Description of chemical systems by means of response functions.

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Article in Journal of mathematical biology, 2025. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Not yet cited in PubMed.

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0citing papers in PubMed

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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

0 citing papers in PubMed.

No citing paper in PubMed yet.

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

3 authors.

E FrancoInstitute for Applied Mathematics, University of Bonn, Endenicher Allee 60, 53115, Bonn, Germany. franco@iam.uni-bonn.de.ORCID 0000-0002-5311-2124

B KepkaInstitute of Mathematics, University of Zürich, Winterthurerstrasse, 190 8057, Zürich, Switzerland.ORCID 0000-0002-0737-8378

J J L VelázquezInstitute for Applied Mathematics, University of Bonn, Endenicher Allee 60, 53115, Bonn, Germany.

Funding

German Science Foundation EXC 2047/1German Science Foundation Project-ID 390685813

6 · The paper itself

Abstract

In this paper we introduce a formalism that allows to describe the response of a part of a biochemical system in terms of renewal equations. In particular, we examine under which conditions the interactions between the different parts of a chemical system, described by means of linear ODEs, can be represented in terms of renewal equations. We show also how to apply the formalism developed in this paper to some particular types of linear and non-linear ODEs, modelling some biochemical systems of interest in biology (for instance, some time-dependent versions of the classical Hopfield model of kinetic proofreading). We also analyse some of the properties of the renewal equations that we are interested in, as the long-time behaviour of their solution. Furthermore, we prove that the kernels characterising the renewal equations derived by biochemical system with reactions that satisfy the detail balance condition belong to the class of completely monotone functions.

Indexed as

Biochemical PhenomenaModels, BiologicalModels, ChemicalKineticsLinear ModelsMathematical ConceptsNonlinear DynamicsSystems BiologyBiochemical systemsNon-Markovian dynamicsRenewal equationsResponse functions

Identifiers

PMID39956846

DOI10.1007/s00285-025-02191-3

PMCPMC11830649

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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.