Examination of Trifluoroethanol Interactions with Trp-Cage through

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Examination of Trifluoroethanol Interactions with Trp-Cage through MD Simulations and Nuclear Overhauser Effects John T. Gerig J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.6b08430 • Publication Date (Web): 29 Sep 2016 Downloaded from http://pubs.acs.org on October 6, 2016

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The Journal of Physical Chemistry

Examination of Trifluoroethanol Interactions with Trp-Cage 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. ABSTRACT. MD simulations of the protein model Trp-cage in 42% TFE-water at 318 K have been carried out with the goal of exploring solvent fluorine-peptide hydrogen nuclear spin cross relaxation. The TFE5 and TFE6 models of trifluoroethanol developed in previous work from this laboratory were used with the TIP5PE model of water. System densities and component translational diffusion coefficients were well-predicted by the simulations, as were many of the cross relaxation parameters ( Σ HF ) for which experimental values are available. However, calculated Σ HF were too small for some hydrogens of the Trp6 indole ring and amino acid hydrogens near this residue in the native structure. Simulations done with unfolded versions of Trp-cage suggest that underestimates of Σ HF are the result of insufficient sampling of conformational motions that expose these hydrogens to interactions with solvent molecules

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during simulations of the native peptide. Consideration of the relative amounts of TFE and water surrounding the Trp-cage structure indicate that the composition of the solvent mixture at distances beyond ~1.5 nm from the surface of the peptide is close to the composition of the bulk solvent but, as observed by others, TFE tends to accumulate preferentially near the surface of the peptide. 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. INTRODUCTION Mixtures of water-soluble organic materials and water can exert strong effects on the conformations of a dissolved biological macromolecule, particularly when the organic component of the solvent is a fluorinated alcohol.

1

Systems containing 2,2,2-trifluoroethanol

(TFE) in water have been widely studied and many mechanisms have been proposed to explain how the presence of TFE alters peptide conformation. Influences of the fluoroalcohol in altering hydrogen bonding and interactions with water molecules, polarity of the solvent, aggregation of the fluoroalcohol and possible molecular crowding effects have been considered. 2-4 These ideas have been extensively explored by experiment and by molecular dynamics simulations.

5-6

Understanding peptide-TFE interactions is challenging because the fluoroalcohol associates with itself 7-9 as well as with dissolved peptides in TFE-water solutions. 7, 10-17 Aggregation of TFE in water may be accompanied by changes in the preferred conformation of the fluoroalcohol. 18 Trp-cage is 20-residue peptide based on extendin-4, a peptide found in the saliva of the Gila monster. 19 It folds to a compact tertiary structure in about 4 µs at 296 K. 20 At low temperatures in water, >90% of Trp-cage molecules are represented by the conformation shown in Figure 1. 21


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Unfolding of this structure in water has been followed by a variety of experiments been the subject of many computational studies.

25-29

21-24

While experimental methods indicate that

thermal unfolding of Trp-cage in water can be described as a two-state process experiments indicate more complexity.

22

and has

30

other

NMR chemical shift data obtained with isotopically

labeled material suggest that at least one on-pathway conformation separates the folded and unfolded forms of the peptide.

24

Contrastingly, a study by Halabis, et al., of changes in

intramolecular 1H{1H} NOEs with sample temperature, while not supporting a two-state model for the unfolding of Trp-cage also does not support more complicated models that involve intermediates for this process.

31

Rather, near the melting temperature of the peptide in water

(~313 K) Trp-cage appears to be present as an ensemble of conformations, each member of which has some structural feature or features of the native state but not all of them. This conclusion is consistent with a MD study of the dynamics of folded and unfolded states of the peptide. 32



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Figure 1. The structure of Trp-cage. The indole ring of Trp6 is sequestered by a collection of hydrophobic resides that includes prolines 12, 17, 18 and 19. 19 Intermolecular nuclear Overhauser effects (NOEs) can be used to probe the interactions of solvent molecules with dissolved species peptides with trifluoroethanol.

11, 13, 37-39

33-36

and have been used to study interactions of

An intermolecular NOE is characterized by a cross

relaxation parameter Σ XY which quantitates magnetic interactions between spin X of the solute and spin Y of the solvent. (The symbol Σ XY for the nuclear spin cross relaxation parameter will be used in this paper to avoid confusion with other uses of the symbol σ .) When the molecules bearing spin X and spin Y are modeled as rotating spheres, theory such as that due to Ayant, et al.

40

shows that Σ 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. There are several reasons why an experimental cross relaxation parameter for the interactions of fluorines of TFE with a hydrogen of a dissolved peptide may be different from the value predicted using theoretical treatments: (1) the local concentration of TFE molecules near a peptide hydrogen may not be the same as that of the bulk system due to the tendency of the fluoroalcohol to preferentially accumulate near a part of the peptide; (2) chemical interactions between solute and solvent such as hydrogen-bonding may persist for times that are long and thus not well-described as diffusive encounters; (3) the diffusion constant of TFE near a peptide may be different from that of TFE in the bulk solvent; or (4) there may be conformational motions of the peptide that regulate the exposure of peptide groups to solvent that are not considered in the simplest theoretical formulations.


