  The assumption of linear response of protein molecules to thermal noise or
structural perturbations, such as ligand binding or detachment, is broadly used
in the studies of protein dynamics. Conformational motions in proteins are
traditionally analyzed in terms of normal modes and experimental data on
thermal fluctuations in such macromolecules is also usually interpreted in
terms of the excitation of normal modes. We have chosen two important protein
motors - myosin V and kinesin KIF1A - and performed numerical investigations of
their conformational relaxation properties within the coarse-grained elastic
network approximation. We have found that the linearity assumption is deficient
for ligand-induced conformational motions and can even be violated for
characteristic thermal fluctuations. The deficiency is particularly pronounced
in KIF1A where the normal mode description fails completely in describing
functional mechanochemical motions. These results indicate that important
assumptions of the theory of protein dynamics may need to be reconsidered.
Neither a single normal mode, nor a superposition of such modes yield an
approximation of strongly nonlinear dynamics.
