MCell-R: A Particle-Resolution Network-Free Spatial Modeling Framework

Part of the Methods in Molecular Biology book series (MIMB, volume 1945)


Spatial heterogeneity can have dramatic effects on the biochemical networks that drive cell regulation and decision-making. For this reason, a number of methods have been developed to model spatial heterogeneity and incorporated into widely used modeling platforms. Unfortunately, the standard approaches for specifying and simulating chemical reaction networks become untenable when dealing with multistate, multicomponent systems that are characterized by combinatorial complexity. To address this issue, we developed MCell-R, a framework that extends the particle-based spatial Monte Carlo simulator, MCell, with the rule-based model specification and simulation capabilities provided by BioNetGen and NFsim. The BioNetGen syntax enables the specification of biomolecules as structured objects whose components can have different internal states that represent such features as covalent modification and conformation and which can bind components of other molecules to form molecular complexes. The network-free simulation algorithm used by NFsim enables efficient simulation of rule-based models even when the size of the network implied by the biochemical rules is too large to enumerate explicitly, which frequently occurs in detailed models of biochemical signaling. The result is a framework that can efficiently simulate systems characterized by combinatorial complexity at the level of spatially resolved individual molecules over biologically relevant time and length scales.

Key words

Rule-based modeling Spatial modeling Particle-based modeling Stochastic simulation Network-free simulation Compartmental modeling 



This work was supported in part by the US National Institutes of Health grants P41GM103712 and R01GM115805.