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As shown in the Supporting Information, cross relaxation parameters ( Σ HF ) describing the interaction of trifluoroethanol with Trp-cage in 42% TFE-water can be significantly underestimated by theoretical treatments, indicating that the assumptions made in deriving such treatments are not realistic for this system. In the present work, MD simulations of Trp-cage in this solvent mixture were undertaken to explore TFE-Trp-cage interactions and how these relate to observed cross relaxation parameters. We find that the modified force fields developed in a previous study of an octapeptide dissolved in TFE-water lead to calculated Σ HF values in agreement with experiment for many hydrogens of Trp-cage at 318 K.

41

However, cross

relaxation parameters for hydrogens of the central Trp6 residue of Trp-cage and other peptide hydrogens near this amino acid are not predicted correctly. It is argued that simulations of 0.100.25 µs duration of the native Trp-cage do not sufficiently sample conformational motions near Trp6 that produce exposure of these hydrogens to solvent.

EXPERIMENTAL SECTION Experimental cross-relaxation parameters ( Σ HF ). Studies of cross relaxation between solvent CF3 fluorines and hydrogens of Trp-cage dissolved in 42% trifluoroethanol-1,1-d2-water (v/v) at 318 K have been previously reported.

39

The sample examined was approximately 5 mM in

peptide and contained a trace amount of acetate. The apparent pH of the sample was 5.0. 3(Trimethylsilyl)propionic acid-d4 was present as a chemical shift reference, with the reference signal set to 0.0 ppm. Data were collected with an instrument operating at a proton frequency of 500.1 MHz. Molecular dynamics (MD) simulations. All simulations were done with GROMACS

42

packages running locally on a SUN SunFire X4600 or on the Stampede system operated at the



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University of Texas, Austin by the NSF-sponsored XSEDE consortium. Parameters for Trp-cage were those of the AMBER99SB-ILDN force field. models TFE5 and TFE6 described previously. simulations.

σ ij =

44

41

43

Parameters for TFE were those of TFE

The TIP5PE water model was used in all

The combination rule for σ non-bonded parameters was the arithmetic mean (

1 (σ ii + σ jj ) as used in the AMBER force fields while the combination rule for ε ij non2

bonded parameters was the geometric mean ( ε ij = (ε iiε jj ) ). 1/2

A cubic simulation cell, approximately 9 nm on a side, was used. It contained one Trp-cage molecule, 2500 trifluoroethanol-d2 molecules, 13981 water molecules and a chloride ion to maintain electrical neutrality. The integration time-step was 0.002 ps. The particle mesh Ewald method for long-range electrostatics was applied 45, as was the long-range correction for the van der Waals interaction described by Allen and Tildesley.

46

Cut-offs for electrostatic and van der

Waals terms were 1.4 nm. The non-bonded interaction list was updated every 5 steps. Periodic boundary conditions were applied. Motion of the model center of mass was corrected every step. Covalent bonds of TFE and the peptide were constrained to constant length by the LINCS procedure 47 while the SETTLE algorithm was used for water. 48 Systems were regulated at 318 K and a pressure of 1 bar by use of the Berendsen temperature (velocity re-scaling) and pressure coupling methods with relaxation time constants of 0.1 and 1 ps, respectively.

49

Simulations to

produce trajectories of 0.10-0.25 µs duration were carried out after initial equilibration for at least 2 ns. Snapshots of the system coordinates for analysis were usually taken at 5 ps intervals.

Starting peptide structures. Coordinates for Trp-cage in its native conformation were those of the first model given for PDB structure 1L2Y (www.rcsb.org/pdb/explore/explore.do? structureId=1l2y). To create an unfolded model of the peptide (unfold1) the native system was


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heated to 598 K for 8 ns then equilibrated to 318 K over 2 ns before starting production calculations. Calculations of a second unfolded model (unfold2) started with the peptide in the fully extended beta conformation. Production calculations of the trajectory were started after the solvated model was equilibrated for 8 ns at 318 K.

Analyses of molecular dynamics trajectories. Programs contained within the GROMACS package were used to compute the system density, peptide radius of gyration (gmx gyrate), peptide solvent-accessible surface areas (gmx sasa) and self-diffusion coefficients of solvent components via the Einstein relationship (gmx msd).

50

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, estimate peptide diffusion coefficients and estimate local diffusion coefficients of solvent molecules as a function of distance from specific peptide hydrogens. A program based on the equations of Ayant, et al.

40

for prediction of solvent cross

relaxation parameters ( Σ HF ) has been previously described. 41 The program naccess 2.1.1, kindly provided by Prof. S. Hubbard (UMIST, www.bioinf.manchester.ac.uk/naccess/) was also used to estimate solvent accessibility of Trp-cage hydrogens. We noted that the accessibilities calculated by the GROMACS routine gave results slightly different from naccess 2.1.1. Computation of correlation functions for TFE fluorine-peptide hydrogen dipolar interactions followed the procedure described previously. correlation effects are negligible,

52-53

41, 51

To summarize, assuming that cross

the collective dipolar relaxation contributions to the cross

relaxation parameter Σ HF that describes relaxation of a solute hydrogen by a group of identical solvent F spins is given by

