Abstract

Recent advances in cytokinin analysis have made it possible to measure the content of 22 cytokinin metabolites in the tissue of developing tobacco seedlings. Individual types of cytokinins in plants are interconverted to their respective forms by several enzymatic activities (5′‐AMP‐isopentenyltransferase, adenosine nucleosidase, 5′‐nucleotidase, adenosine phosphorylase, adenosine kinase, trans‐hydroxylase, zeatin reductase, β‐glucosidase, O‐glucosyl transferase, N‐glucosyl transferase, cytokinin oxidase). This paper reports modelling and measuring of the dynamics of endogenous cytokinins in tobacco plants grown on media supplemented with isopentenyl adenine (IP), zeatin (Z) and dihydrozeatin riboside (DHZR). Differences in phenotypes generated by the three cytokinins are shown and discussed, and the assumption that substrate concentration drives enzyme kinetics underpinned the construction of a simple mathematical model of cytokinin metabolism in developing seedlings. The model was tested on data obtained from liquid chromatography/tandem mass spectrometry cytokinin measurements on tobacco seedlings grown on Murashige and Skoog agar nutrient medium, and on plants grown in the presence of IP, Z and DHZR. A close match was found between measured and simulated data, especially after a series of iterative parameter searches, in which the parameters were set to obtain the best fit with one of the data sets.

Received: 13 November 2002; Returned for revision: 19 December 2002; Accepted: 7 January 2003

INTRODUCTION

Cytokinins (CKs) are chemical substances with the ability to affect plant growth and development. More specifically, CKs influence or regulate cell division, photosynthesis, chloroplast differentiation, chlorophyll degradation, flowering, root initiation and nutrient assimilation/translocation (Brzobohaty et al., 1994; Goltsev et al., 2001; Lexa et al., 2002). To date, dozens of compounds have been recognized as CKs in plants (Letham and Palni, 1983; Mok and Mok, 2001). According to their chemical structure, most fall into one of two major categories: (1) adenine derivatives; and (2) phenylurea derivatives. CKs are found in plant tissues at very low concentrations (0·1–500 pmol g–1 f. wt; Lightfool et al., 1997). Therefore, only with the recent introduction of powerful chromatographic methods combined with mass spectrometry has it been possible to quantify individual CK species. These methods confirmed the previously predicted changes in endogenous CK levels and provided a better understanding of their physiological effects. Here, the occurrence and dynamics of naturally occurring adenine derivatives, especially those of isopentenyl adenine (IP), zeatin (Z) and dihydrozeatin (DHZ) type, are explored. Measurements of CKs in plant tissues, as well as recent advances in CK research, have made possible the construction of a mathematical model of CK dynamics in plant tissues. The interconversions of individual CKs in plants are very complex, and are brought about by enzymes catalysing reaction steps, such as hydroxylation, phosphorylation, hydrolysis, glycosylation and side‐chain reduction (Kaminek, 1992).

This paper shows that many aspects of CK dynamics in plant tissues can be simulated using a relatively simple modelling technique. This is demonstrated by comparison with experimental results obtained in developing tobacco seedling. A set of plants grown on Murashige and Skoog agar nutrient (MS) medium in the presence of 1 µm IP. Changes in endogenous CKs were measured and used to validate the model. To test the model further, endogenous CKs in plants grown on media supplemented with Z and dihydrozeatin riboside (DHZR) were measured. Phenotype alterations caused by the representatives of three types of CKs (IP, Z and DHZR) are documented.

MATERIALS AND METHODS

Growth media, conditions and sample collection

Tobacco seedlings (Petite Havana SR1) were cultured on solid MS medium (Murashige and Skoog, 1962), containing 0·8 % agar (Gibco BRL, Gaithersburg, MD, USA), 1·5 % sucrose, pH 5·7, before autoclaving. Media for CK treatment also contained 1 µm of either IP (Sigma‐ Aldrich, St Louis, MO, USA), Z or DHZR (racemic mixture), both from Apex Organics, Honiton, UK. Seed lings were grown in plastic Petri dishes (9 cm diameter) at 23 °C day/20 °C night and a 16/8 h photoperiod. The photosynthetic photon flux density (PPFD) was approx. 55 µmol m–2 s–1, provided by fluorescent lamps (Sylvania, Erlangen, Germany). For each treatment approx. 100 mg f. wt of seedlings (50–200) was collected 2, 5 and 12 d after germination and immediately frozen in liquid nitrogen. Samples were stored at –85 °C until analysis.

CK extraction and purification

The frozen tissue was ground under liquid nitrogen and extracted overnight at –20 °C with Bieleski solvent (Bieleski, 1964). Deuterium‐labelled CKs were added as internal standards. After clarifying by centrifugation, the extracts were passed through two Sep‐Pak C18 cartridges (Waters Corporation, Milford, MA, USA) connected in series, and the extract evaporated to water phase. After correcting the pH to 6·5, this extract was passed through a DEAE Sephadex column (3 ml, HCO3 form) and a Sep‐Pak C18 cartridge connected in series. The columns were washed and disconnected. CK bases, ribosides and glucosides were eluted from the C18 Sep‐Pak cartridge with 5 ml 80 % (w/w) methanol after two washes with 5 ml of de‐ionized water and 3 ml 10 % (w/w) methanol. The eluted fraction was evaporated to dryness in a Speed Vac concentrator and stored at –20 °C until required for further analysis. DEAE Sephadex columns containing CK phosphates (CK nucleotides) were eluted with 10 ml 1 m NH4HCO3. The sample was neutralized and fractions were passed through to a C18 Sep‐Pak cartridge. CK phosphates were eluted from the C18 Sep‐Pak column with 8 ml 80 % methanol, and this fraction was evaporated to water phase. Four millilitres of 0·1 m Tris (pH 9·6) was added and the sample was treated with alkaline phosphatase (30 min at 37 °C). After neutralization, the solution was passed through a C18 Sep‐Pak cartridge. After washing with 5 ml de‐ionized water and 3 ml 10 % methanol, CK nucleotides were eluted with 5 ml 80 % methanol and evaporated to dryness. Samples were stored at –20 °C until required for further analysis.

Quantitative analysis of CKs

CK fractions were separated and quantified by HPLC (FLUX Rheos 2000 quaternary pump and CTC Analytics HTS PAL autosampler with CSI 6200 Series HPLC Oven) linked to a mass spectrometer (Finnigan LCQ) equipped with an ESI source. Samples (10 µl) were injected onto a C18 column (Phenomenex, AQUA, 2 mm × 250 mm, 5 µm) and eluted with 0·001 % acetic acid (A) and acetonitrile (B). The following gradient profile was used: 5 min, 10 % B then to 17 % in 10 min then to 46 % in 10 min, at a flow rate of 0·2 ml min–1. The column temperature was 30 °C. The effluent was introduced into the ESI source [220 °C, +4·5 kV capillary, sheath gas (N2) 90 units; auxiliary gas (N2) 8 units]. Data acquisition was performed at MS/MS full scan, two microscans at maximum ion time 100 ms.

Mathematical model

Mathematical modelling was carried out according to principles described by Thornley and Johnson (1990). The model consists of 15 metabolic compartments (state variables) for individual CK species, connected by enzyme activities (conversion rates) responsible for the conversion of one chemical form into another (Fig. 1). For clarity, the governing equations and parameter values used in the model are presented in the Appendix. To find numerical solutions for different time points we coded the equations into an algorithm written in the C++ programming language. The algorithm followed the Euclid method in which simulation starts at time t = 0 and proceeds in short time steps, during which it can be reasonably assumed that all state variables remain constant (the time step used in our calculations was Δt = 0·1 h). Conversion rates calculated from the governing equations are applied to define a new state of the system at a new time point. This process is repeated until the end of simulation is reached.

Model calibration

To obtain a better fit between measured and observed data, we used a Monte Carlo calibration algorithm. In this approach, the simulation is repeatedly carried out with variable parameter values and the goodness‐of‐fit is calculated for each run to find a subset of parameter values that give the best fit. The process is then repeated with the new range of parameter values until the range is sufficiently narrow and no further improvement in goodness‐of‐fit is possible.

RESULTS

Phenotype observations

To provide a reliable data set to calibrate and test the mathematical model, tobacco SR1 was grown on MS medium supplemented with IP, Z or DHZR, as described in Materials and Methods. SR1 seedlings grown on MS medium represented a treatment that was expected to contain low concentrations of all the measured CK metabolites. The remaining plants provided data for plant material with increased internal CK concentrations. CK compounds were chosen to provide substrates at different levels of hydroxylation and reduction, and thus to test the validity of the model in as many different conditions as possible. Comparison of control seedlings on MS medium and seedlings treated with 1 µm of the respective CK provided a visual confirmation of the typical CK phenotype. The differences were documented on the same days that the samples were collected for CK analysis (Fig. 2). It is apparent that, in general, CKs caused similar effects, namely: (1) reduced primary root growth; (2) reduction of cotyledon area; and (3) thickening and shortening of the hypocotyl.

