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Stencil Micropatterning of Human Pluripotent Stem Cells for Probing Spatial Organization of Differentiation Fates

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Stochastic modeling of stem-cell dynamics with control.

Zheng Sun¹, Natalia L Komarova

¹Department of Mathematics, University of California Irvine, Irvine, CA 92617, USA.

Mathematical Biosciences

|September 11, 2012

Summary

Stochastic models reveal how negative feedback loops regulate stem cell populations. Nonlinear control, particularly Hill-type, offers tunable parameters to manage cell numbers and reduce fluctuations for robust tissue homeostasis.

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Area of Science:

Mathematical Biology
Systems Biology
Developmental Biology

Background:

Tissue development and homeostasis rely on endogenous control loops to maintain stem and daughter cell numbers.
Cellular dynamics must be robust to perturbations for stable tissue function.

Purpose of the Study:

To analyze stochastic models of stem/daughter cell dynamics with negative control loops.
To investigate how different control mechanisms impact population size regulation and robustness.

Main Methods:

Generalization of the Moran process to model stem/daughter cell dynamics.
Analytical solutions for steady-state expectations and variances.
Analysis of linear, hyperbolic, and Hill-type nonlinear control laws.

Main Results:

Absence of control leads to stem cell extinction or overflow.
Linear control maintains steady state but lacks tunable parameters for population control.
Nonlinear controls (hyperbolic and Hill-type) offer tunable parameters for mean and standard deviation.
Hill-type control shows standard deviation inversely proportional to the Hill coefficient.

Conclusions:

Nonlinear control mechanisms are crucial for precise regulation of stem cell populations.
Ultrasensitive responses (high Hill coefficients) minimize fluctuations, enhancing stability.
These findings have implications for understanding tissue homeostasis and disease mechanisms.