3 3  1  Σ HF = γ H2 γ F2 h 2 − J 0 (ωH − ω F ) + J 2 (ωH + ωF )  4 4  12 


(1)


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where γ H and γ F are gyromagnetic ratios and ωH ωF are Larmor frequencies for protons and fluorines, respectively. The spectral density functions J m (ω ) are written in terms of the Cartesian components of the vector r which connects a Hi-Fj spin pair 54 ∞ ∞  N cut  J m (ω ) = 2 ∫ G m ( t ) e − iωt dt = 2 ∫  ∑ Fijm ( 0 ) Fijm ( t )  e − iωt dt  0 0  j ≠i

(2)

with

Fij = 0

rij 2 − 3zij 2 rij 5

Fij = 1

zij ( xij − iyij ) rij 5

Fij

2

(x =

ij

− iyij )

2

rij 5

The summation in Eq. 2 collects all pair-wise interactions with the target H spin; these are then averaged over the sample. Due to the strong internuclear distance dependence of G m ( t ) , the cross relaxation parameter ( Σ HF ) 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 (ω ) , 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 will capture greater than 99.9% of the interactions that contribute to relaxation. 55 For isotropic liquids, normalized correlation functions ( G m ( t ) / G m ( 0) ) are independent of m and have the same time dependence.

56

Following Feller, et al.,

57

we assumed that the

normalized functions can be represented by a collection of n exponentially decaying functions:


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 t  G m (t ) ≅ ∑ an exp  −  m G (0) n  τn 

(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 (ω ) = 2G m ( 0)τ m (ω )

(4)

with

τ m (ω ) = ∑ n

where

∑a

n

(

anτ n

1 + (ωτ 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

Σ HF = −6.3086x10−8 G 0 (0)τ 0 (ωH − ωF ) + 5.6777 x10−7 G 2 (0)τ 2 (ωH + ωF )

(6)

The units for τ 0 (ωH − ωF ) and τ 2 (ωH + ωF ) 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



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along the trajectory and the process repeated. Resulting Fijm ( 0) Fijm ( t ) values at a given time t were averaged. In the present work the correlation function typically was represented by 1000 points obtained in calculations that averaged 20000-50000 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.

58

(See

http://s-

provencher.com/index.shtml.) The optimum fit to the decay of G m ( t ) / G m ( 0) typically used 4 or 5 exponential terms.

RESULTS Systems studied. Four systems were simulated in this work: (1) Trp-cage starting in the native conformation dissolved in 42% TFE-water in which the TFE molecules were represented by TFE model TFE5;

41

(2) the same system but with TFE represented by the TFE6 model

41

, (3) Trp-

cage starting in a thermally unfolded structure (unfold1) with TFE5 and (4) Trp-cage starting in the fully extended (beta) conformation with TFE5 (unfold2). System densities and translational diffusion coefficients of peptide, TFE and water were calculated for each system. The results are compared to experimental values in Table 1.

Table 1. Calculated Properties of Trp-cage in 42% TFE-d2-water at 318 K Native, TFE5

Native, TFE6

Unfold1, TFE5

Unfold2, TFE5

Experimental

1151.3

1154.9

1151.8

1151.8

1156.9b

Dpeptide x 1010 m2 s-1

2.2 ± 0.2

1.8 ± 0.2

1.7 ± 0.1

1.7 ± 0.2

2.8c

DTFE x 1010 m2 s-1

12.9 ± 0.3

13.1 ± 0.6

12.7 ± 0.3

12.9 ± 0.3

11.0c

DH2O x 1010 m2 s-1

29.0 ± 0.2

29.0 ± 0.2

29.1 ± 0.3

28.9 ± 0.3

27.8c

Densitya, kg m-3

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a

Simulations were done with TFE-d2. Densities calculated for the CF3CD2OH-containing systems were corrected to that of the corresponding CF3CH2OH systems assuming that there is no isotope effect on the volume. b c

Extrapolation of data of Palepu and Clarke for pure 42% TFE-water. 59 Data of Chatterjee and Gerig. 39

Trp-cage in 42% TFE5-water. Previous work in this laboratory indicated that Trp-cage in 42% trifluoroethanol-water has essentially the same conformation at 318 K (somewhat above the melting temperature of the peptide found in pure water

60

) as it does at 278 K .

39

The CD

spectrum of the peptide changes little over this temperature range. Consonant with other reports, fewer intramolecular 1H{1H} NOEs were observed at 318 K compared to lower temperatures. 31 However, there were still a sufficient number of NOE constraints detected at this temperature to confirm that the overall fold of the peptide is virtually the same at 278 K and 318 K in this solvent. 39 Simulation of Trp-cage in 42% TFE-water was done using the native structure (1L2Y) as the starting conformation of the peptide and the TFE5 model of the fluoroalcohol. In TFE5, the Lennard-Jones σ HF parameters for peptide hydrogen-fluorine and TFE methylene hydrogenfluorine interactions are increased 10% over the values calculated by using the standard AMBER parameters. Fifty-nine interproton distances, corresponding to observed intramolecular NOEs between Trp-cage hydrogens separated by 2 or more residues and recorded in Protein Data Bank file 1L2Y

19

, were followed over the course of a 0.25 µs simulation. Figure 2 shows

representative results of these calculations; data for all distances considered are given in the Supporting Information.



