A transcriptomics-based kinetic model for ethylene biosynthesis in tomato (Solanum lycopersicum) fruit: development, validation and exploration of novel regulatory mechanisms

Authors


Summary

  • The gaseous plant hormone ethylene is involved in many physiological processes including climacteric fruit ripening, in which it is a key determinant of fruit quality. A detailed model that describes ethylene biochemistry dynamics is missing. Often, kinetic modeling is used to describe metabolic networks or signaling cascades, mostly ignoring the link with transcriptomic data.
  • We have constructed an elegant kinetic model that describes the transfer of genetic information into abundance and metabolic activity of proteins for the entire ethylene biosynthesis pathway during fruit development and ripening of tomato (Solanum lycopersicum).
  • Our model was calibrated against a vast amount of transcriptomic, proteomic and metabolic data and showed good descriptive qualities. Subsequently it was validated successfully against several ripening mutants previously described in the literature. The model was used as a predictive tool to evaluate novel and existing hypotheses regarding the regulation of ethylene biosynthesis.
  • This bottom-up kinetic network model was used to indicate that a side-branch of the ethylene pathway, the formation of the dead-end product 1-(malonylamino)-1-aminocyclopropane-1-carboxylic acid (MACC), might have a strong effect on eventual ethylene production. Furthermore, our in silico analyses indicated potential (post-) translational regulation of the ethylene-forming enzyme ACC oxidase.

Introduction

The volatile plant hormone ethylene is a small molecule that regulates many aspects of plant development (Vandenbussche et al., 2012), including climacteric fruit ripening (Alexander & Grierson, 2002). In order to achieve better fruit quality and storability, a lot of effort has been devoted to biotechnological and genetic manipulations to control fruit ripening and ethylene-induced senescence (Theologis, 1992; Matas et al., 2009). Although the ethylene biosynthesis pathway and its adjacent Yang cycle are well characterized, an elegant mathematical model that is able to predict fruit ethylene production, based upon the known stoichiometry, and which could aid scientists and agronomists in their quest for preservable and high-quality agricultural products, is lacking.

A mathematical model is now an integral part of systems biology studies (Steuer et al., 2006; Hertog et al., 2011). It allows interpretation of the complex interactions between the different elements of the system (Lucas et al., 2011). These elements can operate at the cellular level only or at different tissues, organs and even between different organisms and their surrounding environment (Keurentjes et al., 2011). Kinetic modeling is a suitable mathematical technique with which to tackle such complex data sets. It has the advantage that one can study the dynamics of a certain system over time (Kitano, 2002). Kinetic modeling is most frequently used to describe metabolic or signaling networks (Lee et al., 2008), ignoring the link with proteomic and transcriptomic data, although such data are an essential part of modern systems biology (Westerhoff & Palsson, 2004; Rohwer, 2012). Limited reports have integrated proteomics and transcriptomics in one model, mainly focusing on the short-term responses of unicellular yeast (Klipp et al., 2005; Liebermeister & Klipp, 2006) or on short-term gibberellin signaling in Arabidopsis thaliana (Middleton et al., 2012). New challenges arise when modeling the complete information transfer of the central dogma of molecular biology (Crick, 1970) during long-term developmental processes (Kooke & Keurentjes, 2012; Prusinkiewicz & Runions, 2012). A previous kinetic model (ETHY) predicting ethylene production of peach (Prunus persica), solely based on fruit dry mass, lacked substantial biochemical information (Genard & Gouble, 2005). We report on a kinetic model that starts from gene expression and that describes abundance and metabolic activity of proteins of the entire ethylene biosynthesis pathway, during the entire developmental and ripening period of tomato (Solanum lycopersicum) fruit, a model system for fruit ripening. The model is validated against well-characterized tomato ripening mutants, and is used to explore in silico several hypotheses regarding the regulation of ethylene biosynthesis.

Materials and Methods

Plant material and biochemical characterization

Tomato fruits (Solanum lycopersicum L. cv Bonaparte) of different stages of maturity were obtained from the Research Station of Vegetable Production (Hoogstraten, Belgium). Ten individual fruits for each maturity stage were sampled, each fruit originating from a different plant. Additionally, the postharvest shelf life (at 18°C and 80% relative humidity) of red ripe fruits was assessed for 12 d. Immediately after sampling, fruit color, firmness and ethylene production were measured (Van de Poel et al., 2012c). On the same day, fruit pericarp tissue was flash-frozen in liquid nitrogen, crushed and stored at −80°C until further analysis. Metabolite, protein activity and gene expression analyses were performed as described in Bulens et al. (2011) and Van de Poel et al. (2012a).

