Cellular automata-based modelling and simulation of biofilm structure on multi-core computers

Abstract

The article presents a mathematical model of biofilm growth for aerobic biodegradation of a toxic carbonaceous substrate. Modelling of biofilm growth has fundamental significance in numerous processes of biotechnology and mathematical modelling of bioreactors. The process following double-substrate kinetics with substrate inhibition proceeding in a biofilm has not been modelled so far by means of cellular automata. Each process in the model proposed, i.e. diffusion of substrates, uptake of substrates, growth and decay of microorganisms and biofilm detachment, is simulated in a discrete manner. It was shown that for flat biofilm of constant thickness, the results of the presented model agree with those of a continuous model. The primary outcome of the study was to propose a mathematical model of biofilm growth; however a considerable amount of focus was also placed on the development of efficient algorithms for its solution. Two parallel algorithms were created, differing in the way computations are distributed. Computer programs were created using OpenMP Application Programming Interface for C++ programming language. Simulations of biofilm growth were performed on three high-performance computers. Speed-up coefficients of computer programs were compared. Both algorithms enabled a significant reduction of computation time. It is important, inter alia, in modelling and simulation of bioreactor dynamics.

Differential equation based minimal model describing metabolic oscillations inBacillus subtilisbiofilms

“…From these calculations, the following conclusions can be drawn. At k 1 G E = k 4 , the two steady states of the simplified system (7) coincide, as in the complete system (1). Since the trivial and nontrivial steady states interchange their stability at that point, it is a transcritical bifurcation.…”

“…System (7) shows two steady states: which is the trivial steady state (TSS), and which is the non-trivial steady state (NTSS).…”

Modeling Biofilms in Water Systems with New Variables: A Review

“…The biomass in the biofilm matrix will move into the compartment and, if the room is full, the extra biomass will move to available compartments nearby. The CA model describes this process mathematically and displays the spatial heterogeneity using a discrete formulation [43,44]. The individual based model, on the other hand, relates the properties of single cells with the biofilms [45].…”

Searching for simple rules in Pseudomonas aeruginosa biofilm formation

“…Although there have been several efforts to model biofilm growth using CA in general [10, 11], here we focused on simple rules to specifically test 2-D spatio-temporal dynamics of P. aeruginosa biofilm in untreated (control) and antibiotic treated conditions.…”