How reliable is the linear noise approximation of gene regulatory networks?
- Background: The linear noise approximation (LNA) is commonly used to predict how noise is regulated and exploited at the cellular level. These predictions are exact for reaction networks composed exclusively of first order reactions or for networks involving bimolecular reactions and large numbers of molecules. It is however well known that gene regulation involves bimolecular interactions with molecule numbers as small as a single copy of a particular gene. It is therefore questionable how reliable are the LNA predictions for these systems. Results: We implement in the software package intrinsic Noise Analyzer (iNA), a system size expansion based method which calculates the mean concentrations and the variances of the fluctuations to an order of accuracy higher than the LNA. We then use iNA to explore the parametric dependence of the Fano factors and of the coefficients of variation of the mRNA and protein fluctuations in models of genetic networks involving nonlinear protein degradation, post-transcriptional, post-translationalBackground: The linear noise approximation (LNA) is commonly used to predict how noise is regulated and exploited at the cellular level. These predictions are exact for reaction networks composed exclusively of first order reactions or for networks involving bimolecular reactions and large numbers of molecules. It is however well known that gene regulation involves bimolecular interactions with molecule numbers as small as a single copy of a particular gene. It is therefore questionable how reliable are the LNA predictions for these systems. Results: We implement in the software package intrinsic Noise Analyzer (iNA), a system size expansion based method which calculates the mean concentrations and the variances of the fluctuations to an order of accuracy higher than the LNA. We then use iNA to explore the parametric dependence of the Fano factors and of the coefficients of variation of the mRNA and protein fluctuations in models of genetic networks involving nonlinear protein degradation, post-transcriptional, post-translational and negative feedback regulation. We find that the LNA can significantly underestimate the amplitude and period of noise-induced oscillations in genetic oscillators. We also identify cases where the LNA predicts that noise levels can be optimized by tuning a bimolecular rate constant whereas our method shows that no such regulation is possible. All our results are confirmed by stochastic simulations. Conclusion: The software iNA allows the investigation of parameter regimes where the LNA fares well and where it does not. We have shown that the parametric dependence of the coefficients of variation and Fano factors for common gene regulatory networks is better described by including terms of higher order than LNA in the system size expansion. This analysis is considerably faster than stochastic simulations due to the extensive ensemble averaging needed to obtain statistically meaningful results. Hence iNA is well suited for performing computationally efficient and quantitative studies of intrinsic noise in gene regulatory networks.…
Author details: | Philipp ThomasORCiD, Hannes MatuschekORCiDGND, Ramon GrimaORCiD |
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URN: | urn:nbn:de:kobv:517-opus4-435028 |
DOI: | https://doi.org/10.25932/publishup-43502 |
ISSN: | 1866-8372 |
Title of parent work (German): | Postprints der Universität Potsdam : Mathematisch Naturwissenschaftliche Reihe |
Publication series (Volume number): | Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe (876) |
Publication type: | Postprint |
Language: | English |
Date of first publication: | 2020/04/09 |
Publication year: | 2013 |
Publishing institution: | Universität Potsdam |
Release date: | 2020/04/09 |
Tag: | Bimolecular Reaction; Fano Factor; Gene Regulatory Network; Reaction Rate Constant; Stochastic Simulation |
Issue: | 876 |
Number of pages: | 17 |
Source: | BMC Genomics 14 (2013) S5 DOI:10.1186/1471-2164-14-S4-S5 |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät |
DDC classification: | 5 Naturwissenschaften und Mathematik / 57 Biowissenschaften; Biologie / 570 Biowissenschaften; Biologie |
6 Technik, Medizin, angewandte Wissenschaften / 61 Medizin und Gesundheit / 610 Medizin und Gesundheit | |
Peer review: | Referiert |
Publishing method: | Open Access |
License (English): | Creative Commons - Namensnennung 2.0 Generic |