Statistical properties of contact vectors

We study the statistical properties of contact vectors, a construct to characterize a protein's structure. The contact vector of an N-residue protein is a list of N integers n_i, representing the number of residues in contact with residue i. We study analytically (at mean-field level) and numerically the amount of structural information contained in a contact vector. Analytical calculations reveal that a large variance in the contact numbers reduces the degeneracy of the mapping between contact vectors and structures. Exact enumeration for lengths up to N=16 on the three dimensional cubic lattice indicates that the growth rate of number of contact vectors as a function of N is only 3% less than that for contact maps. In particular, for compact structures we present numerical evidence that, practically, each contact vector corresponds to only a handful of structures. We discuss how this information can be used for better structure prediction.Comment: 20 pages, 6 figure

Self-Templated Nucleation in Peptide and Protein aggregation

Peptides and proteins exhibit a common tendency to assemble into highly ordered fibrillar aggregates, whose formation proceeds in a nucleation-dependent manner that is often preceded by the formation of disordered oligomeric assemblies. This process has received much attention because disordered oligomeric aggregates have been associated with neurodegenerative disorders such as Alzheimer's and Parkinson's diseases. Here we describe a self-templated nucleation mechanism that determines the transition between the initial condensation of polypeptide chains into disordered assemblies and their reordering into fibrillar structures. The results that we present show that at the molecular level this transition is due to the ability of polypeptide chains to reorder within oligomers into fibrillar assemblies whose surfaces act as templates that stabilise the disordered assemblies.Comment: 4 pages, 3 figure

Processamento de batata (Solanum tuberosum L.) : fritura

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Processamento do purê e néctar de pêssego.

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Comportamento de cultivares chilenas de batata na zona Sul do Rio Grande do Sul.

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The Origin of the Designability of Protein Structures

We examined what determines the designability of 2-letter codes (H and P) lattice proteins from three points of view. First, whether the native structure is searched within all possible structures or within maximally compact structures. Second, whether the structure of the used lattice is bipartite or not. Third, the effect of the length of the chain, namely, the number of monomers on the chain. We found that the bipartiteness of the lattice structure is not a main factor which determines the designability. Our results suggest that highly designable structures will be found when the length of the chain is sufficiently long to make the hydrophobic core consisting of enough number of monomers.Comment: 17 pages, 2 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.

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