Dynamical stability and accuracy of moment closure approximations for bursty gene expression with nonlinear degradation
- 1Harbin Institute of Technology
Abstract
Moment-closure methods provide a widely used approach for approximating low-order statistics of stochastic biochemical reaction networks, but the resulting closed equations may exhibit physically meaningless dynamics. Here, we systematically investigate the stability of second-order moment-closure approximations for a bursty gene expression model with nonlinear protein degradation. We consider the Gaussian, log-normal, and negative-binomial closures. By analyzing the resulting dynamical systems, we show that the Gaussian closure fails the proposed stability criterion for all parameter values, whereas both the log-normal and negative-binomial closures possess a unique physically accessible fixed point and are stable if and only if kB(1 + 2B) [≥] 1, where B is the mean burst size and k is the dimensionless protein synthesis rate. Moreover, this condition is automatically satisfied when the steady-state mean protein copy number is at least one, suggesting that it is mild in biologically relevant regimes. Numerical comparisons over a broad parameter range further show that the negative-binomial closure is the most accurate, while the Gaussian closure is the least accurate. We further develop higher-order negative-binomial moment-closure schemes and demonstrate that increasing the closure order substantially improves predictive accuracy. These results highlight the importance of considering dynamical stability, in addition to numerical accuracy, when assessing moment-closure approximations.
Related
- Rapid early degradation of Cyclin A is important to maintain genomic stability
- Functional specialization and dynamical interaction in human amygdala subregions support fearful-expression processing
- Thermal Stability of Aliphatic and Semiaromatic Polyamides: Tailoring the Choice of Isothermal Aging Temperature by Using Kinetic Models of Degradation
- Cold acclimation of tomato plants is associated with differential expression of genes of the SlLHC family, carotenoid metabolism, and chlorophyll accumulation/degradation.
- Temporal stability for individual differences in both habit learning and expression
BibTeX
@misc{zhou2026dynamical,
title = {{Dynamical stability and accuracy of moment closure approximations for bursty gene expression with nonlinear degradation}},
author = {M. Zhou and C. Jia},
howpublished = {bioRxiv},
year = {2026},
month = sep,
doi = {10.64898/2026.09.30.755644},
url = {https://www.biorxiv.org/content/10.64898/2026.09.30.755644v1},
note = {CC BY},
}
RIS
TY - UNPB
TI - Dynamical stability and accuracy of moment closure approximations for bursty gene expression with nonlinear degradation
AU - M. Zhou
AU - C. Jia
PY - 2026
DA - 2026/09/30
PB - bioRxiv
DO - 10.64898/2026.09.30.755644
UR - https://www.biorxiv.org/content/10.64898/2026.09.30.755644v1
AB - Moment-closure methods provide a widely used approach for approximating low-order statistics of stochastic biochemical reaction networks, but the resulting closed equations may exhibit physically meaningless dynamics. Here, we systematically investigate the stability of second-order moment-closure approximations for a bursty gene expression model with nonlinear protein degradation. We consider the Gaussian, log-normal, and negative-binomial closures. By analyzing the resulting dynamical systems, we show that the Gaussian closure fails the proposed stability criterion for all parameter values, whereas both the log-normal and negative-binomial closures possess a unique physically accessible fixed point and are stable if and only if kB(1 + 2B) [≥] 1, where B is the mean burst size and k is the dimensionless protein synthesis rate. Moreover, this condition is automatically satisfied when the steady-state mean protein copy number is at least one, suggesting that it is mild in biologically relevant regimes. Numerical comparisons over a broad parameter range further show that the negative-binomial closure is the most accurate, while the Gaussian closure is the least accurate. We further develop higher-order negative-binomial moment-closure schemes and demonstrate that increasing the closure order substantially improves predictive accuracy. These results highlight the importance of considering dynamical stability, in addition to numerical accuracy, when assessing moment-closure approximations.
ER -