Transformation of maturity classes into biological age

Because we modeled the entire fruit development and ripening period of tomato, a time stamp was required for every individual tomato that was used for calibrating the model. Fruit mass and fruit color were therefore used to transform all maturity stages into biological age (days) using the approach described in Van de Poel et al. (2012c). Briefly, dynamic models were developed first to describe the mass and color change of tomato fruit as a function of time. By using the inverse models, the biological age of an individual fruit could then be calculated from its mass and color. For postharvest stored fruits, the exact amount of days in storage was added to the biological age of red ripe fruits. This classification method transforms nonequidistant discrete maturity stages into real biological time, allowing the construction of a proper time-dependent kinetic model that spans the entire lifetime of a single fruit.

Model validation against the literature

Because our model was to be validated against data from the literature, an estimation of gene expression level and fruit maturity was essential for validation. In all papers from which data were obtained, gene expression levels were presented by Northern blotting, and hence pixel intensity analysis was performed on these blots, under the assumption that band intensity was linearly correlated with gene expression level. The literature data mainly represented well-defined maturity stages. As the original data with which the model was calibrated also included these maturity stages (see Van de Poel et al., 2012a), an average biological age could be calculated for the corresponding maturity stages and allowed us to position these maturity stages on the continuous biological age axis. This methodology allowed us to obtain a numerical estimate of the timing and intensity of gene expression level described in the literature.

Numerical solutions

Matlab R2009b (The MathWorks Inc., Natick, MA, USA) was used for solving ordinary differential equations and for parameter estimation using normalized data and the weighted least squares criterion. OptiPa, a kinetic modeling tool (Hertog et al., 2007), was run as a Matlab interface using the Runge–Kutta solver for nonstiff systems (ODE45). The behavior of the model was evaluated through a Monte Carlo analysis incorporated in OptiPa. The full model, written in Matlab code, is presented in Supporting Information Notes S1.

Description

Kinetic models allow description of the dynamic changes in time of different components of a biochemical network in relation to each other. Our model focuses on the behavior of the ethylene biosynthesis pathway during long-term fruit development. It is based on the known stochiometry of the ethylene biosynthesis pathway and uses only quantitative gene expression data and the concentration of the substrate S-adenosyl-l-methionine (SAM) as input. This input data are illustrated in Fig. S1. The outputs are enzyme activities, concentrations of metabolites, and, eventually, the ethylene production rate. Fig. 1 illustrates the pathway diagram linking different variables (transcripts, proteins and metabolites) with their corresponding reaction rate constants. All enzymatic conversions as well as the complex process of translation were modeled by mass-action kinetics, which is a simplified version of the Michaelis–Menten equation, under the assumption that substrate concentrations are not saturating. Despite the vast amount of experimental data obtained, it was not possible to estimate Vmax and Km because of the singularity of the Jacobian in the least square estimation indicating overfitting. We therefore decided to use kinetic mass-action equations. This simplification allowed us to reduce the number of unknown variables to 21, without losing any descriptive power while avoiding overfitting.

Figure 1.

Biochemical network of the plant ethylene biosynthesis pathway highlighting the elements of the mathematical model. Solid arrows represent direct conversions, while the dotted arrows indicate more general pathway interactions containing multiple conversion steps. Ethylene (C2H4) is formed from its precursor 1-aminocyclopropane-1-carboxylic acid (ACC) by the enzyme ACC oxidase (ACO) with a rate constant kACO. ACO is encoded mainly by the expression of ACO1 (kt,ACO). ACO1 protein levels are also controlled by protein degradation (kpd,ACO1). The ethylene produced can diffuse out of the cellular tissue through the cell wall/membrane at a certain diffusion rate (kdiff). ACC is synthesized from S-adenosyl-L-methionine (SAM) by multiple ACC synthase (ACS) isoforms (ACS2, ACS4 and ACS6) with their specific rate constants kACS2,4,6. ACS proteins are translated from ACS2, ACS4 and ACS6 transcripts with the same translation constant (kt,ACS). ACS proteins can also easily be degraded through the ubiquitin/proteasome pathway in an isoform-specific way, represented here by the kpd,ACS2,4,6 rate constants. The overall enzymatic ACS activity is the combination of all isoforms (ACS). ACC can also be converted into 1-(malonylamino)-1-aminocyclopropane-1-carboxylic acid (MACC) by ACC-N-malonyltransferase (MACCT), with kMACC being the rate constant. Other ACC derivates (DACC) can also be synthesized (kDACC). For each molecule of ACC, one molecule of 5′ methylthioadenosine (MTA) is formed, which is recycled by the Yang cycle. The first committed step of the Yang cycle is the nucleosidation of MTA by MTA nucleosidase (MTN) (kMTN). MTN is synthesized from MTN transcripts (kt,MTN). MTN protein levels are assumed to be controlled by regular protein degradation (kpd,MTN). MTA is alternatively formed by the decarboxylation of SAM by SAM decarboxylase (SAMdc) (kSAMdc), the first step of the polyamine biosynthesis pathway. Gene expression data were used as model input (green) in combination with SAM content (red), while all other protein (blue) and metabolite (pink) levels are model outputs. The activities of SAMdc and MACCT are incorporated based upon data from the literature and their profiles are illustrated in Supporting Information Fig. S2.

