Limonene Synthase

You can go back to main page of the kinetic model here.

In this model, LIMS is modelled in Escherichia coli and this model is replicating the bacterial system in vivo. As such, in vivo-like conditions such as pH of 7.5 and temperature of 30°C in E. coli is set as the ideal conditions when assigning weights to its parameter. Limonene synthase catalyses the formation of limonene and pyrophosphate from one molecule of geranyl diphosphate (GPP). The following equations show LIMS’s reaction stoichiometry and its corresponding reaction rate using the Michaelis-Menten rate law:

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

Equation Rate

The reversible Michaelis-Menten equation to model the dynamic changes of LimSynth is:

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

where :

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

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
limonene synthase	LimSynth		70.03 kDa , 72.4 kDa  ; 60kDa ; 56 kDa

Parameterisation

Calculating the Equilibrium Constant

Unlike the kinetic parameter values, thermodynamic parameter values such as for equilibrium constant (Keq) are not easily found in literature reports. However, Keq can be calculated from Gibbs Free Energy (ΔG°) using the following equation:

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

where;

Keq	Equilibrium constant
-ΔG°	Gibbs free energy change (kcal/mol)
R	Gas constant (0.0019859 kcal/K/mol)
T	Absolute temperature (298 K)

Gibbs free energy values for LIMS are obtained from MetaCyc (EC 4.2.3.16) is -28.049988 kcal/mol and Equilibrator [1]. Table 2 summarizes the Δ_rG° values found for LIMS and the calculated Keq. These Keq values are given an arbitrary equal weight of 1 as the Δ_rG° values obtained were calculated from a group contribution method and do not have any measurement conditions that would allow us to assess the Keq values according to the weighting scheme set out in (insert link here).

ΔrG°(kcal/mol)	Keq	Error (±)	Source	Weight
-28.050	3.843E+20	N/A	MetaCyc	1
-42.161 ± 2.844	8.711E+30	5.876E+29	Equilibrator	1

Kinetic Parameter Values

Assessing kinetic parameter values. Values for kinetic parameters such as for KmGPP and Kcatforward can be obtained from extensive literature searches. Our findings from literature searches of these parameters are summarised in Table 1. In addition to the parameter values, the measurement conditions such as the pH, temperature and gene source used for the kinetic evaluations are also taken into consideration. Then, in order to assess the plausibility of the parameter values collected, weights are assigned according to different weighting categories as described in Table 2. Final weight for each parameter value is calculated by taking each resulting weight from each category and multiplying it. For example, Lücker et. al. isolated limonene synthase cDNA from lemon (Citrus limon) and functionally expressed them in Escherichia coli. Enzyme assays were conducted at pH 7.0 and 30°C, and the resulting measured KmGPP is at 0.7 µM. This parameter value (KmGPP) is assigned a total weight of 32 (1x1x4x2x4=32) after assessing that:- a) this value was measured in vitro (weight=1), b) limonene synthase isolated was from lemon which is unrelated to E. coli (weight=1), c) limonene synthase measured was from the same EC (EC 4.2.3.16, weight=4), d) measurement pH was within ± 0.5 from the ideal pH of 7.5 (weight=2), and finally e) measurement temperature was at the ideal 30°C (weight=4). The breakdown of weights assigned to each kinetic parameter value found for limonene synthase is shown in Table below.

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

Table 2: Summary of kinetic parameter values retrieved from literature for LIMS

Name	Value	Units	Remarks-References
KmGPP	6.8	µM	This study has isolated and characterised a (-)-limonene synthase recombinant encoded by Cannabis sativa L. cv. ‘Skunk’ trichome mRNA. pH optimum was determined at pH 6.5 and a temperature optimum at 40°C. (Günnewich,, N., 2007)
Kcatforward	0.082	s-1
KmGPP	47.4 ± 3.8	µM	In this study,limonene synthase were cloned from lavender (Lavandula angustifolia) leaves and flowers. Temperature was determined at 30°C and pH at 7.0. (Landmann,C 2007)
Kcatforward	0.012	s-1
KmGPP	6.7	µM	This study reports the kinetic evaluation the native form of LIMS from Mentha spicata. Reaction mixtures were determined at pH 7.0 and temperature of 30°C. Kinetic constants are averaged data sets of triplicate analyses (n=3). (Williams 1998)
Kcatforward	0.024	s-1
Kcatforward	0.3	s-1	In this study, the authors have isolated and purified limonene synthase from both peppermint (Mentha x piperita) and spearmint (Mentha spicata). Enzyme activity was determined at pH 7.0m and temperature 30°C. (Alonso 1992)
KmGPP	1.25	µM	In this study, limonene synthase is characterised and extracted from liverwort (Ricciocarpus natans). The enzyme assay was conducted at pH 6.5 and at temperature of 32°C. (Adam 1996)
KmGPP	0.7	µM	This study isolated limonene synthase cDNA from lemon (Citrus limon) and functionally expressed them in Escherichia coli. Enzyme assays were conducted at pH 7.0 and 30°C. (Lucker 2002)
KmGPP	1.8 ± 0.3	µM	Limonene synthase from purified preparation of glandular trichome seceratory cell clusters from peppermint (Mentha x piperita). Enzyme assays were carried out in buffer pH 7.0, and incubated at 30°C. Data reported are the averages of three independent assays (n=3). (Rajaonarivony 1992)

