Abstract
Biological phenomena at the cellular level can be represented by various types of mathematical formulations. Such representations allow us to carry out numerical simulations that provide mechanistic insights into complex behaviours of biological systems and also generate hypotheses that can be experimentally tested. Currently, we are particularly interested in spatio-temporal representations of dynamic cellular phenomena and how such models can be used to understand biological specificity in functional responses. This review describes the capability and limitations of the approaches used to study spatio-temporal dynamics of cell signalling components.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Angeli D, Ferrell J E Jr and Sontag E D 2004 Detection of multistability, bifurcations, and hysteresis in a large class of biological positive-feedback systems; Proc. Natl. Acad. Sci. USA 101 1822–1827
Batada N N, Shepp L A and Siegmund D O 2004 Stochastic model of protein-protein interaction: why signalling proteins need to be colocalized; Proc. Natl. Acad. Sci. USA 101 6445–6449
Batada N N, Shepp L A, Siegmund D O and Levitt M 2006 Spatial Regulation and the Rate of Signal Transduction Activation; PLoS Comput. Biol. 2 e44
Bhalla U S and Iyengar R 1999 Emergent properties of networks of biological signalling pathways; Science 283 381–387
Bhalla U S and Iyengar R 2001a Functional modules in biological signalling networks; Novartis Found. Symp. 239 4–13; discussion 13–15, 45–51
Bhalla, U S and Iyengar R 2001b Robustness of the bistable behaviour of a biological signalling feedback loop; Chaos 11 221–226
Black J W and Leff P 1983 Operational models of pharmacological agonism; Proc R Soc London B Biol. Sci. 220 141–162
Cussler E L 1994 Diffusion, mass transfer in fluid systems (Cambridge, UK: Cambridge University Press)
Ferrell J E and Xiong W 2001 Bistability in cell signalling: How to make continuous processes discontinuous, and reversible processes irreversible; Chaos 11 227–236
Fong S S, Burgard A P, Herring C D, Knight E M, Blattner F R, Maranas C D and Palsson B O 2005 In silico design and adaptive evolution of Escherichia coli for production of lactic acid; Biotechnol. Bioeng. 91 643–648
Gillespie D T 1977 Exact Stochastic Simulation of Coupled Chemical Reactions; J. Phys. Chem. 81 2340–2361
Hautaniemi S, Kharait S, Iwabu A, Wells A and Lauffenburger D A 2005 Modelling of signal-response cascades using decision tree analysis. Bioinformatics 21 2027–2035
Hodgkin A L and Huxley A F 1952 A quantitative description of membrane current and its application to conduction and excitation in nerve; J. Physiol. 117 500–544
Kenakin T 2004 Efficacy as a vector: the relative prevalence and paucity of inverse agonism; Mol. Pharmacol. 65 2–11
Kowalewski J M, Uhlen P, Kitano H and Brismar H 2006 Modelling the impact of store-operated Ca(2+) entry on intracellular Ca(2+) oscillations; Math Biosci. (in press)
Leff P, Scaramellini C, Law C and McKechnie K 1997 A three-state receptor model of agonist action. Trends Pharmacol. Sci. 18 355–362
Lemerle C, Di Ventura B and Serrano L 2005 Space as the final frontier in stochastic simulations of biological systems; FEBS Lett. 579 1789–1794
Ma’ayan A, Jenkins S L, Neves S, Hasseldine A, Grace E, Dubin-Thaler B, Eungdamrong N J, Weng G, Ram P T, Rice J J, Kershenbaum A, Stolovitzky G A, Blitzer R D and Iyengar R 2005 Formation of regulatory patterns during signal propagation in a Mammalian cellular network; Science 309 1078–83
Mayawala K, Vlachos D G and Edwards J S 2006 Spatial modelling of dimerization reaction dynamics in the plasma membrane: Monte Carlo vs. continuum differential equations; Biophys. Chem. 121 194–208
Papin J A, Hunter T, Palsson B O and Subramaniam S 2005 Reconstruction of cellular signalling networks and analysis of their properties; Nat. Rev. Mol. Cell Biol. 6 99–111
Pertz O, Hodgson L, Klemke R L and Hahn K M 2006 Spatiotemporal dynamics of RhoA activity in migrating cells; Nature (London) 440 1069–1072
Saha K and Schaffer D V 2006 Signal dynamics in Sonic hedgehog tissue patterning; Development 133 889–900
Singh A, Jayaraman A and Hahn J 2006 Modelling regulatory mechanisms in IL-6 signal transduction in hepatocytes; Biotechnol Bioeng. (in press)
Stamatakis M and Mantzaris N V 2006 Modelling of ATP-mediated signal transduction and wave propagation in astrocytic cellular networks; J. Theor. Biol. (in press)
Thiele I, Vo T D, Price N D and Palsson B O 2005 Expanded metabolic reconstruction of Helicobacter pylori (iIT341 GSM/GPR): an in silico genome-scale characterization of single-and double-deletion mutants; J. Bacteriol. 187 5818–5830
Turing A 1952 The Chemical Basis of Morphogenesis. Philos. Trans. R. Soc. Series B 237 37–72
Varma A, Morbidelli M and Wu H 1999 Parametric sensitivity in chemical systems (Cambridge, UK: Cambridge University Press)
Wang Y, Botvinick E L, Zhao Y, Berns M W, Usami S, Tsien R Y and Chien S 2005 Visualizing the mechanical activation of Src; Nature (London) 434 1040–1045
Wiley H S, Shvartsman S Y and Lauffenburger D A 2003 Computational modelling of the EGF-receptor system: a paradigm for systems biology; Trends Cell Biol. 13 43–50
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Rangamani, P., Iyengar, R. Modelling spatio-temporal interactions within the cell. J Biosci 32, 157–167 (2007). https://doi.org/10.1007/s12038-007-0014-3
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12038-007-0014-3