Modeling of spatiotemporal patterns in bacterial colonies (original) (raw)

On the growth of non-motile bacteria colonies: an agent-based model for pattern formation

2019

In the growth of bacterial colonies, a great variety of complex patterns are observed in experiments, depending on external conditions and the bacterial species. Typically, existing models employ systems of reaction-diffusion equations or consist of growth processes based on rules, and are limited to a discrete lattice. In contrast, the two-dimensional model proposed here is an off-lattice simulation, where bacteria are modelled as rigid circles and nutrients are point-like, Brownian particles. Varying the nutrient diffusion and concentration, we simulate a wide range of morphologies compatible with experimental observations, from round and compact to extremely branched patterns. A scaling relationship is found between the number of cells in the interface and the total number of cells, with two characteristic regimes. These regimes correspond to the compact and branched patterns, which are exhibited for sufficiently small and large colonies, respectively. In addition, we characteris...

A Predictive Reaction-Diffusion Based Model of E.coliColony Growth Control

2021

Bacterial colony formations exhibit diverse morphologies and dynamics. A mechanistic understanding of this process has broad implications to ecology and medicine. However, many control factors and their impacts on colony formation remain underexplored. Here we propose a reaction-diffusion based dynamic model to quantitatively describe cell division and colony expansion, where control factors of colony spreading take the form of nonlinear density-dependent function and the intercellular impacts take the form of density-dependent hill function. We validate the model using experimental E. coli colony growth data and our results show that the model is capable of predicting the whole colony expansion process in both time and space under different conditions. Furthermore, the nonlinear control factors can predict colony morphology at both center and edge of the colony.

Continuous and discrete models of cooperation in complex bacterial colonies

1998

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.

Modelling the morphology of migrating bacterial colonies

Physica D: Nonlinear Phenomena, 2010

We present a model which aims at describing the morphology of colonies of Proteus mirabilis and Bacillus subtilis. Our model is based on a cellular automaton which is obtained by the adequate discretisation of a diffusion-like equation, describing the migration of the bacteria, to which we have added rules simulating the consolidation process. Our basic assumption, following the findings of the group of Chuo University, is that the migration and consolidation processes are controlled by the local density of the bacteria. We show that it is possible within our model to reproduce the morphological diagrams of both bacteria species. Moreover, we model some detailed experiments done by the Chuo University group, obtaining a fine agreement.

An (almost) solvable model for bacterial pattern formation

Physica D: Nonlinear Phenomena, 2007

We present a simple model for the description of ring-like concentric structures in bacterial colonies. We model the differences between Bacillus subtilis and Proteus mirabilis colonies by using a different dependence of the duration of the consolidation phase on the concentration of agar. We compare our results to experimental data from these two bacterial species colonies and obtain a good agreement. Based on this analysis, we formulate a hypothesis on the connection of the diffusion constant that appears in the model to the experimental agar concentration.

Reaction-diffusion model for pattern formation in E. coli swarming colonies with slime

Physical Review E, 2005

A new experimental colonial pattern and pattern transition observed in E.coli MG1655 swarming cells grown on semi-solid agar are described. We present a reaction-diffusion model that, taking into account the slime generated by these cells and its influence on the bacterial differentiation and motion, reproduces the pattern and successfully predicts the observed changes when the colonial collective motility is limited. In spite of having small non-hyperflagellated swarming cells, under these experimental conditions E. coli MG1655 can very rapidly colonize a surface, with a low branching rate, thanks to a strong fluid production and a local incremented density of motile, lubricating cells.

Nonlinear Development of Bacterial Colony Modeled with Cellular Automata and Agent Objects

International Journal of Modern Physics C, 2003

Collective dynamical behavior of simple organisms is a very fascinating and important field of study especially in the age of rapid development of nano-and bio-technology. Despite a number of different numerical techniques existing for modeling the uptake of the nutrients, metabolism, maintenance, cell division and growth of bacteria population, none of them can be treated as a universal one. This is because the complex behavior of simple organisms must be studied in different aspects covering totally different spatio-temporal scales. Most of numerical models employ both well known discrete techniques such as diffusion-(reaction)limited algorithms, cellular automata, Monte-Carlo and continuum approaches. In a new model presented here we have combined two techniques. The first one -agent based -has been used for modeling the behavior of an individual bacterium. The agent defines generic features of the bacterium and the ways it interacts (communicates) with the environment and with the neighboring bacteria. The cellular automata is used for modeling the bacterial environment and represent communication layer for the agents, while a fixed two-dimensional grid defines the living space. Despite the entire system is treated as a system with unbounded resources, the resources are limited locally due to congested environment. The growth of the bacterial colony depends on the amount of free space in the closest neighborhood of individuals, which is required for reproduction, and on the availability of nutrients. We have matched the parameters of the model to demonstrate various growth structures developed by bacteria populations. We show that the patterns generated by the bacteria due to their collective behavior reflect the dynamical vitality of population and its fitness factor. We observe that the strongest populations self-organize in rod-like structures, which are reproduced in experimental light microscopy images characteristic for some bioflims and anthrax bacterial colonies.

A local PDE model of aggregation formation in bacterial colonies

Nonlinearity, 2016

We study pattern formation in a model of cyanobacteria motion recently proposed by Galante, Wisen, Bhaya and Levy. By taking a continuum limit of their model, we derive a novel fourth-order nonlinear parabolic PDE equation that governs the behaviour of the model. This PDE is u t = −u xx − u xxxx + α uxuxx u x. We then derive the instability thresholds for the onset of pattern formation. We also compute analytically the spatial profiles of the steady state aggregation density. These profiles are shown to be of the form sech p where the exponent p is related to the parameters of the model. Full numerical simulations give a favorable comparison between the continuum and the underlying discrete system, and show that the aggregation profiles are stable above the critical threshold.