Abstract

The formation mechanism of the growth of bacterial colony is studied by comparing the formation of the bacteria with the patterns obtained by Monte Carlo simulations using the diffusion limited aggregation algorithm. For this purpose, the morphological changes of the growing patterns are controlled by a sticking probability parameter, α, which represents the trajectories of the particles joining to the growing colonies, the complex reactions, and biological dynamics such as concentration of nutrient, temperature, and humidity in the growing environment. Specially, the sticking probability parameter is related to the biological activation and irreversible growth of the bacteria via growth energy for the mobility in the environment and perimeters of the colonies. Morphologies of the aggregation of the bacterial colonies have irregular, fractal, and compact structures. In this study, first, fractal dimensions are assessed for simulations and the real systems. The density of bacteria as ρ in region defined by circle of radius r centered at initial dropping seed from center through the perimeter is computed by using scaling method.  Second, critical exponents of patterns are calculated.  As a function of r, ρ reaches the asymptotic ρ₀ (α) following power-law `r = r₀ + Ar^{­­­ – g} with universal exponents γ = 0.47 for α = 1. The value of the main density for the bacterial patterns has ρ₀ ~ α ^{– β}, where β = 0.32 according to the scaling theory. Finally, the results obtained are found in good agreement with the experiments and can be useful for the researchers studying about bacterial colonization patterns.

Key words: Monte Carlo simulation, diffusion limited aggregation, sticking probability parameter, critical exponent, bacterial colony formation.