  We study the effect of discreteness on various models for patterning in
bacterial colonies. In a bacterial colony with branching pattern, there are
discrete entities - bacteria - which are only two orders of magnitude smaller
than the elements of the macroscopic pattern. We present two types of models.
The first is the Communicating Walkers model, a hybrid model composed of both
continuous fields and discrete entities - walkers, which are coarse-graining of
the bacteria. Models of the second type are systems of reaction diffusion
equations, where the branching of the pattern is due to non-constant diffusion
coefficient of the bacterial field. The diffusion coefficient represents the
effect of self-generated lubrication fluid on the bacterial movement. We
implement the discreteness of the biological system by introducing a cutoff in
the growth term at low bacterial densities. We demonstrate that the cutoff does
not improve the models in any way. Its only effect is to decrease the effective
surface tension of the front, making it more sensitive to anisotropy. We
compare the models by introducing food chemotaxis and repulsive chemotactic
signaling into the models. We find that the growth dynamics of the
Communication Walkers model and the growth dynamics of the Non-Linear diffusion
model are affected in the same manner. From such similarities and from the
insensitivity of the Communication Walkers model to implicit anisotropy we
conclude that the increased discreteness, introduced be the coarse-graining of
the walkers, is small enough to be neglected.
