  From the point of view of statistical mechanics, a full characterisation of a
molecular system requires the experimental determination of its possible
states, their populations and the respective interconversion rates.
Well-established methods can incorporate in molecular dynamics simulations
experimental information about states using structural restraints, and about
populations using thermodynamic restraints. However, it is still unclear how to
include experimental knowledge of interconversion rates. Here we introduce a
method of imposing known rate constants as constraints in molecular dynamics
simulations, which is based on a combination of the maximum entropy and maximum
caliber principles. Starting from an existing ensemble of trajectories,
obtained from either molecular dynamics or enhanced trajectory sampling, this
method provides a minimally perturbed path distribution consistent with the
kinetic constraints, as well as a modified free energy and committor landscape.
We illustrate the application of the method to simple toy systems, as well as
to all atom molecular simulations of peptide association and folding. We find
that by combining experimental rate coefficient data and molecular dynamics
simulations we are able to determine new transition states, reaction mechanisms
and free energies. For instance, in the case of chignolin protein folding we
find that imposing a slower folding rate shifts the transition state to more
native like conformations, while it increases the stability of the unfolded
region.
