Multi-Algorithm Particle Simulations with Spatiocyte

  • Satya N. V. ArjunanEmail author
  • Koichi TakahashiEmail author
Part of the Methods in Molecular Biology book series (MIMB, volume 1611)


As quantitative biologists get more measurements of spatially regulated systems such as cell division and polarization, simulation of reaction and diffusion of proteins using the data is becoming increasingly relevant to uncover the mechanisms underlying the systems. Spatiocyte is a lattice-based stochastic particle simulator for biochemical reaction and diffusion processes. Simulations can be performed at single molecule and compartment spatial scales simultaneously. Molecules can diffuse and react in 1D (filament), 2D (membrane), and 3D (cytosol) compartments. The implications of crowded regions in the cell can be investigated because each diffusing molecule has spatial dimensions. Spatiocyte adopts multi-algorithm and multi-timescale frameworks to simulate models that simultaneously employ deterministic, stochastic, and particle reaction-diffusion algorithms. Comparison of light microscopy images to simulation snapshots is supported by Spatiocyte microscopy visualization and molecule tagging features. Spatiocyte is open-source software and is freely available at .


Mathematical modeling Biophysical simulation Biochemical simulation Particle simulation Multi-algorithm simulation Diffusion 



We thank Masaki Watabe, Hanae Shimo, and Kaizu Kazunari for discussions that led to the improvement of Spatiocyte usage. We also appreciate Kozo Nishida for Spatiocyte software packaging, installation, and documentation assistance.


