Putting proteins back into water

Asymmetry in Polymer-Solvent Interactions Yields Complex Thermoresponsive Behavior

We introduce a lattice framework that incorporates elements of Flory-Huggins solution theory and the q-state Potts model to study the phase behavior of polymer solutions and single-chain conformational characteristics. Without empirically introducing temperature-dependent interaction parameters, standard Flory-Huggins theory describes systems that are either homogeneous across temperatures or exhibit upper critical solution temperatures. The proposed Flory-Huggins-Potts framework extends these capabilities by predicting lower critical solution temperatures, miscibility loops, and hourglass-shaped spinodal curves. We particularly show that including orientation-dependent interactions, specifically between monomer segments and solvent particles, is alone sufficient to observe such phase behavior. Signatures of emergent phase behavior are found in single-chain Monte Carlo simulations, which display heating- and cooling-induced coil-globule transitions linked to energy fluctuations. The framework also capably describes a range of experimental systems. Importantly, and by contrast to many prior theoretical approaches, the framework does not employ any temperature- or composition-dependent parameters. This work provides new insights regarding the microscopic physics that underpin complex thermoresponsive behavior in polymers.

A many-body term improves the accuracy of effective potentials based on protein coevolutionary data

The study of correlated mutations in alignments of homologous proteins proved to be successful not only in the prediction of their native conformation but also in the development of a two-body effective potential between pairs of amino acids. In the present work, we extend the effective potential, introducing a many-body term based on the same theoretical framework, making use of a principle of maximum entropy. The extended potential performs better than the two-body one in predicting the energetic effect of 308 mutations in 14 proteins (including membrane proteins). The average value of the parameters of the many-body term correlates with the degree of hydrophobicity of the corresponding residues, suggesting that this term partly reflects the effect of the solvent.

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.

Sequence determines degree of knottedness in a coarse-grained protein model

Knots are abundant in globular homopolymers but rare in globular proteins. To shed new light on this long-standing conundrum, we study the influence of sequence on the formation of knots in proteins under native conditions within the framework of the hydrophobic-polar lattice protein model. By employing large-scale Wang-Landau simulations combined with suitable Monte Carlo trial moves we show that even though knots are still abundant on average, sequence introduces large variability in the degree of self-entanglements. Moreover, we are able to design sequences which are either almost always or almost never knotted. Our findings serve as proof of concept that the introduction of just one additional degree of freedom per monomer (in our case sequence) facilitates evolution towards a protein universe in which knots are rare.

Generic folding and transition hierarchies for surface adsorption of hydrophobic-polar lattice model proteins

The thermodynamic behavior and structural properties of hydrophobic-polar (HP) lattice proteins interacting with attractive surfaces are studied by means of Wang-Landau sampling. Three benchmark HP sequences (48mer, 67mer, and 103mer) are considered with different types of surfaces, each of which attract either all monomers, only hydrophobic (H) monomers, or only polar (P) monomers, respectively. The diversity of folding behavior in dependence of surface strength is discussed. Analyzing the combined patterns of various structural observables, such as, e.g., the derivatives of the numbers of surface contacts, together with the specific heat, we are able to identify generic categories of folding and transition hierarchies. We also infer a connection between these transition categories and the relative surface strengths, i.e., the ratio of the surface attractive strength to the interchain attraction among H monomers. The validity of our proposed classification scheme is reinforced by the analysis of additional benchmark sequences. We thus believe that the folding hierarchies and identification scheme are generic for HP proteins interacting with attractive surfaces, regardless of chain length, sequence, or surface attraction.

Unifying microscopic mechanism for pressure and cold denaturations of proteins

We study the stability of globular proteins as a function of temperature and pressure through NPT simulations of a coarse-grained model. We reproduce the elliptical stability of proteins and highlight a unifying microscopic mechanism for pressure and cold denaturations. The mechanism involves the solvation of nonpolar residues with a thin layer of water. These solvated states have lower volume and lower hydrogen-bond energy compared to other conformations of nonpolar solutes. Hence, these solvated states are favorable at high pressure and low temperature, and they facilitate protein unfolding under these thermodynamical conditions.