The omission of Michaelis–Menten kinetics has the drawback that substrate- and product-mediated feed-back or feed-forward regulation of enzyme activity is lost. As our model includes all transcriptional feed-back regulation through the incorporation of transcriptomic data (mRNA abundance) and by linking these data to enzymatic activity through protein abundance (and degradation), the main developmental regulatory dynamics are incorporated, yet direct metabolic specific enzymatic regulation is neglected.

From gene expression to protein synthesis

The ethylene biosynthesis pathway (Fig. 1) involves two plant-specific enzymes, named 1-aminocyclopropane-1-carboxylic acid (ACC) synthase (ACS) and ACC oxidase (ACO), which are each encoded by a multigene family (Barry et al., 1996, 2000; Nakatsuka et al., 1998). To identify the key isoforms of both gene families, qPCR profiles were analyzed by the average calibration curve method as explained in the Methods S1 and Fig. S2. These analyses revealed that ACO1 was much more strongly expressed during fruit ripening than the other ACO isoforms (Fig. S3a,b). By contrast, multiple ACS isoforms (ACS2, ACS4 and ACS6) appeared to have similar expression levels (Fig. S3c,d). Therefore, ACO1, ACS2, ACS4 and ACS6 were identified as key genes, and their expression, together with the expression of 5′ methylthioadenosine (MTA) nucleosidase (MTN) which encodes the crucial enzyme of the Yang cycle, were used as input to the model. The model thus incorporated the dynamics of these transcripts (mRNA levels) throughout fruit development, ripening and postharvest storage, indirectly incorporating any transcriptional feed-back or feed-forward regulation originating from ethylene signaling itself. The profiles of these gene expression input data, along with the SAM input data, are presented in Fig. S1. These gene expression data were used to model protein levels (expressed as enzyme activities), assuming a straightforward linear protein translation, solely dependent on gene transcripts. Each gene transcript, expressed as a certain concentration of mRNAp ([mRNAp]), with subscript ‘p’ indicating the protein it encodes, was assumed to yield a certain concentration of the encoded protein ([p]) ((Eqn 1)). The translation rate kt,p into active protein was assumed to be the same for all isoforms of the same gene family (one kt per gene family), ignoring any potential translation regulation by the ribosomal complex. Protein turnover was assumed to be controlled by a protein-specific degradation rate kpd,p (kpd,ACO1, kpd,ACS2, kpd,ACS4, kpd,ACS6 and kpd,MTN) because it has been shown that different ACS isoforms are stabilized by specific phosphorylation mechanisms (Tatsuki & Mori, 2001; Skottke et al., 2011). The overall change in the concentration of active protein was then assumed to be equal to the net balance of translation and degradation:

display math(Eqn 1)

Metabolite turnover

The formed proteins according to Eqn 1 are involved in the enzymatic conversion of their metabolic substrates. The cellular pool of ACC is a result of the net balance between synthesis from SAM by ACS (ACS2, ACS4 and ACS6 with specific conversion rates kACS2,4,6) and conversion to ethylene by ACO, and 1-(malonylamino)-ACC (MACC) formation catalyzed by ACC-N-malonyl transferase (MACCT) with a reaction rate kMACC. It was shown earlier that MACCT activity increased during tomato fruit ripening (Martin & Saftner, 1995). These data were used as an estimate of the MACCT protein content (Fig. S4). Besides MACC formation, ACC can also be converted into other derivates such as γ-glutamyl-ACC (GACC) and jasmonic acid-ACC (JA-ACC) (Martin et al., 1995; Staswick & Tiryaki, 2004). As both derivates are minor moieties and as no enzymatic information is available, both reactions were combined in a single term (derivates of ACC (DACC)) only dependent on the ACC pool with one rate constant (kDACC; (Eqn 2), (Eqn 3), (Eqn 4)).

display math(Eqn 2)
display math(Eqn 3)
display math(Eqn 4)

Ethylene is synthesized from ACC by ACO at some production rate (kACO) and also escapes the fruit with a rate proportional to the ethylene concentration difference within the fruit and its environment according to Fick's law with rate constant kdiff ((Eqn 5)).

display math(Eqn 5)

In practice, math formula is negligible compared with math formula, so the measured ethylene production math formula.

