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Analysis of stochastic stem cell models with control.

Jienian Yang1, Zheng Sun1, Natalia L Komarova1

  • 1Department of Mathematics, University of California Irvine, Irvine, CA 92617, United States.

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|June 16, 2015
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Summary
This summary is machine-generated.

This study models stem cell population dynamics, revealing how regulatory controls impact cell numbers. It provides a general method to calculate mean and variance for stem and differentiated cells in any biological system.

Keywords:
Stem cellsdifferentiated cellsdifferentiationproliferationstochastic modeling

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Area of Science:

  • Mathematical Biology
  • Cell Biology
  • Systems Biology

Background:

  • Stem cell dynamics are crucial for understanding healthy and cancerous tissues.
  • Cellular decisions (proliferation, differentiation, division, death) are regulated by microenvironmental cues.
  • Quantifying the impact of these regulatory mechanisms on cell population numbers is essential.

Purpose of the Study:

  • To investigate how different regulatory control mechanisms influence the mean and variance of stem and differentiated cell populations.
  • To develop a general mathematical framework applicable to various biological systems.
  • To derive explicit expressions for cell number means and variances.

Main Methods:

  • Formulation of moment equations based on the assumption of weak dependencies of regulatory functions near equilibrium.
  • Application of three different closure methods to the moment equations.
  • Derivation of explicit analytical expressions for population means and variances.

Main Results:

  • The variance of cell numbers is an algebraic function of the partial derivatives of regulatory controls with respect to population sizes at equilibrium.
  • Three closure methods yield consistent results for higher-order terms in moment expressions.
  • The derived expressions are validated against existing models and demonstrated with novel examples of positive and negative feedback controls.

Conclusions:

  • The developed methodology provides a versatile tool for analyzing stem cell population dynamics across diverse biological contexts.
  • The findings offer a quantitative understanding of how local cell-cell interactions shape tissue homeostasis and cancer progression.
  • The framework's independence from specific functional forms of regulatory controls enhances its broad applicability.