  1. 1.
    Fange D, Elf J (2006) Noise-induced min phenotypes in E. coli. PLoS Comput Biol 2(6):e80. doi: 10.1371/journal.pcbi.0020080 CrossRefPubMedPubMedCentralGoogle Scholar
  2. 2.
    Hecht I, Kessler DA, Levine H (2010) Transient localized patterns in noise-driven reaction-diffusion systems. Phys Rev Lett 104(15):158301. doi: 10.1103/PhysRevLett.104.158301 CrossRefPubMedPubMedCentralGoogle Scholar
  3. 3.
    Burrage K, Burrage PM, Marquez-lago T, Nicolau DV (2011) Stochastic simulation for spatial modelling of dynamic processes in a living cell. In: Koeppl H, Setti G, di Bernardo M, Densmore D (eds) Design and analysis of biomolecular circuits: engineering approaches to systems and synthetic biology. Springer, New York, NY, pp 43–62. doi: 10.1007/978-1-4419-6766-4 CrossRefGoogle Scholar
  4. 4.
    Klann M, Koeppl H (2012) Spatial simulations in systems biology: from molecules to cells. Int J Mol Sci 13(6):7798–7827. doi: 10.3390/ijms13067798 CrossRefPubMedPubMedCentralGoogle Scholar
  5. 5.
    Schöneberg J, Ullrich A, Noé F (2014) Simulation tools for particle-based reaction-diffusion dynamics in continuous space. BMC Biophys 7(1):11. doi: 10.1186/s13628-014-0011-5 CrossRefPubMedPubMedCentralGoogle Scholar
  6. 6.
    Karr JR, Takahashi K, Funahashi A (2015) The principles of whole-cell modeling. Curr Opin Microbiol 27:18–24. doi: 10.1016/j.mib.2015.06.004 CrossRefPubMedGoogle Scholar
  7. 7.
    Kerr RA, Bartol TM, Kaminsky B, Dittrich M, Chang J-CJ, Baden SB, Sejnowski TJ, Stiles JR (2008) Fast Monte Carlo simulation methods for biological reaction-diffusion Systems in Solution and on surfaces. SIAM J Sci Comput 30(6):3126–3149. doi: 10.1137/070692017 CrossRefPubMedPubMedCentralGoogle Scholar
  8. 8.
    Fange D, Mahmutovic A, Elf J (2012) MesoRD 1.0: Stochastic reaction-diffusion simulations in the microscopic limit. Bioinformatics 28:1–3. doi: 10.1093/bioinformatics/bts584 CrossRefGoogle Scholar
  9. 9.
    Angermann, B. R., Klauschen, F., Garcia, A. D., Prustel, T., Zhang, F., Germain, R. N., & Meier-Schellersheim, M. (2012). Computational modeling of cellular signaling processes embedded into dynamic spatial contexts. Nat Methods, (2011), 1–10. doi: 10.1038/nmeth.1861
  10. 10.
    Drawert B, Engblom S, Hellander A (2012) URDME : a modular framework for stochastic simulation of reaction-transport processes in complex geometries. BMC Syst Biol 6(76):1–17. doi: 10.1186/1752-0509-6-76 Google Scholar
  11. 11.
    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(1):36. doi: 10.1186/1752-0509-6-36 CrossRefPubMedPubMedCentralGoogle Scholar
  12. 12.
    Roberts E, Stone JE, Luthey-Schulten Z (2012) Lattice microbes: high-performance stochastic simulation method for the reaction-diffusion master equation. J Comput Chem. doi: 10.1002/jcc.23130 PubMedCentralGoogle Scholar
  13. 13.
    Andrews SS, Addy NJ, Brent R, Arkin AP (2010) Detailed simulations of cell biology with Smoldyn 2.1. PLoS Comput Biol 6(3):e1000705. doi: 10.1371/journal.pcbi.1000705 CrossRefPubMedPubMedCentralGoogle Scholar
  14. 14.
    Byrne MJ, Waxham MN, Kubota Y (2010) Cellular dynamic simulator: an event driven molecular simulation environment for cellular physiology. Neuroinformatics 8(2):63–82. doi: 10.1007/s12021-010-9066-x CrossRefPubMedPubMedCentralGoogle Scholar
  15. 15.
    Takahashi K, Tanase-Nicola S, ten Wolde PR (2010) Spatio-temporal correlations can drastically change the response of a MAPK pathway. Proc Natl Acad Sci U S A 107(6):2473–2478. doi: 10.1073/pnas.0906885107 CrossRefPubMedPubMedCentralGoogle Scholar
  16. 16.
    Tolle DP, Le Novere N (2010) Meredys, a multi-compartment reaction-diffusion simulator using multistate realistic molecular complexes. BMC Syst Biol 4(1):24. doi: 10.1186/1752-0509-4-24 CrossRefPubMedPubMedCentralGoogle Scholar
  17. 17.
    Schöneberg J, Noé F (2013) ReaDDy—a software for particle-based reaction-diffusion dynamics in crowded cellular environments. PLoS One 8(9):e74261. doi: 10.1371/journal.pone.0074261 CrossRefPubMedPubMedCentralGoogle Scholar
  18. 18.
    Karamitros, M., Luan, S., Bernal, M. A., Allison, J., Baldacchino, G., Davidkova, M., Z. Francis, W. Friedland, V. Ivantchenko, A. Ivantchenko, A. Mantero, P. Nieminem, G. Santin, H.N. Tran, V. Stepan, Incerti, S. (2014). Diffusion-controlled reactions modeling in Geant4-DNA. J Comput Phys, 274, 841–882. doi: 10.1016/
  19. 19.
    Michalski PJ, Loew LM (2016) SpringSaLaD: a spatial, particle-based biochemical simulation platform with excluded volume. Biophys J 110(3):523–529. CrossRefPubMedPubMedCentralGoogle Scholar
  20. 20.
