On the relationship between cell cycle analysis with ergodic principles and age-structured cell population models
| Autor: | Nadine Pollak, Karsten Kuritz, Frank Allgöwer, Daniela Stöhr |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
0301 basic medicine
Statistics and Probability Cell division Cell Population Models Biological 01 natural sciences General Biochemistry Genetics and Molecular Biology Quantitative Biology::Cell Behavior Combinatorics 03 medical and health sciences Stochastic differential equation medicine Animals Humans Ergodic theory Statistical physics 0101 mathematics education Cellular Senescence Mathematics education.field_of_study Number density General Immunology and Microbiology Applied Mathematics Cell Cycle General Medicine Cell cycle 010101 applied mathematics 030104 developmental biology medicine.anatomical_structure Population model Modeling and Simulation General Agricultural and Biological Sciences |
| Zdroj: | Journal of Theoretical Biology. 414:91-102 |
| ISSN: | 0022-5193 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect