Team:UANL Mty-Mexico/Modeling/Silica binding

Silica binding

The silica binding module of our project is based on the expression of a chimeric transmembranal protein, OmpA-L2. This chimeric protein is composed by an OmpA domain (the transmembranal domain) and a L2 domain (the silica binding domain).

For the mathematical representation of the binding to silica particles, we work at the population level and take into account a Verhulst logistic function to describe the kinetics of this process.

The central assumptions for this model and its limitations are the following: we assume that bacteria are in the stationary phase and that the first binding of a bacterial cell to a silica particle occurs in a faster timescale, so that we can safely assume that it occurs immediately. Finally, this model is restricted to the occasions when the size of the particles is greater than that of the cells.

However, as we do not have the proper experimental data, this model will remain only enunciated, with simulations ran with arbitrary parameters.

Core model

We start assuming that the silica particles are spheres, so we have that their volume, density, mass and surface area are related in the following way:

\begin{equation} \large V_{particle} = \frac {4 \cdot \pi \cdot r^{3}}{3} \end{equation} \begin{equation} \large S_{particle} = 4 \cdot \pi \cdot r^{3} \end{equation} \begin{equation} \large V_{total} = \frac{m}{D_{silica}} \end{equation} \begin{equation} \large N_{particle} = \frac{V_{total}}{V_{particle}} \end{equation}

ODEs

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