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Quorum sensing is a system of stimulus and responses correlated to population density that is used by bacteria to coordinate gene-expression. I am looking for a simple computational/mathematical model of quorum sensing that abstracts away from the details of the mechanism implementing it inside the agent, but keeps the key inter-agent properties like diffusion rate, range, and timing.

Is there a standard abstract mathematical model of quorum sensing used by biologists?

I am not interested in the particulars of a specific organism, but would like a general model I could apply to capture the 'gist' for any organism that relies on quorum sensing for part of its behavior.


Bernardini et al. (2007) provided an extension to P-systems incorporating the basics of quorum sensing, and Romero-Campero & Pérez-Jiménez (2008) have used their approach to model bioluminosity in vibrio fischeri. This approach is conceptually appealing to me, but that is because I am predominantly a computer scientists. Although P-system can be used for modeling biological systems (Ardelean & Cavaliere, 2003), they still feel fundamentally computer-science-y and are typically not published in orthodox biological venues. This makes me suspect there is a more standard approach among biologists, probably via dynamic systems and diffusion equations.

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It may not be what you are looking for, but there is a quorum sensing model available here at the EBI repository. –  Alan Boyd Sep 10 '12 at 18:04
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up vote 2 down vote accepted

I found this paper[1], which might be relevant; it uses is a more chemically inspired approach. Another paper[2] also might be interesting, it takes a more dynamical systems approach.

My personal instinct would be to use ordinary differential equations: generate a population of cells in random positions, assign each cell levels of any relevant molecular species, and come up with a list of ODEs that describe the rates of change of the species in a particular cell in terms of gene expression, degradation, and diffusion. You should then be able to simulate the time evolution of the system just by solving the (large) system of ODEs given your initial conditions. Something like the approach in this paper[3] (read the supplemental info), only your cells would move around during the simulation, rather than remaining still as part of a tissue. The implementation would get thorny, because you would have to accommodate the motion of the cells as you solve the ODEs. I imagine that this could be accomplished by simply treating the initial positions of the cells as part of the system's initial conditions and then defining the ODEs that govern the rate of change in each dimension (either randomly, or perhaps they move in a coordinated manner) so that this aspect of the system can evolve during the integration.

References:

  1. Rai N, Anand R, Ramkumar K, Sreenivasan V, Dabholkar S, Venkatesh KV, Thattai M. 2012. Prediction by promoter logic in bacterial quorum sensing. PLoS computational biology 8: e1002361.

  2. Chiang W-Y, Li Y-X, Lai P-Y. 2011. Simple models for quorum sensing: Nonlinear dynamical analysis. Physical Review E 84.

  3. Lubensky DK, Pennington MW, Shraiman BI, Baker NE. 2011. A dynamical model of ommatidial crystal formation. Proceedings of the National Academy of Sciences of the United States of America 108: 11145–50.

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