Localization and energy transfer in nonlinear many-body systems with disorder: the case of corse-grained network models of proteins.

Very little is known concerning the combined effects of nonlinearity
and disorder
in discrete many-body dynamical systems. Yet, they seem to be
characterized by
an extremely rich physics, only partially uncovered and rationalized,
including the recently reported evidences for destruction of Anderson
localization
by virtue of anharmonicity.

Here, we focus on three-dimensional nonlinear coarse-grained models
of proteins, that is dynamical systems disordered in the sense of
spatially heterogeneous (quenched disorder). Our main motivation is to
explore the interplay of nonlinearity and disorder as a possible
source for
mechanisms regulating the striking storage and long-range energy
transfer phenomena occurring in many proteins.

We first examine the properties of Discrete Breathers (DB), i.e.
generic and
robust spatially-localized vibrational modes of nonlinear origin. It
turns out
that they easily self-excite in a given structure, but only at very
few specific
locations. A thorough analysis over a large enzyme database reveals
that the latter
invariably identify catalytic sites, thus suggesting that DBs may play
an active role in effectively storing energy in functional regions
of the protein folds.
An analytical study allows to rationalize the striking site-
selectiveness of
nonlinearity-fostered energy localization in terms of a hierarchy of
excitation
thresholds in the DB spectra, arising as a sheer consequence of
spatial disorder.
In particular, we find that the majority of sites in a given protein
structure
feature spot-dependent energy gaps for local DB excitation, while
few selected locations exist where DBs can be excited at arbitrary
small energies.
Finally, we discuss some recent results on the effects of nonlinearity
in enhancing long-range energy transfer across protein structures.

[1] B. Juanico, Y.-H. Sanejouand, F. Piazza and P. De Los Rios
Discrete breathers in nonlinear network models of proteins
Physical Review Letters - 99, 238104 (2007).


[2] F. Piazza and Y.-H. Sanejouand
Discrete breathers in protein structures
Physical Biology - 5, 026001 (2008).