  Heterogeneity in biological molecules, resulting in molecule-to-molecule
variations in their dynamics and function, is an emerging theme. To elucidate
the consequences of heterogeneous behavior at the single molecule level, we
propose an exactly solvable model in which the unfolding rate due to mechanical
force depends parametrically on an auxiliary variable representing an entropy
barrier arising from fluctuations in internal dynamics. When the rate of
fluctuations, a measure of dynamical disorder, is comparable to or smaller than
the rate of force-induced unbinding, we show that there are two experimentally
observable consequences: non-exponential survival probability at constant
force, and a heavy-tailed rupture force distribution at constant loading rate.
By fitting our analytical expressions to data from single molecule pulling
experiments on proteins and DNA, we quantify the extent of disorder. We show
that only by analyzing data over a wide range of forces and loading rates can
the role of disorder due to internal dynamics be quantitatively assessed.
