We review the principles underpinning the development of mathematical models of the metabolic activities of micro-organisms. Such models are important to understand and chart the substantial contributions made by micro-organisms to geochemical cycles, and also to optimise the performance of bioreactors that exploit the biochemical capabilities of these organisms. We advocate an approach based on the principle of dynamic allocation. We survey the biological background that motivates this approach, including nutrient assimilation, the regulation of gene expression, and the principles of microbial growth. In addition, we discuss the classic models of microbial growth as well as contemporary approaches. The dynamic allocation theory generalises these classic models in a natural manner and is readily amenable to the additional information provided by transcriptomics and proteomics approaches. Finally, we touch upon these organising principles in the context of the transition from the free-living unicellular mode of life to multicellularity.
SchlegelH.G. and ZaboroschC. (1993) General microbiology, 7th edition. Cambridge University Press, Cambridge.
3.
MargulisL. (1993) Symbiosis in cell evolution: microbial communities in the Archean and Proterozoic eons, 2nd edition. W.H. Freeman, New York.
4.
van den BergH.A. (1998) Bull. Math. Biol., 60, 131–150.
5.
HallegraeffG.M. (2010) J. Phycol., 46, 220–235.
6.
HolliganP.M., FernándezE., AikenJ., (1993) Global Biochem. Cycles, 7, 879–900.
7.
van den BergH.A. (2001) Acta Biotheor., 49, 1–21.
8.
NeidhardtF.C., IngrahamJ.L. and SchaechterM. (1990) Physiology of the bacterial cell: a molecular approach.Sinauer Associates, Sunderland, Massachusetts.
9.
BeveridgeT.J. (1989) The structure of bacteria. In: PoindexterJ.S. and LeadbetterE.R. (eds), Bacteria in nature III: structure, physiology, and genetic adaptability, pp. 1–65. Plenum, New York.
10.
PreissJ. (1989) Biochemistry and metabolism of intracellular reserves. In: PoindexterJ.S. and LeadbetterE.R. (eds), Bacteria in nature III: structure, physiology, and genetic adaptability, pp. 189–258. Plenum, New York.
11.
DroopM.R. (1983) Botanica Marina, 24, 99–112.
12.
DroopM.R. (1968) J. Mar. Biol. Assoc., 48, 689–733.
MadiganM.T., MartinkoJ.M., DunlapP.V. and ClarkD.P. (2009) Brock biology of microorganisms, 12th edition. Pearson Benjamin Cummings, San Francisco, CA.
18.
AlvarezH.M. (2016) Biochimie, 120, 28–39.
19.
van den BergH.A., KiselevY.N. and OrlovM.V. (2002) J. Math. Biol., 44, 276–296.
20.
NevO.A. and van den BergH.A. (2017) J. Math. Biol., 74, 409–445.
DavidsonA.L. and ChenJ. (2004) Annu. Rev. Biochem., 73, 241–268.
32.
DeckerK.B. and HintonD.M. (2013) Annu. Rev. Microbiol., 67, 113–139.
33.
LeeD.J., MinchinS.D. and BusbyS.J.W. (2012) Annu. Rev. Microbiol., 66, 125–152.
34.
FisherS.H. and SonensheinA.L. (1991) Annu. Rev. Microbiol., 45, 107–135.
35.
DawesE.A. (1989) Growth and survival of bacteria. In: PoindexterJ.S. and LeadbetterE.R. (eds), Bacteria in nature III: structure, physiology, and genetic adaptability, pp. 67–187. Plenum, New York.
36.
YuraT., NagaiH. and MoriH. (1993) Annu. Rev. Microbiol., 47, 321–350.
37.
DowC.E., RodgerA., RoperD.I. and van den BergH.A. (2013) Integr. Biol., 5, 778.
38.
DowC.E., van den BergH.A., RodgerA. and RoperD.I. (2015) Biochemistry, 54, 3803–3813.
39.
BroughtonC.E., RoperD.I., van den BergH.A. and RodgerA. (2015) Sci. Prog., 98, 131–345.
40.
MeyerH.P., KäppeliO. and FiechterA. (1985) Ann. Rev. Microbiol., 39, 299–319.
41.
van den BergH.A. (2011) Mathematical models of biological systems.Oxford University Press, New York.
42.
PirtS.J. (1965) Proc. Roy. Soc. Lond., 133, 300–302.
GottschalJ.C. (1992) Continuous culture. In: LederbergJ. (ed.), Encyclopaedia of microbiology, Vol. 1, pp. 559–572. Academic Press, San Diego, CA.
46.
de WitR., van den EndeF.P. and van GemerdenH. (1995) FEMS Microbiol. Ecol., 17, 117–136.
47.
HerbertD. (1958) Some principles of continuous culture. In: TunevallG. (ed.), Recent progress in microbiology, pp. 381–396. Almquist & Wiksell, Stockholm.
48.
MarrA.G., NilsonE.H. and ClarkD.J. (1962) Ann. N. Y. Acad. Sci, 102, 536–548.
WhitworthD.E. and CockP.J.A. (2008) Two-component signal transduction systems of the Myxobacteria. In: WhitworthD.E. (ed.), Myxobacteria: multicellularity and differentiation. ASM Press, Washington DC.
63.
KompalaD.S., RamkrishnaD. and TsaoG.T. (1984) Biotechnol. Bioeng., 26, 1272–1281.
64.
KumarK., Mella-HerreraR.A. and GoldenJ.W. (2009) Cold Spring Harb. Perspect. Biol., 2, a000315.
65.
van GemerdenH. (1993) Mar. Geol., 113, 3–25.
66.
BurnatM., HerreroA. and FloresE. (2014) Proc. Natl Acad. Sci. USA, 111, 3823–3828.
