Stationary distributions of systems with discreteness-induced transitions

Bibbona, Enrico; Kim, Jinsu; Wiuf, Carsten

doi:10.1098/rsif.2020.0243

Cited by 10 publications

(8 citation statements)

References 35 publications

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“…Note that these bimodalities cannot be captured by the corresponding deterministic model, which predicted monostability (the result is not shown). Such mismatches between the stochastic and deterministic model have been frequently observed in the presence of timescale separation ( 1, 20, 48 ).…”

Section: Resultsmentioning

confidence: 96%

Derivation of stationary distributions of biochemical reaction networks via structure transformation

Hong

Kim

Al-Radhawi

et al. 2021

Preprint

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Long-term behaviors of biochemical reaction networks (BRNs) are described by steady states in deterministic models and stationary distributions in stochastic models. Unlike deterministic steady states, stationary distributions capturing inherent fluctuations of reactions are extremely difficult to derive analytically due to the curse of dimensionality. Here, we develop a method to derive analytic stationary distributions from deterministic steady states by transforming BRNs to have a special dynamic property, called complex balancing. Specifically, we merge nodes and edges of BRNs to match in- and out-flows of each node. This allows us to derive the stationary distributions of a large class of BRNs, including autophosphorylation networks of EGFR, PAK1, and Aurora B kinase and a genetic toggle switch. This reveals the unique properties of their stochastic dynamics such as robustness, sensitivity and multi-modality. Importantly, we provide a user-friendly computational package, CASTANET, that automatically derives sym- bolic expressions of the stationary distributions of BRNs to understand their long-term stochasticity.

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Section: Resultsmentioning

confidence: 96%

Derivation of stationary distributions of biochemical reaction networks via structure transformation

Hong

Kim

Al-Radhawi

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Note that these bimodalities cannot be captured by the corresponding deterministic model, which predicted monostability. Such mismatches between the stochastic and deterministic model have been frequently observed in the presence of timescale separation 1 , 20 , 47 .…”

Section: Resultsmentioning

confidence: 97%

Derivation of stationary distributions of biochemical reaction networks via structure transformation

et al. 2021

Self Cite

View full text Add to dashboard Cite

Long-term behaviors of biochemical reaction networks (BRNs) are described by steady states in deterministic models and stationary distributions in stochastic models. Unlike deterministic steady states, stationary distributions capturing inherent fluctuations of reactions are extremely difficult to derive analytically due to the curse of dimensionality. Here, we develop a method to derive analytic stationary distributions from deterministic steady states by transforming BRNs to have a special dynamic property, called complex balancing. Specifically, we merge nodes and edges of BRNs to match in- and out-flows of each node. This allows us to derive the stationary distributions of a large class of BRNs, including autophosphorylation networks of EGFR, PAK1, and Aurora B kinase and a genetic toggle switch. This reveals the unique properties of their stochastic dynamics such as robustness, sensitivity, and multi-modality. Importantly, we provide a user-friendly computational package, CASTANET, that automatically derives symbolic expressions of the stationary distributions of BRNs to understand their long-term stochasticity.

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“…(Hoessly and Mazza 2019, § 3)) and with Z Γ the normalising constant. Some other results on the stochastic behavior of CRN beyond complex balance are in (Bibbona et al 2020) or (Levien and Bressloff 2017).…”

Section: Known Results On Stationary Distributionsmentioning

confidence: 99%

“…(Anderson et al 2010;Hoessly and Mazza 2019)). Nonetheless, some examples with stationary distribution of non-product form are available (Levien and Bressloff 2017, § 4.1) or (Bibbona et al 2020), but calculating it or even writing it down in small examples is demanding. -By definition, p 12 (Γ ) = p 21 (Γ ), and condition (B3) requires the functions f 1 i , f 2 i with S i ∈ S 1 ∩ S 2 to be proportional on p S i (Γ ) ⊆ Z ≥0 .…”

Section: Remark 9 [Assumptions I]mentioning

confidence: 99%

Stationary distributions via decomposition of stochastic reaction networks

Hoessly

2021

J. Math. Biol.

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We examine reaction networks (CRNs) through their associated continuous-time Markov processes. Studying the dynamics of such networks is in general hard, both analytically and by simulation. In particular, stationary distributions of stochastic reaction networks are only known in some cases. We analyze class properties of the underlying continuous-time Markov chain of CRNs under the operation of join and examine conditions such that the form of the stationary distributions of a CRN is derived from the parts of the decomposed CRNs. The conditions can be easily checked in examples and allow recursive application. The theory developed enables sequential decomposition of the Markov processes and calculations of stationary distributions. Since the class of processes expressible through such networks is big and only few assumptions are made, the principle also applies to other stochastic models. We give examples of interest from CRN theory to highlight the decomposition.

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Stationary distributions of systems with discreteness-induced transitions

Cited by 10 publications

References 35 publications

Derivation of stationary distributions of biochemical reaction networks via structure transformation

Derivation of stationary distributions of biochemical reaction networks via structure transformation

Derivation of stationary distributions of biochemical reaction networks via structure transformation

Stationary distributions via decomposition of stochastic reaction networks

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