Thermodynamics of Hydration Water around an Antifreeze Protein: A

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Thermodynamics of Hydration Water Around an Antifreeze Protein: A Molecular Simulation Study Hari Pandey, and David M. Leitner J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.7b05892 • Publication Date (Web): 21 Sep 2017 Downloaded from http://pubs.acs.org on September 21, 2017

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The Journal of Physical Chemistry

Thermodynamics of Hydration Water Around an Antifreeze Protein: A Molecular Simulation Study Hari Datt Pandey and David M. Leitner* Department of Chemistry and Chemical Physics Program, University of Nevada, Reno, NV 89557, USA * E-mail: [email protected], Phone: 1-775-784-1968 Abstract We investigate by molecular simulations thermodynamic properties of hydration water and protein, the sensitivity of hydrogen bonds to change in temperature, and hydration water distribution at varying levels of hydration of a hyperactive antifreeze protein, DAFP-1. Hydration water coverage of the protein and partial thermodynamic properties of the hydration water are heterogeneous, different for the water near the ice-binding site (IBS) and the rest of the protein, particularly at low levels of hydration. Overall, we find the partial specific heat of water to be larger at low hydration levels than in the fully hydrated limit, with the separation corresponding roughly to one hydration layer. Differences in the specific heat in the low- and fully-hydrated regions are accounted for by the varying sensitivity of water-water and water-protein hydrogen bonds to change in temperature as a function of hydration, most strikingly near the IBS.

Using values

computed for the specific heat we estimate the partial entropy of the water and protein. We find the partial entropy of DAFP-1 to be greater in the fully hydrated limit than at low levels of hydration, whereas the partial entropy of water is somewhat smaller.

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1. Introduction Longstanding interest in the nature of hydration water around proteins is due in part to the many properties of protein and water that are strongly coupled.1-28

The

importance of protein-water coupling has led to many investigations exploring the relation between hydration water coverage and protein plasticity and function.29-32 Numerous experimental and computational studies, focusing mainly on dynamics and function, have revealed that protein properties found in dilute protein solution are exhibited with as little as about one hydration layer around the protein.32

We address here the thermodynamic

properties of an antifreeze protein (AFP) and its hydration water by molecular simulations. The motivation for this study is fourfold. For the AFP we study there is a region, the icebinding site (IBS), that is distinct from the rest of the protein. As a result, simulations of hydrogen bond dynamics reveal differences near the IBS and elsewhere,33-34 and perhaps there are thermodynamic differences, too. A second property we examine is the origin of the specific heat of the hydration water, in particular contributions of hydrogen bonds between water molecules and those between water and the protein. A third property we consider is heterogeneity in the distribution of water as the protein is hydrated. Finally, large hydration layers have been detected for solvated AFPs by THz spectroscopy,33, 35-37 larger than for other solvated biomolecules.38-45 We would like to examine if there is any parallel in the thermodynamic properties. Early calorimetric measurements of hydrated lysozyme powders revealed that about a layer of water molecules is sufficient for the partial specific heats of protein and hydration water to converge to their values in the dilute solution limit.46 A computational study of thermodynamic properties of hydrated BPTI yielded qualitatively similar results.47

The convergence for such low levels of hydration is consistent with a 2


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percolation model, whereby a threshold corresponding roughly to a percolation network is needed for long-range coverage that yields protein plasticity and thermodynamic properties required for function.32, 48-49 However, the origin of differences between partial specific heats of water in the limit of low hydration and for fully hydrated systems remains unclear, and is something we address in this computational study. AFPs have highly heterogeneous surfaces, part of which is involved in ice binding.50

Effects of that

heterogeneity have been seen, e.g, in computational studies of the dynamics of hydrogen bonding between water molecules near the surface.33-34, 51 We examine where water tends to aggregate, and the extent to which partial thermodynamic properties can be associated with distinct regions of the AFP. In our computational study of hydration thermodynamics we consider a hyperactive AFP from the fire-colored beetle Dendroides Canadensis, DAFP-1, shown in Fig. 1.

AFPs, or ice-binding proteins, enable a variety of organisms to survive in cold

climates via thermal hysteresis activity.52 Hyperactive insect AFPs such as DAFP-1 are right handed β-helical proteins with nearly identical 12- or 13- amino acid repeats.53-55 One region on the surface of the protein is rich in threonines, indicated in Fig. 1. Mutation studies in which some threonines have been replaced by isoleucines indicate a critical role of that surface in the antifreeze activity of the protein.56 Since mutations on that surface, the ice-binding site (IBS), diminish antifreeze activity, AFP activity stems at least in part from local interactions between protein and solvent. Indeed, a general framework for describing antifreeze activity has long been based on a picture of adsorption-inhibition, with additional contributing factors.52 Still, the results of THz studies indicate a longerrange effect, too, i.e., protein-induced retardation of hydrogen bond dynamics extending to

