Tittlke

Supplemental Data S1

Title:Mathematical modeling-guided evaluation of the biochemical, developmental, environmental and genotypic determinants of essential oil composition and yield in peppermint leaves

Authors:Rigoberto Rios-Estepa, Iris Lange, James M. Lee, and B. Markus Lange

INDEX

Page

1. Estimation of enzyme concentrations in individual glandular trichomes

1

2. Estimating developmental dynamics of glandular trichome density

6

3. Kinetic properties of enzymes involved in peppermint monoterpene biosynthesis

7

4. Generating a system of ordinary differential equations to describe kinetic properties of enzymes 9

5. Calculating monoterpenoid essential oil yields for individual glandular trichomes

11

6. Estimating changes in enzyme concentrations based on measurements of gene expression levels12

7. Kinetic model for peppermint monoterpene biosynthesis

14

8. Statistical analysis of goodness of fit between simulated and measured monoterpene profiles26

1.Estimation of enzyme concentrations in individual glandular trichomes

Peppermint glandular trichomes harbor three different cells types termed basal, stalk and secretory cells (Scheme 1). Among these cell types the secretory cells (eight-celled disk highlighted in Scheme 1; only four cells are visible in cross section) are responsible for the biosynthesis of monoterpenes in peppermint. To allow the calculation of enzyme concentrations in the secretory cells (a prerequisite for building Michaelis-Menten-based kinetic models), the volume of these specialized cells had to be determined.

Scheme 1

Enzyme activity

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µ

mol/h/leaf]

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Leaf age [d]

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Enzyme activity

[

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mol/h/leaf]

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1.1Determining the volume of secretory cell clusters

The shape of the secretory cell cluster was approximated by a frustum of a cone. The height of the frustum and the relevant radii were determined experimentally by analyzing 20 microscopic images of peppermint leaf cross sections (average values are given below). The volume of the secretory cell cluster was thus calculated as

V(secretory cell cluster) = 1/3 π h (R2 + R r + r2) = 2.38 x 10-5 µL

where

h = height of frustum = 15 µm

r = radius of frustum at narrower end = 14 µm

R = radius of frustum at wider end = 30 µm (diameter is 60 µm as indicated in Scheme 1)

The volume of an individual secretory cell was obtained as 1/8 of the volume of the entire secretory cell cluster:

V(secretory cell) = 2.74 x 10-5 µL x 1/8 = 2.98 x 10-6 µL

1.2Estimating the volume desities of subcellular compartments

Enzymes involved in peppermint monoterpene biosynthesis are localized to specific subcellular compartment. This means that for the purpose of developing a model, the actual concentration in the appropriate compartment needs to be determined. The volumes of organelles within a secretory cell were estimated by two different approaches using ImageJ software (http://rsb.info.nih.gov/ij). The percentage of micrograph area (volume density) covered by leucoplasts and mitochondria was directly calculated by encircling organelles with a calibrated measuring tool. Such direct measurements using the ImageJ drawing tool were feasible for larger organelles, but were impractical for the tubular smooth ER, which consists of numerous interconnected tubes with narrow diameters. The volume densities of plastids, mitochondria, ER, vacuoles and cytosol were also determined by randomly superimposing a stereological grid overlay on gland cell micrographs and by counting the number of intercepts these organelles made with test points. The grid overlay plug-in for ImageJ was obtained at http://rsb.info.nih.gov/ij/plugins/grid.html. The test points consisted of the intersections of horizontal and vertical lines (the corners of grid squares) separated by spacing representing 1 µm on the micrographs.

Representative micrographs of secretory cells from six different secretory-phase peltate glandular trichomes were used for the morphometric measurements. These were chosen to include both apical and basal regions of gland cells, since there is some polarity in the distribution of organelles [3]. All specimens were preserved by high-pressure freezing and freeze-substitution in order to ensure good preservation of gland cell ultrastructure. However, this method leads to an extraction of low molecular weight lipids during the freeze-substitution process, so that stereological estimates of volume density for vacuolar and cytoplasmic monoterpene droplets could not be obtained.

The directly determined volumes for plastids and mitochondria were very similar to those obtained with volume densities calculations from test-point counts, confirming the quality of our stereological estimates. The average volume density for leucoplasts was 13.3 % area (directly measured) and 13.9 % (stereological test-point intercepts). The difference between these values (0.6 %) is smaller than the standard deviation between leucoplast volume densities for the six individual glandular trichomes (σVd = 3.25 directly measured; σVd = 4.02 when determined using stereological methods). The difference between the estimates for the mitochondrial volumes based on these methods (1.0 %) is slightly larger than the standard deviations between individual glandular trichomes (σVd = 0.6 directly measured; σVd = 0.8 when determined using stereological methods).

Table 1. Volume densities of subcellular compartments in peppermint glandular trichomes.

Organelle

Fraction of cross-sectional area [%]

σVd

Estimated volume per secretory cell

[µL]

Average diameter

[µm]

σdi

Surface area per secretory cell [µm2]

Leucoplasts

13.9

4.02

0.41x 10-6

n.m.

---

---

Mitochondria

4.4

0.6

0.13 x 10-6

0.47 (n=95)

0.11

1.66 x 103

ER

36.5

3.5

1.07x 10-6

0.07 (n=265)

0.04

1.53x 104

Vacuoles

16.2

4.3

0.48 x 10-6

n.m.

---

---

Cytoplasm

20.4

3.1

0.60x 10-6

n.m.

---

---

Other

8.6

---

---

---

---

---

Definitions: σVd, standard deviation of volume density; σdi, standard deviation of average diameter.

The number of point counts required to obtain accurate volume densities were calculated according to published methods (Weibel (1979) in Stereological Methods, Vol 1, Practical Methods for Biological Morphometry, ed Weibel ER (Academic Press, London), 63–100). The required number of point counts (Pc) is proportional to the standard error and is reduced with larger organelle volume density (Vva) and with a larger number of replicate specimens (m) by the equation

Pc = (tα2/(m d2)) ((1-Vva)/Vva))

where

d = Confidence interval (standard error of the mean)

m = Number of replicates

tα = Acceptable error probability

VVa = Organelle volume density

For example, the required number of point counts (per glandular trichome) to obtain a 95 % probability for accuracy within a 10 % confidence interval would be 409.5 (total of 2457 counts) for leucoplasts. Our actual count consisted of 2,266 test-point counts with an average of 378 counts per specimen (with a range of 233 to 476), which results in estimated confidence intervals at the 95% probability level of 10.4 % for leucoplasts, 17.6 % for mitochondria, 9.6 % for vacuoles, and 5.5 % for ER. We also calculated the total surface area of mitochondria and ER within secretory cells by assuming that mitochondria are spherical and the smooth ER consists of narrow cylinders.

1.3Estimating maximum enzyme concentrations in secretory phase glandular trichomes

The laboratory of Rodney Croteau at Washington State University succeeded in cloning the genes corresponding to all enzymes directly involved in the p-menthane pathway of monoterpene biosynthesis in peppermint. Individual genes were expressed in appropriate heterologous expression vectors. The corresponding recombinant enzymes were purified to apparent homogeneity and used to generate highly specific antibodies. Enzyme concentrations were determined by Western Blotting with enzyme extracts obtained at the time of the highest biosynthetic activity. The subcellular localization of monoterpene biosynthetic enzymes was determined by immunocytochemistry with the same antibodies. An overview of these studies is provided in a recent review article (Croteau et al. (2005) Naturwissenschaften 92: 562-577).

Table 2. Maximum concentrations of monoterpene biosynthetic enzymes in peppermint secretory cells.

_______________________________________________________________________________________

Enzyme

Reference

Concentration in

secretory cells [µM]

_______________________________________________________________________________________

Geranyl diphosphate synthase

Turner and Croteau (2004) Plant Physiol. 136: 4215

0.030000

(-)-Limonene synthase

Turner et al. (1999) Plant Physiol. 120: 879

0.017000

(-)-Limonene 3-hydroxylase

Turner and Croteau (2004) Plant Physiol. 136: 4215

0.003000

(-)-trans-Isopiperitenol dehydrogenaseTurner and Croteau (2004) Plant Physiol. 136: 4215

0.900000

(-)-Isopiperitenone reductase

Turner and Croteau, unpublished data

0.340000

(+)-cis-Isopulegone isomerase

Turner and Croteau, unpublished data

0.340000

(+)-Menthofuran synthase

Bertea et al. (2001) Arch. Biochem. Biophys. 390: 279 0.000070

(+)-Pulegone reductase

Turner and Croteau (2004) Plant Physiol. 136: 4215

0.001500

(-)-Menthone:(-)-menthol reductaseTurner and Croteau, unpublished data

0.001100

(-)-Menthone:(+)-neomenthol reductaseTurner and Croteau, unpublished data

0.000011

_______________________________________________________________________________________

1.4Developmental patterns of monoterpene biosynthetic enzyme activities

For the majority of kinetic mathematical models it is assumed that the amounts of biosynthetic enzymes remain constant for the duration of the experimental period. In peppermint glandular trichomes, the biosynthesis of monterpenes involves dynamic changes in the activities of biosynthetic enzymes (Gershenzon et al. (2000) Plant Physiol. 122: 205-214; McConkey et al. (2000) Plant Physiol. 122: 215-224). Genes and enzymes involved in The maximum amount of each enzyme present at the peak of monoterpene biosynthesis (15 d for most enzymes; 20 d for (-)-menthone:menthol reductase) was determined based on immunochemical data as described in 1.3. We thus used the available experimental data on developmental changes in biosynthetic enzyme activities to approximate changes in enzyme amounts with a Gaussian function:

A) Experimental enzyme activity data

B) Example of a Gaussian function to approximate enzyme activity data

Table 6. Extrapolation of protein levels from experimentally determined gene expression levels.

