Oscillation dynamics of MeKS core module containing positive and negative feedback loops with time delay

Abstract

The MeKS core module, as a part of the Bacillus subtilis genetic circuit, consists of the direct positive feedback and ComS-mediated negative feedback loops of ComK. In this paper, based on the four-dimensional MeKS mathematical model proposed by Süel et al., a new model considering the transcription time delay is developed to further study the oscillation dynamics of this module. Combined with theoretical analysis and numerical simulation, the results show that time delay has the ability to induce oscillation of the MeKS core module. However, as the level of the basal expression rate of ComK and the saturating expression rate of ComK increases, i.e. the strength of positive feedback is enhanced, the corresponding oscillating system with time delay becomes stable, which guarantees the competent phenotype of B. subtilis. Interestingly, as the time delay increases, the interlinking system consisted by positive and negative feedback loops can still achieve a widely tunable frequency and a near-constant amplitude. These results are conducive to the analysis of the competence of Bacillus subtilis.