Team:Groningen/Modelling/Arsenic

From 2009.igem.org

(Difference between revisions)
(→The raw model)
(→The raw model: Basic operation of ArsR+ArsD)
Line 14: Line 14:
* Extracellular:
* Extracellular:
-
** [As(III)]
+
** <del>As(III)</del>
-
** [As(V)]
+
** <del>As(V)</del>
* Intracellular:
* Intracellular:
-
** [As(III)]
+
** As(III)
-
** [As(V)]
+
** <del>As(V)</del>
-
** [ArsC]
+
** <del>ArsC</del>
-
** [ArsR unbound] ({{todo}} Do we need this intermediate step?)
+
** ArsD
-
** [ArsR bound to operator]
+
** ArsR
-
** [ArsR bound to As(III)]
+
** ArsR<sub>op</sub> (bound to operator)
-
** [ArsD]?
+
** ArsR<sub>As</sub> (bound to As(III))
The variables above can be related to each other through the following "reactions" and/or equations:
The variables above can be related to each other through the following "reactions" and/or equations:
-
* As(V)<sub>ex</sub> &rarr; As(V)<sub>in</sub>, using phosphate transporters? (Summers2009)
+
* <del>As(V)<sub>ex</sub> &rarr; As(V), using phosphate transporters? ([[Team:Groningen/Literature#Summers2009|Summers2009]])</del>
-
* As(V)<sub>ex</sub> &rarr; As(III)<sub>in</sub>, using ArsC (Summers2009)
+
* <del>As(V)<sub>ex</sub> &rarr; As(III), using ArsC ([[Team:Groningen/Literature#Summers2009|Summers2009]])</del>
-
* As(III)<sub>in</sub> + ArsR<sub>u</sub> &harr; ArsR<sub>As</sub> ???
+
* <del>As(III) &rarr; As(III)<sub>ex</sub>, using ArsAB (helped by ArsD) ([[Team:Groningen/Literature#Summers2009|Summers2009]])</del>
-
* ArsR<sub>u</sub> &harr; ArsR<sub>op</sub> ???
+
* As(III)<sub>in</sub> + ArsR &harr; ArsR<sub>As</sub>
-
* ArsR also controls the production rate of ArsR (and so on).
+
** As(III)<sub>T</sub> = As(III) + ArsR<sub>As</sub>
 +
** d ArsR<sub>As</sub> / dt = k<sub>on</sub> ArsR As(III) - k<sub>off</sub> ArsR<sub>As</sub>
 +
** At equilibrium: ArsR As(III) = (k<sub>off</sub>/k<sub>on</sub>) ArsR<sub>As</sub>
 +
* As(III)<sub>in</sub> + ArsD &harr; ArsD<sub>As</sub>
 +
** K<sub>d</sub> = k<sub>off</sub>/k<sub>on</sub> = 60&micro;M ([[Team:Groningen/Literature#Chen1997|Chen1997]])
 +
* Operator + ArsR &harr; ArsR<sub>op</sub>
 +
** K<sub>d</sub> = k<sub>off</sub>/k<sub>on</sub> = 0.33&micro;M ([[Team:Groningen/Literature#Chen1997|Chen1997]], suspect as the relevant reference doesn't actually seem to give any value for this)
 +
* Operator + ArsD &harr; ArsD<sub>op</sub>
 +
** K<sub>d</sub> = k<sub>off</sub>/k<sub>on</sub> = 65&micro;M ([[Team:Groningen/Literature#Chen1997|Chen1997]])
 +
* Operator &rarr; Operator + ArsR (transcription + translation)
-
Any constants used above are defined here:
+
See [[Team:Groningen/Literature#Chen1997|Chen1997]] for the interplay between ArsR and ArsD.
-
* <math>K_m=6 mg/L</math>
+
{{todo}} Figure out relevant equations for metallochaperone function of ArsD?
-
* <math>V_m=18 mg/(min\cdot g)</math> (note that the gram comes from gram dry cell weight)
+
-
* ???
+
== Kinetic Laws ==
== Kinetic Laws ==

Revision as of 13:18, 9 July 2009

Bold text

Igemhomelogo.png

April
MTWTFSS
    1 2 3 4 5
6 7 8 9 10 11 12
13 14 15 16 17 18 19
20 21 22 23 24 25 26
27 28 29 30
May
MTWTFSS
        1 2 3
4 5 6 7 8 9 10
11 12 13 14 15 16 17
18 19 20 21 22 23 24
25 26 27 28 29 30 31
June
MTWTFSS
1 2 3 4 5 6 7
8 9 10 11 12 13 14
15 16 17 18 19 20 21
22 23 24 25 26 27 28
29 30
July
MTWTFSS
    1 2 3 4 5
6 7 8 9 10 11 12
13 14 15 16 17 18 19
20 21 22 23 24 25 26
27 28 29 30 31
August
MTWTFSS
          1 2
3 4 5 6 7 8 9
10 11 12 13 14 15 16
17 18 19 20 21 22 23
24 25 26 27 28 29 30
31
September
MTWTFSS
  1 2 3 4 5 6
7 8 9 10 11 12 13
14 15 16 17 18 19 20
21 22 23 24 25 26 27
28 29 30
October
MTWTFSS
      1 2 3 4
5 6 7 8 9 10 11
12 13 14 15 16 17 18
19 20 21 22 23 24 25
26 27 28 29 30 31
November
MTWTFSS
            1
2 3 4 5 6 7 8
9 10 11 12 13 14 15
16 17 18 19 20 21 22
23 24 25 26 27 28 29
30

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
  • 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
  • Operator → Operator + ArsR (transcription + translation)

See Chen1997 for the interplay between ArsR and ArsD.

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.
Retrieved from "http://2009.igem.org/Team:Groningen/Modelling/Arsenic"