Limonene Synthase

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Limonene synthase (LIMS) is not native to E. coli and a heterologous LIMS gene from Mentha spicata was engineered into the cell [1].

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


Reaction rate

The reaction rate for LIMS is modelled using the reversible Michaelis-Menten equation [2], 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


Parameterisation

The parameterisation of LIMS for this model was performed according to our DIPPER protocol [3]. Here, we list the thermodynamic and kinetic paramater values obtained from the literature, weights assigned and the log-normal distribution parameter values calculated.

Thermodynamic parameter values

Gibbs free energy values for LIMS are obtained from MetaCyc (EC 4.2.3.16) is -28.049988 kcal/mol [4] and Equilibrator [1]. Table 2 summarizes the ΔrG° values found for LIMS and the calculated Keq. These Keq values are given an arbitrary equal weight of 1 as the ΔrG° 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 [5]
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. [6]
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. [7]
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. [8]
Km_gpp_LIMS 1.25 NaN 16 0 LIMS isolated from Ricciocarpos natans. Kinetics measured at 32°C and pH7.0. [9]
Km_gpp_LIMS 1.8 NaN 32 0 LIMS isolated from Mentha x piperita (peppermint). Kinetics were measured at 30°C. [10]
Table 3: Turnover number values for LIMS
Parameter Value Error Weight Error type Description References
Kcat_LIMS 0.72 NaN 128 0 LIMS gene from Lavandula angustifolia was expressed in E. coli. The kinetics were measured in vitro at 30°C [5]
Kcat_LIMS 7.8 NaN 32 0 LIMS gene from Citrus sinensis (orange) was expressed in E. coli. The enzyme activities were measured in vitro at 20°C and 37°C. [6]
Kcat_LIMS 2.4 NaN 32 0 LIMS gene from Citrus sinensis (orange) was expressed in E. coli. The enzyme activities were measured in vitro at 20°C and 37°C. [6]
Kcat_LIMS 4.92 NaN 32 0 LIMS gene from Cannabis sativa L. var. 'Skunk' plants was expressed in E. coli. The kinetics were measured at 40°C. [7]

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 Kcat 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

Log-normal distribution parameters

The Mode, Confidence Interval (CI) factor, mu and sigma for each parameter distribution is calculated using our scripts as detailed in the DIPPER protocol [3].

Parameter Brenda Add-on Mode CI Factor Mu Sigma
Km_gpp_LIMS ✘ 6.8 7.6504 3.3719 1.2062
Kcat_LIMS ✘ 0.8001 2.6307 0.3424 0.7519
Km_gpp_LIMS ✔
Kcat_LIMS ✔

Log-normal distribution parameter estimation

This section can be found HERE

Simulations

Simulations performed can be found HERE.

References

  1. ↑ Alonso-Gutierrez, J., et al.(2013). "Metabolic engineering of Escherichia coli for limonene and perillyl alcohol production." Metabolic Engineering 19: 33-41.
  2. ↑ Sauro, H. M. (2011). Appendix B: List of Common Rate Laws. Enzyme Kinetics for Systems Biology. United States of America, Future Skills Software: 279-290.
  3. ↑ 3.0 3.1 Tsigkinopoulou, A., et al. (2018). "Defining informative priors for ensemble modeling in systems biology." Nature protocols 13: 2643-2663.
  4. ↑ Latendresse M. (2013). "Computing Gibbs Free Energy of Compounds and Reactions in MetaCyc."
  5. ↑ 5.0 5.1 Landmann, C., et al. (2007). "Cloning and characterization of three terpene synthases from lavender (Lavandula angustifolia)." Archives of Biochemistry and Biophysics 465: 417-429.
  6. ↑ 6.0 6.1 6.2 [Entova, S.](2013). Kinetic characterization, crystallization, and photosynthetic expression of (+)-$R-limonene synthase from C. sinensis. Department of Biochemistry. Massachusetts, Brandeis University. Master's: 55.
  7. ↑ 7.0 7.1 Günnewich, N., Page, J.E., Köllner, T.G., Degenhardt, J., & Kutchan, T.M 2007. "Functional expression and characterization of trichome-specific (-)-limonene synthase and (+)-α-pinene synthase from Cannabis sativa ". Nat. Prod. Comm. 2(3): 223-232.
  8. ↑ Lücker, J., et al. (2002). "Monoterpene biosynthesis in lemon (Citrus limon) cDNA isolation and functional analysis of four monoterpene synthases." Eur. J. Biochem. 269: 3160-3171.
  9. ↑ Adam, K.-P., et al. (1996). "Partial purification and characterization of a monoterpene cyclase, limonene synthase, from the liverwort Ricciocarpus natans." Archives of Biochemistry and Biophysics 332(2): 352-356.
  10. ↑ Rajaonarivony, J. I. M., et al. (1992). "Characterization and mechanism of (4S)-limonene synthase, a monoterpene cyclase from the glandular trichomes of peppermint (Mentha X piperita)." Archives of Biochemistry and Biophysics 296(1): 49-57.
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