ArticleJournal of mathematical biology2011
An exact stochastic hybrid model of excitable membranes including spatio-temporal evolution.
Article in Journal of mathematical biology, 2011. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 6 papers.
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.
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.
Who cites it
6 citing papers in PubMed.
- Stochastic Hybrid Systems in Cellular Neuroscience.Journal of mathematical neuroscience · 2018Review
- Numerical Approach to Spatial Deterministic-Stochastic Models Arising in Cell Biology.PLoS computational biology · 2016Article
- Mutual and asynchronous anticipation and action in sports as globally competitive and locally coordinative dynamics.Scientific reports · 2015Article
- Stochastic representations of ion channel kinetics and exact stochastic simulation of neuronal dynamics.Journal of computational neuroscience · 2015Article
- Adiabatic reduction of a model of stochastic gene expression with jump Markov process.Journal of mathematical biology · 2014Article
- Stochastic synchronization of neuronal populations with intrinsic and extrinsic noise.Journal of mathematical neuroscience · 2011Article
Corrections and comments
PubMed lists nothing against this paper. Absence here is not a guarantee, only a check that was made.
Authors and funding
2 authors.
Funding
No grant is acknowledged in the PubMed record.
Abstract
In this paper, we present a mathematical description for excitable biological membranes, in particular neuronal membranes. We aim to model the (spatio-) temporal dynamics, e.g., the travelling of an action potential along the axon, subject to noise, such as ion channel noise. Using the framework of Piecewise Deterministic Processes (PDPs) we provide an exact mathematical description-in contrast to pseudo-exact algorithms considered in the literature-of the stochastic process one obtains coupling a continuous time Markov chain model with a deterministic dynamic model of a macroscopic variable, that is coupling Markovian channel dynamics to the time-evolution of the transmembrane potential. We extend the existing framework of PDPs in finite dimensional state space to include infinite-dimensional evolution equations and thus obtain a stochastic hybrid model suitable for modelling spatio-temporal dynamics. We derive analytic results for the infinite-dimensional process, such as existence, the strong Markov property and its extended generator. Further, we exemplify modelling of spatially extended excitable membranes with PDPs by a stochastic hybrid version of the Hodgkin-Huxley model of the squid giant axon. Finally, we discuss the advantages of the PDP formulation in view of analytical and numerical investigations as well as the application of PDPs to structurally more complex models of excitable membranes.
Indexed as
Identifiers
21243359What OpenQuestion holds
Registered trials
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.