Abstract
This work studies two mathematical models for describing the motion of phototactic bacteria, i.e., bacteria that move toward light. Based on experimental observations, we conjecture that the motion of the colony toward light depends on certain group dynamics. These group dynamics are hypothesized to be coordinated through an individual property of each bacterium, which we refer to as excitation. The excitation of each individual bacterium is assumed to change based on the excitation of the neighboring bacteria. Under these assumptions, we propose a (discrete) cellular automaton model and derive an analogous stochastic model for describing the evolution in time of the location of bacteria, the excitation of individual bacteria, and a surface memory effect. We provide simulation results and discuss in detail the role of the various model parameters in controlling the emerging dynamics.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bhaya, D., 2004. Light matters: phototaxis and signal transduction in unicellular cyanobacteria. Mol. Microbiol. 53, 745–754.
Bhaya, D., Bianco, N.R., Bryant, D., Grossman, A.R., 2000. Type IV Pilus biogenesis and motility in the cyanobacterium Synechocystis sp. PCC6803. Mol. Microbiol. 37, 941–951.
Bhaya, D., Takahashi, A., Grossman, A.R., 2001. Light regulation of Type IV Pilus-dependent motility by chemosensor-like elements in Synechocystis PCC 6803. Proc. Natl. Acad. Sci. USA 98, 7540–7545.
Bhaya, D., Levy, D., Requeijo, T., 2008. Group dynamics of phototaxis: interacting stochastic many-particle systems and their continuum limit. In: Benzoni-Gavage, S., Serre, D. (Eds.), Hyperbolic Problems: Theory, Numerics, Applications, Proceedings of the Eleventh International Conference on Hyperbolic Problems, Lyon, 2006, pp. 145–159. Springer, Berlin.
Black, W.P., Xu, Q., Yang, Z., 2006. Type IV Pili function upstream of the dif chemotaxis pathway in Myxococcus xanthus EPS regulation. Mol. Micobiol. 61, 447–456.
Burriesci, M., Bhaya, D., 2008. Tracking phototactic responses and modeling motility of Synechocystis sp. strain PCC6803. J. Photochem. Photobiol. B, Epub ahead of print.
Childress, S., Levandowsky, M., Spiegel, E., 1975. Pattern formation in a suspension of swimming microorganisms: equations and stability theory. J. Fluid Mech. 69, 591–613.
Keller, E.F., Segel, L.A., 1971. Traveling band of chemotactic bacteria: a theoretical analysis. J. Theor. Biol. 30, 235–248.
Levy, D., Requeijo, T., 2008. Modeling group dynamics of phototaxis: from particle systems to PDEs. Discrete Contin. Dyan. Syst. B 9, 108–128.
Li, Y., Sun, H., Ma, X., Lu, A., Lux, R., Zusman, D., Shi, W., 2003. Extracellular polysaccharides mediate pilus retraction during social motility of Myxococcus xanthus. Proc. Natl. Acad. Sci. USA 100, 5443–5448.
Lu, A., Cho, K., Black, W.P., Duan, X.Y., Lux, R., Yang, Z., Kalan, H.B., Zusman, D.R., Shi, W., 2005. Exopolysaccharide biosynthesis genes required for social motility in Myxococcus xanthus. Mol. Microbiol. 55, 206–220.
Maree, A., Panfilov, A., Hogeweg, P., 1999. Phototaxis during the slug stage of Dictyostelium discoideum: a model study. Proc. R. Soc. Lond. B 266, 1351–1360.
Masuda, S., Ono, T.A., 2004. Biochemical characterization of the major adenylyl cyclase cya 1, in the cyanobacterium Synechocystis sp. PCC 6803. FEBS Lett. 577, 255–258.
Masuda, S., Ono, T.A., 2005. Adenylyl cyclase activity of cya1 from the cyanobacterium Synechocystis sp. strain PCC 6803 is inhibited by bicarbonate. J. Bacteriol. 187, 5032–5035.
Oelschläger, K., 1989. On the derivation of reaction-diffusion equations as limit dynamics of systems of moderately interacting stochastic many-particle processes. Probab. Theory Relat. Fields 82, 565–586.
Ohmori, M., Okamoto, S., 1979. Photomovement of motile microorganisms. Photochem. Photobiol. 29, 423–437.
Stevens, A., 2000a. A stochastic cellular automaton modeling gliding and aggregation of myxobacteria. SIAM J. Appl. Math. 61, 172–182.
Stevens, A., 2000b. The derivation of chemotaxis equations as limit dynamics of moderately interacting stochastic many-particle systems. SIAM J. Appl. Math. 61, 183–212.
Terauchi, K., Ohmori, M., 1999. An adenylate cyclase, cya1, regulates cell motility in the cyanobacterium Synechocystis sp. PCC 6803. Plant Cell Physiol. 40, 248–251.
Yoshimura, H., Yanagisawa, S., Kanehisa, M., Ohmori, M., 2002a. Screening for the target gene of cyanobacterial cAMP receptor protein SYCRP1. Mol. Microbiol. 43, 834–853.
Yoshimura, H., Yoshihara, S., Okamoto, S., Ikeuchi, M., Ohmori, M., 2002b. A cAMP receptor protein, SYCRP1, is responsible for the cell motility of Synechocystic sp. PCC 6803. Plant Cell. Physiol. 43, 460–463.
Youderian, P., Hartzell, P.L., 2006. Transposon insertions of Magellan-4 that impair social gliding motility in Myxococcus xanthus. Genetics 172, 1397–1410.
Yu, R., Kaiser, D., 2007. Gliding motility and polarized slime secretion. Mol. Microbiol. 63, 454–467.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Levy, D., Requeijo, T. Stochastic Models for Phototaxis. Bull. Math. Biol. 70, 1684–1706 (2008). https://doi.org/10.1007/s11538-008-9314-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11538-008-9314-5