Research

Overview

Broadly speaking, my research interests are in the field of statistical physics and nonlinear dynamical systems, most recently with particular emphasis on problems inspired by molecular biology. I have contributed to biological physics and mathematics in different contexts, from the study of protein dynamics from single-molecule experimental reconstructions to the development of a dual-series approach for the solution of mixed-boundary problems modeling encounter reactions between complex macromolecules in solution. A background in theoretical physics, I have acquired along the years a special expertise in the field of nonlinear discrete dynamical systems, where I contributed in particular to the understanding of the peculiar properties of a class of space-localized periodic orbits known as discrete breathers (DB) in a variety of spatially extended systems. Recently, inspired by the vast and crucial open problem of storage and directed transfer of energy in proteins, I have introduced a simple model with the idea of probing the role of nonlinear effects in such phenomena. The first results of this activity confirm that discrete breathers are easily excitable even in media as heterogeneous as protein structures. In particular, distinct features of DBs (such as their excitation energy threshold) show to be tightly connected with the peculiar topological properties of the protein folds (i.e. as specified by the connectivity graph describing their equilibrium structures), so that the intriguing possibility that space-modulated, non-linear dynamical effects might regulate specific biological functions emerges naturally. For example, we find that, at variance with translationally invariant extended systems, DBs in a disordered medium exhibit a whole hierarchy of excitation thresholds. While in a Hamiltonian system whose equilibrium structure is a regular lattice the lowest energies of DB orbits are dictated by the space dimension and the type of nonlinearity only, in a disordered system all properties of DB families become site-dependent. In other words, also the geography of the connectivity rules determines, among other properties, the energy gaps of DB dispersion relations. Remarkably, in proteins corresponding to connectivity graphs of thousands of vertexes, a handful of special sites typically host DB families that have vanishing energy thresholds and that are, as a consequence, most easily excitable. The rich future follow ups of the above research line hold promise of shedding utterly new light into basic problems in molecular biology, such as ATP-fueled enzyme catalysis and the functioning of molecular motors. Moreover, from a theoretical point of view, our model ventures into the rather unexplored field of discrete dynamical systems with spatial disorder. More generally, indeed, we study networks of nonlinear oscillators with given connectivity rules or, in other words, complex networks of nonlinear oscillators. In the case of proteins, the connectivity rules are provided by the contact graphs specified by the equilibrium structures (e.g. as solved through X-ray crystallography). However, our theoretical framework can be readily extended to arbitrary connectivity rules. Therefore, from a fundamental point of view, we shall explore basic properties of localized periodic orbits (such as existence and linear stability) in complex networks as functions of the topological characteristics of the underlying graph - more precisely, in a context where localization is to be measured in the graph-theoretical sense of distances, i.e. the minimum number of edges between two selected vertexes. The application to protein dynamics can then be recovered as a special case where the graph is embedded in three-dimensional Euclidean space.

Selected topics