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distances on the nm scale from the protein surface, and may potentially contribute to or at least be a consequence of the mechanism of antifreeze activity.33 In this computational study we begin with DAFP-1 and systematically hydrate the protein. At each level of hydration we compute thermodynamic properties, including specific heats, entropy and free energy of mixing water and protein. Values of the partial thermodynamic properties of water and protein are calculated at each level of hydration and compared with values for the isolated protein and for a water cluster comparable in size to the solvated protein. The systems we study are really clusters rather than bulk systems. Specific heats at constant volume of many types of clusters, including van der Waals clusters, water clusters, and metallic clusters, have been calculated classically and quantum mechanically taking the cluster volume as constant over a simulation,57-61 with one goal to explore how bulk properties emerge from finite systems. The volume of the cluster remains essentially constant as long as there is no evaporation from the cluster. Our calculations are carried out with this approach. We shall see that while there are some quantitative differences in values of the thermodynamic properties of the water cluster compared to the bulk, the qualitative trends we find for the hydrated protein are the same as in calorimetric studies of protein powders,46 and quantitative differences are small. For example, we find the weight fraction protein where partial thermodynamic properties reach their fully hydrated limit to be similar to values found for other proteins by experimental measurements of hydrated proteins.62-64 Moreover, we explore the origin of differences in the partial specific heats in the low and fully hydrated limits, with focus on the sensitivity of water-water and water-protein hydrogen bonds to change in temperature as a function of protein hydration.

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In previous computational work on DAFP-1 distinct dynamics of water near the IBS was found compared to water elsewhere around the protein, as well as differences in the vibrational density of states of the water.33, 51 The variability over different regions is not unlike that found in earlier computational studies of other proteins.65-66 The IBS of DAFP-1 contains only hydrophobic and non-charged polar side chains; all of the charged groups lie on the non-IBS. We thus find that when little water is present in the system it tends to aggregate near the non-IBS. We examine if there is also any distinction in the thermodynamic properties of water in these regions. In fact, we find small differences in the specific heat of the water in contact with the IBS and the water in contact with the non-IBS, which we attribute to differences in the configurational contribution to the specific heat arising from the distinct sensitivity of water-protein hydrogen bonds to change in temperature in these two regions. In the following section we discuss the computational methods used to model hydrated DAFP-1.

In Sec. 3 we summarize the thermodynamic properties that we

address. In Sec. 4 we present and discuss results of the thermodynamic and hydrogen bond properties we compute for DAFP-1. We conclude in Sec. 5.

2. Computational Methods The initial structure for the 83-residue DAFP-1 was created as described in Ref. [33]. DAFP-1 was solvated with 4000 TIP5P water molecules in a cubic box. All of the MD simulations were carried out using the GROMACS software package.67

Following

energy minimization, a 1 ns NVT simulation was run, followed by a 5 ns NPT simulation, then a 5 ns NPT production run to obtain a density converged isothermal–isobaric ensemble. The simulations were carried out at a pressure of 1 bar and temperature of 5



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300K. This temperature is close to that at which the subsystems containing the hydrated protein were studied, so that the structures should provide a good starting point for those simulations. This system is a parent system for all the subsystems we have studied in this work. We derived 20 subsystems containing 0 to 1600 water molecules from the parent system for the subsequent simulations. For each system the water molecules closest to the protein were kept, so the 300 nearest water molecules for DAFP-1 with 300 waters, etc. It was more convenient for some of the molecular modeling to use TIP3P water, so we replaced all the TIP5P water molecules by TIP3P water in each subsystem without altering the position of each water molecule. While different water models may have effects on structures of unfolded proteins we do not expect much of an effect on the folded structure when using either of these water models.68 Different water models may also influence the structure of solvation water and the characteristic of the solvation interface, but we do not expect any such perturbation to affect our results or conclusions. Each subsystem was then energy minimized and we carried out a 200 ps NVT simulation, followed by a 500 ps NVT production run with coupling temperature ranging from 270 - 310 K in intervals of 10 K. For these simulations, a cubic box of length 5.2 nm was used, the same size as the box at the end of the NPT simulations. Results for the specific heats did not change significantly when we calculated them after a 200 ps production run, and the values we report are for the longer 500 ps simulation. We checked that no evaporation occurred during the simulations.

This was done by

determining the minimum distance from the surface of the protein within which all water molecules are found, which is plotted for three of the systems at 310 K in Fig. S1. We find this distance to fluctuate very little over the course of the simulations, all within a range of 0.7 Å. We calculated the average total energy at each temperature and performed 6


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a linear fit to get the derivative of energy with respect to temperature, i.e., the specific heat, Cv. Similarly we calculated the average number of hydrogen bonds, N, for each system at 270 K, 280 K, 290 K, 300 K and 310 K, using a standard hydrogen bond criterion specified below. Finally, normal modes were computed for the systems with 0, 50, 100, 200, 250, 300, 400, 500, 600 and 800 water molecules and for the water cluster following energy minimization, which was a sufficient set of systems to estimate the vibrational contribution to the entropy. To compare with thermodynamic properties of a water cluster of size similar to that of the hydrated protein, we repeated the above procedure on a cluster containing 1512 TIP3P water. This number is close to the maximum number of water molecules of 1600 around the hydrated protein that we studied, and was the number extracted within a volume selected to remove roughly 1600 water molecules from a box of water. Thermodynamic properties of the water cluster will not change significantly if a somewhat smaller or larger cluster of water molecules were used, as this size lies beyond the range where size-dependent properties of water clusters are found.69 To obtain this water cluster we carried out a 500 ps NVT simulation followed by 1 ns NPT and 1 ns equilibration NPT simulation for a bulk water system containing 16,000 TIP3P water molecules. This total of 2.5 ns molecular dynamics (MD) simulation reproduced an equilibrated ensemble with pressure, 1 bar, temperature, 300K and density, 1.0 g cm-3. We cut out the droplet of water containing 1512 water molecules in such a way that the center of mass of the droplet was very near the center of mass of the whole system. The box size for the water cluster simulations was the same as for the hydrated protein simulations. We checked that no evaporation occurred during the simulations by determining the distance from the center

