Team:Groningen/Modelling/Arsenic

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Our initial ideas on how and what to model can be found at Brainstorm/Modelling.

The raw model

Note: Math support is currently not enabled on this Wiki... (I've asked hq if they can enable it.)

The following variables play an important role in our system (these can be concentrations of substances, the density of the cell, etc.):

• [Hg²⁺] (if we want to accumulate mercury)
•  ???

The variables above can be related to each other through the following "reactions" and/or equations:

• Example of a reaction: Extra_Cellular_Cu -> Intra_Cellular_Cu, with the reaction rate 0.34*(Extra_Cellular_Cu-Intra_Cellular_Cu).
• From REFERENCE: Extra Cellular Hg²⁺ -> Intra Cellular Hg²⁺, described by the differential equation <math>\frac{\partial[M]}{X \partial t}=\frac{V_m[M]}{K_m+[M]}</math>, where X is the cell mass concentration (in g/L). Question: What is [M]? It looks like it should be the concentration outside the cell (in mg/L), but that doesn't make sense, as everything on the right-hand side is positive, suggesting that the concentration outside the cell is growing...

Any constants used above are defined here:

• <math>K_m=6 mg/L</math>
• <math>V_m=18 mg/(min\cdot g)</math> (note that the gram comes from gram dry cell weight)
•  ???

Kinetic Laws

TODO Add references.

TODO Find out how to determine experimentally which is applicable (and if you know, what the parameters are).

Mass Action

Molecules randomly interact, the reaction rate is simply the product of the concentrations of the reactants (multiplied by a constant).

Michaelis-Menten

Applicable to situations where there is a maximum reaction rate (due to needing a catalyst/transporter of which there is only a limited amount for example) under the assumption that there is much more of the "main" reactant than of the catalyst/transporter. Has two constants, the maximum reaction rate and the concentration and which the reaction rate is half the maximum reaction rate.

Michaelis-Menten reversible

TODO

Hill

TODO