Intrinsic Compressibility and Volume Compression in Solvated Proteins by Molecular Dynamics...

Intrinsic Compressibility and Volume Compression in Solvated Proteins by MolecularDynamics Simulation at High PressureAuthor(s): Emanuele Paci and Massimo MarchiSource: Proceedings of the National Academy of Sciences of the United States of America,Vol. 93, No. 21 (Oct. 15, 1996), pp. 11609-11614Published by: National Academy of SciencesStable URL: http://www.jstor.org/stable/40482 .

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Proc. Natl. Acad. Sci. USA Vol. 93, pp. 11609-11614, October 1996 Biophysics

Intrinsic compressibility and volume compression in solvated proteins by molecular dynamics simulation at high pressure

(volume fluctuations/static structure factor)

EMANUELE PACI AND MASSIMO MARCHI*

Section de Biophysique des Prot6ines et des Membranes, Commissariat I l'Energie Atomique, Centre d'Etudes, Saclay, 91191 Gif-sur-Yvette Cedex, France

Communicated by David Chandler, University of California, Berkeley, CA, June 20, 1996 (received for review May 1, 1996)

ABSTRACT Constant pressure and temperature molecular dynamics techniques have been employed to investigate the changes in structure and volumes of two globular proteins, superoxide dismutase and lysozyme, under pressure. Com- pression (the relative changes in the proteins' volumes), computed with the Voronoi technique, is closely related with the so-called protein intrinsic compressibility, estimated by sound velocity measurements. In particular, compression computed with Voronoi volumes predicts, in agreement with experimental estimates, a negative bound water contribution to the apparent protein compression. While the use of van der Waals and molecular volumes underestimates the intrinsic compressibilities of proteins, Voronoi volumes produce results closer to experimental estimates. Remarkably, for two globular proteins of very different secondary structures, we compute identical (within statistical error) protein intrinsic compressions, as predicted by recent experimental studies. Changes in the protein interatomic distances under compression are also investigated. It is found that, on average, short distances compress less than longer ones. This nonuniform contraction underlines the peculiar nature of the structural changes due to pressure in contrast with temperature effects, which instead produce spatially uniform changes in proteins. The structural effects observed in the simulations at high pressure can explain protein compressibility measurements carried out by fluorimetric and hole burning techniques. Finally, the calculation of the proteins static structure factor shows significant shifts in the peaks at short wavenumber as pressure changes. These effects might provide an alternative way to obtain information concerning compressibilities of selected protein regions.

During the past few years, considerable effort has developed to understand the origin of the pressure effects on the structure and volume of proteins (1-3) and to elucidate the mechanism for protein denaturation at high pressure (4, 5). Many experimental techniques have been used to study pressure induced changes in proteins, but only in rare instances has computer simulation been employed. Here, we present a molecular dynamics (MD) investigation of the microscopic compression of two solvated proteins. By simulating these systems in the NPT ensemble at room temperature and at increasing pressures (from 0.1 to 2000 MPa), we were able to compute averages and fluctuations of the protein volumes and relate these microscopic properties to the experimental thermodynamic compressibilities.

Experimentally, the effects of pressure on the protein structure are investigated by probing the corresponding changes in volume and by measuring compressibility, the latter being related to volume fluctuations, protein flexibility and, indirectly, protein functionality (6). Although crystallography

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(7), fluorescence spectroscopy (8), NMR (9), and hole burning (10) experiments have all been used to make estimates of protein compressibility, most of the available compressibility data come from sound velocity measurements (11, 12). Critical investigations of these experimental results have indicated that the compressibility of a protein can be divided into at least two components of opposite sign. Due to compressible cavities and voids in the protein interior, the first component of the protein intrinsic compressibility, f3p, is positive. The remaining term, fHyd, is the contribution to the compressibility due to hydration and bound water. As the compressibility of single amino acids and small peptides in solution is negative (13), fHyd iS thought to be negative. Most recent work (12) has indicated that the isothermal intrinsic compressibility of the protein, defined as the compressibility of the protein interior, is unique for all proteins and is about 3 times smaller than that of water. To distinguish, at a microscopic level, the protein intrinsic compressibility from contributions due to the solvents, the behavior of alternative definitions of protein compressions derived from computer simulation are juxtaposed here with the general experimental results. Although a few simulations of proteins at high pressure (14, 15) have been reported in the past, we carry out here a systematic correlation between experimental protein compressibilities and the simulation results.

