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Keywords:

  • benzenoid network;
  • kinetic modeling;
  • metabolic control analysis;
  • floral volatiles;
  • petunia

Summary

  1. Top of page
  2. Summary
  3. Introduction
  4. Results
  5. Discussion
  6. Concluding remarks
  7. Experimental procedures
  8. Acknowledgements
  9. References
  10. Supporting Information

In recent years there has been much interest in the genetic enhancement of plant metabolism; however, attempts at genetic modification are often unsuccessful due to an incomplete understanding of network dynamics and their regulatory properties. Kinetic modeling of plant metabolic networks can provide predictive information on network control and response to genetic perturbations, which allow estimation of flux at any concentration of intermediate or enzyme in the system. In this research, a kinetic model of the benzenoid network was developed to simulate whole network responses to different concentrations of supplied phenylalanine (Phe) in petunia flowers and capture flux redistributions caused by genetic manipulations. Kinetic parameters were obtained by network decomposition and non-linear least squares optimization of data from petunia flowers supplied with either 75 or 150 mm2H5-Phe. A single set of kinetic parameters simultaneously accommodated labeling and pool size data obtained for all endogenous and emitted volatiles at the two concentrations of supplied 2H5-Phe. The generated kinetic model was validated using flowers from transgenic petunia plants in which benzyl CoA:benzyl alcohol/phenylethanol benzoyltransferase (BPBT) was down-regulated via RNAi. The determined in vivo kinetic parameters were used for metabolic control analysis, in which flux control coefficients were calculated for fluxes around the key branch point at Phe and revealed that phenylacetaldehyde synthase activity is the primary controlling factor for the phenylacetaldehyde branch of the benzenoid network. In contrast, control of flux through the β-oxidative and non-β-oxidative pathways is highly distributed.


Introduction

  1. Top of page
  2. Summary
  3. Introduction
  4. Results
  5. Discussion
  6. Concluding remarks
  7. Experimental procedures
  8. Acknowledgements
  9. References
  10. Supporting Information

Genetic engineering of plant metabolic networks has been successfully used to achieve a desired outcome (Sewalt et al., 1994; Ye et al., 2000; Kebeish et al., 2007; Aluru et al., 2008). However, genetic modification of plants often results in unanticipated consequences on metabolism or little or no net change to the system. For example, down-regulation of various enzymes at the end-points of the lignin biosynthetic pathway did not result in the desired reduction of lignin content (Dwivedi et al., 1994; Halpin et al., 1994; Atanassova et al., 1995; Van Doorsselaere et al., 1995). Similarly, engineering of the glycine betaine biosynthetic pathway in tobacco chloroplasts had limited success because of unanticipated constraints in choline supply (Nuccio et al., 2000; McNeil et al., 2001). Some genetic modifications of plants result in an unexpected alteration of cellular metabolite pools or pathways not directly involved in the modified network, sometimes leading to deleterious effects on plant growth and development (Wu et al., 2006; Dauwe et al., 2007; Napier, 2007). In many cases these problems are due to an incomplete understanding of network dynamics and control even though the general network structure may be known. Thus, the current challenge is to find ways to prevent or overcome these difficulties.

One way to improve the overall success of genetic and metabolic engineering is through the use of computer models of metabolism that provide descriptions of metabolic networks using kinetic equations (Daae et al., 1999; Libourel and Shachar-Hill, 2008). At its simplest, kinetic modeling assigns kinetic parameters for each reaction in the network allowing estimation of product formation at any concentration of intermediate or enzyme in the system. In contrast with steady-state or transient metabolic flux analysis (see for review Morgan and Rhodes, 2002; Colon et al., 2009; Schwender, 2009), kinetic models of metabolism are capable of describing the dynamic behavior within the cell and provide information on regulatory mechanisms, which might not be intuitively known (McNeil et al., 2000b). To date, kinetic models have been used in attempts to analyze plant responses to environmental or genetic perturbations in order to better describe network regulation in photosynthesis (Pearcy et al., 1997; Fridlyand et al., 1998; Fridlyand and Scheibe, 1999; Poolman et al., 2000; Von Caemmerer, 2000; Zhu et al., 2007), central carbon metabolism (Krab, 1995; Thomas et al., 1997a,b; Affourtit et al., 2001) and to a lesser extent plant secondary metabolism (Heinzle et al., 2007; McNeil et al., 2000a,b; Nuccio et al., 2000; Rios-Estepa et al., 2008).

Rational modification of plant metabolic networks can also be assisted by the utilization of metabolic control analysis (MCA), in which the flux control coefficients (FCCs) are calculated to determine the level of control that an individual enzyme activity imposes on each flux in a network (Kacser and Burns, 1973; Fell, 1997). FCCs can be obtained in multiple ways and one approach is with a valid kinetic model that includes values for steady-state intracellular substrate concentrations and kinetic parameters for each enzyme in the pathway (Stephanopoulos et al., 1998; Morgan and Rhodes, 2002). Kinetic parameters for enzymes in a metabolic network can be obtained by two different experimental approaches depending on the extent of information available about the system. For well described networks or sub-networks, kinetic parameters (Km, Vmax, Ki) of all enzymes involved can be obtained by in vitro characterization (Daae et al., 1999; Curien et al., 2003; Reed et al., 2004; Wu et al., 2006; Uys et al., 2007; Rios-Estepa et al., 2008). For networks with limited information, kinetic parameters of enzymes are estimated via their iterative adjustment to maximize the goodness of fit between the experimental and simulated metabolite and/or labeling data (McNeil et al., 2000b; Nuccio et al., 2000; Rios-Estepa et al., 2008). We pursued the latter approach to develop a kinetic model of the benzenoid network in petunia flowers (Figure 1) for which several biochemical steps remain unknown. The model’s ability to predict network response to genetic perturbations was experimentally validated by prediction of metabolite pool size and labeling data from transgenic petunia flowers in which benzyl CoA:benzyl alcohol/phenylethanol benzoyltransferase (BPBT) was down-regulated using a RNAi approach (Orlova et al., 2006). The kinetic parameters estimated by the model were then used for MCA of the benzenoid network in which FCCs were determined for fluxes in the system at three concentrations of exogenously supplied Phe.

