaction of solvent fluorine spins with peptide hydrogens. The symbol  HF will be reserved for the collision diameter parameter used in the Lennard-Jones 12-6 function representing the nonbonded interaction of a solvent fluorine with a peptide hydrogen.


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Figure 1. Views of the structure of Trp-cage (PDB 1L2Y) in pure water at 296 K. The indole ring of residue 6Trp (red) is sequestered by a collection of hydrophobic resides that includes prolines 12, 17, 18 and 19.30



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EXPERIMENTAL SECTION

Experimental cross-relaxation parameters (  HF ). Studies of cross-relaxation between TFE fluorines and hydrogens of Trp-cage dissolved in 42% trifluoroethanol-1,1-d2-water (v/v) at 298 K and pH 5 have been previously reported.23 3-(Trimethylsilyl)-propionic acid-d4 was present in the samples examined as a chemical shift reference. Most experimental peptide-CF3 cross-relaxation parameters are small at 298 K and could not be estimated with high accuracy due to spectral noise; practical considerations such as available instrument time and unavoidable instrumental drifts limited the S/N improvements that could be achieved by signal averaging.

Starting structures. Starting coordinates for Trp-cage were those of the first model given for PDB structure 1L2Y (www.rcsb.org/pdb/explore/explore.do?structureId=1l2y).30 Force field parameters for Trp-cage were those of the AMBER99SB-ILDN force field.31 The model of 3(trimethylsilyl)propanoic acid (TSP) was constructed using PyMol (PyMOL Molecular Graphics System, Version 2, Schrödinger, LLC, https://pymol.org/2/support). Atomic charges were taken from the YASARA AutoSmiles server (http://www.yasara.org/); charges on the carboxyl group were adjusted slightly so that the sum of all charges for the molecule was -1. Other force field parameters were taken from the AMBER99SB-ILDN collection. Lennard-Jones parameters for silicon were those of Li, et al.32 Table S1 of the Supporting Information gives force field parameters for TSP. Trifluoroethanol model TFE5, described previously,29, 33 and the TIP5P-Ew water model were used in all simulations.34 The combination rule for  non-bonded parameters was the arithmetic mean (  ij 

1  ii   jj  as used in the AMBER force fields while the 2

combination rule for  ij non-bonded parameters was the geometric mean (  ij   ii jj  ). 1/2


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Molecular dynamics (MD) simulations. All simulations were done with GROMACS (Versions 5.1-2 and 2016.4)35 running locally and on the COMET system at UC San Diego (part of the NSF-sponsored XSEDE consortium) as described previously.29

A cubic simulation cell approximately 8.5 nm on a side was used. It contained one Trp-cage or TSP molecule, 2500 trifluoroethanol-d2 molecules, 13981 water molecules, and a sodium ion (placed by the gmx ion routine) to maintain electrical neutrality. Periodic boundary conditions were applied and motion of the model center of mass was corrected at each step. It was assumed that artifacts caused by the periodic boundary conditions and the finite size of the simulation cell were negligible.36 Covalent bonds of TFE and the peptide were constrained to constant length by the LINCS procedure37-38 while the SETTLE algorithm was used to constrain bond lengths of water.39 Systems were regulated at 298 K by velocity rescaling40 and at a pressure of 1 bar by use of the Berendsen pressure coupling method41, with relaxation time constants of 0.1 and 1 ps, respectively. The particle mesh Ewald (PME) method for long-range electrostatics was used.42 Cut-offs for electrostatic and van der Waals terms were 1.4 nm. Periodic boundary conditions were applied. Motion of the model center of mass was corrected every 5 steps while the integration time step was 0.002 ps. Simulations to produce trajectories of 0.1-0.3 µs duration were carried out. Snapshots of the system coordinates for analysis of solvent interactions were usually taken at 10 ps intervals. Models were extensively equilibrated until solvent molecules appeared to be well-mixed.



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Random initial atom velocities were then assigned and, after an additional  2 ns equilibration, production runs initiated.

Analyses of molecular dynamics trajectories. Programs contained within the GROMACS package were used to compute the system density and self-diffusion coefficients of solvent components via the Einstein relationship (gmx msd).43 Locally developed programs were used to obtain internuclear distances as a function of time, estimate durations of solvent interactions, count local populations of solvent molecules and estimate local diffusion coefficients of solvent molecules as a function of distance from a specific peptide hydrogen. A program based on the equations of Ayant, et al. 28 for prediction of solvent cross-relaxation parameters (  HF ) has been previously described.33

Computation of the cross-relaxation parameter  HF that describes dipole-dipole relaxation of a solute hydrogen by a group of identical solvent F spins followed the procedure described previously.33 To summarize, assuming that cross correlation effects are negligible,44-45 the collective dipolar relaxation contributions to  HF is given by

3 3  1   HF   H2  F2 h2  J 0 H  F   J 2 H  F   4 4  12 


(1)

