Paper List

Journal: ArXiv Preprint
Published: Unknown
Systems BiologyComputational Biology

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

Department of Mathematical Analysis and Numerical Mathematics, Comenius University, Slovakia | University of Edinburgh, UK

Iryna Zabaikina, Ramon Grima
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The 30-Second View

IN SHORT: This paper addresses the core challenge of distinguishing genuine stochastic dynamics of gene regulatory networks from artifacts introduced by imperfect molecular detection in single-cell experiments.

Innovation (TL;DR)

  • Methodology Extends the binomial capture model from simple gene expression to general gene regulatory networks (GRNs) with explicit regulation, enabling analysis of technical noise in complex systems.
  • Theory Establishes precise mathematical conditions under which technical noise leads to a renormalization (rescaling) of kinetic rates versus when it introduces non-absorbable distortions.
  • Methodology Derives results valid for networks of arbitrary connectivity and under time-dependent kinetic rates, significantly generalizing previous steady-state analyses.

Key conclusions

  • Technical noise systematically reduces the apparent mean burst size of gene products by a factor of p (the capture probability), e.g., from b(t) to b(t)*p.
  • Rate renormalization occurs when promoter-state transitions are on a distinct timescale (much slower/faster) than other reactions or under high transcription factor abundance.
  • The framework shows that for the telegraph model, the observed mRNA dynamics are equivalent to the true system with a renormalized transcription rate: k₃(t) → p*k₃(t).
Background and Gap： Prior analyses of binomial capture models were limited to simple, non-regulatory gene expression models, leaving a critical gap in understanding how technical noise distorts the inferred dynamics of complex, interacting regulatory networks.

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.