image

Figure 1.  Schematic of the condensed benzenoid network reactions in petunia. Arrows represent flux (v) and grey font and the abbreviation ‘ex’ indicates emitted volatiles. Abbreviations used: BA, benzoic acid; Balc, benzyl alcohol; Bald, benzyl aldehyde; BBa, benzylbenzoate BA moiety; BBb, benzylbenzoate BAlc moiety; CA, cinnamic acid; Chor, chorismic acid; Coum, coumaric acid; Eug, eugenol; Ieug, isoeugenol; MB, methylbenzoate; PEBa, phenylethyl benzoate BA moiety; PEBb, phenylethyl benzoate 2-phenylethanol moiety; Phald, phenylacetaldehyde; Phe, phenylalanine; Phepyr, phenylpyruvate; Pheth, phenylethanol. Note that ExPhe is the exogenous supply of Phe.

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Results

  1. Top of page
  2. Summary
  3. Introduction
  4. Results
  5. Discussion
  6. Concluding remarks
  7. Experimental procedures
  8. Acknowledgements
  9. References
  10. Supporting Information

Development of the kinetic model

Flowers of many plant species emit volatile compounds to attract pollinators and maximize their reproductive success (Dudareva and Pichersky, 2006; Knudsen and Gershenzon, 2006; Pichersky et al., 2006). Flowers of Petunia hybrida cv Mitchell emit high levels of benzenoid/phenylpropanoid compounds (Kolosova et al., 2001; Verdonk et al., 2003; Boatright et al., 2004; Orlova et al., 2006). While enzymes responsible for the final biosynthetic step of many petunia scent volatiles have been characterized (Negre et al., 2003; Boatright et al., 2004; Kaminaga et al., 2006; Koeduka et al., 2006), less is known about the entire biochemical pathways leading to these compounds and the overall regulation of carbon distribution within the network. As a part of the ongoing effort to understand how flux is controlled in this network, a combination of isotopic labeling, metabolic flux analysis, and targeted genetic engineering was previously applied (Boatright et al., 2004; Orlova et al., 2006). This approach has now been extended to develop a kinetic model that can simulate whole network responses to different concentrations of supplied Phe in petunia flowers and capture flux redistributions caused by genetic perturbations. The intracellular and extracellular benzenoid metabolite pools and their fractional isotope enrichments from feeding experiments with two concentrations of 2H5-Phe were quantified over 4-h time courses, during which the endogenous Phe pool expanded approximately linearly from 0.5 μmol gFW−1 (time 0 h) to 30 μmol·gFW−1 when supplied with 75 mm2H5-Phe, and to 96 μmol·gFW−1 when supplied with 150 mm2H5-Phe. The experimentally obtained data were used to develop a kinetic model of the benzenoid network in petunia as described below.

Changes in Phe pool size suggest tight regulation of PAL in petunia flowers

In petunia flowers, a key branch point at the beginning of the benzenoid network is at Phe, which can be converted to either trans-cinnamic acid (CA) by phenylalanine ammonia lyase (PAL) or to phenylacetaldehyde (Phald) by phenylacetaldehyde synthase (PAAS), which catalyzes both Phe decarboxylation and oxidation (Kaminaga et al., 2006). When a range of concentrations of 2H5-Phe was supplied to petunia flowers a proportional increase in the observed metabolite pool of Phald and compounds belonging to that branch of the network occurred while there was only a slight increase in the observed pool size of most endogenous compounds downstream of CA. These results could be explained by feedback inhibition of PAL, which catalyzes the conversion of Phe to CA. PAL kinetic properties and regulation vary among plant species (Koukol and Conn, 1961; Camm and Towers, 1973; Sato et al., 1982; Mavandad et al., 1990; Dubery and Smit, 1994; MacDonald and D’Cunha, 2007), which made it necessary to determine the type of inhibition imposed on the PAL isoform most likely involved in the benzenoid network in petunia flowers. A full-length cDNA encoding petunia PAL1 (AY705976) and a partial cDNA encoding petunia PAL2 (CO805160) were recently reported by Verdonk et al. (2003). A search of our petunia petal-specific EST database for sequences with homology to petunia PALs revealed an additional cDNA with nucleotide sequence 76 and 85% identical to PAL1 and PAL2, respectively. Quantitative real-time RT-PCR revealed that PAL1 is the most highly expressed among the three PAL isoforms in 2-day-old petunia corollas (Figure 2), thus PAL1 was used for kinetic analysis.

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Figure 2.  Quantitative real-time PCR for absolute quantification of the expression of three petunia PAL isoforms in 2-day-old petal tissue harvested during the day.

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Kinetic evaluation of affinity-purified recombinant petunia PAL1 protein revealed that the enzyme has an apparent Km value for Phe of 160 ± 35 μm, which is within the range of Km values previously reported for other plant PAL enzymes (30 μm to 15 mm; Camm and Towers, 1973). While kinetic properties of plant PAL are often deviant and anomalous (Hanson and Havir, 1970; Khan et al., 1987; Dubery and Smit, 1994) petunia PAL1 exhibited normal Michaelis–Menten kinetics similar to three PAL isoforms from alfalfa (Jorrin and Dixon, 1990). To determine the type of PAL inhibition by CA, PAL activity was measured with Phe as substrate (0.5–10 mm) and varying concentrations of CA (0–750 μm). The inhibition mechanism was evaluated using the Lineweaver–Burk method, which revealed competitive inhibition by CA with Ki of approximately 65 ± 10 μm. Therefore, the equation for competitive inhibition was included in the model.