    Hellander A, Hellander S, Lötstedt P (2012) Coupled mesoscopic and microscopic simulation of stochastic reaction-diffusion processes in mixed dimensions. Multiscale Model Simul 10(2):585–611. doi: 10.1137/110832148 CrossRefGoogle Scholar
  21. 21.
    Klann M, Ganguly A, Koeppl H (2012) Hybrid spatial Gillespie and particle tracking simulation. Bioinformatics 28(18):i549–i555. doi: 10.1093/bioinformatics/bts384 CrossRefPubMedPubMedCentralGoogle Scholar
  22. 22.
    Robinson M, Andrews SS, Erban R (2015) Multiscale reaction-diffusion simulations with Smoldyn. Bioinformatics 31(14):2406–2408. CrossRefPubMedPubMedCentralGoogle Scholar
  23. 23.
    Arjunan SNV, Kaizu K, Takahashi K. Spatiocyte: a stochastic particle simulator for filament, membrane and cytosolic reaction-diffusion processes. In preparation.Google Scholar
  24. 24.
    Arjunan SNV, 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. doi: 10.1007/s11693-009-9047-2 CrossRefPubMedGoogle Scholar
  25. 25.
    Gibson MA, Bruck J (2000) Efficient exact stochastic simulation of chemical systems with many species and many channels. J Phys Chem A 104(9):1876–1889. doi: 10.1021/jp993732q CrossRefGoogle Scholar
  26. 26.
    Arjunan SNV (2013) A guide to modeling reaction-diffusion of molecules with the E-cell system. In: Arjunan SNV, Tomita M, Dhar PK (eds) E-cell system: basic concepts and applications. Springer Science & Business Media, New York, NYCrossRefGoogle Scholar
  27. 27.
    King GF, Rowland SL, Pan B, Mackay JP, Mullen GP, Rothfield LI (1999) The dimerization and topological specificity functions of MinE reside in a structurally autonomous C-terminal domain. Mol Microbiol 31(4):1161–1169. doi: 10.1046/j.1365-2958.1999.01256.x CrossRefPubMedGoogle Scholar
  28. 28.
    Ma L-Y, King G, Rothfield L (2003) Mapping the MinE site involved in interaction with the MinD division site selection protein of Escherichia coli. J Bacteriol 185(16):4948–4955. doi: 10.1128/JB.185.16.4948-4955.2003 CrossRefPubMedPubMedCentralGoogle Scholar
  29. 29.
    Loose M, Fischer-Friedrich E, Herold C, Kruse K, Schwille P (2011) Min protein patterns emerge from rapid rebinding and membrane interaction of MinE. Nat Struct Mol Biol 18(5):577–583. doi: 10.1038/nsmb.2037 CrossRefPubMedGoogle Scholar
  30. 30.
    Park K-T, Wu W, Battaile KP, Lovell S, Holyoak T, Lutkenhaus J (2011) The Min oscillator uses MinD-dependent conformational changes in MinE to spatially regulate cytokinesis. Cell 146(3):396–407. doi: 10.1016/j.cell.2011.06.042 CrossRefPubMedPubMedCentralGoogle Scholar
  31. 31.
    Shimo H, Arjunan SNV, Machiyama H, Nishino T, Suematsu M, Fujita H, Tomita M, Takahashi K (2015) Particle simulation of oxidation induced band 3 clustering in human erythrocytes. PLoS Comput Biol 11(6):e1004210. doi: 10.1371/journal.pcbi.1004210 CrossRefPubMedPubMedCentralGoogle Scholar
  32. 32.
    Watabe M, Arjunan SNV, Fukushima S, Iwamoto K, Kozuka J, Matsuoka S, Shindo Y, Ueda M, Takahashi K (2015) A computational framework for bioimaging simulation. PLoS One 10(7):e0130089. doi: 10.1371/journal.pone.0130089 CrossRefPubMedPubMedCentralGoogle Scholar
  33. 33.
    Varma A, Huang KC, Young KD (2008) The Min system as a general cell geometry detection mechanism: branch lengths in Y-shaped Escherichia coli cells affect Min oscillation patterns and division dynamics. J Bacteriol 190(6):2106–2117. doi: 10.1128/JB.00720-07 CrossRefPubMedPubMedCentralGoogle Scholar
  34. 34.
    Schweizer J, Loose M, Bonny M, Kruse K, Monch I, Schwille P (2012) Geometry sensing by self-organized protein patterns. Proc Natl Acad Sci 109(38):15283–15288. doi: 10.1073/pnas.1206953109 CrossRefPubMedPubMedCentralGoogle Scholar
  35. 35.
    Halatek J, Frey E (2014) Effective 2D model does not account for geometry sensing by self-organized proteins patterns. Proc Natl Acad Sci 111(18):E1817–E1817. doi: 10.1073/pnas.1220971111 CrossRefPubMedPubMedCentralGoogle Scholar
  36. 36.
    Wu F, van Schie BGC, Keymer JE, Dekker C (2015) Symmetry and scale orient Min protein patterns in shaped bacterial sculptures. Nat Nanotechnol 10(8):719–726. doi: 10.1038/nnano.2015.126 CrossRefPubMedPubMedCentralGoogle Scholar
  37. 37.
    Zieske K, Schwille P (2015) Reconstituting geometry-modulated protein patterns in membrane compartments. Methods Cell Biol 128:149–163. doi: 10.1016/bs.mcb.2015.02.006 CrossRefPubMedGoogle Scholar
  38. 38.
    Zieske K, Schweizer J, Schwille P (2014) Surface topology assisted alignment of Min protein waves. FEBS Lett 588(15):2545–2549. doi: 10.1016/j.febslet.2014.06.026 CrossRefPubMedGoogle Scholar

Copyright information

© Springer Science+Business Media LLC 2017

Authors and Affiliations

  1. 1.Laboratory for Biochemical SimulationRIKEN Quantitative Biology CenterSuitaJapan

Personalised recommendations