Phase Behavior of a Lattice Hydrophobic Oligomer in Explicit Water † ⊥ ‡ ◇ § Santiago Romero-Vargas Castrillon,́*, , Silvina Matysiak, Frank H
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Article pubs.acs.org/JPCB Phase Behavior of a Lattice Hydrophobic Oligomer in Explicit Water † ⊥ ‡ ◇ § Santiago Romero-Vargas Castrillon,́*, , Silvina Matysiak, Frank H. Stillinger, Peter J. Rossky, † and Pablo G. Debenedetti † Department of Chemical and Biological Engineering, Princeton University, Princeton, New Jersey 08544, United States ‡ Fischell Department of Bioengineering, University of Maryland, College Park, Maryland 20742, United States ◇ Department of Chemistry, Princeton University, Princeton, New Jersey 08544, United States § Institute for Computational Engineering & Sciences and Department of Chemistry and Biochemistry, University of Texas at Austin, Austin, Texas 78712, United States *S Supporting Information ABSTRACT: We investigate the thermodynamics of hydrophobic oligomer collapse using a water-explicit, three-dimensional lattice model. The model captures several aspects of protein thermodynamics, including the emergence of cold- and thermal- unfolding, as well as unfolding at high solvent density (a phenomenon akin to pressure-induced denaturation). We show that over a range of conditions spanning a ≈14% increase in solvent density, the oligomer transforms into a compact, strongly water-penetrated conformation at low temperature. This contrasts with thermal unfolding at high temperature, where the system “denatures” into an extended random coil conformation. We report a phase diagram for hydrophobic collapse that correctly captures qualitative aspects of cold and thermal unfolding at low to intermediate solvent densities. 1. INTRODUCTION conditions, the driving force for folding is entropy-dominated, Many self-assembly processes in aqueous solution, from the generally accepted to be brought about by the formation of a formation of vesicles and micelles to protein folding, are driven more ordered hydration layer around hydrophobic moieties, by the aversion of hydrophobic moieties for water, the so-called within which water exhibits a lower hydrogen bond entropy and 5−7,9 hydrophobic effect. The importance of the hydrophobic effect enthalpy. By folding the polypeptide into a compact in biological self-assembly processes was first proposed in 1959 structure with reduced solvent contact, the entropy of the by Kauzmann,1 who conjectured that hydrophobic interactions, system is maximized. At high temperatures, the native state is the tendency of hydrophobic moieties to aggregate in water, are destabilized with respect to the unfolded state through the large the primary driving force behind the folding of a native entropy increase in the unraveled amino acid chain. A similar polypeptide into a biologically active protein. This conjecture is phenomenon, cold unfolding,8 has been observed at low now regarded as a well-accepted fact based on a number of temperatures, where the impact of solvent entropy loss is observations. First, hydrophobic amino acids are found at the reduced, and the unfolded state is stabilized by enthalpy. Cold core of the native structure, where they avoid contact with unfolding is akin to the low-temperature solubility of water, and water-soluble proteins do not fold to active hydrophobic solutes.8 structures in apolar solvents. More importantly, the solution The “liquid hydrocarbon” model1 described above success- thermodynamics of small hydrocarbons in water exhibits many 2−4 fully describes the T-dependence of protein unfolding but fails similarities with the thermodynamics of protein unfolding. to rationalize the pressure (p) dependence. The volume change In both instances, there is a large positive increase in the heat of thermal unfolding is positive at low p and negative at high p; capacity upon hydrocarbon dissolution (or protein unfolding), on the other hand, the volume change upon hydrocarbon signaling that both ΔH and TΔS increase with temperature. dissolution in water exhibits exactly the opposite behavior: This in turn implies that the T-dependence of the unfolding 10−12 11 Δ negative at low p and positive at high p. Hummer et al., free energy ( Gu) is parabolic, decreasing to negative values at both high and low temperatures. using computer simulations, have rationalized the observed Proteins exist in their native, biologically active state only pressure dependence by invoking an inverted liquid hydro- within a limited temperature range that is described closely by carbon model (conceptualized as the transfer of water to a pure the T-dependence of the free energy of unfolding. Close to Δ room temperature and ambient pressure, Gu for proteins Received: April 23, 2012 traverses a maximum and the native state is marginally stable Revised: June 19, 2012 Δ 3 ( Gu per residue is