Additional issues concerning the intrinsic compressibility of proteins are raised by high pressure experiments on proteins carried out with techniques other than velocimetry. Although measurements of f3p from hole burning experiments are in agreement with sound velocity estimates, fluorimetric deter- mination of distances between trytophan and heme groups in different heme proteins have led to intrinsic compressibilities higher than that of water. In contrast, x-ray crystallography applied to atmospheric and high pressure crystals of lysozyme resulted in an overall f3p that is one order of magnitude lower than that of water and one-third of that estimated from sound velocity experiments. Thus, an additional goal of this study is to address these experimental issues by characterizing the pressure effects on the protein interatomic distances derived from constant pressure MD simulations in light of the above experimental results.

MATERIALS AND METHODS

MD Simulations. All results reported in this paper were derived from a series of MD simulations of solvated superoxide dismutase (SOD) and of the tetragonal crystal of hen egg white lysozyme at constant temperature and pressure, carried out at 300 K and 0.1, 1000, and 2000 MPa. Average pressures and temperature were kept constant using an extended Lagrangian method, the application of which to solvated protein has been discussed in ref. 16. The extended Lagrangian equations of

Abbreviations: MD, molecular dynamics; SOD, superoxide dismutase; SPC, simple point charge model. *To whom reprint requests should be addressed.

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11610 Biophysics: Paci and Marchi Proc. Natl. Acad. Sci. USA 93 (1996)

motion were integrated using a Verlet-based algorithm (17) modified to treat velocity-dependent forces (18). A time step of 1.5 fs was used. Full periodic boundary conditions were used.

The solvated SOD protein was prepared and equilibrated for 300 ps in the microcanonical ensemble at 300 K, as described in ref. 19. The final system consisted of a SOD protein surrounded by 1457 water molecules and four Na+ ions for electroneutrality. The orthorombic box had dimensions a = 43.01 A, b = 62.56 A, and c = 35.19 A.

The simulation box used for lysozyme contained only one elementary cell of its tetragonal crystal (7). It was generated by applying symmetry operations to the x-ray coordinates of the crystal asymmetric unit and by adding, at a later time, 1946 water molecules and 64 Cl- ions to fill the voids and to reach electroneutrality, respectively. The final system consisted of a tetragonal simulation box of dimensions a = 79.1 A and c = 37.9 A containing eight lysozyme molecules, 3154 water molecules, and 64 Cl- ions. As for SOD, lysozyme was equilibrated in the NVE ensemble at about 300 K for 300 ps.

All water molecules contained in the systems were modeled by a simple point charge model (SPC; 19). The CHARMM version 20 united atom force field (20, 21) was used to handle the interactions among the protein atoms. Standard Lennard- Jones sum rules were adopted for mixed interactions between solvent and solute. We adopted a spherical cutoff at 9.0 A with a third order spline between 8.5 and 9 A. All covalent bonds were kept rigid in the MD simulations using SHAKE (22). For the Cu-Zn active site of SOD, the ab initio-based electrostatic model of Shen et al. (23) was used.

The runs in the NPT ensemble were started by fixing the external pressure and temperature of the system at the atmospheric value of 0.1 MPa and 300 K and reequilibrating for -50 ps. For solvated SOD, three MD runs were performed, each lasting 120 ps, at pressure P = 0.1, 1000, and 2000 MPa and temperature T = 300 K. For the lysozyme crystal, MD runs were carried out for 120 ps each at pressures P = 0.1 and 1000 MPa and temperature T = 300 K. After each modification of the pressure, both systems were relaxed for additionally 80 ps. We also performed three simulations of 686 molecules of pure water at the same thermodynamic conditions to compute the protein apparent volume discussed in this paper. While for SOD and water, only isotropic fluctuations of the volume (24) were allowed, for lysozyme, the cell shape and dimensions could change (25) during the runs. For details on the imple- mentation of the method, see ref. 16.

