A water-explicit lattice model of heat-, cold-, and pressure-induced protein unfolding

Implicit water model within the Zimm-Bragg approach to analyze experimental data for heat and cold denaturation of proteins

Studies of biopolymer conformations essentially rely on theoretical models that are routinely used to process and analyze experimental data. While modern experiments allow study of single molecules in vivo, corresponding theories date back to the early 1950s and require an essential update to include the recent significant progress in the description of water. The Hamiltonian formulation of the Zimm-Bragg model we propose includes a simplified, yet explicit model of water-polypeptide interactions that transforms into the equivalent implicit description after performing the summation of solvent degrees of freedom in the partition function. Here we show that our model fits very well to the circular dichroism experimental data for both heat and cold denaturation and provides the energies of inter- and intra-molecular H-bonds, unavailable with other processing methods. The revealed delicate balance between these energies determines the conditions for the existence of cold denaturation and thus clarifies its absence in some proteins.

Temperature-Controlled Liquid-Liquid Phase Separation of Disordered Proteins

The liquid-liquid phase separation (LLPS) of intrinsically disordered proteins (IDPs) is a commonly observed phenomenon within the cell, and such condensates are also highly attractive for applications in biomaterials and drug delivery. A better understanding of the sequence-dependent thermoresponsive behavior is of immense interest as it will aid in the design of protein sequences with desirable properties and in the understanding of cellular response to heat stress. In this work, we use a transferable coarse-grained model to directly probe the sequence-dependent thermoresponsive phase behavior of IDPs. To achieve this goal, we develop a unique knowledge-based amino acid potential that accounts for the temperature-dependent effects on solvent-mediated interactions for different types of amino acids. Remarkably, we are able to distinguish between more than 35 IDPs with upper or lower critical solution temperatures at experimental conditions, thus providing direct evidence that incorporating the temperature-dependent solvent-mediated interactions to IDP assemblies can capture the difference in the shape of the resulting phase diagrams. Given the success of the model in predicting experimental behavior, we use it as a high-throughput screening framework to scan through millions of disordered sequences to characterize the composition dependence of protein phase separation.

Comparative Study of the Effects of Temperature and Pressure on the Water-Mediated Interactions between Apolar Nanoscale Solutes

We perform molecular dynamics simulations to study the effects of temperature and pressure on the water-mediated interaction (WMI) between two nanoscale (apolar) graphene plates at 240 ≤ T ≤ 400 K and -100 ≤ P ≤ 1200 MPa. These are thermodynamic conditions relevant to, for example, cooling-, heating-, compression-, and decompression-induced protein denaturation. We find that at all ( T, P) studied, the potential of mean force between the graphene plates, as a function of plate separation r, exhibits local minima at specific plate separations r = r _n that can accommodate n water layers ( n = 0,1,2,3). In particular, our results show that isobaric cooling and isothermal compression have a similar effect on WMI between the plates; both processes tend to suppress the attraction and ultimate collapse of the graphene plates by kinetically trapping the plates at the metastable states with r = r _n ( n > 0). In addition, isobaric heating and isothermal decompression also have a similar effect; both processes tend to reduce the range and strength of the interactions between the graphene plates. Interestingly, at low temperatures, the WMI between the plates is affected by crystallization. However, crystallization depends deeply on the water model considered, SPC/E and TIP4P/2005 water models, with the crystallization occurring at different ( T, P) conditions, into different forms of ice.

Differential Scanning Calorimetry Analysis of the Effects of Heat and Pressure on Protein Denaturation in Soy Flour Mixed with Various Types of Plasticizers

The effects of heat and pressure on protein denaturation in soy flour were explored by an experimental design that used pressure (atmospheric to 600 MPa), temperature (room to 90 °C), time (1 to 60 min), and type of aqueous plasticizer (NaCl, sucrose, betaine, and lactobionic acid (LBA)) as factors. When 50% (w/w) soy flour-water paste was high hydrostatic pressure (HHP)-treated for 20 min at 25 °C, the treatment at 200 MPa showed a small effect on denaturation of only the 7S soy globulin, but the treatment at 600 MPa showed a significant effect on denaturation of both the 7S and 11S soy globulins. The treatment at 60 °C showed a less-pronounced effect on denaturation of the 11S globulin, even at 600 MPa, but that at 90 °C showed a similar extent of denaturation of the 11S globulin at 600 MPa to that at 25 °C. Chaotropic 2N NaCl, 50% sucrose-, 50% betaine-, or 50% LBA-water solutions showed protective effects on protein denaturation during HHP treatment at 25 °C. Although LBA enhanced the extent of thermostability of soy protein less than did 2N NaCl, LBA exhibited better stabilization against pressure. The results from DSC analysis demonstrated that thermostable soy proteins were not always barostable.

