Computer Simulation of Water Sorption on Flexible Protein Crystals

The first simulation study of water sorption on a flexible protein crystal is presented, along with a new computational approach for calculating sorpt...
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Computer Simulation of Water Sorption on Flexible Protein Crystals Jeremy C. Palmer and Pablo G. Debenedetti* Department of Chemical and Biological Engineering, Princeton University, Princeton, New Jersey 08544, United States S Supporting Information *

ABSTRACT: The first simulation study of water sorption on a flexible protein crystal is presented, along with a new computational approach for calculating sorption isotherms on compliant materials. The flexible ubiquitin crystal examined in the study exhibits appreciable sorption-induced swelling during fluid uptake, similar to that reported in experiments on protein powders. A completely rigid ubiquitin crystal is also examined to investigate the impact that this swelling behavior has on water sorption. The water isotherms for the flexible crystal exhibit Type II-like behavior with sorption hysteresis, which is consistent with experimental measurements on protein powders. Both of these behaviors, however, are absent in the rigid crystal, indicating that modeling flexibility is crucial for predicting water sorption behavior in protein systems. Changes in the enthalpy of adsorption, specific volume, and internal protein fluctuations that occur during sorption in the flexible crystal are also shown to compare favorably with experiment. SECTION: Physical Processes in Nanomaterials and Nanostructures

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require homogenization of the GCMC and MD parts to ensure microscopic reversibility.9,13 As a result, few simulation studies have examined water sorption on proteins. Branco et al.14 and Wedberg et al.15 successfully modeled the hydration of isolated proteins by using MD to simulate water sorption explicitly from a surrounding vapor phase. Most sorption experiments, however, are performed on protein powders and crystals that are usually modeled as semi-infinite, periodic materials,16 prohibiting phase boundaries from being simulated explicitly. The only computational study found in the literature that simulated water sorption on a periodic protein matrix was performed by Sandler and coworkers,17 who used GCMC to examine the hydration of a rigid lysozyme crystal. In this Letter, the first simulation study of water sorption on a flexible protein crystal is presented, along with a new computational approach for calculating sorption isotherms on compliant materials. The proposed approach was inspired by experimental techniques such as the isopiestic method1 and dynamic vapor sorption.14 These experiments are conveniently modeled by considering a protein sample immersed in an infinite reservoir containing a vapor mixture of water and nonadsorbing carrier gas (e.g., dry air or nitrogen), as illustrated in Figure 1a. Because the thermodynamic state of the reservoir is fixed, it imposes a constant isotropic stress on the boundary of the protein phase that is equal to the bulk pressure, σbulk = Pbulk. Although fluid and heat are exchanged during sorption, the number of proteins in the sample remains constant because of their low volatility. Consequently, osmotic equilibrium is established when the temperature and the chemical potential of

apor sorption techniques have been widely used for more than half a century to investigate water’s role in governing the structure, dynamics and biological activity of proteins.1 Because these methods permit control over the adsorbed water content in protein systems, they have facilitated numerous studies of the protein hydration process. Such investigations have revealed that proteins in partially hydrated powders and crystals often behave differently from proteins in solution. Dehydration effects are generally important below ∼0.4 g water/g protein and include significant changes in the specific volume, heat capacity, elastic modulus, unfolding temperature, and enzymatic activity of proteins.1−4 The reported onset of glassy dynamics also suggests that internal fluctuations are suppressed in partially dehydrated proteins.5,6 Uncovering the molecular origins of these dehydration effects is essential to advancing strategies for preserving proteinbased therapeutics, protecting against extreme environmental conditions, and promoting self-repair.7 This task is difficult to achieve by empirical means alone because many experimental techniques lack the spatial and temporal resolution required to probe the nanoscale behavior of proteins. Because molecular simulation techniques are well-equipped to study nanoscale systems,8 they have the potential to complement experimental efforts to understand protein hydration. There are, however, methodological challenges in applying these techniques to study proteins and other materials, such as polymers and metal−organic frameworks, which swell and undergo significant structural transformations during fluid sorption.9−12 The standard method, grand canonical Monte Carlo (GCMC), requires that the sorbent material be rigid during fluid uptake.8 Existing hybrid techniques9,13 that use molecular dynamics (MD) to relax these constraints intermittently during GCMC simulations are challenging to implement because they © 2012 American Chemical Society

