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A Multi-stage Representation of Cell Proliferation as a Markov Process
Christian A Yates1, Matthew J Ford2,3, Richard L Mort4
1Department of Mathematical Sciences, Centre for Mathematical Biology, University of Bath, Claverton Down, Bath, BA2 7AY, UK. c.yates@bath.ac.uk.
Bulletin of Mathematical Biology
|October 15, 2017
Summary
Gillespie's algorithm is widely used but inaccurate for cell proliferation models. This study proposes a modified cell cycle model to restore the Markov property, enabling accurate stochastic simulations of cell proliferation using Gillespie's algorithm.
Area of Science:
- Computational Biology
- Systems Biology
- Mathematical Biology
Background:
- Gillespie's algorithm is a standard for stochastic simulation in well-mixed biological systems.
- Its application to cell proliferation is problematic due to cell cycle's history-dependent nature, violating the Markov process assumption.
- Experimental cell cycle time distributions show less variance than the exponential distribution assumed by the standard algorithm.
Purpose of the Study:
- To propose a novel method for modeling cell cycles compatible with Gillespie's algorithm.
- To restore the memoryless property required for accurate stochastic simulation of cell proliferation.
- To demonstrate the impact of accurate cell cycle modeling on biological process simulations.
Main Methods:
- Decomposing the cell cycle into multiple independent, exponentially distributed stages.
- Developing a revised mathematical model for cell cycle dynamics.
- Analytically exploring the consequences of the revised model.
- Re-simulating existing spatial and non-spatial cellular proliferation models with the new approach.
Main Results:
- The proposed method successfully restores the Markov property to cell cycle modeling.
- The adapted model more accurately approximates cell cycle time distributions.
- Simulations show that using the correct cell cycle time distribution significantly impacts model outcomes, both quantitatively and qualitatively.
- The modified approach allows for the efficient use of Gillespie's algorithm in cell proliferation studies.
Conclusions:
- The revised cell cycle model provides a mathematically sound and computationally efficient way to simulate cellular proliferation using Gillespie's algorithm.
- Accurate representation of cell cycle time distributions is crucial for reliable modeling of biological processes involving cell division.
- This adaptation benefits both computational modelers and experimental biologists by enhancing the accuracy of stochastic simulations in cell proliferation.