On the relationship between cell cycle analysis with ergodic principles and age-structured cell population models . Kuritz, K., Stöhr, D., Pollak, N., & Allgöwer, F. J.\ Theor.\ Biol., 414:91-102, 2017. ![On the relationship between cell cycle analysis with ergodic principles and age-structured cell population models [link]](https://bibbase.org/img/filetypes/link.svg "link")
Paper doi abstract bibtex Cyclic processes, in particular the cell cycle, are of great importance in cell biology. Continued improvement in cell population analysis methods like fluorescence microscopy, flow cytometry, CyTOF or single-cell omics made mathematical methods based on ergodic principles a powerful tool in studying these processes. In this paper, we establish the relationship between cell cycle analysis with ergodic principles and age structured population models. To this end, we describe the progression of a single cell through the cell cycle by a stochastic differential equation on a one dimensional manifold in the high dimensional dataspace of cell cycle markers. Given the assumption that the cell population is in a steady state, we derive transformation rules which transform the number density on the manifold to the steady state number density of age structured population models. Our theory facilitates the study of cell cycle dependent processes including local molecular events, cell death and cell division from high dimensional "snapshot" data. Ergodic analysis can in general be applied to every process that exhibits a steady state distribution. By combining ergodic analysis with age structured population models we furthermore provide the theoretic basis for extensions of ergodic principles to distribution that deviate from their steady state.
@ARTICLE{ist:kuritz17a,
author = {Kuritz, K. and St{\"o}hr, D. and Pollak, N. and Allg{\"o}wer, F.},
title = {On the relationship between cell cycle analysis with ergodic principles
and age-structured cell population models },
journal = {J.\ Theor.\ Biol.},
year = {2017},
volume = {414},
pages = {91-102},
abstract = {Cyclic processes, in particular the cell cycle, are of great importance
in cell biology. Continued improvement in cell population analysis
methods like fluorescence microscopy, flow cytometry, CyTOF or single-cell
omics made mathematical methods based on ergodic principles a powerful
tool in studying these processes. In this paper, we establish the
relationship between cell cycle analysis with ergodic principles
and age structured population models. To this end, we describe the
progression of a single cell through the cell cycle by a stochastic
differential equation on a one dimensional manifold in the high dimensional
dataspace of cell cycle markers. Given the assumption that the cell
population is in a steady state, we derive transformation rules which
transform the number density on the manifold to the steady state
number density of age structured population models. Our theory facilitates
the study of cell cycle dependent processes including local molecular
events, cell death and cell division from high dimensional "snapshot"
data. Ergodic analysis can in general be applied to every process
that exhibits a steady state distribution. By combining ergodic analysis
with age structured population models we furthermore provide the
theoretic basis for extensions of ergodic principles to distribution
that deviate from their steady state.},
doi = {10.1016/j.jtbi.2016.11.024},
issn = {0022-5193},
pubtype = {journal},
url = {http://www.sciencedirect.com/science/article/pii/S0022519316304040}
}
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Continued improvement in cell population analysis methods like fluorescence microscopy, flow cytometry, CyTOF or single-cell omics made mathematical methods based on ergodic principles a powerful tool in studying these processes. In this paper, we establish the relationship between cell cycle analysis with ergodic principles and age structured population models. To this end, we describe the progression of a single cell through the cell cycle by a stochastic differential equation on a one dimensional manifold in the high dimensional dataspace of cell cycle markers. Given the assumption that the cell population is in a steady state, we derive transformation rules which transform the number density on the manifold to the steady state number density of age structured population models. Our theory facilitates the study of cell cycle dependent processes including local molecular events, cell death and cell division from high dimensional \"snapshot\" data. 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Continued improvement in cell population analysis\n\tmethods like fluorescence microscopy, flow cytometry, CyTOF or single-cell\n\tomics made mathematical methods based on ergodic principles a powerful\n\ttool in studying these processes. In this paper, we establish the\n\trelationship between cell cycle analysis with ergodic principles\n\tand age structured population models. To this end, we describe the\n\tprogression of a single cell through the cell cycle by a stochastic\n\tdifferential equation on a one dimensional manifold in the high dimensional\n\tdataspace of cell cycle markers. Given the assumption that the cell\n\tpopulation is in a steady state, we derive transformation rules which\n\ttransform the number density on the manifold to the steady state\n\tnumber density of age structured population models. Our theory facilitates\n\tthe study of cell cycle dependent processes including local molecular\n\tevents, cell death and cell division from high dimensional \"snapshot\"\n\tdata. Ergodic analysis can in general be applied to every process\n\tthat exhibits a steady state distribution. 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