A Novel Computational Method for Two-State Transcription Model with Non-Exponential ON and OFF Durations (CSIAM Transactions on Applied Mathematics, 2024)
The fluctuation of mRNA molecule numbers within an isogenic cell population is primarily attributed to randomly switching between active (ON) and inactive(OFF) periods of gene transcription. In most studies the waiting-times for ON or OFFstates are modeled as exponential distributions. However, increasing data suggest thatthe residence durations at ON or OFF are non-exponential distributed for which thetraditional master equations cannot be presented. By combining Kolmogorov forwardequations with alternating renewal processes, we present a novel method to computethe average transcription level and its noise by circumventing the bottleneck of masterequations under gene ON and OFF switch. As an application, we consider lifetimes ofOFF and ON states having Erlang distributions. We show that: (i) multiple steps fromOFF to ON force the oscillating transcription while multiple steps from ON to OFFaccelerate the transcription, (ii) the increase of steps between ON and OFF rapidlyreduces the transcription noise to approach its minimum value. This suggests thata large number of steps between ON and OFF are not needed in the model to capturethe stochastic transcription data. Our computation approach can be further used totreat a series of transcription cycles which are non-lattice distributed.