Acta Biotheoretica

, Volume 61, Issue 1, pp 3–19 | Cite as

Multiscale Analysis of Biological Systems

Regular Article


It is argued that multiscale approaches are necessary for an explanatory modeling of biological systems. A first step, besides common to the multiscale modeling of physical and living systems, is a bottom-up integration based on the notions of effective parameters and minimal models. Top-down effects can be accounted for in terms of effective constraints and inputs. Biological systems are essentially characterized by an entanglement of bottom-up and top-down influences following from their evolutionary history. A self-consistent multiscale scheme is proposed to capture the ensuing circular causality. Its differences with standard mean-field self-consistent equations and slow-fast decompositions are discussed. As such, this scheme offers a way to unravel the multilevel architecture of living systems and their regulation. Two examples, genome functions and biofilms, are detailed.


Multiscale approaches Effective models Regulation Circular causality Self-consistent equations Integrative biology Systems biology 



This work has been funded by the Agence Nationale de la Recherche, SYSCOMM program, grant DISCO 09-SYSC-003 and by the Institut National de la Santé et de la Recherche Médicale, grant MICROMEGAS PC201104. It also greatly benefited from discussions during the XXXI seminar of the Société Francophone de Biologie Théorique, 15–18 May 2011, Autrans, France, and from the comments of two anonymous referees. I thank all the members of my team “Multiscale modeling of living matter” and especially Jean-Marc Victor for numerous fruitful discussions.