Enzyme WT - GH^WT - LL

Z=100; W=0.05; GN(max)=10151; S0=1900Z=1500; W=0.05; GN(max)=7004; S0=950

Gene Exp.Strd. [Enz] in theGene Exp.Protein Exp.[Enz] in theGene Exp.Protein Exp.[Enz] in theGene Exp.Protein Exp.[Enz] in the

LevelErrormodel [

µ

M]*vs. WT-GHvs. WT-GHmodel [

µ

M]vs. WT-GHvs. WT-GHmodel [

µ

M]vs. WT-GHvs. WT-GHmodel [

µ

M]

DXS #29.911.350.030000.560.820.024621.121.030.030860.660.870.02612

DXR7.040.520.022500.310.640.014471.901.190.026721.541.120.02527

CMK6.192.210.022500.560.820.018472.261.240.027881.261.060.02395

HDS28.621.350.500000.580.830.414722.421.260.630203.181.340.67108

LS5.181.890.017000.730.900.015301.471.110.018881.621.140.01937

L3H7.182.180.003002.641.290.003860.400.720.002153.841.400.00420

PR0.170.820.001509.501.670.0025114.281.790.002691.711.160.00173

MFS16.661.850.000073.301.350.000092.101.220.000096.351.550.00011

Enzyme MFS7a - GHMFS7a - LWMFS7a - LLMFS7a - LL/HT

Z=10; W=0.05; GN(max)=12382; S0=1900Z=200; W=0.05; GN(max)=7593; S0=1500Z=400; W=0.05; GN(max)=$; S0=1100 Z=400; W=0.05; GN(max)=5920; S0=950

Gene Exp.Protein Exp.[Enz] in theGene Exp.Protein Exp.[Enz] in theGene Exp.Protein Exp.[Enz] in theGene Exp.Protein Exp.[Enz] in the

vs. WT-GHvs. WT-GHmodel [

µ

M]vs. WT-GHvs. WT-GHmodel [

µ

M]vs. WT-GHvs. WT-GHmodel [

µ

M]vs. WT-GHvs. WT-GHmodel [

µ

M]

DXS #0.580.830.024930.720.900.026890.780.920.027560.790.920.02768

DXR0.690.880.019860.410.720.016280.460.760.017080.410.730.01632

CMK0.700.890.019941.061.010.022741.871.180.026600.670.870.01960

HDS0.420.730.365570.850.940.472151.021.000.499881.141.030.51627

LS0.230.550.009380.400.720.012220.270.600.010220.440.750.01274

L3H0.350.670.002021.681.150.003450.140.400.001210.780.920.00275

PR6.861.570.0023610.881.710.002572.391.260.001881.261.060.00160

MFS0.140.400.000031.331.080.000080.170.460.000030.170.460.00003

* Enzyme concentrations of DXS, LS, L3H, PR and MFS were determined experimentally based on Western analyses.

# Gene/enzyme identifiers as in Fig. 1 of manuscript

^ Abbreviations and acronyms: WT, wild-type; GH, greenhouse-grown; LL, grown under low light conditions in growth chamber; LW, grown under drought conditions in greenhouse;

LL/HT, grown under low light and high night temperature conditions in growth chambers; MFS7, transgenic lines with reduced (+)-menthofuran synthase gene expression levels;

Z, factor to account for (+)-menthofuran retained in secretory cells; W, factor to account for (+)-pulegone retained in secretory cells; GN(max), number of glandular trichomes at 30 d;

S0, total amount of available substrate for monoterpene biosynthesis (calculated based on experimentally determined essential oil yields).

$ The value used for the simulation in Fig. 5 of the main manuscript corresponds to an estimated amount of 7,500 glanudlar trichomes at 30 d. The (more accurate) experimentally

determined value is 8,262 glandular trichomes at 30 d.

WT - LL/HT

Z=1500; W=0.05; GN(max)=5017; S0=850

WT - LW

Z=400; W=0.05; GN(max)=7273; S0=1200

-5

5

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35

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b

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The Gaussian function represents the following variables:

f(t) = a x exp (-(t-b)2)/2c2)

where

a = Concentration of enzyme in glandular trichomes [µM] (parameter in the model)

t = Time after leaf emergence [s] (variable in the model)

b = Factor defining the the center of the Gaussian peak for enzyme activity [s] (parameter in the model)

c = Factor defining the width of the Gaussian peak for enzyme activity at half maximum [s] (parameter in the model)

C) Example of the use of two Gauss functions to approximate enzyme activity data

To approximate the curve for developmental patterns of enzyme activities with non-Gaussian shapes we used more than one Gaussian function. The pattern of (+)-pulegone reductase activity will serve as an example (plot of Gaussian graph with gray dotted lines):

The Gaussian function was further modified to account for the volume density of the subcellular compartment in which each enzyme resides (Table 3). This factor (“Comp” in the model) was taken directly from Table 1 (e.g., leucoplasts account for roughly 13.9 % of the area of an actively oil-secreting secretory cell, which means that the “Comp” factor in the model would be 0.139). The notation of the Gaussian function in the model is thus:

f(t) = Comp x a x exp (-(t-b)2)/2c2)

Table 3. Subcellular localization of enzymes involved in peppermint monoterpene biosynthesis.

_______________________________________________________________________________________

EnzymeCompartment Reference

_______________________________________________________________________________________

1-Deoxy-D-xylulose 5-phosphate synthaseLeucoplastsLange et al. (1998) Proc. Natl. Acad. Sci. USA 95: 2100

1-Deoxy-D-xylulose 5-phosphate reductoisomeraseLeucoplastsLange et al. (1999) Arch. Biochem. Biophys. 365: 170

2C-Methyl-D-erythritol 4-phosphate cytidyltransferaseLeucoplastsRohdich et al. (2000) Proc. Natl. Acad.Sci. USA 97: 6451

4-(Cytidine 5’-diphospho)-2C-methyl-D-erythritolLeucoplastsLange et al. (1999) Proc. Natl. Acad. Sci. USA 96: 13714

4-phosphate kinaseRohdich et al. (2000) Proc. Natl. Acad.Sci. USA 97: 8251

2C-Methyl-D-erythritol 2,4-cyclodiphosphate synthaseLeucoplastsGao et al. (2006) J. Biochem. Mol. Biol. 39: 502

(E)-4-Hydroxy-3-methyl-but-2-enyl diphosphate synthaseLeucoplastsQuerol et al. (2002) FEBS Lett. 514: 343

(E)-4-Hydroxy-3-methyl-but-2-enyl diphosphate reductaseLeucoplastsHsieh et al. (2005) Plant Physiol. 138: 641

Isopentenyl diphosphate isomeraseLeucoplastsTurner and Croteau (2004) Plant Physiol. 136: 4215

(-)-Limonene synthase

LeucoplastsTurner et al. (1999) Plant Physiol. 120: 879

(-)-Limonene 3-hydroxylaseERTurner and Croteau (2004) Plant Physiol. 136: 4215

(-)-trans-Isopiperitenol dehydrogenase

MitochondriaTurner and Croteau (2004) Plant Physiol. 136: 4215

(-)-Isopiperitenone reductaseCytosolTurner and Croteau, unpublished data

(+)-Menthofuran synthaseERBertea et al. (2001) Arch. Biochem. Biophys. 390: 279

(+)-Pulegone reductase CytosolTurner and Croteau (2004) Plant Physiol. 136: 4215

(-)-Menthone:(-)-menthol reductaseCytosolTurner and Croteau, unpublished data

(-)-Menthone:(+)-neomenthol reductaseCytosolTurner and Croteau, unpublished data

_______________________________________________________________________________________

2.Estimating developmental dynamics of glandular trichome density

Glandular trichome density and distribution depend on the developmental status of the leaf under investigation, which has been studied in detail by Rodney Croteau’s laboratory (Turner et al. (2000) Plant Physiol. 124: 655-663). We expanded the studies to investigate glandular trichome distributions on leaves of plants grown under various environmental conditions (Scheme 2).