However, these effects were not present in all combinations of age and treatment. The most striking deviations from the typical phenotype were observed on day 12. In IP‐treated seedlings, there was a sudden increase in root growth. Root growth was inhibited on all days in Z‐ and DHZR‐treated plants; inhibition caused by Z was complete. Surprisingly, hypocotyl thickening and shortening was absent in DHZR‐treated seedlings on all days. The hypocotyl was altered in IP‐ and Z‐treated seedlings. In IP‐treated seedlings we also observed a pear‐shaped deformation at the base of the hypocotyl. MS‐grown control seedlings did not display any of these effects. On day 12 it was also clear that they developed slightly faster than treated seedlings.

Cytokinin measurements

The mathematical model constructed in this paper (see the Appendix) is based on the presence of several chemical forms of CKs in the plant. Using a liquid chromatography/tandem mass spectrometry (LC/MS/MS) separation and detection system we were able to measure the concentration of 22 different CK metabolites in plant tissue. The results of these measurements are given in Table 1. Clearly, all CK treatments considerably increased internal CK levels of the tobacco plants. When compared with the MS medium‐grown control, total CKs increased 230–320‐fold on MS+IP, 20‐fold on MS+Z and 130–200‐fold on MS+ DHZR. The CK metabolites that accumulated most were the N‐7‐glucosides. The proportion of N‐glucosides in total CKs increased from day 2 to day 12 in all treatments (15–41 % on MS; 92–98 % on MS+IP; 55–83 % on MS+Z; 80–98 % on MS+DHZR). In addition, bases of the CK type that were fed to the seedlings from the medium also increased considerably.

To evaluate the phenotype of seedlings it was important to know the concentration of active CKs. As a first approximation, the sum of CK bases, ribosides and phosphates was calculated. The summary data, presented in Table 2, show that the percentage of active CKs in total CKs decreased from day 2 to day 12 (67–43 % on MS; 9–2 % on MS+IP; 45–15 % on MS+Z; 19–2 % on MS+DHZR). When comparing individual CK treatments, DHZR‐treated seedlings displayed a unique accumulation pattern, with preferential accumulation of phosphates on day 2. A similar but weaker effect could be seen on MS+Z medium as well. Because the content of active Z derivatives [Z + zeatin riboside (ZR) + zeatin riboside 5′‐monophosphate (ZRP)] in the seedlings correlated extremely well with the observed phenotype, we also calculated this characteristic (Table 2). The highest content of active Z derivatives was found in seedlings grown on MS+Z medium at all ages (10–1200× MS). On day 2, IP‐treated plants contained more active Z derivatives (80× MS) than DHZR‐treated plants (35× MS), while untreated seedlings had the lowest content. In contrast, on day 12, active Z derivative concentrations on MS, MS+IP and MS+DHZR were similar.

Simulation results

To test the robustness of the model presented in the Appendix, the data for MS and MS+IP treatments were compared first with simulations with semi‐arbitrary Vmax and Km values for all CK‐converting enzymes (Vmax = 10; Km = 100). Figure 3A shows that, without any fine‐tuning, the model provides only a fair fit to the data set, with some metabolites being more than four orders of magnitude off‐range. The ability to predict some metabolites even by this crude approach probably stems from the topology of the model and the presence of several irreversible conversions in the case of N‐glucosides. To obtain a universal measure of the goodness‐of‐fit we first calculated the logarithm of the ratio between measured and simulated values for each CK compartment. Then, we calculated the sum of squares of these values. The square root of the sum was chosen as a measure of total deviation for the whole data set. This can be expressed mathematically as

3 15

S2 = log([CKij]measured/[CKij]simulated)2(1)

j = 1 i = 1

where [CKij] is the concentration of CK metabolite i on day j. The value obtained for the simulation and measurements on MS+IP medium presented in Fig. 3A was S2 = 152·1.

Subsequently, a calibration step was carried out, using the same MS and MS+IP data. Relying on a Monte Carlo algorithm we searched for the best combination of Vmax, Km and ipu (IP uptake rate) values in more than 10 million simulations. The deviation of measured and simulated data improved considerably. The total deviation after calibration with MS data was only S2 = 33·2. The total deviation after calibration with IP data was only S2 = 19·5 (Fig. 3B). This translates to a mean log(error) per metabolite of approx. 0·6, i.e. less than one order of magnitude. This fit was found to be satisfactory and a sensitivity analysis was carried out on the new model to show the importance of individual parameters on the accuracy of the model. These results are presented in Fig. 4. The model is most sensitive to changes in ipu, which represents the input of CKs into the system, and Vmax and Km for N‐glucosyltransferase (GluN) and adenosine nucleosidase (Ns). The least influential parameter is Vmax and Km for COX and β‐glucosidase (GluO).

The above‐described Monte Carlo optimization yielded Vmax and Km values for the model that best represent the situation in IP‐treated seedlings. Relative magnitudes of these parameters are apparent from the diagram presented in Fig. 5. It can be readily seen that Vmax values for transformations between bases, ribosides, phosphates and glucosides of respective CKs are much higher than the values for any of the hydroxylation and reduction steps. When parameters from models calibrated with MS+IP data and MS data were compared, some interesting differences were found. While most of the Vmax and Km values were in the same range, Vmax values for adenosine phosphorylase (APP), O‐glucosyltransferase (GluOT), zeatin reductase (Red) and trans‐hydroxylase (TH) were 10–20 times lower in the MS+IP‐calibrated model than in the MS‐calibrated model.

The calibrated and sensitivity‐tested version of the model was then subjected to yet another test. We studied the ability of the calibrated model to predict internal levels of CKs in the two remaining CK‐feeding experiments, MS+Z and MS+DHZR. Figure 6 shows satisfactory behaviour of the model. The goodness‐of‐fit is better for MS+Z data (S2 = 48·2) than MS+DHZR data (S2 = 62·5).

DISCUSSION

The main aim of the work reported here was to feed SR1 seedlings with various CK types and show that corresponding changes in internal CK metabolites could be simulated with a relatively simple mathematical model. When growing seedlings for analysis, interesting differences in the overall appearance of the seedlings between CK treatments were observed. These differences are discussed in relation to the collected data. The appearance of CK‐fed seedlings documented in Fig. 2 not only shows typical CK effects, but also provides an opportunity to examine subtle differences between individual treatments. Special attention was paid to root growth, hypocotyl growth and cotyledon expansion.

As for the roots, MS+IP and MS+Z treatments fully inhibited primary root development on day 2. Seedlings growing on MS+DHZR displayed only partial root inhibition. A simple conclusion for the observations at this age would be that DHZR was not as active in our system as IP or Z. This has been shown earlier in different biological systems (Letham et al., 1983). However, after observing the same seedlings on day 12, it became apparent that the situation was more complex. Surprisingly, all seedlings from MS+IP treatments started developing late primary roots. Hence, a better explanation for this phenomenon, other than simple activity differences, was sought. Examination of CK measurement data presented in Tables 1 and 2 indicated that the best common denominator for the data and the observed root phenotypes was the content of active Z derivatives in the samples. As expected, this characteristic was highest in the MS+Z treatment. Accordingly, MS+Z seedlings shown in Fig. 2 lacked primary root on all three dates. Following the same rule, day 2 seedlings grown on MS+DHZR showed the weakest inhibition of root growth of all three feeding treatments. The same seedlings had the lowest Z‐derivative content (Table 2). Appearance of the primary root in IP‐treated seedlings coincided with the decline of active Z derivatives compared with wild‐type levels. This led to the hypothesis that the internal concentration of Z derivatives determines, to a great extent, the effect of externally applied non‐zeatin CKs. This scenario assumes that Z bases, ribosides and phosphates are more efficient inhibitors of root growth than the corresponding derivatives of IP and DHZ. Z has been reported as the most active of naturally occurring CKs (Letham et al., 1983). Moreover, the strong effect of Z was present regardless of the total CK content. For instance, plants fed with Z displayed the strongest root inhibition, but had the second lowest CK content after MS‐grown seedlings. This not only supports the hypothesis regarding higher Z‐derivative activity, but also raises a new question, namely why the total CK content was much lower in MS+Z than that in MS+IP and MS+DHZR treatments. One possibility is that Z was under more stringent control by CK‐degrading enzymes, such as cytokinin oxidase (COX) (Henson, 1978; Hare and van Staden, 1994). This explanation has a slight drawback, since IP and isopentenyl adenine riboside (IPR) are even better substrates for COX (Armstrong, 1994). However, total CK levels stayed high when seedlings were fed with IP and accumulated high levels of IP in the tissues (Table 1). One explanation would be that conversion to isopentenyl adenine N‐glucoside (IPNG), which is not available for oxidation by COX (Letham and Palni, 1983), was relatively fast and prevented a similar decline in total CK levels. Indeed, IPNG was the most accumulated of the three glucosides in all of the feeding treatments. Alternatively, IP may not have been as efficient in inducing COX activity as Z. Kaminek and Armstrong (1990) measured 40 % higher activation of COX by Z compared with IP. This possibility should be further tested experimentally in future.

