Related papers: Local Interactions and Protein Folding: A Model St…
It is known that the stochastic generators of effective processes associated with the unconditioned dynamics of rare events might consist of non-local interactions; however, it can be shown that there are special cases for which these…
We propose a novel method for the determination of the effective interaction potential between the amino acids of a protein. The strategy is based on the combination of a new optimization procedure and a geometrical argument, which also…
We investigate one-dimensional harmonically trapped two-component systems for repulsive interaction strengths ranging from the non-interacting to the strongly interacting regime for Fermi-Fermi mixtures. A new and powerful mapping between…
We introduce a family of particle systems on sparse graphs where local interactions occur via hitting times, providing a dynamic and tractable model for default cascades in large sparsely-connected financial networks. Building on the…
We present a simple model of protein folding dynamics that captures key qualitative elements recently seen in all-atom simulations. The goals of this theory are to serve as a simple formalism for gaining deeper insight into the physical…
Lattice models, for their coarse-grained nature, are best suited for the study of the ``designability problem'', the phenomenon in which most of the about 16,000 proteins of known structure have their native conformations concentrated in a…
The kinetic behavior of a three-dimensional off-lattice heteropolymer model is studied in terms of the time dependence of the average mean-square displacement between configurations. It is found that at short time-scales similar behavior is…
A microscopic theory of the free energy barriers and folding routes for minimally frustrated proteins is presented, greatly expanding on the presentation of the variational approach outlined previously [J. J. Portman, S. Takada, P. G.…
The hydrophobic-polar (HP) model represents proteins as binary strings embedded in lattices, with fold quality measured by an energy score. We prove that the optimal fold energy is not monotonic under concatenation for several standard…
We discuss recent theoretical developments in the study of simple lattice models of proteins. Such models are designed to understand general features of protein structures and mechanism of folding. Among the topics covered are (i) the use…
Many complex structures and stochastic patterns emerge from simple kinetic rules and local interactions, and are governed by scale invariance properties in combination with effects of the global geometry. We consider systems that can be…
On the study of protein folding, our understanding about the protein structures is limited. In this paper we find one way to characterize the compact structures of lattice protein model. A quantity called Partnum is given to each compact…
It has recently been demonstrated that many biological networks exhibit a scale-free topology where the probability of observing a node with a certain number of edges (k) follows a power law: i.e. p(k) ~ k^-g. This observation has been…
We study the thermodynamic behavior of a simple off-lattice model for protein folding. The model is two-dimensional and has two different ``amino acids''. Using numerical simulations of all chains containing eight or ten monomers, we…
A coarse grained model of a random polypeptide chain, with only discrete torsional degrees of freedom and Hookean springs connecting pairs of hydrophobic residues is shown to display stretched exponential relaxation under Metropolis…
The dynamical rules in auxiliary stochastic process that generates the biased ensemble of rare events are non-local. For the systems with one type of particle, it is shown that there are special cases for which the generators of effective…
We present a numerical study of dynamical correlations (structure factors) of the long-range generalization of the Fermi-Pasta-Ulam oscillator chain, where the strength of the interaction between two lattice sites decays as a power $\alpha$…
Spatial pattern formation is a key feature of many natural systems in physics, chemistry and biology. The essential theoretical issue in understanding pattern formation is to explain how a spatially homogeneous initial state can undergo…
The capacity of proteins to interact specifically with one another underlies our conceptual understanding of how living systems function. Systems-level study of specificity in protein-protein interactions is complicated by the fact that the…
Free-energy landscapes for short peptides -- specifically for variants of the pH Low Insertion Peptide (pHLIP) -- in the heterogeneous environment of a lipid bilayer or cell membrane are constructed, taking into account a set of dominant…