Designability of lattice model heteropolymers

Protein folds are highly designable, in the sense that many sequences fold to the same conformation. In the present work we derive an expression for the designability in a 20 letter lattice model of proteins which, relying only on the Central Limit Theorem, has a generality which goes beyond the simple model used in its derivation. This expression displays an exponential dependence on the energy of the optimal sequence folding on the given conformation measured with respect to the lowest energy of the conformational dissimilar structures, energy difference which constitutes the only parameter controlling designability. Accordingly, the designability of a native conformation is intimately connected to the stability of the sequences folding to them.Comment: in press on Phys. Rev.

Random walks in the space of conformations of toy proteins

Monte Carlo dynamics of the lattice 48 monomers toy protein is interpreted as a random walk in an abstract (discrete) space of conformations. To test the geometry of this space, we examine the return probability $P(T)$, which is the probability to find the polymer in the native state after $T$ Monte Carlo steps, provided that it starts from the native state at the initial moment. Comparing computational data with the theoretical expressions for $P(T)$ for random walks in a variety of different spaces, we show that conformational spaces of polymer loops may have non-trivial dimensions and exhibit negative curvature characteristic of Lobachevskii (hyperbolic) geometry.Comment: 4 pages, 3 figure

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

Protein folding rates correlate with heterogeneity of folding mechanism

By observing trends in the folding kinetics of experimental 2-state proteins at their transition midpoints, and by observing trends in the barrier heights of numerous simulations of coarse grained, C-alpha model, Go proteins, we show that folding rates correlate with the degree of heterogeneity in the formation of native contacts. Statistically significant correlations are observed between folding rates and measures of heterogeneity inherent in the native topology, as well as between rates and the variance in the distribution of either experimentally measured or simulated phi-values.Comment: 11 pages, 3 figures, 1 tabl

Patterns of genomic loss of heterozygosity predict homologous recombination repair defects in epithelial ovarian cancer

Background: Defects in BRCA1, BRCA2, and other members of the homologous recombination pathway have potential therapeutic relevance when used to support agents that introduce or exploit double-stranded DNA breaks. This study examines the association between homologous recombination defects and genomic patterns of loss of heterozygosity (LOH). Methods: Ovarian tumours from two independent data sets were characterised for defects in BRCA1,BRCA2, and RAD51C, and LOH profiles were generated. Publically available data were downloaded for a third independent data set. The same analyses were performed on 57 cancer cell lines. Results: Loss of heterozygosity regions of intermediate size were observed more frequently in tumours with defective BRCA1 or BRCA2 (P=10−11). The homologous recombination deficiency (HRD) score was defined as the number of these regions observed in a tumour sample. The association between HRD score and BRCA deficiency was validated in two independent ovarian cancer data sets (P=10−5 and 10−29), and identified breast and pancreatic cell lines with BRCA defects. Conclusion: The HRD score appears capable of detecting homologous recombination defects regardless of aetiology or mechanism. This score could facilitate the use of PARP inhibitors and platinum in breast, ovarian, and other cancers

Geometrically Reduced Number of Protein Ground State Candidates

Geometrical properties of protein ground states are studied using an algebraic approach. It is shown that independent from inter-monomer interactions, the collection of ground state candidates for any folded protein is unexpectedly small: For the case of a two-parameter Hydrophobic-Polar lattice model for $L$-mers, the number of these candidates grows only as $L^2$. Moreover, the space of the interaction parameters of the model breaks up into well-defined domains, each corresponding to one ground state candidate, which are separated by sharp boundaries. In addition, by exact enumeration, we show there are some sequences which have one absolute unique native state. These absolute ground states have perfect stability against change of inter-monomer interaction potential.Comment: 9 page, 4 ps figures are include