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Exact Distribution of Threshold Crossing Times for Protein Concentrations: Implication for Biological Timekeeping
Journal
Physical Review Letters
ISSN
00319007
Date Issued
2022-01-28
Author(s)
Rijal, Krishna
Prasad, Ashok
Singh, Abhyudai
Das, Dibyendu
Abstract
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-Formula Presented 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.
Volume
128