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of mass to the edge of the water cluster, which is plotted in Fig. S1. Fluctuations of this distance are very small, all within a range of 0.5 Å over the course of the simulations. Each of the above MD simulations was performed with a 1 fs time step and 0.1 K coupling constant. The topology parameters for the MD simulations were extracted from the AMBER-03 force field. The cut-off distances, the short-range neighbor list, Coulomb cut-off and LJ cut-off, were 1 nm in our simulation. The grid method for updating the neighbor list, Verlet method for cut-off scheme, all directional periodic boundary condition and all bond constraints with the SHAKE linear constraint solver were applied throughout the simulation process. The coordinate trajectory over the simulation was obtained by saving structures each 10 fs of the simulation. The kinetic and potential energy over the simulation was calculated at each of these saved points to calculate the average total energy. For the hydrogen bond criterion we used a donor-acceptor distance criterion with cut-off radius 0.35 nm, hydrogen-donor-acceptor angle cutoff of 30˚, bin width angle distribution of 1 degree and bin width distance distribution of 0.005 nm to calculate the number of hydrogen bonds for each trajectory and temperature. The time average of the time dependent hydrogen bond data was calculated as the average number of hydrogen bonds in each subsystem at each coupling temperature. To calculate the number of water molecules over the ice binding site and the rest of the protein, we defined a plane tangential to the ice-binding site, the threonine rich surface, and then counted the number of water molecules over the surface. In this way the ice-binding site of DAFP-1 is made up of 24 residues, with the remaining residues of the 83 total making up the non-ice binding region. These are listed in the SI. The calculation of the number of water molecules was investigated from the 500 ps canonical trajectory 8


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each 50 ps. The number that we report is an average over these 10 points at 300 K. All of the MD simulations were carried out using the GROMACS software package.67

3. Thermodynamic properties The thermodynamic properties of hydrated DAFP-1 that we compute by molecular simulations include the specific heat, Cv, and entropy, S. We consider two subsystems, water (W) and protein (P), and we label the partial thermodynamic properties of each as

XW and X P , respectively. The weight fraction water and protein in the system is denoted, respectively, wW and wP .

For thermodynamic property, X, expressed per unit mass of

the mixture, we write

X = wP X P + wW XW .

(1)

Defining X 0j as the property per unit mass of pure component j, we write the change in X due to mixing water and protein as

∆X = X − ( wP X P0 + wW XW0 ) .

(2)

For the specific heat of the system, Cv, we compute the internal energy, U, from 270 K to 310 K by the MD simulations described in the previous section and take the temperature derivative. For the entropy, S, we follow a procedure used in previous work on BPTI.47 We calculate the entropy in harmonic approximation, Snm, in terms of the normal modes, .

(3)

A harmonic approximation should provide a reasonable estimate to the entropy of the system at low temperature, in practice below the apparent dynamical transition, which

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occurs around 200 K. We thus use Eq. (3) to estimate the entropy to 200 K, and at higher temperature, T, we estimate the entropy simply as

 T  S = Snm ( 200K ) + Cv ln  ,  200K 

(4)

where for Cv we use the value obtained from the molecular dynamics simulations. In the analysis of the specific heat, Cv, we separate contributions from the vibrations, Cv,vib, and a configurational contribution, Cv,conf, where for simplicity we take Cv = Cv,vib + Cv,conf.

Since the simulations are classical we use for the vibrational

contribution to the specific heat Cv,vib = 6R = 0.6623 cal/g ⋅ K . For the configurational contributions we assume a uniform hydrogen bond energy, ε, and calculate in the simulations the number of hydrogen bonds, N, at temperatures from 270 K to 310 K, so that we estimate for the configurational contribution, Cv,conf,

Cv,conf = ε

dN . dT

(5)

While of course just an approximation to the configurational contribution to the specific heat, we shall see that Eq. (5) yields a reasonable estimate to the hydrogen bond energy using Cv and dN/dT calculated by MD simulations, after subtracting Cv,vib = 6R.

4. Results and Discussion Fig. 1(a) illustrates a snapshot of the protein with 300 hydration water molecules. More water molecules appear to be concentrated away from the ice-binding site (IBS) than near it, which is supported by our analysis of water molecules near each of the two regions. The reason, as discussed further below, is the relative hydrophobicity of the IBS. In Fig. 1(b) we plot the average fraction of water molecules near the IBS of DAFP-1 and 10