Protein Volumes. Early experimental investigations (26) of changes in volume upon protein folding prompted, more than 20 years ago, the development of techniques to compute the volumes of protein residues directly from x-ray structures. The so-called molecular volume was originally proposed by Rich- ards (27). It is based on the static view of a protein as a collection of atomic hard spheres, each having a core radius corresponding to the atom van der Waals radius. Thus, the molecular volume is defined as the volume of space enclosed by a molecular surface constructed as the contact surface between the van der Waals surface of the protein and a water molecule probe, represented by a hard sphere of 1.4-A radius. When the probe is simultaneously in contact with more than one atom of the protein, the interior-facing part of the probe is used as the contact surface.

According to its definition, the molecular volume takes into account solvent effects on rigid protein structures without explicitly including solvent molecules in the calculation. This was a clear computational advantage in early times, as compared with the calculation of Voronoi volumes (28), which requires, instead, the knowledge of the position of the solvent molecules around the protein to determine the volume associated with the surface residues. Indeed, computing the unique Voronoi polyhedra associated to a given distribution of atoms corresponds in spirit to constructing a Wigner-Seitz cell for

each atom. This can be carried out in a meaningful way only for homogeneous and infinite systems. As shown by earlier studies on liquids (29, 30), the use of Voronoi volumes can provide unambiguous structural information. The Voronoi approach has also been applied to static protein structure derived from x-ray crystallography to determine the volume of interior residues (31).

In this study, we have used the MD-generated configurations of the solvated proteins at different pressures to directly compute van der Waals, molecular, and Voronoi volumes for the concerned part of the system. Standard software was used to compute van der Waals (32) and molecular (33) volumes for the set of van der Waals radii given in ref. 34. As for the Voronoi volumes, their calculation was carried out using the recursive algorithm described in ref. 35. No explicit hydrogens were included in the Voronoi volume calculations.

RESULTS

Apparent and Intrinsic Compressibility. The adiabatic compressibility of a solution is determined experimentally from the Laplace equation:

1 f3 2 [1]

pU

Here, p is the solution density and u is the sound velocity in the medium. Any change in concentration or structure of the solution is reflected by a change in the sound velocity. Exper- imentally, the partial adiabatic compressibility of the solute is obtained by measuring the sound velocity and the density of the solution at different solute concentration and extrapolating to zero concentration, namely (11):

1p V- __

V_ = o > ) [2]

where ,B and f3w are the adiabatic compressibilities of the solution and of the pure solvent, respectively, c is the concentration of the solute, V< is the partial specific volume of the solute, and vo is the apparent volume fraction of the solvent in solution. For solvated proteins, fp3 includes contributions both from the protein interior and from the surface residues interacting with the solvent. Thus, even in the limit of small solute concentration, p,B is known experimentally as the protein apparent compressibility.

For most of the globular proteins investigated, p,B is positive. At least two contributions of opposing signs contribute to fP3: the compressibility of the protein interior, or protein intrinsic compressibility (f3p), and the change in compressibility due to water-protein interaction (IHyd)-i.e.,

p = fp + Hyd [3]

Solvation effects and water penetration at the protein surface cause the latter contribution to be negative, while pressure effects on voids and cavities in the protein globule produce, instead, a positive O3p.

A relation between intrinsic and apparent compressibilities has been used in the experimental literature by writing ,B, the adiabatic compressibility of the system, as the sum of the partial compressibilities of its components multiplied by their volume fractions. Here, we consider a contributions from the protein, O3p, the bulk water, 13w, and the water bound to the surface residues, ,pw. Namely (36):

,B = , + vp[,Bp - 3(A + 1) + AfBp_, [4]

where v1, is the protein fractional volume and A is the ratio between the bound water fractional volume and vp. It must be



Biophysics: Paci and Marchi Proc. Natl. Acad. Sci. USA 93 (1996) 11611

38000

E 33000

> G-OMolecular 0... EVan der Waals <- -*Voronoi

A--Apparent

28000 0 1000 2000

Pressure (MPa) FIG. 1. Volumes of the SOD dimer as a function of pressure. Different protein volumes are compared.

realized that although Eq. 4 cannot be rigorously derived, it has the advantage of providing an expression for the apparent protein compressibility which can be used to easily extract 3p from sound velocimetry results. Indeed, when solvation effects are neglected (i.e., A = 0), fP is equal to Op. Thus, the hydration contribution to , in Eq. 3 is:

fHyd - A(fw - fpw) [51

Since hydration effects reduce the compressibility of bound water with respect to bulk water, a consequence of Eq. 3 is that protein intrinsic compressibility is higher than its apparent value. The same equation also holds for isothermal compressibilities (12).

