Linear-noise approximation and the chemical master equation agree up to second-order moments for a class of chemical systems

Grima, Ramon

doi:10.1103/physreve.92.042124

Cited by 51 publications

(51 citation statements)

References 23 publications

(42 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Our framework relies on three main approximations: the linear-noise approximation, the separation between timescales of the intrinsic and extrinsic fluctuations, and the small extrinsic noise expansion. First, the LNA will give an accurate approximation of the CME when the molecular species populations are sufficiently large, when the nonlinearity in the reaction rates is sufficiently weak or else for special classes of biochemical systems ( [32]; see discussion later). Second, our theory requires the extrinsic fluctuations to be slow with respect to the system's intrinsic dynamics.…”

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

Extending the linear-noise approximation to biochemical systems influenced by intrinsic noise and slow lognormally distributed extrinsic noise

et al. 2019

Self Cite

View full text Add to dashboard Cite

It is well known that the kinetics of an intracellular biochemical network is stochastic. This is due to intrinsic noise arising from the random timing of biochemical reactions in the network as well as due to extrinsic noise stemming from the interaction of unknown molecular components with the network and from the cell's changing environment. While there are many methods to study the effect of intrinsic noise on the system dynamics, few exist to study the influence of both types of noise. Here we show how one can extend the conventional linear-noise approximation to allow for the rapid evaluation of the molecule numbers statistics of a biochemical network influenced by intrinsic noise and by slow lognormally distributed extrinsic noise. The theory is applied to simple models of gene regulatory networks and its validity confirmed by comparison with exact stochastic simulations. In particular we show how extrinsic noise modifies the dependence of the variance of the molecule number fluctuations on the rate constants, the mutual information between input and output signalling molecules and the robustness of feed-forward loop motifs.

show abstract

Section: Discussionmentioning

confidence: 99%

“…However, as the current system is linear (i.e. it contains no bimolecular reactions), the LNA will give the exact expressions for the mean and variance independent of the value of Ω [32]. For this reason, we have chosen Ω = 1 here.…”

Section: A Nonlinear Effects Of Extrinsic Fluctuations On a Linear Mmentioning

confidence: 99%

Extending the linear-noise approximation to biochemical systems influenced by intrinsic noise and slow lognormally distributed extrinsic noise

et al. 2019

Self Cite

View full text Add to dashboard Cite

show abstract

“…Indeed, the huge complexity of biological systems, their dependence on a large number of variables and the system-to-system variability make the unraveling of these issues, whether using experimental or computational approaches, a highly non-trivial task.More specifically, while the noise control is relatively well understood for small and simple networks, it is still far from clear how the fluctuations propagate through more general and complicated networks and what is the link of the network topology and complexity with the noise buffering or amplification. Different investigations addressed these issues from various perspectives, for example by characterizing the stochastic properties of the chemical reaction networks (CRNs) and studying the propagation of the fluctuations [21,23,24,25]. From a physics-oriented perspective, other studies analyzed the connection between the non-equilibrium thermodynamic properties of the network and the noise level [26,27,28].…”

mentioning

confidence: 99%

Deciphering noise amplification and reduction in open chemical reaction networks

Pucci

Rooman

2018

Preprint

View full text Add to dashboard Cite

The impact of random fluctuations on the dynamical behavior a complex biological systems is a longstanding issue, whose understanding would shed light on the evolutionary pressure that nature imposes on the intrinsic noise levels and would allow rationally designing synthetic networks with controlled noise. Using the Itō stochastic differential equation formalism, we performed both analytic and numerical analyses of several model systems containing different molecular species in contact with the environment and interacting with each other through mass-action kinetics. These systems represent for example biomolecular oligomerization processes, complex-breakage reactions, signaling cascades or metabolic networks. For chemical reaction networks with zero deficiency values, which admit a detailed-or complex-balanced steady state, all molecular species are uncorrelated. The number of molecules of each species follow a Poisson distribution and their Fano factors, which measure the intrinsic noise, are equal to one. Systems with deficiency one have an unbalanced non-equilibrium steady state and a non-zero S-flux, defined as the flux flowing between the complexes multiplied by an adequate stoichiometric coefficient. In this case, the noise on each species is reduced if the flux flows from the species of lowest to highest complexity, and is amplified is the flux goes in the opposite direction. These results are generalized to systems of deficiency two, which possess two independent non-vanishing S-fluxes, and we conjecture that a similar relation holds for higher deficiency systems.

show abstract

“…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%

“…II and Appendix). Recent theoretical development [32] shows that LNA is not only limited to high copy number but also exact up to second moments of any chemical species involved in a second-order reaction. 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.…”

Section: Introductionmentioning

confidence: 99%

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

Maity

Chaudhury

Banik

2017

Entropy

View full text Add to dashboard Cite

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.

show abstract

Linear-noise approximation and the chemical master equation agree up to second-order moments for a class of chemical systems

Cited by 51 publications

References 23 publications

Extending the linear-noise approximation to biochemical systems influenced by intrinsic noise and slow lognormally distributed extrinsic noise

Extending the linear-noise approximation to biochemical systems influenced by intrinsic noise and slow lognormally distributed extrinsic noise

Deciphering noise amplification and reduction in open chemical reaction networks

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

Contact Info

Product

Resources

About