Multi-Level Modeling and Simulation of Cellular Systems: An Introduction to ML-Rules

  • Tobias Helms
  • Tom Warnke
  • Adelinde M. UhrmacherEmail author
Part of the Methods in Molecular Biology book series (MIMB, volume 1945)


ML-Rules is a rule-based language for multi-level modeling and simulation. ML-Rules supports dynamic nesting of entities and applying arbitrary functions on entity attributes and content, as well as for defining kinetics of reactions. This allows describing and simulating complex cellular dynamics operating at different organizational levels, e.g., to combine intra-, inter-, and cellular dynamics, like the proliferation of cells, or to include compartmental dynamics like merging and splitting of mitochondria or endocytosis. The expressiveness of the language is bought with additional efforts in executing ML-Rules models. Therefore, various simulators have been developed from which the user and automatic procedures can select. The experiment specification language SESSL facilitates design, execution, and reuse of simulation experiments. The chapter illuminates the specific features of ML-Rules as a rule-based modeling language, the implications for an efficient execution, and shows ML-Rules at work.

Key words

Computational biology Rule-based modeling Multi-level modeling Cell biological systems Stochastic simulation Experiment specification 


  1. 1.
    Sargent RG (2013) Verification and validation of simulation models. J Simul 7:12–24CrossRefGoogle Scholar
  2. 2.
    Maus C (2013) Toward accessible multilevel modeling in systems biology: a rule-based language concept. PhD thesis, University of RostockGoogle Scholar
  3. 3.
    Maus C, Rybacki S, Uhrmacher AM (2011) Rule-based multi-level modeling of cell biological systems. BMC Syst Biol 5:166CrossRefGoogle Scholar
  4. 4.
    Warnke T, Helms T, Uhrmacher AM (2015) Syntax and semantics of a multi-level modeling language. In: Proceedings of the 3rd ACM SIGSIM conference on principles of advanced discrete simulation (PADS), pp 133–144Google Scholar
  5. 5.
    Wiegert RG (1988) Holism and reductionism in ecology: hypotheses, scale and systems models. Oikos 53:267–269CrossRefGoogle Scholar
  6. 6.
    Noble D (2008) The music of life: biology beyond genes. Oxford University Press, OxfordGoogle Scholar
  7. 7.
    Campbell DT (1974) ‘Downward causation’ in hierarchically organised biological systems. In: Ayala FJ, Dobzhansky T (eds) Studies in the philosophy of biology: reduction and related problems. Palgrave, LondonGoogle Scholar
  8. 8.
    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 20:3289–3291CrossRefGoogle Scholar
  9. 9.
    Danos V, Laneve C (2004) Formal molecular biology. Theor Comput Sci 325:69–110CrossRefGoogle Scholar
  10. 10.
    Haack F, Lemcke H, Ewald R, Rharass T, Uhrmacher AM (2015) Spatio-temporal model of endogenous ROS and raft-dependent WNT/beta-catenin signaling driving cell fate commitment in human neural progenitor cells. PLoS Comput Biol 11:e1004106CrossRefGoogle Scholar
  11. 11.
    Gillespie DT (1977) Exact stochastic simulation of coupled chemical reactions. J Phys Chem 81:2340–2361CrossRefGoogle Scholar
  12. 12.
    Oury N, Plotkin GD (2013) Multi-level modelling via stochastic multi-level multiset rewriting. Math Structures Comput Sci 23:471–503CrossRefGoogle Scholar
  13. 13.
    John M, Lhoussaine C, Niehren J, Versari C (2011) Biochemical reaction rules with constraints. Lect Notes Comput Sci 6602:338–357CrossRefGoogle Scholar
  14. 14.
    Bittig A, Uhrmacher AM (2017) ML-Space: hybrid spatial Gillespie and particle simulation of multi-level rule-based models in cell biology. IEEE/ACM Trans Comput Biol Bioinform 14:1339–1349CrossRefGoogle Scholar
  15. 15.
    Faeder JR, Blinov ML, Goldstein B, Hlavacek WS (2005) Rule-based modeling of biochemical networks. Complexity 10:22–41CrossRefGoogle Scholar
  16. 16.
    Jones SP (ed) (2003) Haskell 98 language and libraries: the revised report. Cambridge University Press, CambridgeGoogle Scholar
  17. 17.