Computational investigation of cold denaturation in the Trp-cage miniprotein

The functional native states of globular proteins become unstable at low temperatures, resulting in cold unfolding and impairment of normal biological function. Fundamental understanding of this phenomenon is essential to rationalizing the evolution of freeze-tolerant organisms and developing improved strategies for long-term preservation of biological materials. We present fully atomistic simulations of cold denaturation of an α-helical protein, the widely studied Trp-cage miniprotein. In contrast to the significant destabilization of the folded structure at high temperatures, Trp-cage cold denatures at 210 K into a compact, partially folded state; major elements of the secondary structure, including the α-helix, are conserved, but the salt bridge between aspartic acid and arginine is lost. The stability of Trp-cage's α-helix at low temperatures suggests a possible evolutionary explanation for the prevalence of such structures in antifreeze peptides produced by cold-weather species, such as Arctic char. Although the 310-helix is observed at cold conditions, its position is shifted toward Trp-cage's C-terminus. This shift is accompanied by intrusion of water into Trp-cage's interior and the hydration of buried hydrophobic residues. However, our calculations also show that the dominant contribution to the favorable energetics of low-temperature unfolding of Trp-cage comes from the hydration of hydrophilic residues.

Consistent Treatment of Hydrophobicity in Protein Lattice Models Accounts for Cold Denaturation

The hydrophobic effect stabilizes the native structure of proteins by minimizing the unfavorable interactions between hydrophobic residues and water through the formation of a hydrophobic core. Here, we include the entropic and enthalpic contributions of the hydrophobic effect explicitly in an implicit solvent model. This allows us to capture two important effects: a length-scale dependence and a temperature dependence for the solvation of a hydrophobic particle. This consistent treatment of the hydrophobic effect explains cold denaturation and heat capacity measurements of solvated proteins.

Contribution of Water to Pressure and Cold Denaturation of Proteins

The mechanisms of cold and pressure denaturation of proteins are matter of debate and are commonly understood as due to water-mediated interactions. Here, we study several cases of proteins, with or without a unique native state, with or without hydrophilic residues, by means of a coarse-grain protein model in explicit solvent. We show, using Monte Carlo simulations, that taking into account how water at the protein interface changes its hydrogen bond properties and its density fluctuations is enough to predict protein stability regions with elliptic shapes in the temperature-pressure plane, consistent with previous theories. Our results clearly identify the different mechanisms with which water participates to denaturation and open the perspective to develop advanced computational design tools for protein engineering.

A coarse-grained protein model in a water-like solvent

Simulations employing an explicit atom description of proteins in solvent can be computationally expensive. On the other hand, coarse-grained protein models in implicit solvent miss essential features of the hydrophobic effect, especially its temperature dependence, and have limited ability to capture the kinetics of protein folding. We propose a free space two-letter protein (“H-P”) model in a simple, but qualitatively accurate description for water, the Jagla model, which coarse-grains water into an isotropically interacting sphere. Using Monte Carlo simulations, we design protein-like sequences that can undergo a collapse, exposing the “Jagla-philic” monomers to the solvent, while maintaining a “hydrophobic” core. This protein-like model manifests heat and cold denaturation in a manner that is reminiscent of proteins. While this protein-like model lacks the details that would introduce secondary structure formation, we believe that these ideas represent a first step in developing a useful, but computationally expedient, means of modeling proteins.

Thermal stability of hydrophobic helical oligomers: a lattice simulation study in explicit water

We investigate the thermal stability of helical hydrophobic oligomers using a three-dimensional, water-explicit lattice model and the Wang-Landau Monte Carlo method. The degree of oligomer helicity is controlled by the parameter ε(mm) < 0, which mimics monomer-monomer hydrogen bond interactions leading to the formation of helical turns in atomistic proteins. We vary |ε(mm)| between 0 and 4.5 kcal/mol and therefore investigate systems ranging from flexible homopolymers (i.e., those with no secondary structure) to helical oligomers that are stable over a broad range of temperatures. We find that systems with |ε(mm)| ≤ 2.0 kcal/mol exhibit a broad thermal unfolding transition at high temperature, leading to an ensemble of random coils. In contrast, the structure of conformations involved in a second, low-temperature, transition is strongly dependent on |ε(mm)|. Weakly helical oligomers are observed when |ε(mm)| ≤ 1.0 kcal/mol and exhibit a low-temperature, cold-unfolding-like transition to an ensemble of strongly water-penetrated globular conformations. For higher |ε(mm)| (1.7 kcal/mol ≤ |ε(mm)| ≤ 2.0 kcal/mol), cold unfolding is suppressed, and the low-temperature conformational transition becomes a "crystallization", in which a "molten" helix is transformed into a defect-free helix. The molten helix preserves ≥50% of the helical contacts observed in the "crystal" at a lower temperature. When |ε(mm)| = 4.5 kcal/mol, we find that conformational transitions are largely suppressed within the range of temperatures investigated.

