Bacteria are able to respond to environmental signals by changing their rulesof movement. When we take into account chemical signals in the environment,this behaviour is often called chemotaxis. At the individual-level, chemotaxisconsists of several steps. First, the cell detects the extracellular signalusing receptors on its membrane. Then, the cell processes the signalinformation through the intracellular signal transduction network, and finallyit responds by altering its motile behaviour accordingly. At the populationlevel, chemotaxis can lead to aggregation of bacteria, travelling waves orpattern formation, and the important task is to explain the population-levelbehaviour in terms of individual-based models. It has been previously shownthat the transport equation framework is suitable for connecting differentlevels of modelling of bacterial chemotaxis. In this paper, we couple thetransport equation for bacteria with the (parabolic/elliptic) equation for theextracellular signals. We prove global existence of solutions for the generalhyperbolic chemotaxis models of cells which process the information about theextracellular signal through the intracellular biochemical network and interactby altering the extracellular signal as well. The conditions for globalexistence in terms of the properties of the signal transduction model aregiven.
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