ArticleJournal of theoretical biology2012
Simplification of reversible Markov chains by removal of states with low equilibrium occupancy.
Article in Journal of theoretical biology, 2012. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 9 papers.
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Who cites it
9 citing papers in PubMed.
- A Reliability Assessment Method for Complex Systems Based on Non-Homogeneous Markov Processes.Sensors (Basel, Switzerland) · 2024Article
- Article
- Modeling cell line-specific recruitment of signaling proteins to the insulin-like growth factor 1 receptor.PLoS computational biology · 2019Article
- Data-driven modeling of mitochondrial dysfunction in Alzheimer's disease.Cell calcium · 2018Article
- Stochastic shielding and edge importance for Markov chains with timescale separation.PLoS computational biology · 2018Article
- State aggregation for fast likelihood computations in molecular evolution.Bioinformatics (Oxford, England) · 2017Article
- Analyzing and Quantifying the Gain-of-Function Enhancement of IP3 Receptor Gating by Familial Alzheimer's Disease-Causing Mutants in Presenilins.PLoS computational biology · 2015Article
- Measuring edge importance: a quantitative analysis of the stochastic shielding approximation for random processes on graphs.Journal of mathematical neuroscience · 2014Article
- A data-driven model of a modal gated ion channel: the inositol 1,4,5-trisphosphate receptor in insect Sf9 cells.The Journal of general physiology · 2012Article
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Authors and funding
3 authors.
Funding
Abstract
We present a practical method for simplifying Markov chains on a potentially large state space when detailed balance holds. A simple and transparent technique is introduced to remove states with low equilibrium occupancy. The resulting system has fewer parameters. The resulting effective rates between the remaining nodes give dynamics identical to the original system's except on very fast timescales. This procedure amounts to using separation of timescales to neglect small capacitance nodes in a network of resistors and capacitors. We illustrate the technique by simplifying various reaction networks, including transforming an acyclic four-node network to a three-node cyclic network. For a reaction step in which a ligand binds, the law of mass action implies a forward rate proportional to ligand concentration. The effective rates in the simplified network are found to be rational functions of ligand concentration.
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