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Stochastic Reaction–Diffusion Processes with Embedded Lower-Dimensional Structures

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Abstract

Small copy numbers of many molecular species in biological cells require stochastic models of the chemical reactions between the molecules and their motion. Important reactions often take place on one-dimensional structures embedded in three dimensions with molecules migrating between the dimensions. Examples of polymer structures in cells are DNA, microtubules, and actin filaments. An algorithm for simulation of such systems is developed at a mesoscopic level of approximation. An arbitrarily shaped polymer is coupled to a background Cartesian mesh in three dimensions. The realization of the system is made with a stochastic simulation algorithm in the spirit of Gillespie. The method is applied to model problems for verification and two more detailed models of transcription factor interaction with the DNA.

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Acknowledgements

This work has been supported by the Swedish Research Council (SH, SW), the European Research Council (JE), and the NIH grant for StochSS with number 1R01EB014877-01 (SH).

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Authors and Affiliations

  1. Division of Scientific Computing, Department of Information Technology, Uppsala University, P.O. Box 337, 75105, Uppsala, Sweden

    Siyang Wang, Stefan Hellander & Per Lötstedt

  2. Division of Computational and Systems Biology, Department of Cell and Molecular Biology, Science for Life Laboratory, Uppsala University, P.O. Box 596, 75124, Uppsala, Sweden

    Johan Elf

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  1. Siyang Wang
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  4. Per Lötstedt
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Correspondence to Per Lötstedt.

Appendix

Appendix

Table 7 Biochemical parameters in Sect. 4
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Table 8 Discretization parameters in Sect. 4
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Wang, S., Elf, J., Hellander, S. et al. Stochastic Reaction–Diffusion Processes with Embedded Lower-Dimensional Structures. Bull Math Biol 76, 819–853 (2014). https://doi.org/10.1007/s11538-013-9910-x

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