  In this paper we propose a novel theoretical framework for interpreting
long-range dynamical correlations unveiled in proteins through NMR
measurements. The theoretical rationale relies on the hypothesis that
correlated motions in proteins may be reconstructed as large-scale, collective
modes sustained by long-lived nonlinear vibrations known as discrete breathers
(DB) localized at key, hot-spot sites. DBs are spatially localized modes, whose
nonlinear nature hinders resonant coupling with the normal modes, thus
conferring them long lifetimes as compared to normal modes. DBs have been
predicted to exist in proteins, localized at few $hotspot$ residues typically
within the stiffest portions of the structure. We compute DB modes analytically
in the framework of the nonlinear network model, showing that the displacement
patterns of many DBs localized at key sites match to a remarkable extent the
experimentally uncovered correlation blueprint. The computed dispersion
relations prove that it is physically possible for some of these DBs to be
excited out of thermal fluctuations at room temperature.
  Based on our calculations, we speculate that transient energy redistribution
among the vibrational modes in a protein might favor the emergence of DB-like
bursts of long-lived energy at hot-spot sites with lifetimes in the ns range,
able to sustain critical, function-encoding correlated motions. More generally,
our calculations provide a novel quantitative tool to predict fold-spanning
dynamical pathways of correlated residues that may be central to allosteric
cross-talk in proteins.
