Stochastic modelling of transcriptional bursting modulated by transcription-factor binding: the Ace1p–CUP1 system in yeast

Stochastic modelling of transcriptional bursting modulated by transcription-factor binding: the Ace1p–CUP1 system in yeast

Mathematical biology: stochastic modelling of gene expression and transcriptional bursting

2026

Deven Parmar (author); Prof. Bärbel Finkenstädt (supervisor)

Genetically identical cells in the same conditions can contain different numbers of messenger RNA (mRNA) molecules from the same gene, as transcription and mRNA degradation are stochastic events. We ask how the way a transcription factor controls a gene shapes this variation between cells, using the copper-responsive yeast gene CUP1 and its transcription factor Ace1p as the biological setting. We develop a model in five stages: constitutive production; a promoter that switches between OFF and ON; activation controlled by a fixed Ace1p input; explicit Ace1p binding at the four CUP1 response elements; and a reduced two-state model whose activation rate is a Hill function of the input. For each stage we derive the steady-state mean and Fano factor (variance divided by mean) and check them against exact Gillespie simulations. When the input controls only how often the promoter switches ON, a stronger input raises the mean and lowers the Fano factor, whilst the mean burst size stays fixed. Following binding at four sites shows that the input also lengthens ON periods, so it changes burst size as well as burst frequency. With the illustrative parameters used here, a Hill reduction calibrated to the four-site model reproduces its mean to within about 10% over the inputs studied, but underestimates the Fano factor by up to about 19% and overestimates the burst frequency by up to about 168%. Preserving the average mRNA level therefore does not preserve the variation between cells.

mathematical biology, stochastic modelling, gene expression, transcriptional bursting, transcription factors, Ace1p, CUP1, yeast, Gillespie algorithm, Fano factor, model reduction