Another metabolite‐specific effect seen in this work was hypocotyl thickening and elongation. These differences were only visible on day 12, when MS+DHZR treatment had no effect on the hypocotyl, while MS+IP treatment resulted in especially massive hypocotyls with a pear‐shaped thickening at the base. These results suggest that the process of hypocotyl thickening was under control of IP‐ and Z‐like compounds, but not DHZ derivatives.

In all three feeding treatments, exposure to external CKs resulted in preferential accumulation of N‐7‐glucosides. Both, N‐7‐ and N‐9‐glucosides are considered extremely stable and biologically inactive in normal plants (McGaw and Burch, 1995). Because their formation is irreversible, they seem to represent an inactive form synthesized when endogenous CKs exceed a certain threshold. In contrast, O‐glucosides represent an inactive form of CKs which could serve as a storage form that could be released by β‐glucosidases (Brzobohaty et al., 1993; Kaminek et al., 1997). In previous reports for tobacco callus tissue, levels of zeatin O‐glucoside (ZOG) and zeatin riboside O‐glucoside (ZROG) were found to be markedly increased upon expression or de‐repression of a CK biosynthetic ipt gene (Motyka et al., 1996; Redig et al., 1997). Surprisingly, in the system reported here, there was no dramatic accumulation of O‐glucosides (Table 1). It is thought that the seedlings in these experiments switched to N‐glucosylation on media supplemented with CKs. Examination of apparent Vmax and Km values of GluN and GluOT obtained from model calibration (see the Appendix) shows that GluOT was estimated to have higher Km and lower Vmax. As also seen in Fig. 5, this means that of these two enzymes, which compete for the same substrates, GluN is strongly favoured. The reason for the switch to N‐7‐glucosylation is not known and should be studied further. Perhaps the plants in this study were in a mode where irreversible inactivation was more important than storage.

Another goal of this work was to examine the potential of modelling to predict endogenous CK pools. The initial experiments showed that, while the possible range for CK concentration covered in this work was six orders of magnitude large (0·01–10 000 pmol g–1 f. wt), incorporat ing the generally accepted scheme for CK metabolism (Kaminek, 1992) into a model with unknown parameter values resulted in an average simulation error of three to four orders of magnitude. This means that the topology of the metabolic network is only partially able to explain the observed data. To obtain a better fit, the model had to be optimized by calibrating the Vmax and Km values of individual enzymes. Upon such calibration with MS+IP data, the average error was less than one order of magnitude. Similar goodness‐of‐fit was obtained also for Z‐ and DHZR‐treated seedlings.

The measures of error for IP data, combined with the non‐calibrated and MS+IP‐calibrated models, were used to estimate how individual components contribute to the total variance of the samples (S2 = 270·6). Taking into account the topology of the model (uniform Vmax and Km values), 44 % of the total variance in IP data can explained. Calibration of the model eliminates another 37 %, while the remaining 7 % of the variance remains unexplained. The unexplained portion is 34 % for Z data and 18 % for DHZ data. This shows the potential of using the modelling approach in future, especially with calibrated versions of the model. As more information becomes available for individual enzymes, for the genes that encode them and for the manner in which these are regulated, modelling will become more precise. Although endogenous CKs can now be measured with a precision of about 50 %, there is still room for further improvement in the predictive ability of this kind of model.

One of the advantages of modelling is the ability to derive parameter values from complex data without direct measurements of the parameters in question. In this way, during the calibration of the model, it is possible to obtain the apparent Vmax and Km values for key CK‐converting enzymes. Because of the simplifications used to construct the model, these values differ from values obtained in vitro (Table 3; Mok and Martin, 1994). The apparent Km values derived from the calibration are 100–1000 times lower than measured values. Most of this discrepancy might be eliminated by considering non‐equal distribution of CKs in individual plant tissues and within subcellular compartments inside a single cell. The assumption that certain CK metabolites are preferentially present in specific subcellular compartments might change their estimated local concentration by 10–100‐fold. For example, tobacco chloroplasts at the end of the dark phase accumulate a 10–300‐fold higher level of CK metabolites when compared with their content in the whole leaf homogenate with the degree of enrichment dependent on the nature of the particular metabolite (Benkova et al., 1999). Furthermore, kinetic parameters of the individual enzymes might depend critically on the nature of the reaction medium. Most in vitro assays performed with purified enzyme preparations are conducted in simple aqueous solutions, while active water content is extremely low in some subcellular compartments, e.g. in chloroplasts. Thus, it has been found that lowering water content in an in vitro assay, by addition of an inert polymer, decreases Km and increases kcat for hydrolysis of ZOG by the maize β‐glucosidase Zm‐p60·1 (Zouhar and Brzobohaty, unpubl. res.). Though it is unlikely that all predictions generated by the model will turn out to be correct, the results represent a challenge for experimenters aiming to understand in detail the mechanisms controlling subcellular compartmentation of CK metabolism and factors affecting kinetic parameters of the enzymes involved. Interestingly, most enzymes showing high apparent Km after calibrations were also reported to have higher Km values in the literature.

The apparent values obtained from the calibration are readily visible in Fig. 5. For instance, we observed a relatively low Vmax for the phosphorylase that converts CK bases into their respective ribosides. This means that feeding seedlings with bases should result in an increase in the corresponding base concentration, but it is relatively difficult to convert these to their ribosides or phosphates. On the other hand, phosphates and ribosides fed to the plants should be readily converted to the corresponding bases. This deduction can easily be confirmed by reference to the data in Table 1. When the distribution of CKs fed between the bases and ribosides are considered, in the MS+Z treatment on day 2 about 98 % was found in Z and 2 % in ZR. In contrast, MS+DHZR treatment resulted in only 86 % present in the form of DHZR and as much as 14 % present as DHZ.

Calibration of the model with two different data sets (MS and MS+IP) showed major differences in four Vmax parameters only. This was sufficient for a relatively inaccurate fit between MS data and MS+IP simulation (Fig. 3B) or vice versa. The parameters responsible for the differences were Vmax values for APP, GluoT, Red and TH. Whether these enzymes are indeed down‐regulated in the presence of CKs is not known. However, down‐regulation of GluOT in the presence of IP could be responsible for the observed preferential accumulation of N‐glucosides.

As for other uses of the model, it is envisaged that it could be used to evaluate changes in endogenous CKs when working with transgenic plants or mutants in CK‐associated genes. Such plants may have an altered CK content or signalling and will be invaluable in elucidating the molecular mechanism of CK signalling in plants (Hare et al., 1997). In their recent review, Mok and Mok (2001) also stressed the need for detailed knowledge of CK‐converting enzymes and regulatory genes. In their opinion, the presentation of all measurable CK components allows for a myriad of interpretations, but how such data sets relate to active CK levels is not obvious. At present, the CK model assumes that Vmax values (with the exception of COX) do not change in time. It is felt that there are not enough data available to build in regulatory mechanisms of this kind. When such information becomes available, the precision of model predictions could improve. While enzymes such as adenosine kinase act on a range of substrates, and their activity may not depend on CK levels in plants, enzymes more specific for CK metabolism, such as zeatin reductase, could be under tighter regulatory control.

In this paper, a modelling approach was used to address some of these shortcomings. It was shown that modelling can make complex data for individual metabolites more meaningful. Moreover, using special calibration techniques, the model was used in conjunction with such data to estimate biochemical and other parameters. This is a useful approach in cases where information on enzymes or transport rates is limited.

ACKNOWLEDGEMENTS

These results were achieved with the help of the grants from the Grant Agency of the Academy of Sciences of the Czech Republic (A5004001), Academy of Sciences of the Czech Republic (Z5004920) and Ministry of Education of the Czech Republic (MSM143100008, LN00A081).

APPENDIX

Model structure

The model was constructed based on a scheme proposed by Kaminek (1992). We adapted the scheme to cover all the metabolites that were analysed by LC/MS/MS (Fig. 1), recognizing the fact that many of the enzymes present in the scheme are able to act on several CK substrates in parallel. Our scheme also reflects the fact that only certain CKs are substrates for COX.