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.

Competition for hydrogen-bond formation in the helix-coil transition and protein folding

The problem of the helix-coil transition of biopolymers in explicit solvents, such as water, with the ability for hydrogen bonding with a solvent is addressed analytically using a suitably modified version of the Generalized Model of Polypeptide Chains. Besides the regular helix-coil transition, an additional coil-helix or reentrant transition is also found at lower temperatures. The reentrant transition arises due to competition between polymer-polymer and polymer-water hydrogen bonds. The balance between the two types of hydrogen bonding can be shifted to either direction through changes not only in temperature, but also by pressure, mechanical force, osmotic stress, or other external influences. Both polypeptides and polynucleotides are considered within a unified formalism. Our approach provides an explanation of the experimental difficulty of observing the reentrant transition with pressure and underscores the advantage of pulling experiments for studies of DNA. Results are discussed and compared with those reported in a number of recent publications with which a significant level of agreement is obtained.

A theoretical analysis on characteristics of protein structures induced by cold denaturation

Yeast frataxin is a protein exhibiting cold denaturation at an exceptionally high temperature (280 K). We show that the microscopic mechanism of cold denaturation, which has recently been suggested by us [Yoshidome and Kinoshita, Phys. Rev. E 79, 030905(R) (2009)], is also applicable to yeast frataxin. The hybrid of the angle-dependent integral equation theory combined with the multipolar water model and the morphometric approach is employed for calculating hydration thermodynamic quantities of the protein with a prescribed structure. In order to investigate the characteristics of the cold-denatured structures of yeast frataxin, we consider the entropy change upon denaturation comprising the loss of the water entropy and the gain in the protein conformational entropy. The minimum and maximum values of the conformational-entropy gain (i.e., the range within which the exact value lies) are estimated via two routes. The range of the water-entropy loss is then determined from the entropy change experimentally obtained [Pastore et al., J. Am. Chem. Soc. 129, 5374 (2007)]. We calculate the water-entropy loss upon the transition from the native structure to a variety of unfolded structures. We then select the unfolded structures for which the water-entropy loss falls within the determined range. The selection is performed at cold and heat denaturation temperatures of yeast frataxin. The structures characterizing cold and heat denaturations are thus obtained. It is found that the average values of the radius of gyration, excluded volume, and water-accessible surface area for the cold-denatured structures are almost the same as those for the heat-denatured ones. We theoretically estimate the cold denaturation temperature of yeast frataxin from the experimental data for the enthalpy, entropy, and heat-capacity changes upon denaturation. The finding is that the temperature is considerably higher than 273 K. These results are in qualitatively good accord with the experimental observations.

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 hydrophobic effect and its role in cold denaturation

The hydrophobic effect is considered the main driving force for protein folding and plays an important role in the stability of those biomolecules. Cold denaturation, where the native state of the protein loses its stability upon cooling, is also attributed to this effect. It is therefore not surprising that a lot of effort has been spent in understanding this phenomenon. Despite these efforts, many unresolved fundamental aspects remain. In this paper we review and summarize the thermodynamics of proteins, the hydrophobic effect and cold denaturation. We start by accounting for these phenomena macroscopically then move to their atomic-level description. We hope this review will help the reader gain insights into the role played by the hydrophobic effect in cold denaturation.

Microscopic mechanism for cold denaturation

We elucidate the mechanism of cold denaturation through constant-pressure simulations for a model of hydrophobic molecules in an explicit solvent. We find that the temperature dependence of the hydrophobic effect induces, facilitates, and is the driving force for cold denaturation. The physical mechanism underlying this phenomenon is identified as the destabilization of hydrophobic contact in favor of solvent-separated configurations, the same mechanism seen in pressure-induced denaturation. A phenomenological explanation proposed for the mechanism is suggested as being responsible for cold denaturation in real proteins.

