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Life sciences through mathematical models

  • Life, New Materials and Plasmonics
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Abstract

This article discusses some of the basic principles of mathematical modeling in life sciences, and in particular the special features that make the modeling task fundamentally different from the traditional reductive modeling. The intricacies of the modeling in living systems are elucidated by simple and tractable examples that underline the problems of parametric models and the issue of non-scalability of the models.

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References

  • Anderson PW (1972) More is different. Science 177:393–396

    Article  CAS  Google Scholar 

  • Aubert A, Costalat R, Magistretti PJ, Pellerin L (2005) Brain lactate kinetics: modeling evidence for neuronal lactate uptake upon activation. Proc Natl Acad Sci USA 102:16448–16453

    Article  CAS  Google Scholar 

  • Beauchemin C, Samuel J, Tuszynski J (2005) A simple cellular automaton model for influenza A viral infections. J Theor Biol 232:223–234

    Article  CAS  Google Scholar 

  • Calvetti D, Somersalo E (2006) Large-scale statistical parameter estimation in complex systems with an application to metabolic models. Multiscale Model Simul 5:1333–1366

    Article  Google Scholar 

  • Calvetti D, Somersalo E (2010) Subjective knowledge or objective belief? An oblique look to bayesian methods. In: Large-scale inverse problems and quantification of uncertainty. Wiley, New York, pp 33–70

  • Calvetti D, Somersalo E (2012) Computational mathematical modeling: an integrated approach across scales (vol. 17). SIAM, Philadelphia

    Google Scholar 

  • Calvetti D, Somersalo E (2013) Quantitative in silico analysis of neurotransmitter pathways under steady state conditions. Front Endocrinnol 4:137

    Google Scholar 

  • Calvetti C, Cheng Y, Somersalo E (2015) A spatially distributed computational model of brain cellular metabolism. J Theor Biol (to appear)

  • Cobelli C, Renard E, Kovatchev B (2011) Artificial pancreas: past, present, future. Diabetes 60:2672–2682

    Article  CAS  Google Scholar 

  • Gilbert N (2008) Agent-based models (No. 153). Sage, New York

    Google Scholar 

  • Gardner M (1970) Mathematical games. The fantastic combinations of John Conway’s new solitaire game “life”. Sci Am 223:120–123

    Article  Google Scholar 

  • Hadamard J (1902) Sur les problèmes aux dérivèes partielles et leur signification physique. Princeton Univ Bull 13(1902):49–52

    Google Scholar 

  • Heino J, Calvetti D, Somersalo E (2010) Metabolica: a statistical research tool for analyzing metabolic networks. Compt Methods Program Biomed 97:151–167

    Article  Google Scholar 

  • Immonen T, Gibson R, Leitner T, Miller MA, Arts EJ, Somersalo E, Calvetti D (2012) A hybrid stochasticdeterministic computational model accurately describes spatial dynamics and virus diffusion in HIV-1 growth competition assay. J Theor Biol 312:120–132

    Article  Google Scholar 

  • Immonen T, Somersalo E, Calvetti D (2014) Modeling HIV-1 dynamics and fitness in cell culture across scales. Bull Math Biol 76:486–514

    Article  Google Scholar 

  • LeBaron B (2006) Agent-based computational finance. Handb Comput Econ 2:1187–1233

    Article  Google Scholar 

  • Mertsching H, Walles T, Hofmann M, Schanz J, Knapp WH (2005) Engineering of a vascularized scaffold for artificial tissue and organ generation. Biomaterials 26:6610–6617

    Article  CAS  Google Scholar 

  • Ndanguza D, Tchuenche JM, Haario H (2013) Statistical data analysis of the 1995 Ebola outbreak in the Democratic Republic of Congo. Afrika Mat 24:55–68

    Article  Google Scholar 

  • Newton RG (1993) What makes nature tick?. Harvard University Press, Cambridge

    Google Scholar 

  • Simpson IA, Carruthers A, Vannucci SJ (2007) Supply and demand in cerebral energy metabolism: the role of nutrient transporters. J Cereb Blood Flow Metab 27:1766–1791

    Article  CAS  Google Scholar 

  • Tegmark M (2008) The mathematical universe. Found Phys 38:101–150

    Article  Google Scholar 

  • Von Neumann J (1951) The general and logical theory of automata. Cereb Mech Behav 1:41

    Google Scholar 

  • Wigner EP (1960) The unreasonable effectiveness of mathematics in the natural sciences. Richard courant lecture in mathematical sciences delivered at New York University, May 11, 1959. Commun Pure Appl Math 13:1–14

    Article  Google Scholar 

  • Wigner EP (1995) The unreasonable effectiveness of mathematics in the natural sciences. In: philosophical reflections and syntheses. Springer, Berlin Heidelberg, pp 534–549

  • Wolfram S (2002) A new kind of science. Wolfram Media, Chapaign

    Google Scholar 

Download references

Acknowledgments

The work of Daniela Calvetti was partly supported by Grant number 246665 from the Simons Foundation, and the work of Erkki Somersalo was partly supported by NSF Grant DMS 1016183.

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Authors and Affiliations

  1. Department of Mathematics, Applied Mathematics, and Statistics, Case Western Reserve University, Cleveland, OH, USA

    Daniela Calvetti & Erkki Somersalo

Authors
  1. Daniela Calvetti
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  2. Erkki Somersalo
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Corresponding author

Correspondence to Daniela Calvetti.

Additional information

This contribution is the written, peer-reviewed version of a paper presented in one of the two conferences “From Life to Life: Through New Materials and Plasmonics”, Accademia Nazionale dei Lincei in Rome on June 23, 2014, and at NanoPlasm 2014: New Frontiers in Plasmonics and NanoOptics—Cetraro (CS) on June 16–20, 2014.

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Calvetti, D., Somersalo, E. Life sciences through mathematical models. Rend. Fis. Acc. Lincei 26 (Suppl 2), 193–201 (2015). https://doi.org/10.1007/s12210-015-0422-5

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  • DOI: https://doi.org/10.1007/s12210-015-0422-5

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