Starts 6 Mar 2008 11:00
Ends 6 Mar 2008 20:00
Central European Time
Main Building Seminar Room
Strada Costiera, 11 I - 34151 Trieste (Italy)
Discrete breathers (DB) are spatially-localized, time-periodic vibrations that arise under general conditions in discrete, extended nonlinear systems. While much is known concerning their existence and stability in spatially periodic media, much less is known about the interplay of nonlinearity and spatial heterogeneity in disordered systems, where localization of vibrational energy is also fostered as a result of breaking of translational invariance. We introduce a coarse-grained, topology-based nonlinear network model of protein dynamics with the aim of investigating the interplay of spatial disorder and nonlinearity in biological molecules. DB solutions, characterized both numerically with the surface cooling technique and analytically, show that localization of energy occurs generically also in the presence of disorder, but is a site-dependent and, on a larger scale, a fold-dependent process. In particular, we find that, as a sheer consequence of disorder, a non-zero energy gap for exciting a DB at a given site either exists or not. Interestingly, in the former case, the gaps arise as a result of the impossibility of exciting small-amplitude modes in the first place. In the latter case, a small subset of linear localized modes act as accumulation points, whereby DBs can be continued to arbitrary small energies, while unavoidably approaching one of such normal modes. Remarkably, our cooling simulations show that localized modes of nonlinear origin form spontaneously in the stiffest parts of the structure. Analytic calculations further reveal that such regions are also the sectors where DBs are characterized by the smallest energy gaps. Besides being interesting per se, such results provide a straightforward way for interpreting the recently discovered link between local stiffness of proteins and enzymatic activity. They strongly suggest that nonlinear vibrational modes may play an important role in enzyme function, allowing for a ready energy storage channel during the catalytic process.
  • M. Poropat