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

We investigate the effect of temperature and pressure on polypeptide conformational stability using a two-dimensional square lattice model in which water is represented explicitly. The model captures many aspects of water thermodynamics, including the existence of density anomalies, and we consider here the simplest representation of a protein: a hydrophobic homopolymer. We show that an explicit treatment of hydrophobic hydration is sufficient to produce cold, pressure, and thermal denaturation. We investigate the effects of the enthalpic and entropic components of the water-protein interactions on the overall folding phase diagram, and show that even a schematic model such as the one we consider yields reasonable values for the temperature and pressure ranges within which highly compact homopolymer configurations are thermodynamically stable.

The correlation of cold denaturation temperature with surface stability factor of proteins

Cold denaturation is an intriguing phenomenon in protein denaturation for elucidating protein accessible surface area (ASA). Compared to the impact of protein surface, the importance of protein-water interactions in cold denaturation may be ruled out significantly. Here, based on the ASA, we have defined a new factor, the surface stability factor (SSF). From the SSF, in combination with the cold denaturation temperature (T(g')) or temperature at DeltaS = 0 (T(s)) of a given protein, one can predict the percent of hydrophobic surface area (H), percent of total surface there on positive and negative charge sum (effective charge) be zero (C), percent of patches hydrophobicity (HP) and others critical surface parameters without any need to the crystallographic data.

Low-temperature-induced swelling of a hydrophobic polymer: A lattice approach

The authors investigate equilibrium properties of a simple model of hydrophobic polymer in aqueous solution by means of dynamic Monte Carlo simulations. The solvent is described by a simplified two-dimensional model, defined on a triangular lattice, which has been previously shown to account for most thermodynamic anomalies of pure water and of hydrophobic solvation for monomeric solutes. The polymer is modeled as a self-avoiding walk on the same lattice. In this framework, the degrees of freedom of water are taken into account explicitly, and in principle there is no need to introduce effective self-contact interactions for the polymer in order to mimic the hydrophobic effect. In certain conditions, the authors observe low-temperature-induced swelling, i.e., expansion of the polymer globule upon decreasing temperature. The authors discuss the relationship between this phenomenon and the anomalous properties of the solvent.

Effective interactions between chaotropic agents and proteins

Chaotropic agents are cosolutes that can disrupt the hydrogen bonding network between water molecules and reduce the stability of the native state of proteins by weakening the hydrophobic effect. In this work, we represent the chaotropic agent as a factor that reduces the amount of order in the structures formed by water molecules, both in the bulk and the hydration shells around hydrophobic amino acids. In this framework we show that low chaotrope concentrations lead to a destabilization of the native state of proteins, and that high concentrations induce complete denaturation. We also find that the reduction of the number of bulk ordered states of water molecules can give origin to an effective interaction between chaotropic molecules and proteins.

On the hydration heat capacity change of benzene

The heat capacity change associated with the hydration of benzene is a large and positive quantity, but it is significantly smaller than that associated with the hydration of an alkane having the same accessible surface area of benzene, the corresponding alkane. This large difference merits attention and should be rationalized. This task is performed by means of the two-state Muller's model for the reorganization of H-bonds. It results that: (a) the hydration shell of both hydrocarbons consists of H-bonds that are enthalpically stronger but slightly more broken than those in bulk water; (b) the hydration shell of benzene consists, on average, of enthalpically slightly weaker H-bonds with respect to the corresponding alkane. The latter feature, due to the presence of the weak benzene-water H-bonds, is the physical cause of the large difference in the hydration heat capacity change, according to the two-state Muller's model.

Low-temperature and high-pressure induced swelling of a hydrophobic polymer-chain in aqueous solution

We report molecular dynamics simulations of a hydrophobic polymer-chain in aqueous solution between 260 K and 420 K at pressures of 1 bar, 3000 bar, and 4500 bar. The simulations reveal a hydrophobically collapsed structure at low pressures and high temperatures. At 3000 bar and about 260 K and at 4500 bar and about 260 K, however, an abrupt transition to a swelled state is observed. The transition is driven by a smaller volume and a remarkably strong lower enthalpy of the swelled state, indicating a steep positive slope of the corresponding transition line. The swelling is strongly stabilized by the energetically favorable state of water in the polymer's hydrophobic first hydration shell at low temperatures. This finding is consistent with the observation of a positive heat capacity of hydrophobic solvation. Moreover, the slope and location of the estimated swelling transition line for the collapsed hydrophobic chain coincides remarkably well with the cold denaturation transition of proteins.