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where  H and  F are gyromagnetic ratios and H and F are Larmor frequencies for protons and fluorines, respectively. The spectral density functions J m   are written in terms of the Cartesian components of the vector r which connects a Hi-Fj spin pair 46    N cut  J m    2  G m  t  e  it dt  2    Fijm  0  Fijm  t   e  it dt  0 0  j i

(2)

with Fij  0

rij 2  3 zij 2 rij 5

Fij  1

zij  xij  iyij  rij 5

Fij

2

x 

ij

 iyij 

2

rij 5

The summation in Eq. 2 collects pair-wise interactions with the target H spin which are then averaged over the sample. Due to the strong internuclear distance dependence of G m  t  , the cross-relaxation parameter

is dominated by interactions of a peptide hydrogen with near-neighbor F

spins in the solvent. To reduce the computational effort required to evaluate J m ( ) , calculations were limited to the F spins that lie within a cut-off distance ( rcut ) from the H spin. There will be N cut fluorines within this sphere. For the present work, we considered all interactions with trifluoroethanol fluorines that were within 3 nm of the solute hydrogen. It has been shown that a 3 nm cut-off captures greater than 99.9% of the interactions that contribute to relaxation.47 For isotropic liquids, normalized correlation functions ( G m  t  / G m  0  ) are independent of m and have the same time dependence.48 We assumed that the



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normalized functions can be represented by a collection of n exponentially decaying functions:49  t  G m (t )   an exp    m G (0) n  n 

(3)

By approximating the decay of G m  t  / G m  0  in this way, the Fourier transform of G m  t  leads to

J m    2G m  0  m  

(4)

with

 m     n

where

a

n



an n

1   n 

2

(5)



 1.

n

Collecting terms, the cross-relaxation parameter arising from solvent fluorine atoms interacting with a solute peptide hydrogen is given by

 HF  6.3086 x104 G 0 (0) 0 H  F   5.6777 x105 G 2 (0) 2 H  F 

(6)

The units for  0 H  F  and  2 H  F  are ps. To compute G m  t  for a selected peptide hydrogen, contents of the simulation box (and its periodic images) for a MD trajectory snapshot taken at a time defined as t = 0 were translated so that the hydrogen of interest was at the center of the box. TFE fluorines within 3 nm of a peptide hydrogen in the simulation box were determined. Diffusion of the peptide and the selected solvent fluorines was followed in subsequent snapshots which were translated the same amount as the first. The quantities F 0 , F 1 and F 2 were evaluated for the initial snapshot and at each subsequent time step (t). The quantity Fijm  0  Fijm  t  was evaluated and stored so that it was associated with the time t . The snapshot chosen to represent t = 0 was then advanced one frame along the trajectory and the process repeated. Resulting Fijm  0  Fijm  t  values at a given time t -12ACS Paragon Plus Environment

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were averaged. In the present work the correlation function typically was represented by 1000 points obtained in calculations that averaged 20000-30000 evaluations of each time point. Fitting of G m  t  / G m  0  computed from a MD trajectory to a sum of exponential functions used a local version of Provencher’s program DISCRETE.50 (See http://sprovencher.com /index.shtml.) The optimum fit to the decay of G m  t  / G m  0  typically used 4 or 5 exponential terms. In the present work, the magnitudes of G 0 (0) and G 2 (0) ranged from 102 to 103 while

 0 and  2 ranged from 30-500 ps. Thus, the expression for  HF (Eq. 6) typically leads to a relatively small value for  HF as a difference between two larger quantities.

Strategy. MD simulations must reproduce a range of chemical phenomena in this system if they are to lead to calculated intermolecular NOEs that agree with experimental results. Such phenomena include the conformational dynamics of Trpcage and the dynamics of interaction of each solvent component with the peptide and with each other. The time scales for these may range from seconds to picoseconds. Braun and Steinhauser have pointed out that relatively long simulations might be required to produce reliable estimates of intermolecular cross-relaxation terms.25 In an attempt to obtain ergodic results in a practical amount of time,51 we averaged the results of 10 independent simulations of 0.1-0.3 s duration each in the hope that the considerations indicated will be sufficiently accounted for.

RESULTS -13ACS Paragon Plus Environment


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TSP in 42% TFE-water. A small amount of the NMR chemical shift reference 3(trimethyl-silyl)propanoic acid (TSP) was present in the samples examined. Predictions of the system density, translational diffusion coefficients (DTSP, DTFE, DH2O) and the solvent fluorine-TSP methyl proton cross-relaxation parameter  HF for TSP dissolved in 42% TFE-water were based on MD simulations. Results are shown in Table 1. Diffusion coefficients calculated from the MD trajectories were within 20% of the experimental values for this system. Previous work suggested that small adjustments of the force field parameters for fluorine could improve the agreement between calculated and experimental parameters in simulations of materials dissolved in trifluoroethanolwater.29, 33 We explored adjustments of the non-bonded Lennard-Jones parameter  H F with the goal of improving the ============= Insert Table 1. ============= Table 1. Calculated Properties of Solutes in 42% TFE-d2-Water at 298 K Solute TSP Density, kg m-3 1178.62a (1167.84) DTrp-cage, m2 s-1, x 1010 DTSP, m2 s-1, x 3.5  0.9 1010 DTFE, m2 s-1 7.06  0.1 10 x 10 DH2O, m2 s-1 15.9  0.1 10 x 10