Recycling of MTA

For each molecule of ACC produced, one molecule of MTA is also synthesized. This MTA moiety is recycled by the Yang cycle, the first crucial step of which is the conversion of MTA into 5′-methylthioribose (MTR) by MTN with a rate constant kMTN ((Eqn 6)). (Eqn 6) incorporates the amount of MTA produced by all three ACS isoforms (ACS2, ACS4 and ACS6) with the same rate constants as for ACC formation (kACS2,4,6) from (Eqn 2). Additionally, MTA can be produced by the biosynthesis of polyamines (spermine and spermidine) (Mattoo et al., 2010), the first step of which is the decarboxylation of SAM by SAM decarboxylase (SAMdc) with a rate constant kSAMdc. It was shown previously that SAMdc activity increased transiently at the start of fruit ripening (Morilla et al., 1996) (Fig. S4).

display math(Eqn 6)

It was also assumed that a basal amount of MTA (MTAb) was continuously present and could not participate in the Yang cycle. This assumption was introduced after carefully analyzing the model output for MTA. It is known that MTA levels are strictly controlled as they have a feed-back effect on MTN and presumably also on ACS (Burstenbinder et al., 2010; Van de Poel et al., 2012a). If MTA levels are not under strict control, vascular disorders and impaired fertility can occur (Waduwara-Jayabahu et al., 2012). These biological explanations might support our data-driven introduction of a controlled amount of basal MTA.

Results

Model calibration

The formulated model was calibrated against the proteomic and metabolic data recently published (Van de Poel et al., 2012a). The ODEs presented in (Eqn 1), (Eqn 2), (Eqn 3), (Eqn 4), (Eqn 5), (Eqn 6) were solved in OptiPa, a user-friendly ODE solver run in a Matlab interface (Hertog et al., 2007). The ODEs were dynamically solved, allowing us to model the entire time-dependent developmental dynamics of the ethylene biosynthesis pathway. Fig. 2 shows the results for all the measured metabolites and proteins of the ethylene biosynthesis pathway and the Yang cycle (dots), including the model predictions (line). The model explained 83% of the observed variation. Given the large biological variation observed in fruit, this is remarkably good. The estimated parameter values and their standard deviations are shown in Table S1. All introduced parameters were reliably estimated except kDACC, which showed a standard deviation larger than the estimated value. Analyzing these parameter estimates showed that ACS4 appears to be less important than ACS2, because kpd,ACS4 is much larger than kpd,ACS2 and because kACS4 is smaller than kACS2. This is consistent with the proposed gene regulatory model that positions ACS4 expression mainly in the transition stage between system 1 and 2 ethylene biosynthesis, while ACS2 expression is ethylene dependent and mostly occurs during system 2 (Barry et al., 2000). ACS6 also seems to be less important for the synthesis of ACC, because its reaction rate constant (kACS6) was very low. These observations were supported by calculation of the portion of ACC formed by the individual ACS isoforms, not taking into account any ACC consumption (Fig. S5).

Figure 2.

Results of the kinetic model describing tomato fruit ethylene biosynthesis. Modeled (line) and measured (dots) values are shown for (a) ethylene production, (b) 1-aminocyclopropane-1-carboxylic acid (ACC) concentrations, (c) 1-(malonylamino)-1-aminocyclopropane-1-carboxylic acid (MACC) concentrations, (d) 5′ methylthioadenosine (MTA) concentrations, (e) ACC oxidase (ACO) activity, (f) ACC synthase (ACS) activity and (g) MTA nucleosidase (MTN) activity during tomato fruit development, ripening and postharvest storage. Individual points were plotted using the biological age (d) calculated for each individual fruit. Maturity stages are indicated by different colors: S, small; M, medium; IMG, immature green; MG, mature green; BR, breaker; LO, light orange; O, orange; P, pink; R, red; RR, red ripe; RR + X, red ripe + X days of postharvest storage.

