  Bacteria are able to respond to environmental signals by changing their rules
of movement. When we take into account chemical signals in the environment,
this behaviour is often called chemotaxis. At the individual-level, chemotaxis
consists of several steps. First, the cell detects the extracellular signal
using receptors on its membrane. Then, the cell processes the signal
information through the intracellular signal transduction network, and finally
it responds by altering its motile behaviour accordingly. At the population
level, chemotaxis can lead to aggregation of bacteria, travelling waves or
pattern formation, and the important task is to explain the population-level
behaviour in terms of individual-based models. It has been previously shown
that the transport equation framework is suitable for connecting different
levels of modelling of bacterial chemotaxis. In this paper, we couple the
transport equation for bacteria with the (parabolic/elliptic) equation for the
extracellular signals. We prove global existence of solutions for the general
hyperbolic chemotaxis models of cells which process the information about the
extracellular signal through the intracellular biochemical network and interact
by altering the extracellular signal as well. The conditions for global
existence in terms of the properties of the signal transduction model are
given.
