Accounting for extrinsic variability in the estimation of stochastic rate constants

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SUMMARY Single‐cell recordings of transcriptional and post‐transcriptional processes reveal the inherent stochasticity of cellular events. However, to a large extent, the observed variability in isogenic cell populations is due to extrinsic factors, such as difference in expression capacity, cell volume and cell cycle stage—to name a few. Thus, such experimental data represents a convolution of effects from stochastic kinetics and extrinsic noise sources. Recent parameter inference schemes for single‐cell data just account for variability because of molecular noise. Here, we present a Bayesian inference scheme that deconvolutes the two sources of variability and enables us to obtain optimal estimates of stochastic rate constants of low copy‐number events and extract statistical information about cell‐to‐cell variability. In contrast to previous attempts, we model extrinsic noise by a variability in the abundance of mass‐conserved species, rather than a variability in kinetic parameters. We apply the scheme to a simple model of the osmostress‐induced transcriptional activation in budding yeast.