Action functional gradient descent algorithm for estimating escape paths in stochastic chemical reaction networks

Gagrani, Praful; Smith, Eric

doi:10.1103/physreve.107.034305

Cited by 3 publications

(2 citation statements)

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“…This simple characterization lends support to this particular definition of autocatalysis, which also has been adapted, e.g. in [43,44].…”

Section: Discussionsupporting

confidence: 65%

Unstable cores are the source of instability in chemical reaction networks

Vassena,

Stadler

2024

Proc. R. Soc. A.

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In biochemical networks, complex dynamical features such as superlinear growth and oscillations are classically considered a consequence of autocatalysis. For the large class of parameter-rich kinetic models, which includes generalized mass action kinetics and Michaelis–Menten kinetics, we show that certain submatrices of the stoichiometric matrix, so-called unstable cores, are sufficient for a reaction network to admit instability and potentially give rise to such complex dynamical behaviour. The determinant of the submatrix distinguishes unstable-positive feedbacks, with a single real-positive eigenvalue, and unstable-negative feedbacks without real-positive eigenvalues. Autocatalytic cores turn out to be exactly the unstable-positive feedbacks that are Metzler matrices. Thus there are sources of dynamical instability in chemical networks that are unrelated to autocatalysis. We use such intuition to design non-autocatalytic biochemical networks with superlinear growth and oscillations.

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“…This simple characterization lends support to this particular definition of autocatalysis, which also has been adapted, e.g. in [43,44].…”

Section: Discussionsupporting

confidence: 65%

Unstable cores are the source of instability in chemical reaction networks

Vassena,

Stadler

2024

Proc. R. Soc. A.

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“…Evaluating a non-stationary functional CGF or LDF for currents entails either solving Hamiltonian equations (66) with unstable directions both forward and backward in time [69,70,[107][108][109], or possibly functional gradient descent [110], either method involving considerable numerical effort at stabilization. Here we perform the evaluation only for steady states, where the rate of accumulation of improbability along paths involves an expression in − L analogous to that from ψ for single-time fluctuations.…”

Section: Integral Expression For the Functional Bregman Divergencesmentioning

confidence: 99%

Rules, hypergraphs, and probabilities: the three-level analysis of chemical reaction systems and other stochastic stoichiometric population processes

Smith,

Andersen

2023

Preprint

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We consider problems in the functional analysis and evolution of combinatorial chemical reaction networks as rule-based, or three-level systems. The first level consists of rules, realized here as graph-grammar representations of reaction mechanisms. The second level consists of stoichiometric networks of molecules and reactions, modeled as hypergraphs. At the third level is the stochastic population process on molecule counts, solved for dynamics of population trajectories or probability distributions. Earlier levels in the hierarchy generate later levels combinatorially, and as a result constraints imposed in earlier and smaller layers can propagate to impose order in the architecture or dynamics in later and larger layers. We develop general methods to study rule algebras, emphasizing system consequences of symmetry; decomposition methods of flows on hypergraphs including the stoichiometric counterpart to Kirchhoff’s current decomposition and work/dissipation relations studied in [1]; and the large-deviation theory for currents in a stoichiometric stochastic population process, deriving additive decompositions of the large-deviation function that relate a certain Kirchhoff flow decomposition to the extended Pythagorean theorem from information geometry. The latter result allows us to assign a natural probabilistic cost to topological changes in a reaction network of the kind produced by selection for catalyst-substrate specificity. We develop as an example a model of biological sugar-phosphate chemistry from a rule system published in [2]. It is one of the most potentially combinatorial reaction systems used by biochemistry, yet one in which two ancient, widespread and nearly unique pathways have evolved in the Calvin-Benson cycle and the Pentose Phosphate pathway, which are additionally nearly reverses of one another. We propose a probabilistic accounting in which physiological costs can be traded off against the fitness advantages that select them, and which suggests criteria under which these pathways may be optimal.

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