Dynamical properties and path dependence in a gene-network model of cell differentiation
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Dynamical properties and path dependence in a gene-network model of cell differentiation Michele Braccini1
· Andrea Roli1,4
· Marco Villani2,4
· Roberto Serra2,3,4
© The Author(s) 2020
Abstract In this work, we explore the properties of a control mechanism exerted on random Boolean networks that takes inspiration from the methylation mechanisms in cell differentiation and consists in progressively freezing (i.e. clamping to 0) some nodes of the network. We study the main dynamical properties of this mechanism both theoretically and in simulation. In particular, we show that when applied to random Boolean networks, it makes it possible to attain dynamics and path dependence typical of biological cells undergoing differentiation. Keywords Boolean networks · Cell differentiation · Path dependence · Epigenetics · Methylation
1 Introduction The co-existence of different cell types, which share the same genome, in a multicellular organism, and the processes of progressive cell differentiation raise challenging theoretical issues. The possibility that the same set of genes, with the same type of reciprocal influences, gives rise to very different phenotypes is associated to the fact that not all the genes are active in every cell type, i.e. to the existence of different stable activation patterns of the same set of genes. An important question which naturally raises concerns how these stable patterns are determined, among the huge amount of states which are possible in principle. It is well-known that active genes interfere with the activation of other genes, through proteins or other gene products like, e.g. miRNA. Therefore, it is natural to associate the stable patterns, i.e. the cell types, to the attractors of the dynamical system which describes the Communicated by Tomas Veloz.
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Michele Braccini [email protected]
1
Department of Computer Science and Engineering, Campus of Cesena - Alma Mater Studiorum Università di Bologna, Cesena, Italy
2
Department of Physics, Informatics and Mathematics, Università di Modena e Reggio Emilia, Modena, Italy
3
Institute for Advanced Study (IAS), University of Amsterdam, Amsterdam, The Netherlands
4
European Centre for Living Technology, Venice, Italy
complex web of interactions among genes, RNA, proteins, other gene products and other molecules in the cell. There are beautiful models of various parts of this system; for example, some describe in detail the steps which lead from DNA to mRNA to ribosomes, and some describe the details of the regulation processes. They are very well suited to describe in-depth the translation and transcription processes, but here we are rather interested in global activation patterns of thousands of heterogeneous entities. Therefore, it is mandatory to introduce some simplifications to keep the model manageable and meaningful. One interesting possibility (pioneered by Stuart Kauffman about 50 years ago) is that of simplifying the picture to that of a network of interacting genes only, without explicitly taking into account th
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