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.

Theory predicts that the approach of catastrophic thresholds in natural systems (e.g., ecosystems, the climate) may result in an increasingly slow recovery from small perturbations, a phenomenon called critical slowing down. We used replicate laboratory populations of the budding yeast Saccharomyces cerevisiae for direct observation of critical slowing down before population collapse. We mapped the bifurcation diagram experimentally and found that the populations became more vulnerable to disturbance closer to the tipping point. Fluctuations of population density increased in size and duration near the tipping point, in agreement with the theory. Our results suggest that indicators of critical slowing down can provide advance warning of catastrophic thresholds and loss of resilience in a variety of dynamical systems.

Knowledge of the elastic properties of DNA is required to understand the structural dynamics of cellular processes such as replication and transcription. Measurements of force and extension on single molecules of DNA have allowed direct determination of the molecule's mechanical properties, provided rigorous tests of theories of polymer elasticity, revealed unforeseen structural transitions induced by mechanical stresses, and established an experimental and conceptual framework for mechanical assays of enzymes that act on DNA. However, a complete description of DNA mechanics must also consider the effects of torque, a quantity that has hitherto not been directly measured in micromanipulation experiments. We have measured torque as a function of twist for stretched DNA--torsional strain in over- or underwound molecules was used to power the rotation of submicrometre beads serving as calibrated loads. Here we report tests of the linearity of DNA's twist elasticity, direct measurements of the torsional modulus (finding a value approximately 40% higher than generally accepted), characterization of torque-induced structural transitions, and the establishment of a framework for future assays of torque and twist generation by DNA-dependent enzymes. We also show that cooperative structural transitions in DNA can be exploited to construct constant-torque wind-up motors and force-torque converters.

Microorganisms typically form diverse communities of interacting species, whose activities have tremendous impact on the plants, animals and humans they associate with. The ability to predict the structure of these complex communities is crucial to understanding and managing them. Here, we propose a simple, qualitative assembly rule that predicts community structure from the outcomes of competitions between small sets of species, and experimentally assess its predictive power using synthetic microbial communities composed of up to eight soil bacterial species. Nearly all competitions resulted in a unique, stable community, whose composition was independent of the initial species fractions. Survival in three-species competitions was predicted by the pairwise outcomes with an accuracy of ~90%. Obtaining a similar level of accuracy in competitions between sets of seven or all eight species required incorporating additional information regarding the outcomes of the three-species competitions. Our results demonstrate experimentally the ability of a simple bottom-up approach to predict community structure. Such an approach is key for anticipating the response of communities to changing environments, designing interventions to steer existing communities to more desirable states and, ultimately, rationally designing communities de novo.