Received: August 4, 2012 Accepted: September 7, 2012 Published: September 7, 2012 2713

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Figure 1. (a) Schematic illustrating the thermodynamic conditions imposed on protein samples during water vapor sorption experiments. The protein sample is immersed in an infinite reservoir containing a bulk vapor phase that consists of a nonadsorbing carrier gas and water (green and red spheres, respectively). Sorption brings the protein sample into osmotic equilibrium with the reservoir, which remains at constant temperature, pressure and composition. (b) Crystallographic structure of the ubiquitin crystal examined in this study, projected onto the xy plane, with the bounds of the unit cell represented as a rectangular box. Several neighboring periodic images are shown, and the four ubiquitin monomers comprising the unit cell are rendered using different colors. For clarity, only a small fraction of the hydrating water is shown.

control the final converged value of Nw in each configuration. The GCMC steps add and remove water, while the proteins are held rigid, and the subsequent MD simulations relax the system at constant Nw. This controls the rate of water uptake, giving the system time to equilibrate at each new hydration level. In the second stage, a long (Np,Nw,P,T) MD simulation is initiated from each of the configurations to equilibrate the system and perform sampling. A Parrinello−Rahman18 barostat is used during the (Np,Nw,P,T) MD simulations, allowing the system to deform anisotropically to balance the external isotropic stress (i.e., pressure). The same approach could also be used to study the influence of an anisotropic stress applied to the system during sorption. Finally, the saved MD trajectories are analyzed to calculate μw for each simulated value of Nw. This last step is readily achieved for aqueous systems using Bennett’s method,19 which is a test particle insertion/deletion technique that is parallelizable on CPU and GPU architectures20 and easy to implement with an existing GCMC code. Because enforcing microscopic reversibility is only necessary to correctly sample ensemble properties, the MD relaxation steps are always accepted during the initial GCMC-MD procedure. As a result, this part of the proposed approach can be implemented using a small external script to execute each cycle without modifying existing GCMC and MD software. Another key aspect of the method is that the dynamical properties of the system can be examined during the isotherm calculation process because the number of water molecules does not fluctuate during sampling with MD. This is in contrast with other hybrid methods that directly sample open ensembles, where system dynamics are constantly perturbed by water insertions and deletions. The proposed method is demonstrated by computing sorption isotherms for SPC/E water 21 on a P21 2 12 1 orthorhombic crystal of ubiquitin that was constructed from

each component are equal in both phases, and the stresses are balanced, that is, Tp = Tbulk, μi,p = μi,bulk, and σp = −Pbulk. This equilibrium state corresponds to a minimum in the osmotic potential for the protein phase, Ωos, under the constraint dNp = 0, d Ωos = d(Npμp ) = VdPbulk − SdT − Nwdμw − Ncdμc = 0 (1)

where Ni is the number of molecules of species i and the subscripts p, w, and c denote the protein, water, and carrier gas, respectively. According to Gibbs’ phase rule only three of the four intensive variables, μw, μc, T, and Pbulk, on the right side eq 1 can be chosen independently for the two-phase, threecomponent system because the remaining variable is constrained by the equation of state, Pbulk = f(μw,μc,T). In practice, however, the last term of eq 1 can be omitted because Nc ≈ 0 in the protein phase near ambient temperature. As a result, the only thermodynamic effect of the carrier gas is to maintain isobaric conditions while μw is varied. This is achieved experimentally by altering the vapor phase composition at ambient pressure. The above analysis is rigorous and useful for understanding the thermodynamic principles behind experimental sorption measurements on proteins. Simulation of osmotic equilibrium in the (Np,μw,P,T) ensemble, however, is usually performed using hybrid MC techniques9,13 that are challenging to implement, as previously discussed. Alternatively, the key measurement obtained from such experiments, the sorption isotherm (Nw vs μw), can be calculated using a three-stage process. First, a series of protein configurations with different water loadings is prepared from an initially dehydrated protein crystal. This is done in a quasi-reversible manner by performing alternating cycles of short GCMC and (Np,Nw,P,T) MD simulations, imposing a constant μw during the GCMC steps to 2714

