SummaryCommunicating cells can coordinate their gene expressions to form spatial patterns, generating order from disorder. Ubiquitous “secrete-and-sense cells” secrete and sense the same molecule to do so. Here we present a modeling framework—based on cellular automata and mimicking approaches of statistical mechanics—for understanding how secrete-and-sense cells with bistable gene expression, from disordered beginnings, can become spatially ordered by communicating through rapidly diffusing molecules. Classifying lattices of cells by two “macrostate” variables—“spatial index,” measuring degree of order, and average gene-expression level—reveals a conceptual picture: a group of cells behaves as a single particle, in an abstract space, that rolls down on an adhesive “pseudo-energy landscape” whose shape is determined by cell-cell communication and an intracellular gene-regulatory circuit. Particles rolling down the landscape represent cells becoming more spatially ordered. We show how to extend this framework to more complex forms of cellular communication.
Living systems, particularly multicellular systems, often seem hopelessly complex. But recent studies have suggested that beneath this complexity, there may be unifying quantitative principles that we are only now starting to unravel. All cells interact with their environments and with other cells. Communication among cells is a primary means for cells to interact with each other. The complexity of these multicellular systems, due to the large numbers of cells and the diversity of intracellular and intercellular interactions, makes understanding multicellular systems a daunting task. To overcome this challenge, we will likely need judicious simplifications and conceptual frameworks that can reveal design principles that are shared among diverse multicellular systems.Here we review some recent progress towards developing such frameworks. Concise definition of subjectOne of the important challenges in biology is quantitatively explaining how multicellular systems' behaviours arise from the genetic circuits inside each cell and the interactions among these cells. Communication among cells is one of the primary means for cells to interact with each other. One cell can influence how the other cell behaves by "talking" to that cell, for example, through a secretion of a signalling molecule that the other cell can respond to. Each cell can typically communicate with multiple cells located at various locations. Thus we can represent multicellular systems as complex communication grids. Discovering common principles that govern such multicellular communication grids is crucial for tying together a wide range of multicellular systems such as tissues, embryos and populations of microbes, under a common quantitative framework. But it has been difficult to find such principles. One difficulty is that we do not yet have generally applicable strategies for judiciously reducing the number of parameters in a multicellular system with a large number of intracellular and intercellular
How living systems generate order from disorder is a fundamental question 1-5 . Metrics and ideas from physical systems have elucidated order-generating collective dynamics of mechanical, motile, and electrical living systems such as bird flocks and neuronal networks 6-8 . But suitable metrics and principles remain elusive for many networks of cells such as tissues that collectively generate spatial patterns via chemical signals, genetic circuits, and dynamics representable by cellular automata 1,9-11 . Here we reveal such principles through a statistical mechanics-type framework for cellular automata dynamics in which cells with ubiquitous genetic circuits generate spatial patterns by switching on and off each other's genes with diffusing signalling molecules. Lattices of cells behave as particles stochastically rolling down a pseudo-energy landscapedefined by a spin glass-like Hamiltonian -that is shaped by "macrostate" functions and genetic circuits. Decreasing the pseudo-energy increases the spatial patterns' orderliness. A new kinetic trapping mechanism -"pathway trapping" -yields metastable spatial patterns by preventing minimization of the particle's pseudo-energy. Noise in cellular automata reduces the trapping, thus further increases the spatial order. We generalize our framework to lattices with multiple types of cells and signals. Our work shows that establishing statistical mechanics of computational algorithms can reveal collective dynamics of signal-processing in biological and physical networks.
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