Trp-cage Experimental 1179.24a (1168.17) (1183.34)b 1.01  0.4 0.755c -

3.76c

6.88  0.2

5.86c

15.8  0.1

13.4c


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-1 3 TSP HF s x 10

6.4  0.4

4.5c

a The value for the corresponding undeuterated TFE system is given in parentheses. b The experimental density for 42% v/v TFE-water given is the average of interpolations of the data of Gente and La Mesa52, Palepu and Clarke53 and Harris, et al.54-55 c Experimental data are from Chatterjee and Gerig.23 =================

agreement between calculated and observed  HF for TSP. (Results given in the Supporting Information, Table S2.) Increases in  H F did lead to better agreement but at the cost of poorer predictions of system density and diffusion coefficients. Variation in the Lennard-Jones  HF was also explored; changes of as much a 50% had no significant effect on the system density but slightly altered calculated diffusion coefficients. It was decided to retain the original TFE5 fluorine parameters for the work described here.

An analysis of the distribution of solvent components about the methyl hydrogens of TSP was carried out by considering the solvent shells around these hydrogens shown in Figure 2. The average numbers of TFE fluorines and water molecules in a given solvent shell of TSP over the course of an MD trajectory were calculated; results for replicate simulations were averaged to give the results shown in Table 2. Simulations of TSP in 42% TFE-water indicate that TFE molecules preferentially accumulate near the TSP methyl groups. This observation is consonant with the reported observation that TFE preferentially interacts with the alkyl portion of the amino acid L-leucine in TFE-water



mixtures, presumably as a result of dispersion interactions between hydrogens of the solute and fluorines of TFE.56

=============== Insert Figure 2. =============== Cross-relaxation parameters  HF arising from interaction of the methyl hydrogens of TSP with TFE fluorines were calculated using the available MD trajectories. The average result (6.4  0.4 x 10 -3 s-1) agrees fairly well with the experimental value (4.8  0.5 x 10-3 s-1) and that

calculated from the formulation of Ayant, et al. (4.3 x 10-3 s-1).28


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Figure 2. Spheres defining shells of solvent centered on a hydrogen of TSP or Trpcage. A portion of each solvent shell would be occupied by all or part of the solute. Sphere radii are spaced by 0.492 nm, the diameter of a rapidly rotating TFE molecule.23, 57

For 42% TFE in water, the ratio of the number of water to TFE molecules in

homogeneously mixed solvent is 1.864.

============= Insert Table 2. =============



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Table 2. Calculated average solvent occupancy of spheres centered on hydrogens of TSP and Trp-cage at 298 Ka

TSP-CH3b

Shell 1 to 0.492 nm nm 4.268 (1.031)

Shell 2 0.492-0.984 nm 40.71 (1.497)

Shell 3 0.984-1.476 nm 99.04 (1.881)

Shell 4 1.476-1.968 nm 191.48 (1.907)

Shell 5 1.968-3.000 nm 853.10 (1.863)

1AsnHB2 1AsnHB3 2LeuH 2LeuHB3 2LeuQD1 3TyrH 3TyrHB2 3TyrHB3 4IleH 4IleQD1 5GlnH 5GlnQB 6TrpH 6TrpHD1 6TrpHE1 6TrpHE3 6TrpHH2 6TrpHZ2 6TrpHZ3 7LeuH 9AspH 12ProHB3 17ProHB3 18ProHA 18ProHB3 20SerH

1.435 (5.994) 1.213 (5.320) 0.477 (11.62) 0.710 (6.024) 2.864 (2.193) 0.273 (9.662) 1.640 (1.908) 2.312 (1.146) 0.387 (3.056) 4.309 (0.721) 0.217 (7.737) 1.273 (2.872) 0.286 (3.061) 0.502 (3.682) 0.597 (1.594) 0.697 (0.201) 3.871 (0.329) 2.341 (0.327) 3.113 (0.347) 0.064 (0.335) 0.215 (5.828) 4.914 (0.655) 4.726 (0.695) 0.247 (3.674) 1.481 (0.983) 1.314 (4.624)

27.13 (2.145) 26.92 (2.058) 24.79 (2.198) 23.86 (2.181) 25.82 (2.113) 22.97 (2.088) 23.09 (1.892) 24.66 (1.660) 25.74 (1.693) 30.90 (1.526) 22.94 (1.899) 20.38 (2.247) 19.17 (1.725) 21.88 (1.250) 28.70 (1.034) 27.36 (0.876) 31.45 (1.006) 30.01 (0.996) 31.35 (0.956) 25.42 (1.127) 23.56 (1.728) 34.93 (1.123) 34.91 (1.257) 27.58 (1.090) 28.88 (1.117) 28.60 (1.856)