Unifying temperature effects on the growth rate of bacteria and the stability of globular proteins

The specific growth rate constant for bacterial growth does not obey the Arrhenius-type kinetics displayed by simple chemical reactions. Instead, for bacteria, steep convex curves are observed on an Arrhenius plot at the low- and high-temperature ends of the biokinetic range, with a region towards the middle of the growth range loosely approximating linearity. This central region has been considered by microbiologists to be the "normal physiological range" for bacterial growth, a concept whose meaningfulness we now question. We employ a kinetic model incorporating thermodynamic terms for temperature-induced enzyme denaturation, central to which is a term to account for the large positive heat capacity change during unfolding of the proteins within the bacteria. It is now widely believed by biophysicists that denaturation of complex proteins and/or other macromolecules is due to hydrophobic hydration of non-polar compounds. Denaturation is seen as the process by which enthalpic and entropic forces becomes imbalanced both at high and at low temperatures resulting in conformational changes in the enzyme structure that expose hydrophobic amino acid groups to the surrounding water molecules. The "thermodynamic" rate model, incorporating the heat capacity change and its effect on the enthalpy and entropy of the system, fitted 35 sets of data for psychrophilic, psychrotrophic, mesophilic and thermophilic bacteria well, resulting in biologically meaningful estimates for the important thermodynamic parameters. As these results mirror those obtained by biophysicists for globular proteins, it appears that the same or a similar mechanism applies to bacteria as applies to proteins.

Temperature Dependence of Three-Body Hydrophobic Interactions: Potential of Mean Force, Enthalpy, Entropy, Heat Capacity, and Nonadditivity

Temperature-dependent three-body hydrophobic interactions are investigated by extensive constant-pressure simulations of methane-like nonpolar solutes in TIP4P model water at six temperatures. A multiple-body hydrophobic interaction is considered to be (i) additive, (ii) cooperative, or (iii) anti-cooperative if its potential of mean force (PMF) is (i) equal to, (ii) smaller than, or (iii) larger than the corresponding pairwise sum of two-methane PMFs. We found that three-methane hydrophobic interactions at the desolvation barrier are anti-cooperative at low to intermediate T, and vary from essentially additive to slightly cooperative at high T. Interactions at the contact minimum are slightly anti-cooperative over a wider temperature range. Enthalpy, entropy, and heat capacity are estimated from the computed PMFs. Contrary to the common expectation that burial of solvent-accessible nonpolar surface area always leads to a decrease in heat capacity, the present results show that the change in heat capacity upon three-methane association is significantly positive at the desolvation barrier and slightly positive at the contact minimum. This suggests that the heat capacity signature of a hydrophobic polymer need not vary uniformly nor monotonically with conformational compactness. Ramifications for protein folding are discussed.

Analysis of PIN1 WW domain through a simple statistical mechanics model

We have applied a simple statistical mechanics Go-like model to the analysis of the PIN1 WW domain, resorting to mean field and Monte Carlo techniques to characterize its thermodynamics, and comparing the results with the wealth of available experimental data. PIN1 WW domain is a 39-residue protein fragment which folds on an antiparallel beta-sheet, thus representing an interesting model system to study the behavior of these secondary structure elements. Results show that the model correctly reproduces the two-state behavior of the protein, and also the trends of the experimental phi(T) values. Moreover, there is a good agreement between Monte Carlo results and the mean field ones, which can be obtained with a substantially smaller computational effort.