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Figure 2. Changes of the Trp6HD1-Pro18HA distance (Panel A) and the Tyr3HA-Pro19HB2 distance (Panel B) over the course of a simulation of Trp-cage in 42% TFE-water. The TFE5 model of trifluoroethanol was used. The average interproton distances for these cases were 0.36 nm and 0.56 nm, respectively. The corresponding distances calculated from the static 1L2Y model of Trp-cage in 90%H2O/10%D2O are 0.38 and 0.51 nm. 19 It was seen that the Trp-cage structure is highly mobile under the conditions studied, with some interhydrogen distances changing by as much as a factor of 6 over the course of the simulation. However, in virtually all cases, as shown in the Supporting Information, an average 1

H-1H distance was close to the corresponding distance found in the 1L2Y structure (Figure 1)

and within the constraint distance determined from 1H-1H intramolecular NOE experiments. The average radius of gyration (RG) of Trp-cage calculated from the 0.25 µs simulation (50,000 snapshots) was 0.72 nm, with a maximum and minimum RG of 0.77 and 0.67 nm,


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respectively. These data may be compared to the RG calculated for the PDB structure 1L2Y, 0.73 nm. Intermolecular peptide hydrogen-solvent fluorine cross relaxation parameters ( Σ HF ) were calculated using the 0.25 µs trajectory. These are summarized in Figure 3 and given in Table S2 of the Supporting Information. It was found that many calculated Σ HF agreed with experimental values within the estimated experimental uncertainty. However, calculated Σ HF for some hydrogens of the Trp-cage tryptophan indole ring and hydrogens near Trp6 in the tertiary of structure (Gln5, Pro12, Ser14, Pro18, Pro19) are not well-predicted by the calculations, in many cases being significantly smaller than the corresponding experimental values.

Figure 3. Comparison of observed (black symbols) and calculated (red symbols) cross relaxation parameters ( Σ HF ) for interactions of trifluoroethanol fluorines with Trp-cage hydrogens in a



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sample of the peptide dissolved in 42% TFE-water at 318 K. Data were calculated from a 0.25 µs simulation that used the TFE5 model of the fluoroalcohol. The error bars represent estimated ± 25% errors in the experimental data. Signals for some peptide hydrogens, indicated by asterisks, are overlapped in the experimental spectrum. In those cases, the data shown are the averages of the calculated data for two overlapped hydrogens. See the Supporting Information for more details.

Cross-relaxation terms for the hydrogens of Trp-cage in 42% TFE-water at 318 K were also calculated using the formulation of Ayant, et al..

40

A single static structure of the peptide was

considered (1L2Y); the radius of the sphere representing a TFE molecule was taken as 0.246 nm61 and the sum of the experimental translational diffusion coefficients of Trp-cage and TFE was used. Results of these calculations are given in Table S2 of the Supporting Information. These calculations generally underestimate Σ HF , presumably because a single static structure of the peptide does not explore the range of peptide conformations and their attendant solvent interactions found in a dynamic system. Trp-cage in 42% TFE6-water. Simulation of Trp-cage in 42% TFE-water was also done using the TFE6 model of trifluoroethanol. In this case, the Lennard-Jones σ HF parameters for peptide hydrogen-fluorine and TFE methylene hydrogen-fluorine interactions were the same as those of the TFE5 model while the Lennard-Jones ε HF parameters are decreased by 50%. The density of the system and the translational diffusion coefficients of the components are slightly altered by the change in the ε HF parameter (Table 1).


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Peptide hydrogen-solvent fluorine cross relaxation parameters were calculated using the results from the 0.1 µs simulation done; the data are given in the Supporting Information. As was found in calculations of Σ HF for an octapeptide in 40% TFE-water

41

, the TFE6 model of the

fluoroalcohol leads to Σ HF values that are similar to those found when using TFE5 (Figure S1 in the Supporting Information). The poor agreement between calculated Σ HF and experimental values for some hydrogens of Trp-cage obtained with the TFE5 model noted above was not improved by using the TFE6 model. The average radius of gyration of Trp-cage calculated for the 0.10 µs simulation in TFE6water (20,000 snapshots) was 0.72 nm. On average, the conformation of the peptide in TFE6/water appears to be little altered from that found in the TFE5-water simulation although differences in TFE-peptide interactions in the TFE5-water and TFE6-water simulations are sufficient to change calculated Σ HF values. Unfolded Trp-cage in 42% TFE5-water. The smaller than expected calculated cross-relaxation parameters for interaction of TFE with hydrogens of Trp6 and some other hydrogens of Trp-cage could be the result of shielding of the these hydrogens from solvent interactions by the tertiary structure of the peptide during the simulation. To access the impacts of such protection from solvent, simulations that started with the peptide in substantially unfolded conformations were carried out. With the first model (unfold1) as the starting structure, over the course of a 0.1 µs simulation, the peptide took on a hairpin conformation, with the Tyr3 and Trp6 sidechains solvent exposed. A second simulation (unfold2) began with the peptide in the fully extended βconformation. After equilibration for 8 ns, a dynamics run of 0.1 µs was carried out. During this time the peptide took on more compact conformations that usually left the sidechain of Trp6



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exposed to solvent molecules. Figure 4 shows the structure of Trp-cage observed at the end of the unfold1 and unfold2 simulations.

