Intertemporal trade-off between population growth rate and carrying capacity during public good production

Public goods are biomolecules that benefit cellular populations, such as by providing access to previously unutilized resources. Public good production is energetically costly. To reduce this cost, populations control public good biosynthesis, for example using density-dependent regulation accomplished by quorum sensing. Fitness costs and benefits of public good production must be balanced, similar to optimal investment decisions used in economics. We explore the regulation of a public good that increases the carrying capacity, through experimental measurements of growth in Escherichia coli and analysis using a modified logistic growth model. The timing of public good production showed a sharply peaked optimum in population fitness. The 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 goods, in the form of increased carrying capacity.