  1. 1.
    Chylek LA, Harris LA, Tung C-S, Faeder JR, Lopez CF, Hlavacek WS (2013) Rule-based modeling: a computational approach for studying biomolecular site dynamics in cell signaling systems. Wiley Interdiscip Rev Syst Biol Med 6(1):13–36CrossRefGoogle Scholar
  2. 2.
    Gillespie DT (1977) Exact stochastic simulation of coupled chemical reactions. J Phys Chem 81(25):2340–2361CrossRefGoogle Scholar
  3. 3.
    Funahashi A, Matsuoka Y, Jouraku A, Morohashi M, Kikuchi N, Kitano H (2008) CellDesigner 3.5: a versatile modeling tool for biochemical networks. Proc IEEE 96(8):1254–1265CrossRefGoogle Scholar
  4. 4.
    Hoops S et al (2006) COPASI--a COmplex PAthway SImulator. Bioinformatics 22(24):3067–3074CrossRefGoogle Scholar
  5. 5.
    Bartol TM et al (2015) Computational reconstitution of spine calcium transients from individual proteins. Front Synaptic Neurosci 7:17CrossRefGoogle Scholar
  6. 6.
    Kerr RA, Levine H, Sejnowski TJ, Rappel W-J (2006) Division accuracy in a stochastic model of Min oscillations in Escherichia coli. Proc Natl Acad Sci U S A 103(2):347–352CrossRefGoogle Scholar
  7. 7.
    Takahashi K, Arjunan SNV, Tomita M (2005) Space in systems biology of signaling pathways – towards intracellular molecular crowding in silico. FEBS Lett 579(8):1783–1788CrossRefGoogle Scholar
  8. 8.
    Takahashi K, Tanase-Nicola S, ten Wolde PR (Feb. 2010) Spatio-temporal correlations can drastically change the response of a MAPK pathway. Proc Natl Acad Sci U S A 107(6):2473–2478CrossRefGoogle Scholar
  9. 9.
    Moraru II et al (2008) Virtual Cell modelling and simulation software environment. IET Syst Biol 2(5):352–362CrossRefGoogle Scholar
  10. 10.
    Hattne J, Fange D, Elf J (2005) Stochastic reaction-diffusion simulation with MesoRD. Bioinformatics 21(12):2923–2924CrossRefGoogle Scholar
  11. 11.
    Gillespie DT, Hellander A, Petzold LR (2013) Perspective: stochastic algorithms for chemical kinetics. J Chem Phys 138(17):170901–144908CrossRefGoogle Scholar
  12. 12.
    Drawert B et al (2016) Stochastic simulation service: bridging the gap between the computational expert and the biologist. PLoS Comput Biol 12(12):e1005220CrossRefGoogle 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):e1000705CrossRefGoogle Scholar
  14. 14.
    Kerr RA et al (2008) Fast Monte Carlo simulation methods for biological reaction-diffusion systems in solution and on surfaces. SIAM J Sci Comput 30(6):3126–3149CrossRefGoogle Scholar
  15. 15.
    Hlavacek WS, Faeder JR, Blinov ML, Perelson AS, Goldstein B (2003) The complexity of complexes in signal transduction. Biotechnol Bioeng 84(7):783–794CrossRefGoogle Scholar
  16. 16.
    Sneddon MW, Faeder JR, Emonet T (2011) Efficient modeling, simulation and coarse-graining of biological complexity with NFsim. Nat Methods 8(2):177–183CrossRefGoogle Scholar
  17. 17.
    Blinov ML, Faeder JR, Goldstein B, Hlavacek WS (2004) BioNetGen: software for rule-based modeling of signal transduction based on the interactions of molecular domains. Bioinformatics 20(17):3289–3291CrossRefGoogle Scholar
  18. 18.
    Danos V, Feret J, Fontana W, Krivine J (2007) Scalable simulation of cellular signaling networks. Lect Notes Comput Sci 4807:139–157CrossRefGoogle Scholar
  19. 19.
    Meier-Schellersheim M, Xu X, Angermann B, Kunkel EJ, Jin T, Germain RN (2006) Key role of local regulation in chemosensing revealed by a new molecular interaction-based modeling method. PLoS Comput Biol 2:0710–0724CrossRefGoogle Scholar
  20. 20.
    Chylek LA, Harris LA, Faeder JR, Hlavacek WS (2015) Modeling for (physical) biologists: an introduction to the rule-based approach. Phys Biol 12(4):045007CrossRefGoogle Scholar
  21. 21.
    Faeder JR, Blinov ML, Hlavacek WS (2009) Rule-based modeling of biochemical systems with BioNetGen. Methods Mol Biol 500:113–167CrossRefGoogle Scholar
  22. 22.
    Boutillier P et al (2018) The Kappa platform for rule-based modeling. Bioinformatics 34(13):i583–i592CrossRefGoogle Scholar
  23. 23.
    Angermann BR et al (2012) Computational modeling of cellular signaling processes embedded into dynamic spatial contexts. Nat Methods 9:283–289CrossRefGoogle Scholar
  24. 24.
    Harris LA, Hogg JS, Faeder JR (2009) Compartmental rule-based modeling of biochemical systems. In: Proceedings of the 2009 Winter Simulation Conference (WSC), pp 908–919Google Scholar
  25. 25.
    Lis M, Artyomov MN, Devadas S, Chakraborty AK (2009) Efficient stochastic simulation of reaction–diffusion processes via direct compilation. Bioinformatics 25(17):2289–2291CrossRefGoogle Scholar
  26. 26.
    Sorokina O, Sorokin A, Armstrong JD, Danos V (2013) A simulator for spatially extended kappa models. Bioinformatics 29(23):3105–3106CrossRefGoogle Scholar
  27. 27.
    Andrews SS (2017) Smoldyn: particle-based simulation with rule-based modeling, improved molecular interaction and a library interface. Bioinformatics 33(5):710–717CrossRefGoogle Scholar
  28. 28.
    Michalski PJ, Loew LM (2016) SpringSaLaD: a spatial, particle-based biochemical simulation platform with excluded volume. Biophys J 110(3):523–529CrossRefGoogle Scholar
  29. 29.
    Grünert G, Ibrahim B, Lenser T, Lohel M, Hinze T, Dittrich P (2010) Rule-based spatial modeling with diffusing, geometrically constrained molecules. BMC Bioinformatics 11(1):307CrossRefGoogle Scholar
  30. 30.
    Grünert G, Dittrich P (2011) Using the SRSim software for spatial and rule-based modeling of combinatorially complex biochemical reaction systems, vol. 6501, pp 240–256Google Scholar
