Kinetics
We modeled our enzyme reactions in propane pathway with Michaelis-Menten enzyme kinetics. It is widely used in this kind of modeling and assumes that the reaction enzyme catalyses is rapid compared to the enzyme and substrate joining together and leaving each other. The very basic equation for irreversible one substrate reaction is \[ \text{rate} = \frac{V_{max}[S]}{K_{cat}+[S]}, \] where \([S]\) is substrate concentration. \( V_{max} \) tells us .... and \( K_{cat} \) .... . Only few of our reactions follow this very basic equation, and for the most of them we need to use multisubstrate reaction kinetics. (reference for the book?)
pic of our pathway here to make things more clear. Do we want pictures with highlited enzymes in every subcategory?
AtoB
2\(\cdot\)Acetyl-CoA \(\rightarrow\) Acetoacetyl-CoA + CoA
\[ \frac{K_{cat}^{AtoB} \cdot [AtoB] \cdot [Acetyl\text{-}CoA]^2}{[Acetyl\text{-}CoA]^2+2\cdot K_{M}^{AtoB:Acetyl\text{-}CoA}\cdot [Acetyl\text{-}CoA]} \]
Constant |
Value |
Source |
To note |
\( K_{cat}^{AtoB} \) |
10653 1/min |
link |
Forward reaction |
\( K_{M}^{AtoB:Acetyl\text{-}CoA} \) |
0.00047 mol/l |
link |
Is there something special about this? |
FadB2
Acetoacetyl-CoA + NADPH + H\(^+\) \(\rightarrow\) 3-Hydroxybutyryl-CoA + NADP\(^+\)
\[ \frac{[Acetoacetyl\text{-}CoA]\cdot [NADPH]-\frac{[3\text{-}hydroxybutyryl\text{-}CoA]\cdot [NADP^+]}{K_{eq}}}
{\frac{K_{M}^{FadB2:Acetoacetyl\text{-}CoA}\cdot K_{M}^{FadB2:NADPH}}{K_{cat1}^{FadB2}\cdot [FadB2]}+\frac{K_{M}^{FadB2:NADPH}\cdot [Acetoacetyl\text{-}CoA]}{K_{cat1}^{FadB2}\cdot [FadB2]}+\frac{ K_{M}^{FadB2:Acetoacetyl\text{-}CoA}\cdot [NADPH]}{K_{cat1}^{FadB2}\cdot [FadB2]}+\frac{K_{M}^{FadB2:Acetoacetyl\text{-}CoA}\cdot [NADP^+]}{K_{eq}\cdot K_{cat2}^{FadB2}\cdot [FadB2]}+} \]
\[ \cdots \frac{}{+\frac{K_{M}^{FadB2:NADP^+}\cdot [3\text{-}hydroxybutyryl\text{-}CoA]}{K_{eq}\cdot K_{cat2}^{FadB2}\cdot [FadB2]}+\frac{[Acetoacetyl\text{-}CoA]\cdot [NADPH]}{K_{cat1}^{FadB2}\cdot [FadB2]}+\frac{[NADP^+]\cdot [3\text{-}hydroxybutyryl\text{-}CoA]}{K_{eq}\cdot K_{cat2}^{FadB2}\cdot [FadB2]}}\]
Constant |
Value |
Source |
To note |
\( K_{cat1}^{FadB2} \) |
0.677 1/min |
link |
Forward reaction |
\( K_{cat2}^{FadB2} \) |
0.723 1/min |
link |
Reverse reaction |
\( K_{M}^{FadB2:Acetoacetyl\text{-}CoA} \) |
65.6 mol/l |
link |
Forward reaction |
\( K_{M}^{FadB2:NADPH} \) |
50 mol/l |
link |
Forward reaction |
\( K_{M}^{FadB2:3\text{-}Hydroxybutyryl\text{-}CoA} \) |
43.5 mol/l |
link |
Reverse reaction |
\( K_{M}^{FadB2:NADP^+} \) |
29.5 mol/l |
link |
Reverse reaction |
Hdb
Acetoacetyl-CoA + NADPH + H\(^+\) \(\rightarrow\) 3-Hydroxybutyryl-CoA + NADP\(^+\)
\[ \frac{K_{cat}^{Hdb}\cdot [Hbd] \cdot [Acetoacetyl\text{-}CoA]\cdot [NADPH]}{[Acetoacetyl\text{-}CoA]\cdot [NADPH] + K_{M}^{Hdb:NADPH}\cdot [Acetoacetyl\text{-}CoA]+K_{M}^{Hdb:Acetoacetyl\text{-}CoA}\cdot [NADPH]} \]
Constant |
Value |
Source |
To note |
\( K_{cat}^{Hdb} \) |
336.4 1/min |
link |
Forward reaction |
\( K_{M}^{Hdb:Acetoacetyl\text{-}CoA} \) |
5e-5 mol/l |
link |
Is there something special about this? |
\( K_{M}^{Hdb:NADPH} \) |
7e-5 mol/l |
link |
Is there something special about this? |
Crt
3-hydroxybutyryl-CoA \(\rightarrow\) Crotonyl-CoA + H\( _2\)O
\[ \frac{K_{cat}^{Crt}\cdot [Crt]\cdot [3\text{-}hydroxybutyryl\text{-}CoA]}{K_{M}^{Crt:3\text{-}Hydroxybutyryl\text{-}CoA} +[3\text{-}hydroxybutyryl\text{-}CoA]} \]