Kinetic parameter estimation by network decomposition

Michaelis–Menten equations were assumed for all enzyme kinetics except PAL as discussed in the previous section, and most emission rates were assumed as first order diffusion reactions. By including mechanistically correct kinetic equations we were able to generate a more biologically realistic model with predictive capabilities.

The mass balance and isotope enrichment balance equations for the benzenoid network were constructed, resulting in a highly complex system of non-linear differential equations. The kinetic parameters were estimated through non-linear least squares optimization combined with network decomposition into subnetworks as described by Rizzi et al. (1997). The overall modeling framework applied to the system described here is shown in Figure 3.

image

Figure 3.  Overall framework used to determine the kinetic parameters for the kinetic model of the benzenoid network in petunia.

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It was necessary to decompose the benzenoid network into subnetworks because the large number of unknown parameters led to poor differential equation stability and multiple optima when attempting to solve all differential equations simultaneously. The experimentally obtained pool sizes and isotopic abundances were used for optimization, in which the objective was to minimize the sums of the squares of the difference between the simulated and experimental data. In summary, once the parameters were obtained for a particular subnetwork the network size was increased and the parameters were updated and a new set of parameters were obtained for this larger network, the whole process was repeated until the largest network and the final parameter estimates were obtained. A single set of kinetic parameters were obtained (Table 1), which simultaneously accommodated labeling and pool size data obtained for all endogenous and exogenous network metabolites at the 75 and 150 mm concentrations of supplied 2H5-Phe (Figures 4a and S1). Sensitivity analysis was performed on the model simulations by determining the 95% confidence intervals for the estimated parameters (Table 1). The confidence intervals were estimated using the concepts of linearized statistics as described in Antoniewicz et al. (2006). It was necessary to show that the kinetic parameters could describe network behavior at low concentrations of supplied Phe as well as the high concentrations so they could be applied to the system at estimated in planta concentrations. Therefore, the determined kinetic parameters were used for a model simulation of petunia flowers supplied with 25 mm2H5-Phe, which is closer to the ∼5 mmin planta concentration of Phe (Boatright et al., 2004; Orlova et al., 2006). The model simulation adequately accounted for the time course of experimentally obtained pool sizes and labeling patterns of petunia flowers fed with 25 mm2H5-Phe (Figure 4b).

Table 1.   Model-optimized kinetic parameters (Vmax, Km, and Ki) for reactions in the benzenoid network of petunia based on pool size and labeling data from two feeding experiments with control petunia flowers
  K m and Ki values (nmol·gFW−1)Confidence intervals  V max (Vm) and diffusion rates (K) (nmol·gFW−1 min−1)Confidence intervals
LBUBLBUB
  1. For specific reaction see Figure 1, in which number associated with Vm, Km, or Ki corresponds to the vn reaction in the network scheme. Note that v12 = v14; v13 = v15; v31 = v32; and v33 = v34. LB is lower bound and UB is upper bound.

K m239.939.79939.955 V m25.50.00092.057
K m311006.06053.30019573.070 V m38.97.13811.066
K m4391.80.0001055.430 V m42.70.2415.156
K m560.446.28674.437 V m51.4E–080.0002.298
K m84.70.00051.141Vm80.60.0001.470
K m13133.10.000941.830 V m131.30.0005.389
K m140.70.000781.599 V m141.30.0002.547
K m166.90.000120.017 V m165.30.00030.709
K m1726.40.000341.957 V m170.0080.0000.022
K m1842.90.000112.565 V m1817.22.30232.128
K m20203.60.0002289.579 V m2026.50.000262.512
K m256.30.00030.862 V m250.20.0000.689
K m2757.40.000165.555 V m279.00.00019.007
K m32309.20.0002901.522 V m321.60.0002.385
K m350.30.00057.734 V m350.50.0004.584
K m362944.20.000463598.160 V m3614.90.000435.130
K m3714.80.000132.043 V m374.90.0004.414
K m542.1E–70.000175.611 V m540.80.0002.435
K m570.0060.000606.071 V m570.20.0003.025
K m633.93.7044.094 V m630.90.0009.403
K m62833.40.00028089.133 V m620.00.00045.054
K i64.80.00053.437 K1a4.61.8827.388
     K1b0.0010.000540.002
     K190.10.0230.237
     K300.20.0800.226
     K340.0100.0000.011
     K490.0020.0010.002
     K500.0010.0000.003
     K510.0030.0020.004
     K580.0010.0010.001
     K620.0050.0040.006
     K643.30.00045.396
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Figure 4.  Kinetic model simulation and experimentally obtained pool size and percent labeling data of representative metabolites in control petunia flowers. (a) Pool size and isotopic abundances are shown for endogenous Pheth, BA, endogenous and exogenous MB obtained from feeding experiments with 75 mm (open circles) and 150 mm (solid circles) 2H5-Phe. Simulations for labeling curves and pool sizes (lines) at 75 mm (dashed lines) and 150 mm (solid lines) 2H5-Phe were generated by the kinetic model expressions. (b) Simulated and experimentally obtained pool size and labeling patterns for Phald at 25 mm (dotted lines and solid triangles), 75 mm (dashed lines and open circles), and 150 mm (solid lines and solid circles) 2H5-Phe. A single set of kinetic parameters accommodated system behavior at low concentrations of 2H5-Phe in addition to the high concentrations. Data points are the average over 3–4 biological replicates. Error bars are ±standard error of the mean.

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Model validation using transgenic petunia plants

The predictive capability of the kinetic model of the benzenoid network in petunia was evaluated by comparing simulated and experimental data obtained from feeding experiments with 2H5-Phe in BPBT RNAi transgenic petunia flowers, in which biosynthesis of benzyl benzoate (BB) and phenylethyl benzoate (PEB) were down-regulated to undetectable levels (Orlova et al., 2006). The expectation was that the model would be able to capture the pool size and flux redistributions observed in actual BPBT RNAi flowers supplied with 150 mm2H5-Phe over a 4-h time course (Orlova et al., 2006).