Figure 4. Conformations of Trp-cage at the end of 0.1 µs MD trajectories at 318 K in 42% TFEd2-water: (A) unfold1 simulation; (B) unfold2 simulation. The average radius of gyration (RG) of Trp-cage during the unfold1 simulation was 0.81 nm while over the unfold2 simulation it was 0.83 nm, consistent with the presence of expanded, nonnative conformations of Trp-cage during these calculations. The calculated system density and translation diffusion coefficients of TFE and water during the simulations of the unfold1 and unfold2 systems were close to those found in simulations of the native peptide (Table 1) while the calculated diffusion coefficients of Trp-cage (Dpeptide) in the non-native systems were somewhat smaller than Dpeptide found with the native structure, consistent with a larger average RG for the peptide in these systems. The solvent accessible surface area (SASA) provides a geometric measure of the exposure of atoms of a molecule to solvent. 62-63 Average accessible surface areas of the hydrogens of native and unfolded Trp-cage conformations over the trajectories available were calculated using a


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solvent probe of 0.246 nm. 61 Some results are given in Table 2. The SASA calculations confirm that all hydrogens of the tryptophan residue of native Trp-cage, on average, are completely or partially protected from solvent interactions during the course of a 0.25 µs simulation despite the mobility of the peptide. Solvent accessibility to these hydrogens is restored to some extent when the tertiary structure of the peptide is disrupted, with the accessible surface areas for these hydrogens in the unfold1 and unfold2 systems sometimes approaching those of free tryptophan.

Table 2. Calculated average solvent accessible surface areas (SASA, nm2)a Tryptophan

1L2Yb

Nativec

Unfold1d

Unfold2d

5GlnH

-

0.

0.

0.034

0.020

6TrpH

-

0.

0.

0.004

0.003

6TrpHD1

0.303

0.053

0.008

0.147

0.045

6TrpHE1

0.395

0.

0.001

0.268

0.170

6TrpHE3

0.162

0.

0.

0.073

0.022

6TrpHZ3

0.434

0.

0.029

0.333

0.161

6TrpHH2

0.429

0.

0.112

0.382

0.294

6TrpHZ2

0.366

0.053

0.018

0.313

0.221

18ProHA

-

0.

0.

0.005

0.006

18ProQD

-

0.263

0.155

0.174

0.198

18ProHG3

-

0.210

0.190

0.066

0.178

19ProQD

-

0.

0.041

0.314

0.163

System Hydrogen

a

All SASAs were calculated with the GROMACS routine gmx sasa. The radius of the probe sphere representing a TFE solvent molecule was 0.246 nm. b

A single conformation corresponding to the first structure given in the PDB file 1L2Y was calculated.



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Page 18 of 44

The average SASA for each hydrogen was calculated from a trajectory at 318 K of 0.25 µs duration (50000 frames).

c

The average SASA for each hydrogen was calculated from a trajectory at 318 K of 0.10 µs duration (20000 frames).

d

It is recognized that the system has not reached conformational equilibrium during the course of the short unfold1 and unfold2 simulations; these were intended only to explore qualitatively the effects of reduced peptide tertiary structure of solvent cross relaxation effects. Calculated cross relaxation terms for interactions of solvent TFE with the hydrogens of the models of unfolded Trp-cage are compared to experimental values in Figure 5 and in Table S3 of the Supporting Information. It is seen that more fully exposing hydrogens of the Trp6 ring and other peptide hydrogens to solvent produced increases in Σ HF . These results support the conclusion that the observed small calculated cross relaxation terms for the 5GlnH, 6TrpH, 6TrpHD1, 6TrpHE1, 6TrpHE3, 12ProHD3, 18ProHA and 19ProQG hydrogens of native Trp-cage relative to the experimental values imply that the simulation starting with the native structure and used to obtain the data in Figure 3 did not sufficiently sample conformational changes of the peptide that expose these atoms to solvent molecules.


Page 19 of 44

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Figure 5. Comparison of observed (black symbols) and calculated cross relaxation parameters ( Σ HF ) for interactions of trifluoroethanol fluorines with Trp-cage hydrogens in systems containing unfolded peptide in 42% TFE-water at 318 K. Green symbols represent data from the unfold1 simulations while blue symbols convey the unfold2 results. Data were calculated from 0.10 µs simulations that used the TFE5 model of the fluoroalcohol. The error bars represent estimated ± 25% errors in the experimental data. Signals for some peptide hydrogens, indicated by asterisks, are overlapped in the experimental spectrum. In those cases, the data shown are the averages of the calculated data for two overlapped hydrogens. The arrow at 18ProHA indicates that the datum for the unfold2 result is off-scale at -2.96 x 10-3 s-1.



