Reduction for Stochastic Biochemical Reaction Networks with Multiscale Conservations

Kim, Jae Kyoung; Rempała, Grzegorz A.; Kang, Hye-Won

doi:10.1137/16m1099443

Cited by 21 publications

(18 citation statements)

References 57 publications

(208 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A singular perturbation-theory-based method has also recently been used to obtain a reduced stochastic description (22). There are also several formal results that have been mathematically proven for reaction systems in various scenarios (23)(24)(25)(26).…”

Section: Introductionmentioning

confidence: 99%

Revisiting the Reduction of Stochastic Models of Genetic Feedback Loops with Fast Promoter Switching

Holehouse

Grima

2019

Biophysical Journal

View full text Add to dashboard Cite

Propensity functions of the Hill type are commonly used to model transcriptional regulation in stochastic models of gene expression. This leads to an effective reduced master equation for the mRNA and protein dynamics only. Based on deterministic considerations, it is often stated or tacitly assumed that such models are valid in the limit of rapid promoter switching. Here, starting from the chemical master equation describing promoter-protein interactions, mRNA transcription, protein translation, and decay, we prove that in the limit of fast promoter switching, the distribution of protein numbers is different than that given by standard stochastic models with Hill-type propensities. We show the differences are pronounced whenever the protein-DNA binding rate is much larger than the unbinding rate, a special case of fast promoter switching. Furthermore, we show using both theory and simulations that use of the standard stochastic models leads to drastically incorrect predictions for the switching properties of positive feedback loops and that these differences decrease with increasing mean protein burst size. Our results confirm that commonly used stochastic models of gene regulatory networks are only accurate in a subset of the parameter space consistent with rapid promoter switching.

show abstract

Section: Introductionmentioning

confidence: 99%

Revisiting the Reduction of Stochastic Models of Genetic Feedback Loops with Fast Promoter Switching

Holehouse

Grima

2019

Biophysical Journal

View full text Add to dashboard Cite

show abstract

“…For instance, Grima et al [40], Chow et al [41], as well as some others [42,43] have applied this idea to construct approximate, stochastic Michaelis-Menten enzyme kinetic networks and even the gene regulatory networks [44]. As some of the authors of this article argued in their recent work ( [19]), such approximate stochastic models using intensities derived from the deterministic limits may in some sense be better approximations of the underlying stochastic networks than the deterministic QSSAs. Our derivations presented here could be used to further justify this statement, at least for networks satisfying certain scaling conditions [45,46,47], including those presented in Table 1.…”

Section: Discussionmentioning

confidence: 98%

“…We show that these QSSAs are a consequence of the law of large numbers for the stochastic reaction network under different scaling regimes. A similar approach has been recently taken in [19] with respect to a particular type of QSSA (tQSSA, see below in Section 2). However, our current derivation is different in that it entirely avoids a spatial averaging argument used in [19].…”

mentioning

confidence: 99%

“…A similar approach has been recently taken in [19] with respect to a particular type of QSSA (tQSSA, see below in Section 2). However, our current derivation is different in that it entirely avoids a spatial averaging argument used in [19]. Such an argument requires additional assumptions that are difficult to verify in practice.The paper is organized as follows.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Quasi-Steady-State Approximations Derived from the Stochastic Model of Enzyme Kinetics

