Delineation of the Native Basin in Continuum Models of Proteins

We propose two approaches for determining the native basins in off-lattice models of proteins. The first of them is based on exploring the saddle points on selected trajectories emerging from the native state. In the second approach, the basin size can be determined by monitoring random distortions in the shape of the protein around the native state. Both techniques yield the similar results. As a byproduct, a simple method to determine the folding temperature is obtained.Comment: REVTeX, 6 pages, 5 EPS figure

Dynamical chaos and power spectra in toy models of heteropolymers and proteins

The dynamical chaos in Lennard-Jones toy models of heteropolymers is studied by molecular dynamics simulations. It is shown that two nearby trajectories quickly diverge from each other if the heteropolymer corresponds to a random sequence. For good folders, on the other hand, two nearby trajectories may initially move apart but eventually they come together. Thus good folders are intrinsically non-chaotic. A choice of a distance of the initial conformation from the native state affects the way in which a separation between the twin trajectories behaves in time. This observation allows one to determine the size of a folding funnel in good folders. We study the energy landscapes of the toy models by determining the power spectra and fractal characteristics of the dependence of the potential energy on time. For good folders, folding and unfolding trajectories have distinctly different correlated behaviors at low frequencies.Comment: 8 pages, 9 EPS figures, Phys. Rev. E (in press

Nonlinear AC resistivity in s-wave and d-wave disordered granular superconductors

We model s-wave and d-wave disordered granular superconductors with a three-dimensional lattice of randomly distributed Josephson junctions with finite self-inductance. The nonlinear ac resistivity of these systems was calculated using Langevin dynamical equations. The current amplitude dependence of the nonlinear resistivity at the peak position is found to be a power law characterized by exponent $\alpha$. The later is not universal but depends on the self-inductance and current regimes. In the weak current regime $\alpha$ is independent of the self-inductance and equal to 0.5 or both of s- and d-wave materials. In the strong current regime this exponent depends on the screening. We find $\alpha \approx 1$ for some interval of inductance which agrees with the experimental finding for d-wave ceramic superconductors.Comment: 4 pages, 5 figures, to appear in Phys. Rev. Let

Universal geometrical factor of protein conformations as a consequence of energy minimization

The biological activity and functional specificity of proteins depend on their native three-dimensional structures determined by inter- and intra-molecular interactions. In this paper, we investigate the geometrical factor of protein conformation as a consequence of energy minimization in protein folding. Folding simulations of 10 polypeptides with chain length ranging from 183 to 548 residues manifest that the dimensionless ratio (V/(A)) of the van der Waals volume V to the surface area A and average atomic radius of the folded structures, calculated with atomic radii setting used in SMMP [Eisenmenger F., et. al., Comput. Phys. Commun., 138 (2001) 192], approach 0.49 quickly during the course of energy minimization. A large scale analysis of protein structures show that the ratio for real and well-designed proteins is universal and equal to 0.491\pm0.005. The fractional composition of hydrophobic and hydrophilic residues does not affect the ratio substantially. The ratio also holds for intrinsically disordered proteins, while it ceases to be universal for polypeptides with bad folding properties.Comment: 6 pages, 1 table, 4 figure

Aging Effect in Ceramic Superconductors

A three-dimensional lattice of the Josephson junctions with a finite self-conductance is employed to model ceramic superconductors. Using Monte Carlo simulations it is shown that the aging disappears in the strong screening limit. In the weeak screening regime aging is present even at low temperatures. For intermediate values of the self-inductance aging occurs at intermediate temperatures interval but is suppressed entirely at high and low temperatures. Our results are in good agreement with experiments.Comment: 5 pages, 5 eps figures, to appear in Physical Review Letter

Finite size effects on thermal denaturation of globular proteins

Finite size effects on the cooperative thermal denaturation of proteins are considered. A dimensionless measure of cooperativity, Omega, scales as N^zeta, where N is the number of amino acids. Surprisingly, we find that zeta is universal with zeta = 1 + gamma, where the exponent gamma characterizes the divergence of the susceptibility for a self-avoiding walk. Our lattice model simulations and experimental data are consistent with the theory. Our finding rationalizes the marginal stability of proteins and substantiates the earlier predictions that the efficient folding of two-state proteins requires the folding transition temperature to be close to the collapse temperature.Comment: 3 figures. Physical Review Letters (in press

Folding in two-dimenensional off-lattice models of proteins

Model off-lattice sequences in two dimensions are constructed so that their native states are close to an on-lattice target. The Hamiltonian involves the Lennard-Jones and harmonic interactions. The native states of these sequences are determined with a high degree of certainty through Monte Carlo processes. The sequences are characterized thermodynamically and kinetically. It is shown that the rank-ordering-based scheme of the assignment of contact energies typically fails in off-lattice models even though it generates high stability of on-lattice sequences. Similar to the on-lattice case, Go-like modeling, in which the interaction potentials are restricted to the native contacts in a target shape, gives rise to good folding properties. Involving other contacts deteriorates these properties.Comment: REVTeX, 9 pages, 8 EPS figure