91.31 (1.803) 91.53 (1.796) 92.03 (1.733) 94.07 (1.673) 86.88 (1.856) 96.82 (1.643) 97.05 (1.636) 94.79 (1.703) 92.48 (1.799) 86.07 (1.959) 94.78 (1.731) 87.50 (1.831) 102.21 (1.628) 106.46 (1.522) 101.88 (1.546) 194.24 (1.675) 97.34 (1.581) 191.75 (1.548) 193.77 (1.661) 98.00 (1.725) 101.10 (1.550) 97.37 (1.597) 92.88 (1.668) 101.91 (1.557) 99.78 (1.554) 95.59 (1.586)

190.08 (1.798) 191.01 (1.797) 197.04 (1.749) 197.71 (1.761) 198.63 (1.727) 197.40 (1.777) 196.41 (1.801) 197.11 (1.793) 198.45 (1.764) 191.49 (1.815) 199.88 (1.756) 207.52 (1.691) 198.21 (1.796) 193.12 (1.881) 192.13 (1.893) 194.24 (1.862) 192.05 (1.898) 191.75 (1.895) 193.77 (1.874) 194.10 (1.812) 196.39 (1.813) 189.84 (1.831) 188.28 (1.843) 192.54 (1.889) 192.91 (1.884) 192.94 (1.802)

853.51 (1.858) 853.16 (1.863) 847.21 (1.885) 844.92 (1.894) 845.68 (1.891) 845.60 (1.891) 845.76 (1.889) 846.38 (1.888) 847.32 (1.884) 854.54 (1.857) 845.57 (1.890) 844.17 (1.876) 843.43 (1.900) 841.25 (1.909) 840.64 (1.876) 843.56 (1.898) 842.78 (1.902) 841.60 (1.906) 844.15 (1.896) 843.56 (1.773) 843.56 (1.899) 842.66 (1.903) 847.33 (1.908) 841.34 (1.907) 841.68 (1.911) 842.91 (1.902)

Hydrogen

a

The first number given is the average number of TFE fluorine atoms in a solvent

shell. The number in parentheses is the ratio of the average number of water molecules to the average number of TFE atoms in the shell. The nominal value for this ratio for homogeneous solvent is 13981/(3*2500) = 1.864. (See Experimental Section.) A ratio


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smaller than this for a solvent shell indicates preferential accumulation of TFE in that shell. b

Results for four independent simulations were averaged for the TSP results. Results

from 10 simulations were averaged for the Trp-cage results. Trp-cage in 42% TFE-water. Simulations of Trp-cage in 42% TFE-water were done with a computational model that featured sufficient solvent molecules to provide a layer ~ 4 nm between the peptide and the walls of the simulation box. Parameters for the solvent components of the force field were identical to those used with TSP. Calculated diffusion coefficients for solvent components and the system density agreed with experimental values to better than  20% (Table 1). Selective solvation of the hydrogens of Trp-cage was explored with reference to the solvent shells defined in Figure 2. Some results of this analysis are given in Table 2; more results are available in the Supporting Information (Table S3). These calculations indicate that most peptide N-H hydrogens of Trp-cage, although protected from interactions with solvent molecules to varying extents, are preferentially solvated by water molecules at close range. Consistent with the tendency for hydrophobic groups in TFE-water mixtures to be preferentially solvated by the fluoroalcohol,58 most other peptide hydrogens appear to be in environments that are slightly or strongly enriched in TFE. The propensity for preferential solvent interactions near any hydrogen of Trp-cage rapidly dissipates as the distance from the hydrogen to the bulk solvent increases, with the computed composition of the solvent mixture at distances greater than ~1.5 nm from the peptide hydrogen being essentially that of the bulk solvent. Lifetimes of TFE-solute interactions. Analysis of TFE contacts with TSP and Trp-cage was done for four or more independent simulations by following the behavior of individual TFE molecules in the simulations after they enter solvent sphere 1. The number of such contacts made at a solute hydrogen per second was counted, giving a notion of the solvent exposure of the hydrogen. For hydrogens of TSP and many hydrogens of the peptide, the majority of TFE molecules entering the first solvent sphere leave within 10 ps of the initial encounter. However, -19ACS Paragon Plus Environment


for Trp-cage, depending on the hydrogen, a fraction of TFE encounters persist for times up to ~7000 ps. Table 3 presents data regarding TFE contacts for selected hydrogens; a more extensive compilation is given in Table S4 of the Supporting Information. The analysis of TFE contacts with Trp-cage hydrogens confirms that backbone atoms of the peptide are relatively shielded from contacts with solvent. The numbers of TFE contacts with hydrogens 6TrpH and 6TrpHD1 of the peptide are small due to the protected position of these atoms in the tertiary structure (Figure 1). However, essentially all TFE encounters with hydrogens 6TrpH and 6TrpHD1 persist for times longer than 20 ps (Table 3). TFE contacts with the sidechain hydrogens of 5Gln are also notably persistent. =============== Insert Table 3. =============== Solvent diffusion near solutes. Intermolecular nuclear dipole-dipole relaxation depends critically on the mutual diffusion of the interacting partners.59 Experimentation and MD simulations indicate that diffusion of solvent water is slowed near the surface of proteins. 3, 32, 57, 60-63.