It is noteworthy that, during ripening, the ACC content (Fig. 2b) is slightly overestimated. These higher ACC model values are caused by the need to realize a high ethylene production rate during ripening. This suggests the existence of some additional regulatory step, such as, for example, inter-tissue ACC transport, not described in the literature and hence not included in the current model. Additionally, there is an overestimation of ACO activity during early fruit development (Fig. 2e). Although gene expression is already high during these stages, no enzymatic activity could be measured in vitro, resulting in an inconsistency between ACO1 expression and protein activity. During the process of model development, additional scenarios were considered to improve this overestimation of ACO, without substantial improvements. In one trial, different isoforms were incorporated for ACO protein translation, while in another trial the effect of ascorbic acid, an essential effector of ACO activity (Rocklin et al., 2004), on ACO activity was evaluated. The inconsistency between ACO1 expression and protein activity is further elaborated on in the Discussion.

To further analyze the effect of the uncertainty of the estimated model parameter values, a Monte Carlo simulation was performed (Fig. S6). The Monte Carlo method allows a statistical evaluation of the model outcome for higher rates of uncertainty. Here to, the distribution of the estimated parameter values was used as input for the Monte Carlo simulation to randomly generate 1000 samples of the model parameter vector respecting the observed distributions and covariance structure of the model parameters. For every sample, the model was numerically solved, and eventually the probability density function of all model outputs was estimated and presented as a heat plot (Fig. S6). The parameter kDACC was omitted from the Monte Carlo analysis because its confidence interval contained zero. Most of the modeled variables show a narrow distribution over the entire ripening profile, indicating that the model structure is relatively well defined, with the overall model behavior being conserved throughout a wide range of parameter value combinations. While at some maturity stages the distribution is wider than at other stages, this is reflecting the uncertainty in the parameter values as a result of either the inherent biological variability observed in the experimental data (e.g. in the case of ACC concentrations towards the end of storage) or some less constraining data (e.g. in the case of the starting concentrations of ACS). In the case of ACS, this does not affect the overall performance of the model, indicating its robustness.

Model validation using known ethylene mutants

Transgenic or mutant tomato plants that are ethylene- or ripening-impaired are a rich source of data with which to validate our model. These genetic perturbations can be incorporated into the model without any model modifications, because gene expression levels serve as the model input. The corresponding simulated response of the ethylene biosynthesis pathway should match that of the transgenic tomato fruit. Several mutants, for which both gene expression data and ethylene biosynthesis data are documented in the literature, were used to validate the model.

A first example is the well-known rin mutant (ripening inhibitor). RIN is a MADS-box transcription factor that was identified as a crucial regulator of fruit ripening (Vrebalov et al., 2002; Martel et al., 2011). It was also shown that RIN can interact with the promoter of ACS2 and ACS4 (Fujisawa et al., 2011). Expression of both ACS2 and ACS4 was found to be severely inhibited in the rin mutant (Barry et al., 2000; Kitagawa et al., 2005), while ACS6 expression was up-regulated during ripening (Barry et al., 2000). This information was used to reduce ACS2 and ACS4 expression in our model to zero, and to up-regulate ACS6 expression during ripening to the same level as observed in mature green fruit as was shown by Barry et al. (2000). The model predicted lower fruit ethylene production, ACS activity, ACO activity, and ACC and MACC concentrations, which all match previously published results (Terai, 1993; Kitagawa et al., 2005, 2006) (Fig. 3a–e).

Figure 3.

Model validation through simulating well-characterized ethylene mutants. The model (left y-axis; lines) and results adapted from the literature (right y-axis; bars) are shown for the wild type (wt) (black) and mutants (red/green). Model predictions for the rin (ripening inhibitor) mutant (a–e), the 1-aminocyclopropane-1-carboxylic acid (ACC) oxidase 1 (ACO1) RNAi mutant (f, g), the never-ripe (nr) mutant (h) and the APETALLA2a (AP2a) mutant (i) are shown for ethylene production (a, f, h, i), ACO activity (b, g), ACC synthase (ACS) activity (c), ACC concentrations (d) and 1-(malonylamino)-1-aminocyclopropane-1-carboxylic acid (MACC) concentrations (e) during the entire developmental period. Bars illustrate the published profiles for the wt and rin, ACO1 RNAi, nr and AP2a mutants, respectively (Lanahan et al., 1994; Barry et al., 2005; Kitagawa et al., 2005, 2006; Xiong et al., 2005; Chung et al., 2010) for discrete maturity stages. These stages were allocated to the graph based on the corresponding average biological age ± SD for that stage. Maturity stages: S, small; M, medium; IMG, immature green; MG, mature green; BR, breaker; LO, light orange; O, orange; P, pink; R, red; RR, red ripe; RR + X, red ripe + X days of postharvest storage.

