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Go to PNAS Homepage > Current Issue > vol. 111 no. 10 > Jinzhi Lei, E880–E887, doi: 10.1073/pnas.1324267111

Mathematical model of adult stem cell regeneration with cross-talk between genetic and epigenetic regulation
Jinzhi Leia, Simon A. Levinb,1, and Qing Niec
Author Affiliations

Contributed by Simon A. Levin, January 7, 2014 (sent for review September 4, 2013)

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Significance

This paper examines how adult stem cells maintain their ability to carry out a complex set of tasks, including tissue regeneration and replacement of defective cells. To do so, stem cell populations must coordinate differentiation, proliferation, and cell death (apoptosis) to maintain an appropriate distribution of epigenetic states. Using the tools of applied mathematics, and borrowing from the theory of intergenerational transfer of resources, this paper shows how control strategies during cell division should be chosen to maximize expected performance, utilizing cross-talk between genetic and epigenetic regulation and performance criteria during homeostasis. Heterogeneous proliferation, a mixed strategy in which not all cells have the same proliferation probability, is shown to increase robustness, and hence long-term performance.

Abstract
Adult stem cells, which exist throughout the body, multiply by cell division to replenish dying cells or to promote regeneration to repair damaged tissues. To perform these functions during the lifetime of organs or tissues, stem cells need to maintain their populations in a faithful distribution of their epigenetic states, which are susceptible to stochastic fluctuations during each cell division, unexpected injury, and potential genetic mutations that occur during many cell divisions. However, it remains unclear how the three processes of differentiation, proliferation, and apoptosis in regulating stem cells collectively manage these challenging tasks. Here, without considering molecular details, we propose a genetic optimal control model for adult stem cell regeneration that includes the three fundamental processes, along with cell division and adaptation based on differential fitnesses of phenotypes. In the model, stem cells with a distribution of epigenetic states are required to maximize expected performance after each cell division. We show that heterogeneous proliferation that depends on the epigenetic states of stem cells can improve the maintenance of stem cell distributions to create balanced populations. A control strategy during each cell division leads to a feedback mechanism involving heterogeneous proliferation that can accelerate regeneration with less fluctuation in the stem cell population. When mutation is allowed, apoptosis evolves to maximize the performance during homeostasis after multiple cell divisions. The overall results highlight the importance of cross-talk between genetic and epigenetic regulation and the performance objectives during homeostasis in shaping a desirable heterogeneous distribution of stem cells in epigenetic states.

fitness function optimization robustness dynamic programming systems biology
Footnotes
1To whom correspondence should be addressed. E-mail: slevin@princeton.edu.
Author contributions: J.L., S.A.L., and Q.N. designed research; J.L. and Q.N. performed research; J.L., S.A.L., and Q.N. contributed new reagents/analytic tools; J.L. and Q.N. analyzed data; and J.L., S.A.L., and Q.N. wrote the paper.

The authors declare no conflict of interest.

See Commentary on page 3653.

This article contains supporting information online at http://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1324267111/-/DCSupplemental.

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Collective dynamics of stem cell populations
Proc. Natl. Acad. Sci. USA 2014 111 (10) 3653-3654
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Published online before print February 5, 2014, doi: 10.1073/pnas.1324267111
PNAS March 11, 2014 vol. 111 no. 10 E880-E887
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Physical Sciences
Applied Mathematics
Biological Sciences
Systems Biology

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