Our drylab has been working to simulate different processes in biofilm formation. The reason is that, for the purpose of enhancing biological activity in a bioreactor, biofilm induction is a pillar in the project.

Specifically, two kinds of simulations regarding biofilm formation have been performed. One of the simulations consists in a microscopic prediction of biofilm growth. The other pursues to study the population kinetics of cultures containing planktonic and biofilm cells.

MICROSCOPIC PREDICTION OF BIOFILM GROWTH

In this simulation, analysis of biofilm formation involves analyzing the bacteria as individual, discrete particles.

The prediction starts modelling a 3D liquid space in which one or more bacteria are attached to a solid wall. Notably, these bacteria can reflect in their shape the form of real rod-shaped cells, like Pseudomonas putida. In this way, they are considered cylindrical tubes of length ranging from “L0” to “2L0 + σ”, with semi-spheres of radius “σ/2” at both ends (Figure 1).

The software predicts the growth in size of the initial bacteria over time, until the cells reach the critical length (“2L0 + 2σ”). At that point, cell division occurs (Figure 1). This process of growth and division is repeated again and again.

Figure 1. Initial cell size (upper part), maximum cell size (medium) and cell division (bottom).

How bacterial consumption of the limiting substrate affects cell and biofilm growth

The velocity in wich, at a given point in time, each cell grows in length is proposed to be:

Equation 1. Bacterial length growth rate equation.

Where v is the length growth rate of the bacteria in question, k is a proportionality constant, p represents the limiting substrate consumption rate by the cell, and L depicts its length.

Therefore, the length growth rate of a bacterium is inversely proportional to its length. The reason for this is in turn how p is defined:

Equation 2. Limiting substrate consumption rate equation.

Where pmax corresponds to the maximum length growth rate per bacterial length unit, S is the limiting substrate concentration in the area surrounding the bacterium, and M depicts the limiting substrate concentration at which half of the maximum length growth rate is achieved.

To model that bigger cells would uptake more limiting substrate than smaller cells, equation 2 shows that p is linearly dependent on the length of the bacterium (L). However, the simulation models that bacterial length growth (v) is indepedent from the actual length of the bacterium. As v depends on p and p is dependent on L, it is necessary in turn for v to be inversely proportional to L (equation 1).

Initially, the limiting substrate is evenly distributed in the three dimensional space. However, bacterial consumption creates gradients of the limiting substrate. This causes cells to grow at lower velocities in regions where less limiting substrate is present. The software also includes Fick's diffusion equations to incorporate how these mass gradients spontaneously tend to disappear. Because of these multiple factors, each bacterium in the biofilm grows at its own, time-dependent velocity to reach the critical length and divide.

What holds the bacteria together

The bacteria in the program are attracted to each other and to the solid wall, to reflect the action of adhesins (i.e LaPA), which are transmembranal proteins that enable adherance to form a biofilm.

However, it exists simultaneously a certain repulsion force, to emulate in this way the superficial tension of the cells and wall (Figure 2).

Figure 2. Superficial-tension related forces.

At the same time, the position of each cell is also affected by thermal agitation-associated diffusion. Brownian motion equations are included to this end.

POPULATION KINETICS OF CULTURES CONTAINING PLANKTONIC AND BIOFILM CELLS

In a bioreactor containing bacteria with the ability to form biofilms, some of the cells will exist in planktonic state and others in biofilm state.

We propose here a model to describe how the planktonic and biofilm populations grow, and how they interact. That is, how a dynamic transition between both states exists. As shown later, this model yet simple has been shown to correspond to experimental results.