Skip to main content
SpringerLink
Log in

Multiscale Stochastic Reaction–Diffusion Modeling: Application to Actin Dynamics in Filopodia

  • Original Article
  • Published:
Bulletin of Mathematical Biology Aims and scope Submit manuscript

Abstract

Two multiscale (hybrid) stochastic reaction–diffusion models of actin dynamics in a filopodium are investigated. Both hybrid algorithms combine compartment-based and molecular-based stochastic reaction–diffusion models. The first hybrid model is based on the models previously developed in the literature. The second hybrid model is based on the application of a recently developed two-regime method (TRM) to a fully molecular-based model, which is also developed in this paper. The results of hybrid models are compared with the results of the molecular-based model. It is shown that both approaches give comparable results, although the TRM model better agrees quantitatively with the molecular-based model.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  • Andrews, S. (2005). Serial rebinding of ligands to clustered receptors as exemplified by bacterial chemotaxis. Phys. Biol., 2, 111–122.

    Article  Google Scholar 

  • Andrews, S., & Bray, D. (2004). Stochastic simulation of chemical reactions with spatial resolution and single molecule detail. Phys. Biol., 1, 137–151.

    Article  Google Scholar 

  • Arjunan, S., & Tomita, M. (2010). A new multicompartmental reaction–diffusion modeling method links transient membrane attachment of E. coli MinE to E-ring formation. Syst. Synth. Biol., 4(1), 35–53.

    Article  Google Scholar 

  • Cao, Y., Li, H., & Petzold, L. (2004). Efficient formulation of the stochastic simulation algorithm for chemically reacting systems. J. Chem. Phys., 121(9), 4059–4067.

    Article  Google Scholar 

  • Engblom, S., Ferm, L., Hellander, A., & Lötstedt, P. (2009). Simulation of stochastic reaction–diffusion processes on unstructured meshes. SIAM J. Sci. Comput., 31, 1774–1797.

    Article  MathSciNet  MATH  Google Scholar 

  • Erban, R., & Chapman, S. J. (2007). Reactive boundary conditions for stochastic simulations of reaction–diffusion processes. Phys. Biol., 4(1), 16–28.

    Article  Google Scholar 

  • Erban, R., & Chapman, S. J. (2009). Stochastic modeling of reaction–diffusion processes: algorithms for bimolecular reactions. Phys. Biol., 6(4), 046001.

    Article  Google Scholar 

  • Erban, R., Chapman, S. J., & Maini, P. (2007). A practical guide to stochastic simulations of reaction–diffusion processes, 35 pages, arXiv:0704.1908.

  • Ferm, L., Hellander, A., & Lötstedt, P. (2010). An adaptive algorithm for simulation of stochastic reaction–diffusion processes. J. Comput. Phys., 229, 343–360.

    Article  MathSciNet  MATH  Google Scholar 

  • Flegg, M., Chapman, J., & Erban, R. (2012). The two-regime method for optimizing stochastic reaction–diffusion simulations. J. R. Soc. Interface, 9(70), 859–868.

    Article  Google Scholar 

  • Flegg, M., Rüdiger, S., & Erban, R. (2013). Diffusive spatio-temporal noise in a first-passage time model for intracellular calcium release. J. Chem. Phys. doi:10.1063/1.4796417.

    Google Scholar 

  • Flekkøy, E., Feder, J., & Wagner, G. (2001). Coupling particles and fields in a diffusive hybrid model. Phys. Rev. E, 64, 066302.

    Article  Google Scholar 

  • Franz, B., Flegg, M., Chapman, J., & Erban, R. (2013, to appear). Multiscale reaction–diffusion algorithms: PDE-assisted Brownian dynamics. SIAM J. Appl. Math. arXiv:1206.5860.

    Google Scholar 

  • Gibson, M., & Bruck, J. (2000). Efficient exact stochastic simulation of chemical systems with many species and many channels. J. Phys. Chem. A, 104, 1876–1889.

    Article  Google Scholar 

  • Gillespie, D. (1977). Exact stochastic simulation of coupled chemical reactions. J. Phys. Chem., 81(25), 2340–2361.

    Article  Google Scholar 

  • Hattne, J., Fange, D., & Elf, J. (2005). Stochastic reaction–diffusion simulation with MesoRD. Bioinformatics, 21(12), 2923–2924.

    Article  Google Scholar 

  • Hepburn, I., Chen, W., Wils, S., & De Schutter, E. (2012). STEPS: efficient simulation of stochastic reaction–diffusion models in realistic morphologies. BMC Syst. Biol., 6, 36.

    Article  Google Scholar 

  • Ho, C.-P. (2012). Multi-scale reaction diffusion simulations in biology. M.Sc. Thesis, University of Oxford.

