Acta Biotheoretica

, Volume 61, Issue 3, pp 291–303 | Cite as

How to Build a Multiscale Model in Biology

Original Article

Abstract

Biological processes span several scales in space, from the single molecules to organisms and ecosystems. Multiscale modelling approaches in biology are useful to take into account the complex interactions between different organisation levels in those systems. We review several single- and multiscale models, from the most simple to the complex ones, and discuss their properties from a multiscale point of view. Approaches based on master equations for stochastic processes, individual-based models, hybrid continuous-discrete models and structured PDE models are presented.

Keywords

Multiscale model Master equation Reaction-diffusion equation Hybrid modelling Individual-based modelling Structured PDE 

References

  1. IMAG (Interagency Modeling and Analysis Group) (2012) What exactly is multiscale modeling? http://www.imagwiki.nibib.nih.gov/mediawiki/index.php?title=What_exactly_is_Multiscale_Modeling
  2. Anderson A (2005) A hybrid mathematical model of solid tumour invasion: the importance of cell adhesion. Math Med Biol 22(2):163–186CrossRefGoogle Scholar
  3. Anderson A, Weaver A, Cummings P, Quaranta V (2006) Tumor morphology and phenotypic evolution driven by selective pressure from the microenvironment. Cell (Cambridge, MA, US) 127(5):905–915CrossRefGoogle Scholar
  4. Battogtokh D, Aihara K, Tyson JJ (2006) Synchronization of eukaryotic cells by periodic forcing. Phys Rev Lett 96(14):148,102CrossRefGoogle Scholar
  5. Bekkal Brikci F, Clairambault J, Ribba B, Perthame B (2008) An age-and-cyclin-structured cell population model for healthy and tumoral tissues. J Math Biol 57(1):91–110CrossRefGoogle Scholar
  6. Benzekry S (2011) Mathematical analysis of a two-dimensional population model of metastatic growth including angiogenesis. J Evol Equ 11(1):187–213CrossRefGoogle Scholar
  7. Bernard S, Gonze D, Čajavec B, Herzel H, Kramer A (2007) Synchronization-induced rhythmicity of circadian oscillators in the suprachiasmatic nucleus. PLOS Comput Biol 3(4):e68CrossRefGoogle Scholar
  8. Billy F, Ribba B, Saut O, Morre-Trouilhet H, Colin T, Bresch D, Boissel JP, Grenier E, Flandrois JP (2009) A pharmacologically based multiscale mathematical model of angiogenesis and its use in investigating the efficacy of a new cancer treatment strategy. J Theor Biol 260(4):545–562CrossRefGoogle Scholar
  9. Byrne H, Drasdo D (2009) Individual-based and continuum models of growing cell populations: a comparison. J Math Biol 58(4):657–687CrossRefGoogle Scholar
  10. Chauvière A, Preziosi L, Verdier C (2009) Cell mechanics: from single scale-based models to multiscale modeling, vol. 32. Chapman & Hall/CRC, LondonGoogle Scholar
  11. Cristini V, Lowengrub J (2010) Multiscale modeling of cancer: an integrated experimental and mathematical modeling approach. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  12. Deisboeck T, Stamatakos G (2010) Multiscale cancer modeling. vol. 34. Chapman & Hall/CRC, LondonCrossRefGoogle Scholar
  13. Dial KP, Greene E, Irschick DJ (2008) Allometry of behavior. Trends Ecol Evol 23(7):394–401CrossRefGoogle Scholar
  14. Doumic M (2007) Analysis of a population model structured by the cells molecular content. Math Model Nat Phenom 2(3):121–152CrossRefGoogle Scholar
  15. Drasdo D, Höhme S (2005) A single-cell-based model of tumor growth in vitro: monolayers and spheroids. Phys Biol 2:133CrossRefGoogle Scholar
  16. Drasdo D, Kree R, McCaskill J (1995) Monte Carlo approach to tissue-cell populations. Phys Rev E 52(6):6635CrossRefGoogle Scholar
  17. Drasdo D, Loeffler M (2001) Individual-based models to growth and folding in one-layered tissues: intestinal crypts and early development. Nonliner Anal 47(1):245–256CrossRefGoogle Scholar
  18. Françoise JP (2005) Oscillations en biologie: analyse qualitative et modèles, vol. 46. Springer, BerlinGoogle Scholar
  19. Friedman A, Kao CY, Shih CW (2009) Asymptotic phases in a cell differentiation model. J Differ Equ 247(3):736–769CrossRefGoogle Scholar
  20. Friedman A, Kao CY, Shih CW (2012) Asymptotic limit in a cell differentiation model with consideration of transcription. J Differ Equ 252(10):5679–5711CrossRefGoogle Scholar
  21. Galle J, Loeffler M, Drasdo D (2005) Modeling the effect of deregulated proliferation and apoptosis on the growth dynamics of epithelial cell populations in vitro. Biophys J 88(1):62–75CrossRefGoogle Scholar
  22. Gatenby R, Gawlinski E (1996) A reaction-diffusion model of cancer invasion. Cancer Res 56(24):5745Google Scholar
  23. Gunawardena J (2012) A linear framework for time-scale separation in nonlinear biochemical systems. PLOS One 7(5):e36,321CrossRefGoogle Scholar
