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

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

Information Loss in Coarse Graining of Polymer Configurations via Contact Matrices

Contact matrices provide a coarse grained description of the configuration omega of a linear chain (polymer or random walk) on Z^n: C_{ij}(omega)=1 when the distance between the position of the i-th and j-th step are less than or equal to some distance "a" and C_{ij}(omega)=0 otherwise. We consider models in which polymers of length N have weights corresponding to simple and self-avoiding random walks, SRW and SAW, with "a" the minimal permissible distance. We prove that to leading order in N, the number of matrices equals the number of walks for SRW, but not for SAW. The coarse grained Shannon entropies for SRW agree with the fine grained ones for n <= 2, but differs for n >= 3.Comment: 18 pages, 2 figures, latex2e Main change: the introduction is rewritten in a less formal way with the main results explained in simple term

Genetic divergence in biomass sorghum genotypes through agronomic and physicalchemical characters.

The present research aimed to evaluate the genetic divergence in 34 sorghum biomass genotypes via agronomic and physicochemical characters. The design used was randomized blocks with three replications. The agronomic and physical-chemical characteristics evaluated were: days for flowering, number of stems, plant height, number of leaves, green mass production, dry mass production, determination of total ash, determination of volatile content, insoluble lignin and determination of fixed carbon content. The data were submitted to analysis of variance and then, to estimate divergence,the generalized Mahalanobisdistance was used as a measure of dissimilarity. Based on this matrix, the methods of Tocher's optimization clusters and the Hierarchical method of Average Grouping Between Groups (UPGMA) were used, and analysis of canonical variables, and the projection based on the first two canonical variables arranged in two-dimensional space. Singh criterion was also used to quantify the relative contribution of these characteristics to genetic divergence. The evaluated genotypes showed significant differences for all the evaluated characteristics. The combination between the 201429B001 and 201429B028 (394.98) genotype pairs was the most divergent and the combination between the 201429B015 and 201429B031 (6.31) genotypes was the most similar. The grouping generated by the Tocher Optimization method, hierarchical UPGMA and graphical dispersion showed similarity in the grouping of genotypes. The first two canonical variables were sufficient to explain about 81.78% of the total variation observed. Theresults showed a wide genetic diversity among the 34 genotypes of sorghum biomass

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

Effect of spatial bias on the nonequilibrium phase transition in a system of coagulating and fragmenting particles

We examine the effect of spatial bias on a nonequilibrium system in which masses on a lattice evolve through the elementary moves of diffusion, coagulation and fragmentation. When there is no preferred directionality in the motion of the masses, the model is known to exhibit a nonequilibrium phase transition between two different types of steady states, in all dimensions. We show analytically that introducing a preferred direction in the motion of the masses inhibits the occurrence of the phase transition in one dimension, in the thermodynamic limit. A finite size system, however, continues to show a signature of the original transition, and we characterize the finite size scaling implications of this. Our analysis is supported by numerical simulations. In two dimensions, bias is shown to be irrelevant.Comment: 7 pages, 7 figures, revte

Modeling study on the validity of a possibly simplified representation of proteins

The folding characteristics of sequences reduced with a possibly simplified representation of five types of residues are shown to be similar to their original ones with the natural set of residues (20 types or 20 letters). The reduced sequences have a good foldability and fold to the same native structure of their optimized original ones. A large ground state gap for the native structure shows the thermodynamic stability of the reduced sequences. The general validity of such a five-letter reduction is further studied via the correlation between the reduced sequences and the original ones. As a comparison, a reduction with two letters is found not to reproduce the native structure of the original sequences due to its homopolymeric features.Comment: 6 pages with 4 figure

Als mutations in FUS cause neuronal dysfunction and death in caenorhabditis elegans by a dominant gain-of-function mechanism

It is unclear whether mutations in fused in sarcoma (FUS) cause familial amyotrophic lateral sclerosis via a loss-of-function effect due to titrating FUS from the nucleus or a gain-of-function effect from cytoplasmic overabundance. To investigate this question, we generated a series of independent Caenorhabditis elegans lines expressing mutant or wild-type (WT) human FUS. We show that mutant FUS, but not WT-FUS, causes cytoplasmic mislocalization associated with progressive motor dysfunction and reduced lifespan. The severity of the mutant phenotype in C. elegans was directly correlated with the severity of the illness caused by the same mutation in humans, arguing that this model closely replicates key features of the human illness. Importantly, the mutant phenotype could not be rescued by overexpression of WT-FUS, even though WTFUS had physiological intracellular localization, and was not recruited to the cytoplasmic mutant FUS aggregates. Our data suggest that FUS mutants cause neuronal dysfunction by a dominant gain-of-function effect related either to neurotoxic aggregates of mutant FUS in the cytoplasm or to dysfunction in its RNA-binding functions

Metastability of native proteins and the phenomenon of amyloid formation

An experimental determination of the thermodynamic stabilities of a series of amyloid fibrils reveals that this structural form is likely to be the most stable one that protein molecules can adopt even under physiological conditions. This result challenges the conventional assumption that functional forms of proteins correspond to the global minima in their free energy surfaces and suggests that living systems are conformationally as well as chemically metastable. © 2011 American Chemical Society

Rational design of a conformation-specific antibody for the quantification of A beta oligomers

The accurate quantification of the amounts of small oligomeric assemblies formed by the amyloid β (Aβ) peptide represents a major challenge in the Alzheimer’s field. There is therefore great interest in the development of methods to specifically detect these oligomers by distinguishing them from larger aggregates. The availability of these methods will enable the development of effective diagnostic and therapeutic interventions for this and other diseases related to protein misfolding and aggregation. We describe here a single-domain antibody able to selectively quantify oligomers of the Aβ peptide in isolation and in complex protein mixtures from animal models of disease