  Most biochemical reactions in living cells rely on diffusive search for
target molecules or regions in a heterogeneous overcrowded cytoplasmic medium.
Rapid re-arrangements of the medium constantly change the effective diffusivity
felt locally by a diffusing particle and thus impact the distribution of the
first-passage time to a reaction event. Here, we investigate the effect of
these dynamic spatio-temporal heterogeneities onto diffusion-limited reactions.
We describe a general mathematical framework to translate many results for
ordinary homogeneous Brownian motion to heterogeneous diffusion. In particular,
we derive the probability density of the first-passage time to a reaction event
and show how the dynamic disorder broadens the distribution and increases the
likelihood of both short and long trajectories to reactive targets. While the
disorder slows down reaction kinetics on average, its dynamic character is
beneficial for a faster search and realization of an individual reaction event
triggered by a single molecule.
