Computational modelling of quorum sensing using cascade delay

Abstract: The scope of this project was to implement a quorum sensing model capable of synchronised oscillations from the article ”A synchronized quorum of genetic clocks” [1] in the software framework URDME [2]. The model consists of a system of partial differential equations describing time delayed and coupled biochemical reactions. In URDME, the time delay system was formed using a cascade of reactions in which the rate of each reaction was set so that the expected total time for all reactions in the cascade corresponds to a certain delay time. One reason for this cascade delay model is that it might better capture the inherently stochastic nature of the delay mechanism in the quorum sensing network, as opposed to a model using explicit delays.Another reason is simplicity of implementation, as delays are not explicitly supported in URDME. After initial tests suggested that the cascade delay model gave satisfying results, it was incorporated into the quorum sensing model from the article, which was implemented by rewriting the differential equations as a system of biochemical reactions. Simulations in one and two dimensions were then done, with both stochastic and deterministic solution methods. The one dimensional and two dimensional simulations yielded distinct synchronised oscillations with a cascade delay containing five sub-reactions. Several results from the simulations of the original article could be reproduced. From the results, it was concluded that the proposed cascade delay model was successful in modelling the delayed reactions in the quorum sensing network. In future studies, it is suggested that the individual cells, in which most of the reactions in the quorum sensing network happen, are modelled with greater resolution.