Dataset Information

How reliable is the linear noise approximation of gene regulatory networks?

ABSTRACT:

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-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.

SUBMITTER: Thomas P

PROVIDER: S-EPMC3849541 | biostudies-literature | 2013

REPOSITORIES: biostudies-literature

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Publications

How reliable is the linear noise approximation of gene regulatory networks?

Thomas Philipp P Matuschek Hannes H Grima Ramon R

BMC genomics 20131001

<h4>Background</h4>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 h ...[more]

PMID: 24266939

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Project description:BackgroundStochastic fluctuations in molecular numbers have been in many cases shown to be crucial for the understanding of biochemical systems. However, the systematic study of these fluctuations is severely hindered by the high computational demand of stochastic simulation algorithms. This is particularly problematic when, as is often the case, some or many model parameters are not well known. Here, we propose a solution to this problem, namely a combination of the linear noise approximation with optimisation methods. The linear noise approximation is used to efficiently estimate the covariances of particle numbers in the system. Combining it with optimisation methods in a closed-loop to find extrema of covariances within a possibly high-dimensional parameter space allows us to answer various questions. Examples are, what is the lowest amplitude of stochastic fluctuations possible within given parameter ranges? Or, which specific changes of parameter values lead to the increase of the correlation between certain chemical species? Unlike stochastic simulation methods, this has no requirement for small numbers of molecules and thus can be applied to cases where stochastic simulation is prohibitive.ResultsWe implemented our strategy in the software COPASI and show its applicability on two different models of mitogen-activated kinases (MAPK) signalling -- one generic model of extracellular signal-regulated kinases (ERK) and one model of signalling via p38 MAPK. Using our method we were able to quickly find local maxima of covariances between particle numbers in the ERK model depending on the activities of phospho-MKKK and its corresponding phosphatase. With the p38 MAPK model our method was able to efficiently find conditions under which the coefficient of variation of the output of the signalling system, namely the particle number of Hsp27, could be minimised. We also investigated correlations between the two parallel signalling branches (MKK3 and MKK6) in this model.ConclusionsOur strategy is a practical method for the efficient investigation of fluctuations in biochemical models even when some or many of the model parameters have not yet been fully characterised.

Project description:Evolution requires phenotypic variation in a population of organisms for selection to function. Gene regulatory processes involved in organismal development affect the phenotypic diversity of organisms. Since only a fraction of all possible phenotypes are predicted to be accessed by the end of development, organisms may evolve strategies to use environmental cues and noise-like fluctuations to produce additional phenotypic diversity, and hence to enhance the speed of adaptation. We used a generic model of organismal development --gene regulatory networks-- to investigate how different levels of noise on gene expression states (i.e. phenotypes) may affect access to new, unique phenotypes, thereby affecting phenotypic diversity. We studied additional strategies that organisms might adopt to attain larger phenotypic diversity: either by augmenting their genome or the number of gene expression states. This was done for different types of gene regulatory networks that allow for distinct levels of regulatory influence on gene expression or are more likely to give rise to stable phenotypes. We found that if gene expression is binary, increasing noise levels generally decreases phenotype accessibility for all network types studied. If more gene expression states are considered, noise can moderately enhance the speed of discovery if three or four gene expression states are allowed, and if there are enough distinct regulatory networks in the population. These results were independent of the network types analyzed, and were robust to different implementations of noise. Hence, for noise to increase the number of accessible phenotypes in gene regulatory networks, very specific conditions need to be satisfied. If the number of distinct regulatory networks involved in organismal development is large enough, and the acquisition of more genes or fine tuning of their expression states proves costly to the organism, noise can be useful in allowing access to more unique phenotypes.

Project description:BackgroundReverse engineering gene networks and identifying regulatory interactions are integral to understanding cellular decision making processes. Advancement in high throughput experimental techniques has initiated innovative data driven analysis of gene regulatory networks. However, inherent noise associated with biological systems requires numerous experimental replicates for reliable conclusions. Furthermore, evidence of robust algorithms directly exploiting basic biological traits are few. Such algorithms are expected to be efficient in their performance and robust in their prediction.ResultsWe have developed a network identification algorithm to accurately infer both the topology and strength of regulatory interactions from time series gene expression data in the presence of significant experimental noise and non-linear behavior. In this novel formulism, we have addressed data variability in biological systems by integrating network identification with the bootstrap resampling technique, hence predicting robust interactions from limited experimental replicates subjected to noise. Furthermore, we have incorporated non-linearity in gene dynamics using the S-system formulation. The basic network identification formulation exploits the trait of sparsity of biological interactions. Towards that, the identification algorithm is formulated as an integer-programming problem by introducing binary variables for each network component. The objective function is targeted to minimize the network connections subjected to the constraint of maximal agreement between the experimental and predicted gene dynamics. The developed algorithm is validated using both in silico and experimental data-sets. These studies show that the algorithm can accurately predict the topology and connection strength of the in silico networks, as quantified by high precision and recall, and small discrepancy between the actual and predicted kinetic parameters. Furthermore, in both the in silico and experimental case studies, the predicted gene expression profiles are in very close agreement with the dynamics of the input data.ConclusionsOur integer programming algorithm effectively utilizes bootstrapping to identify robust gene regulatory networks from noisy, non-linear time-series gene expression data. With significant noise and non-linearities being inherent to biological systems, the present formulism, with the incorporation of network sparsity, is extremely relevant to gene regulatory networks, and while the formulation has been validated against in silico and E. Coli data, it can be applied to any biological system.

Dataset Information

How reliable is the linear noise approximation of gene regulatory networks?

Background

Results

Conclusion

Publications

How reliable is the linear noise approximation of gene regulatory networks?

Similar Datasets

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