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.

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

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

Cooperativity and the origins of rapid, single-exponential kinetics in protein folding

The folding of naturally occurring, single domain proteins is usually well-described as a simple, single exponential process lacking significant trapped states. Here we further explore the hypothesis that the smooth energy landscape this implies, and the rapid kinetics it engenders, arises due to the extraordinary thermodynamic cooperativity of protein folding. Studying Miyazawa-Jernigan lattice polymers we find that, even under conditions where the folding energy landscape is relatively optimized (designed sequences folding at their temperature of maximum folding rate), the folding of protein-like heteropolymers is accelerated when their thermodynamic cooperativity enhanced by enhancing the non-additivity of their energy potentials. At lower temperatures, where kinetic traps presumably play a more significant role in defining folding rates, we observe still greater cooperativity-induced acceleration. Consistent with these observations, we find that the folding kinetics of our computational models more closely approximate single-exponential behavior as their cooperativity approaches optimal levels. These observations suggest that the rapid folding of naturally occurring proteins is, at least in part, consequences of their remarkably cooperative folding

Native geometry and the dynamics of protein folding

In this paper we investigate the role of native geometry on the kinetics of protein folding based on simple lattice models and Monte Carlo simulations. Results obtained within the scope of the Miyazawa-Jernigan indicate the existence of two dynamical folding regimes depending on the protein chain length. For chains larger than 80 amino acids the folding performance is sensitive to the native state's conformation. Smaller chains, with less than 80 amino acids, fold via two-state kinetics and exhibit a significant correlation between the contact order parameter and the logarithmic folding times. In particular, chains with N=48 amino acids were found to belong to two broad classes of folding, characterized by different cooperativity, depending on the contact order parameter. Preliminary results based on the G\={o} model show that the effect of long range contact interaction strength in the folding kinetics is largely dependent on the native state's geometry.Comment: Proceedings of the BIFI 2004 - I International Conference, Zaragoza (Spain) Biology after the genome: a physical view. To appear in Biophysical Chemistr