In this study, we did not attempt to compute partial properties such as protein partial volume or compressibilities as such calculations, by requiring a series of simulations at increasingly smaller protein concentration, would be compu- tationally too heavy. For sake of comparison with properties of water, we have instead computed the relative compression of the protein with respect to simulated SPC water. As shown in ref. 16, the compressibility of SPC water is very close to the experimental one. The compression, k, is related to compressibility in the limit of infinitely small change in pressure by:

kp 2

lim p [61 P2 --- PI P2 - P

where kpj is the fractional change in volume due to a pressure change P2 - P1, namely:

IP2 (V7)Pl - (Vj1P2 k ) ~[7] Pi (V)p1

where ( ) stands for statistical average in the chosen ensemble (NPT in our case).

In Fig. 1 the protein volumes for SOD computed at 0.1, 1000, and 2000 MPa are shown. As expected, van der Waals volume is almost constant with changes in pressure. In addition,

although at atmospheric pressure molecular, Voronoi and apparent volume are very close, their properties with respect to changes in pressure are strikingly different. This is better shown in Table 1, where we present the volume compressions calculated for the hydrated SOD and the lysozyme crystal. Their relative values with respect to compressions of SPC water are also included. Typically, errorst on Voronoi and apparent compressions are close to 5 and 15%, respectively. Since changes in molecular volumes are smaller than for Voronoi and apparent volumes, the corresponding errors are larger and on the order of 20%. The observed decorrelation time for volumes was 2 ps, which is small compared with the length of our simulations (120 ps). More details on volume convergence and errors are reported in ref. 16.

We first observe that the compression of the proteins molecular volumes is consistently smaller than that of the apparent volumes at all pressures. On the contrary, k computed from the Voronoi volume is always larger for both proteins. Thus, the hydration contribution to the apparent k values computed from the Voronoi volumes, 'Kyd in the table, is negative, as predicted from experimental estimates of the difference between apparent and intrinsic compressibilities (11, 12). On the contrary, a positive contribution is obtained if molecular volume is used instead of Voronoi volume (see column labeled k')tm in Table 1).

The similarity of behavior between protein intrinsic and Voronoi volumes with respect to changes in pressure is also supported by the calculation of the protein hydration or the ratio between the weight of the bound water and the weight of the protein. Indeed, if we adopt the Voronoi compression as the intrinsic protein compression and use a value of the bound water compression within zero and one-third of that of bulk water (47), protein hydration can be estimated directly from Eqs. 3 and 5. While for SOD, A is within 0.12-0.19 g of H20 per g of protein, the estimated hydration for the lysozyme crystal is higher and ranges between 0.21 and 0.31 g of H20 per

tUnless otherwise stated, by error we refer to the maximum error- i.e., three times the standard deviation a.




Table 1. Protein compression of SOD and lysozyme

Compressions

Apparent Molecular Voronoi

Absolute Relative Absolute Relative Absolute Relative kMyd kHyd

Lysozyme kl.?l ? 0.04 0.19 0.031 0.15 0.091 0.44 0.04 -0.25

SOD ko.?p? 0.055 0.26 0.022 0.10 0.098 0.47 0.16 -0.21 k0820 0.037 0.41 0.021 0.23 0.048 0.53 0.18 -0.12

The protein compressions are computed from apparent, molecular, and Voronoi volumes. The values in the first column of each item are the absolute com ressions. In the second column, we report the compression relative to SPC water at the same pressures. Items mHyd and kHyd are the hydration contributions relative to SPC water compression obtained using molecular and Voronoi volumes, respectively. Mean SPC water volume at 0.1, 1000, and 2000 MPa was computed from additional simulations described in ref. 18.

g of protein. This trend is consistent with the experimental estimates of 0.23 and 0.33 for solvated SOD (37) and lysozyme (7), respectively.

