Investment in secreted enzymes during nutrient-limited growth is utility dependent

during growth on a protein substrate that requires extracellular digestion by secreted proteases. We identified a quantitative relationship between the rate of increase of cellular biomass under nutrient-limiting growth conditions and the rate of increase in investment in secreted proteases. Production of secreted proteases is stimulated by secreted signals that convey information about the utility of secreted proteins during nutrient-limited growth. Growth modeling using this relationship recapitulated the observed kinetics of bacterial growth on a protein substrate. The proposed regulatory strategy suggests a rationale for quorum-sensing-dependent stimulation of the production of secreted enzymes whereby investment in secreted enzymes occurs in proportion to the utility they confer. Our model provides a framework that can be applied toward understanding bacterial growth in many environments where growth rate is limited by the availability of nutrients.