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crystallographic data (PDB ID: 1UBQ).22 Ubiquitin was chosen because it is a prototypical globular protein used in many fundamental simulation and experimental studies. The unit cell, shown projected onto the xy plane in Figure 1b, contains four ubiquitin monomers interspersed with pores up to ∼0.8 nm in size that permit water to adsorb. Simulations were performed on a double unit cell that was modeled using the CHARMM 22 force field.23 The double cell was created by replicating the original system along the z axis, producing a simulation box with initial dimensions of Lx × Ly × 2Lz = 5.084 nm × 4.277 nm × 5.790 nm. After hydrating the protein system with SPC/E water, it was equilibrated under ambient conditions with MD. Becasue sorption measurements usually start with freeze-dried proteins, the iterative GCMC-MD procedure was used to dehydrate the crystal, bringing its final water content to 0.04 g/g. This was followed by re-equilibration of the system using MD. Next, a series of GCMC-MD simulations was performed to rehydrate the system, producing configurations with water loadings ranging from ∼0.05 to 0.34 g/g. From each of these configurations, a 50 ns (Np,Nw,P,T) MD simulation was initiated to propagate the trajectory. An anisotropic Parrinello−Rahman18 barostat was used during the MD simulations to allow the x, y, and z dimensions of the unit cell to fluctuate independently in accordance with the ubiquitin crystal’s orthorhombic symmetry. Finally, the saved trajectories from the MD simulations were analyzed to calculate μw and other properties. Desorption was examined in a similar fashion, except that the GCMC-MD simulations were initiated from a fully hydrated protein configuration from the adsorption isotherm. To assess the importance of protein flexibility, GCMC was used to calculate isotherms for a rigid crystal with proteins frozen in their crystallographic positions, corresponding to a hydrated state. Because the protein crystal is fully expanded in this configuration, it has a large specific volume and solvent accessible surface area, which are calculated to be 1.11 cm3/g and 940 m2/g, respectively. Additional technical details of the isotherm and geometric calculations are provided as Supporting Information (SI). The sorption isotherms for the rigid and flexible crystals are shown in Figure 2a and are reported as a function of relative sat humidity, RH(%) = 100 × exp((μw − μsat w )/(RT)), where μw is the chemical potential of water in pure saturated vapor at the same temperature. The value of μsat w was calculated from the reported vapor pressure of SPC/E water,24 0.01 bar, using the ideal gas law. According to the IUPAC convention,25 the adsorptions isotherms for the rigid and flexible crystals show Type I and Type II-like behavior with hysteresis, respectively. The initial rise in both isotherms in the 0−10% RH range is due to sorption on energetically attractive sites inside and on the surface of the proteins. This begins at lower RH in the rigid crystal because the structure has a greater accessible surface area for water to adsorb. After the rise, water starts to fill the larger pores in the rigid structure and continues to adsorb gradually until the crystal’s maximum capacity of ∼1350 water molecules is reached. In contrast, the isotherm for the flexible protein matrix exhibits a bend after the initial rise due to the complete filling of small residual pores in the dehydrated structure. This is followed by steady water adsorption as the pores and protein matrix begin to swell. The isotherm also never saturates because the flexible crystal eventually dissolves as the hydration level increases, forming a dilute solution. Experimental adsorption isotherms for protein powders also frequently show Type II-like

