Graphs, random sums, and sojourn time distributions, with application to ion-channel modeling
type: Item
instance of: scholarly article
title: Graphs, random sums, and sojourn time distributions, with application to ion-channel modeling
zbMATH Open document ID: 0734.92010
DOI: 10.1016/0025-5564(90)90056-5
published in: Mathematical Biosciences
publication date: 1990-01-01T00:00:00Z
review text: For modelling of ion-channel kinetics and drug-receptor interactions the distribution of a sojourn time in a subset of the state space of a stochastic process is derived in which sojourn times in an individual state are independent and identically distributed. Transitions between states follow a Markov chain. The state space and possible transitions of the stochastic process are represented by a graph identified with an underlying chemical kinetic scheme. A sojourn time in a composition state is expressed as a random sum. The random sum structure of the required sojourn time can be derived algorithmically on the basis of graph operations. This random sum method is legitimate if there are no correlations between sojourn times in adjacent composition states. But also for cases where correlation is weak the random-sum approach may provide useful approximations. A standard five-state model of a single ion channel is used to illustrate the ideas and to discuss results.
reviewed by: J.Peil
Mathematics Subject Classification ID: 92C45
Mathematics Subject Classification ID: 60J20
Mathematics Subject Classification ID: 92C99
Mathematics Subject Classification ID: 92E10
zbMATH DE Number: 4215767
zbMATH Keywords: sojourn time distributions
zbMATH Keywords: kinetic parameter estimation
zbMATH Keywords: sequential models of nicotinic receptor kinetics
zbMATH Keywords: composition of states
zbMATH Keywords: ion-channel kinetics
zbMATH Keywords: drug-receptor interactions
zbMATH Keywords: random-sum approach
zbMATH Keywords: five-state model of a single ion channel
Wikidata QID: Q51725445
author: Robert O. Edeson
author: Geoffrey F. Yeo
author: Robin K. Milne
author: Barry W. Madsen
MaRDI profile type: Publication
full work available at URL: 0025-5564(90)90056-5
OpenAlex ID: W2029941861
cites work: Aggregated Markov processes incorporating time interval omission
cites work: On aggregated Markov processes
cites work: Parallel concepts in graph theory
cites work: Q4076577
cites work: Ion channel kinetics: A model based on fractal scaling rather than multistate Markov processes
cites work: Q5661516
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description: scientific article; zbMATH DE number 4215767