State variables

State variables represent levels of individual metabolites at any time during the simulation. For the sake of simplicity, the proposed model disregards plant growth. This should be a reasonable approximation, since the turnover rates of individual compartments are relatively high, compared with the seedling growth rate. For example, it was calculated that on day 2 (MS+Z treatment), the half‐life for the Z pool was approx. 2·5 h. All the contributing processes could theoretically double the Z pool size in 4·5 h; however, growth doubles the size of the seedling in the same treatment only in about 60 h (as calculated from seedling fresh weights on day 2 and day 5). The following is a list of all used state variables: IP, IPR, IPRP, IPNG, Z, ZR, ZRP, ZOG, ZROG, ZNG (zeatin N‐glucoside), DHZ, DHZR, dihydrozeatin riboside 5′‐monophosphate (DHZRP), dihydrozeatin riboside O‐glucoside (DHZROG), dihydrozeatin N‐glucoside (DHZNG).

Initially, all state variables are set to zero. Trying to set these to a more realistic value would have had a negligible effect on the result of the simulation, since the simulated processes are driven mainly by uptake and Δ2‐isopentenyl pyrophosphate: 5′‐AMP isopenthenyltransferase (IPT) activity. According to the scheme in Fig. 1, state variables are modified at every time step during the simulation according to the following equations:

ΔIP/Δt = ipt + ipu + ipNs – ipAPP – ipTH – ipGluN – ipCOX

ΔIPR/Δt = ipNt + ipAPP – ipKin – ipNs – iprTH – iprCOX

ΔIPRP/Δt = ipt + ipKin – ipNt – iprpTH

ΔIPNG/Δt = ipGluN

ΔZ/Δt = zu + ipTH + zNs + zGluO – zAPP – zRed – zGluOT – zGluN – zCOX

ΔZR/Δt = iprTH + zNt + zAPP + zrGluO – zKin – zNs – zrGluOT – zrCOX

ΔZRP/Δt = iprpTH + zKin – zNt

ΔZOG/Δt = zGluOT – zGluO

ΔZROG/Δt = zrGluOT – zrGluO

ΔZNG/Δt = zGluN

ΔDHZ/Δt = zRed + dhzNs – dhzAPP – dhzGluN

ΔDHZR/Δt = dhzru + dhzAPP + dhzNt + dhzrGluO – dhzKin – dhzrGluOT – dhzNs

ΔDHZRP/Δt = dhzKin – dhzNt

ΔDHZROG/Δt = dhzrGluOT – dhzrGluO

ΔDHZNG/Δt = dhzGluN

where Kin = adenosine kinase and Nt = 5′‐nucleotidase.

Governing rate equations

The following equations were used to calculate rates of conversions in the model. The rates depend on substrate concentration according to the well‐known Michaelis–Menten kinetics that provide for initial linear response to increasing substrate concentration and subsequent saturation with the substrate. In simulation of COX activity, literature data were accounted for that show the enzyme to be inducible by IP‐ and Z‐type bases and ribosides (Hare and van Staden, 1994). This was done by making Vmax COX hyperbolically proportional to the sum of these four inducers. Because the same data show Km for IP to be lower than that for Z, we used an arbitrary factor of 1·5 to modify Km COX when used with Z and ZR substrates.

dhzAPP = Vmax APP × DHZ/(Km APP + DHZ)

dhzGluN = Vmax GluN × DHZ/(Km GluN + DHZ)

dhzKin = Vmax Kin × DHZR/(Km Kin + DHZR)

dhzNs = Vmax Ns × DHZR/(Km Ns + DHZR)

dhzNt = Vmax Nt × DHZRP/(Km Nt + DHZRP)

dhzrGluO = Vmax GluO × DHZROG/(Km GluO + DHZROG)

dhzrGluOT = Vmax GluOT × DHZR/(Km GluOT + DHZR)

ipAPP = Vmax APP × IP/(Km APP + IP)

ipCOX = Vmax COX × IP/(Km COX + IP)

ipGluN = Vmax GluN × IP/(Km GluN + IP)

ipNs = Vmax Ns × IPR/(Km Ns + IPR)

ipNt = Vmax Nt × IPRP/(Km Nt + IPRP)

ipTH = Vmax TH × IP/(Km TH + IP)

iprCOX = Vmax COX × IPR/(Km COX + IPR)

iprTH = Vmax TH × IPR/(Km TH + IPR)

iprpTH = Vmax TH × IPRP/(Km TH + IPRP)

VmaxCOX = Vmax k × (IP + IPR + Z + ZR)/(Km k + IP + IPR + Z + ZR)

zAPP = Vmax APP × Z/(Km APP + Z)

zCOX = Vmax COX × Z/(1·5 × Km COX + Z)

zGluN = Vmax GluN × Z/(Km GluN + Z)

zGluO = Vmax GluO × ZOG/(Km GluO + ZOG)

zGluOT = Vmax GluOT × Z/(Km GluOT + Z)

zKin = Vmax Kin × ZR/(Km Kin + ZR)

zNs = Vmax Ns × ZR/(Km Ns + ZR)

zNt = Vmax Nt × ZRP/(Km Nt + ZRP)

zRed = Vmax Red × Z/(Km Red + Z)

zrGluO = Vmax GluO × ZROG/(Km GluO + ZROG)

zrGluOT = Vmax GluOT × ZR/(Km GluOT + ZR)

zrCOX = Vmax COX × ZR/(1·5 × Km COX + ZR)

Parameter values

Parameter values are shown in Table A1. They were obtained from a series of Monte Carlo calibration cycles as described in Materials and Methods and used in simulations of IP (Fig. 3), Z and DHZ data (Fig. 6)A1

Fig. 1. The CK simulation model. Adenosine 5′‐monophosphate and isopentenyl pyrophosphate are maintained at constant concentrations. The other 15 rectangles represent state variables corresponding to the main CK compounds. Arrows represent their biochemical conversions catalysed by enzymes (black, unidirectional; grey, bidirectional; white, uptake and oxidation). The metabolic network used for construction of the model was adapted from Kaminek (1992) to fit the set of known enzymes and possibilities to measure metabolite concentration experimentally. Enzyme names are used as defined in the list of abbreviations. ipu, isopentenyl adenine uptake; zu, trans‐zeatin uptake, dhzru, dihydrozeatin riboside uptake.

Fig. 1. The CK simulation model. Adenosine 5′‐monophosphate and isopentenyl pyrophosphate are maintained at constant concentrations. The other 15 rectangles represent state variables corresponding to the main CK compounds. Arrows represent their biochemical conversions catalysed by enzymes (black, unidirectional; grey, bidirectional; white, uptake and oxidation). The metabolic network used for construction of the model was adapted from Kaminek (1992) to fit the set of known enzymes and possibilities to measure metabolite concentration experimentally. Enzyme names are used as defined in the list of abbreviations. ipu, isopentenyl adenine uptake; zu, trans‐zeatin uptake, dhzru, dihydrozeatin riboside uptake.

Fig. 2. The effect of isopentenyl adenine, trans‐zeatin and dihydro zeatin riboside on the morphology and development of SR1 tobacco seedlings grown on MS medium. The three rows represent seedlings of different ages (day 2, day 5 and day 12 after germination). The first column (MS) shows control seedlings grown in absence of external CKs. The other columns show seedlings grown on MS medium supplemented with 1 µm isopentenyl adenine (MS+IP), 1 µmtrans‐zeatin (MS+Z) and 1 µm dihydrozeatin riboside (MS+DHZR). The displayed seedlings were chosen as representative samples from more than 100 individuals. The scale bar = 1 mm.

Fig. 2. The effect of isopentenyl adenine, trans‐zeatin and dihydro zeatin riboside on the morphology and development of SR1 tobacco seedlings grown on MS medium. The three rows represent seedlings of different ages (day 2, day 5 and day 12 after germination). The first column (MS) shows control seedlings grown in absence of external CKs. The other columns show seedlings grown on MS medium supplemented with 1 µm isopentenyl adenine (MS+IP), 1 µmtrans‐zeatin (MS+Z) and 1 µm dihydrozeatin riboside (MS+DHZR). The displayed seedlings were chosen as representative samples from more than 100 individuals. The scale bar = 1 mm.

Fig. 3. Comparison of data simulated by the mathematical model and experimental measurements. Data shown are for the MS‐grown control (open triangle) and the MS+IP treatment sampled on day 2 (open circles), day 5 (grey circles) and day 12 (closed circles). Simulations were carried out (A) before calibration of the model with equal Vmax (= 10) and Km (= 100) values for all the key enzymes represented in the model and (B) after calibration of the model with data from the MS+IP treatment. Symbols occurring close to the diagonal line (1 : 1) represent a perfect match between simulated and measured data. For completeness of the presentation, metabolites which were below the limit of detection were replaced by a value of 0·01.