Figure 2. (a) Water sorption isotherms for the rigid (red symbols) and flexible (blue symbols) ubiquitin crystals. Circles and squares denote state points on the adsorption and desorption branches, respectively. Lines are shown to guide the eye. (b) Enthalpy of adsorption for the rigid and flexible crystals compared with experimental measurements on bovine serum albumin,26 α-chymotrypsin,27 and lysozyme.28

behavior, similar to that observed for the flexible crystal. This agreement is not surprising because Tarek et al.16 have demonstrated that simulated crystal and powder systems exhibit similar physical properties. Whereas the adsorption and desorption isotherms for the rigid structure are identical, the two branches for the flexible crystal exhibit a slight hysteresis similar to that routinely observed in experimental isotherms for protein systems.1,2 Although the reasons for the hysteresis are not entirely clear,1,2 it has been explained in other materials by the presence of thermodynamic metastability arising from capillary condensation8 and structural transitions.8−12 To understand this behavior, work is currently in progress to calculate water isotherms for systems, such as lysozyme powders, where considerable experimental sorption data is available for comparison. These systems are more challenging to simulate because of their significantly larger size. The enthalpy of adsorption, ΔHads = RT − (∂H/∂Nw)T, was also calculated for the protein crystals from the adsorption data using a numerical differentiation procedure described elsewhere.29 This quantity contains information regarding the adsorption energetics and can be measured experimentally using calorimetry or calculated from isotherm data. Figure 2b shows the simulated results along with experimental data for three different proteins.26−28 The enthalpy of vaporization, ΔHvap, for the SPC/E model and real water have been subtracted from the simulated and experimental results, respectively, so that the data in Figure 2b approach zero for a dilute protein solution. 2715

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Figure 3. (a) Specific volume (blue circles) and solvent accessible surface area (green squares) of the flexible ubiquitin crystal as a function on hydration level. (b,c) Configuration of the protein crystal at hydration levels of 0.21 and 0.31 g/g. Regions shaded in red, green, and blue denote values of the local pore size function, d(r), in the range of [0.28,0.4), [0.4,0.6), and [0.6,1.0) nm, respectively.

increases the SASA and appears to begin near ∼0.13 g/g, where the slope of the curve changes. Despite these changes in the crystal environment, the protein monomers did not undergo any significant structural transformations during hydration. This suggests that they are either stable during hydration or that such changes are not observable on the simulated times scales. Residue mean-square fluctuations (MSFs) were also calculated from the adsorption simulations to investigate the effects of hydration on protein dynamics. The reported MSF profiles were averaged over all eight of the protein monomers in the crystal and include only contributions from heavy atoms on the residues. Figure 4 shows the MSF profiles at different

The appreciable decrease in ΔHads at low hydration coincides with the initial rise in the isotherms because the most attractive adsorption sites are being populated with water. Growing evidence indicates that the physical properties of this strongly bound water significantly influence protein behavior.5,30 As a result, previous sorption studies have noted the onset of numerous dehydration effects in this region.1,2 The remarkable similarity between the ΔHads curves for the flexible crystal and all three experimental systems also supports empirical observations that despite fulfilling unique biological functions proteins have almost universal thermophysical properties.1,2 The large ΔHads values for the rigid crystal are consistent with its strong propensity to adsorb water. However, the fact that ΔHads does not reach ΔHvap suggests that the rigidity of the structure prevents the confined water from exhibiting bulk-like properties. This would appear to be spurious behavior because it is not observed in either the flexible crystal or experimental protein systems. The specific volume, ν, and solvent accessible surface area (SASA) of the flexible crystal are shown along the adsorption branch in Figure 3a. Configurations of the protein crystal at moderate and high hydration levels are also presented in Figures 3b,c, respectively. The configurations are overlaid with plots showing the local pore size function, d(r), along a thin cross section of the crystal 0.5 nm in width. This function is defined as the diameter of the largest sphere that can encompass point r without overlapping with the protein matrix.31 Overlap occurs if the sphere intersects with water’s reentrant surface on the protein. A simple method for calculating d(r) was described in a previous Letter.32 As detailed in the Figure caption, local d(r) values are represented by the colors of the shaded regions. As a result of sorption-induced swelling, the specific volume increases by ∼25% along the adsorption isotherm. This is consistent with X-ray and optical measurements on lysozyme crystals that show a ∼25% increase in volume over the same RH range.33 As illustrated in Figure 3b,c, most of the swelling occurs as adsorbing water expands existing pores in the crystal. As a consequence, the largest pore size in the crystal increases from 0.57 to 0.77 nm during sorption. New regions of accessible void space are also created as water intrudes into the contact regions between adjacent protein monomers, causing them to separate and expose a greater fraction of their surface to water. As shown in Figure 3a, this process significantly

