Discrete and Continuum Multiscale Behaviour in Bacterial Communication - Multiscale Computer Modeling in Biomechanics and Biomedical Engineering - page 314

being made up of individual cells. 4 We conclude by revisiting some aspects of
these phenomena and noting some obvious omissions.
Delay effects ( Sect. 2 ) have a significant impact on the time dependence of the
initial stages of the behaviour of an autoinductive process. Discreteness ( Sect. 3 )
by contrast has little influence on the rate of upregulation but can affect signifi-
cantly the extent to which initial quorum-sensing behaviour (say) is localised.
Wave propagation and pinning ( Sect. 4 ) make explicit how discreteness can block
propagation of a switch in phenotype and hence whether or not an entire popu-
lation may upregulate or downregulate in response to the state of a subpopulation. 5
It scarcely need be said that numerous potentially important effects have been
ignored, even at the level of generic modelling (combinations of discreteness and
delays, stochastic behaviour etc.): applications to systems biology of such multi-
scale spatio-temporal systems can be expected to continue to raise a wide variety
of novel mathematical challenges.
Acknowledgments SJ thanks the MRC for funding in the form of a Special Training in Bio-
medical Informatics Fellowship and both authors the BBSRC for support under the SysMO and
SysMO2 initiatives (COSMIC and COSMIC 2).
References
1. Cheung, J.K., Keyburn, A.L., Carter, G.P., Lanckriet, A.L., An Immerseel, F., Moore, R.J.,
Rood, J.I: The VirSR two-component signal transduction system regulates NetB toxin
production in Clostridium perfringens. Infect. Immun. 78, 3064-3072 (2010)
2. Cooksley, C.M., Davis, I.J., Winzer, K., Chan, W.C., Peck, M.W., Minton, N.P.: Regulation
of neurotoxin production and sporulation by a putative agrBD signaling system in proteolytic
Clostridium botulinum. Appl. Environ. Microb. 76, 4448-4460 (2010)
3. Dold, J.W.: Analysis of the early stage of thermal runaway. Q. J. Mech. Appl. Math. 38,
361-387 (1985)
4. Fujii, T., Ingham, C., Nakayama, J., Beerthuyzen, M., Kunuki, R., Molenaar, D., Sturme, M.,
Vaughan, E., Kleerebezem, M., de Vos, W.: Two homologous Agr-like quorum-sensing
systems cooperatively control adherence, cell morphology, and cell viability properties in
Lactobacillus plantarum WCFS1. J. Bacteriol. 190, 7655-7665 (2008)
5. Henke, J.M., Bassler, B.L.: Bacterial social engagements. Trends Cell Biol. 14, 648-656
(2004)
6. Hocking, L.M., Stewartson, K., Stuart, J.T., Brown, S.N.: A nonlinear instability burst in
plane parallel flow. J. Fluid Mech. 51, 705-735 (1972)
7. Jabbari, S., King, J.R., Koerber, A.J., Williams, P.: Mathematical modelling of the agr
operon in Staphylococcus aureus. J. Math. Biol. 61, 17-54 (2010)
4 The quorum-sensing phenomena described above allow bacterial populations to function in
some regards as multicellular organisms, and the types of qualitative phenomena that we have
sought to classify are of course also relevant to plants, fungi and animals.
5 Discreteness means that it is only meaningful for an entire cell or compartment, rather than an
infinitesimally small part of one, to become upregulated, an effect that cannot of course be
captured by continuum models.