  1. Acharya A, Sawant A (2006) On a computational approach for the approximate dynamics of averaged variables in nonlinear ODE systems: toward the derivation of constitutive laws of the rate type. J Mech Phys Solids 54:2183–2213CrossRefGoogle Scholar
  2. Anderson PW (1972) More is different. Sci Agric 177:393–396CrossRefGoogle Scholar
  3. Artstein Z (1999) Singularly perturbed ordinary differential equations with nonautonomous fast dynamics. J Dyn Differ Equ 11:297–318CrossRefGoogle Scholar
  4. Auger P, de la Parra RB, Poggiale JC, Sánchez E, Sanz L (2008) Aggregation methods in dynamical systems and applications in population and community dynamics. Phys Life Rev 5:79–105CrossRefGoogle Scholar
  5. Bancaud A, Wagner G, Conde e Silva N, Lavelle C, Wong H, Mozziconacci J, Barbi M, Sivolob A, Le Cam E, Mouawad L, Viovy JL, Victor JM, Prunell A (2007) Nucleosome chiral transition under positive torsional stress in single chromatin fibers. Mol Cell 27:135–147CrossRefGoogle Scholar
  6. Bécavin C, Barbi M, Victor JM, Lesne A (2010) Transcription within condensed chromatin: steric hindrance facilitates elongation. Biophys J 98:824–833CrossRefGoogle Scholar
  7. Ben Arous G, Owhadi H (2003) Multiscale homogenization with bounded ratios and anomalous slow diffusion. Comm Pure Appl Math 56:80–113CrossRefGoogle Scholar
  8. Ben Haïm E, Lesne A, Victor JM (2001) Chromatin: a tunable spring at work inside chromosomes. Phys Rev E 64:051921CrossRefGoogle Scholar
  9. Bogoliubov NN, Mitropolskii YA (1961) Asymptotic methods in the theory of nonlinear oscillations. Gordon and Breach, New YorkGoogle Scholar
  10. Bystricky K, Heun P, Gehlen L, Langowski J, Gasser SM (2004) Long-range compaction and flexibility of interphase chromatin in budding yeast analyzed by high-resolution imaging techniques. Proc Natl Acad Sci USA 101:16495–16500CrossRefGoogle Scholar
  11. Castiglione P, Falcioni M, Lesne A, Vulpiani A (2008) Chaos and coarse-graining in statistical mechanics. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  12. Deygout C, Lesne A, Campillo F, Rapaport A (2013) Homogenised model linking microscopic and macroscopic dynamics of a biofilm: application to growth in a plug flow reactor. Ecol Model 250:15–24Google Scholar
  13. Dieckmann U, Law R (2000) Relaxation projections and the method of moments. In: Dieckmann U, Law R, Metz JAJ (eds) The geometry of ecological interactions: simplifying spatial complexity. Cambridge University Press, Cambridge, pp 412–455CrossRefGoogle Scholar
  14. E W, Engquist B (2003) The heterogeneous multiscale methods. Comm Math Sci 1:87–132Google Scholar
  15. E W, Ren W, Vanden-Eijnden E (2009) A general strategy for designing seamless multiscale methods. J Comput Phys 228:5437–5453Google Scholar
  16. El Hajji M, Rapaport A (2009) Practical coexistence of two species in the chemostat—a slow-fast characterization. Math Biosci 218:33–39CrossRefGoogle Scholar
  17. Ellis GFR (2005) Physics, complexity, and causality. Nat Biotechnol 435:743CrossRefGoogle Scholar
  18. Hänggi P, Talkner P, Borkovec M (1990) Reaction rate theory: fifty years after Kramers. Rev Mod Phys 62:251–342CrossRefGoogle Scholar
  19. Gardiner CW (1983) Handbook of stochastic methods. Springer, BerlinCrossRefGoogle Scholar
  20. Gaveau B, Lesne A, Schulman LS (1999) Spectral signatures of hierarchical relaxation. Phys Lett A 258:222–228CrossRefGoogle Scholar
  21. Givon D, Kupferman R, Stuart A (2004) Extracting macroscopic dynamics: model problems and algorithms. Nonlinearity 17:R55–R127CrossRefGoogle Scholar
  22. Hersen P, Andersen K, Elbelrhiti H, Andreotti B, Claudin P, Douady S (2004) Corridors of barchan dunes: stability and size selection. Phys Rev E 69:011304CrossRefGoogle Scholar
  23. Hornung U (1997) Homogenization and porous media. Springer, BerlinCrossRefGoogle Scholar
  24. Jenuwein T, Allis CD (2001) Translating the histone code. Sci Agric 293:1074–1080CrossRefGoogle Scholar
  25. Karsenti E, Nedelec F, Surrey T (2006) Modelling microtubule patterns. Nat Cell Biol 8:1204–1211CrossRefGoogle Scholar
  26. Kratky O, Porod G (1949) Röntgenuntersuchung gelöster Fadenmoleküle. Rec Trav Chim Pays-Bas 68:1106–1123CrossRefGoogle Scholar
  27. Laguës M, Lesne A (2011) Scale invariance. Springer, BerlinGoogle Scholar
  28. Langevin P (1908) On the theory of Brownian motion. C.R. Acad Sci (Paris) 146:530–533. Reprinted in Am J Phys 65:1079–1081 (1997)Google Scholar
  29. Lemarchand A, Lesne A, Mareschal M (1995) Langevin approach to a chemical wave-front: selection of the propagation velocity by internal noise. Phys Rev E 51:4457–4465CrossRefGoogle Scholar
  30. Lesne A (1998) Renormalization methods. Wiley, New-YorkGoogle Scholar
  31. Lesne A (2006) Multiscale approaches. In: Françoise JP, Naber G, Tsun TS (eds) Encyclopedia of mathematical physics. Elsevier, Amsterdam, pp 465–482CrossRefGoogle Scholar