less than 1/10kBT). Under these Published: July 23, 2012 © 2012 American Chemical Society 9540 dx.doi.org/10.1021/jp3039237 | J. Phys. Chem. B 2012, 116, 9540−9548 The Journal of Physical Chemistry B Article hydrocarbon phase), with protein folds destabilized by pressure well as the data analysis methodology, are presented in section because of water penetration of the hydrophobic core.12 3. Results and discussion, followed by a summary and Molecular simulation studies have revealed considerable conclusions are presented in sections 4 and 5, respectively. insight into the mechanisms by which a protein becomes unfolded or denatured. In particular, atomistic molecular 2. LATTICE MODEL dynamics (MD) simulations have provided microscopic We study a system at infinite dilution, consisting of a single information about, e.g., the role of hydrophobic interactions 13 hydrophobic oligomer in explicit water. The main goal of our in the formation of the protein hydrophobic core and the work is to study the conformational states of solvated collapse of multidomain proteins,14 the formation of secondary- − oligomers. Since transitions are strongly cooperative and structural features such as α-helices and β-hairpins,15 18 the 19 involve the concerted motion of a large number of water role of water in pressure-induced denaturation, and the molecules and oligomer residues, the time required to sample mechanisms of protein unfolding due to denaturants such as 20−25 51 these is fairly long. As in numerous previous studies, we urea. Despite the ever-increasing computational power, choose a lattice representation of the system, which reduces the however, the long time scales characterizing protein dynamics degrees of freedom by constraining molecular positions to the impose limits on the scope of fully atomistic simulations. lattice geometry. This coarse-graining significantly reduces the 20−25 An alternative approach espouses minimalist models computational resources required to analyze the problem. where the protein structure and dynamics are constrained to a Previous studies using lattice models have yielded many lattice, significantly reducing the degrees of freedom relative to insights into protein thermodynamics. We should emphasize, continuum MD simulations at the expense of detail. Lattice however, that, apart from a handful of examples,21,22 most 20 models such as the HP model have revealed that sequences investigations included water only implicitly. Our study folding into a unique native conformation can emerge from a distinguishes itself in that water is represented explicitly on simple two-letter, hydrophobic/hydrophilic, amino acid alpha- the lattice. bet. Nevertheless, implicit solvent models without temperature- The protein−water system is projected onto a body-centered dependent effective interactions cannot capture effects such as cubic lattice, which can be alternatively conceptualized as two 21 26,27 cold denaturation. Recently, Patel et al. formulated a 2-D interpenetrating tetrahedral lattices. Each site possesses eight lattice model of homo- and heteropolymers in explicit water nearest neighbors (nn), placed at a distance 31/2 on the vertices and carried out simulations using flat-histogram Monte Carlo of the cube, so that relative coordinate alternatives [±1, ±1, 28,29 techniques. The authors showed that upon explicit ±1] describe virtual bonds between nn lattice sites. Water incorporation of the thermodynamics of hydrophobic solvation molecules are described using a modified version of the model (namely, the entropic penalty and enthalpic bonus upon by Roberts and Debenedetti,33,34 which captures many of liquid interfacial HB formation), the model exhibits cold-, thermal-, water’s properties, including the density anomaly and the 26 and pressure-induced oligomer unfolding. The model was hypothesized existence of two distinct supercooled liquid subsequently extended and refined on a 3-D lattice by Matysiak phases. We have verified that our simulations are conducted 30 et al. Extension to three dimensions resulted in several under conditions where solvent-phase separation does not improvements, most importantly the ability to correctly capture affect analysis of oligomer stability (see Supporting Informa- the hydrogen-bond topology of hydration water. The 3-D tion). The lattice site representing the water oxygen atom is lattice model also enables the study of protein secondary fitted with four bonding arms (two proton donors and two structure in a realistic manner. In this respect, the model by proton acceptors) arranged tetrahedrally. Molecules interact Matysiak et al.30 builds on the pioneering work of Skolnick et − with their nn sites through hydrogen bonding (HB) al.,23 25 who proposed a family of lattice models that could interactions on the tetrahedral directions. Non-hydrogen- produce the secondary-structural