Responsive lysogeny under nonproductive phage binding

Upon infecting a bacterial cell, temperate phages make a decision between lysis and lysogeny. While research has previously explored how phages sense environmental information to make this choice, most studies have focused on modelling known mechanisms that impact the decision. These mechanisms tell us what environmental information the phage does respond to, but not what it should respond to, as the signals sensed by the phage may serve as proxies for other sources of information. Here, using a mechanism-agnostic population dynamics model, we find that irreversible phage binding to lysogens protects sensitive host cells from infection. This results in lysogens being an additional environmental factor that the phage should sense while making its decision to undergo lysis or lysogeny. Using this model, we derive a responsive lysogeny probability for phages that respond to both cell and lysogen densities optimized towards invading phage-occupied systems, and show that it is more capable of invading and resisting invasion than phage with fixed lysogeny probabilities across different environmental conditions.