Scheme 2. Distribution of glandular trichomes on levaes of wild-type plants grown under greenhouse conditions. The blue line graph indicates the experimentally determined number of glandular trichomes for each leaf size class (± standard error). The broken black line depicts the logistic function used to approximate glandular trichome numbers (for details see text).

0200040006000800010000010203040Glandular trichome countDays after leaf emergence

To account for developmental dynamics in trichome density, we introduced a logistic function, the most common sigmoid curve, to approximate the curve shown in Scheme 2. This function specifies an initial lag phase, then grows steeply but, because of limits in the size of the glandular trichome population, eventually levels off at the later stages of leaf development. Based on more recent data, there is no drop in the total number of glandular trichomes at later stages of development, when plants are grown under greenhouse conditions (indicated by the red dotted line in Scheme 2). Thus, a logistic function is an appropriate approach to approximate this curve. The function was selected based on manual trial and error experiments.

The expression for the logistic function for the number of glandular trichomes (GN) as a function of time after leaf emergence is:

GN(t) = a / (1 + c x expkt)

where

t = Time after leaf emergence [s] (variable in the model)

a = Number of glandular trichomes on a fully expanded leaf (parameter in the model)

c = Number of times the initial gland population must grow to reach “a” (parameter in the model)

k = Factor determining the slope during the growth phase of the curve (parameter in the model)

The values used for the parameters a, c, and k in the model are listed in Table 4.

Table 4. Parameters to approximate dynamics of glandular trichome formation using a logistic function.

Experiment

Parameter a

Parameter c

Parameter k

WT-GH (wild-type grown under greenhouse conditions)

1

8 x 104

1.11 x 10-5

WT-LW (wild-type grown under low water conditions)

0.7

8 x 104

1.11 x 10-5

WT-LL (wild-type grown under low light conditions)

0.73

8 x 104

1.11 x 10-5

WT-LL/HT (wild type treated with combination of low water and high night temperature conditions)

0.53

8 x 104

1.11 x 10-5

MFS7a-GH (MFS7a line grown under greenhouse conditions)

1.15

8 x 104

1.11 x 10-5

MFS7a-LL (MFS7a lines grown under low light conditions)

0.8262

8 x 104

1.11 x 10-5

L3H20-GH (L3H20 line grown under greenhouse conditions; Model 1)

1

8 x 104

1.11 x 10-5

L3H-GH (L3H20 line grown under greenhouse conditions; Model 2; approximation of delayed glandular trichome formation)

1.09*

8 x 104*

1.11 x 10-5*

* For this experiment GN was set to 0.21 (experimentally observed lag phase) for 0-15 d, and the logistic function (with above listed parameters) was used to approximate GN from 15-40 d.

3.Kinetic properties of enzymes involved in peppermint monoterpene biosynthesis

The laboratory of Rodney Croteau at Washington State University determined the kinetic properties of all enzymes involved in the peppermint p-menthane monoterpene biosynthetic pathway. Values listed in Table 1 reflect data obtained using in vitro assays with either purified recombinant or purified native enzymes. Values for the enzymes involved in the methylerythritol pathway, which provides the precursors for monoterpene biosynthesis, were taken from the literature. Some of the kinetic constants had to be estimated as no relevant information could be obtained directly from the literature. The following rationales were use in these parameter estimations:

(-)-Limonene 3-hydroxylase - Kcat value estimated based on published data for other terpene hydroxylases, including premnaspirodiene oxygenase.

(+)-cis-Isopulegone isomerase – the mechanism of enzyme resembles that of ketosteroid isomerase; the Kcat value of this enzyme ranges between 1.4 and 3.8; we used an average value of Kcat=2.5 for simulations.

(+)-Menthofuran synthase - Km and Kcat values taken from published work on psoralen synthase, a cytochrome P450-dependent monooxygenase with the highest known sequence identity to (+)-menthofuran synthase.

Table 5. Kinetic properties of enzymes involved in peppermint monoterpene biosynthesis (numbering of enzymes as in Fig. 1 of main manuscript).

_______________________________________________________________________________________

Enzyme

Km Kcat References

[mM] [s-1]

_______________________________________________________________________________________

(1) 1-Deoxy-D-xylulose 5-phosphate synthase (GAP) 0.068 1.9Eubanks and Poulter (2003) Biochemistry 42: 1140-1149

(Pyruvate) 0.44 1.9Eubanks and Poulter (2003) Biochemistry 42: 1140-1149

(2) 1-Deoxy-D-xylulose 5-phosphate (DXP) 0.132 4.4Rohdich et al. (2006) FEBS J. 273: 4446-4458

reductoisomerase

(MEP) 0.972 1.6Rohdich et al. (2006) FEBS J. 273: 4446-4458

(3) 2C-Methyl-D-erythritol 4-phosphate

0.5 26Rohdich et al. (2000) PNAS 97: 6451-6456

cytidyltransferase

(4) 4-(Cytidine 5’-diphospho)-2C-methyl-D- 0.1 1Bernal et al. (2005) Anal. Biochem. 250: 245-251.

erythritol 4-phosphate kinase

(5) 2C-Methyl-D-erythritol 2,4-cyclodiphosphate 0.252 3.4Rohdich et al. (2001) Eur. J. Biochem. 268: 3190-3197

synthase

Shi et al. (2007) Biochem. Mol. Biol. 40: 911-920

(6) (E)-4-Hydroxy-3-methyl-but-2-enyl

0.42 0.4Kollas et al. (2002) FEBS Lett. 532: 432-436

diphosphate synthase

(7) (E)-4-Hydroxy-3-methyl-but-2-enyl

0.03 3.7Altincicek et al. (2002) FEBS Lett. 532: 437-440

diphosphate reductase

Graewert et al. (2004) J.Am.Chem.Soc. 126: 12847-12855

(8) Isopentenyl diphosphate isomerase (DMAPP) 0.0051 0.018Ramos-Valdivia et al. (1997) Eur.J.Biochem. 249: 161-170

(IPP) 0.017 0.89Ramos-Valdivia et al. (1997) Eur.J.Biochem. 249: 161-170

(9) Geranyl diphosphate synthase

(DMAPP) 0.054 48Burke et al. (1999) PNAS 96: 13062-13067

(IPP) 0.026 48Burke et al. (1999) PNAS 96: 13062-13067

(10) (-)-Limonene synthase

0.020 0.3Alonso et al. (1992) J. Biol. Chem. 267: 7582-7587

(11) (-)-Limonene 3-hydroxylase

0.018 1.5*Karp et al. (1990) Arch. Biochem. Biophys. 276: 219-226

Takahashi et al. (2007) J. Biol. Chem. 282: 31744-31754

(12) (-)-trans-Isopiperitenol dehydrogenase

0.072 0.002Ringer et al. (2005) Plant Physiol. 137: 863-872

(13) (-)-Isopiperitenone reductase

0.001 1.3Ringer et al. (2003) Arch. Biochem. Biophys. 4186: 80-92

(14) (+)-cis-Isopulegone isomerase

0.27 2.5*Kjonaas et al. (1985) Arch. Biochem. Biophys. 238: 49-60

(15) (+)-Menthofuran synthase

0.03* 2.0*Larbat et al. (2007) J. Biol. Chem. 282: 542-554.

(16) (+)-Pulegone reductase

0.0023 1.8Ringer et al. (2003) Arch. Biochem. Biophys. 4186: 80-92

(17) (-)-Menthone:(-)-menthol reductase (menthone) 0.003 0.6Davis et al. (2005) Plant Physiol. 137: 873-881

((+)-isomenthone) 0.041 0.6Davis et al. (2005) Plant Physiol. 137: 873-881

(18) (-)-Menthone:(+)-neomenthol reductase (menthone) 0.674 0.06Davis et al. (2005) Plant Physiol. 137: 873-881

((+)-isomenthone) 1.0 0.06Davis et al. (2005) Plant Physiol. 137: 873-881

_________________________________________________________________________________________________________

* These values could not be obtained from the literature and have thus been estimated.

4.Generating a system of ordinary differential equations to describe kinetic properties of enzymes

The Michaelis-Menten rate equation, as developed by Briggs and Haldane (Fersht (1985) In: Enzyme structure and mechanism, Ed 2. New York: W.H. Freeman), allows calculating the change of the concentration of a metabolite based on the rate of enzymatic formation and turnover. Using the monoterpene pathway intermediate (-)-trans-isopiperitenol as an example we obtain the following:

where

Kc11, Kcat(limonene 3-hydroxylase); E11, Concentration(limonene 3-hydroxylase); Kc12, Kcat(trans-isopiperitenol dehydrogenase); IPPol, (-)-trans-isopiperitenol; LM, (-)-limonene; KM11, Km(limonene 3-hydroxylase); KM12, Km(trans-isopiperitenol dehydrogenase).