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the average fraction computed over the simulation near the non-IBS as a function of wP at 300 K. We see that for low levels of hydration water the fraction of water near the IBS is smaller than the hydrated limit, increasing gradually to about 0.21 as wP decreases to about 0.62, which corresponds to about 300 water molecules. For more water, i.e., smaller

wP , the fraction of water around the IBS remains at 0.21. We have assigned 24 of the 83 residues to the IBS (see SI), or 0.29 of the 83 residues that make up the surface of the protein. Since the fraction of water around the IBS is smaller than the fraction of residues on the IBS the water molecules are found somewhat disproportionately near the non-IBS of the protein. All the IBS side chains are either hydrophobic or polar and all of the side chains with charged groups are found in the non-IBS, which would explain the propensity for water molecules near the latter. Earlier computational studies have shown that when there are few water molecules hydrating a protein those molecules tend to aggregate near charged groups.47 It is likely that, at low levels of hydration, the position of the water molecules in our systems resembles the position in the solvated system. For the protein systems hydrated by N water molecules studied here, where the initial structures were those N water molecules closest to the protein, the water molecules near the charged groups do not migrate much around the protein during the simulation of the partially hydrated protein. In Fig. 2 we plot the specific heat of hydrated DAFP-1 as a function of weight fraction protein, wP . We see that the specific heat of the system decreases monotonically as wP increases, reaching a value of 0.494 cal g-1 K-1 for the dry protein. Also plotted is the value of Cv computed for a cluster of 1512 water molecules, which was found to be 1.125 cal g-1 K-1. There appear to be two regions where Cv varies approximately linearly

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with wP . The more convincing linear variation lies where wP ≈ 0.23 – 0.62, or from 300 – 1600 water molecules around the protein. A linear fit to those data yields in this region, Cv = 1.0983 cal g-1 K-1 - 0.4920 wP . Extrapolating to pure water we find that Cv for a water cluster is 1.0983 cal g-1 K-1 , about 2.5% smaller than the value of 1.125 cal g-1 K-1 we calculated for a cluster of water molecules that is of comparable size. In this region, we find for the protein the partial specific heat in the hydrated limit to be 0.606 cal g-1 K-1, a 23% increase over the partial specific heat of the protein in the limit of low hydration. The other region where the data appear to vary linearly, perhaps only approximately so, is in the limit of low hydration. Using the data for the dry protein and the data for hydration with 50 to 250 water molecules we obtain the linear fit, Cv = 1.260 cal g-1 K-1 – 0.7634 wP . This linear fit gives 0.4966 cal/g ⋅ K for the partial specific heat of the protein in the limit of low hydration, essentially the same as the value of 0.494 cal g-1 K-1 computed for the dry protein itself. The intercept of Cv = 1.260 cal g-1 K-1 gives a value for the partial specific heat of water that, in the limit of low hydration, is 15% larger than the specific heat of water in the fully hydrated limit. To explore further what properties influence differences in the partial specific heat of the water in the limit of low hydration, where wP is greater than about 0.62, and the fully hydrated limit, corresponding to at least 300 water molecules, we focus on the hydrogen bonds. We begin with the average number of hydrogen bonds, N, calculated over the course of a simulation divided by the number of water molecules in the system at 300 K, which we plot in Fig. 3. There we see that at low hydration, with fewer than 300 waters, N is greater than its value in the hydrated limit, which is about 1.6 for these systems. N decreases from about 1.9 to 1.6 with decreasing wP until about wP ≈ 0.6, or

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300 water molecules, then the number remains fairly constant around 1.6 for smaller wP . The value N = 1.6 corresponds to 3.2 hydrogen bonds extending from each water molecule on average, i.e., twice the number of hydrogen bonds over all water molecules, since there are two water molecules per bond. In simulations the average number of hydrogen bonds is found to be 3.2 or larger,70 so for the systems we have studied the number of hydrogen bonds extending from each water molecule may be somewhat smaller than in the bulk due to surface effects. We have broken up N into contributions from water-water and water-protein hydrogen bonds, which is also plotted in Fig. 3. At low levels of hydration the number of water-water hydrogen bonds is much smaller than the number of water-protein hydrogen bonds, which make up, e.g., about three-quarters of the hydrogen bonds when there are about 50 water molecules around DAFP-1. As the hydration level increases more waterwater hydrogen bonds form.

With about 150 water molecules around DAFP-1 the

contribution of water-water and water-protein hydrogen bonds is about the same. When there are about 300 water molecules hydrating the protein the number of water-water and water-protein hydrogen bonds per water molecule apparently sums to yield about 1.6 hydrogen bonds per water molecule in the system. The specific heat has contributions from vibrations of the water network and from configurational changes in hydrogen bonds with temperature. We thus seek to explain the variation in Cv with wP by examining trends in dN/dT. In Fig. 4 we plot dN/dT vs. wP , where N(T) is the average number of hydrogen bonds calculated during the MD simulation at each temperature, T. We have computed dN/dT for each system and divided by the number of waters to get dN/dT per water in the system. Those values are multiplied by 1000, to be of order 1, so we plot in Fig. 4 dN/dT per 1000 waters, which we have broken 13



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down into dN/dT for water-water hydrogen bonds (blue), water-protein hydrogen bonds (black) and their sum (red). We note that while we have also calculated dN/dT for proteinprotein hydrogen bonds, we found those values to be at least two orders of magnitude smaller than those computed for water-water and water-protein hydrogen bonds and thus neglect protein-protein hydrogen bonds in Fig. 4 and in the following discussion. As wP approaches 1, where there is relatively little water, the hydrogen bonds involving water molecules are mainly between water and protein. For weight fraction protein 0.8 or greater only water-protein hydrogen bonds contribute to dN/dT.

