Limonene Synthase

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Enzyme	Pathway	Keq	Kcat	VmaxF	KmSub1	KmSub2	[Sub1]	[Sub2]	VmaxR	KmProd1	KmProd2	[Prod1]	[Prod2]

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

Strategies for estimating the kinetic parameter values

Calculating the Equilibrium Constant

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

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

Kinetic Parameter Values

Values for the kinetic parameter required to simulate this model can be obtained from published and unpublished literature.

A more detailed descriptions of the values listed above can be found here , where I've linked and highlighted where these data came from.

Km Values

Km (mM)	Unit	Substrate / Product	Directionality	Organism	References
0.00125	mM	GPP	forward	Ricciocarpos natans	Ref
0.0018	mM	GPP	forward	Mentha piperita	Ref
0.00625	mM	GPP	forward	Cannabis sativa L.	Ref
0.00496	mM	GPP	forward	Cannabis sativa L.	Ref
0.0031	mM	GPP	forward	Citrus limon	ref
0.016	mM	GPP	forward	Escherichia coli	Ref
0.0068	mM	GPP	forward	Cannabis sativa L.	Ref
0.0067	mM	GPP	forward	Cannabis sativa L.	Ref

μ :-5.05354 , σ : 0.49474

Vmax values

Vmax	Unit	Directionality	Organism	References
0.08	µmol/min/mg	forward	Cannabis sativa L.	References
0.13	µmol/min/mg	forward	Cannabis sativa L.	References
0.4748	µmol/min/mg	forward	Citrus limon	References
Vmax	Unit	Directionality	Organism	References
Vmax	Unit	Directionality	Organism	References
Vmax	Unit	Directionality	Organism	References

Kcat values

Kcat	Unit	Organism	Reference
0.3	s-1	Mentha piperita & Mentha spicata	Alonso 1992
0.08	s-1	Cannabis sativa L.	Reference
0.14	s-1	Cannabis sativa L.	Reference
0.02	s-1	E. coli	Reference
0.082	s-1	Cannabis sativa L.	Reference
0.081	s-1	Cannabis sativa L.	Reference
Kcat	Unit	Organism	Reference
Kcat	Unit	Organism	Reference
Kcat	Unit	Organism	Reference

Extracting Information from Limonene Production Rates

The production rates would reflect on the flux for this enzyme, and this would provide provide the insights on the Vmax of this enzyme.

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

Simulations

these are mock simulation results