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Page 20 of 44

Selective solvation of Trp-cage. Beyond accessibility considerations, in mixed solvent systems such as 42% TFE-water, preferential interactions of the peptide with one solvent component may be present. To explore the solvent environment of Trp-cage in 42% TFE-water we imagined five concentric spheres centered on a peptide hydrogen of interest. The first sphere (Shell 1) had a radius of 0.492 nm (roughly the diameter of a sphere representing a TFE molecule

61

); three

additional spheres (Shells 2 to 4) with radii that were multiples of 0.492 nm were also considered while a larger fifth sphere (Shell 5) had a radius of 3 nm, the cut-off distance used in the Σ HF calculations. Part of each sphere will be occupied by atoms of the peptide in addition to TFE and water molecules. The average number of TFE fluorines and the ratio of the number of water molecules to the number of fluorines near the hydrogens mentioned in Table 2, calculated from a 0.25 µs simulation of the native Trp-cage in TFE5-water, are given in Table 3; results for all hydrogens of Trp-cage in this solvent and in TFE6-water are given in the Supporting Information (Tables S4 and S5).


Page 21 of 44

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Table 3. Calculated solvent composition near hydrogens of native Trp-cage in 42%TFE-water at 318 Ka Trp-cage

Shell 1

Shell 2

Shell 3

Shell 4

Shell 5

hydrogen

to 0.492 nm

0.492-0.984 nm

0.984-1.476 nm

1.476-1.968 nm

1.968-3.000 nm

5GlnH

0.266 (5.026)

24.55 (1.581)

91.02 (1.790)

194.05 (1.774)

832.43 (1.862)

6TrpH

0.543 (1.366)

18.88 (1.723)

97.52 (1.686)

193.87 (1.795)

831.71 (1.865)

6TrpHD1

1.023 (1.768)

18.69 (1.600)

99.93 (1.631)

191.97 (1.821)

831.32 (1.867)

6TrpHE1

0.553 (2.367)

25.14 (1.254)

95.65 (1.678)

190.25 (1.846)

831.01 (1.868)

6TrpHZ2

2.231 (0.504)

27.08 (1.173)

94.55 (1.674)

187.92 (1.877)

830.01 (1.872)

6TrpHH2

3.364 (0.503)

28.54 (1.165)

92.59 (1.676)

187.44 (1.886)

829.14 (1.876)

6TrpHZ3

2.116 (0.661)

29.47 (1.090)

91.04 (1.716)

188.79 (1.880)

829.67 (1.873)

6TrpHE3

0.185 (0.886)

26.08 (1.032)

95.47 (1.724)

189.52 (1.864)

830.35 (1.871)

18ProHA

4.624 (3.355)

24.62 (1.318)

95.80 (1.672)

191.24 (1.832)

830.33 (1.870)

18ProQD

3.224 (0.735)

29.55 (1.316)

89.79 (1.732)

189.36 (1.832)

829.92 (1.873)

18ProHG3

3.365 (0.903)

28.19 (1.343)

91.27 (1.675)

189.38 (1.846)

829.15 (1.876)

19ProQD

2.796 (2.176)

20.31 (1.740)

98.61 (1.604)

192.11 (1.818)

830.61 (1.870)

a

Results shown are average values obtained with a 0.25 µs simulation (50000 frames) of Trp-

cage in 42% TFE5-water. The first number given is the average number of TFE5 fluorines present in the shell while the number in parentheses is the ratio of the average number of water molecules present to the average number of TFE fluorine atoms present. The ratio of water molecules to fluorines in the bulk solvent mixture was 1.864. A ratio larger than this for a solvent shell indicates a solvent mixture that locally is enriched in water molecules while an environment rich in TFE fluorines is characterized by a ratio less than this.



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Page 22 of 44

The simulations show that the solvent composition around Trp-cage hydrogens is near the composition of the bulk TFE-water solvent at distances greater than ~ 1.5 nm from the peptide (Shells 4 and 5). Closer to the peptide, preferential accumulation of TFE near the surface of the peptide is apparent (Shells 2 and 3), in agreement with many previous studies of peptides indicating formation of a TFE-enriched layer around peptides in TFE-water.

12, 14

The number

and identity of solvent molecules in contact with a peptide hydrogen (Shell 1) is variable. In simulations done with both TFE5 and TFE6, the backbone atoms of Trp-cage (N-H, CαH, CβH) generally are preferentially solvated by water molecules in Shell 1 while hydrogen atoms of sidechains, particularly those of hydrophobic residues, are primarily solvated by TFE. As a result of the strong dependence of the F m on H-F internuclear distance (Eq. 2), there is a strong correlation between the calculated average number of fluorine atoms found in solvent shell 1 and the value of the coefficients G 0 ( 0 ) and G 2 ( 0 ) of Eq.10 (See Figure S2.). The factors τ 0 (ωH − ωF ) and τ 2 (ωH + ωF ) of Eq. 10 reflect the diffusive translation of near-neighbor and more distant TFE molecules and depend in a complex way on the populations of TFE molecules in solvent shell 1 and beyond (Figure S3). However, a rough linear correlation of calculated cross relaxation parameters ( Σ HF ) and the number of TFE molecules present on average in shell 1 is found (Figure 6), suggesting that experimental solvent-solute cross relaxation parameters could be used to diagnose the nature of TFE interactions with Trp-cage at 318 K. At lower temperatures where molecular motions are slower, the frequency dependence of

τ 0 (ωH − ωF ) and τ 2 (ωH + ωF ) may vitiate use of an observed Σ HF in this way. 64-65


Page 23 of 44

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Figure 6. Dependence of calculated Trp-cage-TFE cross relation parameters ( Σ HF ) on the calculated average number of fluorines in solvent shell 1 over a 0.25 µs simulation of the native peptide in 42%TFE5-water at 318 K. Solvent diffusion near Trp-cage. Calculations and experimentation indicate that diffusion of solvent water molecules near proteins is slowed by factors of 2-4 relative to diffusion in the bulk solvent.