The

magnitude of dN/dT for water-protein hydrogen bonds is noticeably greater at low levels of hydration than at higher levels, apparently due to a greater sensitivity of water-protein hydrogen bonds to changes in temperature at low hydration. As the level of hydration increases, the contribution of water-protein hydrogen bonds to dN/dT diminishes and the contribution of water-water hydrogen bonds increases. By wP ≈ 0.7, the magnitude of dN/dT for water-water hydrogen bonds is greater than that for water-protein hydrogen bonds, and the values diverge further with increasing hydration. With the addition of at least 300 water molecules ( wP ≈ 0.6) the sum of the two contributions to dN/dT reaches a value of about -2.7 K-1 per 1000 water molecules. With roughly two hydration layers, or wP ≈ 0.4, the magnitude of dN/dT for water-protein hydrogen bonds becomes far smaller than that for water-water hydrogen bonds, which indicates that, for this level of hydration and beyond, the configurational contribution to the specific heat is largely due to the water-water hydrogen bonds. While there are significant fluctuations in dN/dT around -2.7 per 1000 water molecules as more water is added to the system, the average value does not appear to change much. The same value, -2.7 K-1, is found for the water cluster. Overall, the 14


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hydrated limit appears to be reached when for all hydrogen bonds dN/dT reaches a value of about -2.7 K-1 per 1000 water molecules. We can use dN/dT ≈ -2.7 K-1 per 1000 waters to estimate the configurational contribution to the specific heat of the water and the hydrogen bond strength, ε, with Eq. (5). Since for this value of dN/dT, where the hydration levels are large, almost all of the hydrogen bonds are between water molecules, we are thus estimating the hydrogen bond strength between water molecules.

The simulations are classical so we use for the

vibrational contribution to the specific heat, Cv,vib = 6R = 0.6623 cal g-1 K-1.

For the

cluster of water molecules we found Cv to be 1.0983 cal g-1 K-1. Taking the difference between Cv and Cv,vib to get Cv,conf gives Cv,conf = 0.4360 cal g-1 K-1, or 39.7% of the specific heat of water. With that value we use Eq. (5) to estimate ε, recognizing that there are two water molecules for each hydrogen bond. For the dN/dT we have calculated we thus need to divide the right hand side of Eq. (5) by 2 to account for 2 water molecules per hydrogen bond. For dN/dT = -2.7 K-1 per 1000 water molecules, we find for the average energy of each hydrogen bond the value, ε = -5.8 kcal mol-1. This ε is comparable to the value, -5.6 kcal mol-1, we have calculated for the hydrogen bonds of the water cluster as the change in potential energy with the change in hydrogen bond number. For hydrogen bonds between TIP3P water the depth of the potential71 is -6.6 kcal mol-1 and the hydrogen bond energy can be as high as -4.6 kcal mol-1 for the angles and bond lengths of our hydrogen bond criterion. For two systems, one DAFP-1 with 300 water molecules and the other DAFP-1 with 100 water molecules, we have calculated dN/dT for water-IBS and water-non-IBS hydrogen bonds, i.e., we have broken down dN/dT into contributions from hydrogen bonds between water and the IBS and water and the non-IBS, respectively. The system 15



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with 300 water molecules represents a fully hydrated system, whereas the system with 100 water molecules represents a system with little hydration. We have only used the final structure of our simulation for this analysis, so that N is not an average in this case, but the values we found were very close to the average. E.g., for 300 water molecules at 300 K we found N to be 155.7 on average, and 155 in the final structure. For the system with 300 water molecules we find 82% of dN/dT to arise from water-IBS hydrogen bonds, the rest from water-non-IBS.

Thus, the configurational

contribution to the specific heat from water-protein hydrogen bonds is due more to waterIBS hydrogen bonds than water-non-IBS. We thus expect that the partial specific heat, and the entropy, of the water surrounding the IBS to be somewhat larger than the partial specific heat of water near the non-IBS. That conclusion is consistent with the greater hydrophilic character of the non-IBS, where all charged groups of DAFP-1 are located. Since about 40% of the specific heat corresponds to configurational contributions, and about 30% of that is due to water-protein hydrogen bonds for wP ≈ 0.6 (Fig. 4), the partial specific heat for water at the IBS could be as much as 10% greater than for water at the non-IBS. The difference would be substantially smaller for water not directly in contact with the protein, where water-protein hydrogen bonds do not contribute to the configurational contribution to the specific heat and entropy. In the limit of low hydration the configurational contribution to the partial specific heat of water is due entirely to water-protein hydrogen bonds, as seen in Fig. 4. We find for DAFP-1 hydrated by 100 water molecules that dN/dT is due entirely to water-IBS hydrogen bonds. The magnitude of dN/dT for hydrogen bonds between water and the rest of the protein is negligible by comparison. Therefore, the relatively high value of the partial specific heat of hydration water in the limit of low hydration is due to the high 16


