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A Review of Stochastic and Deterministic Modeling of Stem Cell Dynamics

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Abstract

Purpose of Review

This paper briefly describes recent mathematical models that use stochastic and deterministic approaches to understand stem cell dynamics and how these models are utilized to study the roles of stem cells’ dynamics in cancer and aging.

Recent Findings

Stochastic compartmental models have been developed to investigate the generalized double-hit mutant production under the influence of different types of stem cell divisions. More specialized examination of the generation, spread, and optimizing structure of 2-hit mutants in the colon crypts has also been conducted. The recent introduction of a hybrid stochastic-deterministic model creates innovative approaches to studying carcinogenesis, while other stochastic models interested in the stem cell renewal process have explored the phenomenon of aging.

Summary

The results of these studies indicate that asymmetric stem cell divisions increase the probability of mutants production and their fixation probability. Moreover, the hybrid stochastic-deterministic model demonstrates how a low rate of dedifferentiation can significantly accelerate carcinogenesis. Finally, a stochastic model for the stem cell renewal process behind aging shows that the fixation probability of an altered stem cell with a longer cell cycle than the rest is higher than other stem cells.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, Mount Holyoke College, 50 College St, South Hadley, 01075, MA, USA

    Shaojun Gong

  2. Department of Mathematics and Statistics, University of Massachusetts Amherst, 710 N Pleasant St, Amherst, 01003, MA, USA

    Leili Shahriyari

Authors
  1. Shaojun Gong
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Contributions

SG carried out the study and drafted the manuscript; LS designed and supervised the study. All authors gave final approval for publication.

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Correspondence to Leili Shahriyari.

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Gong, S., Shahriyari, L. A Review of Stochastic and Deterministic Modeling of Stem Cell Dynamics. Curr Stem Cell Rep 9, 1–8 (2023). https://doi.org/10.1007/s40778-023-00225-4

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