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Simple mathematical model of gene expression has been studied thoroughly in this paper. We assume that protein synthesis and protein decay are deterministic in nature whereas transition from active to inactive state is totally stochastic. The probability distribution function of transcript number is calculated and evidence of binary and graded response has been observed for different reaction rates. Slow and fast kinetics have been studied explicitly. Different rate constants play a significant role in calculating distribution function (PDF) and mean value of TF regulated gene expression. It is seen that rate constants control the variance as well. A small change in the value of the rate constant gives a significant change in average protein value. The randomness of gene expression is reduced with increasing value of one of the rate constants. The main focus of this paper is to observe the effect of rate constants in transcription factor regulated gene expression.

Effect of Rate Constants in TF Regulated Gene Expression