Imperfect molecular detection renormalizes apparent kinetic rates in stochastic gene regulatory networks

TL;DR

This paper extends binomial models of molecular capture to complex gene regulatory networks, revealing how imperfect detection affects observed kinetics and can lead to rate renormalization or misinterpretation of gene expression dynamics.

Contribution

It provides a systematic analysis of how imperfect molecular detection influences observed gene regulatory network kinetics, including conditions for rate renormalization.

Findings

Capture effects can renormalize certain kinetic rates.

Rate renormalization occurs with high transcription factor abundance.

Technical noise can distort perceived gene expression dynamics.

Abstract

Imperfect molecular detection in single-cell experiments introduces technical noise that obscures the true stochastic dynamics of gene regulatory networks. While binomial models of molecular capture provide a principled description of imperfect detection, they have so far been analyzed only for simple gene-expression models that do not explicitly account for regulation. Here, we extend binomial models of capture to general gene regulatory networks to understand how imperfect capture reshapes the observed time-dependent statistics of molecular counts. Our results reveal when capture effects correspond to a renormalization of a subset of the kinetic rates and when they cannot be absorbed into effective rates, providing a systematic basis for interpreting noisy single-cell measurements. In particular, we show that rate renormalization emerges either under significant transcription factor abundance or when promoter-state transitions occur on a distinct (much slower or faster) timescale than other reactions. In these cases, technical noise causes the apparent mean burst size of synthesized gene products to appear reduced while transcription factor binding reactions appear faster. These effects hold for gene regulatory networks of arbitrary connectivity and remain valid under time-dependent kinetic rates.