Extending the minimal model of metabolic oscillations in Bacillus subtilis biofilms

Effects of noise and harmonic excitation on the growth of Bacillus subtilis biofilm

We study the dynamic growth behaviors of Bacillus subtilis biofilms by using a stochastic delay differential equation similar to the Mackey-Glass equation. We observe a wealth of dynamic behavior from a mathematical perspective. Firstly, the change of the time delay (i.e. the time that the growth state of the periphery to affect the stress of the interior cells needs and the time required for the stress signal coming from the interior to reach the peripheral cells) and the external excitation (i.e. the change in temperature) frequency will influence the size of Bacillus subtilis biofilm and the collective growth of the cell community. We also found the resonance phenomena in mathematics, which is of great help in understanding the behavior of stress levels in the biofilm periphery. Secondly, the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by using the normal form theory and the center manifold reduction. Numerical simulations are carried out to ensure theoretical results. Finally, the effects of noise on stress levels in the biofilm periphery are analyzed and reveal more complex dynamics of the system.

Modelling population dynamics in a unicellular social organism community using a minimal model and evolutionary game theory

Most unicellular organisms live in communities and express different phenotypes. Many efforts have been made to study the population dynamics of such complex communities of cells, coexisting as well-coordinated units. Minimal models based on ordinary differential equations are powerful tools that can help us understand complex phenomena. They represent an appropriate compromise between complexity and tractability; they allow a profound and comprehensive analysis, which is still easy to understand. Evolutionary game theory is another powerful tool that can help us understand the costs and benefits of the decision a particular cell of a unicellular social organism takes when faced with the challenges of the biotic and abiotic environment. This work is a binocular view at the population dynamics of such a community through the objectives of minimal modelling and evolutionary game theory. We test the behaviour of the community of a unicellular social organism at three levels of antibiotic stress. Even in the absence of the antibiotic, spikes in the fraction of resistant cells can be observed indicating the importance of bet hedging. At moderate level of antibiotic stress, we witness cyclic dynamics reminiscent of the renowned rock–paper–scissors game. At a very high level, the resistant type of strategy is the most favourable.