et al. 2019

Self Cite

View full text Add to dashboard Cite

In this paper we derive several quasi steady-state approximations (QSSAs) to the stochastic reaction network describing the Michaelis-Menten enzyme kinetics. We show how the different assumptions about chemical species abundance and reaction rates lead to the standard QSSA (sQSSA), the total QSSA (tQSSA), and the reverse QSSA (rQSSA) approximations. These three QSSAs have been widely studied in the literature in deterministic ordinary differential equation (ODE) settings and several sets of conditions for their validity have been proposed. By using multiscaling techniques introduced in [1, 2] we show that these conditions for deterministic QSSAs largely agree with the ones for QSSAs in the large volume limits of the underlying stochastic enzyme kinetic network.In chemistry and biology, we often come across chemical reaction networks where one or more of the species exhibit a different intrinsic time scale and tend to reach an equilibrium state quicker than others. Quasi steady state approximation (QSSA) is a commonly used tool to simplify the description of the dynamics of such systems. In particular, QSSA has been widely applied to the important class of reaction networks known as the Michaelis-Menten models of enzyme kinetics [3,4,5].Traditionally the enzyme kinetics has been studied using systems of ordinary differential equations (ODEs). The ODE approach allows one to analyze various aspects of the enzyme dynamics such as asymptotic stability. However, it ignores the fluctuations of the enzyme reaction network due to intrinsic noise and instead focuses on the averaged dynamics. If accounting for this intrinsic noise is required, the use of an alternative stochastic reaction network approach may be more appropriate, especially when some of the species have low copy numbers or when one is interested in predicting the molecular fluctuations of the system. It is well-known that such molecular fluctuations in the species with small numbers, and stochasticity in general, can lead to interesting dynamics. For instance, in a recent paper [6], Perez et al. gave an account of how intrinsic noise controls and alters the dynamics, and steady state of morphogen-controlled bistable genetic switches. Stochastic models have been strongly advocated by many in recent literature [7,8,9,10,11,12]. In this paper, we consider such stochastic models in the context of QSSA and the Michaelis-Menten enzyme kinetics and relate them to the deterministic ones that are well-known from the chemical physics literature.The QSSAs are very useful from a practical perspective. They not only reduce the model complexity, but also allow us to better relate it to experimental measurements by averaging out the unobservable or difficult-to-measure species. A substantial body of work has been published to justify such QSSA reductions in deterministic models, typically by means of perturbation theory [13,14,15,16,17,18]. In contrast to this approach, we derive here the QSSA reductions using stochastic multiscaling techniques [1,2]. Although our approac...

show abstract

“…We also investigated the accuracy of the stochastic simulations performed with both models. Specifically, we compared the stochastic simulations using the Gillespie algorithm based on the propensity functions from either the original full model (described in Table S1), the sQ model (Table S2), or the tQ model (Table S3) for 9 different conditions [31][32][33][34][35][36] : E T is either lower than, similar to, or higher than K M , and S T is also either lower than, similar to, or higher than K M (Fig. 1).…”

Section: /13mentioning

confidence: 99%

Beyond the Michaelis-Menten equation: Accurate and efficient estimation of enzyme kinetic parameters

Choi

Rempała²,

Kim³

2017

Preprint

Self Cite

View full text Add to dashboard Cite

Examining enzyme kinetics is critical for understanding cellular systems and for using enzymes in industry. The MichaelisMenten equation has been widely used for over a century to estimate the enzyme kinetic parameters from reaction progress curves of substrates, which is known as the progress curve assay. However, this canonical approach works in limited conditions, such as when there is a large excess of substrate over enzyme. Even when this condition is satisfied, the identifiability of parameters is not always guaranteed, and often not verifiable in practice. To overcome such limitations of the canonical approach for the progress curve assay, here we propose a Bayesian approach based on an equation derived with the total quasi-steady-state approximation. In contrast to the canonical approach, estimates obtained with this proposed approach exhibit little bias for any combination of enzyme and substrate concentrations. Importantly, unlike the canonical approach, an optimal experiment to identify parameters with certainty can be easily designed without any prior information. Indeed, with this proposed design, the kinetic parameters of diverse enzymes with disparate catalytic efficiencies, such as chymotrypsin, fumarase, and urease, can be accurately and precisely estimated from a minimal amount of timecourse data. A publicly accessible computational package performing the Bayesian inference for such accurate and efficient enzyme kinetics is provided.

show abstract

Reduction for Stochastic Biochemical Reaction Networks with Multiscale Conservations

Cited by 21 publications

References 57 publications

Revisiting the Reduction of Stochastic Models of Genetic Feedback Loops with Fast Promoter Switching

Revisiting the Reduction of Stochastic Models of Genetic Feedback Loops with Fast Promoter Switching

Quasi-Steady-State Approximations Derived from the Stochastic Model of Enzyme Kinetics

Beyond the Michaelis-Menten equation: Accurate and efficient estimation of enzyme kinetic parameters

Contact Info

Product

Resources

About