Dynamics Mechanism Driven By Time Delay In The Competence Gene Regulatory Circuit Of Bacillus Subtilis

Bacillus subtilis is a non-pathogenic microorganism,which has the application values in industry,agriculture,medicine and health,food health,etc.For example,it can be used as a new type of vaccine carrier and started to be used for vaccines such as tetanus and anthrax.Specially,when Bacillus subtilis is in a special physiological state,the competence,DNA molecules in the external environment can enter the cell to participate in inheritance,,which is what makes it important and widely used.Therefore,numerous scholars and experts have begun to pay attention to the composition and dynamic mechanism of gene regulatory networks or circuits that enter and exit the competence of Bacillus subtilis.A large number of studies have shown that time delay in the process of gene expression is inevitable,which often causes great variations in the dynamic properties of the system.However,in the Bacillus subtilis competent gene regulatory circuits,the regulatory effect of time delay has received little attention.Therefore,studying the dynamic mechanism of the Bacillus subtilis competent gene regulatory circuit with time delay has great practical significance.This article mainly studies the effects of time delay,parameters,and their combinations on the Bacillus subtilis wild-type gene regulatory circuit and the hypothetical gene regulatory CircuitOne that a positive feedback loop was added.Based on the corresponding mathematical model established by the predecessors,some time delay terms were were considered,the theoretical analysis and numerical simulation were explained respectively.The main results as show as follows.First and foremost,for WT gene regulatory circuit,the time delay has the ability to induce circuit oscillations.However,the corresponding oscillatory system with time delay becomes stable with the increase of the rates of basic expression of comK and the saturation expression of comK,i.e.the positive feedback intensity,which guarantees the phenotype of the competent state of Bacillus subtilis.Additionally,for the hypothetical CircuitOne,Time delay also has the effect that causing the oscillations of core factors.Moreover,some parameters in the model can also regulate the dynamic behavior of core factors.After the addition of time delay,the effect of the parameters has varied significantly,such as dynamic characteristics or critical values have been changed,and even the action of the original parameters have been directly eliminated.These results mentioned above will help to analyze how to maintain the competence and serve for the effective use of Bacillus subtilis.