A comparative analysis of noise properties of stochastic binary models for a self-repressing and for an externally regulating gene

This manuscript presents a comparison of noise properties exhibited by two stochastic binary models for: (ⅰ) a self-repressing gene; (ⅱ) a repressed or activated externally regulating one. The stochastic models describe the dynamics of probability distributions governing two random variables, namely, protein numbers and the gene state as ON or OFF. In a previous work, we quantify noise in protein numbers by means of its Fano factor and write this quantity as a function of the covariance between the two random variables. Then we show that distributions governing the number of gene products can be super-Fano, Fano or sub-Fano if the covariance is, respectively, positive, null or negative. The latter condition is exclusive for the self-repressing gene and our analysis shows the conditions for which the Fano factor is a sufficient classifier of fluctuations in gene expression. In this work, we present the conditions for which the noise on the number of gene products generated from a self-repressing gene or an externally regulating one are quantitatively similar. That is important for inference of gene regulation from noise in gene expression quantitative data. Our results contribute to a classification of noise function in biological systems by theoretically demonstrating the mechanisms underpinning the higher precision in expression of a self-repressing gene in comparison with an externally regulated one