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Diffusion-limited reactions in dynamic heterogeneous media

Author

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  • Yann Lanoiselée

    (CNRS—Ecole Polytechnique, University Paris-Saclay)

  • Nicolas Moutal

    (CNRS—Ecole Polytechnique, University Paris-Saclay)

  • Denis S. Grebenkov

    (CNRS—Ecole Polytechnique, University Paris-Saclay)

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.

Suggested Citation

  • Yann Lanoiselée & Nicolas Moutal & Denis S. Grebenkov, 2018. "Diffusion-limited reactions in dynamic heterogeneous media," Nature Communications, Nature, vol. 9(1), pages 1-16, December.
    • Handle: RePEc:nat:natcom:v:9:y:2018:i:1:d:10.1038_s41467-018-06610-6
    DOI: 10.1038/s41467-018-06610-6
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    Cited by:

    1. Gorka Muñoz-Gil & Giovanni Volpe & Miguel Angel Garcia-March & Erez Aghion & Aykut Argun & Chang Beom Hong & Tom Bland & Stefano Bo & J. Alberto Conejero & Nicolás Firbas & Òscar Garibo i Orts & Aless, 2021. "Objective comparison of methods to decode anomalous diffusion," Nature Communications, Nature, vol. 12(1), pages 1-16, December.
    2. Mutothya, Nicholas Mwilu & Xu, Yong, 2021. "Mean first passage time for diffuse and rest search in a confined spherical domain," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 567(C).
    3. Ahamad, Nabi & Debnath, Pallavi, 2020. "Rouse model in crowded environment modeled by “diffusing diffusivity”," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 549(C).
    4. Janczura, Joanna & Burnecki, Krzysztof & Muszkieta, Monika & Stanislavsky, Aleksander & Weron, Aleksander, 2022. "Classification of random trajectories based on the fractional Lévy stable motion," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).

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