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Bull Math Biol. 2018 May;80(5):1345-1365. doi: 10.1007/s11538-017-0283-4. Epub 2017 May 15.

Stability of Control Networks in Autonomous Homeostatic Regulation of Stem Cell Lineages.

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Department of Mathematics, University of California Irvine, Irvine, CA, 92697, USA.
Department of Mathematics and Statistics, University of Victoria, Victoria, BC, V8W 2Y2, Canada.


Design principles of biological networks have been studied extensively in the context of protein-protein interaction networks, metabolic networks, and regulatory (transcriptional) networks. Here we consider regulation networks that occur on larger scales, namely the cell-to-cell signaling networks that connect groups of cells in multicellular organisms. These are the feedback loops that orchestrate the complex dynamics of cell fate decisions and are necessary for the maintenance of homeostasis in stem cell lineages. We focus on "minimal" networks that are those that have the smallest possible numbers of controls. For such minimal networks, the number of controls must be equal to the number of compartments, and the reducibility/irreducibility of the network (whether or not it can be split into smaller independent sub-networks) is defined by a matrix comprised of the cell number increments induced by each of the controlled processes in each of the compartments. Using the formalism of digraphs, we show that in two-compartment lineages, reducible systems must contain two 1-cycles, and irreducible systems one 1-cycle and one 2-cycle; stability follows from the signs of the controls and does not require magnitude restrictions. In three-compartment systems, irreducible digraphs have a tree structure or have one 3-cycle and at least two more shorter cycles, at least one of which is a 1-cycle. With further work and proper biological validation, our results may serve as a first step toward an understanding of ways in which these networks become dysregulated in cancer.


Homeostasis regulation; Mathematical modeling; Stem cells

[Available on 2019-05-01]

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