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sensitivity of hydrogen bonds between water and the IBS as the temperature is changed. Those hydrogen bonds are apparently stabilized when more hydration water is present, and the configurational contribution to the partial specific heat of water is then largely due to hydrogen bonds between water molecules when the protein is fully hydrated. As pointed out, the magnitude of dN/dT for protein-protein hydrogen bonds is much smaller than for water-water and water-protein hydrogen bonds. However, we found that the partial specific heat of the protein in the fully hydrated limit is more than 20% larger than the partial specific heat of the protein in the limit of low hydration. The sizable increase in the partial specific heat of the protein when the hydrated limit is reached cannot be explained by changes of hydrogen bonding with temperature, at least not using the hydrogen bond definition adopted here. Other configurational contributions to the specific heat, including changes in van der Waals interactions with temperature, may play a greater role. We use the specific heats calculated for the hydrated protein to estimate the entropy using Eq. (3) and (4). In Fig. 5(a) we plot Snm(200 K), Snm (300 K), and S(300 K) where the former two were calculated using Eq. (3), and S(300 K) was computed with Eq. (4). We fit the entropy data in the hydrated limit, i.e., DAFP-1 hydrated with at least 300 water molecules. This gives for Snm(200 K) the result Snm(200 K) = 0.4079 cal g-1 K-1 0.1928 wP . For Snm(300 K) we find by fitting the same range of data Snm(300 K) = 0.5798 cal g-1 K-1 - 0.2695 wP . For S calculated with Eq. (4) we find for the same range S (300 K) = 0.8637 cal g-1 K-1 - 0.4119 wP . We thereby find for the entropy of water 0.8637 cal g-1 K-1, which matches the value we find for the water cluster, 0.8655 cal g-1 K-1. Both are close to the actual standard entropy of liquid water, which is 0.9288 cal g-1 K-1, or 7% below the actual value. We note that our result could be larger if we chose a somewhat 17



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lower temperature for the dynamical transition than 200 K, which is of course very plausible. We note also that the entropy computed with normal modes at 300 K is fairly similar to the standard entropy of ice, 0.5444 cal g-1 K-1. For the protein in the hydrated limit we find a partial entropy of 0.4518 cal g-1 K-1. In the low-hydration region, i.e., wP > 0.6, we find by fitting the data, S(300 K) = 0.9468 cal g-1 K-1 - 0.5413 wP . For the protein we find a lower value of the partial entropy of 0.4045 cal g-1 K-1 in the limit of low hydration, so the partial entropy of the protein increases by about 12% when it is hydrated. For water in the low-hydration limit we find the partial entropy to be 0.9468 cal g-1 K-1, about a 9 % increase in entropy over water in the fully hydrated limit. Finally, we calculate the entropy of mixing, ∆S, for DAFP-1 and water using the fitted values for S(300 K) in Eq. (2) for the hydrated and low-hydration regions, i.e., above and below wP of 0.62, respectively. The result is plotted in Fig. 5(b), where we also plot ∆S using the data plotted in Fig. 5(a). Based on the two linear fits to the computed entropy we see that the entropy of mixing increases as water is added to the protein until about 300 water molecules around the protein, then decreases as more water is added. While 300 water molecules is roughly the number that would cover the protein with one hydration layer, we have seen that a disproportionate amount of water is found away from the IBS, so that the distribution is not uniform. We find the entropy of mixing to make a much greater contribution to the free energy of mixing at 300 K than the energy of mixing (SI), except possibly at low levels of hydration. The energy of mixing at 300 K (Fig. S2) could reasonably be fit to a straight line over the full range of hydration, in which case ∆U is 0, but if we fit the data for 300 water molecules or more we find U = -423.99 cal g-1 + 290.88 wP in the hydrated region, whereas we fit to U = -442.64 cal g-1 + 309.69 wP in the 18


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low-hydration region. For the hydrated region we find ∆U to be more than two orders of magnitude smaller than T∆S at 300 K, but in the region of low hydration it is negative and about 70% of the value of T∆S, which reflects a significant drop in U with addition of water to about 100 water molecules (Fig. S2). Overall, we find that the separation between the bulk hydration limit and the lowhydration region occurs where the entropy of mixing is a maximum and the free energy of mixing is a minimum. The free energy of mixing is largely due to the entropy of mixing when the number of water molecules added is sufficient for roughly a complete hydration layer around the protein.

5. Conclusions We have computed thermodynamic properties of hydration water around the antifreeze protein DAFP-1 by molecular simulations and normal mode analysis. We find the specific heat of the hydrated protein around 300 K to vary linearly with weight fraction protein, wP , when wP is about 0.6 or smaller, corresponding to about 300 or more water molecules around the protein. For fewer hydration water molecules the specific heat also appears to vary fairly linearly with wP , but with a different slope than at higher levels of hydration. In the hydrated region the partial specific heat of the water is the same as the specific heat of a water cluster of about the same size. In the region of lower hydration the partial specific heat of the hydration water is about 10% larger. The partial specific heat of DAFP-1 is lower in the region of little hydration and over 20% greater in the fully hydrated limit.

The separation between the low and fully hydrated limit of wP ≈ 0.6,

about 300 water molecules around DAFP-1, is similar to wP found for other proteins. 19



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Isothermal calorimetric measurements on lysozyme, human serum albumin, βlactoglobulin and chymotrypsinogen A reveal fully hydrated values of partial enthalpies and free energies are reached where wP ≈ 0.5,62, 64 and densitometry studies indicate fully hydrated values of partial volumes are again reached where wP ≈ 0.5.63 While we find values of the thermodynamic properties of the hydration water to largely approach bulk values when there is enough water for roughly a full hydration layer, the distribution of water molecules around the protein is not uniform, with a propensity for water to cluster around the non-IBS. This is consistent with a hydrophobic IBS. Indeed, sum-frequency generation spectroscopy measurements reveal strikingly the hydrophobic nature of the IBS of DAFP-1, which is found in the experiments to lie at the air-water interface, whereas the non-IBS is found immersed in water.55 There have been previous studies of the temperature-dependence of protein-solvent interactions on the IBS of other hyperactive APFs, in particular CfAFP.