Role of hydrophobic hydration in protein stability: a 3D water-explicit protein model exhibiting cold and heat denaturation

We investigate the microscopic mechanism of cold and heat denaturation using a 3D lattice model of a hydrated protein in which water is represented explicitly. The water model, which incorporates directional bonding and tetrahedral geometry, captures many aspects of water thermodynamics and properly describes hydrophobic hydration around apolar solutes because the hydrogen bonding rules in the model were gleaned from off-lattice atomistic simulations of water around representative protein structures. By incorporating local chain stiffness in the protein model, a homopolymer can fold into a β-hairpin. It is shown that the homopolymer can be folded by either attractive interactions between the monomers or as a direct consequence of the entropic cost of forming interfacial hydrogen bonds in the solvent. However, cold denaturation is not observed if the collapse transition is induced by intramolecular attractions. We further find that it is the changes in hydrophobic hydration with decreasing temperature that drive cold unfolding and that the overall process is enthalpically driven, whereas heat denaturation is entropically driven.

Hydrophobic nanoconfinement suppresses fluctuations in supercooled water

We perform very efficient Monte Carlo simulations to study the phase diagram of a water monolayer confined in a fixed disordered matrix of hydrophobic nanoparticles between two hydrophobic plates. We consider different hydrophobic nanoparticle concentrations c. We adopt a coarse-grained model of water that, for c = 0, displays a first-order liquid-liquid phase transition (LLPT) line with negative slope in the pressure-temperature (P-T) plane, ending in a liquid-liquid critical point at about 174 K and 0.13 GPa. We show that upon increase of c the liquid-gas spinodal and the temperature of the maximum density line are shifted with respect to the c = 0 case. We also find dramatic changes in the region around the LLPT. In particular, we observe a substantial (more than 90%) decrease of isothermal compressibility, thermal expansion coefficient and constant-pressure specific heat upon increasing c, consistent with recent experiments. Moreover, we find that a hydrophobic nanoparticle concentration as small as c = 2.4% is enough to destroy the LLPT for P ≥ 0.16 GPa. The fluctuations of volume apparently diverge at P ≈ 0.16 GPa, suggesting that the LLPT line ends in an LL critical point at 0.16 GPa. Therefore, nanoconfinement reduces the range of P-T where the LLPT is observable. By increasing the hydrophobic nanoparticle concentration c, the LLPT becomes weaker and its P-T range smaller. The model allows us to explain these phenomena in terms of a proliferation of interfaces among domains with different local order, promoted by the hydrophobic effect of the water-hydrophobic-nanoparticle interfaces.

Understanding the role of hydrogen bonds in water dynamics and protein stability

The mechanisms of cold and pressure denaturation of proteins are a matter of debate, but it is commonly accepted that water plays a fundamental role in the process. It has been proposed that the denaturation process is related to an increase of hydrogen bonds among hydration water molecules. Other theories suggest that the causes of denaturation are the density fluctuations of surface water, or the destabilization of hydrophobic contacts as a consequence of water molecule inclusions inside the protein, especially at high pressures. We review some theories that have been proposed to give insight into this problem, and we describe a coarse-grained model of water that compares well with experiments for proteins' hydration water. We introduce its extension for a homopolymer in contact with the water monolayer and study it by Monte Carlo simulations in an attempt to understand how the interplay of water cooperativity and interfacial hydrogen bonds affects protein stability.

Large decrease of fluctuations for supercooled water in hydrophobic nanoconfinement

Using Monte Carlo simulations, we study a coarse-grained model of a water layer confined in a fixed disordered matrix of hydrophobic nanoparticles at different particle concentrations c. For c=0, we find a first-order liquid-liquid phase transition (LLPT) ending in one critical point at low pressure P. For c>0, our simulations are consistent with a LLPT line ending in two critical points at low and high P. For c=25%, at high P and low temperature, we find a dramatic decrease of compressibility, thermal expansion coefficient, and specific heat. Surprisingly, the effect is present also for c as low as 2.4%. We conclude that even a small presence of hydrophobic nanoparticles can drastically suppress thermodynamic fluctuations, making the detection of the LLPT more difficult.

