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

Thomas, Philipp; Matuschek, Hannes; Grima, Ramon

doi:10.1186/1471-2164-14-s4-s5

Cited by 38 publications

(51 citation statements)

References 55 publications

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“…In this case, the system description with uncorrelated white noise in the Ito interpretation does not predict correctly the system behavior. This is not surprising because it has been known that for second-order reactions, the FPE with independent white noise is not accurate (Grima et al, 2011;Thomas et al, 2013). Different approaches have been introduced to resolve the discrepancy, exemplified by the colored noise approximations (Shahrezaei et al, 2008).…”

Section: Discussionmentioning

confidence: 99%

An open-loop approach to calculate noise-induced transitions

Maleki

Becskei

2017

Journal of Theoretical Biology

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Section: Discussionmentioning

confidence: 99%

An open-loop approach to calculate noise-induced transitions

Maleki

Becskei

2017

Journal of Theoretical Biology

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“…To examine the a priori estimated upper bound for truncation error, we follow Eqn. (22) and (23) to assign values of α i = k s and β i+1 = k d (i + 1) for this network. We compute the a priori upper error bound for different truncations using Eqn.…”

Section: Birth-death Processmentioning

confidence: 99%

“…To examine a priori estimated upper bounds for the truncation errors in MEG 1 and MEG 2 , we follow Eqn. (22) and (23) to assign values of α i = k e and β (i+1) = k m (i + 1) for the M EG 1 . Because of the dependency of protein synthesis on the mRNA copy numbers, we set α i = 64 · k t and β i+1 = k d (i + 1) following Eqn.…”

Section: Single Gene Expression Modelmentioning

confidence: 99%

“…To examine a priori estimated upper bounds for the truncation errors in MEG 1 and MEG 2 , we follow Eqn. (22) and (23) to assign values of α i = k sA and β (i+1) = [(i + 1) − 2] · k dA for the M EG 1 , where the subscript (i + 1) is the total copy number of species A in the system. The subtraction of 2 is necessary because up to 2 copies of A can be protected from degradation by binding to GeneB.…”

Section: Genetic Toggle Switchmentioning

confidence: 99%

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State Space Truncation with Quantified Errors for Accurate Solutions to Discrete Chemical Master Equation

2016

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The discrete chemical master equation (dCME) provides a general framework for studying stochasticity in mesoscopic reaction networks. Since its direct solution rapidly becomes intractable due to the increasing size of the state space, truncation of the state space is necessary for solving most dCMEs. It is therefore important to assess the consequences of state space truncations so errors can be quantified and minimized. Here we describe a novel method for state space truncation. By partitioning a reaction network into multiple molecular equivalence groups (MEG), we truncate the state space by limiting the total molecular copy numbers in each MEG. We further describe a theoretical framework for analysis of the truncation error in the steady state probability landscape using reflecting boundaries. By aggregating the state space based on the usage of a MEG and constructing an aggregated Markov process, we show that the truncation error of a MEG can be asymptotically bounded by the probability of states on the reflecting boundary of the MEG. Furthermore, truncating states of an arbitrary MEG will not undermine the estimated error of truncating any other MEGs. We then provide an overall error estimate for networks with multiple MEGs. To rapidly determine the appropriate size of an arbitrary MEG, we also introduce an a priori method to estimate the upper bound of its truncation error. This a priori estimate can be rapidly computed from reaction rates of the network, without the need of costly trial solutions of the dCME. As examples, we show results of applying our methods to the four stochastic networks of 1) the birth and death model, 2) the single gene expression model, 3) the genetic toggle switch model, and 4) the phage lambda bistable epigenetic switch model. We demonstrate how truncation errors and steady state probability landscapes can be computed using different sizes of the MEG(s) and how the results validate out theories. Overall, the novel state space truncation and error analysis methods developed here can be used to ensure accurate direct solutions to the dCME for a large number of stochastic networks.

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“…The fluctuations associated with at least one of the species participating in each of the second-order reaction are Poissonian and uncorrelated with the fluctuations of other species. Also, LNA remains valid for faster activation and deactivation (or synthesis and degradation) rates of the corresponding components compared to the coarse-grained (steady state) time scale [30][31][32][33][34][35][36][37][38][39][40].…”

Section: Introductionmentioning

confidence: 99%

Information Theoretical Study of Cross-Talk Mediated Signal Transduction in MAPK Pathways

Maity

Chaudhury

Banik

2017

Entropy

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Abstract:Biochemical networks having similar functional pathways are often correlated due to cross-talk among the homologous proteins in the different networks. Using a stochastic framework, we address the functional significance of the cross-talk between two pathways. A theoretical analysis on generic MAPK pathways reveals cross-talk is responsible for developing coordinated fluctuations between the pathways. The extent of correlation evaluated in terms of the information theoretic measure provides directionality to net information propagation. Stochastic time series suggest that the cross-talk generates synchronisation in a cell. In addition, the cross-interaction develops correlation between two different phosphorylated kinases expressed in each of the cells in a population of genetically identical cells. Depending on the number of inputs and outputs, we identify signal integration and signal bifurcation motif that arise due to inter-pathway connectivity in the composite network. Analysis using partial information decomposition, an extended formalism of multivariate information calculation, also quantifies the net synergy in the information propagation through the branched pathways. Under this formalism, signature of synergy or redundancy is observed due to the architectural difference in the branched pathways.

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

Cited by 38 publications

References 55 publications

An open-loop approach to calculate noise-induced transitions

An open-loop approach to calculate noise-induced transitions

State Space Truncation with Quantified Errors for Accurate Solutions to Discrete Chemical Master Equation

Information Theoretical Study of Cross-Talk Mediated Signal Transduction in MAPK Pathways

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