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Supporting Information
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A transcriptomics based kinetic model for ethylene biosynthesis in tomato fruit:
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development, validation and exploration of novel regulatory mechanisms
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Bram Van de Poel, Inge Bulens, Maarten L.A.T.M. Hertog, Bart M. Nicolai, Annemie H. Geeraerd
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Overview
Supporting Figures
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Supporting Figure S1. Model input data. ................................................................................................ 2
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Supporting Figure S2. Illustration of the average calibration method..................................................... 3
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Supporting Figure S3. Comparison qPCR results analyzed by the normal calibration method and the
average calibration method. .................................................................................................................... 4
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Supporting Figure S4. Input data adapted from literature. ...................................................................... 5
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Supporting Figure S5. Distribution of ACC production by the three individual ACS isoforms. ............ 6
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Supporting Figure S6. Monte Carlo evaluation of the model.................................................................. 7
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Supporting Figure S7. The behaviour of the fTRAN and fDEG function during the entire fruit development
period. ...................................................................................................................................................... 8
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Supporting Tables
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Supporting Table S1. Estimated parameter values and their units .......................................................... 9
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Supporting Table S2. Estimated parameter values of fTRAN and fDEG. .................................................... 10
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Supporting Methods
Supporting Methods S1. Explanation of the average calibration method for qPCR analysis. .............. 11
Supporting Notes
Supporting Notes S1. Overview of the model in Matlab code. ............................................................. 13
Supporting References
Supporting References S1 ..................................................................................................................... 15
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Supporting Figures
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Supporting Figure S1. Model input data. Overview of the input data used by the model for (a)
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SAM content (nmol mg protein-1), (b) ACO1 expression (relative copies), (c) ACS2
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expression (relative copies), (d) ACS4 expression (relative copies), (e) ACS6 expression
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(relative copies) and (f) MTN expression (relative copies) during tomato fruit development,
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ripening and postharvest storage. A linear interpolation method is used between the data
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points in order to get intermediate input values.
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Supporting Figure S2. Theoretical illustration of the average calibration method. Two
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different reference genes are analyzed (Ref gene A (green) and Ref gene B (red)) and for both
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genes a dilution series was made ranging from 1 to 0.01 transcript copies (= gene specific
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calibration curve). Both the qPCR profiles (a) and the calculated calibration curves (b) are
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shown for both genes and their average expression (blue). For both genes an unknown sample
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was also included (UA and UB). Based upon the gene specific calibration curve, a Cq value of
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the unknown samples were calculated. Supporting Figure S3A shows how the average qPCR
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profile is constructed from gene A and B for each dilution point. Supporting Figure S3b
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shows the average calibration curve, calculated from the two independent calibration curves
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of gene A and B. The average calibration curve allows to calculate an average expression
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(Cq,Avg) level for the unknown samples UA and UB. This method shows that sample UA is ±
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2.106 times more expressed than sample UB, relative to their average expression. Gene A is
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thus identified as the most important gene in this theoretical example.
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Supporting Figure S3. Comparison qPCR results analyzed by the normal calibration method
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and the average calibration method. Relative gene expression profile of all ACO (a, b) and
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ACS (c, d) isoforms with the gene specific calibration method (a, c) and the average
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calibration method (b, d). Maturity stage annotations: S. small fruit, M. medium fruit, IMG.
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immature green fruit, MG. mature green fruit, BR. breaker fruit, LO. light orange fruit, O.
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orange fruit, P. pink fruit, R. red fruit, RR. red ripe fruit, RR + X. red ripe fruit + X days post
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harvest (X = 3, 5, 7, 10 and 12 days).
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Supporting Figure S4. Input data adapted from literature. Profiles of MACCT activity (nmol
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h-1 mg protein-1) and SAMdc activity (nmol h-1 mg protein-1) used as model input and adopted
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from (Martin et al., 1995; Morilla et al., 1996).
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Supporting Figure S2. Distribution of ACC production by the three individual ACS isoforms
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ACS2 (black), ACS4 (red) and ACS6 (blue).
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Supporting Figure S3. Monte Carlo simulation of the model. Heat plots representing the
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distribution results from a Monte Carlo simulation for (a) ethylene production (nmol h-1 mg
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protein-1), (b) ACC levels (nmol mg protein-1), (c) MACC levels (nmol mg protein-1), (d)
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MTA levels (nmol mg protein-1), (e) ACO activity (nmol h-1 mg protein-1), (f) ACS activity
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(nmol h-1 mg protein-1) and (g) MTN activity (nmol h-1 mg protein-1) during tomato fruit
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development, ripening and postharvest storage.
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Supporting Figure S4. The behaviour of the fTRAN (a) and fDEG (b) function during the entire
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fruit development period.
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Supporting Tables
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Supporting Table S1. Estimated parameter values and their units; including initial values of model independent
variables.