Figure 4. Mean-square fluctuations of the protein residues in the flexible crystal shown at different levels of hydration. The first five profiles, starting from the bottom, are simulation results for hydration levels of 0.06, 0.17, 0.21, 0.26, and 0.34 g/g, respectively. The top black line shows the MSF profile derived from diffuse X-ray scattering measurements on a fully hydrated ubiquitin crystal.22 The profiles are offset by 0.01 nm for clarity, and the bars at the top denote the location of residues that form β-strands (green) and α-helices (blue). The vertical location of these bars is irrelevant.

hydration levels along with a profile calculated from X-ray scattering measurements on a fully hydrated ubiquitin crystal.22 The appearance of several peaks in the simulated profiles shows that fluctuations increase in residues that border the pores in the crystal, indicating that water sorption in these regions is responsible for the increased mobility. A similar lubricating effect has been observed in dielectric spectroscopy6,34 and neutron scattering34 experiments, which show an increase in internal protein fluctuations during hydration. The magnitude 2716

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(10) Ghoufi, A.; Maurin, G.; Ferey, G. Physics Behind the GuestAssisted Structural Transitions of a Porous Metal-Organic Framework Material. J. Phys. Chem. Lett. 2010, 1, 2810−2815. (11) Neimark, A. V.; Coudert, F. X.; Boutin, A.; Fuchs, A. H. StressBased Model for the Breathing of Metal-Organic Frameworks. J. Phys. Chem. Lett. 2010, 1, 445−449. (12) Triguero, C.; Coudert, F. X.; Boutin, A.; Fuchs, A. H.; Neimark, A. V. Mechanism of Breathing Transitions in Metal-Organic Frameworks. J. Phys. Chem. Lett. 2011, 2, 2033−2037. (13) Banaszak, B. J.; Faller, R.; de Pablo, J. J. Simulation of the Effects of Chain Architecture on the Sorption of Ethylene in Polyethylene. J. Chem. Phys. 2004, 120, 11304−11315. (14) Branco, R. J. F.; Graber, M.; Denis, V.; Pleiss, J. Molecular Mechanism of the Hydration of Candida Antarctica Lipase B in the Gas Phase: Water Adsorption Isotherms and Molecular Dynamics Simulations. ChemBioChem 2009, 10, 2913−2919. (15) Wedberg, R.; Abildskov, J.; Peters, G. H. Protein Dynamics in Organic Media at Varying Water Activity Studied by Molecular Dynamics Simulation. J. Phys. Chem. B 2012, 116, 2575−2585. (16) Tarek, M.; Tobias, D. J. The Dynamics of Protein Hydration Water: A Quantitative Comparison of Molecular Dynamics Simulations and Neutron-Scattering Experiments. Biophys. J. 2000, 79, 3244−3257. (17) Hu, Z.; Jiang, J.; Sandler, S. I. Water in Hydrated Orthorhombic Lysozyme Crystal: Insight from Atomistic Simulations. J. Chem. Phys. 2008, 129, 075105. (18) Parrinello, M.; Rahman, A. Polymorphic Transitions in Single Crystals: A New Molecular Dynamics Method. J. Appl. Phys. 1981, 52, 7182−7190. (19) Bennett, C. H. Efficient Estimation of Free Energy Differences from Monte Carlo Data. J. Comput. Phys. 1976, 22, 245−268. (20) Daly, K. B.; Benziger, J. B.; Debenedetti, P. G.; Panagiotopoulos, A. Z. Massively Parallel Chemical Potential Calculations on Graphics Processing Units. Comput. Phys. Commun. 