Studies of Bacterial Branching Growth using Reaction-Diffusion Models for Colonial Development

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 pres

Modeling branching and chiral colonial patterning of lubricating bacteria

In nature, microorganisms must often cope with hostile environmental conditions. To do so they have developed sophisticated cooperative behavior and intricate communication capabilities, such as: direct cell-cell physical interactions via extra-membrane polymers, collective production of extracellular "wetting" fluid for movement on hard surfaces, long range chemical signaling such as quorum sensing and chemotactic (bias of movement according to gradient of chemical agent) signaling, collective activation and deactivation of genes and even exchange of genetic material. Utilizing these capabilities, the colonies develop complex spatio-temporal patterns in response to adverse growth conditions. We present a wealth of branching and chiral patterns formed during colonial development of lubricating bacteria (bacteria which produce a wetting layer of fluid for their movement). Invoking ideas from pattern formation in non-living systems and using ``generic'' modeling we are able to reveal novel survival strategies which account for the salient features of the evolved patterns. Using the models, we demonstrate how communication leads to self-organization via cooperative behavior of the cells. In this regard, pattern formation in microorganisms can be viewed as the result of the exchange of information between the micro-level (the individual cells) and the macro-level (the colony). We mainly review known results, but include a new model of chiral growth, which enables us to study the effect of chemotactic signaling on the chiral growth. We also introduce a measure for weak chirality and use this measure to compare the results of model simulations with experimental observations.Comment: 50 pages, 24 images in 44 GIF/JPEG files, Proceedings of IMA workshop: Pattern Formation and Morphogenesis (1998

Continuous and discrete models of cooperation in complex bacterial colonies

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.Comment: 16 pages, 10 figures in 13 gif files, to be published in proceeding of CMDS

SkyMapper SEDs of nearby galaxies: quenching and bursting probed by a change index for star formation

The wish list of astronomers includes a tool that reveals quenching of star formation in galaxies directly as it proceeds. Here, we present a proof-of-concept for a new quenching-and-bursting diagnostic, a "change index" for star formation, that requires only photometric data, provided they include filters such as the violet $uv$ bands used by SkyMapper. The index responds mostly to changes in star-formation rate on a timescale of 20 to 500 Myr and is nearly insensitive to dust extinction. It works effectively to distances of 100 to 150 Mpc. We explore its application to eight example galaxies in SkyMapper DR2, including known E+A and Seyfert-1 galaxies. Owing to the degeneracies inherent in broad-band photometry, the change index can only be a qualitative indicator of changes in star-formation rate. But once the SkyMapper Southern Survey is complete, the change index will be available for every spatial resolution element of every galaxy in the Southern sky within its working distance range.Comment: 20 pages, 14 figures, submitted to PAS

Information flow and optimization in transcriptional control

In the simplest view of transcriptional regulation, the expression of a gene is turned on or off by changes in the concentration of a transcription factor (TF). We use recent data on noise levels in gene expression to show that it should be possible to transmit much more than just one regulatory bit. Realizing this optimal information capacity would require that the dynamic range of TF concentrations used by the cell, the input/output relation of the regulatory module, and the noise levels of binding and transcription satisfy certain matching relations. This parameter-free prediction is in good agreement with recent experiments on the Bicoid/Hunchback system in the early Drosophila embryo, and this system achieves ~90% of its theoretical maximum information transmission.Comment: 5 pages, 4 figure

Spatio-selection in Expanding Bacterial Colonies

Segregation of populations is a key question in evolution theory. One important aspect is the relation between spatial organization and the population's composition. Here we study a specific example -- sectors in expanding bacterial colonies. Such sectors are spatially segregated sub-populations of mutants. The sectors can be seen both in disk-shaped colonies and in branching colonies. We study the sectors using two models we have used in the past to study bacterial colonies -- a continuous reaction-diffusion model with non-linear diffusion and a discrete ``Communicating Walkers'' model. We find that in expanding colonies, and especially in branching colonies, segregation processes are more likely than in a spatially static population. One such process is the establishment of stable sub- population having neutral mutation. Another example is the maintenance of wild-type population along side with sub-population of advantageous mutants. Understanding such processes in bacterial colonies is an important subject by itself, as well as a model system for similar processes in other spreading populations

Lubricating Bacteria Model for Branching growth of Bacterial Colonies

Various bacterial strains (e.g. strains belonging to the genera Bacillus, Paenibacillus, Serratia and Salmonella) exhibit colonial branching patterns during growth on poor semi-solid substrates. These patterns reflect the bacterial cooperative self-organization. Central part of the cooperation is the collective formation of lubricant on top of the agar which enables the bacteria to swim. Hence it provides the colony means to advance towards the food. One method of modeling the colonial development is via coupled reaction-diffusion equations which describe the time evolution of the bacterial density and the concentrations of the relevant chemical fields. This idea has been pursued by a number of groups. Here we present an additional model which specifically includes an evolution equation for the lubricant excreted by the bacteria. We show that when the diffusion of the fluid is governed by nonlinear diffusion coefficient branching patterns evolves. We study the effect of the rates of emission and decomposition of the lubricant fluid on the observed patterns. The results are compared with experimental observations. We also include fields of chemotactic agents and food chemotaxis and conclude that these features are needed in order to explain the observations.Comment: 1 latex file, 16 jpeg files, submitted to Phys. Rev.