Four-states phase diagram of proteins

A four states phase diagram for protein folding as a function of temperature and solvent quality is derived from an improved 2-d lattice model taking into account the temperature dependence of the hydrophobic effect. The phase diagram exhibits native, globule and two coil-type regions. In agreement with experiment, the model reproduces the phase transitions indicative of both warm and cold denaturations. Finally, it predicts transitions between the two coil states and a critical point.Comment: 7 pages, 5 figures. Accepted for publication in Europhysics Letter

Origin of entropy convergence in hydrophobic hydration and protein folding

An information theory model is used to construct a molecular explanation why hydrophobic solvation entropies measured in calorimetry of protein unfolding converge at a common temperature. The entropy convergence follows from the weak temperature dependence of occupancy fluctuations for molecular-scale volumes in water. The macroscopic expression of the contrasting entropic behavior between water and common organic solvents is the relative temperature insensitivity of the water isothermal compressibility. The information theory model provides a quantitative description of small molecule hydration and predicts a negative entropy at convergence. Interpretations of entropic contributions to protein folding should account for this result.Comment: Phys. Rev. Letts. (in press 1996), 3 pages, 3 figure

Warm and Cold Denaturation in the Phase Diagram of a Protein Lattice Model

Studying the properties of the solvent around proteins, we propose a much more sophisticated model of solvation than temperature-independent pairwise interactions between monomers, as is used commonly in lattice representations. We applied our model of solvation to a 16-monomer chain constrained on a two-dimensional lattice. We compute a phase diagram function of the temperature and a solvent parameter which is related to the pH of the solution. It exhibits a native state in which the chain coalesces into a unique compact conformation as well as a denatured state. Under certain solvation conditions, both warm and cold denaturations occur between the native and the denatured states. A good agreement is found with the data obtained from calorimetric experiments, thereby validating the proposed model.Comment: 7 pages, 2 figure

Growth of fat slits and dispersionless KP hierarchy

A "fat slit" is a compact domain in the upper half plane bounded by a curve with endpoints on the real axis and a segment of the real axis between them. We consider conformal maps of the upper half plane to the exterior of a fat slit parameterized by harmonic moments of the latter and show that they obey an infinite set of Lax equations for the dispersionless KP hierarchy. Deformation of a fat slit under changing a particular harmonic moment can be treated as a growth process similar to the Laplacian growth of domains in the whole plane. This construction extends the well known link between solutions to the dispersionless KP hierarchy and conformal maps of slit domains in the upper half plane and provides a new, large family of solutions.Comment: 26 pages, 6 figures, typos correcte

Construction of Reversible Lattice Molecular Automata

Several cellular automata (CA) models have been developed to simulate self-organization of multiple levels of structures. However, they do not obey microscopic reversibility and conservation laws. In this paper, we describe the construction of a reversible lattice molecular automata (RLMA) model, which simulates molecular interaction and self-organization of higher-order structures. The model's strict reversibility entails physically relevant conservation laws, and thus opens a way to precise application and validation of the methods from statistical physics in studying the necessary conditions for such multiple levels of self-organization.Comment: 29 pages, 20 figure

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 non-polar 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.Comment: 11 pages, 10 figures; some rearrangement of introduction and discussion sections, streamlining of formalism and general compression; to appear in Phys. Rev.

A 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 ($\approx2$ kbar), 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.Comment: 4 pages for double column and single space. 3 figures Added references Changed conten

Quantifying Self-Organization with Optimal Predictors

Despite broad interest in self-organizing systems, there are few quantitative, experimentally-applicable criteria for self-organization. The existing criteria all give counter-intuitive results for important cases. In this Letter, we propose a new criterion, namely an internally-generated increase in the statistical complexity, the amount of information required for optimal prediction of the system's dynamics. We precisely define this complexity for spatially-extended dynamical systems, using the probabilistic ideas of mutual information and minimal sufficient statistics. This leads to a general method for predicting such systems, and a simple algorithm for estimating statistical complexity. The results of applying this algorithm to a class of models of excitable media (cyclic cellular automata) strongly support our proposal.Comment: Four pages, two color figure

The effect of local thermal fluctuations on the folding kinetics: a study from the perspective of the nonextensive statistical mechanics

Protein folding is a universal process, very fast and accurate, which works consistently (as it should be) in a wide range of physiological conditions. The present work is based on three premises, namely: ($i$) folding reaction is a process with two consecutive and independent stages, namely the search mechanism and the overall productive stabilization; ($ii$) the folding kinetics results from a mechanism as fast as can be; and ($iii$) at nanoscale dimensions, local thermal fluctuations may have important role on the folding kinetics. Here the first stage of folding process (search mechanism) is focused exclusively. The effects and consequences of local thermal fluctuations on the configurational kinetics, treated here in the context of non extensive statistical mechanics, is analyzed in detail through the dependence of the characteristic time of folding ($\tau$) on the temperature $T$ and on the nonextensive parameter $q$.The model used consists of effective residues forming a chain of 27 beads, which occupy different sites of a $3-$D infinite lattice, representing a single protein chain in solution. The configurational evolution, treated by Monte Carlo simulation, is driven mainly by the change in free energy of transfer between consecutive configurations. ...Comment: 19 pages, 3 figures, 1 tabl

Lattice model for cold and warm swelling of polymers in water

We define a lattice model for the interaction of a polymer with water. We solve the model in a suitable approximation. In the case of a non-polar homopolymer, for reasonable values of the parameters, the polymer is found in a non-compact conformation at low temperature; as the temperature grows, there is a sharp transition towards a compact state, then, at higher temperatures, the polymer swells again. This behaviour closely reminds that of proteins, that are unfolded at both low and high temperatures.Comment: REVTeX, 5 pages, 2 EPS figure