Studying pressure denaturation of a protein by molecular dynamics simulations

Many globular proteins unfold when subjected to several kilobars of hydrostatic pressure. This "unfolding-up-on-squeezing" is counter-intuitive in that one expects mechanical compression of proteins with increasing pressure. Molecular simulations have the potential to provide fundamental understanding of pressure effects on proteins. However, the slow kinetics of unfolding, especially at high pressures, eliminates the possibility of its direct observation by molecular dynamics (MD) simulations. Motivated by experimental results-that pressure denatured states are water-swollen, and theoretical results-that water transfer into hydrophobic contacts becomes favorable with increasing pressure, we employ a water insertion method to generate unfolded states of the protein Staphylococcal Nuclease (Snase). Structural characteristics of these unfolded states-their water-swollen nature, retention of secondary structure, and overall compactness-mimic those observed in experiments. Using conformations of folded and unfolded states, we calculate their partial molar volumes in MD simulations and estimate the pressure-dependent free energy of unfolding. The volume of unfolding of Snase is negative (approximately -60 mL/mol at 1 bar) and is relatively insensitive to pressure, leading to its unfolding in the pressure range of 1500-2000 bars. Interestingly, once the protein is sufficiently water swollen, the partial molar volume of the protein appears to be insensitive to further conformational expansion or unfolding. Specifically, water-swollen structures with relatively low radii of gyration have partial molar volume that are similar to that of significantly more unfolded states. We find that the compressibility change on unfolding is negligible, consistent with experiments. We also analyze hydration shell fluctuations to comment on the hydration contributions to protein compressibility. Our study demonstrates the utility of molecular simulations in estimating volumetric properties and pressure stability of proteins, and can be potentially extended for applications to protein complexes and assemblies.

The effect of hydrogen bonding on the solvent-mediated interaction of composite plates

When two solute particles in water sufficiently approach each other, the disruption of water-water hydrogen bonds in their first hydration layers gives rise to an additional contribution to their overall interaction. Here we present a probabilistic approach to examining interactions between two identical parallel plates whereof the surfaces are covered with uniformly distributed hydrophobic and hydrophilic sites. The proposed approach allows one to determine the average number of hydrogen bonds per water molecule in the first hydration shell of a plate. Because of the constraint imposed by the proximity to the plate, a water molecule forms less hydrogen bond in this shell than in the bulk medium. As a result, the water molecules prefer the latter to the former, even though a bond is stronger in the former than in the latter. The interplay of these factors results in an additional contribution to the overall plate interaction which is attractive and naturally short-range, appearing only when the distance between the plates is smaller than five lengths of a hydrogen bond. At a given distance, it monotonically increases from 0 to its maximum value as the fraction of hydrophobic surface area on a plate increases from 0 to 1. When this fraction is 0.5, this contribution can be up to two orders of magnitude larger than the van der Waals interaction (depending on the water density in the vicinity of a plate).

The effect of sequence on the conformational stability of a model heteropolymer in explicit water

We investigate the properties of a two-dimensional lattice heteropolymer model for a protein in which water is explicitly represented. The model protein distinguishes between hydrophobic and polar monomers through the effect of the hydrophobic monomers on the entropy and enthalpy of the hydrogen bonding of solvation shell water molecules. As experimentally observed, model heteropolymer sequences fold into stable native states characterized by a hydrophobic core to avoid unfavorable interactions with the solvent. These native states undergo cold, pressure, and thermal denaturation into distinct configurations for each type of unfolding transition. However, the heteropolymer sequence is an important element, since not all sequences will fold into stable native states at positive pressures. Simulation of a large collection of sequences indicates that these fall into two general groups, those exhibiting highly stable native structures and those that do not. Statistical analysis of important patterns in sequences shows a strong tendency for observing long blocks of hydrophobic or polar monomers in the most stable sequences. Statistical analysis also shows that alternation of hydrophobic and polar monomers appears infrequently among the most stable sequences. These observations are not absolute design rules and, in practice, these are not sufficient to rationally design very stable heteropolymers. We also study the effect of mutations on improving the stability of the model proteins, and demonstrate that it is possible to obtain a very stable heteropolymer from directed evolution of an initially unstable heteropolymer.