Far Eastern Mathematical Journal

To content of the issue


2D reaction-diffusion model of quorum sensing characteristics during all phases of bacterial growth


Y. Shuai, A.G. Maslovskaya, C. Kuttler

2022, issue 2, P. 232-237
DOI: https://doi.org/10.47910/FEMJ202231


Abstract
The paper is devoted to the development of a 2D reaction-diffusion model of the bacterial communication process due to the quorum sensing observed during all bacterial growth phases. The mathematical model is presented by an initial-boundary value problem for a system of semilinear partial differential equations modified in view of the multiphase character of population dynamics. The model is implemented by the finite element method using the COMSOL Multiphysics platform. The results of simulations of chemical compounds characterizing quorum sensing are presented on an example of the bacterial species of Pseudomonas putida under variation of parameters of mortality intensity.

Keywords:
reaction-diffusion model of quorum sensing, bacterial growth, finite-element modelling, simulation of chemical compounds

Download the article (PDF-file)

References

[1] J. D. Dockery, J.P. Keener, “A mathematical model for quorum sensing in Pseudomonas aeruginosa", Bull. Math. Biol., 63, (2001), 1585-1639.
[2] J. Muller, C. Kuttler, B. A. Hense , M. Rothballer, A. Hartmann, “Cell-cell communication by quorum sensing and dimension-reduction", J. Math. Biol., 53, (2006), 672-702.
[3] G. Telford, D. Wheeler, P. Williams, P. T. Tomkins, P. Appleby, H. Sewell, G. S. Stewart, B. W. Bycroft, D. I. Pritchard., “The Pseudomonas aeruginosa quorum-sensing signal molecule N-(3-oxododecanoyl)-L-homoserine lactone has immunomodulatory activity", Infect Immun., 66(1), (1998), 36-42.
[4] A. B. Goryachev, “Understanding bacterial cell-cell communication with computational modeling", Chem. Rev., 111, (2011), 238-250.
[5] J. Perez-Velazquez, M. Golgeli, R. Garcia-Contreras, “Mathematical modelling of bacterial quorum sensing: a review", Bull. Math. Biol., 76, (2016), 1585-1639. [6] Ch. Kuttler, “Reaction-diffusion equations and their application on bacterial communication", In: Handbook of Statistics (Chapter 4), 37, (2017), 55-91.
[7] Ch. Kuttler, A. Maslovskaya, “Computer simulation of communication in bacterial populations under external impact of signal-degrading enzymes", Proc. of the CEUR “Workshop Proceedings", 2783, (2020), 163-179.
[8] Ch. Kuttler, A. Maslovskaya, “Wave effects in stochastic time lagging reaction-diffusion model of quorum-sensing in bacterial populations", Proc. IEEE Int. Conf. Days on Diffraction, 2020, 62-67.
[9] Ch. Kuttler, A. Maslovskaya, “Hybrid stochastic fractional-based approach to modeling bacterial quorum sensing", Applied Mathematical Modelling, 93, (2021), 360-375.
[10] Ch. Kuttler, A. Maslovskaya, L. Moroz, “Numerical simulation of time-fractional diffusion wave processes applied to communication in bacterial populations", Proc. of the IEEE, “Days on Diffraction", 2021, 114-119.
[11] J. M. N. Llorens, A. Tormo, E. Martinez-Garcia, “Stationary phase in gram-negative bacteria", FEMS Microbiol. Rev., 2010, 476-495.
[12] M. Peleg, M.G. Corradini, “Microbial growth curves: what the models tell us and what they cannot", Critical Reviews in Food Science and Nutrition, 51(10), (2011), 917(45).
[13] Md. S. Munna, Z. Zeba, R. Noor, “Inuence of temperature on the growth of Pseudomonas putida", Stamford Journal of Microbiology, 5(1), (2015), 9-12.
[14] N. Shen, M. Jiang, P. Wei, “The kinetic study on the production of hydantoinase and n-carbamoylase by Pseudomonas JS-01", Journal of Nanjing University of Chemical Technology, 23, (2001), 36-39.

To content of the issue