Many considerations relating to the structural, chemical and dynamical heterogeneity of the

surface are responsible for the slowing.64-66. The approach of Pettit and co-workers was used to explore diffusion of TFE and water near the surface of TSP and Trp-cage.67-68 The calculations suggest a slight retardation of translational diffusion of TFE near TSP while diffusion of TFE and is slowed by as much as a factor of 7 when a solvent molecule is near certain Trp-cage hydrogens, similar to results obtained for this system at 318 K.29, 33 Diffusion of water molecules is also slowed in parallel with slowing of TFE molecules. Typical results are shown in Figure 3; further results are provided in the Supporting Information (Table S5). Reduction of the translational diffusion of both solvent components is largest for solvent near the peptide N-H and HD1 hydrogens of the 6Trp residue, consistent with the high percentage of solvent molecules that persist for relatively long times in the solvent shells of these hydrogens (Table 3). ================ Insert Figure 3. ================ -20ACS Paragon Plus Environment

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Table 3. Calculated average TFE contacts with hydrogens of TSP and selected Trp-cage hydrogens in 42% TFE5-water at 298 K Total TFE-peptide hydrogen contacts, x 10-10, s-1

Long-lived TFE-peptide hydrogen contacts, x 10-10, s-1

TSP

7.57  0.80

~0

1AsnHB2 1AsnHB3 2LeuH 2LeuHB3 2LeuQD1 3TyrH 3TyrHB2 3TyrHB3 3TyrQD 3TyrQE 4IleH 4IleQD1 5GlnH 5GlnQB 5GlnQG 6TrpH 6TrpHD1 6TrpHE1 6TrpHE3 6TrpHH2 6TrpHZ2 6TrpHZ3 7LeuH 9AspH 9AspHA 9AspHB2 9AspHB3 12ProHB3 17ProHB3 18ProHB3 18ProHA 20SerH

2.24  0.21 1.86  0.16 0.79  0.32 0.91  0.30 2.18  0.28 0.55  0.26 1.42  0.41 1.58  0.34 1.61  0.30 2.03  0.33 0.84  0.36 2.97  0.40 0.33  0.14 1.05  0.11 1.44  0.23 0.11  0.10 0.17  0.12 0.52  0.21 0.74  0.52 2.38  0.45 1.55  0.35 2.11  0.47 * 0.35  0.23 1.47  0.22 0.62  0.30 0.91  0.29 2.92  0.41 2.93  0.41 1.60  0.50 0.39  0.31 1.38  0.37

0.03  0.01 0.04  0.02 0.04  0.02 0.05  0.02 0.17  0.09 0.03  0.03 0.15  0.08 0.26  0.20 0.14  0.06 0.14  0.06 ~0 0.12  0.04 0.01  0.01 0.21  0.12 0.12  0.06 0.14  0.11 0.17  0.18 0.01  0.01 0.14  0.15 0.45  0.10 0.37  0.06 0.32  0.19 * 0.02  0.02 0.18  0.09 0.17  0.20 0.18  0.04 0.61  0.06 0.40  0.07 0.13  0.18 ~0 0.13  0.03

Percent

Average duration, long-lived contacts, ps

Maximum duration, long-lived contact, ps

1 2 5 5 8 11 11 16 9 7

92 123 216 214 167 157 205 201 207 148

258 410 670 685 1930 560 862 1332 3950 1290

4 3 20 17 100 100 2 19 19 24 15 * 6 12 27 20 21 14 8

105 84 432 195 135 233 101 342 159 367 211 * 109 168 444 197 200 128 149

860 208 6870 6840 1160 2920 830 6490 1310 1950 6500 * 380 1600 3420 2580 1610 960 2200

9

197

1210

* Very few contacts detected in solvent shell 1.


