Abstract
Quantitative modeling of spatiotemporal dynamics of cells facilitates understanding and engineering of biological systems. Using a synthetic bacterial ecosystem as a workbench, we present the approach to mathematically simulate the spatiotemporal population dynamics of the ecosystem. A description of ecosystem’s genetic construction and model development is firstly given. Parameter estimation and computational approach for the derived partial differential equations (PDEs) are then given. Spatiotemporal pattern formation is computed by numerically solving the PDE model. Biodiversity of the ecosystem and its impacts by cellular seeding distance and motility are computed according to the cell distribution patterns.
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References
Hanahan D, Weinberg RA (2000) The hallmarks of cancer. Cell 100:57–70
Aldridge BB, Burke JM, Lauffenburger DA, Sorger PK (2006) Physicochemical modelling of cell signalling pathways. Nat Cell Biol 8:1195–1203
Kholodenko BN (2006) Cell-signalling dynamics in time and space. Nat Rev 7:165–176
Tyson JJ, Chen KC, Novak B (2003) Sniffers, buzzers, toggles and blinkers: dynamics of regulatory and signaling pathways in the cell. Curr Opin Cell Biol 15:221–231
Yao G, Lee TJ, Mori S, Nevins JR, You L (2008) A bistable Rb-E2F switch underlies the restriction point. Nat Cell Biol 10:476–482
Song H, Smolen P, Av-Ron E, Baxter DA, Byrne JH (2006) Bifurcation and singularity analysis of a molecular network for the induction of long-term memory. Biophys J 90:2309–2325
Bhalla US, Iyengar R (1999) Emergent properties of networks of biological signaling pathways. Science 283:381–387
Roenneberg T, Chua EJ, Bernardo R, Mendoza E (2008) Modelling biological rhythms. Curr Biol 18:R826–R835
Iglesias PA, Devreotes PN (2008) Navigating through models of chemotaxis. Curr Opin Cell Biol 20:35–40
Levchenko A, Iglesias PA (2002) Models of eukaryotic gradient sensing: application to chemotaxis of amoebae and neutrophils. Biophys J 82:50–63
Onsum MD, Rao CV (2009) Calling heads from tails: the role of mathematical modeling in understanding cell polarization. Curr Opin Cell Biol 21:74–81
Shvartsman SY, Coppey M, Berezhkovskii AM (2008) Dynamics of maternal morphogen gradients in Drosophila. Curr Opin Genet Dev 18:342–347
Umulis D, O’Connor MB, Othmer HG (2008) Robustness of embryonic spatial patterning in Drosophila melanogaster. Curr Top Dev Biol 81:65–111
Koch AJ, Meinhardt H (1994) Biological pattern formation: from basic mechanisms to complex structures. Rev Mod Phys 66:1481–1507
Kholodenko BN (2009) Spatially distributed cell signalling. FEBS Lett 583:4006–4012
Neves SR, Iyengar R (2009) Models of spatially restricted biochemical reaction systems. J Biol Chem 284:5445–5449
Neves SR, Tsokas P, Sarkar A, Grace EA, Rangamani P, Taubenfeld SM, Alberini CM, Schaff JC, Blitzer RD, Moraru II, Iyengar R (2008) Cell shape and negative links in regulatory motifs together control spatial information flow in signaling networks. Cell 133:666–680
Freeman M (2000) Feedback control of intercellular signalling in development. Nature 408:313–319
Edelstein-Keshet L (1988) Mathematical models in biology. McGraw-Hill Companies
Birtwistle MR, Kholodenko BN (2009) Endocytosis and signalling: a meeting with mathematics. Mol Oncol 3:308–320
Bird RB, Stewart WE, Lightfoot EN (2001) Transport phenomena, 2nd edn. Wiley
Balagadde FK, Song H, Ozaki J, Collins CH, Barnet M, Arnold FH, Quake SR, You L (2008) A synthetic Escherichia coli predator-prey ecosystem. Mol Syst Biol 4:187
Reeves GT, Muratov CB, Schupbach T, Shvartsman SY (2006) Quantitative models of developmental pattern formation. Dev Cell 11:289–300
Camilli A, Bassler BL (2006) Bacterial small- molecule signaling pathways. Science 311:1113–1116
Taylor RJ (1984) Predation. Chapman and Hall Ltd, New York, NY
Morton KW, Mayers DF (2005) Numerical solution of partial differential equations: an introduction, 2nd edn. Cambridge University Press, Cambridge
Slepchenko BM, Schaff JC, Macara I, Loew LM (2003) Quantitative cell biology with the Virtual Cell. Trends Cell Biol 13:570–576
van Schijndel J (2008) Integrated modeling using MatLab, Simulink and COMSOL: with heat, air and moisture applications for building physics and systems. VDM Verlag Dr. Müller
Zimmerman WBJ (2006) Multiphysics modeling with finite element methods. World Scientific Publishing Company
Ford RM, Lauffenburger DA (1991) Analysis of chemotactic bacterial distributions in population migration assays using a mathematical model applicable to steep or shallow attractant gradients. Bull Math Biol 53:721–749
Lauffenburger DA (1991) Quantative studies of bacterial chemotaxis and microbial population dynamics. Microb Ecol 22:175–185
Woodward DE, Tyson R, Myerscough MR, Murray JD, Budrene EO, Berg HC (1995) Spatio-temporal patterns generated by Salmonella typhimurium. Biophys J 68:2181–2189
Murray JD (2005) Mathematical biology, vol 2. Oxford University Press
Peet R (1974) The measurement of species diversity. Annu Rev Ecol Syst 5:285–307
Song H, Payne S, Gray M, You L (2009) Spatiotemporal modulation of biodiversity in a synthetic chemical-mediated ecosystem. Nat Chem Biol 5:929–935
Collins CH, Leadbetter JR, Arnold FH (2006) Dual selection enhances the signaling specificity of a variant of the quorum-sensing transcriptional activator LuxR. Nat Biotechnol 24:708–712
Keller EF, Segel LA (1971) Traveling bands of chemotactic bacteria: a theoretical analysis. J Theor Biol 30:235–248
Kaufmann GF, Sartorio R, Lee SH, Rogers CJ, Meijler MM, Moss JA, Clapham B, Brogan AP, Dickerson TJ, Janda KD (2005) Revisiting quorum sensing: discovery of additional chemical and biological functions for 3-oxo-N-acylhomoserine lactones. Proc Natl Acad Sci USA 102:309–314
Acknowledgments
This study was supported by a Startup Grant (H.S.), AcRF TIER 1 Grant (H.S.), the National Institute of Health (5R01CA118486, L.Y.), a David and Lucile Packard Fellowship (L.Y.), and a DuPont Young Professor Award (L.Y.).
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Song, H., You, L. (2012). Modeling Spatiotemporal Dynamics of Bacterial Populations. In: Liu, X., Betterton, M. (eds) Computational Modeling of Signaling Networks. Methods in Molecular Biology, vol 880. Humana Press, Totowa, NJ. https://doi.org/10.1007/978-1-61779-833-7_11
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DOI: https://doi.org/10.1007/978-1-61779-833-7_11
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