dorsal/arxiv
View SchemaA family tree of Markov models in systems biology
| Authors | Mukhtar Ullah, Olaf Wolkenhauer |
|---|---|
| Categories | |
| ArXiv ID | q-bio/0610003 |
| URL | https://arxiv.org/abs/q-bio/0610003 |
| DOI | 10.1049/iet-syb:20070017 |
| Journal | IET Syst Biol. 1 (2007) 247-254 |
Abstract
Motivated by applications in systems biology, we seek a probabilistic framework based on Markov processes to represent intracellular processes. We review the formal relationships between different stochastic models referred to in the systems biology literature. As part of this review, we present a novel derivation of the differential Chapman-Kolmogorov equation for a general multidimensional Markov process made up of both continuous and jump processes. We start with the definition of a time-derivative for a probability density but place no restrictions on the probability distribution, in particular, we do not assume it to be confined to a region that has a surface (on which the probability is zero). In our derivation, the master equation gives the jump part of the Markov process while the Fokker-Planck equation gives the continuous part. We thereby sketch a {}``family tree'' for stochastic models in systems biology, providing explicit derivations of their formal relationship and clarifying assumptions involved.
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"abstract": "Motivated by applications in systems biology, we seek a probabilistic\nframework based on Markov processes to represent intracellular processes. We\nreview the formal relationships between different stochastic models referred to\nin the systems biology literature. As part of this review, we present a novel\nderivation of the differential Chapman-Kolmogorov equation for a general\nmultidimensional Markov process made up of both continuous and jump processes.\nWe start with the definition of a time-derivative for a probability density but\nplace no restrictions on the probability distribution, in particular, we do not\nassume it to be confined to a region that has a surface (on which the\nprobability is zero). In our derivation, the master equation gives the jump\npart of the Markov process while the Fokker-Planck equation gives the\ncontinuous part. We thereby sketch a {}``family tree\u0027\u0027 for stochastic models in\nsystems biology, providing explicit derivations of their formal relationship\nand clarifying assumptions involved.",
"arxiv_id": "q-bio/0610003",
"authors": [
"Mukhtar Ullah",
"Olaf Wolkenhauer"
],
"categories": [
"q-bio.QM"
],
"doi": "10.1049/iet-syb:20070017",
"journal_ref": "IET Syst Biol. 1 (2007) 247-254",
"title": "A family tree of Markov models in systems biology",
"url": "https://arxiv.org/abs/q-bio/0610003"
},
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