To provide an additional corroboration to the intimate relation between intrinsic and Voronoi volumes, we notice that the Voronoi compressions of SOD and of the lysozyme crystal, between 0.1 and 1000 MPa, are identical within simulation error. In light of the structural differences between the two proteins, this result is remarkable. Indeed, SOD is a ,3-sheet dimeric protein while lysozyme is monomeric and predomi- nantly a-helical. This finding is consistent with recent studies on the intrinsic compressibility of proteins and small peptides by the regression method (12). Based on the analysis of the correlation between isothermal partial compressibilities and molecular surface area, it was found that the intrinsic compressibility of globular proteins depends very weakly on the size and structural characteristics of the proteins. This suggests that the value of the protein intrinsic compressibility is common to all globular proteins and is about one-third that of water. This compares with our computed protein compression, which was half that of water.

Since the constant pressure MD simulation techniques used in this study sample directly from the NPT ensemble (16, 38), we have been able to compute not only volume averages, but also volume fluctuations. In the past, protein volume fluctuations were estimated by relating them to protein isothermal compressibility, (3p, with the equation (39):

< 5V2 > = VkBTt3,B [8]

where kB is the Boltzmann constant, T is the temperature, and V is the protein volume. This equation follows directly by considering either that the protein alone samples the distribution characteristic of a NPT ensemble or that the coupling between the protein and the solvent volume is negligible. Unfortunately, these assumptions are not true in general. We verified indeed that the coupling between protein and solvent Voronoi volumes was not at all negligible and that the cross fluctuations were of the same order of magnitude as the fluctuations of the two volumes alone. We present in Table 2 the calculated fluctuations of the cell volume and the protein

Table 2. Volume fluctuations

P, MPa Svc/Vc x100 6Vv/Vv, x100

Lysozyme 0.1 0.23 0.27 1000 0.26 0.22

SOD 0.1 0.43 0.37 1000 0.23 0.26 2000 0.19 0.20

Relative volume fluctuations for the simulation cell volume (Vc) and the protein Voronoi volume (Vv) were computed from constant pressure simulations described in the text. P is the external pressure used given in MPa.

Voronoi volume. Statistical errors on volume fluctuations are higher than those reported for compressions and are in the order of 30%. Although no estimate exists for SOD, the computed volume fluctuation of lysozyme is close to the experimental estimate of -0.3% obtained in ref. 7. In addition, volume fluctuations in SOD are larger that in lysozyme. This contrasts with the common experimental view (40) that 8-sheet domains are less flexible than a-helical domains under compression.

Distance Changes Under Pressure and Compressibility. Protein intrinsic compressibility can also be estimated from techniques sensitive to changes in distances between atoms of the protein. In particular, fluorescence spectroscopy (8) has been used to probe donor-acceptor distances in heme proteins as a function of pressure, and the resulting underlying compressibility was found to be comparable to that of bulk water. To interpret the difference of this result with those obtained by sound velocimetry, we have investigated how distances among the Ca of SOD change with pressure. In Fig. 2, we report the value of the volume compression between 0.1 and 1000 MPa for each pair of Ca, assuming isotropic compression. We first notice that for all distances, the compression greatly fluctuates and can assume both positive and negative values. These fluctuations are larger for short Ca-Ca distances below 20 A and become narrower as the distances increase. The range of compressions obtained in this way lays between -1.5 and 0.7. It is clear from this result that a single distance

0.7~~~~~~00

0 A0

^:; 0 _20 20 40 ..... ~ ~ .C .:.i no .

0 CO disanc j eX

FIG. 2. Volume compression between 0.1 and 1000 MPa computed from the contraction of the Ca-Ca distances. Each point in the plot corresponds to a pair of Ca atoms. (Inset) The average compression versus the Ca-Ca distance.



Biophysics: Paci and Marchi Proc. Natl. Acad. Sci. USA 93 (1996) 11613

contraction can never provide an accurate estimate of protein compression.