66-68

The difference equation of Pettit and co-workers

69-70

was used to explore solvent

diffusion near the surface of Trp-cage in 42% TFE-water. Some results of these calculations for hydrogens of the tryptophan residue in the native conformation of Trp-cage are shown in Figure 8; additional results from the native and unfold2 simulations are given in the Supporting Information (Table S6). It was generally found that diffusion of TFE molecules appears to slow by as much as a factor of ~4 as they approach the peptide backbone hydrogens (N-H, Cα-H, Cβ-H). Slowing of diffusion is less when TFE approaches a side chain hydrogen. The dependence of diffusion on distance to the peptide surface appears to be similar for native and unfolded peptide. It has previously been



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Page 24 of 44

argued that the slowing of diffusion near the peptide is likely not related to accumulation of TFE near the peptide. 41

Figure 8. Calculated translational diffusion coefficients for TFE as a function of distance from a Trp-cage hydrogen in 42% TFE-water at 318 K. The results were obtained using the TFE5 model of the fluoroalcohol. The black, cyan, red and green symbols represent data for the 6TrpH, 6TrpHB3, 6TrpHD1 and 6TrpHH2 hydrogens, respectively.

Long-lived TFE interactions with Trp-cage. Our original report of intermolecular NOE studies of the interactions of TFE with Trp-cage included the suggestion that some of the Σ HF observed could be influenced by the formation of long-lived TFE-peptide complexes. A mean residence time of 0.5-1.0 ns appeared to be consistent with the available data. TFE interactions was more closely considered in the present work.


39

The impact of long-lived

Page 25 of 44

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Encounters of TFE molecules with Trp-cage were examined using the approach described previously

51

in which individual TFE molecules in the simulation box are followed as they

approach then depart the peptide. A TFE-peptide interaction was assumed to persist as long as the distance between a TFE fluorine and a peptide hydrogen of interest was less than 0.5 nm. At 318 K, some TFE interactions with Trp-cage, defined in this way, persisted for as long as ~4 ns, although the average interaction time was ~0.1 ns. The simulations thus confirmed that TFE molecules can be close to a peptide hydrogen for long times. However, as was found in an octapeptide-TFE system,

41

during these contacts, the TFE molecules rotate rapidly, thus

modulating peptide hydrogen-solvent fluorine distances and greatly reducing potential contributions of such contacts to the relaxation of the peptide hydrogen. It was concluded that, contrary to our earlier suggestion, while persistent interactions of the fluoroalcohol with Trpcage are possible, it is unlikely that these long-lived contacts with TFE molecules are an important aspect of understanding the differences between observed and calculated Σ HF parameters for Trp-cage in TFE-water.

DISCUSSION Previous work showed that small adjustment of the Lennard-Jones σ parameters for trifluoroethanol led to improved predictions of TFE fluorine-peptide hydrogen cross relaxation parameters, calculated using MD simulations, of an octapeptide dissolved in 40% TFE-water at sample temperatures of 278 and 298 K. 41 We find in the present work that these force fields lead to good predictions of Σ HF for interactions of TFE with many of the hydrogens of a larger peptide, Trp-cage, dissolved in 42% TFE-water at 318 K. Good results are obtained for both backbone hydrogens as well as those of many sidechains on the surface of the peptide.



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Page 26 of 44

Translational diffusion coefficients and system densities for the Trp-cage system predicted from simulations are close to experimental values (Table 1). Agreement of calculated and experimental Σ HF hydrogens of Trp-cage implies that motions of the peptide and the solvent molecules near a particular peptide hydrogen are appropriately accounted for in 0.1-0.2 µs simulations. However, calculated Σ HF for some hydrogens of Trpcage are much smaller than experimental values. Results shown in Figures 3 and 4 implies that a calculated cross relaxation parameter smaller than the experimental value at 318 K means that the subject peptide hydrogen did not sample the solvent over the course of a simulation to the same extent it does in the experimental system. Simulations starting with models of Trp-cage that have less tertiary structure than the native peptide (unfold1, unfold2) show that a Trp-cage hydrogen fully exposed to solvent molecules would have at cross relaxation constant of 6 - 8 x 10-3 s-1 at 318 K in 42% TFE-water. Thus, although the Trp-cage structure appears to be highly mobile in 42% TFE-water at 318 K, some hydrogens of the Trp6 indole ring and peptide hydrogens near them, appear to not be exposed to solvent for long enough in a simulation of 0.25

µs duration that a Σ HF as large as that found experimentally can develop. Several µs at 318 K are likely required for Trp-cage in pure water to transition to an unfolded state that presumably would expose these hydrogens to additional solvent interactions. The presence of trifluoroethanol would lengthen this unfolding time since the fluoroalcohol tends to stabilize the elements of tertiary structure found in Trp-cage. Thus, the simulations of 0.10-0.25

µs duration reported here are insufficient for reliable prediction of solvent cross relaxation parameters for some peptide hydrogens. Elber has recently noted that time scales accessible to conventional MD simulations are often too short to address many molecular events and that extending these time scales to simulations of protein conformational changes that take place on


Page 27 of 44

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the microsecond time scale is still a "significant feat on readily accessible computers".

