An Analytical Approach to the Protein Designability Problem

We present an analytical method for determining the designability of protein structures. We apply our method to the case of two-dimensional lattice structures, and give a systematic solution for the spectrum of any structure. Using this spectrum, the designability of a structure can be estimated. We outline a heirarchy of structures, from most to least designable, and show that this heirarchy depends on the potential that is used.Comment: 16 pages 4 figure

Protein and DNA sequence determinants of thermophilic adaptation

Prokaryotes living at extreme environmental temperatures exhibit pronounced signatures in the amino acid composition of their proteins and nucleotide compositions of their genomes reflective of adaptation to their thermal environments. However, despite significant efforts, the definitive answer of what are the genomic and proteomic compositional determinants of Optimal Growth Temperature of prokaryotic organisms remained elusive. Here the authors performed a comprehensive analysis of amino acid and nucleotide compositional signatures of thermophylic adaptation by exhaustively evaluating all combinations of amino acids and nucleotides as possible determinants of Optimal Growth Temperature for all prokaryotic organisms with fully sequences genomes.. The authors discovered that total concentration of seven amino acids in proteomes, IVYWREL, serves as a universal proteomic predictor of Optimal Growth Temperature in prokaryotes. Resolving the old-standing controversy the authors determined that the variation in nucleotide composition (increase of purine load, or A+G content with temperature) is largely a consequence of thermal adaptation of proteins. However, the frequency with which A and G nucleotides appear as nearest neighbors in genome sequences is strongly and independently correlated with Optimal Growth Temperature. as a result of codon bias in corresponding genomes. Together these results provide a complete picture of proteomic and genomic determinants of thermophilic adaptation.Comment: in press PLoS Computational Biology; revised versio

Mapping of mutation-sensitive sites in protein-like chains

In this work we have studied, with the help of a simple on-lattice model, the distribution pattern of sites sensitive to point mutations ('hot' sites) in protein-like chains. It has been found that this pattern depends on the regularity of the matrix that rules the interaction between different kinds of residues. If the interaction matrix is dominated by the hydrophobic effect (Miyazawa Jernigan like matrix), this distribution is very simple - all the 'hot' sites can be found at the positions with maximum number of closest nearest neighbors (bulk). If random or nonlinear corrections are added to such an interaction matrix the distribution pattern changes. The rising of collective effects allows the 'hot' sites to be found in places with smaller number of nearest neighbors (surface) while the general trend of the 'hot' sites to fall into a bulk part of a conformation still holds.Comment: 15 pages, 6 figure

Reply to Comment on "Criterion that Determines the Foldability of Proteins"

We point out that the correlation between folding times and $\sigma = (T_{\theta } - T_{f})/T_{\theta }$ in protein-like heteropolymer models where $T_{\theta }$ and $T_{f}$ are the collapse and folding transition temperatures was already established in 1993 before the other presumed equivalent criterion (folding times correlating with $T_{f}$ alone) was suggested. We argue that the folding times for these models show no useful correlation with the energy gap even if restricted to the ensemble of compact structures as suggested by Karplus and Shakhnovich (cond-mat/9606037).Comment: 6 pages, Latex, 2 Postscript figures. Plots explicitly showing the lack of correlation between folding time and energy gap are adde

Is Heteropolymer Freezing Well Described by the Random Energy Model?

It is widely held that the Random Energy Model (REM) describes the freezing transition of a variety of types of heteropolymers. We demonstrate that the hallmark property of REM, statistical independence of the energies of states over disorder, is violated in different ways for models commonly employed in heteropolymer freezing studies. The implications for proteins are also discussed.Comment: 4 pages, 3 eps figures To appear in Physical Review Letters, May 199

Two-Dimensional Polymers with Random Short-Range Interactions

We use complete enumeration and Monte Carlo techniques to study two-dimensional self-avoiding polymer chains with quenched ``charges'' $\pm 1$. The interaction of charges at neighboring lattice sites is described by $q_i q_j$. We find that a polymer undergoes a collapse transition at a temperature $T_{\theta}$, which decreases with increasing imbalance between charges. At the transition point, the dependence of the radius of gyration of the polymer on the number of monomers is characterized by an exponent $\nu_{\theta} = 0.60 \pm 0.02$, which is slightly larger than the similar exponent for homopolymers. We find no evidence of freezing at low temperatures.Comment: 4 two-column pages, 6 eps figures, RevTex, Submitted to Phys. Rev.

Localization in simple multiparticle catalytic absorption model

We consider the phase transition in the system of n simultaneously developing random walks on the halfline x>=0. All walks are independent on each others in all points except the origin x=0, where the point well is located. The well depth depends on the number of particles simultaneously staying at x=0. We consider the limit n>>1 and show that if the depth growth faster than 3/2 n ln(n) with n, then all random walks become localized simultaneously at the origin. In conclusion we discuss the connection of that problem with the phase transition in the copolymer chain with quenched random sequence of monomers considered in the frameworks of replica approach.Comment: 17 pages in LaTeX, 5 PostScript figures; submitted to J.Phys.(A): Math. Ge