Snowdrift game dynamics and facultative cheating in yeast

Abstract

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.

Cooperation and cheating in microbial exoenzyme production – Theoretical analysis for biotechnological applications

“…Under a wide range of physiological conditions, it rather is a snowdrift game and can even turn into a harmony game. For the special case of yeast invertase, this has been shown both experimentally and theoretically by Gore et al [30]. Notably, a snowdrift game occurs when cell density is neither very low nor very high.…”

“…In particular, the area of the harmony game is smaller than in spatially heterogeneous setups because δ is then smaller, while the area of the Prisoner's Dilemma is larger. Gore et al [30] studied this case both experimentally and theoretically. They modeled this by an efficiency of capture, ε, and by raising the payoff for defectors and cheaters to an exponent α being a phenomenological (not necessarily integer) parameter.…”

“…As mentioned above, stable cooperation arises naturally in the snowdrift game. Gore et al [30] showed by experiments (again with baker's yeast) that a stable coexistence between invertasesecreting and non-secreting yeast cells can be established even in well-mixed cultures. They concluded that generally a snowdrift game applies and supported this by a phenomenological mathematical model, which implies Prisoner's Dilemma, snowdrift, or harmony games depending on parameter values.…”

Evolution of gene network activity by tuning the strength of negative-feedback regulation

“…To test these hypotheses, we ran 16 separate competition experiments in duplicate for 48 h in the first environment. Then, we changed the environment to the second type and continued these competitions for another 44 h. We took FACS snapshots to quantify YFP versus tdTomato fractions at the beginning and at the end of each environmental exposure, measured cell densities and diluted the cultures as necessary to keep the densities low, and entered these FACS and OD 600 measurements into a metric 18 to quantify relative fitness values across the 16 genetic backgrounds (Methods). Figure 5 and Supplementary Fig.…”

“…For this, we used the following metric 18 where f i and f f are the fraction of YFP-containing cells at the beginning and at the end of each environment, while OD i and OD f are the initial and final densities of the mixture (by taking into account the dilutions). Fig.…”