Vmax values

Vmax	Unit	Directionality	Organism	Organism	References
0.08	µmol/min/mg	forward	Cannabis sativa L.
0.12 ± 0.01	µmol/min/mg	forward	Cannabis sativa
0.4748	µmol/min/mg	forward	Citrus limon		References
0.53	µM/min	forward	Citrus sinensis	200µM GPP, 20°C, [E]: 0.07µM, pH7.5
0.64	µM/min	forward	Citrus sinensis	200µM GPP, 37°C, [E]: 0.26µM, pH7.5
19	µmol/h/mg	forward	Mentha x piperita & Mentha spicata	Maximum specific activity, 1-10µg protein per mixture, pH &.0, 30°C	References

Kcat values

Parameter	Direction	Substrate	Value	Unit	Method	M_w	Organism	O_w	Expression_vector	E_w	Enzyme	En_w	pH	P_w	Temperature	T_w	Total_weight	Description	Reference
Kcat	Forward	GPP	0.0004	1/s	in vitro (+2)	2	Unrelated (+0)	0	E.coli (+4)	4	Identical (+4)	4	7.0 (+4)	4	different temperature (+0)	0	128	Protein from Mentha sp, expressed in E.coli and truncated (R59), pH7.0, 1-50 mg [E], 25 µM [GPP], limonene produced 94%, 2% myrcene, pinene	Williams1998
Kcat	Forward	GPP	0.0004	1/s	in vitro (+2)	2	Unrelated (+0)	0	E.coli (+4)	4	Identical (+4)	4	7.0 (+4)	4	different temperature (+0)	0	128	Protein from Mentha sp. expressed in E.coli , truncated R58P59, pH7.0, 1-50 mg [E], 25 µM [GPP], limonene produced 94%, 2% myrcene, pinene	Williams1998
Kcat	Forward	GPP	0.0004	1/s	in vitro (+2)	2	Unrelated (+0)	0	E.coli (+4)	4	Identical (+4)	4	7.0 (+4)	4	different temperature (+0)	0	128	Protein from Mentha sp. expressed in E.coli , truncated R58A59, pH7.0, 1-50 mg [E], 25 µM [GPP], limonene produced 94%, 2% myrcene, pinene	Williams1998
Kcat	Forward	GPP	0.0004	1/s	in vitro (+2)	2	Unrelated (+0)	0	E.coli (+4)	4	Identical (+4)	4	7.0 (+4)	4	different temperature (+0)	0	128	Protein from Mentha sp. expressed in E.coli , S60, pH7.0, 1-50 mg [E], 25 µM [GPP], limonene produced 94%, 2% myrcene, pinene	Williams1998
Kcat	Forward	GPP	0.002	1/s	in vitro (+2)	2	Unrelated (+0)	0	E.coli (+4)	4	Identical (+4)	4	7.0 (+4)	4	different temperature (+0)	0	128	Protein from Mentha sp. expressed in E.coli preprotein, pH7.0, 1-50 mg [E], 25 µM [GPP], limonene produced 94%, 2% myrcene, pinene	Williams1998
Kcat	Forward	GPP	0.0024	1/s	in vitro (+2)	2	Unrelated (+0)	0	E.coli (+4)	4	Identical (+4)	4	7.0 (+4)	4	different temperature (+0)	0	128	Protein from Mentha sp. expressed in E.coli wt, pH7.0, 1-50 mg [E], 25 µM [GPP], limonene produced 94%, 2% myrcene, pinene	Williams1998
Kcat	Forward	GPP	0.0034	1/s	in vitro (+2)	2	Unrelated (+0)	0	E.coli (+4)	4	Identical (+4)	4	7.0 (+4)	4	different temperature (+0)	0	128	Protein from Mentha sp. expressed in E.coli E57, pH7.0, 1-50 mg [E], 25 µM [GPP], limonene produced 94%, 2% myrcene, pinene	Williams1998
