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Team:Groningen/Modelling/Arsenic
From 2009.igem.org
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Our initial ideas on how and what to model can be found at Brainstorm/Modelling.
Usage of graphs in wiki: Graphs
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.):
- Extracellular:
-
As(III) -
As(V)
-
- Intracellular:
- As(III)
-
As(V) -
ArsC - ArsD
- ArsR
- ArsRop (bound to operator)
- ArsRAs (bound to As(III))
The variables above can be related to each other through the following "reactions" and/or equations:
-
As(V)ex → As(V), using phosphate transporters? (Summers2009) -
As(V)ex → As(III), using ArsC (Summers2009) -
As(III) → As(III)ex, using ArsAB (helped by ArsD) (Summers2009) - As(III)in + ArsR ↔ ArsRAs
- As(III)T = As(III) + ArsRAs
- d ArsRAs / dt = kon ArsR As(III) - koff ArsRAs
- At equilibrium: ArsR As(III) = (koff/kon) ArsRAs
- As(III)in + ArsD ↔ ArsDAs
- Kd = koff/kon = 60µM (Chen1997)
- Operator + ArsR ↔ ArsRop
- Kd = koff/kon = 0.33µM (Chen1997, suspect as the relevant reference doesn't actually seem to give any value for this)
- Operator + ArsD ↔ ArsDop
- Kd = koff/kon = 65µM (Chen1997)
- Operator → Operator + ArsR (transcription + translation)
See Chen1997 for the interplay between ArsR and ArsD. The following derives an equation for the concentration of free Operators (which is directly related to the amount of ArsR and ArsD produced) based on ArsR and ArsD (utilizing the same kind of equilibrium assumption as in the derivation of the Michaelis-Menten equation in Alon2007:
ArsR*As=Kd1*ArsRAs ArsD*As=Kd2*ArsDAs ArsR*Op=Kd3*ArsROp ArsD*Op=Kd4*ArsDOp OpT = Op + ArsROp + ArsDOp ArsD*Op=Kd4*(OpT-Op-ArsROp) ArsD*Op/Kd4=OpT-Op-ArsR*Op/Kd3 (1+ArsR/Kd3+ArsD/Kd4)*Op=OpT Op = OpT/(1+ArsR/Kd3+ArsD/Kd4)
TODO Figure out relevant equations for metallochaperone function of ArsD?
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/binding site 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
- Generalization of Michaelis-Menten. More detail.
