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Various bacterial strains exhibit colonial branching patterns during growth on thin poor substrates. The growth can be either diffusion-limited or kinetic-limited, according to the imposed growth conditions. We present experimental observations of patterns exhibited by the bacterial strains Paenibacillus dendritiformis and Paenibacillus vortex. All manners of branching patterns are observed, the three main being: (I) basic branching; (2) chiral branching; (3) vortex branching. We show that the following biological features can explain the spectrum of observed patterns: (1) Formation of a lubricating fluid. (2) Food chemotactic. (3) Attractive and repulsive chemotactic signaling. (4) Flagella handedness. (5) Transition into pre-spore state. In the theoretical studies we employ knowledge drawn from branching patterning in non-living systems and the mathematical properties of reaction-diffusion models and atomistic models. The above can be used not just to describe existing biological understanding, but also to derive new understanding. For example, reaction-diffusion models that include bacterial density and nutrient concentration, can exhibit branching dynamics if the growth term is a meta-stable fixed point or if the diffusion is state dependent. We show that biologically the growth term has to be an unstable fixed point, but that state-dependent diffusion can represent the lubrication fluid excreted by the bacteria.

In this paper, we study the effect of discreteness on various models for patterning in bacterial colonies (finite-size effect) and present two types of models to describe the growth of the bacterial colonies. The first model presented is the Communicating Walkers model (CWm), a hybrid model composed of both continuous fields and discrete entities — walkers, which are coarse-graining of the bacteria; coarse-graining may amplify the discreteness inherent to the biological system. 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. The representation of bacteria by a density field neglects their discreteness altogether. We implement the discreteness of the bacteria 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. The cutoff affects the dynamics by decreasing the effective surface tension of the front, making it more sensitive to anisotropy and decreasing the fractal dimension of the evolving patterns. We compare the continuous and semi-discrete models by introducing food chemotaxis and repulsive chemotactic signaling into the models. We find that the growth dynamics of the CWm and the growth dynamics of the Non-Linear Diffusion model (one of the continuous models) are affected in the same manner. From such similarities and from the insensitivity of the CWm to implicit anisotropy, we conclude that even the increased discreteness, introduced by the coarse-graining of the walkers, is small enough to be neglected. There are advantages and disadvantages to the two types of models. Employing both of them in parallel enables us to conclude that the discreteness of the bacteria does not significantly affect the growth dynamics (no finite-size effect).

Bacterial colonies must often cope with unfavourable environmental conditions. To do so, they have developed sophisticated modes of cooperative behaviour. It has been found that such behaviour can cause bacterial colonies to exhibit complex growth patterns similar to those observed during non-equilibrium growth processes in non-living systems; some of the qualitative features of the latter may be invoked to account for the complex patterns of bacterial growth. Here we show that a simple model of bacterial growth can reproduce the salient features of the observed growth patterns. The model incorporates random walkers, representing aggregates of bacteria, which move in response to gradients in nutrient concentration and communicate with each other by means of chemotactic 'feedback'. These simple features allow the colony to respond efficiently to adverse growth conditions, and generate self-organization over a wide range of length scales.

We investigate a discrete model consisting of self-propelled particles that obey simple interaction rules. We show that this model can self-organize and exhibit coherent localized solutions in one- and in two-dimensions.In one-dimension, the self-organized solution is a localized flock of finite extent in which the density abruptly drops to zero at the edges.In two-dimensions, we focus on the vortex solution in which the particles rotate around a common center and show that this solution can be obtained from random initial conditions, even in the absence of a confining boundary. Furthermore, we develop a continuum version of our discrete model and demonstrate that the agreement between the discrete and the continuum model is excellent., 4 pages, 5 figures

During the course of evolution, bacteria have developed sophisticated cooperative behavior and intricate communication capabilities [1-3]. Utilizing these capabilities, bacterial colonies develop complex spatio-temporal patterns in response to adverse growth conditions. It is now understood that the study of cooperative self-organization of bacterial colonies is an exciting new multidisciplinary field of research, necessitating the merger of biological information with the physics of non-equilibrium processes and the mathematics of non-linear dynamics. At this stage, several experimental systems have been identified, and preliminary modeling efforts are making significant progress in providing a framework for the understanding of experimental observations [4-12]. This endeavour is not limited to bacteria alone. Studies have been performed of other types of microorganisms as well, such as amoeba [13] and yeast [14]

Various bacterial strains exhibit colonial branching patterns during growth on poor substrates. These patterns reflect bacterial cooperative self-organization and cybernetic processes of communication, regulation and control employed during colonial development. One method of modeling is the continuous, or coupled reaction-diffusion approach, in which continuous time evolution equations describe the bacterial density and the concentration of the relevant chemical fields. In the context of branching growth, this idea has been pursued by a number of groups. We present an additional model which includes a lubrication fluid excreted by the bacteria. We also add fields of chemotactic agents to the other models. We then present a critique of this whole enterprise with focus on the models' potential for revealing new biological features., Comment: 1 latex file, 40 gif/jpeg files (compressed into tar-gzip). Physica A, in press