Three enzymes in the monoterpene pathway catalyze fully reversible reactions: 1-deoxy-D-xylulose 5-phosphate reductoisomerase (DXR), isopentenyl diphosphate isomerase and (-)-menthone:(+)-neomenthol reductase. The formalism for these reactions is different. For example, the time-dependent change in the concentration of 1-deoxy-D-xylulose 5-phosphate is calculated as follows:

Formation

Turnover

where

(for turnover of 1-deoxy-D-xylulose 5-phosphate by DXR)

Kc2f, Kcat(1-deoxy-D-xyxlulose 5-phosphate reductoisomerase; forward reaction); Kc2r, Kcat(1-deoxy-D-xyxlulose 5-phosphate reductoisomerase; reverse reaction); KM2f, Km(1-deoxy-D-xyxlulose 5-phosphate reductoisomerase; forward reaction); KM2r, Km(1-deoxy-D-xyxlulose 5-phosphate reductoisomerase; reverse reaction); E2, Concentration(1-deoxy-D-xyxlulose 5-phosphate reductoisomerase); DOXP, 1-deoxy-D-xylulose 5-phosphate; ME4P, 2C-methyl-D-erythritol 4-phosphate.

The reaction catalyzed by (+)-pulegone reductase yields (-)-menthone and (+)-isomenthone in a 10 : 1 ratio. We used two separate expressions for these reactions (basically treating the two reactions as being catalyzed by two different enzymes).

The enzyme (-)-menthone:(-)-menthol reductase accepts two substrates ((-)-menthone and (+)-isomenthone) and converts them into two different products ((-)-menthol and (+)-neoisomenthol). Since the mechanism of this reaction is unknown, these two reactions are treated as being catalyzed by two different enzymes. The same is true for the enzyme (-)-menthone:(+)-neomenthol reductase (substrates: (-)-menthone and (+)-isomenthone; products: (+)-neomenthol and (+)-isomenthol).

Two enzymes involved in peppermint monoterpene biosynthesis are known to be affected by competitive feedback inhibition: isopentenyl diphosphate isomerase and (+)-pulegone reductase. As an example, modified Michaelis-Menten rate equations are used to account for the effect of the competitive inhibitor (+)-menthofuran on the turnover of (+)-pulegone by (+)-pulegone reductase. In addition to assessing the inhibition of (+)-pulegone reductase by (+)-menthofuran, we also considered substrate inhibition (as determined experimentally):

where

Kc14, Kcat((+)-isopulegone isomerase); E14, Concentration((+)-isopulegone isomerase); KM14, Km((+)-isopulegone isomerase); CIPUL, (+)-cis-isopulegone; Kc15, Kcat((+)-menthofuran synthase); E15, Concentration((+)-menthofuran synthase); KM15, Km((+)-menthofuran synthase); MF, (+)-menthofuran; Kc16a, Kcat((+)-pulegone reductase; (-)-menthone-forming); E16a, Concentration((+)-pulegone reductase; (-)-menthone-forming); KM16a, Km((+)-pulegone reductase; (-)-menthone-forming); PUL,(+)-pulegone; Kc16b, Kcat((+)-pulegone reductase; (+)-isomenthone-forming); E16b, Concentration((+)-pulegone reductase; (+)-isomenthone-forming); KM16b, Km((+)-pulegone reductase; (+)-isomenthone-forming); Kis, substrate inhibition constant of (+)-pulegone on (+)-pulegone reductase; Kic, feedback competitive inhibition constant for (+)-menthofuran on (+)-pulegone reductase.

The above expression (d[PUL]/dt) also contains two additional factors “w” and “z”, which account for the fact that (+)-pulegone reductase (PR) can be affected by substrate inhibition (w-factor) and competitive inhibition by the pathway side product (+)-menthofuran. In a recent publication (Rios-Estepa et al. (2008) Proc. Natl. Acad. Sci. USA 105: 2818-2823) we reported that the concentration of (+)-menthofuran was roughly 400 µM in secretory cells obtained from plants grown under greenhouse conditions. Based on the experimentally determined monoterpene profiles of these plants, inhibitiory effects on PR were negligible. The z-factor is used to modify the actual (+)-menthofuran concentration in secretory cells. Our measurements indicated that the concentration of this compound in secretory cells (which is where PR is present) is 100 times less than in the essential oil that accumulates extracellularly in the subcuticular cavity. The expression for competitive inhibition of PR contains the (+)-menthofuran concentration in the denominator (see above). A z-factor of 100 (which is used for greenhouse conditions) thus reduces the effect of competitive inhibition to reflect our experimental data. Under low light conditions, the total concentration of (+)-menthofuran in secretory cells was determined as 20 mM, with an estimated concentration of 6 mM in the cytosol. The latter value corresponds to the solubility product of (+)-menthofuran in aqueous solutions (Fichan et al. (1999) J. Chem. Eng. Data 44: 56-62). Based on electron microscopic images the remaining (+)-menthofuran appears to partition into membranes (data not shown). Based on these experimental measurements, the (+)-menthofuran concentration in the cytosol of secreotry cells (which is the location of (+)-pulegone reductase) is 15-fold higher when plants are grown under low light conditions compared to greenhouse-grown plants. This is reflected in a 15-fold higher z-factor value (1,500 for plants grown under low light). The concentration of (+)-menthofuran in secretory cells of plants grown under low water conditions is also higher than in greenhouse-grown plants but the increase is only 4-fold (which is reflected in a 4-fold higher z-factor). The MFS7a mutant line accumulates (+)-menthofuran at only very low levels (10-fold less than wild-type grown under greenhouse conditions) and the z-factor was thus adjusted to 10. In stress-treated conditions MFS7a plants (+)-menthofuran is accumulated to higher levels than in green-house-grown plants (20-fold higher under low light and 40-fold higher under low light; reflected in a 20- and 40-fold higher z-value, respectively) but remains significantly below the corresponding levels in wild-type plants. The factor “w” is used in an analogous fashion to account for the actual concentration of (+)-pulegone in secretory cells. Based on experimental data (Rios-Estepa et al. (2008) Proc. Natl. Acad. Sci. USA 105: 2818-2823) the concentration of (+)-pulegone in secretory cells is 5 % of the total concentration in glandular trichomes and we thus use a w-factor of 0.05 to adjust the (+)-pulegone concentration in the expression for substrate inhibition. It was also observed experimentally that the (+)-pulegone concentration in secretory cells was only marginally affected by environmental conditions and we therefore use a w-factor of 0.05 for all simulations.

5.Calculating monoterpenoid essential oil yields for individual glandular trichomes

Our model simulates monoterpene composition and yield for individual trichomes, which is then extrapolated to the entire leaf using a logistic function that accounts for the number and developmental distribution on glandular trichomes (see 2. for details). The key constraints for our model are experimentally determined monoterpene levels. It is thus essential to be able to extrapolate from these macroscopic measurements (essential oil distillations from entire leaves) to the scale of an individual trichome. In other words, we needed to determine the storage capacity of a glandular trichome.

The volume of the essential oil-filled subcuticular cavity of mature glandular trichomes (Scheme 1, Lower Panel) was originally calculated based on the approximation of its shape as a hemisphere (2/3 π r3). However, we noticed that, using this approach, the amount of oil was significantly underestimated. We thus modified our estimation of the oil storage cavity by approximating it as a sphere (volume: 4/3 π r3) minus the volume of the secretory cells (see 1.1 for details). Trichomes were divided into three different classes: large (75-82 μm diameter; average radius 39 μm), medium (65-74 μm diameter; average radius 35 μm) and small (50-64 μm diameter; average radius 30 μm). The volumes were thus calculated as 2.25 x 10-4 µl (large-sized trichomes), 1.56 x 10-4 µl (medium-sized trichomes) or 0.73 x 10-4 µl (small-sized trichomes). Using this calculation the amount of oil was slightly overestimated, potentially because of the presence of a previously described non-oil mucilage layer surrounding the seceretory cells, as indicated by black dots in Scheme 3 (Turner et al. (2000) Plant Physiol. 124: 665-680). This was corrected by introducing a factor of 0.94, which led to accurate representations of oil volumes (2.03 x 10-4 µl for large-sized trichomes, 1.40 x 10-4 µl for medium-sized trichomes) or 0.66 x 10-4 µl for small-sized trichomes).

Scheme 3

0

10

20

30

0102030405060

Enzyme activity

[

µ

mol/h/leaf]

Leaf age [d]

(+)-cis-Isopulegoneisomerase

Y (-)-Isopiperitenonereductase

X (-)-trans-Isopiperitenoldehydrogenase

+(+)-Pulegonereductase

-(-)-Menthonereductase

▲(-)-Limonene 3-hydroxylase

■(-)-Limonene synthase

0

10

20

30

0102030405060

Enzyme activity

[

µ

mol/h/leaf]

Leaf age [d]

(+)-cis-Isopulegoneisomerase

Y (-)-Isopiperitenonereductase

X (-)-trans-Isopiperitenoldehydrogenase

+(+)-Pulegonereductase

-(-)-Menthonereductase

▲(-)-Limonene 3-hydroxylase

■(-)-Limonene synthase

For example, leaves of peppermint plants grown under greenhouse conditions contained 39 % large, 57 percent medium and 4 % small glandular trichomes at 30 d after leaf emergence. A total of 10151 glandular trichomes was counted, thus indicating a distribution of 3,959 large (39 %), 5786 medium (57 %), and 406 small (4 %) glandular trichomes. In order to calculate the amount of oil per leaf, the number of glandular trichomes in each size category was multiplied by the appropriate trichome volume (e.g, 3,959 (number of large trichomes per leaf) x 2.08 x 10-4 µl (volume of individual large trichome) = 0.822 µl per leaf). The known density of peppermint essential oil (0.9) then allows us to estimate essential oil yield (in µg per leaf). These types of calculations are the basis of all tables shown in the main manuscript.