In a second validation trial, two ACO1 silencing lines (full and medium silencing) generated with RNAi were used (Xiong et al., 2005). Based on pixel intensity analysis of northern blots, as explained in the 'Materials and Methods' section, ACO1 expression was reduced to almost zero (1% of wild-type (WT) expression; full silencing) and intermediately (11% of WT expression; medium silencing). The model output showed that both ethylene production and ACO activity are reduced by silencing ACO1 and, evidently, full silencing has a stronger effect than medium silencing, matching previously published results (Xiong et al., 2005) (Fig. 3f,g).

A third ripening-impaired mutant is the never-ripe (nr) mutant which is caused by a single point amino acid mutation in the ethylene-binding site of the ethylene receptor ETR3 (Wilkinson et al., 1995). This causes reduced ethylene susceptibility, resulting in lower ethylene production and a delayed ripening process (Lanahan et al., 1994; Hackett et al., 2000; Barry et al., 2005). In the nr mutant, ACS2 expression is reduced and delayed (Barry et al., 2000), while ACS4 expression and ACO1 expression are only delayed for c. 5 d (Alba et al., 2005). Based on pixel intensity analysis, the expression of ACS2 was reduced to 35% of the WT expression level, and the expression of ACS2, ACS4 and ACO1 was delayed for 5 d. Fig. 3(h) shows that the predicted ethylene production is indeed delayed and reduced, similar to the trend that was observed for the nr mutant (Lanahan et al., 1994; Barry et al., 2005).

A final ethylene-impaired transgenic tomato line is an RNAi silencing line of APETALLA2a (AP2a), which is a negative regulator of fruit ripening. AP2a is an APETALLA transcription factor that regulates fruit size and carotenoid content, and inhibits ethylene biosynthesis (Chung et al., 2010; Karlova et al., 2011). It was shown in AP2a RNAi silencing lines that ACO1, ACS2 and ACS4 gene expression was up-regulated (Chung et al., 2010), as was expression of several members of the ethylene signal transduction pathway (Karlova et al., 2011). Again, pixel intensity analysis of northern blot results for ACO1, ACS2 and ACS4 (Chung et al., 2010) allowed their expression to be augmented 1.9-, 7.1- and 5.7-fold, respectively, based on the average increase in expression throughout fruit development. Fig. 3(i) shows that the model predicts a higher ethylene production rate during ripening for AP2a silencing lines, similar to the results previously reported by Chung et al. (2010).

These four examples, using diverse mutant and transgenic data from the literature, show that the model responds accurately to alterations in gene expression without any modification of the model structure or parameters. This independent validation confirms that the model is a realistic in silico representation of the ethylene biosynthesis pathway in tomato.

Discussion

More and more plant scientists use mathematical models to facilitate their research and to gain a better insight into complex biological processes (Prusinkiewicz & Runions, 2012). Well-constructed models can be used to test old hypotheses or to formulate new ones and explore novel ideas, often where wet-lab data are hard to obtain, contributing to the development of scientific theories. In the area of fruit development and ripening, some work has already been done in the framework of so-called virtual fruit (Gutierrez et al., 2005; Genard et al., 2007). The current work contributes to this concept by modeling the important ethylene hormonal biosynthesis pathway. The constructed model only uses gene expression data to predict all intermediate proteins and metabolites of the ethylene biosynthesis pathway downstream of SAM. Gene expression can now be detected easily using fast and accurate techniques. Furthermore, gene expression is the source for downstream translation, according to the central dogma of molecular biology (Crick, 1970). This transfer of genetic information towards proteins and eventual metabolic activity, will be reflected by the eventual physiological state of a cell/organism. Modelling this information transfer allows a holistic representation of what really happens in a cell, and essential for incorporation in network models. By incorporating expression data for genes encoding the key enzyme of the ethylene biosynthesis pathway in the network model, all feed-back regulation of the ethylene signaling pathway is implicitly incorporated. Because the constructed ethylene model fitted the calibration data very well, explaining up to 83% of total variation, and because the independent validation against tomato mutant data from the literature was successful, we believe that our model is suitable for further scientific exploration. In the next sections, old and new hypotheses are examined using our model, and several model extensions are suggested, paving the way for novel experimental discoveries in plant science.

