@Article{CSIAM-AM-5-2,
author = {Zheng, Manyi and Zhishan, Qiu and Jiao, Feng and Sun, Qiwen},
title = {A Novel Computational Method for Two-State Transcription Model with Non-Exponential ON and OFF Durations},
journal = {CSIAM Transactions on Applied Mathematics},
year = {2024},
volume = {5},
number = {2},
pages = {295--319},
abstract = {<p style="text-align: justify;">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 OFF
states are modeled as exponential distributions. However, increasing data suggest that
the residence durations at ON or OFF are non-exponential distributed for which the
traditional master equations cannot be presented. By combining Kolmogorov forward
equations with alternating renewal processes, we present a novel method to compute
the average transcription level and its noise by circumventing the bottleneck of master
equations under gene ON and OFF switch. As an application, we consider lifetimes of
OFF and ON states having Erlang distributions. We show that: (i) multiple steps from
OFF to ON force the oscillating transcription while multiple steps from ON to OFF
accelerate the transcription, (ii) the increase of steps between ON and OFF rapidly
reduces the transcription noise to approach its minimum value. This suggests that
a large number of steps between ON and OFF are not needed in the model to capture
the stochastic transcription data. Our computation approach can be further used to
treat a series of transcription cycles which are non-lattice distributed.</p>},
issn = {2708-0579},
doi = {https://doi.org/10.4208/csiam-am.SO-2023-0049},
url = {https://global-sci.com/article/91020/a-novel-computational-method-for-two-state-transcription-model-with-non-exponential-on-and-off-durations}
}