First passage time in post-transcriptional regulation by multiple small RNAs

A stochastic vs deterministic perspective on the timing of cellular events

Cells are the fundamental units of life, and like all life forms, they change over time. Changes in cell state are driven by molecular processes; of these many are initiated when molecule numbers reach and exceed specific thresholds, a characteristic that can be described as "digital cellular logic". Here we show how molecular and cellular noise profoundly influence the time to cross a critical threshold-the first-passage time-and map out scenarios in which stochastic dynamics result in shorter or longer average first-passage times compared to noise-less dynamics. We illustrate the dependence of the mean first-passage time on noise for a set of exemplar models of gene expression, auto-regulatory feedback control, and enzyme-mediated catalysis. Our theory provides intuitive insight into the origin of these effects and underscores two important insights: (i) deterministic predictions for cellular event timing can be highly inaccurate when molecule numbers are within the range known for many cells; (ii) molecular noise can significantly shift mean first-passage times, particularly within auto-regulatory genetic feedback circuits.

Exact Distribution of Threshold Crossing Times for Protein Concentrations: Implication for Biological Timekeeping

Stochastic protein accumulation up to some concentration threshold sets the timing of many cellular physiological processes. Here we obtain the exact distribution of first threshold crossing times of protein concentration, in either Laplace or time domain, and its associated cumulants: mean, variance, and skewness. The distribution is asymmetric, and its skewness nonmonotonically varies with the threshold. We study lysis times of E. coli cells for holin gene mutants of bacteriophage-λ and find a good match with theory. Mutants requiring higher holin thresholds show more skewed lysis time distributions as predicted. The theory also predicts a linear relationship between infection delay time and host doubling time for lytic viruses, that has recently been experimentally observed.

First passage time properties of miRNA-mediated protein translation

An important function of microRNAs in gene regulation is to repress the protein synthesis in a multi-step process with implications in timing efficiency of the regulatory network. We propose a stochastic description of translation-initiation mechanism and solve for the steady state distribution of protein number in the linear regime. The time-dependent moments have been approximately calculated and the role of miRNAs in determining the First Passage Time (FPT) properties of protein dynamics has been established. We analytically show that the modulation of slow rates of the translation process will result in efficient and robust timing mechanism. For a general nonlinear model our numerical simulation results are in qualitative agreement with the linear model.