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A three-dimensional lattice model of a protein is used to investigate the properties required for its folding to the native state. The polypeptide chain is represented as a 27 bead heteropolymer whose lowest energy (native) state can be determined by an exhaustive enumeration of all fully compact conformations. A total of 200 sequences with random(More)
The number of all possible conformations of a polypeptide chain is too large to be sampled exhaustively. Nevertheless, protein sequences do fold into unique native states in seconds (the Levinthal paradox). To determine how the Levinthal paradox is resolved, we use a lattice Monte Carlo model in which the global minimum (native state) is known. The(More)
In this paper we introduce a novel method of deriving a pairwise potential for protein folding. The potential is obtained by an optimization procedure that simultaneously maximizes thermodynamic stability for all proteins in the database. When applied to the representative dataset of proteins and with the energy function taken in pairwise contact(More)
Here we present an approximate analytical theory for the relationship between a protein structure's contact matrix and the shape of its energy spectrum in amino acid sequence space. We demonstrate a dependence of the number of sequences of low energy in a structure on the eigenvalues of the structure's contact matrix, and then use a Monte Carlo simulation(More)
Here, we provide an analysis of molecular evolution of five of the most populated protein folds: immunoglobulin fold, oligonucleotide-binding fold, Rossman fold, alpha/beta plait, and TIM barrels. In order to distinguish between "historic", functional and structural reasons for amino acid conservations, we consider proteins that acquire the same fold and(More)
To address the question of how the geometry of a protein's native conformation affects its folding and stability, we studied three model 36-mers on a cubic lattice. The native structure of one of these model 36-mers consisted mostly of local contacts, while that of a second consisted mostly of non-local contacts. The third native structure had a typical(More)
We propose a model that explains the hierarchical organization of proteins in fold families. The model, which is based on the evolutionary selection of proteins by their native state stability, reproduces patterns of amino acids conserved across protein families. Due to its dynamic nature, the model sheds light on the evolutionary time-scales. By studying(More)
Classical population genetics a priori assigns fitness to alleles without considering molecular or functional properties of proteins that these alleles encode. Here we study population dynamics in a model where fitness can be inferred from physical properties of proteins under a physiological assumption that loss of stability of any protein encoded by an(More)
There have been considerable attempts in the past to relate phenotypic trait--habitat temperature of organisms--to their genotypes, most importantly compositions of their genomes and proteomes. However, despite accumulation of anecdotal evidence, an exact and conclusive relationship between the former and the latter has been elusive. We present an(More)
BACKGROUND Many attempts have been made to resolve in time the folding of model proteins in computer simulations. Different computational approaches have emerged. Some of these approaches suffer from insensitivity to the geometrical properties of the proteins (lattice models), whereas others are computationally heavy (traditional molecular dynamics). (More)