71

Additional efforts will be required to determine if simulations of Trp-cage in TFE-water can lead to correct predictions of all experimentally observed cross relaxation parameters.

CONCLUSIONS MD simulations of Trp-cage in 42% TFE-water at 318 K using the TFE5 or TFE6 models of trifluoroethanol lead to calculated peptide hydrogen-solvent fluorine cross relaxation parameters ( Σ HF ) that agree with experimental values for many of the hydrogens of the peptide. Calculated

Σ HF for the most internalized hydrogens of the Trp6 indole ring and a few others nearby in the tertiary structure are not well-predicted by these calculations. It is shown that this is likely due to lack of conformational changes sufficient to expose of these hydrogens to solvent molecules over the course a 0.25 µs simulation. Examination of the distribution of solvent molecules around Trp-cage confirms the tendency of TFE molecules to congregate near the surface of the peptide. Translational diffusion of TFE appears to slow near the peptide surface although this may be unrelated to the accumulation of fluoroalcohol. The calculations suggest that encounters of Trpcage solvent TFE molecules may persist for nanoseconds, peptide hydrogen-solvent fluorine dipolar interactions during these encounters likely are not the source of disproportionate values of calculated cross relaxation parameters.

ASSOCIATED CONTENT Supporting Information The Supporting Information provides interproton distances in Trp-cage averaged over the course of a 0.25 µs simulation at 318 K, a comparison of observed and calculated Trp-cage hydrogen-TFE fluorine intermolecular cross-relaxation parameters ( Σ HF ) calculated from



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Page 28 of 44

simulations using the TFE5 and TFE6 models of trifluoroethanol, calculated cross relaxation parameters for unfolded Trp-cage models (unfold1, unfold2), average occupancy of the solvent shells calculated from simulations that used the TFE5 and TFE6 fluoroalcohol models, the dependence of G 0 ( 0 ) on the average number of TFE fluorines in solvent shell 1, and the dependence of calculated ΣHF on the average occupancy of solvent shell 1 and the dependence of the diffusion coefficient of TFE on the distance of the fluoroalcohol from the Trp-cage surface. This material is available free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION Corresponding author E-mail: [email protected] Telephone: 805-893-2113. FAX: 805-893-4120

Notes The author declares no competing financial interest.

ACKNOWLEDGMENTS 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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TOC Graphic



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Figure 1. The structure of Trp-cage. The indole ring of Trp6 is sequestered by a collection of hydrophobic resides that includes prolines 12, 17, 18 and 19.19 Figure 1 239x265mm (300 x 300 DPI)

ACS Paragon Plus Environment

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Figure 2. Changes of the Trp6HD1-Pro18HA distance (Panel A) and the Tyr3HA-Pro19HB2 distance (Panel B) over the course of a simulation of Trp-cage in 42% TFE-water. The TFE5 model of trifluoroethanol was used. The average interproton distances for these cases were 0.36 nm and 0.56 nm, respectively. The corresponding distances calculated from the static 1L2Y model of Trp-cage in 90%H2O/10%D2O are 0.38 and 0.51 nm.19 Figure 2 91x107mm (300 x 300 DPI)



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Figure 3. Comparison of observed (black symbols) and calculated (red symbols) cross relaxation parameters (ΣHF ) for interactions of trifluoroethanol fluorines with Trp-cage hydrogens in a sample of the peptide dissolved in 42% TFE-water at 318 K. Data were calculated from a 0.25 µs simulation that used the TFE5 model of the fluoroalcohol. The error bars represent estimated ± 25% errors in the experimental data. Signals for some peptide hydrogens, indicated by asterisks, are overlapped in the experimental spectrum. In those cases, the data shown are the averages of the calculated data for two overlapped hydrogens. See the Supporting Information for more details. Figure 3 206x267mm (300 x 300 DPI)


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Figure 4. Conformations of Trp-cage at the end of 0.1 µs MD trajectories at 318 K. (A) unfold1 simulation; (B) unfold2 simulation. Figure 4 173x116mm (300 x 300 DPI)



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Figure 5. Comparison of observed (black symbols) and calculated cross relaxation parameters (ΣHF ) for interactions of trifluoroethanol fluorines with Trp-cage hydrogens in systems containing unfolded peptide in 42% TFE-water at 318 K. Green symbols represent data from the unfold1 simulations while blue symbols convey the unfold2 results. Data were calculated from a 0.10 µs simulation that used the TFE5 model of the fluoroalcohol. The error bars represent estimated ± 25% errors in the experimental data. Signals for some peptide hydrogens, indicated by asterisks, are overlapped in the experimental spectrum. In those cases, the data shown are the averages of the calculated data for two overlapped hydrogens. Figure 5 199x258mm (300 x 300 DPI)


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153x145mm (300 x 300 DPI)



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Examination of Trifluoroethanol Interactions with Trp-Cage through

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