Uncertainty Quantification in Stochastic Dynamical Gene Regulatory Networks
- 1KU Leuven/BioTeC+
Abstract
The dynamics of gene regulatory networks are governed by intrinsic noise, stemming from the random nature of biochemical reactions, and by extrinsic noise, arising from fluctuations in cellular components and environmental conditions. Together, these sources can compromise the reliability of predictive computational models if not properly accounted for, and capturing both effects within a single framework remains a non-trivial task in computational biology. In this work, we propose an uncertainty quantification framework that addresses these two contributions jointly: intrinsic stochasticity is described through a partial integro-differential equation (PIDE) for the protein probability density function, whereas extrinsic noise is represented as parametric uncertainty in the kinetic parameters. The propagation of the uncertainty is carried out via an intrusive polynomial chaos expansion (PCE), in which the PCE coefficients are obtained from a stochastic Galerkin projection of the PIDE, yielding a coupled deterministic system that is solved with standard numerical methods. We illustrate the approach on a positive autoregulatory gene network with one and two uncertain kinetic parameters. The proposed approach accurately reproduces the mean, variance, and full protein probability density function, including the bimodal distributions, at a substantially lower computational cost.
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BibTeX
@misc{galleguillos2026uncertainty,
title = {{Uncertainty Quantification in Stochastic Dynamical Gene Regulatory Networks}},
author = {F. Pizarro Galleguillos and S. Bhonsale and J. VAN IMPE},
howpublished = {bioRxiv},
year = {2026},
month = aug,
doi = {10.64898/2026.08.31.747806},
url = {https://www.biorxiv.org/content/10.64898/2026.08.31.747806v1},
note = {CC BY-NC-ND},
}
RIS
TY - UNPB
TI - Uncertainty Quantification in Stochastic Dynamical Gene Regulatory Networks
AU - F. Pizarro Galleguillos
AU - S. Bhonsale
AU - J. VAN IMPE
PY - 2026
DA - 2026/08/31
PB - bioRxiv
DO - 10.64898/2026.08.31.747806
UR - https://www.biorxiv.org/content/10.64898/2026.08.31.747806v1
AB - The dynamics of gene regulatory networks are governed by intrinsic noise, stemming from the random nature of biochemical reactions, and by extrinsic noise, arising from fluctuations in cellular components and environmental conditions. Together, these sources can compromise the reliability of predictive computational models if not properly accounted for, and capturing both effects within a single framework remains a non-trivial task in computational biology. In this work, we propose an uncertainty quantification framework that addresses these two contributions jointly: intrinsic stochasticity is described through a partial integro-differential equation (PIDE) for the protein probability density function, whereas extrinsic noise is represented as parametric uncertainty in the kinetic parameters. The propagation of the uncertainty is carried out via an intrusive polynomial chaos expansion (PCE), in which the PCE coefficients are obtained from a stochastic Galerkin projection of the PIDE, yielding a coupled deterministic system that is solved with standard numerical methods. We illustrate the approach on a positive autoregulatory gene network with one and two uncertain kinetic parameters. The proposed approach accurately reproduces the mean, variance, and full protein probability density function, including the bimodal distributions, at a substantially lower computational cost.
ER -