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Figure 3. Calculated TFE translational diffusion coefficients as a function of distance from a solute hydrogen atom in 42% TFE-water at 298 K. The black, cyan, blue and red symbols represent data for the TSP methyl hydrogens, the hydrogens of the 2LeuQD2 methyl group, 6TrpH and 18ProHA, respectively. The translational diffusion coefficient for TFE in the bulk solvent at 298 K is 6.88 x 10-10 m2 s-1. ================= Conformational motions of Trp-cage. Neidigh, et al. obtained the structure of Trp-cage in water at 296 K by standard constraint satisfaction methods, the constraints being distances between pairs of hydrogens of the peptide obtained from 1H{1H} nuclear Overhauser effects.30 Changes in the long-range, intra-peptide ( di , d j ( j  i  1) ) distances used in the structure determination of Trp-cage were followed in the present work during the course of MD simulations. About two-thirds of these distances oscillated ± 50% about their mean values, with the mean close to the constraint distance used in calculations of the tertiary structure of the peptide (See Table S6 in the Supporting Information.). However, some Trp-cage intra-hydrogen distances were longer than those reported for the structure in water.30. These distances usually involved hydrogens of 3Tyr, 6Trp, 7Leu and 18Pro. Using the distance between the Tyr3CZ and Trp6HE3 atoms of Trp-cage as a diagnostic, examination of MD trajectories showed the presence of appreciable amounts of a Trp-cage conformation in which the tyrosine-3 ring is turned away from proximity to the tryptophan-6 ring to a more open orientation. Figure 4 shows -23ACS Paragon Plus Environment


variation of this inter-atom distance during a simulation of 0.2 s duration. Structures of the peptide observed at times over the course of this simulation are shown in Figure 5. Beyond the change in position of the 3Tyr aromatic ring, comparing Figure 1 and the closed structure in Figure 5 shows that parts of the peptide structure in 42% TFE-water move away from the ideal turn conformations found between 9Asp to 15Gly in water. =============== Insert Figure 4. ===============

Figure 4. Conformation changes in Trp-cage during a simulation of the peptide in 42% TFEwater at 298 K ================ Insert Figure 5. ================


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Figure 5. Conformations of Trp-cage appearing during the simulation that led to Figure 4: (A) conformation at 0.103 s, (B) conformation at 0.176 s. ============== Transition from the tyrosine-closed to a long-lived, tyrosine-open structure of Trp-cage appears to take place 1-5 times per s, with the open structure persisting for times up to the order of 0.05 s. The detection of persistent tyrosine-open structures depended on the starting conditions for a simulation and long-lived conformations of this type were not detected in all simulations done. However, short-lived excursions of the peptide into the tyrosine-open conformation, such observed in Figure 4 between 0.01 and 0.09 s, were seen in all trajectories. Interaction of the solvent components with Trp-cage in closed and open conformation was examined by the TFE and water counting exercise described earlier. Results are given in the Supporting Information (Table S3). Considering data from 20 segments of 9 trajectories where one of the tyrosine positions was persistent, differences in the average number of water and TFE molecules interacting with 3Tyr, 6Trp and 18Pro residues were observed but these barely exceeded the standard deviations of the counts. Solute hydrogen-solvent fluorine cross-relaxation. Experimental peptide hydrogen-solvent fluorine cross-relaxation parameters (  HF ) for hydrogens of TSP and Trp-cage were reported previously.23 Many of these NOEs are small and not always as reliable as desired due to the noise level of the experimental spectra. All available data at 298 K was re-evaluated for the -25ACS Paragon Plus Environment


present work. Although a few values for  HF have been updated, most are essentially as given in the earlier paper. An estimated error of ± 0.5 s-1 has been assigned to all experimental  HF . Cross-relaxation parameters  HF arising from interaction of the various hydrogens of Trpcage with TFE fluorines were calculated from 10 independent MD trajectories of 0.1-0.3 s duration. Average values of  HF for hydrogens of Trp-cage whose proton NMR signals could be confidently assigned are given in Table S7 of the Supporting Information and are shown graphically in Figures 6 and 7. Standard errors of the mean calculated  HF are shown in the Figures (red bars). Some of these deviations are large, although the average calculated  HF may agree with the corresponding experimental value. For other peptide hydrogens, the mean value of

 HF is far from the corresponding experimental result. Most notably, calculated  HF for the 5GlnQB and 6TrpHD1 hydrogens are seriously in error. ============== Insert Figure 6. Insert Figure 7. ============== A program based on the equations of Ayant, et al.28 for prediction of solvent cross-relaxation terms from the exposure of solute hydrogens to a continuum model of the solvent was used to estimate  HF for hydrogens of a single structure of Trp-cage found in the PDB, as described previously.33 These results are also given in Figures 6 and 7. While generally of the correct magnitude,  HF for sidechain hydrogens estimated in this way are typically less than the experimental  HF .


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Figure 6. Comparison of experimental cross-relaxation parameters (  HF ) for interactions of peptide backbone hydrogens of Trp-cage with fluorines of TFE in 42% TFE-water at 298 K (black symbols) to the average  HF calculated from MD simulations (red symbols). Results from 10 MD trajectories of 0.1-0.3 s length were averaged. The red error bars indicate the standard deviations of these results. The black error bars correspond to assumed experimental errors of  0.5 s-1. Values of  HF calculated using the equations of Ayant, et al. and a single static structure of Trp-cage (PDB 1L2Y) are represented by the cyan symbols. Signals for 2LeuH and 8LysH, as well as 10GlyH and 13SerH, are not resolved in the experimental spectra. Data shown for these are the averages of calculations for the individual hydrogens.