NMR

measurements indicate temperature-dependent protein-solvent interactions at the IBS consistent with hydrophobic hydration.72 Hydrophobic hydration on the IBS is consistent with the trends in dN/dT for hydrogen bonds observed in our simulations. Results of previous molecular simulations of hyperactive insect AFPs at different temperature also reflect temperature-dependent interaction energies at the IBS. Nutt and Smith,34 and Kuffel, et al.,73 found the hydration water to be more structured around the IBS of CfAFP than elsewhere around the protein, most strikingly at low temperature. Nutt and Smith34 also observed the hydrogen bond dynamics to be more retarded around the IBS than elsewhere around the protein, again mainly at low temperature. The latter is consistent with more recent studies on other hyperactive insect AFPs,51 including DAFP-1.33

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Differences in the specific heat in the low- and fully-hydrated regions are accounted for by differences in the sensitivity of hydrogen bonds to change in temperature as a function of wP . We found the magnitude of dN/dT, where N is the average number of hydrogen bonds, increases with decreasing wP from 1.0 to about 0.6, at which point it does not change on average as more water is added. However, the origin of dN/dT varies as water is added. At low levels of hydration, the magnitude of dN/dT is mediated by water-protein hydrogen bonds and is relatively large compared to the magnitude of dN/dT in the fully hydrated limit, giving rise to a partial specific heat of water that is larger than in the bulk limit. The main source of the relatively large magnitude of dN/dT at low levels of hydration is the water-protein hydrogen bonds at the IBS, where water is less tightly bound to the protein than at the non-IBS. Since water-protein hydrogen bonds contribute significantly to the partial specific heat of the hydration water at low levels of hydration, the specific heat of the hydration water near the IBS is greater than near the non-IBS. Differences in values of thermodynamic properties of water molecules in distinct regions or binding pockets around other proteins have been observed in previous molecular simulation studies,74-76 e.g., for waters in the five binding pockets of Interleukin-1β.74 Tightly bound water molecules that have been studied by molecular simulations77-83 contribute to thermal84-86 and thermodynamically-driven processes,79 e.g. entropy-driven cooperativity in some proteins.87-88 It is unclear if small differences in values of the thermodynamic properties of hydration water around the IBS and non-IBS of DAFP-1 contribute to function or are simply a consequence of their different chemical properties. Either way, it would be interesting if those differences could be observed experimentally. Perhaps THz-calorimetry, which has recently revealed local changes in

21



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solvation free energies of alcohol chains,89 could differentiate values of thermodynamic properties in different regions of this protein. Using the values computed for the specific heat, the entropy of the hydrated protein was estimated. The partial entropy of the protein is greater in the fully hydrated limit, and the partial entropy of water is somewhat smaller. The origin of the larger partial entropy of water at low levels of hydration can again be attributed to the water near the IBS, for which the partial specific heat is relatively large due to the sensitivity of the water-protein hydrogen bonds there to change in temperature.

The relatively loosely

bound water molecules or isolated clusters at the IBS exhibit a particularly high partial specific heat and entropy at low levels of hydration. Only when a hydration layer forms are hydrogen bonds involving the IBS more stable, consistent with a percolation network model for the hydration water32, 48-49 where the onset of long-range water coverage yields thermodynamic properties that start to converge to values in the dilute solution limit.

Supporting Information Table of DAFP-1 residues assigned either to ice-binding site or non-ice binding site, figure plotting distance within which water molecules are found in system, and figure plotting internal energy versus weight fraction protein.

Acknowledgements The authors thank Dr. Yao Xu for providing structures of DAFP-1 and for helpful conversations. Support from NSF grant CHE-1361776 is gratefully acknowledged.

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Behavior and Flexibility of Folded Peptides Remain Intact. J. Chem. Theor. Comp. 2010, 6, 3569 - 3579. 69. Buck, U.; Pradzynski, C. C.; Zeuch, T.; Dieterich, J. M.; Hartke, B., A Size Resolved Investigation of Large Water Clusters. Phys. Chem. Chem. Phys. 2014, 16, 6859 - 6871. 70. Kumar, R.; Schmidt, J. R.; Skinner, J. L., Hydrogen Bonding Definitions and Dynamics in Liquid Water. J. Chem. Phys. 2007, 126, 204107. 71. Buck, M.; Karplus, M., Hydrogen Bond Energetics: A Simulation and Statistical Analysis of N-Methyl Acetamide (Nma), Water, and Human Lysozyme. J. Phys. Chem. B 2001, 105, 11000 - 11015. 72. Hong, J.; Hu, Y.; Li, C.; Jia, Z.; Xia, B.; Jin, C., NMR Characterizations of the Ice Binding Surface of an Antifreeze Protein. PLoS One 2010, 5, e15682. 73. Kuffel, A.; Czapiewski, D.; Zielkiewicz, J., Unusual Structural Properties of Water within the Hydration Shell of Hyperactive Antifreeze Protein. J. Chem. Phys. 2014, 141, 055103. 74. Raman, E. P.; MacKerell, A. D., Rapid Estimation of Hydration Thermodynamics of Macromolecular Regions. J. Chem. Phys. 2013, 139, 055105. 75. Nguyen, C. N.; Young, T. K.; Gilson, M. K., Grid Inhomogeneous Solvation Theory: Hydration Structure and Thermodynamics of the Miniature Receptor Cucurbit[7]Uril. J. Chem. Phys. 2012, 137, 044101. 76. Drake, J. A.; Harris, R. C.; Pettitt, B. M., Solvation Thermodynamics of Oligoglycine with Respect to Chain Length and Flexibility. Biophys. J. 2016, 111, 756 767. 77. Gnanasekaran, R.; Agbo, J. K.; Leitner, D. M., Communication Maps Computed for Homodimeric Hemoglobin: Computational Study of Water-Mediated Energy Transport in Proteins. J. Chem. Phys. 2011, 135, art. no. 065103. 78. Gnanasekaran, R.; Xu, Y.; Leitner, D. M., Dynamics of Water Clusters Confined in Proteins: A Molecular Dynamics Simulation Study of Interfacial Waters in a Dimeric Hemoglobin. J. Phys. Chem. B 2010, 114, 16989 - 96. 79. Leitner, D. M., Water-Mediated Energy Dynamics in a Homodimeric Hemoglobin. J. Phys. Chem. B 2016, 120, 4019 - 4027. 80. Agbo, J. K.; Gnanasekaran, R.; Leitner, D. M., Communication Maps: Exploring Energy Transport through Proteins and Water. Isr. J. Chem. 2014, 54, 1065 - 1073. 81. Xu, Y.; Leitner, D. M., Vibrational Energy Flow through the Green Fluorescent Protein-Water Interface: Communication Maps and Thermal Boundary Conductance. J. Phys. Chem. B 2014, 118, 7818 -7826. 28