Kosmotropes and chaotropes: modelling preferential exclusion, binding and aggregate stability

Kosmotropic cosolvents added to an aqueous solution promote the aggregation of hydrophobic solute particles, while chaotropic cosolvents act to destabilise such aggregates. We discuss the mechanism for these phenomena within an adapted version of the two-state Muller-Lee-Graziano model for water, which provides a complete description of the ternary water/cosolvent/solute system for small solute particles. This model contains the dominant effect of a kosmotropic substance, which is to enhance the formation of water structure. The consequent preferential exclusion both of cosolvent molecules from the solvation shell of hydrophobic particles and of these particles from the solution leads to a stabilisation of aggregates. By contrast, chaotropic substances disrupt the formation of water structure, are themselves preferentially excluded from the solution, and thereby contribute to solvation of hydrophobic particles. We use Monte Carlo simulations to demonstrate at the molecular level the preferential exclusion or binding of cosolvent molecules in the solvation shell of hydrophobic particles, and the consequent enhancement or suppression of aggregate formation. We illustrate the influence of structure-changing cosolvents on effective hydrophobic interactions by modelling qualitatively the kosmotropic effect of sodium chloride and the chaotropic effect of urea.

Solvent-induced micelle formation in a hydrophobic interaction model

We investigate the aggregation of amphiphilic molecules by adapting the two-state Muller-Lee-Graziano model for water, in which a solvent-induced hydrophobic interaction is included implicitly. We study the formation of various types of micelle as a function of the distribution of hydrophobic regions at the molecular surface. Successive substitution of nonpolar surfaces by polar ones demonstrates the influence of hydrophobicity on the upper and lower critical solution temperatures. Aggregates of lipid molecules, described by a refinement of the model in which a hydrophobic tail of variable length interacts with different numbers of water molecules, are stabilized as the length of the tail increases. We demonstrate that the essential features of micelle formation are primarily solvent-induced, and are explained within a model which focuses only on the alteration of water structure in the vicinity of the hydrophobic surface regions of amphiphiles in solution.

Effective interactions cannot replace solvent effects in a lattice model of proteins

Protein folding and protein design are among the most challenging problems of the past ten years in biophysics and molecular biology. For a given protein, it is possible to extract, from existing protein databases, a set of specific (i.e., belonging to the investigated protein) effective amino-acid (AA) interactions able to stabilize the native state. On the other hand, attempts to find global effective AA interactions, which would be able to stabilize all proteins at once, failed. Using a simple lattice model where the solvent degrees of freedom are (semi)explicitly taken into account, we show that the absence of global effective AA interactions is due to the solvent and that on this lattice model the solvent effects cannot be reproduced by amino-acid effective interactions.

Possible mechanism for cold denaturation of proteins at high pressure

We study cold denaturation of proteins at high pressures. Using multicanonical Monte Carlo simulations of a model protein in a water bath, we investigate the effect of water density fluctuations on protein stability. We find that above the pressure where water freezes to the dense ice phase (approximately 2 kbars) the mechanism for cold denaturation with decreasing temperature is the loss of local low-density water structure. We find our results in agreement with data of bovine pancreatic ribonuclease A.

Non-arrhenius behavior in the unfolding of a short, hydrophobic alpha-helix. Complementarity of molecular dynamics and lattice model simulations

The unfolding of the last, C-terminal residue of AcNH(2)-(l-Leu)(11)-NHMe in its alpha-helical form has been investigated by measuring the variation of free energy involved in the alpha(R) to beta conformational transition. These calculations were performed using large-scale molecular dynamics simulations in conjunction with the umbrella sampling method. For different temperatures ranging from 280 to 370 K, the free energy of activation was estimated. Concurrently, unfolding simulations of a homopolypeptide formed by twelve hydrophobic residues were carried out, employing a three-dimensional lattice model description of the peptide, with a temperature-dependent interaction potential. Using a Monte Carlo approach, the lowest free energy conformation, an analogue of a right-handed alpha-helix, was determined in the region where the peptide chain is well ordered. The free energy barrier separating this state from a distinct, compact conformation, analogue to a beta-strand, was determined over a large enough range of temperatures. The results of these molecular dynamics and lattice model simulations are consistent and indicate that the kinetics of the unfolding of a hydrophobic peptide exhibits a non-Arrhenius behavior closely related to the temperature dependence of the hydrophobic effect. These results further illuminate the necessity to include a temperature dependence in potential energy functions designed for coarse-grained models of proteins.