2012, 183, 2054−2062. (21) Berendsen, H. J. C.; Grigera, J. R.; Straatsma, T. P. The Missing Term in Effective Pair Potentials. J. Phys. Chem. 1987, 91, 6269−6271. (22) Vijaykumar, S.; Bugg, C. E.; Cook, W. J. Structure of Ubiquitin Refined at 1.8 Å Resolution. J. Mol. Biol. 1987, 194, 531−544. (23) MacKerell, A. D.; Bashford, D.; Bellott, M.; Dunbrack, R. L.; Evanseck, J. D.; Field, M. J.; Fischer, S.; Gao, J.; Guo, H.; Ha, S.; et al. All-Atom Empirical Potential for Molecular Modeling and Dynamics Studies of Proteins. J. Phys. Chem. B 1998, 102, 3586−3616. (24) Vega, C.; Abascal, J. L. F.; Nezbeda, I. Vapor-Liquid Equilibria from the Triple Point up to the Critical Point for the New Generation of Tip4p-Like Models: Tip4p/Ew, Tip4p/2005, and Tip4p/Ice. J. Chem. Phys. 2006, 125, 34503. (25) Sing, K. S. W.; Everett, D. H.; Haul, R. A. W.; Moscou, L.; Pierotti, R. A.; Rouquerol, J.; Siemieniewska, T. Reporting Physisorption Data for Gas Solid Systems with Special Reference to the Determination of Surface-Area and Porosity (Recommendations 1984). Pure Appl. Chem. 1985, 57, 603−619. (26) Amberg, C. H. Heats of Adsorption of Water Vapor on Bovine Serum Albumin. J. Am. Chem. Soc. 1957, 79, 3980−3984. (27) Sirotkin, V. A.; Khadiullina, A. V. Hydration of α-Chymotrypsin: Excess Partial Enthalpies of Water and Enzyme. Thermochim. Acta 2011, 522, 205−210. (28) Bone, S. Dielectric and Gravimetric Studies of Water Binding to Lysozyme. Phys. Med. Biol. 1996, 41, 1265−1275. (29) Vuong, T.; Monson, P. A. Monte Carlo Simulation Studies of Heats of Adsorption in Heterogeneous Solids. Langmuir 1996, 12, 5425−5432. (30) Nucci, N. V.; Pometun, M. S.; Wand, A. J. Site-Resolved Measurement of Water-Protein Interactions by Solution Nmr. Nat. Struct. Mol. Biol. 2011, 18, 245−U315. (31) Gelb, L. D.; Gubbins, K. E. Pore Size Distributions in Porous Glasses: A Computer Simulation Study. Langmuir 1999, 15, 305−308. (32) Palmer, J. C.; Moore, J. D.; Brennan, J. K.; Gubbins, K. E. Simulating Local Adsorption Isotherms in Structurally Complex

and position of the peaks also agree with the experimental MSF profile, suggesting that the simulations provide a reasonable description of the fluctuations in the fully hydrated crystal. In summary, the first simulated water isotherms for a flexible protein crystal were calculated for ubiquitin using a new MDdriven procedure. The isotherms for the flexible ubiquitin crystal exhibit Type II-like behavior with sorption hysteresis that is consistent with experiments on protein powders. The proposed procedure also successfully captures the swelling of the crystal during hydration and shows semiquantitative agreement with experiment in predicting the adsorption enthalpy, specific volume changes, and residue fluctuations. These promising results suggest that the method may be a valuable tool for exploring the thermodynamic and dynamic properties of proteins during hydration, and that it may also find wider application in examining sorption-induced structural changes in other compliant materials.

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ASSOCIATED CONTENT

S Supporting Information *

Technical details of the computational methods. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The financial support of Unilever U.K. Central Resources and the National Science Foundation (grant NSF CHE 0908265 to P.G.D.) is gratefully acknowledged. Computations were performed at the Terascale Infrastructure for Groundbreaking Research in Engineering and Science (TIGRESS) facility at Princeton University.

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REFERENCES

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