Model simulations were performed to obtain accurate initial pool predictions for benzenoid metabolites in BPBT RNAi flowers, in which BB and PEB pools were depleted. In these simulations the network was first allowed to attain a steady-state based on control flower starting pools with fixed Phe concentration at the approximate in planta level (5 mm) followed by an in silico perturbation in which the Vmax values for BPBT (v12 and v32, Figure 1) were set to zero. After the network attained a new steady state, the fold changes in simulated starting pool sizes between control and transgenic steady states were in close agreement to the fold changes of observed starting pools between control and transgenic petunia flowers (Table 2). The simulated fold difference was applied to the pools of control flowers to obtain predicted starting pool values for the BPBT RNAi flowers. The predicted starting pool values were then incorporated into the kinetic model for a more accurate simulation of a 4-h time course (0, 30, 60, 120, and 240 min) of labeling and pool sizes in BPBT RNAi flowers supplied with 150 mm2H5-Phe. The model-simulated data were then compared with experimental data previously obtained for BPBT RNAi petunia flowers (Orlova et al., 2006) and found to be in excellent agreement (Figures 5 and S2). In order to further demonstrate the accuracy of the model predictions, log-transformed simulated and predicted data were plotted against each other for linear regression analysis (Figure 6). Data were log transformed so that data in different scales such as concentration, rate, and percent isotopic abundance can be compared. The slope of 1.17 and the R2 value of 0.82 are near 1, indicating that the model predictions are in close agreement with the observed data.

Table 2.   Observed versus simulated fold change of initial metabolite pools (End.) in control and BPBT RNAi transgenic petunia flowers
MetaboliteObserved fold changeSimulated fold change
BA0.70.9
End. Bald1.01.5
End. Balc5.05.2
End. Ieug1.31.9
End. MB0.80.7
End. Phald1.12.3
End. Pheth1.92.4
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Figure 5.  Kinetic model simulation and experimentally obtained pool size and percent labeling data of representative metabolites in transgenic BPBT RNAi petunia flowers. Simulations for labeling curves and pool sizes (lines) at 150 mm2H5-Phe were generated by the kinetic model expressions in response to an in silico knockout of BPBT and superimposed upon observed pool size and isotopic abundances (circles) for endogenous Pheth, BA, endogenous MB, and endogenous BB obtained from feeding experiments with 150 mm2H5-Phe in transgenic BPBT RNAi petunia flowers. Data points are the average over 3–4 biological replicates. Error bars are ±standard error of the mean.

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image

Figure 6.  Log–log plot of simulated versus experimental data. The log–log scale was chosen to encompass the whole range of data which varies from fractional enrichments (on scale of 1), average pool sizes in the range of 10–400 nm and Phe pool sizes in the range of 100 000 nm. The intercept of the log–log plot describes the slope of simulated versus experimental data on the normal scale, and calculated as 10(intercept from log–log plot). Using this approach it was found that simulated versus experimental data has a slope of 1.17 which is close to 1.

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Metabolic control analysis of the benzenoid network

Based on kinetic parameters determined by the developed kinetic model, metabolic control analysis was performed for the benzenoid network in petunia flowers in which FCCs for fluxes in the system were calculated. In general, a FCC describes the extent of systemic flux control imposed by the activity of a single enzyme in the network and the enzyme with the largest FCC exerts the largest control of flux (Stephanopoulos et al., 1998).

Flux control coefficients for volatile emission fluxes

An important concept in MCA is that the FCCs are local properties, thus for the same network the FCC will be different under different conditions. Therefore, the FCC for fluxes through the benzenoid network in petunia flowers were calculated from kinetic model simulations at high (150 mm), intermediate (25 mm), and low (5 mm) concentrations of exogenously supplied Phe to understand the distribution of flux control as a function of Phe supply. At all concentrations of supplied Phe the flux toward methylbenzoate (MB, v30) emission had distributed control among several network parameters. Strong positive control was exerted by the exogenous supply of Phe (ExPhe) and activity of PAL (Vm6), BPBT (Vm14), and enzymes responsible for conversion of BB to benzoic acid (BA) and benzyl alcohol (Balc) (Vm13), CA to benzaldehyde (Bald, Vm18) and Bald to BA (Vm20) on flux towards methylbenzoate emission (Figure 7a). The calculated FCCs showed that as Phe supply increases control shifts to other enzymes in the network. For example, the control of ExPhe on flux towards MB emission decreased from 0.42 to 0.17 when the simulated Phe supply increased from 5 to 150 mm (Figure 7a). In addition, as Phe supply increased the control on MB emission shifted from enzymes involved in the β-oxidative pathway of BA biosynthesis (Vm13) to those involved in the non-β-oxidative pathway (Vm18) indicating saturation within the non-β-oxidative pathway at high Phe supply.

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Figure 7.  Flux control coefficients calculated for representative emission fluxes. FCCs calculated for flux toward emission of MB (a), Ieug (b), and BB (c), where ExPhe is the exogenous concentration of supplied Phe and Vmx corresponds to the reaction in the benzenoid network (Figure 1) exerting control on the particular emission flux. White is 5 mM Phe, grey is 25 mM Phe and black is 150 mM Phe.

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Flux control coefficients calculated for flux toward isoeugenol (Ieug) emission over the range of Phe concentrations revealed that, when Phe supply is limiting, positive flux control is distributed among PAL (Vm6), trans-cinnamic acid 4-hydroxylase (C4H, Vm8), isoeugenol synthase (IGS, Vm35), and ExPhe, with C4H having the highest FCC (0.81). Although negative flux control over Ieug emission was distributed between BPBT (Vm14) and Bald formation from CA (Vm18) the magnitude of their FCCs are low (−0.1 and −0.19, respectively), indicating that there is little effect of the β-oxidative and non-β-oxidative pathways on Ieug emission (Figure 7b). These FCCs suggest a bottleneck around C4H. Thus, in order to increase flux toward Ieug emission at in planta concentrations of Phe it would be necessary to increase C4H activity. This notion was reinforced by calculating FCCs at higher concentrations of exogenously supplied Phe, in which flux toward Ieug emission became predominantly controlled by the activities of C4H (FCC = 0.3) and IGS (FCC = 0.8). This result was also supported by recent findings (Koeduka et al., 2009) showing that, although flux toward either eugenol (Eug) or Ieug could be altered by down-regulation of either eugenol synthase (EGS) or IGS, the net amount of emitted Eug and Ieug did not change in response to the genetic perturbation.