    Priami C (1995) Stochastic π-calculus. Comput J 38:578–589CrossRefGoogle Scholar
  18. 18.
    Mazemondet O, John M, Leye S, Rolfs A, Uhrmacher AM (2012) Elucidating the sources of β-catenin dynamics in human neural progenitor cells. PLoS ONE 7:e42792CrossRefGoogle Scholar
  19. 19.
    Tyson JJ (1991) Modeling the cell division cycle: cdc2 and cyclin interactions. Proc Natl Acad Sci USA 88:7328–7332CrossRefGoogle Scholar
  20. 20.
    Gibson MA, Bruck J (2000) Efficient exact stochastic simulation of chemical systems with many species and many channels. J Chem Phys 104:1876–1889CrossRefGoogle Scholar
  21. 21.
    Danos V, Feret J, Fontana W, Krivine J (2007) Scalable simulation of cellular signaling networks. Lect Notes Comput Sci 4807:139–157CrossRefGoogle Scholar
  22. 22.
    Sneddon MW, Faeder JR, Emonet T (2011) Efficient modeling, simulation and coarse-graining of biological complexity with NFsim. Nat Methods 8:177–183CrossRefGoogle Scholar
  23. 23.
    Forgy CL (1982) Rete: a fast algorithm for the many pattern/many object pattern match problem. Artif Intell 19:17–37CrossRefGoogle Scholar
  24. 24.
    Krivine J, Milner R, Troina A (2008) Stochastic bigraphs. Electron Notes Theor Comput Sci 218:73–96CrossRefGoogle Scholar
  25. 25.
    Helms T, Luboschik M, Schumann H, Uhrmacher AM (2013) An approximate execution of rule-based multi-level models. Lect Notes Comput Sci 8130:19–32CrossRefGoogle Scholar
  26. 26.
    Cao Y, Gillespie DT, Petzold LR (2005) The slow-scale stochastic simulation algorithm. J Chem Phys 122:14116CrossRefGoogle Scholar
  27. 27.
    Weinan E, Liu D, Vanden-Eijnden E (2005) Nested stochastic simulation algorithm for chemical kinetic systems with disparate rates. J Chem Phys 123:194107CrossRefGoogle Scholar
  28. 28.
    Helms T, Wilsdorf P, Uhrmacher AM (2018) Hybrid simulation of dynamic reaction networks in multi-level models. In: SIGSIM-PADS ’18: proceedings of the 2018 ACM SIGSIM conference on principles of advanced discrete simulation. ACM Press, New York, pp 133–144CrossRefGoogle Scholar
  29. 29.
    Helms T, Warnke T, Maus C, Uhrmacher AM (2017) Semantics and efficient simulation algorithms of an expressive multilevel modeling language. ACM Trans Model Comput Simul 27:8CrossRefGoogle Scholar
  30. 30.
    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:e1003544CrossRefGoogle Scholar
  31. 31.
    Helms T, Ewald R, Rybacki S, Uhrmacher AM (2015) Automatic runtime adaptation for component-based simulation algorithms. ACM Trans Model Comput Simul 26:7CrossRefGoogle Scholar
  32. 32.
    Leye S, Himmelspach J, Uhrmacher AM (2009) A discussion on experimental model validation. In: Al-Dabass D, Orsoni A, Brentnall A, Abraham A, Zobel R (eds) UKSim 2009: eleventh international conference on computer modelling and simulation. IEEE, Los Alamitos, pp 161–167Google Scholar
  33. 33.
    Ewald R, Uhrmacher AM (2014) SESSL: a domain-specific language for simulation experiments. ACM Trans Model Comput Simul 24:11CrossRefGoogle Scholar
  34. 34.
    Lukasiewycz M, Glaß M, Reimann F, Teich J (2011) Opt4J—a modular framework for meta-heuristic optimization. In: Krasnogor N (ed) GECCO ’11: Proceedings of the 13th annual conference on genetic and evolutionary algorithms. ACM Press, New York, pp 1723–1730Google Scholar
  35. 35.
    Clarke EM, Faeder JR, Langmead CJ, Harris LA, Jha SK, Legay A (2008) Statistical model checking in BioLab: applications to the automated analysis of T-cell receptor signaling pathway. Lect Notes Comput Sci 5307:231–250CrossRefGoogle Scholar
  36. 36.
    Peng D, Warnke T, Haack F, Uhrmacher AM (2016) Reusing simulation experiment specifications to support developing models by successive extension. Simul Model Pract Theory 68:33–53CrossRefGoogle Scholar

Copyright information

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

Authors and Affiliations

  • Tobias Helms
    • 1
  • Tom Warnke
    • 1
  • Adelinde M. Uhrmacher
    • 1
    Email author
  1. 1.Institute of Computer ScienceUniversity of RostockRostockGermany

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