The origin of cooperation is a central challenge to our understanding of evolution1–3. Microbial interactions can be manipulated in ways that animal interactions cannot, thus leading to growing interest in microbial models of cooperation4–10 and competition11,12. In order for the budding yeast S. cerevisiae to grow on sucrose, the disaccharide must first be hydrolyzed by the enzyme invertase13,14. This hydrolysis reaction is performed outside of the cytoplasm in the periplasmic space between the plasma membrane and the cell wall. Here we demonstrate that the vast majority (~99%) of the monosaccharides created by sucrose hydrolysis diffuse away before they can be imported into the cell, thus making invertase production and secretion a cooperative behavior15,16. A mutant cheater strain that does not produce invertase is able to take advantage of and invade a population of wildtype cooperator cells. However, over a wide range of conditions, the wildtype cooperator can also invade a population of cheater cells. Therefore, we observe coexistence between the two strains in well-mixed culture at steady state resulting from the fact that rare strategies outperform common strategies—the defining features of what game theorists call the snowdrift game17. A model of the cooperative interaction incorporating nonlinear benefits explains the origin of this coexistence. We are able to alter the outcome of the competition by varying either the cost of cooperation or the glucose concentration in the media. Finally, we note that glucose repression of invertase expression in wildtype cells produces a strategy which is optimal for the snowdrift game—wildtype cells cooperate only when competing against cheater cells.

Cells that secrete and sense the same signaling molecule are ubiquitous. To uncover the functional capabilities of the core ‘secrete-and-sense’ circuit motif shared by these cells, we engineered yeast to secrete and sense the mating pheromone. Perturbing each circuit element revealed parameters that control the degree to which the cell communicated with itself versus with its neighbors. This tunable interplay of self- and neighbor-communication enables cells to span a diverse repertoire of cellular behaviors. These include a cell being asocial by responding only to itself, social through quorum sensing and an isogenic population of cells splitting into social and asocial subpopulations. A mathematical model explained these behaviors. The versatility of the secrete-and-sense circuit motif may explain its recurrence across species.

An important challenge in systems biology is to quantitatively describe microbial growth using a few measurable parameters that capture the essence of this complex phenomenon. Two key events at the cell membrane – extracellular glucose sensing and uptake – initiate the budding yeast’s growth on glucose. However, conventional growth models focus almost exclusively on glucose uptake. Here we present results from growth-rate experiments that cannot be explained by focusing on glucose uptake alone. By imposing a glucose uptake rate independent of the sensed extracellular glucose level, we show that despite increasing both the sensed glucose concentration and uptake rate, the cell’s growth rate can decrease or even approach zero. We resolve this puzzle by showing that the interaction between glucose perception and import, not their individual actions, determines the central features of growth and characterize this interaction using a quantitative model. Disrupting this interaction by knocking out two key glucose sensors significantly changes the cell’s growth rate, yet uptake rates are unchanged. This is due to a decrease in burden that glucose perception places on the cells. Our work shows that glucose perception and import are separate and pivotal modules of yeast growth whose interplay can be precisely tuned and measured.

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.

'Secrete-and-sense cells' can communicate by secreting a signaling molecule while also producing a receptor that detects the molecule. The cell can potentially 'talk' to itself ('self-communication') or talk to neighboring cells with the same receptor ('neighbor communication'). The predominant forms of secrete-and-sense cells are self-communicating 'autocrine cells', which are largely found in animals, and neighbor-communicating 'quorum sensing cells', which are mostly associated with bacteria. While assumed to function independently of one another, recent studies have discovered quorum-sensing organs and autocrine-signaling microbes. Moreover, similar types of genetic circuit control many autocrine and quorum-sensing cells. Here, we outline these recent findings and explain how autocrine and quorum sensing are two sides of a many-sided 'dice' created by the versatile secrete-and-sense cell.

Motivated by the ever-increasing experimental effort devoted to the properties of frustrated quantum magnets in a magnetic field, we present a careful and detailed theoretical analysis of a onedimensional version of this problem, a frustrated ladder with a magnetization plateau at m = 1/2. We show that even for purely isotropic Heisenberg interactions, the magnetization curve exhibits a rather complex behavior that can be fully accounted for in terms of simple elementary excitations. The introduction of anisotropic interactions (e.g., Dzyaloshinskii-Moriya interactions) modifies significantly the picture and reveals an essential difference between integer and fractional plateaux. In particular, anisotropic interactions generically open a gap in the region between the plateaux, but we show that this gap closes upon entering fractional plateaux. All of these conclusions, based on analytical arguments, are supported by extensive Density Matrix Renormalization Group calculations.

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.

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