MCA revealed strong positive control on flux toward BB emission (v58) by BPBT (Vm14) and strong negative control by the rate of catabolism (or turnover) of BB to Balc and BA (Vm13) (Figure 1 and 7c). This finding indicates that when there is greater turnover of BB to other endogenous metabolites there will be lower emission and vice versa. Interestingly, there is remarkably negligible control of BB emission by ExPhe, which exerts control on most other emission fluxes. This suggests that in order to significantly alter flux toward BB emission it is only necessary to target the enzymes involved in endogenous BB biosynthesis (Vm14) and degradation (Vm13).

Flux control coefficients for the branch point fluxes around phenylalanine

FCCs calculated over the range of supplied Phe concentrations revealed important differences in the distribution of control over the Phe branch point. At all concentrations of supplied Phe, positive control over the Phe[RIGHTWARDS ARROW]CA flux (v6) is distributed among the enzyme activities governing the reactions for CA[RIGHTWARDS ARROW]Bald (Vm18), BCoA/Balc[RIGHTWARDS ARROW]BB (BPBT, Vm14), Phe[RIGHTWARDS ARROW]CA (PAL, Vm6), CA[RIGHTWARDS ARROW]Coum (C4H, Vm8), and the exogenous supply of Phe (ExPhe), with only slight negative control by Phe[RIGHTWARDS ARROW]Phald (PAAS, Vm3) (Figure 8a). This result indicates that a perturbation, such as an increase, of any one of these enzyme activities alone will only result in slight modification of Phe[RIGHTWARDS ARROW]CA flux (v6), and a more dramatic change would be observed by increasing all five positively controlling parameters. However, control over the Phe[RIGHTWARDS ARROW]Phald flux (v3) is distributed between PAAS (Vm3) and ExPhe with only a slight negative control by PAL (Vm6) (Figure 8b). The calculation of FCCs at the three concentrations of supplied Phe showed that PAAS activity becomes the primary controlling parameter when the Phe supply is non-limiting. This number indicates that alteration of PAAS activity would result in nearly proportional changes to the Phe[RIGHTWARDS ARROW]Phald flux (v3) as well as the other fluxes in the Phald branch of the network, but minimally affect fluxes in the CA branch of the network. This finding is in agreement with the result discussed earlier that PAL is tightly regulated by feedback inhibition of CA.

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Figure 8.  Flux control coefficients calculated for fluxes around the Phe branch point. FCCs calculated for flux toward formation of CA (a) and Phald (b), in which ExPhe is the exogenous concentration of supplied Phe and Vmx corresponds to the reaction in the benzenoid network (Figure 1) exerting control on the particular emission flux. White is 5 mM Phe, grey is 25 mM Phe and black is 150 mM Phe.

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Discussion

  1. Top of page
  2. Summary
  3. Introduction
  4. Results
  5. Discussion
  6. Concluding remarks
  7. Experimental procedures
  8. Acknowledgements
  9. References
  10. Supporting Information

Model development and validation

A goal of plant systems biology is to create tools that will allow one to make useful qualitative and quantitative predictions about the effects of a genetic or environmental perturbation on plant metabolism. Predictive modeling is a powerful tool to test scientific hypotheses, which in turn improves understanding of metabolic regulation and can lead to more successful genetic engineering of plant metabolism. The approach presented here for kinetic modeling of the benzenoid network in petunia flowers is a useful method of evaluating in vivo kinetic parameters, which allow for the accurate prediction of network response to a specific genetic perturbation. Breaking this complex network down into subnetworks in addition to non-linear least squares optimization was a particularly novel approach to generate a kinetic model of a plant metabolic network and determine in vivo kinetic parameters for uncharacterized network reactions. This is in contrast to the more common approach of using previously published, in vitro characterized kinetic parameters, which often leads to inadequate description of in vivo behavior (Mulquiney et al., 1999) and less accurate prediction of network response to a genetic perturbation. Also, in contrast to similar approaches for kinetic modeling of plant metabolic networks, which commonly use only one concentration of labeled substrate (Nuccio et al., 2000; Heinzle et al., 2007; Uys et al., 2007), the kinetic parameters for the petunia benzenoid network were determined based on data sets obtained at various concentrations of supplied substrate. In addition, our model contained a variety of kinetic equations including those for competitive inhibition, transport rates and Michaelis–Menten kinetics, which improved the robustness, biological accuracy and predictive capability of the model. The use of Michaelis–Menten kinetic expressions instead of power law kinetics (Heinzle et al., 2007) was especially important for accurate predictive capability as Michaelis–Menten kinetic parameters are valid over a wide range of substrate concentrations. Indeed, the model was able to predict system behavior when petunia flowers were supplied with a low concentration of 2H5-Phe (25 mm) (Figure 4b). Moreover, model validation with transgenic BPBT RNAi petunia plants revealed the model’s capability to predict network response to the down-regulation of BPBT, which eliminated the endogenous BB and PEB metabolite pools (Figure 5). As more experimental information becomes available about specific biochemical steps in the benzenoid network the kinetic model will be refined, in particular by expanding reaction steps that are currently lumped and including kinetic expressions for inhibition when appropriate. As the model becomes more sophisticated it can be expanded to include equations that will allow prediction of intracellular transport mechanisms and network response to rhythmic, post-transcriptional, and post-translational effects.

