zbMATH — the first resource for mathematics

Cell-cell communication by quorum sensing and dimension-reduction. (English) Zbl 1113.92022
Summary: Several bacterial taxa change their behavior if the population density exceeds a certain threshold. This phenomenon is the consequence of a communication system between the bacteria and is called quorum sensing (QS). Up to now, this phenomenon is mostly modeled at the population level. However, new experimental techniques allow for single cell analysis. We introduce a modeling approach for the description of this QS system, including a discussion of the regulatory network and its bistable behavior. Based on this single-cell model we develop and analyze a spatially structured model for a cell population. Special attention is given to the scaling behavior w.r.t. the cell size (leading to an approximation theorem for stationary solutions) and its consequences for the interpretation of cell communication (QS versus diffusion sensing). Concluding, we apply the modeling approach to spatially structured experimental data.

92C37 Cell biology
35Q92 PDEs in connection with biology, chemistry and other natural sciences
35A35 Theoretical approximation in context of PDEs
Full Text: DOI
[1] Adams R., Fournier J. (2003). Sobolev Spaces. Elsevier, Amsterdam · Zbl 1098.46001
[2] Bassler B. (1999). How bacteria talk to each other: regulation of gene expression by quorum sensing. Curr. Opin. Microbiol. 2:582–587
[3] Daniels R., Vanderleyden J., Michiels J. (2004). Quorum sensing and swarming migration in bacteria. FEMS Microbiol. Rev. 28:261–289
[4] Dockery J., Keener J. (2001). A mathematical model for quorum sensing in Pseudomonas aeruginosa. Bull. Math. Biol. 63:95–116 · Zbl 1323.92123
[5] Eberhard A., Burlingame A., Eberhard C., Kenyon G., Nealson K., Oppenheimer N. (1981). Structural identification of autoinducer of Photobacterium fischeri luciferase. Biochemistry 20:2444–2449
[6] Fuqua C., Greenberg P.E. (2002). Listening on bacteria: acyl-homoserine lactone signalling. Nat. Rev. 3:685–695
[7] Gantner, S.: Mikrobielle Ökologie N-Acyl-L-Homoserinlacton-produzierender Bakterien in der Rhizosphäre von Tomatenpflanzen. PhD Thesis, Ludwig-Maximilian-Universität München (2003)
[8] Gray K., Greenberg E. (1992). Physical and functional maps of the luminescence gene cluster in an autoinducer-deficient Vibrio fischeri strain isolated from a squid light organ. J. Bacteriol. 174:4384–4390
[9] Kaplan H., Greenberg E. (1985). Diffusion of autoinducers is involved in regulation of the Vibrio fischeri luminescence system. J. Bacteriol. 163:1210–1214
[10] Koerber A., King J., Williams P. (2005). Deterministic and stochastic modelling of endosome escape by Staphylococcus aureus: ”quorum” sensing by a single bacterium. J. Math. Biol. 50:440–488 · Zbl 1114.92041
[11] Kuo A., Blough N., Dunlap P. (1994). Multiple N-acyl-L-homoserine lactone autoinducers of luminescence in the marine symbiotic bacterium Vibrio fischeri. J. Bacteriol. 176:7558–7565
[12] Lupp C., Ruby E. (2004). Vibrio fischeri LuxS and AinS: comparative study of two signal synthases. J. Bacteriol. 186:3873–3881
[13] Lupp C., Ruby E. (2005). Vibrio fischeri uses two quorum-sensing systems for the regulation of early and late colonization factors. J. Bacteriol. 187:3620–3629
[14] Lupp C., Urbanowski M., Greenberg E., Ruby E. (2003). The Vibrio fischeri quorum-sensing systems ain and lux sequentially induce luminescence gene expression and are important for persistence in the squid host. Mol. Microbiol. 50:319–331
[15] Miller M., Bassler B. (2001). Quorum sensing in bacteria. Annu. Rev. Microbiol. 55:165–199
[16] Nealson K., Platt T., Hastings J. (1970). Cellular control of the synthesis and activity of the bacterial luminescent system. J. Bacteriol. 104:313–322
[17] Ravn L., Christensen A., Molin S., Givskov M., Gram L. (2001). Methods for detecting acylated homoserine lactones produced by Gram-negative bacteria and their application in studies of AHL-production kinetics. J. Microbiol. Methods 44:239–251
[18] Redfield R.J. (2002). Is quorum sensing a side effect of diffusion sensing? Trends Microbiol. 10:365–370
[19] Renardy M., Rogers R.C. (1992). An Introduction to Partial Differential Equations. Springer, Berlin Heidelberg New York · Zbl 0917.35001
[20] Riedel K., Hentzer M., Geisenberger O., Huber B., Steidle A., Wu H., Hoiby N., Givskov M., Molin S., Eberl L. (2001). N-acylhomoserine-lactone-mediated communication between Pseudomonas aeruginosa and Burkholderia cepacia in mixed biofilms. Microbiology 147:3249–3262
[21] Ruby E., Lee K.-H. (1998). The Vibrio fischeri-Euprymna scolopes light organ association: current ecological paradigms. Appl. Environ. Microbiol. 64(3):805–812
[22] Schaefer A., Val B., Hanzelka B., Cronan J., Greenberg E. (2000). Detection, purification and structural elucidation of acylhomoserine lactone inducer of Vibrio fischeri luminescence and other related molecules. Method. Enzymol. 305:288–301
[23] Sharma A., Sahgal M., Johri B. (2003). Microbial communication in the rhizosphere: operation of quorum sensing. Curr. Sci. 85:1164–1172
[24] Steidle A., Sigl K., Schuhegger R., Ihring A., Schmid M., Gantner S., Stoffels M., Riedel K., Givskov M., Hartmann A., Langebartels C., Eberl L. (2001). Visualization of N-Acylhomoserine lactone-mediated cell-cell communication between bacteria colonizing the tomato rhizosphere. Appl. Environ. Microbiol. 67:5761–5770
[25] Steidle A., Allesen-Holm M., Riedel K., Berg G., Givskov M., Molin S., Eberl L. (2002). Identification and characterization of an N-Acylhomoserine Lactone-dependent quorum-sensing system in Pseudomonas putida strain IsoF. Appl. Environ. Microbiol. 68:6371–6382
[26] Thyson J., Othmer H. (1978). The dynamics of feedback control circuits in biochemical pathways. Progr. Theor. Biol. 5:1–62
[27] Walter W. (1964). Differential- und Integral-Ungleichungen. Springer, Berlin Heidelberg New York · Zbl 0119.12205
[28] Ward J., King J., Koerber A., Croft J., Socket R., Williams P. (2004). Cell-signalling repression in bacterial quorum sensing. Math. Med. Biol. 21:169–204 · Zbl 1055.92017
[29] Waters C., Bassler B. (2005). Quorum sensing: Cell-to-cell communication in bacteria. Annu. Rev. Cell. Dev. Biol. 21:319–346
[30] Whitehead N., Barnard A., Slater H., Simpson N., Salmond G. (2001). Quorum-sensing in Gram-negative bacteria. FEMS Microbiol. Rev. 25:365–404
[31] You L., Cox R.S. III, Weiss R., Arnold F.A. (2004). Programmed population control by cell-cell communication and regulated killing. Nature 428:868–871
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.