Fig. 3. Comparison of data simulated by the mathematical model and experimental measurements. Data shown are for the MS‐grown control (open triangle) and the MS+IP treatment sampled on day 2 (open circles), day 5 (grey circles) and day 12 (closed circles). Simulations were carried out (A) before calibration of the model with equal Vmax (= 10) and Km (= 100) values for all the key enzymes represented in the model and (B) after calibration of the model with data from the MS+IP treatment. Symbols occurring close to the diagonal line (1 : 1) represent a perfect match between simulated and measured data. For completeness of the presentation, metabolites which were below the limit of detection were replaced by a value of 0·01.

Fig. 4. Sensitivity analysis for the MS+IP‐calibrated model. Panels show the goodness‐of‐fit of the calibrated model when individual parameters (A, Vmax values and uptake rate ipu; B, Km values) are varied by a factor of 0·2–3. The flat, more open curves represent parameters with smaller effect on the overall behaviour of the model.

Fig. 4. Sensitivity analysis for the MS+IP‐calibrated model. Panels show the goodness‐of‐fit of the calibrated model when individual parameters (A, Vmax values and uptake rate ipu; B, Km values) are varied by a factor of 0·2–3. The flat, more open curves represent parameters with smaller effect on the overall behaviour of the model.

Fig. 5. Graphical representation of Vmax and Km values obtained by calibration of the model using data from the MS+IP treatment. Rectangles represent state variables corresponding to the main CK compounds. Arrows represent their biochemical conversions catalysed by enzymes. Thickness of individual arrows is proportional to the Vmax of the represented enzyme. The size of the circle associated with the arrow is inversely proportional to the Km; small circles therefore represent low affinity for the substrate.

Fig. 5. Graphical representation of Vmax and Km values obtained by calibration of the model using data from the MS+IP treatment. Rectangles represent state variables corresponding to the main CK compounds. Arrows represent their biochemical conversions catalysed by enzymes. Thickness of individual arrows is proportional to the Vmax of the represented enzyme. The size of the circle associated with the arrow is inversely proportional to the Km; small circles therefore represent low affinity for the substrate.

Fig. 6. Comparison of data simulated by the mathematical model and experimental measurements. Data shown are for MS+Z (A) and MS+DHZR (B) treatments sampled on day 2 (open circles), day 5 (grey circles) and day 12 (closed circles). Simulations were carried out after calibration of the model with data from the MS+IP treatment. Symbols occurring close to the diagonal line (1 : 1) represent a perfect match between simulated and measured data. For completeness of the presentation, metabolites which were below the limit of detection were replaced by a value of 0·01.

Fig. 6. Comparison of data simulated by the mathematical model and experimental measurements. Data shown are for MS+Z (A) and MS+DHZR (B) treatments sampled on day 2 (open circles), day 5 (grey circles) and day 12 (closed circles). Simulations were carried out after calibration of the model with data from the MS+IP treatment. Symbols occurring close to the diagonal line (1 : 1) represent a perfect match between simulated and measured data. For completeness of the presentation, metabolites which were below the limit of detection were replaced by a value of 0·01.

Table 1.

Endogenous CK content (pmol g f. wt–1) in seedlings of SR1 tobacco grown on MS medium with or without addition of 1 µm isopentenyl adenine (MS+IP), 1 µmtrans‐zeatin (MS+Z) or 1 µm dihydrozeatin riboside (MS+DHZR)

