Optimal prediction of folding rates and transition state placement from native state geometry

A variety of experimental and theoretical studies have established that the folding process of monomeric proteins is strongly influenced by the topology of the native state. In particular, folding times have been shown to correlate well with the contact order, a measure of contact locality. Our investigation focuses on identifying additional topologic properties that correlate with experimentally measurable quantities, such as folding rates and transition state placement, for both two- and three-state folders. The validation against data from forty experiments shows that a particular topologic property which measures the interdepedence of contacts, termed cliquishness or clustering coefficient, can account with significant accuracy both for the transition state placement and especially for folding rates, the linear correlation coefficient being $r=0.71$. This result can be further improved to $r=0.74$, by optimally combining the distinct topologic information captured by cliquishness and contact order.Comment: Revtex, 15 pages, 8 figure

A clustering algorithm for multivariate data streams with correlated components

Common clustering algorithms require multiple scans of all the data to achieve convergence, and this is prohibitive when large databases, with data arriving in streams, must be processed. Some algorithms to extend the popular K-means method to the analysis of streaming data are present in literature since 1998 (Bradley et al. in Scaling clustering algorithms to large databases. In: KDD. p. 9-15, 1998; O'Callaghan et al. in Streaming-data algorithms for high-quality clustering. In: Proceedings of IEEE international conference on data engineering. p. 685, 2001), based on the memorization and recursive update of a small number of summary statistics, but they either don't take into account the specific variability of the clusters, or assume that the random vectors which are processed and grouped have uncorrelated components. Unfortunately this is not the case in many practical situations. We here propose a new algorithm to process data streams, with data having correlated components and coming from clusters with different covariance matrices. Such covariance matrices are estimated via an optimal double shrinkage method, which provides positive definite estimates even in presence of a few data points, or of data having components with small variance. This is needed to invert the matrices and compute the Mahalanobis distances that we use for the data assignment to the clusters. We also estimate the total number of clusters from the data.Comment: title changed, rewritte

Low energy solutions for singularly perturbed coupled nonlinear systems on a Riemannian manifold with boundary

Let (M,g) be asmooth, compact Riemannian manifold with smooth boundary, with n= dim M= 2,3. We suppose the boundary of M to be a smooth submanifold of M with dimension n-1. We consider a singularly perturbed nonlinear system, namely Klein-Gordon-Maxwell-Proca system, or Klein-Gordon-Maxwell system of Scrhoedinger-Maxwell system on M. We prove that the number of low energy solutions, when the perturbation parameter is small, depends on the topological properties of the boundary of M, by means of the Lusternik Schnirelmann category. Also, these solutions have a unique maximum point that lies on the boundary

Non degeneracy of critical points of the Robin function with respect to deformations of the domain

We show a result of genericity for non degenerate critical points of the Robin function with respect to deformations of the domai

A multiplicity result for double singularly perturbed elliptic systems

We show that the number of low energy solutions of a double singularly perturbed Schroedinger Maxwell system type on a smooth 3 dimensional manifold (M,g) depends on the topological properties of the manifold. The result is obtained via Lusternik Schnirelmann category theory

Probing the entanglement and locating knots in ring polymers: a comparative study of different arc closure schemes

The interplay between the topological and geometrical properties of a polymer ring can be clarified by establishing the entanglement trapped in any portion (arc) of the ring. The task requires to close the open arcs into a ring, and the resulting topological state may depend on the specific closure scheme that is followed. To understand the impact of this ambiguity in contexts of practical interest, such as knot localization in a ring with non trivial topology, we apply various closure schemes to model ring polymers. The rings have the same length and topological state (a trefoil knot) but have different degree of compactness. The comparison suggests that a novel method, termed the minimally-interfering closure, can be profitably used to characterize the arc entanglement in a robust and computationally-efficient way. This closure method is finally applied to the knot localization problem which is tackled using two different localization schemes based on top-down or bottom-up searches.Comment: 9 pages, 7 figures. Submitted to Progress of Theoretical Physic