Rewriting Theory for the Life Sciences: A Unifying Theory of CTMC Semantics

Behr, Nicolas; Krivine, Jean

doi:10.1007/978-3-030-51372-6_11

Cited by 12 publications

(9 citation statements)

References 41 publications

(183 reference statements)

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“…The first domain is rule-based modeling [ 110 ] which recognizes the finitary-to-infinitary mappings exhibited here between CRN generators and state spaces as a widely generalizable organizing principle. The algebra and combinatorics of non-commutative rule systems is a very active area of study [ 77 , 128 , 129 , 130 , 131 ] which connects to chemistry, systems biology, theories of algorithms, process calculus, and much more. A thermodynamics of rule-based systems that expands the conceptual scope of science will not be a reduction to their consequences for heat generation.…”

Section: Discussionmentioning

confidence: 99%

Intrinsic and Extrinsic Thermodynamics for Stochastic Population Processes with Multi-Level Large-Deviation Structure

Smith

2020

Entropy

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A set of core features is set forth as the essence of a thermodynamic description, which derive from large-deviation properties in systems with hierarchies of timescales, but which are not dependent upon conservation laws or microscopic reversibility in the substrate hosting the process. The most fundamental elements are the concept of a macrostate in relation to the large-deviation entropy, and the decomposition of contributions to irreversibility among interacting subsystems, which is the origin of the dependence on a concept of heat in both classical and stochastic thermodynamics. A natural decomposition that is known to exist, into a relative entropy and a housekeeping entropy rate, is taken here to define respectively the intensive thermodynamics of a system and an extensive thermodynamic vector embedding the system in its context. Both intensive and extensive components are functions of Hartley information of the momentary system stationary state, which is information about the joint effect of system processes on its contribution to irreversibility. Results are derived for stochastic chemical reaction networks, including a Legendre duality for the housekeeping entropy rate to thermodynamically characterize fully-irreversible processes on an equal footing with those at the opposite limit of detailed-balance. The work is meant to encourage development of inherent thermodynamic descriptions for rule-based systems and the living state, which are not conceived as reductive explanations to heat flows.

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Section: Discussionmentioning

confidence: 99%

Intrinsic and Extrinsic Thermodynamics for Stochastic Population Processes with Multi-Level Large-Deviation Structure

Smith

2020

Entropy

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“…The composites γ 1 • h 1 and γ 2 • h 1 are pushout complements of f 1 • α 1 and g 1 • α 2 , respectively, and hence by [12, proposition 12], they are also FPBCs. It follow that the upper half of (22) is indeed the underlying diagram in G of both the derivations in (9) and the upper half of (10). For the lower half of (22) to also be a derivation, f 2 must be a match, so we need to show that it is monic.…”

Section: B3 Proof Of Lemma 2 (Backward Modularity)mentioning

confidence: 90%

“…As the theory can handle adhesive categories in general and sesqui-pushout rewriting [5], it offers an treatment of irreversible rewrites alternative to the one presented in this paper. (The rule-algebraic approach can also handle application conditions [9]). It will need further work to precisely pinpoint how these two threads of work articulate both at the theoretical and at the implementation levels.…”

Section: Related Workmentioning

confidence: 99%

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Rate Equations for Graphs

Danos¹,

Heindel²,

Honorato-Zimmer³

et al. 2020

Computational Methods in Systems Biology

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In this paper, we combine ideas from two different scientific traditions: 1) graph transformation systems (GTSs) stemming from the theory of formal languages and concurrency, and 2) mean field approximations (MFAs), a collection of approximation techniques ubiquitous in the study of complex dynamics. Using existing tools from algebraic graph rewriting, as well as new ones, we build a framework which generates rate equations for stochastic GTSs and from which one can derive MFAs of any order (no longer limited to the humanly computable). The procedure for deriving rate equations and their approximations can be automated. An implementation and example models are available online at https://rhz.github.io/fragger. We apply our techniques and tools to derive an expression for the mean velocity of a two-legged walker protein on DNA.

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“…The derivation of indefinitely large types spaces in a generator by rules defines a second infinitary-to-finitary map, in which the finite range is the rule algebra [59,94]. Rules specify equivalence classes of reactions, and from their algebra it is possible to extract the statistics of common features across multiple reactions, or to compute the interdependencies of reactions without solving for complete states of the system [95].…”

Section: Managing Combinatorial State Spaces Algebraically With Rulesmentioning

confidence: 99%

Beyond fitness: selection and information flow through the constructive steps in lifecycles

Smith

2021

Preprint

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The replicator is the fundamental abstraction of evolutionary genetics. Only for replicators do Darwin's concept of fitness as differential reproductive success, and the formalization by Fisher and Price in terms of apportionment of descendant populations to ancestors, coincide without ambiguity or potential conflict. The organization of the Price equation, causal interpretations of Fisher's Fundamental Theorem and its relatives, and the abstraction of fitness as the sole channel through which information flows in from environments to form the adapted states of evolving populations, all follow from properties of replicators imposed artificially on the genetics of more complex lifecycles. Here it is shown how to generalize this role of the replicator to the autocatalytic flows in the generators of Stoichiometric Populations Processes, and to generalize from the unique summary statistic of fitness to a class of summary statistics that appear as regression coefficients against the autocatalytic flows associated with reproduction, including replication but also including constructive operations beyond simple copying. Both the statistical construction and the causal interpretation of Fisher's Theorem and the Price Equation generalize from replicators and fitness to the wider class of regressions. Ad hoc corrections for mis-specified fitness models, which the conventional Price equation groups with "environment" effects, become part of a Fisher covariance on the basis of flows, which takes on a consistent causal interpretation in terms of an expanded concept of selection recognizing distributed information. A measure is derived for the information in the trajectory of a population evolving under a stoichiometric stochastic process, as the large-deviation function for that trajectory from a null model. The interpretation of fitness and other regression coefficients as channels for causation and information flow is derived from their inner product with the gradient of the trajectory entropy.

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Rewriting Theory for the Life Sciences: A Unifying Theory of CTMC Semantics

Cited by 12 publications

References 41 publications

Intrinsic and Extrinsic Thermodynamics for Stochastic Population Processes with Multi-Level Large-Deviation Structure

Intrinsic and Extrinsic Thermodynamics for Stochastic Population Processes with Multi-Level Large-Deviation Structure

Rate Equations for Graphs

Beyond fitness: selection and information flow through the constructive steps in lifecycles

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