Limonene Synthase

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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 reaction rate for LIMS is modelled using the reversible Michaelis-Menten equation, and is shown below:

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

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

Table 2: Km for GPP values for LIMS

Parameter	Value	Error	Weight	Error type	Description	References
Km_gpp_LIMS	47.4	3.8	128	0	LIMS gene from Lavandula angustifolia was expressed in E. coli. The kinetics were measured in vitro at 30°C
Km_gpp_LIMS	130	NaN	32	0	LIMS gene from Citrus sinensis (orange) was expressed in E. coli. The Km was measured in vitro at 20°C.	Entova2013
Km_gpp_LIMS	6.8	NaN	32	0	LIMS gene from Cannabis sativa L. var. 'Skunk' plants was expressed in E. coli. The kinetics were measured at 40°C.
Km_gpp_LIMS	0.7	NaN	128	0	LIMS gene from Citrus limon (lemon) was expressed in E. col. Kinetics were measured in vitro at 30°C.	Lucker2002
Km_gpp_LIMS	1.25	NaN	16	0	LIMS isolated from Ricciocarpos natans. Kinetics measured at 32°C and pH7.0.
Km_gpp_LIMS	1.8	NaN	32	0	LIMS isolated from Mentha x piperita (peppermint). Kinetics were measured at 30°C.	Rajaonarivony1992

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.