A dynamic mathematical model has been developed and validated to describe the synthesis of pectate lyases (Pels), the major virulence factors in Dickeya dadantii. This work focuses on the simultaneous modeling of the metabolic degradation of pectin by Pel enzymes and the genetic regulation of pel genes by 2-keto-3-deoxygluconate (KDG), a catabolite product of pectin that inactivates KdgR, one of the main repressors of pel genes. This modeling scheme takes into account the fact that the system is composed of two time-varying compartments: the extracellular medium, where Pel enzymes cleave pectin into oligomers, and the bacterial cytoplasm where, after internalization, oligomers are converted to KDG. Using the quasi-stationary state approximations, the model consists of some nonlinear differential equations for which most of the parameters could be estimated from the literature or from independent experiments. The few remaining unknown parameters were obtained by fitting the model equations against a set of Pel activity data. Model predictions were verified by measuring the time courses of bacterial growth, Pel production, pel mRNA accumulation, and pectin consumption under various growth conditions. This work reveals that pectin is almost totally consumed before the burst of Pel production. This paradoxical behavior can be interpreted as an evolutionary strategy to control the diffusion process so that as soon as a small amount of pectin is detected by the bacteria in its surroundings, it anticipates more pectin to come. The model also predicts the possibility of bistable steady states in the presence of constant pectin compounds. Dickeya dadantii (ex Erwinia chrysanthemi) is a soft rottingGram-negative bacterium that attacks a wide range of plant species, including many crops of economical importance. These bacteria are found on plant surfaces and in soil where they may enter the plant via wound sites or through natural openings. During infection, D. dadantii first colonizes the intercellular space (apoplast) where they can remain latent until conditions become favorable for the development of the disease. Soft rot, the visible symptom, is mainly due to the degradation of pectin present in the plant cell wall. D. dadantii can utilize pectin as its sole carbon and energy source (Fig.

A linear chain of cells is considered in which calcium (Ca2+) fluctuations within a cell are described by a simple minimal model. Cells are coupled together by bidirectional paracrine signaling via calcium oscillations. Two typical zones of propagation are observed: a transition zone and a regular zone. The transition zone exhibits the same phenomena that can be observed in single cells, pairs or triplets of cells. Within the regular zone, simple periodic oscillations of calcium propagate and the Ca2+ signal is similar from one cell to another (same amplitude and same frequency). But, the signals are separated by a slight phase shift characterizing the propagation of Ca2+ waves due to the type of coupling used. We also consider the colonization of the lattice by the abnormal oscillations of sick cells.

The enterobacteria Erwinia chrysanthemi and other soft-rot Erwiniae cause soft-rot disease in plants by secreting extracellular enzymes among which the main virulence factors are pectate lyases (Pels). These pectic enzymes are produced by the activation of the pel genes whose transcription is controlled by a complex regulatory network. Using the knowledge acquired in a previous work, a simplified regulatory network is proposed, keeping only the key variables for the transition to pathogenicity. We identify that the core mechanism for the onset of Pel is governed by a small metabolico-genetic network involving the repressor KdgR and the inductor KDG. Next we consider that the triggering of Pel synthesis is relayed by a quorum sensing (QS) phenomenon describing the ability of bacteria to use the size and density of their colonies to regulate the production of pectate lyases. The simplified network is described by only a few differential equations, thereby allowing the use of standard bifurcation analysis in the phase space. From this modeling emerges a qualitative but generic mechanism for the transition to virulence of a pectinolytic bacterium when it infects a plant.

In this paper, numerical simulation of calcium waves in a network of cells coupled together by a paracrine signaling is investigated. The model takes into account the long-range interaction between cells due to the action of extracellular messengers, which provide links between first-neighbor cells, but also on cells located far away from the excited cell. When considering bidirectional coupling, the long-range interaction influences neither the frequency nor the amplitude of oscillations, contrary to one-directional coupling. The long-range interaction influences the speed of propagation of Ca2+ waves in the network and induces enlargement of the transition zone before the steady regime of propagation is attained. We also investigate the long-range effects on the colonization of a given niche by a pathogenic microorganism signal on calcium wave propagation in the network.