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42828-AC7
Molecular Simulation and Statistical Mechanical Studies of Pressure Effects on Proteins

Shekhar Garde, Rensselaer Polytechnic Institute

Background: The structure, thermodynamics, and dynamics of biomolecules in solution are intimately connected to their function. Our understanding of fundamental aspects of biomolecules has come from quantifying their response to systematic perturbations in the extended thermodynamic space. Over the past decade, resulting from the development of high pressure experimental technology, hydrostatic pressure has emerged as an important dimension in which to perturb biomolecules.  Experiments show that proteins unfold at high pressures leading to water-swollen molten globule like ensemble. Also, the kinetics of folding-unfolding are significantly slowed down at high pressures. Lastly, protein aggregates or protein-protein complexes (or multimeric units) can be particularly sensitive to pressure, dissociating at moderate to high pressures. That proteins unfold at high pressures appears counterintuitive at first and is also at odds with the prediction of the simple “hydrophobic transfer” model. Thus, fundamental understanding of pressure effects on proteins and their complexes presents an important challenge. In addition, there are several fundamental questions in liquid state theory relating to the behavior of water at interfaces. Understanding the pressure dependence of water structure and dynamics at interfaces provides another probe of interfaces.

Our studies: We have followed two directions.

(1)   Firstly, we have focused on pressure effects on fundamental water-mediated interactions (e.g., hydrophobic interactions) over the extended pressure temperature space. Specifically, we have performed molecular simulation studies to obtain the free energy of hydrophobic interactions (as quantified by methane-methane potentials of mean force) over the entire liquid state phase space of water.  These calculations show that near ambient temperatures, increasing pressure distinctly weakens the strength of hydrophobic interactions, consistent with lower thermodynamic stability of proteins at higher pressures.  Qualitatively, with increasing pressure, the “open” hydrogen bonded structure of liquid water is changed in such a way as to weaken hydrophobic interactions. 

More recently, we have studied an exciting aspect of hydrophobicity, namely, its lengthscale dependence.  Studies from David Chandler’s group at Berkeley have pointed to interesting lengthscale dependence of hydrophobic hydration with increasing size of the solute. We find that pressure effects on the hydration of small and large solutes are different – the hydration shells of larger solutes (or large hydrophobic patches on proteins) have higher compressibility compared to small solutes.  More interestingly, we find that the local compressibility of water near hydrophobic solutes displays a non-monotonic dependence on solute size. Specifically, it goes through a minimum for solutes comparable to size of methane.  We are preparing a manuscript based on this to be sent to Physical Review Letters.  Broadly, our observations are consistent with the experimental observations that protein-protein complexes with significant hydrophobic interface are more sensitive to pressure. 

(2)   Secondly, we have performed atomically detailed simulations of protein Staphyloccocal Nuclease with focus on its volumetric properties and on thermodynamics of pressure unfolding. Given that the timescales of unfolding of proteins at high pressures can range from seconds to hours and longer, brute force molecular dynamics are severely limited.  Instead, we developed an algorithm (where water molecules are gradually inserted into protein interior) that generated ensemble of states from fully folded to partially folded to unfolded. By simulating these states in separate simulations, we calculated partial molar volumes of the protein in the folded and unfolded ensemble.  These volumetric data, combined with a thermodynamic cycle, allows prediction of the pressure-dependent free energy of unfolding of this protein.  Our predictions of the wild type protein as well as for its mutants are in good agreement with experimental results.

These calculations and similar studies on non-ionic micelles allowed us to accurately measure from simulations the compressibility properties of protein interiors and of micelle cores. We found that whereas micelles are highly compressible (with compressibility about 50% of liquid hexane), protein interiors are comparatively incompressible with compressibilities similar to those of solid polymeric materials. We were able to relate these observations to the fluctuations, and specifically the widths of cavity size distribution in these media correlate well with the observed compressibility (see Molecular Physics, 105:2, 189-199, 2007.)

Currently, we are exploring studies of folding-unfolding of hydrophobic (alkane-like) polymers to explore mechanistic aspects of pressure effect on hydrophobically driven folding.

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