Metabolic control analysis

The MCA presented here for the benzenoid network in petunia flowers reflects the notion that instead of a single rate-limiting step, network control is often distributed among several network parameters (Fell, 1997; Kacser and Burns, 1973; Rios-Estepa and Lange, 2007). In general, MCA can generate new hypotheses that can then be tested by developed kinetic models and ultimately validated in planta via targeted metabolic engineering. MCA was recently performed on the metabolic network involved in sucrose accumulation in sugarcane culm (Uys et al., 2007). Through this analysis a hypothesis was generated that alteration of the activity of enzymes with the largest control over futile cycling would result in decreased futile cycling but increased sucrose accumulation in the vacuole. This hypothesis was reinforced after testing various in silico scenarios with their kinetic model providing direction for future metabolic engineering to improve sucrose accumulation in sugarcane culm. Similarly, the FCCs calculated for the Phe branch-point in the benzenoid network in petunia generated the hypothesis that alteration of PAAS activity will significantly alter flux toward the formation of Phald, Pheth, and PEB, but flux toward the other branches in the network will remain unaltered (Figure 8); however, this hypothesis has yet to be validated in planta. Overall, the results of our study and others show the utility of MCA in combination with kinetic modeling to direct future metabolic engineering strategies.

Concluding remarks

  1. Top of page
  2. Summary
  3. Introduction
  4. Results
  5. Discussion
  6. Concluding remarks
  7. Experimental procedures
  8. Acknowledgements
  9. References
  10. Supporting Information

In order to be able to achieve a desired outcome from targeted metabolic engineering, it is now necessary to manipulate a system as a whole and consider the response of the entire metabolic network to a specific perturbation. Many times the genetic modification of a specific enzyme in a network fails to produce an obvious phenotypic change due to compensation from an alternative pathway, gene redundancy or highly distributed network control. Kinetic models are able to overcome these complications by providing a deeper understanding of network structure and regulation which otherwise would not be intuitively known (Nuccio et al., 2000; Rios-Estepa et al., 2008). The kinetic modeling approach presented here for the benzenoid network in petunia can be widely applied to networks of similar complexity in other plant systems. With a valid kinetic model in hand, one is able to simulate dozens of in silico metabolic engineering strategies to obtain a precise target to achieve a desired outcome, ultimately saving labor and expense.

Experimental procedures

  1. Top of page
  2. Summary
  3. Introduction
  4. Results
  5. Discussion
  6. Concluding remarks
  7. Experimental procedures
  8. Acknowledgements
  9. References
  10. Supporting Information

Labeling experiments with 2H5-Phe and volatile sampling

Feeding experiments were performed on 3–4 biological replications as described previously (Boatright et al., 2004). Corollas from 2-day-old control flowers were placed on moist filter paper supplied with 25, 75, or 150 mm deuterium-labeled phenylalanine (l-phenylalanine-ring-2H5; Cambridge Isotope Laboratories, Inc., http://www.isotope.com) (total 10 corollas per each experiment) and emitted volatiles were collected after 30, 60, 120, and 240 min during the day (10 a.m. to 2 p.m.) using a closed-loop stripping method (Donath and Boland, 1995; Dudareva et al., 2005). To determine the internal pools of volatiles, 1 g of 2-day-old corolla tissue were extracted after scent collection with 10 ml of dichloromethane, concentrated to 180 μl, and analyzed by GC-MS (Boatright et al., 2004).

Organic and amino acids analysis

To determine pools and labeling of organic and amino acids 0.5 g of petal tissue was extracted by a methanol:chloroform:water phase separation as described previously (Orlova et al., 2006). Organic acids were further separated by extraction with ethyl acetate acidified with 1 N HCl, concentrated, derivatized with BSTFA (Sigma, http://www.sigmaaldrich.com) and analyzed by GC-MS (Boatright et al., 2004). Amino acids were purified by ion exchange chromatography, concentrated, derivatized by HFBI and analyzed by GC-MS as described previously (Boatright et al., 2004). Internal standards were hydroxyproline for the amino acid fraction and 4-chlorobenzoic acid for the organic acid fraction.

Computer modeling of 2H5-Phe labeling data and estimation of Vmax and Km

A simple Michaelis–Menten type reaction mechanism was assumed for most of the enzyme kinetics:

  • image(1)

where v is the velocity of the enzyme catalyzed reaction, S is the substrate concentration in nmol·gFW−1, Vmax is the maximum reaction velocity (nmol·gFW−1 min−1, and Km is the substrate concentration at ½Vmax. However, the kinetic equation for a two substrate reaction was also modeled when appropriate using the following equation:

  • image(2)

where A is the concentration of one substrate and B is the concentration of the other substrate, both in nmol gFW−1.

Most scent compound emission rates were assumed as first order diffusion reactions given by:

  • image(3)

where K is the coefficient (min−1) and A is the emitted compound (nmol·gFW−1).

A diffusion reaction was also assumed for the uptake rate of Phe as an inverse correlation was observed between the uptake rate and internal Phe concentration, where external Phe uptake rate decreased as internal Phe concentration increased. Therefore, the following equation was used to describe Phe uptake:

  • image(4)

where K1 is the diffusion coefficient, Pheex is the external Phe concentration (mmol·L−1), Pheint is the intracellular Phe concentration (nmol·gFW−1) and K1b is the conversion factor that converts the Pheint into concentration units of mmol·L−1.

Network decomposition into subnetworks was applied as described in Rizzi et al. (1997). Solving for subnetworks entails that the time course of pool size and labeling data be provided for the component that acts as substrate for a particular subnetwork. Empirical equations were fitted to pool size and labeling patterns for all the species using the CURVEFIT tool of MATLAB (2007). The empirical equations are simply used to fit the data over a time course and have no biological significance, but provide a smooth fit representation of the experimental data. Table S1 lists some of these empirical expressions used for the simulation.

