  A rigorous understanding of how multicellular behaviors arise from the
actions of single cells requires quantitative frameworks that bridge the gap
between genetic circuits, the arrangement of cells in space, and
population-level behaviors. Here, we provide such a framework for a ubiquitous
class of multicellular systems - namely, "secrete-and-sense cells" that
communicate by secreting and sensing a signaling molecule. By using formal,
mathematical arguments and introducing the concept of a phenotype diagram, we
show how these cells tune their degrees of autonomous and collective behavior
to realize distinct single-cell and population-level phenotypes; these
phenomena have biological analogs, such as quorum sensing or paracrine
signaling. We also define the "entropy of population," a measurement of the
number of arrangements that a population of cells can assume, and demonstrate
how a decrease in the entropy of population accompanies the formation of
ordered spatial patterns. Our conceptual framework ties together diverse
systems, including tissues and microbes, with common principles.
