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A dynamic mathematical model has been developed and validated to describe thesynthesis of pectate lyases (Pels), the major virulence factors in Dickeyadadantii. This work focuses on the simultaneous modeling of the metabolicdegradation of pectin by Pel enzymes and the genetic regulation of pel genes by2-keto-3-deoxygluconate (KDG), a catabolite product of pectin which inactivatesKdgR, one of the main repressors of pel genes. This modeling scheme takes intoaccount the fact that the system is composed of two time-varying compartments:the extracellular medium, where Pel enzymes cleave pectin into oligomers, andthe bacterial cytoplasm where, after internalization, oligomers are convertedto KDG. Using the quasi-stationary state approximations, the model consists ofsome nonlinear differential equations for which most of the parameters could beestimated from the literature or from independent experiments. The fewremaining unknown parameters were obtained by fitting the model equationsagainst a set of Pel activity data. Model predictions were verified bymeasuring the time courses of bacterial growth, Pel production, pel mRNAaccumulation and pectin consumption under various growth conditions. This workreveals that pectin is almost totally consumed before the burst of Pelproduction. This paradoxical behaviour can be interpreted as an evolutionarystrategy to control the diffusion process so that as soon as a small amount ofpectin is detected by the bacteria in its surroundings it anticipates morepectin to come. The model also predicts the possibility of bistable steadystates in the presence of constant pectin compounds.

Towards a Quantitative Modeling of the Synthesis of the Pectate Lyases, Essential Virulence Factors in Dickeya Dadantii