==================



Figure 7. Comparison of experimental cross-relaxation parameters (  HF ) for interactions of peptide sidechain hydrogens of Trp-cage with TFE in 42% TFE-water at 298 K (black symbols) to  HF calculated from MD simulations (red symbols). Results of calculations done with 10 independent trajectories of 0.1-0.3 s length were averaged. The red error bars indicate the standard deviations of these results. The black error bars correspond to assumed errors of  0.5 s-1. Values of  HF calculated using the equations of Ayant, et al. and a single static structure of Trp-cage (PDB 1L2Y) are represented by the cyan symbols. Signals for the methyl groups of 2Leu, 4Ile and 7Leu are not wellresolved and experimental data shown for these are the average of NOEs calculated at various points in this region of the experimental spectrum.

===================


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DISCUSSION The force field used for the calculations described here was also used in a study of Trp-cage in the same solvent system at 318 K29 and is based on a conventional force field for simulations of peptides in water. The predicted densities and component translational diffusion coefficients at 298 K calculated using this force field agree somewhat less well with experiment than was the case at the higher temperature, although the calculated quantities at 298 K are still within 20% or better of experimental data. We explored adjustment of the parameters for non-bonded interactions of fluorine with the solute in simulations at 298 K but could not find values for these parameters that simultaneously led to improvement in the agreement between observed and calculated system densities and the translational diffusion coefficients of the solvent components.

Our simulations suggest that previously unrecognized conformational changes of Trp-cage take place in 42%TFE-water (Figure 5), with solvent component interactions with the hydrogens of Trp-cage being conformation-dependent (Table S3). We are unaware of any experimental evidence bearing on this point. It is not known if the persistence of a given conformation or the interactions of the water and TFE solvent components are correctly predicted by the force field used or how important are these conformations to defining experimental values of cross-relaxation terms.



Calculations show that most of a calculated cross-relaxation parameter for interaction of TFE with a hydrogen of Trp-cage at 298 K is the result of interactions with solvent fluorines within ~0.9 nm of the hydrogen (solvent shells 1 and 2). A few percent of the total calculated  HF is due to interactions with TFE in solvent shell 3 while a nearly constant contribution of -0.33 x 10-3 s-1 results from H-F dipolar interactions with solvent molecules that lie beyond solvent shell 3. Thus, it is the number of solvent nearneighbors and their dynamics that leads to most of the calculated cross-relaxation parameter of a Trp-cage hydrogen.

It is interesting that for some Trp-cage hydrogens,  HF calculated by an approach that basically treats the solvent as a homogeneous medium that contacts a peptide hydrogen at its van der Waals surface gives a predicted solvent fluorine-peptide hydrogen crossrelaxation parameter that agrees with the  HF derived from the heterogeneous, particulate model of the system used in the MD simulations (Compare red and cyan symbols in Figures 6 and 7.). While many  HF for peptide hydrogen-TFE fluorine solvent interactions calculated by either approach agree reasonably well with experimental observations others do not.

Translational diffusion of both solvent components is predicted from the MD simulations to decrease as TFE or water approach hydrogens of Trp-cage (Figure 3, Table S5). The reductions are largest for hydrogens of residues 5Gln. 6Trp, 9Asp and 18Pro. Calculations based on the equations of Ayant, et al.28 indicate that reduction of -30ACS Paragon Plus Environment

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TFE translational diffusion is expected to lead to a more negative cross-relaxation parameter (  HF ), consonant with observations made for the 6TrpH, 6TrpHD1, and 6TrpHE1 hydrogens. Thus, reasons for at least part of discrepancies between experimental and calculated  HF parameters for this system may lie in the aspects of the simulations that define motions of solvent molecules near the Trp-cage surface.

Simulations must correctly reproduce a number of characteristics of a peptidetrifluoro-ethanol-water system if there is to be any hope of making reliable predictions of peptide-solvent cross- relaxation phenomena. These considerations include the following. [1] The Trp-cage structure is dynamic and it is only on average that the tertiary structure is consistent with intramolecular 1H{1H} NOEs and other constraints. The populations of various conformations of the peptide present, and their interconversion rates, may not be correctly reproduced by the MD force field used. [2] In the simulations, TFE and water interactions with the peptide are selective, with some parts of the structure preferentially solvated by the fluoroalcohol. It is known that TFE can form specific, long-lived complexes with proteins7, 14, 69 and there are suggestions from the present work that relatively long-lived complexes of TFE with Trp-cage can form in a regio-specific manner. The dynamics of such interactions can influence observed intermolecular 1H{19F} NOEs. [3] Trifluoroethanol accumulates preferentially at the surface of peptides and proteins dissolved in TFE-water mixtures.15, 70 The extent