Biochemical network modeling reveals inconsistencies between ACO1 expression and protein activity

No regulation of ACO protein abundance was incorporated in the model because the current understanding of ethylene biochemistry lacks knowledge about this regulation. Nonetheless, we observed that during fruit development the predicted ACO activity was higher than the measured activity, resulting in an overestimation for ACO during these stages. This discrepancy indicates that there is a disconnection between ACO1 expression and ACO1 activity, suggesting that ACO is differentially regulated either at the translational level or at the post-translational level. To explore this hypothesis, two additional functions were introduced into the model, which control ACO translation (fTRAN) and ACO degradation (fDEG), respectively ((Eqn 7), (Eqn 8)).

display math(Eqn 7)
display math(Eqn 8)

The outcomes of these two functions (fTRAN and fDEG) were multiplied by their corresponding translation and degradation rate constants kt,ACO and kpd,ACO, respectively. The behavior of both functions is illustrated in Fig. S7. Basically, fTRAN leads to lower protein translation during fruit development, while fDEG leads to higher protein degradation during fruit development. Both functions have been optimized to the measured ACO data (Fig. 4) and the estimated parameter values are shown in Table S2. These mathematical functions improved the model significantly and coped with the inconsistency between ACO expression and ACO activity. These in silico explorations indicate that ACO protein regulation during fruit development may be more complex than currently thought.

Figure 4.

The potential regulation of 1-aminocyclopropane-1-carboxylic acid (ACC) oxidase (ACO) protein levels. The effects of the fTRAN (a; blue) and fDEG (b; pink) functions, controlling ACO translation and ACO degradation, respectively, on ACO activity during the entire fruit development period are shown. Maturity stages are indicated by different colors: S, small; M, medium; IMG, immature green; MG, mature green; BR, breaker; LO, light orange; O, orange; P, pink; R, red; RR, red ripe; RR + X, red ripe + X days of postharvest storage.

In silico evaluation of the effect of MACC formation on ethylene production

Next, the developed kinetic model was used to explore some old hypotheses concerning the role of MACC formation during ethylene biosynthesis. This is one of the enduring, intriguing questions in ethylene research, as MACC does not participate in any other known metabolic reaction besides its formation from ACC. Therefore, MACC is considered to be an end-product with no real biochemical function. This assumption was supported by the observation that MACC, like many other waste products, could be translocated from the cytosol into the vacuole and back by ATP-mediated tonoplast carriers (Bouzayen et al., 1988, 1989; Tophof et al., 1989). Nonetheless, a few early studies reported that MACC could be reconverted into ACC by a yet unidentified protein, called MACC hydrolase (MACCH) (Jiao et al., 1986; Hanley et al., 1989). These observations support the hypothesis that MACC formation could regulate the ACC pool and, consequently, ethylene production. As no genetic or protein sequence information is available about MACCT and MACCH, wet-lab approaches are difficult and/or time-consuming, making this a perfect case study for in silico modeling. Our kinetic model was used to investigate whether or not MACC formation and/or MACC hydrolysis could influence ACC concentrations and consequently ethylene production. First, the rate constant of MACCT (kMACC) was assumed to be zero (kMACC = 0) and, secondly, kMACC was increased ten times in value (kMACC = 0.73; Fig. 5a–c). The shutdown of MACC synthesis resulted in an excess amount of ACC and consequently a higher ethylene production rate. When MACC formation was stimulated, both ACC concentrations and ethylene production were drastically reduced, although MACC concentrations did not increase much. These in silico results imply that MACC formation could be a potential regulator of fruit ethylene biosynthesis.

Figure 5.

In silico investigation of the regulatory role of 1-(malonylamino)-1-aminocyclopropane-1-carboxylic acid (MACC) in ethylene biosynthesis. Model predictions for different kMACC values (kMACC = 0.073, kMACC = 0 and kMACC = 0.73; a–c, respectively) for the developed model (black line) and the effect of the introduction of MACC hydrolase (MACCH) for different kMACCH values (kMACCH = 0, kMACCH = 0.025, kMACCH = 0.05, kMACCH = 0.1 and kMACCH = 0.5; d–f, respectively) for (a, d) ethylene production, (b, e) 1-aminocyclopropane-1-carboxylic acid (ACC) concentrations and (c, f) MACC concentrations during the entire developmental period are shown.