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Figures Figure 1. (a) DAFP-1 hydrated by 300 water molecules from two different perspectives. Threonine side chains, which lie on the IBS, are indicated. (b) Fractional coverage of the IBS (triangles) and the rest of the protein (circles) is plotted versus weight fraction protein, wP, at 300 K.

Figure 2. Specific heat, CV, for hydrated DAFP-1 is plotted versus weight fraction protein, wP. Values of CV computed by MD simulations are indicated by filled circles. Linear fits to the data at low hydration (solid line) and fully hydrated limit (dashed line) are also plotted.

Figure 3. The average number of hydrogen bonds, N, per water molecule (red *) computed in the MD simulation at 300 K is plotted versus weight fraction protein, wP. Contributions of water-water (blue circles) and water-protein (black squares) hydrogen bonds are indicated.

Figure 4. dN/dT for water-water (blue circles), water-protein (black squares) hydrogen bonds and both (red *) per 1000 water molecules is plotted versus weight fraction protein, wP. At least 80% of dN/dT for water-protein hydrogen bonds is due to water at the IBS (see text).

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Figure 5. (a) Entropy, S, is plotted versus weight fraction protein, wP, including entropy computed with normal modes at 200 K (*) and 300 K (squares), and entropy computed with Eq. (4) (circles), i.e, Snm(200 K), Snm(300 K) and S(300 K), respectively. Linear fits in the fully hydrated limit are plotted as dashed lines, and a linear fit to the low-hydration region for S(300 K) data is plotted as a solid line. (b) Entropy of mixing, ∆S, is plotted using the S(300 K) data (*) and the linear fits (dashed lines).

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Figure 1 32


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Figure 2

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Figure 3

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Figure 4

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Figure 5

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TOC Graphic

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Figure 1. (a) DAFP-1 hydrated by 300 water molecules from two different perspectives. Threonine side chains, which lie on the IBS, are indicated. 286x168mm (96 x 96 DPI)


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Figure 1. (b) Fractional coverage of the IBS (triangles) and the rest of the protein (circles) is plotted versus weight fraction protein, wP, at 300 K. 254x190mm (72 x 72 DPI)



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Figure 2. Specific heat, CV, for hydrated DAFP-1 is plotted versus weight fraction protein, wP. Values of CV computed by MD simulations are indicated by filled circles. Linear fits to the data at low hydration (solid line) and fully hydrated limit (dashed line) are also plotted. 254x190mm (72 x 72 DPI)


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Figure 3. The average number of hydrogen bonds, N, per water molecule (red *) computed in the MD simulation at 300 K is plotted versus weight fraction protein, wP. Contributions of water-water (blue circles) and water-protein (black squares) hydrogen bonds are indicated. 249x145mm (72 x 72 DPI)



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Figure 4. dN/dT for water-water (blue circles), water-protein (black squares) hydrogen bonds and both (red *) per 1000 water molecules is plotted versus weight fraction protein, wP. At least 80% of dN/dT for water-protein hydrogen bonds is due to water at the IBS (see text). 254x190mm (72 x 72 DPI)


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Figure 5. (a) Entropy, S, is plotted versus weight fraction protein, wP, including entropy computed with normal modes at 200 K (*) and 300 K (squares), and entropy computed with Eq. (4) (circles), i.e, Snm(200 K), Snm(300 K) and S(300 K), respectively. Linear fits in the fully hydrated limit are plotted as dashed lines, and a linear fit to the low-hydration region for S(300 K) data is plotted as a solid line. 254x190mm (72 x 72 DPI)



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Figure 5. (b) Entropy of mixing, ∆S, is plotted using the S(300 K) data (*) and the linear fits (dashed lines). 249x150mm (72 x 72 DPI)


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TOC Graphic 161x132mm (96 x 96 DPI)


Thermodynamics of Hydration Water around an Antifreeze Protein: A

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