Lanoiselée Y, Moutal N, Grebenkov DS. Diffusion-limited reactions in dynamic heterogeneous media.
Nat Commun 2018;
9:4398. [PMID:
30353010 PMCID:
PMC6199324 DOI:
10.1038/s41467-018-06610-6]
[Citation(s) in RCA: 80] [Impact Index Per Article: 13.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/10/2018] [Accepted: 09/11/2018] [Indexed: 12/02/2022] Open
Abstract
Most biochemical reactions in living cells rely on diffusive search for target molecules or regions in a heterogeneous overcrowded cytoplasmic medium. Rapid rearrangements 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 spatiotemporal 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.
“Diffusing diffusivity” concept has been recently put forward to account for rapid structural rearrangements in soft matter and biological systems. Here the authors propose a general mathematical framework to compute the distribution of first-passage times in a dynamically heterogeneous medium.
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