Mathematical Model for Length Control by the Timing of Substrate Switching in the Type III Secretion System

Type III Secretion Systems (T3SS) are complex bacterial structures that provide gram-negative pathogens with a unique virulence mechanism whereby they grow a needle-like structure in order to inject bacterial effector proteins into the cytoplasm of a host cell. Numerous experiments have been performed to understand the structural details of this nanomachine during the past decade. Despite the concerted efforts of molecular and structural biologists, several crucial aspects of the assembly of this structure, such as the regulation of the length of the needle itself, remain unclear. In this work, we used a combination of mathematical and computational techniques to better understand length control based on the timing of substrate switching, which is a possible mechanism for how bacteria ensure that the T3SS needles are neither too short nor too long. In particular, we predicted the form of the needle length distribution based on this mechanism, and found excellent agreement with available experimental data from Salmonella typhimurium with only a single free parameter. Although our findings provide preliminary evidence in support of the substrate switching model, they also make a set of quantitative predictions that, if tested experimentally, would assist in efforts to unambiguously characterize the regulatory mechanisms that control the growth of this crucial virulence factor.Author Summary: The Type III Secretion System (T3SS) is a molecular needle that allows pathogenic bacteria (e.g. Salmonella) to inject proteins into host cells and control their behavior. Two mechanisms have been proposed to explain how bacteria regulate the length of the T3SS needle, but to date neither of these mechanisms has been subjected to any rigorous quantitative analysis. In this work we constructed a mathematical model for one of these mechanisms, namely length control via the timing of substrate switching. We showed that this model is quantitatively consistent with experimental data from S. typhimurium. In addition to providing evidence for the substrate switching mechanism, our work provides a framework for future quantitative evaluation of length control in the T3SS.