6.Estimating changes in enzyme concentrations based on measurements of gene expression levels

The concentrations of enzymes involved in peppermint monoterpene biosynthesis in glandular trichomes were determined for greenhouse growth conditions as described in chapter 1. However, it is not practically feasible to determine enzyme concentrations under various environmental conditions, at different stages of leaf development, and in different transgenic plants. Thus, we approximated differences between greenhouse-grown wild-type plants and experimental plants by acquiring quantitative real-time PCR data regarding the expression of key biosynthetic genes and subsequently extrapolated differences in gene expression levels to changes in enzyme concentrations. This is possible because the Lange and Croteau laboratories at WSU have accumulated a wealth of experimental data regarding the correlation of gene expression levels and enzyme activities (for 5 gene/enzyme pairs) in wild-type peppermint plants at many different developmental stages (Scheme 4).

Scheme 4. Correlation of gene expression and enzyme activity patterns in peppermint leaf glandular trichomes. The x-axis indicates gene expression changes, whereas the y-axis shows enzyme activity changes as fold-change from the value measured at 15 d after leaf emergence.

y = 0.3013ln(x) + 0.9937R² = 0.9529

0.00.51.01.52.00.02.04.06.0

The gene expression and enzyme activity levels measured at 12 d after leaf emergence were set to “1”. All other gene expression/enzyme activity pairs were calculated as a fold-change from this calibrator value. As indicated by an analysis of 32 measured gene expression/enzyme activity pairs throughout leaf development (8 to 40 d after leaf emergence) (Scheme 4), there is a correlation between the change in the levels of a certain transcript and the change in the corresponding enzyme activity. This correlation can be described by the equation y = 0.3013 ln (x) + 0.9937, which is a logarithmic function (R2 = 0.9529). We assume that the same equation can be used to approximate enzyme concentrations from gene expression levels (Table 6).

It is known from various published experiments that, under regular greenhouse conditions, peppermint essential oil biosynthesis is regulated primarily at the transcriptional level (Gershenzon et al. (2000) Plant Physiol. 122: 205-214; McConkey et al. (2000) Plant Physiol. 122: 215-224). One of the exceptions to this rule was identified in our previous work, when we identified the importance of feedback control by the dead-end pathway side product (+)-menthofuran) on (+)-pulegone reductase activity under low light conditions (Rios-Estepa et al. (2008) Proc. Natl. Acad. Sci. USA 105: 2818-2823). In the current study we used the same approach to investigate if additional as yet unknown regulatory processes might need to be considered (which would be the case when modeling and experimental data match poorly). It is important to note that we did not perform any modeling optimizations in the present work. The primary focus of this study was to evaluate the minimum set of experimental data that, when incorporated into our model, generate simulations reflecting experimentally determined monoterpene profiles.

7.Kinetic model for peppermint monoterpene biosynthesis

Our recently published first generation model (Rios-Estepa et al. (2008) Proc. Natl. Acad. Sci. USA 105: 2818-2823) encompassed the core reactions of the p-menthane pathway of monoterpene biosynthesis in peppermint glandular trichomes. The current work builds on this model and extends it to include additional reactions (precursor supply in leucoplasts of glandular trichome cells). Our modeling applies the conservation law of mass to secretory cell as the reaction volume. We did not perform parameter optimizations as kinetic and other parameters were inferred directly from experimental data. Statistical tests (primarily the Chi Square test) were used to evaluate the goodness of fit of simulated versus experimentally determined monoterpene profiles. We are currently not considering transport processes or thermodynamics.

The variation of a metabolite M over time is proportional to the difference between the rate at which it is formed (anabolic reaction, RA) minus the rate at which it is turned over (catabolic reaction, RC). The model combines the mass balances for each individual metabolite of the peppermint monoterpene pathway into a series of stiff ordinary differently equations (ODEs), which must be solved simultaneously:

dM/dt = RA – RC

The metabolite-forming reaction (assuming Michaelis - Menten type kinetics) is defined as:

RA= [EA] kcat) [M]/(KM + [M]),

Our model assumes a limited supply of precursors for monoterpene biosynthesis, pyruvate and glyceraldehydes 3-phosphate ([S0] = ([Pyr] + [GAP]), which is calculated based on the final amount of oil produced by glandular trichomes under various conditions (oil yields are determined experimentally). One option for solving a system of ordinary differential equations in the MATLAB framework is the ode45 solver, which uses the Runge Kutta Higher order method. However, this method does not work well with stiff differential equations (Harman et al. (2000) Advanced Engineering Mathematics with MATLAB®, 2nd Ed., Cengage Learning, Florence, KY). In such cases, the ode15s solver is recommended (http://www.mathworks.com/access/helpdesk/help/pdf_doc/otherdocs/ode_suite.pdf).

For the numerical solution of the stiff ODE system, we wrote a MATLAB program that contains the following files, functions, parameters and variables:

A) Script File

· A set of commands that includes the vector for pathway metabolites, time span, and the vector of initial conditions.

· It calls the function (m-file) that solves the ODEs and produces the graphical outputs (monoterpene profiles).

B) Function ( m-file)

· Inputs: independent variable t (time span); vector of dependent variables x ([Metabolites]).

· Solves the set of ODEs with the initial values given in the vector of initial conditions. Returns the values of the independent variable in the vector t (time span) and the values of the dependent variables in the vector x ([Metabolites]). The vector of independent variables t is not equally spaced because the function (m-file) controls the step size.

C) Parameters

· Kinetic constants of enzymes involved in p-menthane monoterpene biosynthesis. Not optimized because these values were inferred directly from experimental data.

· w-Factor accounts for the small amounts of (+)-pulegone retained in secretory cells (does not change under various environmental conditions). Not optimized because this value was inferred directly from experimental data.

· Reaction volume: volume of secretory cells of glandular trichomes, which was inferred directly from experimental data.

D) Non-constant parameters (variables)

· Independent variable t (time span); dependent variable x ([Metabolites])

· Gauss function to approximate dynamic changes in enzyme concentrations over time (d[E]/dt = f( a1-a18, b1-b18, c1-c18)). Not optimized because the values for parameters a, b and c were inferred directly from experimental data.

· Logistic function to approximate dynamic changes in the distribution of leaf glandular trichomes over time (GN = f(a, c, k)). Not optimized because the values for parameters a, c and k were inferred directly from experimental data.

· z-Factor accounts for the selective retention of (+)-menthofuran in secretory cells under stress conditions (z = f(phenotype, environmental conditions)). Not optimized because this value was inferred directly from experimental data.

7.1Reaction mechanisms utilized in kinetic model of peppermint monoterpene biosynthesis

A mechanism following regular Michaelis-Menten-type kinetics is assumed for all

enzymes with the following exceptions:

(1) Substrate inhibition of (+)-pulegone reductase

(2) Competitive inhibition of (+)-pulegone reductase by (+)-menthofuran

(3) Competitive inhibition of isopentenyl-diphosphate isomerase by GPP

(4) Reversible reaction mechanisms were assumed for 1-Deoxy-D-xylulose-5-

phosphate reductoisomerase and (-)-Menthone:(+)-neomenthol reductase

(5) Bi-bi (two substrates, two products) reaction mechanisms were assumed for

1-deoxy-D-xylulose-5-phosphate synthase (Pyruvate + GAP = DXP + CO2) and

geranyl diphosphate synthase (IPP + DMAPP = GPP + PPi). The former utilizes

an ordered mechanism (Pyr binds first), whereas a random mechanism is assumed

for the latter.

