Limonene Synthase

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Reaction catalysed

$geranyl diphosphate \rightleftharpoons (−)-(4S)-limonene + diphosphate$

Metabolite Background Information

Long metabolite names are abbreviated in the model for clarity and standard identification purposes.

Metabolite	Abbreviation	Chemical Formula	Molar mass (g/mol)	ChEBI	ChEMBL	PubChem
geranyl diphosphate	GPP	C10H20O7P2	314.209	17211	41432	445995
(-)-4S-limonene	Limonene	C10H16	136.24	15384	449062	22311 or 439250
diphosphate	PP	O7P2	173.94			644102

Equation Rate

$V_\mathrm{LimSynth} = Vmax_\mathrm{forward} * \cfrac {\cfrac{[GPP]}{Km_\mathrm{GPP}} * \left ( 1 - \cfrac {[Limonene]*[PP]}{[GPP]*K_\mathrm{eq}} \right )}{1 + \cfrac {[GPP]}{Km_\mathrm{GPP}} + \cfrac {[Limonene]}{Km_\mathrm{Limonene}} + \cfrac {[PP]}{Km_\mathrm{PP}} + \cfrac {[Limonene]*[PP]}{Km_\mathrm{Limonene}*Km_\mathrm{PP}}}$

Parameter	Description	Reference
VLimSynth	Reaction rate for Limonene Synthase	ref
Vmaxforward	Maximum reaction rate towards the production of limonene	ref
KmGPP	Michaelis-Menten constant for GPP	ref
KmLimonene	Michaelis-Menten constant for Limonene	ref
KmPP	Michaelis-Menten constant for PP	ref
Keq	Equilibrium constant	ref
[GPP]	GPP concentration	ref
[Limonene]	Limonene concentration	ref
[PP]	PP concentration	ref

Strategies for estimating the kinetic parameter values

Calculating the Equilibrium Constant

The equilibrium constant can be calculated using the Van't Hoff Isotherm equation:

$K_\mathrm{eq} = exp \left ( \cfrac {-ΔG^{°'}}{RT} \right )$

Failed to parse (Cannot store math image on filesystem.): = exp \left ( \cfrac {-(- 117.36396 \text { kJmol}^{-1})}{ (8.31 \text{ JK}^{-1} \text { mol}^{-1} * 289 K} \right )

Failed to parse (Cannot store math image on filesystem.): = exp \left ( \cfrac { + 117.36396 \text { kJmol}^{-1} }{ 2401.59 \text{ JK}^{-1}\text { mol}^{-1} }\right)

Failed to parse (Cannot store math image on filesystem.): = exp \left ( \cfrac{ 117.364 * 10^3 \text { Jmol}^{-1}}{2401.59 \text{ JK}^{-1}\text { mol}^{-1}} \right)

Failed to parse (Cannot store math image on filesystem.): =exp \left ( 48.8693 \right )

Failed to parse (Cannot store math image on filesystem.): = 1.6736 * 10^{21}

where;

Keq	Equilibrium constant
-ΔG°	Gibbs free energy change. For Limonene Synthase it is -117.364 kJmol-1
R	Gas constant with a value of 8.31 JK-1mol-1
T	Temperature which is always expressed in kelvin

Standard Gibbs Free energy

Standard Gibbs Free energy for Limonene Synthase from MetaCyc (EC 4.2.3.16) is -28.049988 kcal/mol .

SI derived unit for Gibbs free energy is Joules per mol (J mol^-1). 1 kJ·mol⁻¹ is equal to 0.239 kcal·mol⁻¹.

Therefore, the Gibbs free energy for Limonene synthase in kJ mol^-1 is:

Failed to parse (Cannot store math image on filesystem.): \cfrac {1}{0.239 kcal.mol^-1} * -28.049988 kcal.mol^-1

Failed to parse (Cannot store math image on filesystem.): = -117.36396 kJmol^-1

Extracting Information from Limonene Production Rates

Amount produced (mg/L)	Time (H)	Organism	Description	Reaction Flux (µM/s)
5	24	Escherichia coli	Possible reason for the low limonene production might due to the insufficient supply of IPP and DMAPP .	0.0255
335	48	Escherichia coli	Engineered E.coli in which heterologous MVA pathway was installed .	0.8537
35.8	48	Escherichia coli	E.coli was engineered to express GPPS, LS, DXS, and IDI .	0.0912
4.87	48	Escherichia coli	This was the initial titer. The study established a limonene biosynthesis pathway in E.coli using four different polycistronic operons based on 3 vectors with varied expression strength .	0.0124
17.4	48	Escherichia coli	Using a plasmid with DXS and IDI over expressed .	0.0445
430	72	Escherichia coli		0.7306

Published Kinetic Parameter Values

Km (mM)	Vmax	Kcat (s-1)	Kcat/Km	Organism	Description
0.00125	-	-	-	Ricciocarpos natans	GPP -> Limonene
0.0018	-	-	-	Mentha piperita	GPP -> Limonene
0.00625	0.08 µmol/min/mg	0.08	1.5	Cannabis sativa L.	GPP -> Limonene
0.00496	0.13 µmol/min/mg	0.14	2.9	Cannabis sativa L.	GPP -> Limonene
0.0031	0.4748 µmol/min/mg	-	-	Citrus limon	GPP -> Limonene
0.016	-	0.02	-	Escherichia coli	GPP -> Limonene
0.0068	-	0.082	-	Cannabis sativa L.	GPP -> Limonene
0.0067	-	0.081	-	Cannabis sativa L.	GPP -> Limonene

Simulations

I'll insert table of parameter values used in the simulation here.