Kcat	Forward	GPP	0.0036	1/s	in vitro	2	Unrelated (+0)	0	E.coli (+4)	4	Identical (+4)	4	7.0 (+4)	4	different temperature (+0)	0	128	Protein from Mentha sp. expressed in E.coli Q54, pH7.0, 1-50 mg [E], 25 µM [GPP], limonene produced 94%, 2% myrcene, pinene	Williams1998
Kcat	Forward	GPP	0.0037	1/s	in vitro	2	Unrelated (+0)	0	E.coli	4	Identical (+4)	4	7.0 (+4)	4	different temperature (+0)	0	128	Protein from Mentha sp. expressed in E.coli R58, pH7.0, 1-50 mg [E], 25 µM [GPP], limonene produced 94%, 2% myrcene, pinene	Williams1998
Kcat	Forward	GPP	0.02	1/s	in vitro	2	Unrelated	0	E.coli	4	Identical (+4)	4	7.0 (+4)	4	different temperature (+0)	0	128	Protein from Mentha sp. expressed in E.coli recombinant preprotein , pH7.0, 1-50 mg [E], 25 µM [GPP], limonene produced 94%, 2% myrcene, pinene	Williams1998
Kcat	Forward	GPP	0.04	1/s	in vitro	2	Unrelated	0	E.coli	4	Identical (+4)	4	close range (+2)	2	37°C (+4)	4	256	Citrus sinensis, expressed in E.coli 200µM GPP, 37°C, [E]: 0.26µM, pH7.5	Entova2013
Kcat	Forward	GPP	0.082	1/s	in vitro	2	Unrelated	0	E.coli	4	Identical (+4)	4	close range (+2)	2	36°C - 40°C (+2)	2	128	Cannabis sativa L., expressed in E.coli,CsTPS1, pH6.5, 40°C, 1.25 mg [LimSynth] per 500ml assay mixture, 10mM [GPP]	Gunnewich2008
Kcat	Forward	GPP	0.09	1/s	in vitro	2	Unrelated	0	E.coli	4	Identical (+4)	4	close range (+2)	2	36°C - 40°C (+2)	2	128	Cannabis sativa L., expressed in E.coli,Km of 6.25 ± 0.41 µM, pH 6.5, 40°C, [GPP] 0.5 - 25.0 µM used for kinetic parameter determination, kcat 0.09 /s	Gunnewich2008
Kcat	Forward	GPP	0.13	1/s	in vitro	2	Unrelated	0	E.coli	4	Identical (+4)	4	close range (+2)	2	36°C - 40°C (+2)	2	128	Cannabis sativa L., expressed in E.coli,Km of 6.25 ± 0.41 µM, pH 6.5, 40°C, [GPP] 0.5 - 25.0 µM used for kinetic parameter determination, kcat 0.09 /s	Gunnewich2008
Kcat	Forward	GPP	0.13	1/s	in vitro	2	Unrelated	0	E.coli	4	Identical (+4)	4	close range (+2)	2	different temperature (+0)	0	128	Citrus sinensis, expressed in E.coli 200µM GPP, 20°C, [E]: 0.07 mM, pH7.5	Entova2013
Kcat	Forward	GPP	0.3	1/s	in vitro	2	Unrelated	0	E.coli	4	Identical (+4)	4	7.0 (+4)	4	different temperature (+0)	0	128	Mentha piperita & Mentha spicata, expressed in E.coli , pH7.0, 30°C, enzyme assay, 1 -10 mg protein per mixture	Alonso1992
Kcat	Forward	GPP	0.000039	1/s	in vitro	2	Unrelated	0	E.coli	4	Identical (+4)	4	7.0 (+4)	4	37°C (+4)	4	512	Citrus sinensis, expressed in E.coli40mM GPP, 37°C, [E]: 0.3 mM, pH7.0 (check units)	Olsen2011

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

Parameter estimation

This section can be found HERE

Simulations

Simulations performed can be found HERE.