 Medium 
 MS MS+IP MS+Z MS+DHZR 
 Days Days Days Days 
CK type 12 12 12 12 
nd nd 9·4 (10·8; 8·0) 13·6 (15·0; 12·1) 14·5 (5·3; 23·7) 11·9 (5·7; 18·1) 403 (435; 370) 214 (219; 208) 152 (147; 157) 8·3 (8·1; 8·5) 9·2 (7·5; 10·9) 10·3 (8·8; 11·8) 
cZ nd 5·2 (7·3; 3·1) 6·2 (6·9; 5·5) 8·9 (10·1; 7·7) 7·8 (9·1; 6·5) 7·2 (7·7; 6·7) 7·7 (6·4; 9·0) 7·0 (8·7; 5·3) 7·2 (9·8; 4·6) 5·3 (6·5; 4·1) 6·5 (8·3; 4·7) 7·2 (8·8; 5·5) 
IP 0·1* 0·2* 1·3 (1·5; 1·1) 971 (883; 1058) 446 (373; 519) 216 (190; 242) 2·2 (1·2; 3·2) 2·2 (2·4; 2·0) 1·3 (1·1; 1·5) 0·1* 1·2 (0·6; 1·8) 1·2 (0·9; 1·4) 
DHZ 0·7 (1·3; 0·1) 1·6 (0·8; 2·4) nd 1·1 (1·4; 0·8) 0·8 (1·5; 0·1) 1·6* 1·1 (0·7; 1·5) 1·5 (2·3; 0·7) 0·4* 82·0 (85·3; 78·6) 19·9 (16·8; 23·0) 19·9 (26·3; 13·5) 
ZR 0·4* 0·5 (0·4; 0·5) 0·5* 1·5 (1·6; 1·4) nd 0·7 (1·2; 0·2) 6·7 (4·4; 9·0) 0·5 (0·8; 0·2) 1·8 (2·1; 1·5) 0·8 (1·1; 0·5) nd 0·8 (0·5; 1·1) 
cZR 1·8 (1·2; 2·3) 1·1 (1·5; 0·7) 2·2 (1·6; 2·7) 1·6 (1·9; 1·3) 0·4 (0·2; 0·6) 0·7 (0·6; 0·8) 1·7 (1·0; 2·4) nd 0·7 (0·8; 0·6) 1·7 (2·3; 1·1) nd 1·5 (1·2; 1·8) 
IPR nd 0·1* 0·3* 3·0 (2·9; 3·1) 0·5* 0·4* 0·2 (0·1; 0·3) 0·2* 0·2* 0·5* 0·1* 0·4* 
DHZR 1·2 (1·0; 1·4) 2·7 (2·3; 3·1) 1·6 (2·2; 1·0) 0·1* 0·2* nd 2·2 (1·2; 3·2) 4·0 (4·9; 3·1) 2·0 (2·2; 1·8) 504 (598; 409) 291 (200; 382) 184 (164; 204) 
ZRP nd nd 1·6 (1·4; 1·8) 8·6 (7·8; 9·4) 1·3* 1·5 (0·9; 2·1) 61·8 (52·4; 71·2) 16·5 (13·2; 19·8) 8·0 (6·7; 9·3) nd nd 2·1* 
cZRP 11·2 (6·0; 16·4) 3·4 (2·1; 4·6) 0·8 (0·1; 1·5) 4·0 (2·8; 5·2) 0·1* 3·5* 2·3* nd 1·1 (0·6; 1·6) 22·3 (25·2; 19·4) 0·5 (0·3; 0·7) 2·0* 
IPRP 3·4 (2·8; 4·0) 1·9 (2·6; 1·2) 0·5* 26·4 (28·0; 24·8) 6·3 (5·7; 6·9) 6·4 (6·8; 6·0) 0·7* 0·3* 0·7 (0·4; 1·0) 2·9 (0·8; 5·0) nd 0·1* 
DHZRP 15·5 (10·9; 20·1) 16·6 (12·9; 20·3) 4·0 (3·1; 4·9) 2·7 (2·0; 3·4) 2·4 (2·6; 2·2) 45·3 (42·2; 48·4) 6·2 (4·2; 8·2) 5·2 (3·5; 6·9) 19·5 (13·2; 25·8) 665 (629; 701) 53·6 (45·8; 61·4) 23·0 (18·5; 27·5) 
ZOG 1·8 (1·4; 2·1) 9·1 (5·0; 13·2) 9·9 (5·1; 14·6) nd 24·2 (26·7; 21·7) 12·9 (10·0; 15·7) nd 5·9 (8·6; 3·2) 21·0 (18·0; 24·0) 0·9 (0·8; 1·0) 2·1 (1·8; 2·3) 3·6 (6·1; 1·1) 
ZROG 0·1* nd nd 0·6* 1·6* 1·8* nd nd nd nd nd nd 
DHZROG 0·5 (0·3; 0·7) 0·3* 0·5* nd 0·6* 1·0* 0·4* nd 0·3* 51·4 (41·0; 61·8) 30·9 (28·8; 33·0) 32·0 (27·2; 36·8) 
Z7G 2·0 (2·0; 2·0) nd 6·9 (4·8; 9·0) 104 (72; 136) 22·7 (29·0; 16·4) 69·7 (51·5; 87·9) 552 (510; 594) 680 (641; 719) 1019 (904; 1134) 11·1 (6·8; 15·4) nd 20·0 (16·0; 24·0) 
IP7G 6·6 (8·5; 4·7) 5·6 (8·8; 2·4) 16·9 (20·8; 12·9) 12 361 (16 251; 8470) 16 210 (20 114; 12 306) 15 341 (20 701; 9981) 33·5 (29·3; 37·7) 3·8 (6·3; 1·3) 0·9 (0·7; 1·1) 52·7 (47·9; 57·4) 3·0* 3·1 (4·6; 1·6) 
DHZ7G‐1 1·2 (1·0; 1·4) 0·6* 1·0* 12·7 (9·8; 15·6) 2·8 (5·5; 0·1) nd 16·7 (11·2; 22·2) 59·4 (45·2; 73·6) 19·7 (26·4; 12·9) 2738 (1968; 3508) 4471 (2918; 6023) 8822 (5145; 12 499) 
DHZ7G‐2 3·6 (4·3; 2·9) 0·7* nd 19·4 (19·2; 19·6) 30·9 (30·9; 30·9) 34·8 (34·3; 35·3) 11·7 (7·9; 15·5) 9·2 (14·9; 3·5) 10·3 (15·5; 5·1) 2709 (2985; 2432) 2541 (3399; 1683) 4294 (3285; 5303) 
Z9G nd 0·3 (0·5; 0·1) 0·8 (0·9; 0·7) 2·5 (1·9; 3·1) 2·5* 2·5 (2·1; 2·9) 2·5 (2·3; 2·7) 2·5* 2·5 (2·4; 2·6) 2·5 (1·9; 3·1) 0·4 (0·3; 0·5) 2·5 (1·2; 3·7) 
IP9G 0·7 (0·4; 0·9) 0·4* 0·7 (0·5; 0·9) 12·4 (14·9; 9·8) 15·3 (13·9; 16·7) 19·3 (12·8; 25·8) 0·7 (0·4; 1·0) 0·4 (0·3; 0·5) 0·4* 0·8 (0·7; 0·9) 0·6* 0·2* 
DHZ9G 0·4* 0·1* 0·7* 3·1* 0·3* 0·6 (0·3; 0·9) 0·1* 0·2* nd 3·7 (4·6; 2·8) 9·4 (8·9; 9·9) 4·4* 
 Medium 
 MS MS+IP MS+Z MS+DHZR 
 Days Days Days Days 
CK type 12 12 12 12 
nd nd 9·4 (10·8; 8·0) 13·6 (15·0; 12·1) 14·5 (5·3; 23·7) 11·9 (5·7; 18·1) 403 (435; 370) 214 (219; 208) 152 (147; 157) 8·3 (8·1; 8·5) 9·2 (7·5; 10·9) 10·3 (8·8; 11·8) 
cZ nd 5·2 (7·3; 3·1) 6·2 (6·9; 5·5) 8·9 (10·1; 7·7) 7·8 (9·1; 6·5) 7·2 (7·7; 6·7) 7·7 (6·4; 9·0) 7·0 (8·7; 5·3) 7·2 (9·8; 4·6) 5·3 (6·5; 4·1) 6·5 (8·3; 4·7) 7·2 (8·8; 5·5) 
IP 0·1* 0·2* 1·3 (1·5; 1·1) 971 (883; 1058) 446 (373; 519) 216 (190; 242) 2·2 (1·2; 3·2) 2·2 (2·4; 2·0) 1·3 (1·1; 1·5) 0·1* 1·2 (0·6; 1·8) 1·2 (0·9; 1·4) 
DHZ 0·7 (1·3; 0·1) 1·6 (0·8; 2·4) nd 1·1 (1·4; 0·8) 0·8 (1·5; 0·1) 1·6* 1·1 (0·7; 1·5) 1·5 (2·3; 0·7) 0·4* 82·0 (85·3; 78·6) 19·9 (16·8; 23·0) 19·9 (26·3; 13·5) 
ZR 0·4* 0·5 (0·4; 0·5) 0·5* 1·5 (1·6; 1·4) nd 0·7 (1·2; 0·2) 6·7 (4·4; 9·0) 0·5 (0·8; 0·2) 1·8 (2·1; 1·5) 0·8 (1·1; 0·5) nd 0·8 (0·5; 1·1) 
cZR 1·8 (1·2; 2·3) 1·1 (1·5; 0·7) 2·2 (1·6; 2·7) 1·6 (1·9; 1·3) 0·4 (0·2; 0·6) 0·7 (0·6; 0·8) 1·7 (1·0; 2·4) nd 0·7 (0·8; 0·6) 1·7 (2·3; 1·1) nd 1·5 (1·2; 1·8) 
IPR nd 0·1* 0·3* 3·0 (2·9; 3·1) 0·5* 0·4* 0·2 (0·1; 0·3) 0·2* 0·2* 0·5* 0·1* 0·4* 
DHZR 1·2 (1·0; 1·4) 2·7 (2·3; 3·1) 1·6 (2·2; 1·0) 0·1* 0·2* nd 2·2 (1·2; 3·2) 4·0 (4·9; 3·1) 2·0 (2·2; 1·8) 504 (598; 409) 291 (200; 382) 184 (164; 204) 
ZRP nd nd 1·6 (1·4; 1·8) 8·6 (7·8; 9·4) 1·3* 1·5 (0·9; 2·1) 61·8 (52·4; 71·2) 16·5 (13·2; 19·8) 8·0 (6·7; 9·3) nd nd 2·1* 
cZRP 11·2 (6·0; 16·4) 3·4 (2·1; 4·6) 0·8 (0·1; 1·5) 4·0 (2·8; 5·2) 0·1* 3·5* 2·3* nd 1·1 (0·6; 1·6) 22·3 (25·2; 19·4) 0·5 (0·3; 0·7) 2·0* 
IPRP 3·4 (2·8; 4·0) 1·9 (2·6; 1·2) 0·5* 26·4 (28·0; 24·8) 6·3 (5·7; 6·9) 6·4 (6·8; 6·0) 0·7* 0·3* 0·7 (0·4; 1·0) 2·9 (0·8; 5·0) nd 0·1* 
DHZRP 15·5 (10·9; 20·1) 16·6 (12·9; 20·3) 4·0 (3·1; 4·9) 2·7 (2·0; 3·4) 2·4 (2·6; 2·2) 45·3 (42·2; 48·4) 6·2 (4·2; 8·2) 5·2 (3·5; 6·9) 19·5 (13·2; 25·8) 665 (629; 701) 53·6 (45·8; 61·4) 23·0 (18·5; 27·5) 
ZOG 1·8 (1·4; 2·1) 9·1 (5·0; 13·2) 9·9 (5·1; 14·6) nd 24·2 (26·7; 21·7) 12·9 (10·0; 15·7) nd 5·9 (8·6; 3·2) 21·0 (18·0; 24·0) 0·9 (0·8; 1·0) 2·1 (1·8; 2·3) 3·6 (6·1; 1·1) 
ZROG 0·1* nd nd 0·6* 1·6* 1·8* nd nd nd nd nd nd 
DHZROG 0·5 (0·3; 0·7) 0·3* 0·5* nd 0·6* 1·0* 0·4* nd 0·3* 51·4 (41·0; 61·8) 30·9 (28·8; 33·0) 32·0 (27·2; 36·8) 
Z7G 2·0 (2·0; 2·0) nd 6·9 (4·8; 9·0) 104 (72; 136) 22·7 (29·0; 16·4) 69·7 (51·5; 87·9) 552 (510; 594) 680 (641; 719) 1019 (904; 1134) 11·1 (6·8; 15·4) nd 20·0 (16·0; 24·0) 
IP7G 6·6 (8·5; 4·7) 5·6 (8·8; 2·4) 16·9 (20·8; 12·9) 12 361 (16 251; 8470) 16 210 (20 114; 12 306) 15 341 (20 701; 9981) 33·5 (29·3; 37·7) 3·8 (6·3; 1·3) 0·9 (0·7; 1·1) 52·7 (47·9; 57·4) 3·0* 3·1 (4·6; 1·6) 
DHZ7G‐1 1·2 (1·0; 1·4) 0·6* 1·0* 12·7 (9·8; 15·6) 2·8 (5·5; 0·1) nd 16·7 (11·2; 22·2) 59·4 (45·2; 73·6) 19·7 (26·4; 12·9) 2738 (1968; 3508) 4471 (2918; 6023) 8822 (5145; 12 499) 
DHZ7G‐2 3·6 (4·3; 2·9) 0·7* nd 19·4 (19·2; 19·6) 30·9 (30·9; 30·9) 34·8 (34·3; 35·3) 11·7 (7·9; 15·5) 9·2 (14·9; 3·5) 10·3 (15·5; 5·1) 2709 (2985; 2432) 2541 (3399; 1683) 4294 (3285; 5303) 
Z9G nd 0·3 (0·5; 0·1) 0·8 (0·9; 0·7) 2·5 (1·9; 3·1) 2·5* 2·5 (2·1; 2·9) 2·5 (2·3; 2·7) 2·5* 2·5 (2·4; 2·6) 2·5 (1·9; 3·1) 0·4 (0·3; 0·5) 2·5 (1·2; 3·7) 
IP9G 0·7 (0·4; 0·9) 0·4* 0·7 (0·5; 0·9) 12·4 (14·9; 9·8) 15·3 (13·9; 16·7) 19·3 (12·8; 25·8) 0·7 (0·4; 1·0) 0·4 (0·3; 0·5) 0·4* 0·8 (0·7; 0·9) 0·6* 0·2* 
DHZ9G 0·4* 0·1* 0·7* 3·1* 0·3* 0·6 (0·3; 0·9) 0·1* 0·2* nd 3·7 (4·6; 2·8) 9·4 (8·9; 9·9) 4·4* 

