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Geometry of the energy landscape and folding in models of proteins

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Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)

Abstract

A geometric analysis of the global properties of the energy landscape of minimalistic models of polypeptides is presented, which is based on the relation between dynamical trajectories and geodesics of a suitable manifold, whose metric is completely determined by the potential energy. We first consider different sequences in a simple model with only three classes of aminoacids: hydrophobic, polar, and neutral. Some of the sequences have a definite protein-like behavior, i.e., show a folding transition towards a unique native state; the others undergo a hydrophobic collapse without any tendency to select a particular configuration below the collapse temperature. The global geometry of the energy landscape appears to contain relevant information on the behavior of the various sequences: in particular, the fluctuations of the curvature of the landscape, measured by means of numerical simulations, clearly mark the folding transition and allow to distinguish the protein-like sequences from the others 1. The same analysis is then applied to a more refined model, where not only the full aminoacidic sequences are considered but also the different sizes of the residues are effectively taken into account. Such a model is able to describe folding of real proteins to a good degree of accuracy 2. In particular, we consider SH3 and S6 proteins, as well as sequences that do not behave as proteins. The above scenario is completely confirmed, thus suggesting that the geometry of the energy landscape plays an important role in determining folding properties of polypeptides. 1) L.\ N.\ Mazzoni and L.\ Casetti, Phys.\ Rev.\ Lett.\ 97, 218104 (2006).\\ 2) P.\ Das, S.\ Matysiak, and C.\ Clementi, Proc.\ Natl.\ Acad.\ Sci.\ USA 102, 10141 (2005).

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