Derivation of stationary distributions of biochemical reaction networks via structure transformation

Hong, Hyukpyo; Kim, Jinsu; Al-Radhawi, M. Ali; Sontag, Eduardo D.; Kim, Jae Kyoung

doi:10.1101/2021.03.23.436681

Cited by 3 publications

(4 citation statements)

References 63 publications

(84 reference statements)

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“…Unlike the deterministic QSSA (Eq. (3)), the stochastic QSSA, which is the stationary average number conditioned on the total numbers of the bound and unbound species, has a complex form [41,55,56]. For instance, the stochastic QSSA for the number of A ( A ) can be expressed in terms of the dimensionless variables and parameters, X =XΩ, where Ω is the volume of a system (e.g., A =ÃΩ,…”

Section: Resultsmentioning

confidence: 99%

Universally valid reduction of multiscale stochastic biochemical systems using simple non-elementary propensities

Hong

Kim

2021

Preprint

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Biochemical systems consist of numerous elementary reactions governed by the law of mass action. However, experimentally characterizing all the elementary reactions is nearly impossible. Thus, over a century, their deterministic models that typically contain rapid reversible bindings have been simplified with non-elementary reaction functions (e.g., Michaelis-Menten and Morrison equations). Although the non-elementary functions are derived by applying the quasi-steady-state approximation(QSSA) to deterministic systems, they have also been widely used to derive propensities for stochastic simulations due to computational efficiency and simplicity. However, the validity condition for this heuristic approach has not been identified even for the reversible binding between molecules, such as protein-DNA, enzyme-substrate, and receptor-ligand, which is the basis for living cells. Here, we find that the non-elementary propensities based on the deterministic total QSSA can accurately capture the stochastic dynamics of the reversible binding in general. However, serious errors occur when reactant molecules with similar levels tightly bind, unlike deterministic systems.In that case, the non-elementary propensities distort the stochastic dynamics of a bistable switch in the cell cycle and an oscillator in the circadian clock. Accordingly, we derive alternative non-elementary propensities with the stochastic low-state QSSA,developed in this study. This provides a universally valid framework for simplifying multiscale stochastic biochemical systems with rapid reversible bindings, critical for efficient stochastic simulations of cell signaling and gene regulation.

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Section: Resultsmentioning

confidence: 99%

Universally valid reduction of multiscale stochastic biochemical systems using simple non-elementary propensities

Hong

Kim

2021

Preprint

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“…S9). It would be interesting in future work to investigate whether the property can be extended to diverse systems, for instance, having multimodal dynamics such as a toggle switch network with arbitrary waiting time distributions ( 22 , 53 , 54 ).…”

Section: Discussionmentioning

confidence: 99%

Systematic inference identifies a major source of heterogeneity in cell signaling dynamics: The rate-limiting step number

2022

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Identifying the sources of cell-to-cell variability in signaling dynamics is essential to understand drug response variability and develop effective therapeutics. However, it is challenging because not all signaling intermediate reactions can be experimentally measured simultaneously. This can be overcome by replacing them with a single random time delay, but the resulting process is non-Markovian, making it difficult to infer cell-to-cell heterogeneity in reaction rates and time delays. To address this, we developed an efficient and scalable moment-based Bayesian inference method (MBI) with a user-friendly computational package that infers cell-to-cell heterogeneity in the non-Markovian signaling process. We applied MBI to single-cell expression profiles from promoters responding to antibiotics and discovered a major source of cell-to-cell variability in antibiotic stress response: the number of rate-limiting steps in signaling cascades. This knowledge can help identify effective therapies that destroy all pathogenic or cancer cells, and the approach can be applied to precision medicine.

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“…While we focus on the steady states of deterministic systems, the stationary distributions of stochastic systems can also be derived analytically for WR and DZ biochemical reaction networks [22, 24, 33, 34]. It would be interesting in future work to investigate whether the combination of network decomposition and translation can be used to derive stationary distributions analytically for a large class of biochemical reaction networks.…”

Section: Discussionmentioning

confidence: 99%

“…Hence, the method of network translation, which could transform such CRNs into WR and DZ networks while preserving their dynamics, has been developed [13,16,[19][20][21]. It has also been applied to stochastic reaction networks [22]. In practice, however, the process of network translation can be challenging for two reasons: (a) it can be difficult to find a WR and DZ network translation; (b) even after the network translation, the two desired structures are rarely satisfied, in particular for large and complex networks [23,24].…”

Section: Introductionmentioning

confidence: 99%

A framework for deriving analytic long-term behavior of biochemical reaction networks

Hernandez

Lubenia²,

Johnston

et al. 2022

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The long-term behaviors of biochemical systems are described by their steady states. Deriving these states directly for complex networks arising from real-world applications, however, is often challenging. Recent work has consequently focused on network-based approaches. Methods have been developed for transforming biochemical reaction networks into weakly reversible and deficiency zero networks, which allows the analytic steady states to be derived easily. Identifying this transformation, however, can be challenging for large and complex networks. In this paper, we address this difficulty by breaking the network into smaller independent subnetworks and then deriving the analytic steady states of each subnetwork. We show that the analytic steady states of the original network can then be derived by stitching these solutions together. To facilitate this process, we develop a user-friendly and publicly-available package, COMPILES. With our approach, we can easily test the presence of bistability of a CRISPRi toggle switch model, which was previously investigated via tremendous amount of numerical simulations. Furthermore, our approach can be used to identify absolute concentration robustness (ACR), the property of a system to maintain the concentration of particular species at steady state regardless of any initial concentrations. Specifically, our approach completely identifies all the species with and without ACR in a complex insulin model. Our method provides an effective approach to analyzing and understanding complex biochemical systems.

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Derivation of stationary distributions of biochemical reaction networks via structure transformation

Cited by 3 publications

References 63 publications

Universally valid reduction of multiscale stochastic biochemical systems using simple non-elementary propensities

Universally valid reduction of multiscale stochastic biochemical systems using simple non-elementary propensities

Systematic inference identifies a major source of heterogeneity in cell signaling dynamics: The rate-limiting step number

A framework for deriving analytic long-term behavior of biochemical reaction networks

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