A case study on the use of scale separation-based analytic propagators for parameter inference in stochastic gene regulation

Justin Feigelman, Nikola Popovic, Carsten Marr

Research output: Contribution to journalArticlepeer-review


Advances in long-term fluorescent time-lapse microscopy have made it possible to study the expression of individual genes in single cells. In a typical setting, the intensity of one or more fluorescently-labeled proteins is measured at regular time intervals. Such time-courses are inherently noisy due to both measurement noise and intrinsic stochasticity of the underlying gene expression regulation. Fitting stochastic models to time-series data remains a difficult task, partly because analytical and tractable expressions for the transition probabilities cannot usually be derived in closed form.
In the present work, we employ a recently developed approach that is based on geometric singular perturbation theory, as applied to the chemical master equation of a simple two-stage gene expression model, to compute parameter likelihoods using synthetic protein time-series. We study the identifiability of model parameters in this simple setting, and compare the performance of the perturbative (uniform) propagator to a previously published, idealized (zeroth-order) propagator that assumes perfect time-scale separation between degradation of mRNA and protein. We find that both propagators are useful for parameter inference when the scale separation is sufficiently large. However, with decreasing separation, the uniform propagator sometimes yields non-physical negative transition probabilities which render parameter inference difficult. Finally, we discuss the utility of both propagators, and possible extensions thereof, for inference. For computational efficiency, the propagators were implemented in C++ and embedded in Matlab; the code is available upon request.
Original languageEnglish
Pages (from-to)164-173
Number of pages10
JournalJournal of Coupled Systems and Multiscale Dynamics
Issue number2
Publication statusPublished - Jun 2015


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