Use of the Metropolis algorithm to simulate the dynamics of protein chains

The Metropolis implementation of the Monte Carlo algorithm has been developed to study the equilibrium thermodynamics of many-body systems. Choosing small trial moves, the trajectories obtained applying this algorithm agree with those obtained by Langevin's dynamics. Applying this procedure to a simplified protein model, it is possible to show that setting a threshold of 1 degree on the movement of the dihedrals of the protein backbone in a single Monte Carlo step, the mean quantities associated with the off-equilibrium dynamics (e.g., energy, RMSD, etc.) are well reproduced, while the good description of higher moments requires smaller moves. An important result is that the time duration of a Monte Carlo step depends linearly on the temperature, something which should be accounted for when doing simulations at different temperatures.Comment: corrections to the text and to the figure

Protein folding using contact maps

We present the development of the idea to use dynamics in the space of contact maps as a computational approach to the protein folding problem. We first introduce two important technical ingredients, the reconstruction of a three dimensional conformation from a contact map and the Monte Carlo dynamics in contact map space. We then discuss two approximations to the free energy of the contact maps and a method to derive energy parameters based on perceptron learning. Finally we present results, first for predictions based on threading and then for energy minimization of crambin and of a set of 6 immunoglobulins. The main result is that we proved that the two simple approximations we studied for the free energy are not suitable for protein folding. Perspectives are discussed in the last section.Comment: 29 pages, 10 figure

Statistical Properties of Contact Maps

A contact map is a simple representation of the structure of proteins and other chain-like macromolecules. This representation is quite amenable to numerical studies of folding. We show that the number of contact maps corresponding to the possible configurations of a polypeptide chain of N amino acids, represented by (N-1)-step self avoiding walks on a lattice, grows exponentially with N for all dimensions D>1. We carry out exact enumerations in D=2 on the square and triangular lattices for walks of up to 20 steps and investigate various statistical properties of contact maps corresponding to such walks. We also study the exact statistics of contact maps generated by walks on a ladder.Comment: Latex file, 15 pages, 12 eps figures. To appear on Phys. Rev.

Folding, Design and Determination of Interaction Potentials Using Off-Lattice Dynamics of Model Heteropolymers

We present the results of a self-consistent, unified molecular dynamics study of simple model heteropolymers in the continuum with emphasis on folding, sequence design and the determination of the interaction parameters of the effective potential between the amino acids from the knowledge of the native states of the designed sequences.Comment: 8 pages, 3 Postscript figures, uses RevTeX. Submitted to Physical Review Letter

Steric constraints in model proteins

A simple lattice model for proteins that allows for distinct sizes of the amino acids is presented. The model is found to lead to a significant number of conformations that are the unique ground state of one or more sequences or encodable. Furthermore, several of the encodable structures are highly designable and are the non-degenerate ground state of several sequences. Even though the native state conformations are typically compact, not all compact conformations are encodable. The incorporation of the hydrophobic and polar nature of amino acids further enhances the attractive features of the model.Comment: RevTex, 5 pages, 3 postscript figure

Hi-C: A Method to Study the Three-dimensional Architecture of Genomes.

The three-dimensional folding of chromosomes compartmentalizes the genome and and can bring distant functional elements, such as promoters and enhancers, into close spatial proximity 2-6. Deciphering the relationship between chromosome organization and genome activity will aid in understanding genomic processes, like transcription and replication. However, little is known about how chromosomes fold. Microscopy is unable to distinguish large numbers of loci simultaneously or at high resolution. To date, the detection of chromosomal interactions using chromosome conformation capture (3C) and its subsequent adaptations required the choice of a set of target loci, making genome-wide studies impossible 7-10

Design of Force Fields from Data at Finite Temperature

We investigate the problem of how to obtain the force field between atoms of an experimentally determined structure. We show how this problem can be efficiently solved, even at finite temperature, where the position of the atoms differs substantially from the ground state. We apply our method to systems modeling proteins and demonstrate that the correct potentials can be recovered even in the presence of thermal noise.Comment: 10 pages, 1 postcript figure, Late

Nucleosome-mediated cooperativity between transcription factors

Cooperative binding of transcription factors (TFs) to cis-regulatory regions (CRRs) is essential for precision of gene expression in development and other processes. The classical model of cooperativity requires direct interactions between TFs, thus constraining the arrangement of TFs sites in a CRR. On the contrary, genomic and functional studies demonstrate a great deal of flexibility in such arrangements with variable distances, numbers of sites, and identities of the involved TFs. Such flexibility is inconsistent with the cooperativity by direct interactions between TFs. Here we demonstrate that strong cooperativity among non-interacting TFs can be achieved by their competition with nucleosomes. We find that the mechanism of nucleosome-mediated cooperativity is mathematically identical to the Monod-Wyman-Changeux (MWC) model of cooperativity in hemoglobin. This surprising parallel provides deep insights, with parallels between heterotropic regulation of hemoglobin (e.g. Bohr effect) and roles of nucleosome-positioning sequences and chromatin modifications in gene regulation. Characterized mechanism is consistent with numerous experimental results, allows substantial flexibility in and modularity of CRRs, and provides a rationale for a broad range of genomic and evolutionary observations. Striking parallels between cooperativity in hemoglobin and in transcription regulation point at a new design principle that may be used in range of biological systems

Statistical-mechanical lattice models for protein-DNA binding in chromatin

Statistical-mechanical lattice models for protein-DNA binding are well established as a method to describe complex ligand binding equilibriums measured in vitro with purified DNA and protein components. Recently, a new field of applications has opened up for this approach since it has become possible to experimentally quantify genome-wide protein occupancies in relation to the DNA sequence. In particular, the organization of the eukaryotic genome by histone proteins into a nucleoprotein complex termed chromatin has been recognized as a key parameter that controls the access of transcription factors to the DNA sequence. New approaches have to be developed to derive statistical mechanical lattice descriptions of chromatin-associated protein-DNA interactions. Here, we present the theoretical framework for lattice models of histone-DNA interactions in chromatin and investigate the (competitive) DNA binding of other chromosomal proteins and transcription factors. The results have a number of applications for quantitative models for the regulation of gene expression.Comment: 19 pages, 7 figures, accepted author manuscript, to appear in J. Phys.: Cond. Mat