Constant |
Value |
Source |
To note |
\( K_{cat}^{Crt} \) |
1310.8 1/min |
link |
Forward reaction |
\( K_{M}^{Crt:3\text{-}Hydroxybutyryl\text{-}CoA} \) |
3e-5 mol/l |
link |
Is there something special about this? |
Ter
Crotonyl-CoA + NADH + H\( ^+\) \(\rightarrow\) Butyryl-CoA + NAD\( ^+\)
\[ \frac{K_{cat}^{Ter}\cdot [Ter] \cdot [Crotonyl\text{-}CoA]\cdot [NADH]}{[Crotonyl\text{-}CoA]\cdot [NADH] + K_{M}^{Ter:NADH}\cdot [Crotonyl\text{-}CoA]+K_{M}^{Ter:Crotonyl\text{-}CoA}\cdot [NADH] + K_{I}^{Ter:Butyryl\text{-}CoA}\cdot K_{M}^{Ter:NADH}} \]
Constant |
Value |
Source |
To note |
\( K_{cat}^{Ter} \) |
1881.6 1/min |
link |
Forward reaction |
\( K_{M}^{Ter:Crotonyl\text{-}CoA} \) |
2.7e-06 mol/l |
link |
Is there something special about this? |
\( K_{M}^{Ter:NADH} \) |
5.2e-06 mol/l |
link |
Is there something special about this? |
\( K_{I}^{Ter:Butyryl\text{-}CoA} \) |
1.98e-07 mol/l |
link |
Is there something special about this? |
YciA
Butyryl-CoA + H\( _2\)O \(\rightarrow\) Butyrate + CoA
\[ \frac{K_{cat}^{YciA}\cdot [YciA]\cdot [Butyryl\text{-}CoA]}{K_{M}^{YciA:Butyryl\text{-}CoA} +[Butyryl\text{-}CoA]} \]
Constant |
Value |
Source |
To note |
\( K_{cat}^{YciA} \) |
1320 1/min |
link |
Forward reaction |
\( K_{M}^{YciA:Butyryl\text{-}CoA} \) |
3.5e-06 mol/l |
link |
Is there something special about this? |
Car
Butyrate + NADPH + ATP \(\rightarrow\) Butyraldehyde + NADP\(^+\) + AMP + 2P\(_i\)
\[\frac{K_{cat}^{Car}\cdot [Car]\cdot [Butyrate]\cdot [NADPH]\cdot [ATP]}{K_{M}^{Car:Butyrate}\cdot K_{M}^{Car:NADPH}\cdot [ATP]+K_{M}^{Car:ATP}\cdot [Butyrate]\cdot [NADPH]+K_{M}^{Car:NADPH}\cdot [Butyrate]\cdot [ATP]}\]\[\cdots \frac{}{+K_{M}^{Car:Butyrate}\cdot [NADPH]\cdot [ATP]+ [Butyrate]\cdot [NADPH]\cdot [ATP]}\]
Constant |
Value |
Source |
To note |
\( K_{cat}^{Car} \) |
150 1/min |
link |
Forward reaction |
\( K_{M}^{Car:Butyrate} \) |
0.013 mol/l |
link |
Is there something special about this? |
\( K_{M}^{Car:NADPH} \) |
4.8e-05 mol/l |
link |
Is there something special about this? |
\( K_{M}^{Car:ATP} \) |
0.000115 mol/l |
link |
Is there something special about this? |
Sfp
Ado
\[ \frac{K_{cat}^{Ado}\cdot [Ado]\cdot [Butyrate]}{K_{M}^{Ado:Butyrate} +[Butyrate]} \]
Constant |
Value |
Source |
To note |
\( K_{cat}^{Ado} \) |
0.215 1/min |
link |
Forward reaction |
\( K_{M}^{Ado:Butyraldehyde} \) |
0.0101 mol/l |
link |
Is there something special about this? |
Other Constants
This is a table of already known typical concentrations in a cell that we use in our model.
Constant |
Value |
Source |
To note |
[Acetyl-CoA] |
0.00061 mol/l |
link |
Is there something special about this? |
[Acetoacetyl-CoA] |
2.2e-05 mol/l |
link |
Is there something special about this? |
[CoA] |
0.00014 mol/l |
link |
Is there something special about this? |
[NADPH] |
00012 mol/l |
link |
Is there something special about this? |
[NADP\( ^+\)] |
2.1e-06 mol/l |
link |
Is there something special about this? |
[NADH] |
8.3e-05 mol/l |
link |
Is there something special about this? |
[NAD\( ^+\)] |
0.0026 mol/l |
link |
Is there something special about this? |
[ATP] |
0.0096 mol/l |
link |
Is there something special about this? |
[AMP] |
0.00028 mol/l |
link |
Is there something special about this? |
[H\( _2\)O] |
38.85 mol/l |
link |
Is there something special about this? |