مدل شبیه سازی از تشکیل بیوفیلم با سلول های مستقل: تجزیه و تحلیل از نسخه دو بعدی

We introduce a single-cell based simulation model of biofilm growth. Each microbial cell is modelled as an autonomous agent whose behavior is controlled by thermodynamic parameters, mechanical properties, physiological rules and environmental conditions. In the two-dimensional version presented here, a cell is represented by a closed chain of self-avoiding beads linked together using the bond fluctuation algorithm. The cell is thus controlled both by the rigidity of its membrane and a pressure difference. The model is complemented by key features such as the explicit presence of nutrient diffusion and flow, the processes of cell-division and cell-death, and the attractive interactions between the cell and the surface on which the colony grows. Tuning the parameters of the model can lead to the growth and maturation of various types of biofilms. In this first article, we describe the main properties of a two-dimensional version of the model, and we discuss the extension to three dimensions.

Biofilms are a common form of microbial community associated with surfaces in contact with liquids. For example, bacterial biofilms can be found growing in water pipes, on surgical instruments or on tooth surfaces. A distinguishing characteristic of biofilms is the presence of extracellular polymeric substances (EPS) in which the cells are embedded. Mathematical models have been used for the last three decades in order to improve our understanding of the growth and behavior of microbial biofilms. Early models represented biofilms as spatially homogeneous steady-state films containing a single species [1]. Additional features, such as multiple types of nutrients, mixed microbial species and variable biofilm density were later included [2], [3] and [4]. However, most of these models assumed a predetermined biofilm morphology. Consequently, they were unable to account for the experimentally observed 3D structural heterogeneity of the colonies. Furthermore, they made several assumptions about biofilm development. For instance, the direction of biomass displacement was taken to be perpendicular to the substratum, while cell detachment was determined by an arbitrary uniform removal rate or velocity. Such simple models are generally suitable for representing the aggregate activity of a biofilm on many square millimeters of surface area. In recent years, several biofilm numerical models which deal with smaller scales have been proposed. They can be divided into two classes of models, namely the continuum models and the discrete models. The continuum models use a mean-field-type of approach [5], [6] and [7]. Most of the discrete models utilize methods, such as cellular automata, to simulate the rules that govern the lives of microbial cells. These coarse-grained models use a set of local rules governing the growth of the biomass, the displacement of the growing biomass as well as its detachment. These methods produce realistic, structurally heterogeneous biofilms [8], [9], [10], [11], [12], [13], [14] and [15] but a major drawback is that they rely on speculative rules which control the global biomass development [16] instead of the cell themselves. Another sub-class of discrete models are the so-called individual-based (or particle-based) models [17], [18] and [19]. The latter approaches have some similarity with our model in that they consider cells as individual agents.

We have developed a 2D biofilm model using a novel single-cell based approach that represents cells as thermodynamic and mechanical autonomous systems. The current version of the model includes cell-division, cell-death, explicit presence of nutrients, as well as cell–wall and cell–cell interactions. We first examined the physical characteristics of the cells in order to find the range of parameters needed to model realistic cells. Our investigation of the cell structural properties lead to results which could be compared to those obtained by other authors working on related polymer and/or colloidal systems. In addition, cell–wall and cell–cell interaction parameters have been studied, and two kinds of transitions have been pointed out: the unbinding–binding transition and the glassy transition. Our systematic study of the parameters of the model has helped us narrow the parameter phase space. Different colony patterns can be created by changing some parameters such as the cell–cell interaction parameter and the nutrient concentration. These patterns are qualitatively similar to the ones found in the growth of B. subtilis. We have also found that growth dynamics is very sensitive to the nutrient concentration as well as to the cell maturity age (tmaturetmature) and presents a power-law profile. These are preliminary results, and a more complete study of the model is in preparation.