Team:ITB Indonesia/Modeling/Difussion

First thing to do is calculate how much aflatoxin would enter the cell every time. Aflatoxin diffused into cell through simple diffusion mechanism, it means that aflatoxin difusion is drived by concentration gradient.
Assumption :

• Aflatoxin homogenely diffused into cell

Parameters of the equation :

I. Permeability aflatoxin-membrane

Permeability value between solute and solvent can be described through this equation :

To determine the value of diffusivity constant, we use Stoke-Einstein equation

where the radii value of solute (r) can be determined with the help of molecular weight

So, to simplify our equation, we try to find the correlation between diffusivity constant and solute molecular weight. It can be done through dividing two sets of case (diffusion of protein with well-known molecular weight and diffusion of aflatoxin) and the result is

II. Aflatoxin membrane cell area

To simulate the effect of cell growth to diffusion phenomena, we modify the diffusion equation. Membrane cell area will be increased along with cell number, and it affected by cell growth.
We simplify this problem by assuming cell growth is like growing sphere. When the cell number doubled, it can be stated that the membrane cell area and cell volume doubled too.

Cell membrane area can be evaluated every time by this equation :

where the value of A0 represents membrane cell area of one E. coli cell and n is cell number at certain time. The value of n can be determined with cell growth kinetic :

So, the equation’s final form to evaluate cell membrane area every time become :

With the same principle, we can evaluate cell volume every time :

To gather the value of A0 dan V0, we use the data that bacteria has area to volume ratio 3:1 [4]. Cell density and wet cell mass of E. coli can be known from literature

So the value of A0 and V0 is :