and dynamics of these interactions must be captured correctly. [4] Trifluoroethanol in water at concentrations near that used for the present study aggregates into clusters 12, 71

and the nature of the aggregates and their dynamics may play a role in determining

the influence of TFE on biomolecule structure and function as well as the interactions of solvent components with these structures.12-13[5] It is well-recognized that the structure and dynamics of proteins in water are strongly influenced by their hydration shells3-5, 72 and that the dynamics of these hydration shells are perturbed relative to those of pure water.2 Solvent interactions in a mixed solvent such as 42% trifluoroethanol-water add further complications by virtue of the interactions of both solvent components with the biomolecule and with each other. The diffusive behaviour of all of these components must be correctly reproduced, particularly near the peptide surface. [6] Chemical interactions between solute and solvent such as hydrogen-bonding may not be correctly accounted for in the force field used. [7] Simulations may need to be much longer than those done here to get correctly converged results.73 However, the accumulation of numerical errors and the reliability of force field parameters make the reliability of simulation trajectories exceeding a few msec suspect.74

MD simulations may exhibit chaotic behaviour in which small changes in starting conditions for a calculation can lead to widely disparate results,75-77 We attempted to obtain approximately ergotic results for cross-relaxation parameters characterizing TFE-peptide interactions by averaging results obtained from a number of independent but relatively short simulations. Judging by the root mean square deviations of the computed  HF obtained, this approach was -32ACS Paragon Plus Environment

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reasonably successful for about half of the hydrogens of Trp-cage. For other hydrogens, the cross-relaxation parameter obtained had an incorrect average value and/or large standard errors, indicating that facets of the system had not been sufficiently sampled. That a mean  HF value for a peptide hydrogen often is close to the corresponding experimental result (Figures 6 and 7) tends to validate the many assumptions underlying the simulations done and the calculations of cross-relaxation parameters. However, there are notable disagreements between observed and calculated  HF and these likewise signal a faulty appreciation of critical aspects of the system.

In pure water, translational and rotational motions of water molecules in contact with biomolecule surfaces occur on multiple time scales as do the rates of exchange of water molecules between various chemical environments present.65 All of these processes will be modified by the presence of trifluoroethanol molecules. Near-neighbor electronic interactions between TFE and the peptide may not be well-described by force field parameters that are appropriate for modeling bulk solvent mixtures; these may need to be modified for the special environment found at a biomolecule surface. It will be of interest to determine if improvements to the force field such as the inclusion of electronic polarization will lead to improved agreement between calculated and experimental cross-relaxation parameters.



CONCLUSIONS

MD simulations with a reasonable force field indicate selective accumulation of TFE molecules near many hydrogens of the Trp-cage dissolved in 42% TFE-water. Hydrogens of the peptide backbone and residues near the peptide termini are selectively solvated by water. The composition of the solvent about 1.5 nm from the peptide surface is essentially that of the bulk solvent. While solvent molecules generally leave the solvent layer directly in contact with the peptide surface within ~10 ps of making contact, at some positions in the peptide structure TFE molecules may persist in this layer for varying lengths of time up to ~7000 ps. Translational diffusion of TFE and water molecules is slowed near the peptide surface, with the largest slowing associated with persistence of contacts of solvent molecules at the surface. Many peptide hydrogen-solvent fluorine cross-relaxation terms (  HF ) calculated from the MD trajectories agree with experimental results although there are notable failures of such predictions especially for some hydrogens of 6Trp and other nearby residues. Thus, further refinements to the force field or the general approach used are indicated. Appreciable amounts of an "open" conformation of Trp-cage, with the tyrosine ring turned about 180° away from its orientation in the "closed" structure found in water, is present during some of the trajectories calculated for the peptide in 42% TFE-water. Interactions of solvent molecules with the "open" and "closed" structures are different


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but there is insufficient data available at this point to permit quantitative conclusions regarding these differences.



AUTHOR INFORMATION

Corresponding author *E-mail: [email protected] Telephone: 805-893-2113. FAX: 805-893-4120 Notes The author declares no competing financial interest.

SUPPORTING INFORMATION AVAILABLE Force field parameters for 3-(trimethylsilyl)-propionic acid (TSP), indications of the effects of adjusting force field parameters on system density and diffusion, calculated occupancy by solvent molecules and solvent diffusion coefficients of layers surrounding the hydrogens of TSP and Trp-cage, variation of various peptide interhydrogen distances over the course of MD simulations and comparison of observed and calculated solvent fluorine-solute hydrogen cross relaxation parameters are provided.

ACKNOWLEDGMENTS


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The author thanks the UCSB Committee on Research for supporting the initial phases of this work. The work used facilities of the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation grant number OCI-1053575.



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Examination of Trifluoroethanol Interactions with Trp-Cage in

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