The distributed delay rearranges the bimodal distribution at protein level

Abstract

BackgroundIn bimodal distribution, we refer ON to the mode with a higher protein level and OFF to a lower protein level. The traditional wisdom of manipulating the population in each mode is done by adding an inducer or inhibitor to change the protein number. MethodsBy delay stochastic simulation algorithm, we applied transcriptional or translational delay to the gene expression system of toggle switches. We also incorporated distributed delay in the model. From a deterministic aspect, reaction delay does NOT alter the steady-state value. Thus, our approach is different from the conventional method. Significant FindingsThe transcriptional delay rearranged the bimodal distribution at the protein level and the influence of the translational delay is even higher. The increment of delay time pushes more cells to have the protein in the ON mode. Remarkably, the distributed delay of translation guides 98% of cells to have protein in the ON mode. We then displayed the time-course trajectories and discovered the cause leading to the rearrangement of bimodal distribution. We also exclude the possibility that rearrangement of bimodal distribution simply comes from the trivial reason, the change of the input distribution, and concluded that the change of dynamic stochastic processes is crucial.