  31. 31.
    Suderman R, Mitra ED, Lin YT, Erickson KE, Feng S, Hlavacek WS (2018) Generalizing Gillespie’s direct method to enable network-free simulations. Bull Math Biol:1–27Google Scholar
  32. 32.
    Michalski PJ, Loew LM (2012) CaMKII activation and dynamics are independent of the holoenzyme structure: an infinite subunit holoenzyme approximation. Phys Biol 9(3):036010CrossRefGoogle Scholar
  33. 33.
    Hogg JS, Harris LA, Stover LJ, Nair NS, Faeder JR (2014) Exact hybrid particle/population simulation of rule-based models of biochemical systems. PLoS Comput Biol 10(4):e1003544CrossRefGoogle Scholar
  34. 34.
    Le Novère N, Shimizu TS (2001) STOCHSIM: modelling of stochastic biomolecular processes. Bioinformatics (Oxford, England) 17(6):575–576CrossRefGoogle Scholar
  35. 35.
    Colvin J, Monine MI, Gutenkunst RN, Hlavacek WS, Von Hoff DD, Posner RG (2010) RuleMonkey: software for stochastic simulation of rule-based models. BMC Bioinformatics 11:404CrossRefGoogle Scholar
  36. 36.
    Gupta S et al (2018) Spatial stochastic modeling with MCell and CellBlender. In: Munksy B, Hlavacek W, Tsimring L (eds) Quantitative biology: theory, computational methods and examples of models. MIT Press, Cambridge, MAGoogle Scholar
  37. 37.
    Miller CC (1924) The Stokes-Einstein Law for diffusion in solution. Proc R Soc London Ser A, Contain Pap A Math Phys Character 106(740):724–749CrossRefGoogle Scholar
  38. 38.
    Saffman PG, Delbrück M (1975) Brownian motion in biological membranes. Proc Natl Acad Sci U S A 72(8):3111–3113CrossRefGoogle Scholar
  39. 39.
    McKay BD (1981) Practical graph isomorphism. Congr Numer 30:45–87Google Scholar
  40. 40.
    Tapia JJ (2016) A study on systems modeling frameworks and their interoperability. University of Pittsburgh, Pittsburgh, PAGoogle Scholar
  41. 41.
    Sekar JA, Faeder JR (2012) Rule-based modeling of signal transduction: a primer. Methods Mol Biol 880:139–218CrossRefGoogle Scholar
  42. 42.
    Perelson AS, DeLisi C (1980) Receptor clustering on a cell surface. I. theory of receptor cross-linking by ligands bearing two chemically identical functional groups. Math Biosci 48(1–2):71–110CrossRefGoogle Scholar
  43. 43.
    Gilfillan AM, Rivera J (2009) The tyrosine kinase network regulating mast cell activation. Immunol Rev 228(1):149–169CrossRefGoogle Scholar
  44. 44.
    Goldstein B, Faeder JR, Hlavacek WS, Blinov ML, Redondo A, Wofsy C (2002) Modeling the early signaling events mediated by FcepsilonRI. Mol Immunol 38(16–18):1213–1219CrossRefGoogle Scholar
  45. 45.
    Faeder JR et al (2003) Investigation of early events in Fc epsilon RI-mediated signaling using a detailed mathematical model. J Immunol 170:3769–3781CrossRefGoogle Scholar
  46. 46.
    Falkenberg CV, Blinov ML, Azeloglu EU, Neves SR, Iyengar R, Loew LM (2012) A mathematical model for nephrin localization in podocyte foot processes. Biophys J 102(3):593a–594aCrossRefGoogle Scholar
  47. 47.
    Nag A, Monine MI, Faeder JR, Goldstein B (2009) Aggregation of membrane proteins by cytosolic cross-linkers: theory and simulation of the LAT-Grb2-SOS1 system. Biophys J 96(7):2604–2623CrossRefGoogle Scholar
  48. 48.
    Stefan MI, Bartol TM, Sejnowski TJ, Kennedy MB (2014) Multi-state modeling of biomolecules. PLoS Comput Biol 10(9):e1003844CrossRefGoogle Scholar
  49. 49.
    Michalski PJ (2013) The delicate bistability of CaMKII. Biophys J 105(3):794–806CrossRefGoogle Scholar
  50. 50.
    Zwier MC et al (2015) WESTPA: an interoperable, highly scalable software package for weighted ensemble simulation and analysis. J Chem Theory Comput 11(2):800–809CrossRefGoogle Scholar
  51. 51.
    Donovan RM, Sedgewick AJ, Faeder JR, Zuckerman DM (2013) Efficient stochastic simulation of chemical kinetics networks using a weighted ensemble of trajectories. J Chem Phys 139(11):115105CrossRefGoogle Scholar
  52. 52.
    Donovan RM et al (2016) Unbiased rare event sampling in spatial stochastic systems biology models using a weighted ensemble of trajectories. PLoS Comput Biol 12(2):e1004611CrossRefGoogle Scholar
  53. 53.
    Goldstein B, Perelson AS (1984) Equilibrium theory for the clustering of bivalent cell surface receptors by trivalent ligands. Application to histamine release from basophils. Biophys J 45(6):1109–1123CrossRefGoogle Scholar
  54. 54.
    Faeder JR et al (2003) Investigation of early events in FcεRI-mediated signaling using a detailed mathematical model. J Immunol 170(7):3769–3781CrossRefGoogle Scholar
  55. 55.
    Xu W, Smith AM, Faeder JR, Marai GE (2011) RULEBENDER: a visual interface for rule-based modeling. Bioinformatics 27(12):1721–1722CrossRefGoogle Scholar
  56. 56.
    Smith AM, Xu W, Sun Y, Faeder JR, Marai GE (2012) RuleBender: integrated modeling, simulation and visualization for rule-based intracellular biochemistry. BMC Bioinformatics 13(Suppl 8):S3Google Scholar
  57. 57.
    Sekar JAP, Tapia J-J, Faeder JR (2017) Automated visualization of rule-based models. PLoS Comput Biol 13(11):e1005857CrossRefGoogle Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Computational and Systems BiologyUniversity of PittsburghPittsburghUSA
  2. 2.Pittsburgh Supercomputing CenterCarnegie Mellon UniversityPittsburghUSA
  3. 3.Howard Hughes Medical InstituteThe Salk Institute for Biological StudiesLa JollaUSA

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