For each subnetwork, the set of differential equations (mass balances and isotopic enrichment balances) were first solved for the initial guess values of the parameters using either differential equation solver ODE45 in MATLAB that implements an explicit Runge-Kutta-(4,5) formula or stiff solver ODE15s for some networks depending upon the stiffness of the differential equations. The calculated pool sizes and fractional enrichments were fed to an optimizer, where the objective function is the sum of the square of the difference between the experimentally observed and simulated values (which depend on the guessed parameters):

  • image(5)

where N is total number of species in the subnetwork (that is pool sizes and fractional labeling), ZCal is the calculated values and ZExp is the experimental value of a particular experimental species. Thus the objective was to minimize the difference between the simulated and experimental data. The optimization was performed in MATLAB (2007) using LSQNONLIN that implemented non-linear least square optimization using the sub-space trust region algorithm. Once the parameters were obtained for a particular subnetwork, the network size was increased and the parameters were updated and a new set of parameters were obtained for this larger network. The whole process was repeated until the final parameter estimates were obtained. The general form of the differential equations used by the optimizer is:

  • image(6)

where Ci is the concentration of ith species (nmol·gFW−1) and v are the reactions (nmol·gFW−1 min−1) involved in the production and consumption of a particular species. The general isotopic labeling balance is given by:

  • image(7)

where fi represents the fractional labeling of the species.

Steady-state simulation to estimate starting pools

The initial metabolite pools for the BBPT RNAi transgenic line (line 10, Orlova et al., 2006) were determined using the kinetic model developed for the control petunia flowers. In this simulation, the initial concentration of the control data was used as the starting pool and the internal Phe concentration was held constant by setting the rate of formation of Phe (v1) equal to the rate of degradation of Phe, allowing the system to reach a pseudosteady state. Once the steady state was reached an in silico BBPT down-regulation was simulated by setting v14 and v32 equal to a minuscule number, 0.000001 (0 as a whole number led to mathematical instability of the differential equations), and the system was allowed to reach a new pseudosteady state. The fold change in the pool size between the control and transgenic steady states were determined. This fold change was then applied to the initial control pool values by multiplication to calculate the in planta BBPT RNAi petunia initial pools. The predictive capability of this method was determined by comparing the simulated fold change in starting pools to the experimentally determined fold change in starting pools.

Sensitivity analysis: estimation of confidence intervals

The confidence intervals were estimated using sensitivity coefficients, which are the partial derivatives of the simulated values at the optimum solution with respect to the estimated parameters:

  • image(8)

where Jij is the sensitivity of simulated measurement (xi) at the optimum with respect to estimated parameter pj. The sensitivity coefficients were obtained directly from the LSQNONLIN routine in MATLAB, calculated at the optimum. Next the Hessian matrix was calculated, which is defined as:

  • image(9)

The covariance matrix of the estimated parameters can be calculated as:

  • image(10)

where Φ is the value of objective function at the optimum, H−1 is the inverse of the Hessian matrix and n are the number of observations and p are the number of parameters.

In this work it was found that the inverse of the matrix H was not numerically stable and thus Moore Penrose pseudoinverse was used for the calculation inverse of the matrix H. The diagonal elements of the ∑parameters are the variances of the estimated parameters, from which the approximate 95% confidence intervals can be calculated as:

  • image(11)

R2 analysis

Data was log transformed as the log–log scale is able to encompass the whole range of data. The intercept of the log–log plot describes the slope of simulated versus experimental data on the normal scale, and calculated as 10(intercept from log–log plot). Analysis was performed in Microsoft Office Excel™.

Metabolic control analysis

The kinetic model was used for calculation of the flux control coefficients (FCCs), which are defined as:

  • image(12)

where Ej is the enzyme activity or parameter that affects the particular flux Ji (Kacser and Burns, 1973). FCCs are the relative change in the steady-state flux resulting from an infinitesimal change in the activity of an enzyme of the pathway divided by the relative change of the enzymatic activity (Stephanopoulos et al., 1998). The external Phe concentration and each of the enzyme activities (Vm) was perturbed in range of ±10% and the fluxes were evaluated for each perturbation at the steady state. Log–log plots were generated for each of the fluxes and enzyme activity pair, and the slope which is the FCC for the flux /enzyme pair was determined using curve fitting using LSQNONLIN (MATLAB 2007b).

Functional expression of PAL1 in Escherichia coli and purification of recombinant protein

The coding region of petunia PAL1 was amplified by PCR using the forward primer 5′-CCATGGAGTATGCCAATGAAAACTGTA-3′, which introduced an NcoI site at the initiating ATG codon in combination with the reverse primer 5′-GGATCCGCAGAGTGGAAGAGGAGCACC-3′, which introduced a BamHI site downstream of the stop codon and subcloned into the expression vector pET 28a (Novagen, http://www.merck-chemicals.com). Sequencing revealed that no errors had been introduced during PCR amplifications. For functional expression, BL21 Rosetta competent E. coli cells were transformed with the resulting recombinant plasmid and pET vector without an insert as control, and grown in LB medium with 50 μg·ml−1 kanamycin at 37°C. Induction, harvesting, and protein purification by affinity chromatography on nickel–nitriloacetic acid agarose (Qiagen, http://www1.qiagen.com) were performed as described previously (Boatright et al., 2004) with slight modifications. When the culture density reached an OD600 of 0.5, the expression of PAL was induced by addition of isopropyl-1-thio-β-D-galactopyranoside to a final concentration of 0.4 mm. After 24-h incubation with shaking (200 rpm) at 18°C, the E. coli cells were harvested by centrifugation and resuspended in lysis buffer (50 mm potassium phosphate (KPi) pH 8.0, 300 mm NaCl, 10% (v/v) glycerol). PMSF was added and cells were lysed with lysozyme (1 mg·ml−1) and 3-min sonication on ice. After removal of the cellular debris by centrifugation for 15 min at 20 000 g the enzyme in the supernatant was purified by affinity chromatography on nickel–nitriloacetic acid agarose (0.5-ml bed volume) (Qiagen). The Ni–NTA agarose was washed with lysis buffer and the 6xHis-tagged protein was eluted from the column with a gradient of 20 mm KPi (pH 7.5), 500 mm NaCl, and 500 mm imidazole. The eluate fractions (1 ml each) with the highest PAL activity were desalted on NAPTM 5 columns (Amersham Pharmacia Biotech AB, http://www6.gelifesciences.com) into storage buffer (50 mm KPi (pH 7.5) and 10% glycerol (v/v). Fractions with the highest PAL activity were examined by SDS-PAGE gel electrophoresis followed by coomassie brilliant blue staining of the gel. Protein concentrations were determined by the Bradford method using the Bio-Rad (http://www.bio-rad.com/) protein reagent and bovine serum albumin as a standard. Kinetic data were evaluated using Lineweaver–Burk plots.