Metabolites

GAP: Glyceraldehyde-3-phosphate

Pyr: Pyruvate

DOXP: 1-Deoxy-D-xylulose-5-phosphate

MEP4: 2-C-Methyl-D-erythritol 4-phosphate

CDPME: 4-(Cytidine 5'-diphospho)-2-C-methyl-D-erythritol

CDPME2P: 2-Phospho-4-(Cytidine 5'-diphospho)-2-C-methyl-D-erythritol

MecPP: 2-C-Methyl-D-erythritol 2,4-cyclodiphosphate

HMBPP: 4-Hydroxy-3-methylbut-2-en-1-yl diphosphate

DMAPP: Dimethylallyl-pyrophosphate

IPP: Isopentenyl-pyrophosphate

GPP: Geranyl diphosphate

LM: (-)-Limonene

IPPol: (-)-trans-Isopiperitenol

IPPone: (-)-Isopiperitenone

CIPUL: (+)-Cis-Isopulegone

PUL: (+)-Pulegone

MF: (+)-Menthofuran

Imone: (+)-isomenthone

Mone: (-)-Menthone

Nmol: (+)-Neomenthol

Mol(: (-)-Menthol

Imol: (+)-Isomenthol

NIMol: (+)-Neoisomenthol

Species equations

Variation of GAP

Variation of Pyr

Variation of DOXP

Variation of ME4P

Variation of CDPME

Variation of CDPME2P

Variation of MEcPP

Variation of HMBPP

Variation of DMAPP

Variation of IPP

Variation of GPP

Variation of LM

Variation of IPPol

Variation of IPPone

Variation of CIPUL

Variation of PUL

Variation of MF

Variation of IMone

Variation of Mone

Variation of NMol

Variation of Mol

Variation of IMol

Variation of NIMol

7.2Code of reference model for wild-type plants grown under greenhouse conditions

function xdot = mint_MEP6_GH_WT(t,x)

% This function calculates monoterpene amounts (40 day time course) in leaves

% of peppermint WT plants grown in a greenhouse with supplemental lighting from sodium

% vapor lights.

% A mechanism following regular Michaelis-Menten-type kinetics is assumed for all

% enzymes with the following exceptions:

% (1) Substrate inhibition of (+)-pulegone reductase

% (2) Competitive inhibition of (+)-pulegone reductase by (+)-menthofuran

% (3) Competitive inhibition of isopentenyl-diphosphate isomerase by GPP

% (4) Reversible reaction mechanisms were assume for 1-Deoxy-D-xylulose-5-phosphate

% reductoisomerase and (-)-Menthone:(+)-neomenthol reductase

% (5) Bi-bi (two substrates, two products) reaction mechanisms were assumed for

% 1-deoxy-D-xylulose-5-phosphate synthase (Pyruvate + GAP = DXP + Co2) and geranyl

% diphosphate synthase (IPP + DMAPP = GPP + PPi). The former utilizes an ordered mechanism

% (Pyr binds first), whereas a random mechanism is assumed for the latter.

% Metabolite Nomenclature

%[GAP]=x(1) D-Glyceraldehyde 3-Phosphate

%[Pyr]=x(2) Pyruvate

%[DOXP]=x(3) 1-Deoxy-D-xylulose 5-phosphate

%[ME4P]=x(4) 2-C-Methyl-D-erythritol-4-phosphate

%[CDPME]=x(5) 4-(Cytidine 5'-diphospho)-2-C-methyl-D-erythritol

%[CDPME2P]=x(6) 2-Phospho-4-(cytidine 5'-diphospho)-2-C-methyl-D-erythritol

%[MEcPP]=x(7) 2-C-Methyl-D-erythritol-2,4-cyclodiphosphate

%[HMBPP]=x(8) 1-Hydroxy-2-methyl-2-(E)-butenyl 4-diphosphate

%[DMAPP]=x(9) Dimethylallyl-pyrophosphate

%[IPP]=x(10) Isopentenyl diphosphate

%[GPP]=x(11) Geranyl diphosphate

%[LIM]=x(12) (-)-Limonene

%[IPPol]=x(13) (-)-trans-Isopiperitenol

%[IPPone]=x(14) (-)-Isopiperitenone

%[CIPUL]=x(15) (+)-cis-Isopulegone

%[PUL]=x(16) (+)-Pulegone

%[MF]=x(17) (+)-Menthofuran

%[IMone]=x(18) (+)-Isomenthone

%[Mone]=x(19) (-)-Menthone

%[NMol]=x(20) (+)-Neomenthol

%[Mol]=x(21) (-)-Menthol

%[IMol]=x(22) (+)-Isomenthol

%[NIMol]=x(23) (+)-Neoisomenthol

% Kinetic Parameters

% kc units: [1/s] (kc = Kcat)

% KM units: [uM]

% Ki units: [uM]

KM1a = 68; %1-Deoxy-D-xylulose-5-phosphate synthase (DXS) for GAP

kc1a = 1.9;

KM1b = 440; %1-Deoxy-D-xylulose-5-phosphate synthase (DXS) for Pyr

kc1b = 1.9;

Kia = 16; %Dissociation constant for Pyr

KM2f = 132; %1-Deoxy-D-xylulose-5-phosphate reductoisomerase (DXR; forward reaction)

kc2f = 4.4;

KM2r = 972; %1-Deoxy-D-xylulose-5-phosphate reductoisomerase (DXR; reverse reaction)

kc2r = 1.6;

KM3 = 500; %2-C-Methyl-D-erythritol 4-phosphate cytidylyltransferase (MCT)

kc3 = 26;

KM4 = 100; %4-(Cytidine 5'-diphospho)-2-C-methyl-D-erythritol kinase (CMK)

kc4 = 1;

KM5 = 252; %2-C-Methyl-D-erythritol 2,4-cyclodiphosphate synthase (MECPS)

kc5 = 3.4;

KM6 = 420; %4-Hydroxy-3-methylbut-2-en-1-yl diphosphate synthase (HDS)

kc6 = 0.4;

KM7 = 30; %4-Hydroxy-3-methylbut-2-en-1-yl diphosphate reductase (HDR)

kc7 = 3.7;

KM8f = 5.1; %Isopentenyl-diphosphate delta-isomerase for IPP (IPPI; forward reaction)

kc8f =0.018;

KM8r = 17; %Isopentenyl-diphosphate delta-isomerase for DMAPP (IPPI; rev reaction)

kc8r = 0.89;

KM9a = 54; %Geranyl diphosphate synthase (GPPS; DMAPP as substrate)

kc9a = 48;

KM9b = 26; %Geranyl diphosphate synthase (GPPS; IPP as substrate)

kc9b = 48;

KM10 = 20; %(-)-Limonene synthase (LS)

kc10 = 0.3;

KM11 = 18; %(-)-Limonene 3-hyroxylase (L3H)

kc11 = 1.8;

KM12 = 72; %(-)-trans-Isopiperitenol dehydrogenase (IsoDH)

kc12 = 0.002;

KM13 = 1; %(-)-Isopiperitenone reductase (IsoR)

kc13 = 1.3;

KM14 = 270; %(+)-cis-Isopulegone isomerase (IsoI)

kc14 = 2.5;

KM15 = 30; %(+)-Menthofuran synthase (MFS)

kc15 = 2.0;

KM16a = 2.3; %(+)-Pulegone reductase (PR; product: (-)-menthone)

kc16a = 1.8;

KM16b = 2.3; %(+)-Pulegone reductase (PR; product: (+)-isomenthone)

kc16b = 1.8;

KM17a = 3; %(-)-Menthone:(-)-menthol reductase (MMR; substrate: (-)-menthone)

kc17a = 0.6;

KM17b = 41; %(-)-Menthone:(-)-menthol reductase (MMR; substrate: (+)-isomenthone)

kc17b = 0.6;

KM18af = 674; %(-)-Menthone:(+)-neomenthol reductase (MNR; substrate: (-)-menthone);

forward reaction)

kc18af = 0.06;

KM18ar = 1200; %(-)-Menthone:(+)-neomenthol reductase (MNR; substrate: (-)-menthone);

backward reaction)

kc18ar = 0.06;% estimated

KM18b = 1000; %(-)-Menthone:(+)-neomenthol reductase (MNR; substrate: (+)-isomenthone)

kc18b = 0.06;

Kic1=96; % Product inhibition constant (Geranyl diphosphate acting on IPPI)

Kic2=300; % Product inhibition constant ((+)-menthofuran acting on PR)

% Competitive inhibition mechanism

Kis=112; % Substrate Inhibition constant ((+)-pulegone acting on PR)

% Uncompetitive inhibition mechanism

z=100; % Factor to account for the actual concentration of (+)-menthofuran in

secretory cells of glandular trichomes

w=0.05; % Factor to account for the actual concentration of (+)-pulegone in

secretory cells of glandular trichomes

% The model also takes into account that each enzyme shows a particular transient

% pattern of expression. This pattern is approximated by a Gauss function.

%First peak of activity:

%f(x) = Comp * a * exp((-(t-b).^2)/(2*(c)^2))

%where Comp = Factor to adjust for the volume density of the compartment in which a

particular enzyme is active [Dimensionless]

% a = Factor defining the height of the Gaussian peak for enzyme activity

[µM]

% t = Time [s]

% b = Factor defining the position of the center of the Gaussian peak for

enzyme activity [s]

% c = Factor defining the width of the Gaussian peak for enzyme activity at

half maximum [s]

b1=1296000; % Defines the position of the center of the Gaussian peak for enzyme

activity.

% Relevant to the following enzyme activities: LS, L3H, IsoDH, IsoR, IsoI,

MFS, PR

c1=800000; % Defines the width of the Gaussian peak for enzyme activity at half

maximum.