Values represent the mean of LC/MS/MS measurements in two replications (individual measurements shown in parentheses). nd, No CKs detected. Individual CKs were grouped as bases, ribosides, phosphates, O‐glucosides, N‐7‐glucosides and N‐9‐glucosides. DHZ7G‐1 and DHZ7G‐2 are enantiomers of DHZ7G. cZ, cis‐zeatin; DHZ7G and DHZ9G, dihydrozeatin N‐7‐ and N‐9‐glucoside; IP7G and IP9G, isopentenyl adenine N‐7‐ and N‐9‐glucoside; Z7G and Z9G, zeatin N‐7‐ and N‐9‐glucoside. * Data represent a single measurement. CKs were not detected in one of the two replicates.

Table 2.

Summary representation of endogenous CK content (pmol g–1 f. wt) in seedlings of SR1 tobacco grown on MS medium with or without supplementation with 1 µm isopentenyl adenine (MS+IP), 1 µmtrans‐zeatin (MS+Z) and 1 µm dihydrozeatin riboside (MS+DHZR)

 Medium 
 MS MS+IP MS+Z MS+DHZR 
 Days Days Days Days 
Group 12 12 12 12 
Bases 0·8 (1·4; 0·2) 7·0 (8·3; 5·7) 16·9 (19·2; 14·6) 995 (910; 1079) 469 (389; 549) 237 (205; 268) 414 (443; 384) 224 (232; 216) 161 (158; 164) 95·7 (100·0; 91·3) 36·8 (33·2; 40·4) 38·5 (44·8; 32·2) 
Ribosides 3·4 (2·6; 4·1) 4·4 (4·6; 4·5) 4·6 (4·6; 4·5) 6·2 (6·5; 5·9) 1·1 (0·9; 1·3) 1·8 (2·2; 1·4) 10·8 (6·7; 14·9) 4·7 (5·9; 3·5) 4·7 (5·3; 4·1) 507 (602; 411) 291 (200; 382) 187 (166; 207) 
Phosphates 30·1 (19·7; 40·4) 21·9 (17·6; 26·1) 6·9 (5·1; 8·7) 41·7 (40·6; 42·8) 10·1 (9·7; 10·5) 56·7 (53·4; 60·0) 71·0 (59·6; 82·4) 22·0 (17·0; 27·0) 29·3 (20·9; 37·7) 690 (655; 725) 54·1 (46·1; 62·1) 27·2 (22·7; 31·7) 
O‐Glucosides 2·4 (1·8; 2·9) 9·4 (5·3; 13·5) 10·4 (5·6; 15·1) 0·6* 26·4 (28·9; 23·9) 15·7 (12·8; 18·5) 0·4* 5·9 (8·6; 3·2) 21·3 (18·3; 24·3) 52·3 (41·8; 62·8) 33·0 (30·6; 35·3) 35·6 (33·3; 37·9) 
N‐Glucosides 14·5 (16·6; 12·3) 7·7 (11·1; 4·3) 27·0 (28·7; 25·2) 12 515 (16 372; 8657) 16 285 (20 196; 12 373) 15 468 (20 802; 10 134) 617 (561; 673) 755 (710; 800) 1053 (949; 1156) 5518 (5015; 6020) 7025 (6330; 7720) 13 146 (8456; 17 836) 
Total CK 51·0 (42·1; 59·9) 50·5 (46·9; 54·1) 65·7 (63·2; 68·1) 13 558 (17 330; 9785) 16 792 (20 625; 12 958) 15 778 (21 075; 10 481) 1113 (1071; 1155) 1012 (974; 1050) 1269 (1152; 1386) 6862 (6414; 7310) 7440 (6640; 8240) 13 434 (8723; 18 145) 
Z + ZR + ZRP 0·4* 5·7 (7·7; 3·6) 17·7 (19·6; 15·8) 32·6 (34·5; 30·6) 23·6 (15·7; 31·5) 21·3 (15·5; 27·1) 479 (498; 459) 238 (242; 233) 169 (166; 172) 14·4 (15·7; 13·1) 15·7 (15·8; 15·6) 20·4 (20·2; 20·5) 
Active CK 34·2 (23·7; 44·7) 33·4 (30·5; 36·3) 28·4 (28·9; 27·8) 1043 (958; 1128) 481 (400; 561) 294 (260; 328) 496 (510; 482) 251 (255; 247) 195 (185; 205) 1292 (1357; 1227) 382 (279; 485) 253 (234; 271) 
Non‐active CK 16·8 (18·4; 15·2) 17·1 (16·4; 17·8) 37·3 (34·3; 40·3) 12 515 (16 372; 8657) 16 311 (20 225; 12397) 15 484 (20 815; 10153) 617 (561; 673) 761 (719; 803) 1074 (967; 1180) 5570 (5057; 6083) 7058 (6361; 7755) 13 182 (8489; 17 874) 
% Active 65·5 (56·3; 74·6) 66·1 (65·0; 67·1) 43·3 (45·7; 40·8) 8·5 (5·5; 11·5) 3·1 (1·9; 4·3) 2·2 (1·2; 3·1) 44·7 (47·6; 41·7) 24·9 (26·2; 23·5) 15·5 (16·1; 14·8) 19·0 (21·2; 16·8) 5·1 (4·2; 5·9) 2·1 (2·7; 1·5) 
 Medium 
 MS MS+IP MS+Z MS+DHZR 
 Days Days Days Days 
Group 12 12 12 12 
Bases 0·8 (1·4; 0·2) 7·0 (8·3; 5·7) 16·9 (19·2; 14·6) 995 (910; 1079) 469 (389; 549) 237 (205; 268) 414 (443; 384) 224 (232; 216) 161 (158; 164) 95·7 (100·0; 91·3) 36·8 (33·2; 40·4) 38·5 (44·8; 32·2) 
Ribosides 3·4 (2·6; 4·1) 4·4 (4·6; 4·5) 4·6 (4·6; 4·5) 6·2 (6·5; 5·9) 1·1 (0·9; 1·3) 1·8 (2·2; 1·4) 10·8 (6·7; 14·9) 4·7 (5·9; 3·5) 4·7 (5·3; 4·1) 507 (602; 411) 291 (200; 382) 187 (166; 207) 
Phosphates 30·1 (19·7; 40·4) 21·9 (17·6; 26·1) 6·9 (5·1; 8·7) 41·7 (40·6; 42·8) 10·1 (9·7; 10·5) 56·7 (53·4; 60·0) 71·0 (59·6; 82·4) 22·0 (17·0; 27·0) 29·3 (20·9; 37·7) 690 (655; 725) 54·1 (46·1; 62·1) 27·2 (22·7; 31·7) 
O‐Glucosides 2·4 (1·8; 2·9) 9·4 (5·3; 13·5) 10·4 (5·6; 15·1) 0·6* 26·4 (28·9; 23·9) 15·7 (12·8; 18·5) 0·4* 5·9 (8·6; 3·2) 21·3 (18·3; 24·3) 52·3 (41·8; 62·8) 33·0 (30·6; 35·3) 35·6 (33·3; 37·9) 
N‐Glucosides 14·5 (16·6; 12·3) 7·7 (11·1; 4·3) 27·0 (28·7; 25·2) 12 515 (16 372; 8657) 16 285 (20 196; 12 373) 15 468 (20 802; 10 134) 617 (561; 673) 755 (710; 800) 1053 (949; 1156) 5518 (5015; 6020) 7025 (6330; 7720) 13 146 (8456; 17 836) 
Total CK 51·0 (42·1; 59·9) 50·5 (46·9; 54·1) 65·7 (63·2; 68·1) 13 558 (17 330; 9785) 16 792 (20 625; 12 958) 15 778 (21 075; 10 481) 1113 (1071; 1155) 1012 (974; 1050) 1269 (1152; 1386) 6862 (6414; 7310) 7440 (6640; 8240) 13 434 (8723; 18 145) 
Z + ZR + ZRP 0·4* 5·7 (7·7; 3·6) 17·7 (19·6; 15·8) 32·6 (34·5; 30·6) 23·6 (15·7; 31·5) 21·3 (15·5; 27·1) 479 (498; 459) 238 (242; 233) 169 (166; 172) 14·4 (15·7; 13·1) 15·7 (15·8; 15·6) 20·4 (20·2; 20·5) 
Active CK 34·2 (23·7; 44·7) 33·4 (30·5; 36·3) 28·4 (28·9; 27·8) 1043 (958; 1128) 481 (400; 561) 294 (260; 328) 496 (510; 482) 251 (255; 247) 195 (185; 205) 1292 (1357; 1227) 382 (279; 485) 253 (234; 271) 
Non‐active CK 16·8 (18·4; 15·2) 17·1 (16·4; 17·8) 37·3 (34·3; 40·3) 12 515 (16 372; 8657) 16 311 (20 225; 12397) 15 484 (20 815; 10153) 617 (561; 673) 761 (719; 803) 1074 (967; 1180) 5570 (5057; 6083) 7058 (6361; 7755) 13 182 (8489; 17 874) 
% Active 65·5 (56·3; 74·6) 66·1 (65·0; 67·1) 43·3 (45·7; 40·8) 8·5 (5·5; 11·5) 3·1 (1·9; 4·3) 2·2 (1·2; 3·1) 44·7 (47·6; 41·7) 24·9 (26·2; 23·5) 15·5 (16·1; 14·8) 19·0 (21·2; 16·8) 5·1 (4·2; 5·9) 2·1 (2·7; 1·5) 

