Optimal strategy for public good production is set by balancing intertemporal trade-off between population growth rate and carrying capacity

Public goods are biomolecules that contribute to the community welfare. Their production can benefit populations in many ways, such as by providing access to previously unutilized resources. However, public good production has often been energetically costly, resulting in a reduction in the cellular growth rate. To reduce this cost, populations have evolved strategies to regulate biosynthesis of public good. Among these cell densities dependent regulation of public goods, as accomplished by quorum sensing, is a widely studied mechanism. Given that the fitness costs and benefits of public good production must be balanced, adoption of quorum sensing as a regulatory pathway by bacterial cells may have parallels with several economic principles that are used to study optimal investment decisions. Here, we explore the regulation of a public good, whose benefit is an increase in the carrying capacity, through experimental measurements of growth for engineered strains of Escherichia coli and analysis of those results using a modified logistic growth model. By varying the cell density at which the production of the public good was activated, we showed sharply-peaked optimum population fitness. Analysis further revealed that cell density associated with maximum public good benefits was determined by the trade-off between the cost of public good production, in terms of reduced growth rate, and benefits received from public good, in the form of increased carrying capacity. Moreover, our model showed that cells with luxRI quorum sensing seem to upregulate public good expression when the benefits from the production was immediate. These results demonstrate a case where a biological system apparently has evolved to optimize the timing of public good production to account for short-term costs and delays in reaping a future benefit. Author summary Bacteria often cooperate by sharing resources, sometimes referred as public goods. The activity of public good molecules benefits all of the neighboring cells. Here we examine the public good amylase, an enzyme to break down starch into smaller pieces that can be eaten by cells. Amylase production benefits the entire population because it enables growth to a larger population size, but production of this enzyme also has a cost. Enzyme production requires cells to expend energy and cellular resources. To balance the cost and benefit of the production of amylase, cells have likely evolved a strategy to control the timing of the production of public goods. We tested the dependence of population fitness on the timing of amylase production, finding an optimal cell density for amylase production. Finding the balance means that cells have evolved to anticipate future events, such as when simple food sources are depleted. Similar balancing of immediate costs and future benefits has been observed and studied in economics. Our results revealed that cells which use the regulatory strategy quorum sensing to control amylase production have minimized the delay in obtaining a benefit from this public good.