Team:UANL Mty-Mexico/Modeling/broad level

Modeling: broad level approach

The first approach will describe and predict the behavior of the system in a broad abstraction level. Briefly, empirically obtained kinetic constants will be obtained after fitting data to the following ODE set:

\begin{equation} \frac{d[Asac]}{dt} = Vmax_{1}\bigg(\frac{[Asex]}{K_{1}+[Asex]}\bigg) \end{equation} \begin{equation} \frac{d[Asex]}{dt} = -[Asac] \end{equation} \begin{equation} \frac{dUM}{dt} = Vmax_{2}\bigg(\frac{[Asac]}{K_{2}+[Asac]}\bigg) \end{equation}

Where the variables Asac, Asex and UM represent the arsenic accumulated inside the cells, the extracellular arsenic (i.e. the arsenic that remains in the solution) and Miller units, respectively.

This approach will allow us to use the data from relatively simple characterization experiments and can be extended to take into account total cell volume available and the effect of the silica-binding kinetics on this available cell volume.

Note that the equations that describe the change of extracellular arsenic and Miller units through time are a simple Michaelis-Menten model. Nevertheless, this will not be the only scenario considered; we will look for other models to which our data may fit better.