  The concept of a protein diffusing in its free energy folding landscape has
been fruitful for both theory and experiment. Yet the choice of the reaction
coordinate (RC) introduces an undesirable degree of arbitrariness into the
problem. We analyze extensive simulation data of an alpha-helix in explicit
water solvent as it stochastically folds and unfolds. The free energy profiles
for different RCs exhibit significant variation, some having an activation
barrier, others not. We show that this variation has little effect on the
predicted folding kinetics if the diffusivity profiles are properly taken into
account. This kinetic quasi-universality is rationalized by an RC rescaling,
which, due to the reparameterization invariance of the Fokker-Planck equation,
allows the combination of free energy and diffusivity effects into a single
function, the rescaled free energy profile. This rescaled free energy indeed
shows less variation among different RCs than the bare free energy and
diffusivity profiles separately do, if we properly distinguish between RCs that
contain knowledge of the native state and those that are purely geometric in
nature. Our method for extracting diffusivity profiles is easily applied to
experimental single molecule time series data and might help to reconcile
conflicts that arise when comparing results from different experimental probes
for the same protein.
