Evidence map›Paper›PMID 26376889›Full record

ArticleBulletin of mathematical biology2015

Lyapunov Functions, Stationary Distributions, and Non-equilibrium Potential for Reaction Networks.

David F Anderson, Gheorghe Craciun, Manoj Gopalkrishnan, Carsten Wiuf

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In one paragraph

Article in Bulletin of mathematical biology, 2015. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 5 papers.

0numbers the graph read from it
0cells of the map it votes in
5citing papers in PubMed
–field-weighted citation impact
1 · What the graph read from it

What it found

Each row is one number read from the abstract, on the scale the paper reported it, with its interval. Left of the dashed line favours the treatment, right favours the comparator. Under each row is the sentence it came from. New to these charts? A ten-minute tutorial.

The abstract states no effect estimate the extractor could read, or names no intervention and outcome on the map, so this paper lights no cell and moves no belief. It is still indexed, cited and linked below.

2 · The registry

The trial behind it

Trials whose registry record cites this paper, or whose number appears in the abstract. A trial that started after this paper was published is citing it as background, not reporting it.

Neither the registry nor the abstract names a trial number. If this is a trial report, that itself is worth knowing.

3 · Its place in the literature

Who cites it

5 citing papers in PubMed.

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4 · The record

Corrections and comments

PubMed lists nothing against this paper. Absence here is not a guarantee, only a check that was made.

5 · Who and what money

Authors and funding

4 authors.

David F AndersonDepartment of Mathematics, University of Wisconsin-Madison, Madison, WI, USA. anderson@math.wisc.edu.
Gheorghe CraciunDepartment of Mathematics, University of Wisconsin-Madison, Madison, WI, USA. craciun@math.wisc.edu.
Manoj GopalkrishnanSchool of Technology and Computer Science, Tata Institute of Fundamental Research, Mumbai, India. manoj.gopalkrishnan@gmail.com.
Carsten WiufDepartment of Mathematical Sciences, University of Copenhagen, Copenhagen, Denmark. wiuf@math.ku.dk.

Funding

Collaborative Research: Multistability in Biological NetworksR01GM086881 · NIGMS · UNIVERSITY OF WISCONSIN-MADISON · PI CRACIUN, GHEORGHE · 2008 to 2012
$1.5M
NIGMS NIH HHS R01 GM086881NIGMS NIH HHS R01GM086881
6 · The paper itself

Abstract

We consider the relationship between stationary distributions for stochastic models of reaction systems and Lyapunov functions for their deterministic counterparts. Specifically, we derive the well-known Lyapunov function of reaction network theory as a scaling limit of the non-equilibrium potential of the stationary distribution of stochastically modeled complex balanced systems. We extend this result to general birth-death models and demonstrate via example that similar scaling limits can yield Lyapunov functions even for models that are not complex or detailed balanced, and may even have multiple equilibria.

Indexed as

Models, BiologicalKineticsMarkov ChainsMathematical ConceptsMetabolic Networks and PathwaysPopulation DynamicsStochastic ProcessesBirth-death processComplex balancedContinuous time Markov chainDynamical systemLong-term dynamics

Identifiers

PMID26376889
PMCPMC8408763

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Registered trials

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Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.