  32. Lesne A (2007) Discrete vs continuous controversy in physics. Math Struct Comput Sci 17:185–223CrossRefGoogle Scholar
  33. Lesne A, Bécavin C, Victor JM (2012) The condensed chromatin fiber: an allosteric chemo-mechanical machine for signal transduction and genome processing. Phys Biol 9:013001CrossRefGoogle Scholar
  34. Lesne A, Benecke A (2008a) Probability landscapes for integrative genomics. Theor Biol Med Model 5:9CrossRefGoogle Scholar
  35. Lesne A, Benecke A (2008b) Feature context-dependency and complexity reduction in probability landscapes for integrative genomics. Theor Biol Med Model 5:21CrossRefGoogle Scholar
  36. Lesne A, Victor JM (2006) Chromatin fiber functional organization: some plausible models. Eur Phys J E 19:279–290CrossRefGoogle Scholar
  37. Malo M, Cartier-Michaud A, Fabre-Guillevin E, Hutzler G, Delaplace F, Barlovatz-Meimon G, Lesne A (2010) When a collective outcome triggers a rare individual event: a mode of metastatic process in a cell population. Math Pop Stud 17:136–165CrossRefGoogle Scholar
  38. Malo M, Cartier-Michaud A, Charrière-Bertrand C, Gadea G, Anguille C, Supiramaniam A, Lesne A, Delaplace F, Hutzler G, Roux P, Lawrence DA, Barlovatz-Meimon G (2012) Matrix-bound PAI-1 supports membrane blebbing via RhoA-Rock1 signaling. PLoS One 7:e32204CrossRefGoogle Scholar
  39. Marr C, Geertz M, Hütt MT, Muskhelishvili G (2008) Two distinct logical types of network control in gene expression profiles. BMC Syst Biol 2:18CrossRefGoogle Scholar
  40. Mathias JD, Grediac M, Balandraud X (2006) On the bidirectional stress distribution in rectangular bonded composite patches. Int J Solids Struct 43:6921–6947CrossRefGoogle Scholar
  41. Mozziconacci J, Lavelle C, Barbi M, Lesne A, Victor JM (2006) A physical model for the condensation and decondensation of eukaryotic chromosomes. FEBS Lett 580:368–372CrossRefGoogle Scholar
  42. Mozziconacci J, Victor JM (2003) Nucleosome gaping supports a functional structure for the 30 nm chromatin fiber. J Struct Biol 143:72–76CrossRefGoogle Scholar
  43. Murray JD (2003) Mathematical biology (3rd edition). Springer, New YorkGoogle Scholar
  44. Muskhelishvili G, Sobetzko P, Geertz M, Berger M (2010) General organisational principles of the transcriptional regulation system: a tree or a circle?. Mol BioSyst 6:662–676CrossRefGoogle Scholar
  45. Nayfeh AH (1973) Perturbation methods. Wiley, New YorkGoogle Scholar
  46. Nicholson C (2001) Diffusion and related transport mechanisms in brain tissue. Rep Prog Phys 64:815–884CrossRefGoogle Scholar
  47. Polanyi M (1968) Life’s irreducible structure. Sci Agric 160:1308–1312CrossRefGoogle Scholar
  48. Radulescu O, Gorban AN, Zinovyev A, Lilienbaum A (2008) Robust simplifications of multiscale biochemical networks. BMC Syst Biol 2:86CrossRefGoogle Scholar
  49. Sanders J, Verhulst F, Murdock J (2007) Averaging methods in nonlinear dynamical systems. Springer, New YorkGoogle Scholar
  50. Schrödinger E (1944) What is life. Cambridge University Press, CambridgeGoogle Scholar
  51. Simon HA (1962) The architecture of complexity. Proc Am Phil Soc 106:467–482Google Scholar
  52. Sivolob A, Lavelle C, Prunell A (2003) Sequence-dependent nucleosome structural and dynamic polymorphism. Potential involvement of histone H2B N-terminal tail proximal domain. J Mol Biol 326: 49–63CrossRefGoogle Scholar
  53. Spector DL (2003) The dynamics of chromosome; organization and gene regulation. Annu Rev Biochem 72:573–608CrossRefGoogle Scholar
  54. Torquato S (2002) Random heterogeneous materials: microstructure and macroscopic properties. Springer, BerlinCrossRefGoogle Scholar
  55. Travers A, Muskhelishvili G (2005) DNA supercoiling—a global transcriptional regulator for enterobacterial growth. Nat Rev Microbiol 3:157–169CrossRefGoogle Scholar
  56. Van Kampen N (1981) Stochastic processes in physics and chemistry. North-Holland, AmsterdamGoogle Scholar
  57. Werner BT (1999) Complexity in natural landform patterns. Sci Agric 284:102–104CrossRefGoogle Scholar
  58. Wong H, Victor JM, Mozziconacci J (2007) An all-atom model of the chromatin fiber containing linker histones reveals a versatile structure tuned by nucleosomal repeat length. PLoS One 2:e877CrossRefGoogle Scholar
  59. Woodcock CL, Grigoryev SA, Horowitz RA, Whitaker N (1993) A chromatin folding model that incorporates linker variability generates fibers resembling the native structures. Proc Natl Acad Sci USA 90:9021–9025CrossRefGoogle Scholar
  60. Zlatanova J, Bishop TC, Victor JM, Jackson V, van Holde K (2009) The nucleosome family: dynamic and growing. Struct Bond 17:160–171CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.CNRS UMR 7600Université Pierre et Marie Curie-Paris 6Paris Cedex 05France
  2. 2.Institut des Hautes Études ScientifiquesBures-sur-YvetteFrance

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