Abbreviation
Estimated value
Unit
± Std. deviation
0.22 ± 0.07
nmol h-1 mg protein-1 d-1 relative copies-1
kt,ACS
0.028 ± 0.003
nmol h-1 mg protein-1 d-1 relative copies-1
kt,MTN
34.9 ± 8.2
nmol h-1 mg protein-1 d-1 relative copies-1
1.39 ± 0.4
d-1
kpd,ACS2
0.21 ± 0.02
d-1
kpd,ACS4
4.25 ± 0.66
d-1
kpd,ACS6
0.22 ± 0.04
d-1
kpd,MTN
0.16 ± 0.04
d-1
0.0126 ± 0.0009
mg protein h nmol-1 d-1
kACS2
2.2 ± 0.3
mg protein h nmol-1 d-1
kACS4
0.63 ± 0.58
mg protein h nmol-1 d-1
kACS6
0.016 ± 0.005
mg protein h nmol-1 d-1
kMACC
0.073 ± 0.004
mg protein h nmol-1 d-1
kSAMDC
0.22 ± 0.05
mg protein h nmol-1 d-1
kMTN
0.24 ± 0.04
mg protein h nmol-1 d-1
kDACC
0.008 ± 0.011§
d-1
0.04 ± 0.01
nmol h-1 mg protein-1
[MTNini]
75.7 ± 6.7
nmol h-1 mg protein-1
[MTAini]
1.2 ± 0.2
nmol mg protein-1
0.35 ± 0.03
nmol mg protein-1
4.4 ± 1.3
h-1
Protein synthesis kt,ACO
Protein degradation kpd,ACO1
Metabolite synthesis kACO
Initial values [ACS6ini]
Basal MTA level [MTAb]
Ethylene diffusivity kdiff
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§
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omitted from the model. Additional biochemical information about DACC formation could improve the estimation of this parameter.
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
Standard deviation was larger than the estimated parameter value. This indicates that the estimated value of kDACC is uncertain and could be
All other initial values were fixed (see Supporting Notes S1 for values).
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Supporting Table S2. Estimated parameter values of fTRAN and fDEG.
Abbreviation
Estimated value
± Std. deviation
Unit
0.29 ± 0.03
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0.037 ± 0.006
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0.09 ± 0.02
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fDEGini
3.7 ± 0.8
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fDEGmin
0.93 ± 0.02
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fDEGmax
4±1
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fTRAN kTRAN
fTRANini
fDEG kDEG
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Supporting Methods
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Supporting Methods S1. Explanation of the average calibration method for qPCR analysis.
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The implementation of the average calibration method allows cross-comparison of gene
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expression levels of different genes. The theoretical explanation of the average calibration
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method is supported by Supporting Figure S3 that shows real-time qPCR profiles for two
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theoretical genes (genes A and B) and their calibration curves. If one analyzes the expression
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level of sample A with a calibration curve designed in the range of gene A only, it would have
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a Cq,A value of 0.025. This value is much lower than the Cq,B value (0.38) of unknown sample
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B calculated with a gene B-specific calibration curve. For the average calibration method the
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average Cq values for all dilutions points of the gene specific calibration curve are calculated.
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One can now reanalyze the expression level of unknown samples A and B with the new
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average calibration curve. The new expression levels of unknown sample A and B have a
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Cq,Avg value of 14.2 and 0.000065 respectively. This method shows that gene A is much more
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expressed than gene B, relative to the average expression level of both genes, identifying gene
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A as more important than gene B. The method can now be extended and improved by
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calculating the average calibration curve for many stable reference genes. This allows a
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rescaling of unknown genes according to the average expression level of a group of reference
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genes.
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In our study, all performed qPCR runs included a gene specific calibration curve for relative
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quantification. This calibration curve consisted out of a dilution series of a mixed sample,
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allowing quantification of unknown samples in the same expression range of the mixed
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sample. Unfortunately, it is impossible to compare transcription levels of different genes,
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since the calibration curve is gene specific (assessed with the same primers). To overcome
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this, the new average calibration curve was calculated based upon the average expression of
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five different reference genes (GAPDH, ACT, ELF1α, RPL2 and PP2Ac). This new
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calibration curve represents the average expression level of the five reference genes. The
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expression level of all unknown samples was reanalyzed relatively to the average expression
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of the five reference genes and, as such, allows a cross-comparison of relative expression
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levels between different genes.
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Supporting Notes
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Supporting Notes S1. Overview of the model in Matlab code.
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The full model is written in Matlab code and is shown below. It can be run by the OptiPa
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toolbox in a Matlab environment (Hertog et al., 2007). OptiPa is a graphical user interface
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freeware tool designed for solving ordinary differential equations and parameter optimization
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for kinetic modeling.
