Team:Aalto-Helsinki/Kinetics

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 the maximum speed of the enzyme and \( K_{cat} \) ... (how calculated from specific activity!). 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

Vf/Vr: 22,3. Source: Molecular and catalytic properties of the acetoacetyl-coenzyme A thiolase of Escherichia coli; Archives of Biochemistry and Biophysics Volume 176, Issue 1, September 1976, Pages 159–170

\[ \frac{K_{cat}^{AtoB} \cdot [AtoB] \cdot [Acetyl\text{-}CoA]^2}{[Acetyl\text{-}CoA]^2+2\cdot K_{M}^{AtoB:Acetyl\text{-}CoA}\cdot [Acetyl\text{-}CoA]} \]

Constant

Value

Source

To note

\( K_{cat}^{AtoB} \)

10653 1/min

needs checking

Forward reaction

\( K_{M}^{AtoB:Acetyl\text{-}CoA} \)

0.00047 mol/l

Molecular and catalytic properties of the acetoacetyl-coenzyme A thiolase of Escherichia coli; Archives of Biochemistry and Biophysics Volume 176, Issue 1, September 1976, Pages 159–170

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

needs to be checked

Forward reaction

\( K_{cat2}^{FadB2} \)

0.723 1/min

needs to be checked

Reverse reaction

\( K_{M}^{FadB2:Acetoacetyl\text{-}CoA} \)

65.6 mol/l

needs to be checked

Forward reaction

\( K_{M}^{FadB2:NADPH} \)

50 mol/l

needs to be checked

Forward reaction

\( K_{M}^{FadB2:3\text{-}Hydroxybutyryl\text{-}CoA} \)

43.5 mol/l

needs to be checked

Reverse reaction

\( K_{M}^{FadB2:NADP^+} \)

29.5 mol/l

needs to be checked

Reverse reaction

Hdb

Acetoacetyl-CoA + NADPH + H\(^+\) \(\rightarrow\) 3-Hydroxybutyryl-CoA + NADP\(^+\)

Species is Clostridium acetobutylicum, but Clostridium Kluyveri ought to be close enough for comparison.

The specific activity of the 3-hydroxybutyryl-CoA dehydrogenase (forward) as measured in the direction of acetoacetyl-CoA reduction was 478.6 U/mg protein. The rate of the oxidation reaction (reverse) proceeded with 36.6 U / mg protein. Source: Purification and Properties of NADP-Dependent L( +)-3-Hydroxybutyryl-CoA Dehydrogenase from Clostridiurn kluyveri; Eur. J. Biochem. 32,51-56 (1973)

\[ \frac{K_{cat}^{Hdb}\cdot [Hbd] \cdot [Acetoacetyl\text{-}CoA]\cdot [NADPH]}{[Acetoacetyl\text{-}CoA]\cdot [NADPH] + K_{M}^{Hdb:NADPH}\cdot [Acetoacetyl\text{-}CoA]+K_{M}^{Hdb:Acetoacetyl\text{-}CoA}\cdot [NADPH]} \]

Constant

Value

Source

To note

\( K_{cat}^{Hdb} \)

336.4 1/min

Purification and Properties of NADP-Dependent
L( +)-3-Hydroxybutyryl-CoA Dehydrogenase from Clostridiurn kluyveri; Eur. J. Biochem. 32,51-56 (1973)

Forward reaction

\( K_{M}^{Hdb:Acetoacetyl\text{-}CoA} \)

5e-5 mol/l

Purification and Properties of NADP-Dependent
L( +)-3-Hydroxybutyryl-CoA Dehydrogenase from Clostridiurn kluyveri; Eur. J. Biochem. 32,51-56 (1973)

Is there something special about this?

\( K_{M}^{Hdb:NADPH} \)

7e-5 mol/l

Purification and Properties of NADP-Dependent
L( +)-3-Hydroxybutyryl-CoA Dehydrogenase from Clostridiurn kluyveri; Eur. J. Biochem. 32,51-56 (1973)

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

needs checking

Forward reaction

\( K_{M}^{Crt:3\text{-}Hydroxybutyryl\text{-}CoA} \)

3e-5 mol/l

needs checking

Is there something special about this?

Ter

Crotonyl-CoA + NADH + H\( ^+\) \(\rightarrow\) Butyryl-CoA + NAD\( ^+\)

an ordered bi-bi reaction mechanism with NADH binding first. Source: Biochemical and Structural Characterization of the trans-Enoyl-CoA Reductase from Treponema denticola; Biochemistry 2012, 51, 6827−6837

\[ \frac{K_{cat}^{Ter}\cdot [Ter] \cdot [Crotonyl\text{-}CoA]\cdot [NADH]}{[Crotonyl\text{-}CoA]\cdot [NADH] + K_{M}^{Ter:NADH}\cdot [Crotonyl\text{-}CoA]+K_{M}^{Ter:Crotonyl\text{-}CoA}\cdot [NADH] + K_{I}^{Ter:Butyryl\text{-}CoA}\cdot K_{M}^{Ter:NADH}} \]

Constant

Value

Source

To note

\( K_{cat}^{Ter} \)

1881.6 1/min

needs checking

Forward reaction

\( K_{M}^{Ter:Crotonyl\text{-}CoA} \)

2.7e-06 mol/l

70 µmol/l Biochemical and Structural Characterization of the trans-Enoyl-CoA Reductase from Treponema denticola; Biochemistry 2012, 51, 6827−6837

Is there something special about this?

\( K_{M}^{Ter:NADH} \)

5.2e-06 mol/l

Biochemical and Structural Characterization of the trans-Enoyl-CoA Reductase from Treponema denticola; Biochemistry 2012, 51, 6827−6837

Is there something special about this?

\( K_{I}^{Ter:Butyryl\text{-}CoA} \)

1.98e-07 mol/l

needs checking

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

Divergence of Function in the Hot Dog Fold Enzyme Superfamily: The Bacterial Thioesterase YciA; Biochemistry 2008, 47, 2789–2796

Forward reaction

\( K_{M}^{YciA:Butyryl\text{-}CoA} \)

3.5e-06 mol/l

Divergence of Function in the Hot Dog Fold Enzyme Superfamily: The Bacterial Thioesterase YciA; Biochemistry 2008, 47, 2789–2796

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

needs checking

Forward reaction

\( K_{M}^{Car:Butyrate} \)

0.013 mol/l

needs checking

Is there something special about this?

\( K_{M}^{Car:NADPH} \)

4.8e-05 mol/l

needs checking

Is there something special about this?

\( K_{M}^{Car:ATP} \)

0.000115 mol/l

needs checking

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

needs checking

Forward reaction

\( K_{M}^{Ado:Butyraldehyde} \)

0.0101 mol/l

needs checking

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

needs checking

Is there something special about this?

[Acetoacetyl-CoA]

2.2e-05 mol/l

needs checking

Is there something special about this?

[CoA]

0.00014 mol/l

needs checking

Is there something special about this?

[NADPH]

00012 mol/l

needs checking

Is there something special about this?

[NADP\( ^+\)]

2.1e-06 mol/l

needs checking

Is there something special about this?

[NADH]

8.3e-05 mol/l

needs checking

Is there something special about this?

[NAD\( ^+\)]

0.0026 mol/l

needs checking

Is there something special about this?

[ATP]

0.0096 mol/l

needs checking

Is there something special about this?

[AMP]

0.00028 mol/l

needs checking

Is there something special about this?

[H\( _2\)O]

38.85 mol/l

needs checking

Is there something special about this?