On the other hand, if the average of compression is plotted as a function of the Cae-Cae distance, the behavior shown in the Inset of Fig. 2 is observed. Protein compression computed from average distance contraction is always positive, or near zero for short distances, and is also nonuniform within the whole range of interactions. Indeed, compression is smaller for shorter distances and larger for longer ones. Thus, experiments such as photochemical hole shift measurements, which probe average nearest neighbor distances, are likely to underestimate the intrinsic compressibility of proteins. The results presented in Fig. 2 were also confirmed by the high pressure simulations of the lysozyme crystal (data not shown).

The protein nonuniform dilation revealed by our high- pressure simulations is in contrast with x-ray crystallography experiments on the protein thermal expansion (41), which found instead a uniform dilation of interatomic distances. Thus, our result emphasizes the difference in the physical nature of the structural effects induced by pressure with respect to those due to temperature changes.

Evidence of nonuniform dilation can also be gathered by computing the protein static structure factor, S(q), at different pressures. We have evaluated S(q) from the pair correlation function, g(r), as:

sinqr S(q) =1 + 4 r r2pg(r) dr, [9]

with

/N N\

pg (r) = N (r-rij, [10]

where N is the total number of atoms, rij is the distance between every pair of atoms i and j, and p is the average

number density of the protein. We included in the calculation of pg(r) only contributions from nonhydrogen atoms.

We have computed the pair correlation functions of SOD at the three pressures. At small distances, no significant shift in the position of the peaks is noticeable. In addition, beyond 6 A, the pair correlation functions become featureless. More useful to our analysis is the behavior under pressure of S(q), shown in Fig. 3 for P = 0.1 and 1000 MPa. Since some of the static structure factor peaks are due to the periodic distances characteristic of the protein secondary structure, pressure induced peak shift is an indirect measure of the compression of the corresponding secondary structure motifs. Assuming isotropic compression, if si and S2 are the position of the peak at pressure P1 and P2, respectively, the volume compression kpS is computed as:

s 3 _ [11]

Si

In Fig. 3, the shifts of the peaks are appreciable mainly in the region of small and medium wavenumber q (q < 1.5 A-1). In agreement with results of Fig. 2, we find that compression is not uniform over various length scales. Indeed, a first peak observed near 0.3 A-1I at 0.1 MPa shows a volume compression of 0.12 between 0.1 and 1000 MPa, while for the peak at 1.27 A-1, we compute a compression of only 0.06 (see Insets in Fig. 3). The former peak is related to the protein radius of gyration (42, 43). Its larger compression agrees well with the compression computed from the Cae-Cae distance changes in Fig. 2 in the limit of large distances. On the other hand, the peak at 1.27 i-1 is due to a space periodicity of 5 A, which is typical of the distance between the ae carbons of two adjacent f strands. Thus, the calculation of the pressure effects on this peak can provide estimates of the underlying compressibility of the SOD f-sheets, which are the principal motif of the protein secondary structure. This result indicates that measurements of the static structure factor of solvated proteins could, in principle,

'I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~0

S(q) \ It|i\ S(q) 0.25 0.29 0.33 1.2 1.4

5

P=0.1 MPa ____ P=1000 VlPa

I ,I

0 1 1 2 3

q(A ) FIG. 3. Protein static structure factor, S(q), at atmospheric and 1000 MPa pressure. (Insets) On a different scale, the peaks at q 0.3 and

q 1.28 A. Statistical error is within the thickness of the lines.




be used to investigate the intrinsic compressibility of proteins secondary structure. Nevertheless, although experimental de- termination of S(q) by coherent elastic neutron scattering of liquid water at high pressure (44) and of a hydrated protein powder at atmospheric pressure (45) has been carried out in the past, such a technique has not yet been applied to solvated proteins at high pressure.

CONCLUSION

To conclude, our study has emphasized the importance of computer simulations to investigate pressure induced structural modifications in solvated proteins. Hopefully, constant pressure MD combined with Voronoi volume analysis will be used in the future to address some of the long-standing issues concerned with high-pressure studies of proteins, such as anomalous protein compressibilities, enzymatic activity, and protein denaturation. We also hope that our results on the static structure factor of proteins at high pressure will stimu- late experimental work in the field.

We thank Piero Procacci for useful discussions and for helping us in the calculation of the Voronoi volumes.

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Intrinsic Compressibility and Volume Compression in Solvated Proteins by Molecular Dynamics...

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