Design of lattice proteins with explicit solvent

Protein design is important to develop new drugs. As such, a knowledge of the correct model to use to design novel proteins is of the utmost importance. Here we show that a simple model where the solvent degrees of freedom are (semi)explicitly taken into account performs better than other existing models when compared to real data. Some consequences on the criteria to be used for protein design are discussed.

Statistical properties of contact vectors

We study the statistical properties of contact vectors, a construct to characterize a protein's structure. The contact vector of an N-residue protein is a list of N integers n(i), representing the number of residues in contact with residue i. We study analytically (at mean-field level) and numerically the amount of structural information contained in a contact vector. Analytical calculations reveal that a large variance in the contact numbers reduces the degeneracy of the mapping between contact vectors and structures. Exact enumeration for lengths up to N=16 on the three-dimensional cubic lattice indicates that the growth rate of number of contact vectors as a function of N is only 3% less than that for contact maps. In particular, for compact structures we present numerical evidence that, practically, each contact vector corresponds to only a handful of structures. We discuss how this information can be used for better structure prediction.

Cold denaturation of proteins under high pressure

The advantageous usage of the high pressure technique in studies of cold denaturation of proteins is reviewed, with a brief explanation of the theoretical background of this universal phenomenon. Various experimental results are presented and discussed, explaining the plausible image of the cold denatured state of proteins. In order to understand more clearly this phenomenon and protein structure transition in general, several studies on model polymer systems are also reviewed.

Apolar and polar solvation thermodynamics related to the protein unfolding process

Thermodynamics related to hydrated water upon protein unfolding is studied over a broad temperature range (5-125 degrees C). The hydration effect arising from the apolar interior is modeled as an increased number of hydrogen bonds between water molecules compared with bulk water. The corresponding contribution from the polar interior is modeled as a two-step process. First, the polar interior breaks hydrogen bonds in bulk water upon unfolding. Second, due to strong bonds between the polar surface and the nearest water molecules, we assume quantization using a simplified two-state picture. The heat capacity change upon hydration is compared with model compound data evaluated previously for 20 different proteins. We obtain good correspondence with the data for both the apolar and the polar interior. We note that the effective coupling constants for both models have small variations among the proteins we have investigated.

Bethe approximation for a model of polymer solvation

The phase diagram of a recently proposed model for the solvation of monomers and polymers in water is studied in the homopolymer case, and several thermodynamic quantities are computed by means of pair approximation of the cluster variation method, i.e., the Bethe approximation. The model takes into account the water degrees of freedom in a simplified way, so that they can be integrated out analytically. The resulting effective Hamiltonian contains only a temperature-dependent water-monomer interaction and its phase diagram can be easily studied thanks to the simplicity of the Bethe approximation and exhibits, for a hydrophobic polymer, both cold and warm unfolding transitions in a wide region of the parameter space. This suggests that the present one might be a toy-model description of the phase behavior observed experimentally in water solutions of hydrophobic polymers, such as poly-N-isopropylacrylamide (PNIPAM), as well as a step to understand the mechanism of cold unfolding in proteins.

Model for the hydration of nonpolar compounds and polymers

We introduce an exactly solvable statistical-mechanical model of the hydration of nonpolar compounds, based on grouping water molecules in clusters where hydrogen bonds and isotropic interactions occur; interactions between clusters are neglected. Analytical results show that an effective strengthening of hydrogen bonds in the presence of the solute, together with a geometric reorganization of water molecules, are enough to yield hydrophobic behavior. We extend our model to describe a nonpolar homopolymer in aqueous solution, obtaining a clear evidence of both "cold" and "warm" swelling transitions. This suggests that our model could be relevant to describe some features of protein folding.

Cold and warm swelling of hydrophobic polymers

We introduce a polymer model where the transition from swollen to compact configurations is due to interactions between the monomers and the solvent. These interactions are the origin of the effective attractive interactions between hydrophobic amino acids in proteins. We find that in the low and high temperature phases polymers are swollen, and there is an intermediate phase where the most favorable configurations are compact. We argue that such a model captures in a single framework both the cold and the warm denaturation experimentally detected for thermosensitive polymers and for proteins.