  • Hu, L., & Papoian, G. A. (2010). Mechano-chemical feedbacks regulate actin mesh growth in lamellipodial protrusions. Biophys. J., 98(8), 1375–1384.

    Article  Google Scholar 

  • Lan, Y., & Papoian, G. A. (2008). The stochastic dynamics of filopodial growth. Biophys. J., 94, 3839–3852.

    Article  Google Scholar 

  • Lipkova, J., Zygalakis, K., Chapman, J., & Erban, R. (2011). Analysis of Brownian dynamics simulations of reversible bimolecular reactions. SIAM J. Appl. Math., 71(3), 714–730.

    Article  MathSciNet  MATH  Google Scholar 

  • Moro, E. (2004). Hybrid method for simulating front propagation in reaction–diffusion systems. Phys. Rev. E, 69, 060101.

    Article  Google Scholar 

  • Noselli, S. (2002). Drosophila, actin and videotape—new insights in wound healing. Nat. Cell Biol., 4, 251–253.

    Article  Google Scholar 

  • Opplestrup, T., Bulatov, V., Donev, A., Kalos, M., Gilmer, G., & Sadigh, B. (2009). First-passage kinetic Monte Carlo method. Phys. Rev. E, 80(6), 066701.

    Article  Google Scholar 

  • Schaus, T., Taylor, E., & Borisy, G. (2007). Self-organization of actin filament orientation in the dendritic-nucleation/array-treadmilling model. Proc. Natl. Acad. Sci. USA, 104, 7086–7091.

    Article  Google Scholar 

  • Stiles, J., & Bartol, T. (2001). Monte Carlo methods for simulating realistic synaptic microphysiology using MCell. In E. Schutter (Ed.), Computational neuroscience: realistic modeling for experimentalists (pp. 87–127). Boca Raton: CRC Press.

    Google Scholar 

  • van Zon, J., & ten Wolde, P. (2005). Green’s-function reaction dynamics: a particle-based approach for simulating biochemical networks in time and space. J. Chem. Phys., 123, 234910.

    Article  Google Scholar 

  • Wagner, G., & Flekkøy, E. (2004). Hybrid computations with flux exchange. Philos. Trans. R. Soc. A, Math. Phys. Eng. Sci., 362, 1655–1665.

    Article  MathSciNet  MATH  Google Scholar 

  • Yamazaki, D., Kurisu, S., & Takenawa, T. (2005). Regulation of cancer cell motility through actin reorganization. Cancer Sci., 96(7), 379–386.

    Article  Google Scholar 

  • Zhuravlev, P., & Papoian, G. (2009). Molecular noise of capping protein binding induces macroscopic instability in filopodial dynamics. Proc. Natl. Acad. Sci. USA, 106(28), 11570–11575.

    Article  Google Scholar 

  • Zhuravlev, P., & Papoian, G. A. (2011). Protein fluxes along the filopodium as a framework for understanding the growth-retraction dynamics: the interplay between diffusion and active transport. Cell Adhes. Migr., 5(5), 448–456.

    Article  Google Scholar 

  • Zhuravlev, P., Der, B., & Papoian, G. A. (2010). Design of active transport must be highly intricate: a possible role of myosin and ena/VASP for G-actin transport in filopodia. Biophys. J., 98, 1439–1448.

    Article  Google Scholar 

  • Zhuravlev, P., Lan, Y., Minakova, M., & Papoian, G. A. (2012). Theory of active transport in filopodia and stereocilia. Proc. Natl. Acad. Sci. USA, 109, 10849–10854.

    Article  Google Scholar 

Download references

Acknowledgements

The research leading to these results has received funding from the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007–2013)/ ERC grant agreement No. 239870. Radek Erban would also like to thank Brasenose College, University of Oxford, for a Nicholas Kurti Junior Fellowship; the Royal Society for a University Research Fellowship; and the Leverhulme Trust for a Philip Leverhulme Prize. This prize money was used to support a research visit of Garegin Papoian in Oxford. Garegin Papoian was also supported by the National Science Foundation CAREER Award CHE-0846701.

Author information

Authors and Affiliations

  1. Mathematical Institute, University of Oxford, 24-29 St. Giles’, Oxford, OX1 3LB, UK

    Radek Erban & Mark B. Flegg

  2. Department of Chemistry & Biochemistry, University of Maryland, Chemistry Bldg 2216, College Park, MD, 20742-2021, USA

    Garegin A. Papoian

Authors
  1. Radek Erban
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mark B. Flegg
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Garegin A. Papoian
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Radek Erban.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Erban, R., Flegg, M.B. & Papoian, G.A. Multiscale Stochastic Reaction–Diffusion Modeling: Application to Actin Dynamics in Filopodia. Bull Math Biol 76, 799–818 (2014). https://doi.org/10.1007/s11538-013-9844-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11538-013-9844-3

Keywords

Search

Navigation