Distribution of Dangling Ends on the Incipient Percolation Cluster

We study numerically and by scaling arguments the probability P(M)dM that a given dangling end of the incipient percolation cluster has a mass between M and M + dM. We find by scaling arguments that P(M) decays with a power law, P(M)~M^(-(1+k)), with an exponent k=dBf/df, where df and dBf are the fractal dimensions of the cluster and its backbone, respectively. Our numerical results yield k=0.83 in d=2 and k=0.74 in d=3 in very good agreement with theory.Comment: proceedings of the conference "Percolation and Disordered Systems: *Theory and Applications*", Giessen (Germany) 1998, see http://ory.ph.biu.ac.il/PERCOLATION98/ , 4 pages, 3 figures, in press, will be published in Physica

Generating random networks with given degree-degree correlations and degree-dependent clustering

Random networks are widely used to model complex networks and research their properties. In order to get a good approximation of complex networks encountered in various disciplines of science, the ability to tune various statistical properties of random networks is very important. In this manuscript we present an algorithm which is able to construct arbitrarily degree-degree correlated networks with adjustable degree-dependent clustering. We verify the algorithm by using empirical networks as input and describe additionally a simple way to fix a degree-dependent clustering function if degree-degree correlations are given.Comment: 4 pages, 3 figure

Statistical properties of neutral evolution

Neutral evolution is the simplest model of molecular evolution and thus it is most amenable to a comprehensive theoretical investigation. In this paper, we characterize the statistical properties of neutral evolution of proteins under the requirement that the native state remains thermodynamically stable, and compare them to the ones of Kimura's model of neutral evolution. Our study is based on the Structurally Constrained Neutral (SCN) model which we recently proposed. We show that, in the SCN model, the substitution rate decreases as longer time intervals are considered, and fluctuates strongly from one branch of the evolutionary tree to another, leading to a non-Poissonian statistics for the substitution process. Such strong fluctuations are also due to the fact that neutral substitution rates for individual residues are strongly correlated for most residue pairs. Interestingly, structurally conserved residues, characterized by a much below average substitution rate, are also much less correlated to other residues and evolve in a much more regular way. Our results could improve methods aimed at distinguishing between neutral and adaptive substitutions as well as methods for computing the expected number of substitutions occurred since the divergence of two protein sequences.Comment: 17 pages, 11 figure

Stochastic reconstruction of protein structures from effective connectivity profiles.

We discuss a stochastic approach for reconstructing the native structures of proteins from the knowledge of the "effective connectivity", which is a one-dimensional structural profile constructed as a linear combination of the eigenvectors of the contact map of the target structure. The structural profile is used to bias a search of the conformational space towards the target structure in a Monte Carlo scheme operating on a Calpha-chain of uniform, finite thickness. Structure information thus enters the folding dynamics via the effective connectivity, but the interaction is not restricted to pairs of amino acids that form native contacts, resulting in a free energy landscape which does not rely on the assumption of minimal frustration. Moreover, effective connectivity vectors can be predicted more readily from the amino acid sequence of proteins than the corresponding contact maps, thus suggesting that the stochastic protocol presented here could be effectively combined with other current methods for predicting native structures. PACS codes: 87.14.Ee.RIGHTS : This article is licensed under the BioMed Central licence at http://www.biomedcentral.com/about/license which is similar to the 'Creative Commons Attribution Licence'. In brief you may : copy, distribute, and display the work; make derivative works; or make commercial use of the work - under the following conditions: the original author must be given credit; for any reuse or distribution, it must be made clear to others what the license terms of this work are

Comparison of translation loads for standard and alternative genetic codes

<p>Abstract</p> <p>Background</p> <p>The (almost) universality of the genetic code is one of the most intriguing properties of cellular life. Nevertheless, several variants of the standard genetic code have been observed, which differ in one or several of 64 codon assignments and occur mainly in mitochondrial genomes and in nuclear genomes of some bacterial and eukaryotic parasites. These variants are usually considered to be the result of non-adaptive evolution. It has been shown that the standard genetic code is preferential to randomly assembled codes for its ability to reduce the effects of errors in protein translation.</p> <p>Results</p> <p>Using a genotype-to-phenotype mapping based on a quantitative model of protein folding, we compare the standard genetic code to seven of its naturally occurring variants with respect to the fitness loss associated to mistranslation and mutation. These fitness losses are computed through computer simulations of protein evolution with mutations that are either neutral or lethal, and different mutation biases, which influence the balance between unfolding and misfolding stability. We show that the alternative codes may produce significantly different mutation and translation loads, particularly for genomes evolving with a rather large mutation bias. Most of the alternative genetic codes are found to be disadvantageous to the standard code, in agreement with the view that the change of genetic code is a mutationally driven event. Nevertheless, one of the studied alternative genetic codes is predicted to be preferable to the standard code for a broad range of mutation biases.</p> <p>Conclusions</p> <p>Our results show that, with one exception, the standard genetic code is generally better able to reduce the translation load than the naturally occurring variants studied here. Besides this exception, some of the other alternative genetic codes are predicted to be better adapted for extreme mutation biases. Hence, the fixation of alternative genetic codes might be a neutral or nearly-neutral event in the majority of the cases, but adaptation cannot be excluded for some of the studied cases.</p

High quality protein sequence alignment by combining structural profile prediction and profile alignment using SABERTOOTH

<p>Abstract</p> <p>Background</p> <p>Protein alignments are an essential tool for many bioinformatics analyses. While sequence alignments are accurate for proteins of high sequence similarity, they become unreliable as they approach the so-called 'twilight zone' where sequence similarity gets indistinguishable from random. For such distant pairs, structure alignment is of much better quality. Nevertheless, sequence alignment is the only choice in the majority of cases where structural data is not available. This situation demands development of methods that extend the applicability of accurate sequence alignment to distantly related proteins.</p> <p>Results</p> <p>We develop a sequence alignment method that combines the prediction of a structural profile based on the protein's sequence with the alignment of that profile using our recently published alignment tool SABERTOOTH. In particular, we predict the contact vector of protein structures using an artificial neural network based on position-specific scoring matrices generated by PSI-BLAST and align these predicted contact vectors. The resulting sequence alignments are assessed using two different tests: First, we assess the alignment quality by measuring the derived structural similarity for cases in which structures are available. In a second test, we quantify the ability of the significance score of the alignments to recognize structural and evolutionary relationships. As a benchmark we use a representative set of the SCOP (structural classification of proteins) database, with similarities ranging from closely related proteins at SCOP family level, to very distantly related proteins at SCOP fold level. Comparing these results with some prominent sequence alignment tools, we find that SABERTOOTH produces sequence alignments of better quality than those of Clustal W, T-Coffee, MUSCLE, and PSI-BLAST. HHpred, one of the most sophisticated and computationally expensive tools available, outperforms our alignment algorithm at family and superfamily levels, while the use of SABERTOOTH is advantageous for alignments at fold level. Our alignment scheme will profit from future improvements of structural profiles prediction.</p> <p>Conclusions</p> <p>We present the automatic sequence alignment tool SABERTOOTH that computes pairwise sequence alignments of very high quality. SABERTOOTH is especially advantageous when applied to alignments of remotely related proteins. The source code is available at <url>http://www.fkp.tu-darmstadt.de/sabertooth_project/</url>, free for academic users upon request.</p