Values shown are averages of sums calculated from Table 1.

Active CK represent the sum of all CKs except glucosides.

Sums for each replicate shown in parentheses.

* Data represent a single measurement. CKs were not detected in one of the two replicates.

Percentage of active CK is calculated from the total CK content.

Table 3.

Comparison of experimental Km values reported in literature and Km′ values obtained from Monte Carlo calibration of the simulation model, using MS+IP cytokinin data

Enzyme Source Substrate KmmKm′ (nmReference 
APP Wheat germ IP 57 11 Chen and Petschow (1978) 
GluN Radish seedling 150 483 Entsch et al. (1979) 
GluOT Phaseolus seed 200 822 Dixon et al. (1989) 
Kin Arabidopsis seedlings IPR 3·2; 4·8 51 Moffatt et al. (2000) 
 Wheat germ IPR 31 51 Chen and Eckert (1977) 
Ns Wheat germ IPR 2·4 Chen and Kristopeit (1981a
Nt Wheat germ IPRP 3·5; 12·8 702 Chen and Kristopeit (1981b
Red Phaseolus embryo 70; 100 150 Martin et al. (1989) 
Enzyme Source Substrate KmmKm′ (nmReference 
APP Wheat germ IP 57 11 Chen and Petschow (1978) 
GluN Radish seedling 150 483 Entsch et al. (1979) 
GluOT Phaseolus seed 200 822 Dixon et al. (1989) 
Kin Arabidopsis seedlings IPR 3·2; 4·8 51 Moffatt et al. (2000) 
 Wheat germ IPR 31 51 Chen and Eckert (1977) 
Ns Wheat germ IPR 2·4 Chen and Kristopeit (1981a
Nt Wheat germ IPRP 3·5; 12·8 702 Chen and Kristopeit (1981b
Red Phaseolus embryo 70; 100 150 Martin et al. (1989) 

The apparent Km′ values are two to three orders of magnitude lower than the measured ones. Potential sources of the differences are addressed in the Discussion.

Table A1.

ipt 0·16 pmol g–1 f. wt h–1 IPT activity 
ipu (zu, dhzru)* 48·004 pmol g–1 f. wt h–1 Rate of IP (Z, DHZR) uptake from medium 
Km APP 10·884 pmol g–1 f. wt Km of adenosine phosphorylase 
Km COX 10 000 pmol g–1 f. wt Km of CK oxidase 
Km GluN 483·2 pmol g–1 f. wt Km of N‐glucosyl transferase 
Km GluO 848·2 pmol g–1 f. wt Km of β‐glucosidase 
Km GluOT 822·4 pmol g–1 f. wt Km of O‐glucosyltransferase 
Km8718 pmol g–1 f. wt Parameter for COX Vmax 
Km Kin 51·92 pmol g–1 f. wt Kmax of adenosine kinase 
Km Ns 9·472 pmol g–1 f. wt Km of adenosine nucleosidase 
Km Nt 701·6 pmol g–1 f. wt Km of 5′ nucleotidase 
Km Red 150·4 pmol g–1 f. wt Km of zeatin reductase 
Km TH 921·2 pmol g–1 f. wt Km of trans‐hydroxylase 
Vmax APP 12·71 pmol g–1 f. wt h–1 Vmax of adenosine phosphorylase 
Vmax GluN 142·7 pmol g–1 f. wt h–1 Vmax of N‐glucosyl transferase 
Vmax GluO 40·826 pmol g–1 f. wt h–1 Vmax of β‐glucosidase 
Vmax GluOT 15·933 pmol g–1 f. wt h–1 Vmax of O‐glucosyltransferase 
Vmax1259·2 pmol g–1 f. wt h–1 Parameter for COX Vmax 
Vmax Kin 100·36 pmol g–1 f. wt h–1 Vmax of adenosine kinase 
Vmax Ns 99·69 pmol g–1 f. wt h–1 Vmax of adenosine nucleosidase 
Vmax Nt 90·16 pmol g–1 f. wt h–1 Vmax of 5′ nucleotidase 
Vmax Red 19·364 pmol g–1 f. wt h–1 Vmax of zeatin reductase 
Vmax TH 7·291 pmol g–1 f. wt h–1 Vmax of trans‐hydroxylase 
ipt 0·16 pmol g–1 f. wt h–1 IPT activity 
ipu (zu, dhzru)* 48·004 pmol g–1 f. wt h–1 Rate of IP (Z, DHZR) uptake from medium 
Km APP 10·884 pmol g–1 f. wt Km of adenosine phosphorylase 
Km COX 10 000 pmol g–1 f. wt Km of CK oxidase 
Km GluN 483·2 pmol g–1 f. wt Km of N‐glucosyl transferase 
Km GluO 848·2 pmol g–1 f. wt Km of β‐glucosidase 
Km GluOT 822·4 pmol g–1 f. wt Km of O‐glucosyltransferase 
Km8718 pmol g–1 f. wt Parameter for COX Vmax 
Km Kin 51·92 pmol g–1 f. wt Kmax of adenosine kinase 
Km Ns 9·472 pmol g–1 f. wt Km of adenosine nucleosidase 
Km Nt 701·6 pmol g–1 f. wt Km of 5′ nucleotidase 
Km Red 150·4 pmol g–1 f. wt Km of zeatin reductase 
Km TH 921·2 pmol g–1 f. wt Km of trans‐hydroxylase 
Vmax APP 12·71 pmol g–1 f. wt h–1 Vmax of adenosine phosphorylase 
Vmax GluN 142·7 pmol g–1 f. wt h–1 Vmax of N‐glucosyl transferase 
Vmax GluO 40·826 pmol g–1 f. wt h–1 Vmax of β‐glucosidase 
Vmax GluOT 15·933 pmol g–1 f. wt h–1 Vmax of O‐glucosyltransferase 
Vmax1259·2 pmol g–1 f. wt h–1 Parameter for COX Vmax 
Vmax Kin 100·36 pmol g–1 f. wt h–1 Vmax of adenosine kinase 
Vmax Ns 99·69 pmol g–1 f. wt h–1 Vmax of adenosine nucleosidase 
Vmax Nt 90·16 pmol g–1 f. wt h–1 Vmax of 5′ nucleotidase 
Vmax Red 19·364 pmol g–1 f. wt h–1 Vmax of zeatin reductase 
Vmax TH 7·291 pmol g–1 f. wt h–1 Vmax of trans‐hydroxylase 

* Calibration of the model was only carried out using the IP data. When the calibrated model was compared with Z and DHZR data, zu or dhzu were set to the ipu value shown, while the uptake ratios for the other two metabolites were set to zero.

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Author notes

1Masaryk University Brno, Department of Functional Genomics and Proteomics, Kotlářská 2, 611 37 Brno, Czech Republic, 2Institute of Experimental Botany of the Academy of Sciences of the Czech Republic, Rozvojová 135, 165 02 Prague, Czech Republic and 3Institute of Biophysics of the Academy of Sciences of the Czech Republic, Královopolská 135, 612 65 Brno, Czech Republic

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