Enzyme assays

PhPAL1 fractions were assayed for activity with L-[U-14C]Phe (350 mCi·mmol−1) as substrate (American Radiolabeled Chemicals Inc, http://www.arcincusa.com). The standard reaction mixture (100 μl) contained purified PAL1 protein (2.35 μg) and 2 mm L-[U-14C]Phe in 50 μl assay buffer (100 mm Na2B4O7 (pH 8.8) and 2 mm dithiothreitol). After incubation for 30 min at room temperature, the reaction was stopped with 50 μl of 1 N HCl. The product was extracted with 200 μl toluene and 100 μl of the organic phase was counted in a liquid-scintillation counter. The raw data were converted to picokatals (pkat) based on the specific activity of the substrate and efficiency of counting. Controls included assays without enzyme, and background radioactivity produced in these assays was subtracted from all of the results. Assays were done in triplicate. Inhibition studies were performed by varying the concentration of CA at each of a series of concentrations of Phe. Data were presented as double-reciprocal plots of initial velocity (v) versus varying substrate (S) concentrations. In all experiments, an appropriate enzyme concentration was chosen so that the reaction velocity was linear during the incubation time period.

Quantitative real-time PCR

Total RNA from 2-day-old petunia petal tissue was isolated as previously described (Kolosova et al., 2001). Real-time quantitative reverse transcriptase polymerase chain reaction (real-time qRT-PCR) was performed on an Applied Biosystems StepOnePlusTM Real-Time PCR System using SYBR Green fluorescent dye. The primers for the PAL isoforms were designed to amplify an approximately 200-bp amplicon in the 3′ region of the coding sequence and were as follows:

PAL1Fwd 5′-GGCCATGATCAACAACTTGATC-3′

PAL1Rev 5′-CTTCACCATTCTCTTGACTTCATCA-3′

PAL2Fwd 5′-TAATGAATTTAGGAAACCAATCGTG-3′

PAL2Rev 5′-TTCAACTTTAATATCATTTTCTCTAGCAATAC-3′

PAL3Fwd 5′-GGCTGAATTTAGAAAGCCAGTG-3′

PAL3Rev 5′-CATCTTCAGAAAGCTCCACTTTC-3′.

These primers were specific for the individual PAL isoforms. Real-time qRT-PCRs were carried out in 20 μl final volume. The reaction mixture contained Fast SYBR Green Master Mix (Applied Biosystems, http://products.appliedbiosystems.com), forward and reverse primers and either the appropriate DNA gene template to determine standard curve for absolute quantification or the 2-day-old petunia petal cDNA template. The standard curve method was used to determine the absolute target quantity in samples. Real time qRT-PCR conditions were as follows: PAL1: 40 cycles of 95°C 15 sec, 68°C 15 sec, and 72°C 30 sec; PAL2 and PAL3: 40 cycles of 95°C 3 sec, 57°C 15 sec, and 72°C 15 sec. cDNA sample reactions were from three biological replicates of petunia tissue and two technical replicates were performed.

Acknowledgements

  1. Top of page
  2. Summary
  3. Introduction
  4. Results
  5. Discussion
  6. Concluding remarks
  7. Experimental procedures
  8. Acknowledgements
  9. References
  10. Supporting Information

This work is supported by the US National Science Foundation (grant number MCB-0615700 for JAM, ND and DR).

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  2. Summary
  3. Introduction
  4. Results
  5. Discussion
  6. Concluding remarks
  7. Experimental procedures
  8. Acknowledgements
  9. References
  10. Supporting Information
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Supporting Information

  1. Top of page
  2. Summary
  3. Introduction
  4. Results
  5. Discussion
  6. Concluding remarks
  7. Experimental procedures
  8. Acknowledgements
  9. References
  10. Supporting Information

Figure S1. Kinetic model simulation and experimentally obtained pool size and percent labeling data of metabolites in control petunia flowers. Pool size and isotopic abundances are shown for benzenoid metabolites obtained from feeding experiments with 75 mm (open circles) and 150 mm (solid circles) 2H5-Phe. Simulations for labeling curves and pool sizes (lines) at 75 mm (dashed) and 150 mm (solid) 2H5-Phe were generated by the kinetic model expressions.

Figure S2. Kinetic model simulation and experimentally obtained pool size and percent labeling data of benzenoid metabolites in transgenic BPBT RNAi petunia flowers. Simulations for labeling curves and pool sizes (lines) at 150 mm 2H5-Phe were generated by the kinetic model expressions in response to an in silico knockout of BPBT and superimposed upon observed pool size and isotopic abundances (circles) for endogenous and exogenous metabolites obtained from feeding experiments with 150 mm 2H5-Phe in transgenic BPBT RNAi petunia flowers.

Table S1. Empirical fit relations used for the kinetic model simulations. The empirical equations are for data obtained from 75 mm and 150 mm 2H5-Phe feeding concentrations. All equations used in the model are also listed.

Appendix S1. Differential equations used in the model.

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