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%-------------------------------------------------------------------------%
Ethylene Biosynthesis model
%-------------------------------------------------------------------------switch status
case 'step1'
%------------------------------------------------------------------------------------% Initialize variables and parameters
%------------------------------------------------------------------------------------output_var = { 'ACO1' 'ACS2' 'ACS4' 'ACS6' 'MTN' 'ACC' 'MACC' 'DACC' 'MTA'
'ETHint' 'ETHpro' 'ACS'} ;
%------------------------------------------------------------------------------------% Definition of all model parameters. One parameter per row.
% For consistency, these parameters values are set equal to the optimized values
shown in SI Table SI. In practice, initial estimates are to be provided here.
%------------------------------------------------------------------------------------param_DEF = {
'ktaco'
0.22;...
'ktacs'
0.028;...
'ktmtn'
34.9;...
'kpdaco1'
'kpdacs2'
'kpdacs4'
'kpdacs6'
'kpdmtn'
1.39;...
0.21;...
4.25;...
0.22;...
0.16;...
'kaco1'
'kacs2'
'kacs4'
'kacs6'
'kmacc'
'kdacc'
'ksamdc'
'kmtn'
0.0126;...
2.2;...
0.63;...
0.016;...
0.073;...
0.008;...
0.22;...
0.24;...
'ACS60'
'MTN0'
0.04;...
75.7;...
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'MTA0'
1.2;...
'MTAb'
0.35;...
'kdiff'
4.4};
%------------------------------------------------------------------------------------case 'step2'
%------------------------------------------------------------------------------------% Initialize ODEs
%-------------------------------------------------------------y0 = [ 1.5 0 0 ACS60 MTN0 0 1 1 MTA0 0.008] ;
%------------------------------------------------------------------------------------case 'step3'
%------------------------------------------------------------------------------------% Transform experimental data
%------------------------------------------------------------------------------------case 'step4'
%------------------------------------------------------------------------------------% ODE model definition
%------------------------------------------------------------% defining local model constants
%------------------------------------------------------------------------------------% SAM content
SAM=interp1(t_cond,SAM,t);
SAM0=SAM(1);
% Gene expression data
ACO1e=interp1(t_cond,ACO1e,t);
ACS2e=interp1(t_cond,ACS2e,t);
ACS4e=interp1(t_cond,ACS4e,t);
ACS6e=interp1(t_cond,ACS6e,t);
MTNe=interp1(t_cond,MTNe,t);
% SAM decarboxylase activity
SAMdc=interp1(t_cond,SAMdc,t);
SAMdc0=SAMdc(1);
% MACC transferase activity
MACCT=interp1(t_cond,MACCT,t);
%------------------------------------------------------------------------------------% Definition of ODEs
%------------------------------------------------------------------------------------% Protein synthesis
dACO1dt=ktaco*ACO1e-kpdaco1*ACO1;
dACS2dt=ktacs*ACS2e-kpdacs2*ACS2;
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dACS4dt=ktacs*ACS4e-kpdacs4*ACS4;
dACS6dt=ktacs*ACS6e-kpdacs6*ACS6;
dMTNdt=ktmtn*MTNe-kpdmtn*MTN;
% Metabolite production
dACCdt=kacs2*SAM*ACS2+kacs4*SAM*ACS4+kacs6*SAM*ACS6kaco1*ACC*ACO1-kmacc*ACC*MACCT-kdacc*ACC;
dMACCdt=kmacc*ACC*MACCT;
dDACCdt=kdacc*ACC;
dMTAdt=kacs2*SAM*ACS2+kacs4*SAM*ACS4+kacs6*SAM*ACS6kmtn*(MTA-MTAb)*MTN+ksamdc*SAM*SAMdc;
% Ethylene production
dETHintdt=kaco1*ACC*ACO1-kdiff*ETHint;
%------------------------------------------------------------------------------------% Returning all ODE's together as dydt
%------------------------------------------------------------------------------------dydt = [dACO1dt dACS2dt dACS4dt dACS6dt dMTNdt dACCdt dMACCdt
dDACCdt dMTAdt dETHintdt]';
%------------------------------------------------------------------------------------case 'step5'
%------------------------------------------------------------------------------------% Transform ODE model output
%------------------------------------------------------------------------------------ETHpro=ETHint*kdiff;
ACS=ACS2+ACS4+ACS6;
MTA=MTA+MTAb;
%------------------------------------------------------------------------------------end
Supporting References
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1. Martin MN, Cohen JD, Saftner RA (1995). A New 1-Aminocyclopropane-1-Carboxylic AcidConjugating Activity in Tomato Fruit. Plant Physiol 109: 917-926.
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2. Morilla A, Garcia JM, Albi MA (1996). Free polyamine contents and decarboxylase activities during
tomato development and ripening. J Agr Food Chem 44: 2608-2611.
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3. Hertog MLAT, Verlinden BE, Lammertyn J, Nicolai BM (2007) OptiPa, an essential primer to develop
models in the postharvest area. Comput Electron Agr 57: 99-106.
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