% Relevant to the following enzyme activities: LS, L3H, IsoDH, IsoR, IsoI,

MFS, PR

b5=1800000; % Defines the position of the center of the Gaussian peak for enzyme

activity.

% Relevant to the following enzyme activities: MMR, MNR

c5=900000; % Defines the width of the Gaussian peak for enzyme activity at half

maximum.

% Relevant to the following enzyme activities: MMR, MNR

E1=(0.139)*0.03*exp((-(t-b1).^2)/(2*(c1)^2)); % DXS

E2=(0.139)*0.0225*exp((-(t-b1).^2)/(2*(c1)^2)); % DXR

E3=(0.139)*0.5*exp((-(t-b1).^2)/(2*(c1)^2)); % MCT

E4=(0.139)*0.0225*exp((-(t-b1).^2)/(2*(c1)^2)); % CMK

E5=(0.139)*0.5*exp((-(t-b1).^2)/(2*(c1)^2)); % MECPS

E6=(0.139)*0.5*exp((-(t-b1).^2)/(2*(c1)^2)); % HDS

E7a=(0.139)*0.2*exp((-(t-b1).^2)/(2*(c1)^2)); % HDR (product: DMAPP)

E7b=(0.139)*0.04*exp((-(t-b1).^2)/(2*(c1)^2)); % HDR (product: IPP)

E8=(0.139)*0.3*exp((-(t-b1).^2)/(2*(c1)^2)); % IPPI

E9=(0.139)*0.1*exp((-(t-b1).^2)/(2*(c1)^2)); % GPPS

E10= (0.139)*0.017*exp((-(t-b1).^2)/(2*(c1)^2)); % LS

E11= (0.365)*0.003*exp((-(t-b1).^2)/(2*(c1)^2)); % L3H

E12= (0.044)*10*exp((-(t-b1).^2)/(2*(c1)^2)); % IsoDH

E13= (0.204)*0.34*exp((-(t-b1).^2)/((2*c1)^2)); % IsoR

E14= (0.204)*0.34*exp((-(t-b1).^2)/((2*c1)^2)); % IsoI

E15= (0.365)*0.00007*exp((-(t-b1).^2)/(2*(c1)^2)); % MFS

E16a=(0.204)*0.0015*exp((-(t-b1).^2)/(2*(c1)^2)); % PR (product: (-)-menthone)

E16b=(0.204)*0.00015*exp((-(t-b1).^2)/(2*(c1)^2)); % PR (product: (+)-isomenthone)

E17a=(0.204)*0.0011*exp((-(t-b5).^2)/(2*(c5)^2)); % MMR (product: (-)-menthol)

E17b=(0.204)*0.0011*exp((-(t-b5).^2)/(2*(c5)^2)); % MMR (product: (+)-neoisomenthol)

E18a=(0.204)*0.00001*exp((-(t-b5).^2)/(2*(c5)^2)); % MNR (product: (+)-neomenthol)

E18b=(0.204)*0.00001*exp((-(t-b5).^2)/(2*(c5)^2)); % MNR (product: (+)-isomenthol)

% The model also takes into account that the glandular trichome density (GN) changes over time. This behavior is approximated using a logistic function:

c=5*10^5; % parameter approximating slope of exponential phase of sigmoid curve

k=1/8*10^4; % parameter approximating shape of sigmoid curve

GN = 1+ 1/(1+c*exp(-k*t)); % at day 15, gland number is 86.7 % of total gland number at

day 30

%Species Equations

if t< 1296000 % (patterns of enzymes from 0 to 15 days after leaf initiation)

xdot=[GN*(-(kc1b*E1*x(2)*x(1)/(Kia*KM1b+KM1a*x(2)+KM1b*x(1)+x(1)*x(2)))); % Variation of GAP

GN*(-(kc1b*E1*x(2)*x(1)/(Kia*KM1b+KM1a*x(2)+KM1b*x(1)+x(1)*x(2)))); % Variation of Pyruvate (same expression as for GAP) GN*((kc1b*E1*x(2)*x(1)/(Kia*KM1b+KM1a*x(2)+KM1b*x(1)+x(1)*x(2)))-((KM2r*kc2f*E2*x(3)-KM2f*kc2r*E2*x(4))/(KM2f*KM2r+KM2r*x(3)+KM2f*x(4)))); % Variation of DOXP

GN*(((KM2r*kc2f*E2*x(3)-KM2f*kc2r*E2*x(4))/(KM2f*KM2r+KM2r*x(3)+KM2f*x(4)))-(kc3*E3*x(4)/(x(4)+KM3))); % Variation of ME4P

GN*((kc3*E3*x(4)/(x(4)+KM3))-(kc4*E4*x(5)/(x(5)+KM4))); % Variation of CDP-ME

GN*((kc4*E4*x(5)/(x(5)+KM4))-(kc5*E5*x(6)/(x(6)+KM5))); % Variation of CDP-ME2P

GN*((kc5*E5*x(6)/(x(6)+KM5))-(kc6*E6*x(7)/(x(7)+KM6))); % Variation of MEcPP

GN*((kc6*E6*x(7)/(x(7)+KM6))-(kc7*E7a*x(8)/(x(8)+KM7))- (kc7*E7b*x(8)/(x(8)+KM7))); % Variation of HMB-PP

GN*((kc7*E7a*x(8)/(x(8)+KM7))+(kc8f*E8*x(10)/(x(10)+KM8f*(1+(x(11)/Kic1))))-(kc8r*E8*x(9)/(x(9)+KM8r*(1+(x(11)/Kic1))))-((kc9a*E9*KM9b*x(9)+kc9b*E9*KM9a*x(10))/(KM9b*x(9)+KM9a*x(10)+KM9a*KM9b))); %Variation of DMAPP

GN*((kc7*E7b*x(8)/(x(8)+KM7))+(kc8r*E8*x(9)/(x(9)+KM8r*(1+(x(11)/Kic1))))-(kc8f*E8*x(10)/(x(10)+KM8f*(1+(x(11)/Kic1))))-((kc9a*E9*KM9b*x(9)+kc9b*E9*KM9a*x(10))/(KM9b*x(9)+KM9a*x(10)+KM9a*KM9b))); %Variation of IPP

GN*(((kc9a*E9*KM9b*x(9)+kc9b*E9*KM9a*x(10))/(KM9b*x(9)+KM9a*x(10)+KM9a*KM9b))- (kc10*E10*x(11)/(x(11)+KM10))); %Variation of GPP

GN*((kc10*E10*x(11)/(x(11)+KM10))-(kc11*E11*x(12)/(x(12)+KM11))); % Variation of LIM

GN*((kc11*E11*x(12)/(x(12)+KM11))-(kc12*E12*x(13)/(x(13)+KM12))); % Variation of IPPol

GN*((kc12*E12*x(13)/(x(13)+KM12))-(kc13*E13*x(14)/(x(14)+KM13))); % Variation of IPPone

GN*((kc13*E13*x(14)/(x(14)+KM13))-(kc14*E14*x(15)/(x(15)+KM14))); % Variation of CIPUL

GN*((kc14*E14*x(15)/(x(15)+KM14))-(kc16a*E16a*x(16)/(x(16)+KM16a*(1+z*(x(17))/Kic2)))-(kc16b*E16b*x(16)/(x(16)+KM16b*(1+z*(x(17))/Kic2)))-(w*kc16a*E16a*x(16)/(KM16a+x(16)*(1+x(16)/Kis)))-(w*kc16b*E16b*x(16)/(KM16b+x(16)*(1+x(16)/Kis)))-(kc15*E15*x(16)/(x(16)+KM15))); % Variation of PUL

GN*(kc15*E15*x(16)/(x(16)+KM15)); % Variation of MF

GN*((kc16b*E16b*x(16)/(x(16)+KM16b*(1+z*(x(17))/Kic2)))+(w*kc16b*E16b*x(16)/(KM16b+x(16)*(1+x(16)/Kis)))-(kc17b*E17b*x(18)/(x(18)+KM17b))-(kc18b*E18b*x(18)/(x(18)+KM18b))); % Variation of IMone

GN*((kc16a*E16a*x(16)/(x(16)+KM16a*(1+z*(x(17))/Kic2)))+(w*kc16a*E16a*x(16)/(KM16a+x(16)*(1+x(16)/Kis)))-((KM18ar*kc18af*E18a*x(19)-KM18af*kc18ar*E18a*x(20))/(KM18af*KM18ar+KM18ar*x(19)+KM18af*x(20)))-(kc17a*E17a*x(19)/(x(19)+KM17a))); % Variation of Mone

GN*((KM18ar*kc18af*E18a*x(19)-KM18af*kc18ar*E18a*x(20))/(KM18af*KM18ar+KM18ar*x(19)+KM18af*x(20))); % Variation of NMol

GN*(kc17a*E17a*x(19)/(x(19)+KM17a)); % Variation of Mol

GN*(kc18b*E18b*x(18)/(x(18)+KM18b)); % Variation of IMol

GN*(kc17b*E17b*x(18)/(x(18)+KM17b))]; % Variation of NIMol

else t>= 1296000 %(patterns of enzymes from 15 - 40 days after leaf initiation)

% Second peak of enzyme activity:

b2=1814400; % Defines the position of the center of the second Gaussian peak for

enzyme activity.