To incorporate the possible effect of the reverse reaction through MACC hydrolysis, (Eqn 3) was extended with an additional MACC hydrolysis term (;(Eqn 9)).

display math(Eqn 9)

In this equation, MACC is hydrolyzed back into ACC at a certain reaction rate kMACCH. As no information is available about MACCH activity during fruit ripening, we assume that the reaction is solely substrate dependent. This additional term (now with a positive sign) was also incorporated in the equation of ACC synthesis ((Eqn 2)). Different kMACCH values were evaluated to explore different rates of MACC hydrolysis (Fig. 5d,e). MACC content decreased with a larger kMACCH value, while ACC concentrations and the ethylene production rate increased. It would be interesting to obtain more experimental insights into the activity of this enzyme to further unravel the importance of its function, although no genetic or protein sequences are currently known for MACCH. Nonetheless, these in silico simulations illustrate that MACC hydrolysis might potentially act as a controlling step in tomato fruit ethylene biosynthesis.

All in all, these results suggest that MACC plays an important role in regulating the ACC pool. From the literature it is known that immature green tomatoes treated with ethylene have a high MACC production rate, as they still lack the capability to form ethylene (Liu et al., 1985). Additionally, it was shown that 1-MCP (1-methylcyclopropene)-treated mature green tomatoes showed lower concentrations of MACC, which resulted in an accumulation of ACC (Van de Poel et al., 2012b). MACC formation was also differentially regulated during cold storage and 1-MCP treatment of apple (Malus domestica) (Bulens et al., 2012), pear (Pyrus ‘conference’) (Chiriboga et al., 2012) and plum (Prunus ‘Larry Ann’) (Larrigaudiere et al., 2009) fruits. All previous studies combined with our in silico explorations indicate that MACC formation may differentially control ACC concentrations during specific developmental stages and environmental conditions. As ethylene is important for a myriad of developmental processes (Vandenbussche et al., 2012), the role of MACC may be more diverse than anticipated.

Towards a virtual fruit

We have shown that kinetic modeling of biochemical networks, starting from gene expression, is a very powerful tool with which to investigate fundamental questions in plant biology. This is a quantitative explorative tool that allows the scientist to virtually investigate any possible perturbations in the biochemical phenotype of the fruit. Although the developed kinetic model accurately describes the time dynamics of ethylene biosynthesis of an entire tomato fruit, the spatial dynamics of ethylene within a fruit are neglected. Information about tissue-specific ethylene biosynthesis is limited, as most studies have solely focused on pericarp tissue (Matas et al., 2011). More biochemical and molecular information is needed at a tissue and even cellular level to gain further insights into the regulation of fruit ethylene biosynthesis.

Furthermore, one needs to take into account specific ethylene gas diffusion properties. How much ethylene dissolves in the cell and how much diffuses through the intercellular pores is an important parameter that determines the overall tissue gas exchange properties (Cloetens et al., 2006). These diffusion barriers induce an ethylene gas gradient throughout the fruit, which in turn might cause different spatial physiological responses (Colmer, 2003). Diffusion parameters of O2 and CO2 have already been obtained for apple and pear tissue (Ho et al., 2008; Verboven et al., 2008). Similarly, ethylene diffusivity through tomato tissues could also be measured using ultra-sensitive ethylene detection techniques such as laser-based photo-acoustic resonance (Devries et al., 1995). In addition, the 3D multicellular structure of the fruit should be obtained. Modern computed tomography X-ray technology allows rapid and sensitive visualization of cellular and void 3D microstructure at the submicrometer level (Verboven et al., 2008, 2012; Dhondt et al., 2010). This 3D structural information, in combination with the detailed biochemical network model currently developed, would further enable researchers to understand the spatial dynamics of ethylene.

Additionally, one could attempt to quantitatively model the physical binding kinetics of ethylene molecules to the ethylene receptors (O'Malley et al., 2005). Furthermore, current advances in elucidating the molecular biology of the ethylene signal transduction pathway (Lin et al., 2009), are enabling modelers to incorporate the downstream signaling cascade leading to the activation of multiple ethylene response factors (ETRs) and many associated physiological responses (Xu et al., 2008). In this way, the entire ethylene biosynthesis and signal transduction pathway could be plated in silico, a big step forward towards a virtual fruit.

Acknowledgements

This research was funded by the Research Council of KU Leuven (project OT/12/055) and PhD grants from the Institute for the Promotion of Innovation through Science and Technology in Flanders (IWT-Vlaanderen) to B.V.d.P. and I.B. COST action FA1106 is acknowledged for financial support.

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