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Multiscale Modeling of Diffusion in a Crowded Environment

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Abstract

We present a multiscale approach to model diffusion in a crowded environment and its effect on the reaction rates. Diffusion in biological systems is often modeled by a discrete space jump process in order to capture the inherent noise of biological systems, which becomes important in the low copy number regime. To model diffusion in the crowded cell environment efficiently, we compute the jump rates in this mesoscopic model from local first exit times, which account for the microscopic positions of the crowding molecules, while the diffusing molecules jump on a coarser Cartesian grid. We then extract a macroscopic description from the resulting jump rates, where the excluded volume effect is modeled by a diffusion equation with space-dependent diffusion coefficient. The crowding molecules can be of arbitrary shape and size, and numerical experiments demonstrate that those factors together with the size of the diffusing molecule play a crucial role on the magnitude of the decrease in diffusive motion. When correcting the reaction rates for the altered diffusion we can show that molecular crowding either enhances or inhibits chemical reactions depending on local fluctuations of the obstacle density.

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Acknowledgements

This work was supported by the Swedish Research Council Grant 621-2001-3148 and the NIH grant for StochSS with number 1R01EB014877-01. The author would like to thank the Computational Systems Biology group at Uppsala University for fruitful discussions and Markus Eriksson for the Smoldyn simulations.

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  1. Department of Information Technology, Uppsala University, Uppsala, Sweden

    Lina Meinecke

  2. University of California at Irvine, Irvine, CA, USA

    Lina Meinecke

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Meinecke, L. Multiscale Modeling of Diffusion in a Crowded Environment. Bull Math Biol 79, 2672–2695 (2017). https://doi.org/10.1007/s11538-017-0346-6

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