% Relevant to the following enzyme activities: PR

c2=1420000; % Defines the width of the second Gaussian peak for enzyme activity at

half maximum.

% Relevant to the following enzyme activities: PR

b4=2160000; % Defines the position of the center of the second Gaussian peak for

enzyme activity.

% Relevant to the following enzyme activities: IsoDH, IsoR, IsoI

c4=170000; % Defines the width of the second Gaussian peak for enzyme activity at

half maximum.

% Relevant to the following enzyme activities: IsoDH, IsoR, IsoI

E12=(0.044)*1*exp((-(t-b4).^2)/(2*(c4)^2)); % IsoDH

E13=(0.204)*0.0044*exp((-(t-b2).^2)/(2*(c2)^2)); % IsoR

E14=(0.204)*0.0044*exp((-(t-b2).^2)/(2*(c2)^2)); % IsoI

E16a=(0.204)*0.00014*exp((-(t-b2).^2)/(2*(c2)^2)); % PR (product: (-)-menthone)

E16b=(0.204)*0.000014*exp((-(t-b2).^2)/(2*(c2)^2)); % PR (product: (+)-isomenthone)

xdot=[GN*(-(kc1b*E1*x(2)*x(1)/(Kia*KM1b+KM1a*x(2)+KM1b*x(1)+x(1)*x(2)))); % Variation of GAP

GN*(-(kc1b*E1*x(2)*x(1)/(Kia*KM1b+KM1a*x(2)+KM1b*x(1)+x(1)*x(2)))); % Variation of Pyruvate (same expression as for GAP) GN*((kc1b*E1*x(2)*x(1)/(Kia*KM1b+KM1a*x(2)+KM1b*x(1)+x(1)*x(2)))-((KM2r*kc2f*E2*x(3)-KM2f*kc2r*E2*x(4))/(KM2f*KM2r+KM2r*x(3)+KM2f*x(4)))); % Variation of DOXP

GN*(((KM2r*kc2f*E2*x(3)-KM2f*kc2r*E2*x(4))/(KM2f*KM2r+KM2r*x(3)+KM2f*x(4)))-(kc3*E3*x(4)/(x(4)+KM3))); % Variation of ME4P

GN*((kc3*E3*x(4)/(x(4)+KM3))-(kc4*E4*x(5)/(x(5)+KM4))); % Variation of CDP-ME

GN*((kc4*E4*x(5)/(x(5)+KM4))-(kc5*E5*x(6)/(x(6)+KM5))); % Variation of CDP-ME2P

GN*((kc5*E5*x(6)/(x(6)+KM5))-(kc6*E6*x(7)/(x(7)+KM6))); % Variation of MEcPP

GN*((kc6*E6*x(7)/(x(7)+KM6))-(kc7*E7a*x(8)/(x(8)+KM7))- (kc7*E7b*x(8)/(x(8)+KM7))); % Variation of HMB-PP

GN*((kc7*E7a*x(8)/(x(8)+KM7))+(kc8f*E8*x(10)/(x(10)+KM8f*(1+(x(11)/Kic1))))-(kc8r*E8*x(9)/(x(9)+KM8r*(1+(x(11)/Kic1))))-((kc9a*E9*KM9b*x(9)+kc9b*E9*KM9a*x(10))/(KM9b*x(9)+KM9a*x(10)+KM9a*KM9b))); %Variation of DMAPP

GN*((kc7*E7b*x(8)/(x(8)+KM7))+(kc8r*E8*x(9)/(x(9)+KM8r*(1+(x(11)/Kic1))))-(kc8f*E8*x(10)/(x(10)+KM8f*(1+(x(11)/Kic1))))-((kc9a*E9*KM9b*x(9)+kc9b*E9*KM9a*x(10))/(KM9b*x(9)+KM9a*x(10)+KM9a*KM9b))); %Variation of IPP

GN*(((kc9a*E9*KM9b*x(9)+kc9b*E9*KM9a*x(10))/(KM9b*x(9)+KM9a*x(10)+KM9a*KM9b))- (kc10*E10*x(11)/(x(11)+KM10))); %Variation of GPP

GN*((kc10*E10*x(11)/(x(11)+KM10))-(kc11*E11*x(12)/(x(12)+KM11))); % Variation of LIM

GN*((kc11*E11*x(12)/(x(12)+KM11))-(kc12*E12*x(13)/(x(13)+KM12))); % Variation of IPPol

GN*((kc12*E12*x(13)/(x(13)+KM12))-(kc13*E13*x(14)/(x(14)+KM13))); % Variation of IPPone

GN*((kc13*E13*x(14)/(x(14)+KM13))-(kc14*E14*x(15)/(x(15)+KM14))); % Variation of CIPUL

GN*((kc14*E14*x(15)/(x(15)+KM14))-(kc16a*E16a*x(16)/(x(16)+KM16a*(1+z*(x(17))/Kic2)))-(kc16b*E16b*x(16)/(x(16)+KM16b*(1+z*(x(17))/Kic2)))-(w*kc16a*E16a*x(16)/(KM16a+x(16)*(1+x(16)/Kis)))-(w*kc16b*E16b*x(16)/(KM16b+x(16)*(1+x(16)/Kis)))-(kc15*E15*x(16)/(x(16)+KM15))); % Variation of PUL

GN*(kc15*E15*x(16)/(x(16)+KM15)); % Variation of MF

GN*((kc16b*E16b*x(16)/(x(16)+KM16b*(1+z*(x(17))/Kic2)))+(w*kc16b*E16b*x(16)/(KM16b+x(16)*(1+x(16)/Kis)))-(kc17b*E17b*x(18)/(x(18)+KM17b))-(kc18b*E18b*x(18)/(x(18)+KM18b))); % Variation of IMone

GN*((kc16a*E16a*x(16)/(x(16)+KM16a*(1+z*(x(17))/Kic2)))+(w*kc16a*E16a*x(16)/(KM16a+x(16)*(1+x(16)/Kis)))-((KM18ar*kc18af*E18a*x(19)-KM18af*kc18ar*E18a*x(20))/(KM18af*KM18ar+KM18ar*x(19)+KM18af*x(20)))-(kc17a*E17a*x(19)/(x(19)+KM17a))); % Variation of Mone

GN*((KM18ar*kc18af*E18a*x(19)-KM18af*kc18ar*E18a*x(20))/(KM18af*KM18ar+KM18ar*x(19)+KM18af*x(20))); % Variation of NMol

GN*(kc17a*E17a*x(19)/(x(19)+KM17a)); % Variation of Mol

GN*(kc18b*E18b*x(18)/(x(18)+KM18b)); % Variation of IMol

GN*(kc17b*E17b*x(18)/(x(18)+KM17b))]; % Variation of NIMol

End

8. Statistical analysis of goodness of fit between simulated and measured monoterpene profiles

The focus of this study was to evaluate the minimum set of experimental data that, when incorporated into our model, led to simulations reflecting experimentally determined monoterpene profiles. It is important to note that we did not use any model fitting approaches in the present work. All modeling assumptions were inferred directly from experimental data. To assess the validity of our modeling assumptions we performed a very basic goodness of fit analysis. We did not attempt to accurately simulate the entire time course of accumulation for each monoterpene. We were primarily interested in how well we could simulate the composition of monoterpenes at 40 d, which corresponds to the developmental stage when commercially grown peppermint would be harvested for oil extraction. For this analysis we selected the Chi Square goodness of fit test. This test is usually employed when one attempts to fit a statistical model to observed data, and one is assessing how well the model actually reflects the data. In general, the Chi Square test statistic is of the form

where

Oi = observed values (in the context of the present study this refers to simulated data)

Ei = expected values (in the context of the present study this refers to experimental data)

Although this test is commonly used to evaluate frequency distributions (with very large sample sizes), it provided us with an opportunity to apply statistical hypothesis testing to the semi-quantitative evaluation of modeling results. The Chi Square statistic can then be used to calculate a p-value with various online tools (we use the tool at the following URL: http://faculty.vassar.edu/lowry/tabs.html). This calculation requires entry of degrees of freedom, which, in our study, is equal to the number of analytes n (for the statistical analysis the goodness of fit for 5 major p-menthane monoterpenes and a separate “Other” category (all other monoterpenes) was determined; total of 6 analytes) minus “1”. In statistical hypothesis testing the null hypothesis is generally rejected if the p-value is less than 0.05 or 0.01, corresponding to a 5% or 1% probability of obtaining a certain result by chance. In the context of our experiments a non-significant p-value (p > 0.05) means that there are no statistically significant differences between experimentally determined and simulated monoterpene composition at 40 d, indicating a good fit between experimental and simulated data.

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