  24. Hoehme S, Brulport M, Bauer A, Bedawy E, Schormann W, Hermes M, Puppe V, Gebhardt R, Zellmer S, Schwarz M, et al (2010) Prediction and validation of cell alignment along microvessels as order principle to restore tissue architecture in liver regeneration. Proc Natl Acad Sci USA 107(23):10,371CrossRefGoogle Scholar
  25. Hoffmann M, Chang H, Huang S, Ingber D, Loeffler M, Galle J (2008) Noise-driven stem cell and progenitor population dynamics. PLOS One 3(8):e2922CrossRefGoogle Scholar
  26. Kærn M, Elston T, Blake W, Collins J (2005) Stochasticity in gene expression: from theories to phenotypes. Nat Rev Genet 6(6):451–464CrossRefGoogle Scholar
  27. Kaplan D, Glass L (1995) Understanding nonlinear dynamics, vol. 19. Springer, BerlinCrossRefGoogle Scholar
  28. Keller E, Segel L (1970) Initiation of slime mold aggregation viewed as an instability. J Theor Biol 26(3):399–415CrossRefGoogle Scholar
  29. Kepler T, Elston T (2001) Stochasticity in transcriptional regulation: origins, consequences, and mathematical representations. Biophys J 81(6):3116–3136CrossRefGoogle Scholar
  30. Lahutte-Auboin M, Guillevin R, Françoise JP, Vallée JN, Costalat R (2013) On a minimal model for hemodynamics and metabolism of lactate: application to low grade glioma and therapeutic strategies. Acta Biotheor 61(1):79–89CrossRefGoogle Scholar
  31. Lesart A, van der Sanden B, Hamard L, Estève F, Stéphanou A (2012) On the importance of the submicrovascular network in a computational model of tumour growth. Microvasc Res 84(2):188–204CrossRefGoogle Scholar
  32. Macal CM, North MJ (2005) Tutorial on agent-based modeling and simulation. In: proceedings of the 37th conference on winter simulation, pp. 2–15. Winter Simulation ConferenceGoogle Scholar
  33. Magal P, Auger P, Ruan S (2008) Structured population models in biology and epidemiology. 1936. Springer, BerlinCrossRefGoogle Scholar
  34. Newman T, Grima R (2004) Many-body theory of chemotactic cell-cell interactions. Phys Rev E 70(5):051,916Google Scholar
  35. Paulsson J (2005) Models of stochastic gene expression. Phys Life Rev 2(2):157–175CrossRefGoogle Scholar
  36. Perkins T, Swain P (2009) Strategies for cellular decision-making. Mol Syst Biol 5:326CrossRefGoogle Scholar
  37. Powathil G, Gordon K, Hill L, Chaplain M (2012) Modelling the effects of cell-cycle heterogeneity on the response of a solid tumour to chemotherapy: biological insights from a hybrid multiscale cellular automaton model. J Theor Biol 308:1–19Google Scholar
  38. Qu Z, Garfinkel A, Weiss JN, Nivala M (2011) Multi-scale modeling in biology: how to bridge the gaps between scales? Prog Biophys Mol Biol 107(1):21–31CrossRefGoogle Scholar
  39. Railsback S, Grimm V (2011) Agent-based and individual-based modeling: a practical introduction. Princeton University Press, PrincetonGoogle Scholar
  40. Ramis-Conde I, Chaplain M, Anderson A, Drasdo D (2009) Multi-scale modelling of cancer cell intravasation: the role of cadherins in metastasis. Phys Biol 6:016,008CrossRefGoogle Scholar
  41. Ribba B, Colin T, Schnell S (2006) A multiscale mathematical model of cancer, and its use in analyzing irradiation therapies. Theor Biol Med Model 3(1):7CrossRefGoogle Scholar
  42. Ribeiro A, Dai X, Yli-Harja O (2009) Variability of the distribution of differentiation pathway choices regulated by a multipotent delayed stochastic switch. J Theor Biol 260(1):66–76CrossRefGoogle Scholar
  43. Schnell S, Grima R, Maini P (2007) Multiscale modeling in biology new insights into cancer illustrate how mathematical tools are enhancing the understanding of life from the smallest scale to the grandest. Am Sci 95:134–42Google Scholar
  44. Spencer S, Gerety R, Pienta K, Forrest S (2006) Modeling somatic evolution in tumorigenesis. PLOS Comput Biol 2(8):e108CrossRefGoogle Scholar
  45. Treuil JP, Drogoul A, Zucker JD (2008) Modélisation et simulation à base d’agents: exemples commentés, outils informatiques et questions théoriques. DunodGoogle Scholar
  46. Turing A (1952) The chemical basis of morphogenesis. Proc R Soc B 237(641):37–72Google Scholar
  47. Van Kampen N (1992) Stochastic processes in physics and chemistry. Elsevier, North HollandGoogle Scholar
  48. Wikenros C, Sand H, Wabakken P, Liberg O, Pedersen HC (2009) Wolf predation on moose and roe deer: chase distances and outcome of encounters. Acta Theriologica 54(3):207–218CrossRefGoogle Scholar
  49. Wilkinson DJ (2009) Stochastic modelling for quantitative description of heterogeneous biological systems. Nat Rev Genet 10(2):122–133CrossRefGoogle Scholar
  50. Zhang L, Wang Z, Sagotsky J, Deisboeck T (2009) Multiscale agent-based cancer modeling. J Math Biol 58(4):545–559CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Institut Camille Jordan, CNRS UMR 5208Université de LyonVilleurbanneFrance
  2. 2.Équipe Inria DraculaVilleurbanneFrance
  3. 3.Rhône-Alpes Complex Systems Institute (IXXI)LyonFrance

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