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:

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

where :

Parameter	Description	Units
VLimSynth	Reaction rate for Limonene Synthase	μM/min
KcatLIMS	Turnover number for limonene synthase	min-1
KmGPP	Michaelis-Menten constant for GPP	μM
KmLimonene	Michaelis-Menten constant for Limonene	μM
KmPP	Michaelis-Menten constant for PP	μM
Keq	Equilibrium constant	dimensionless
[GPP]	GPP concentration	μM
[Limonene]	Limonene concentration	μM
[PP]	PP concentration	μM

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

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.
forward	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)
forward	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)

BRENDA data

To further enrich the kinetic parameter values for LIMS, parameter values from EC 4 to EC 4.2.3.* that can be obtained from BRENDA is downloaded. These BRENDA data is integrated with the rest of the kinetic parameter values using our ‘BRENDA Add-on’ protocol. In the BRENDA Add-On protocol, we’ve specified six different ‘EC cases’ that are arranged in order of rank. These EC cases are essentially six different datasets of parameter values downloaded from BRENDA that are filtered according to the specific enzyme class and organism of interest. For this case study example, six different ‘EC case’ datasets were downloaded from BRENDA each for Km and Kcat parameters (Tables below).

Table 7: Input matrix for Km values from BRENDA for EC 4.2.3.16

Parameter value and uncertainty is in µM. Each row represents EC case 2 – 6 respectively. EC case 1 is discarded as number of values obtained were <50. .

*Uncertainty values in this table correspond to the standard deviation calculated from SEM reported in literature

** Uncertainty type is multiplicative, therefore ‘1’ is defined.

Parameter value	Uncertainty*	Weight	Uncertainty type**
6.80	14.9566	11.9024	1
49	69.0555	7.4390	1
121	36.1126	2.9756	1
500	36.9586	1.4878	1
300	23.8770	0.5951	1

Input matrix for K_cat values from BRENDA for EC 4.2.3.16

Parameter value and uncertainty is in µM. Each row represents EC case 2 – 6 respectively. EC case 1 is discarded as number of values obtained were <50. .

*Uncertainty values in this table correspond to the standard deviation calculated from SEM reported in literature

** Uncertainty type is multiplicative, therefore ‘1’ is defined.

Parameter value	Uncertainty*	Weight	Uncertainty type**
2.040	38.2439	9.5610	1
17.400	109.1960	5.9756	1
200.698	177.0428	2.3902	1
192.000	44.6715	1.1951	1
168.000	62.4126	0.4780	1

Parameter estimation

This section can be found HERE

Simulations

Simulations performed can be found HERE.