Modeling the temporal dynamics of
monoterpene emission by isotopic labeling in
Quercus ilex leaves
S.M. Noe a,∗, U. Niinemets a, J-P. Schnitzler b
aDepartment of Plant Physiology, Institute of Agricultural and Environmental
Sciences, Estonian University of Life Sciences, Kreutzwaldi 1, EE-51014 Tartu,
Estonia
bResearch Centre Karlsruhe Institute for Meteorology and Climate Research
(IMK-IFU) Kreuzeckbahnstrasse 19, D-82467 Garmisch-Partenkirchen, Germany
Abstract
A mathematical model to study the temporal dynamics of stable isotope 13C in-
corporation into monoterpene molecules, emitted from Mediterranean evergreen
sclerophyll oak Quercus ilex L. leaves, was developed. The box model uses leaf level
gas exchange and monoterpene emission data to assess biochemical and diffusional
processes of the light-dependent monoterpene biosynthesis and emission within the
leaf tissues. We estimated total leaf monoterpene pool exchange half-lifes against
these processes. The slowest response took up to 38 hours, while the fastest response
occurred within one hour, taking the sum of the lumped processes time constants
into account. Separately, the turnover half-lives of the biochemical processes ranged
between 26 minutes up to more than 4 hours. The diffusional processes turnover
times, driven by the physico-chemical properties of the monoterpene molecule, have
been found to range between 32 minutes and 3 hours, depending on the number of
Preprint submitted to Atmospheric Environment 18 March 2010
13C-labeled carbon atoms. As a consequence, the steady state assumption that is
used in many larger scale emission models, may not hold in all cases and the ap-
plication of process-based algorithms is beneficial to overcome such long transient
pool dynamics of light-dependent monoterpene emission.
Key words: stable isotope, 13C, mathematical model, monoterpene emission,
temporal emission dynamics
1 Introduction1
Terpene emissions from leaves of many plant species (Kesselmeier and Staudt,2
1999) play a major role in atmospheric chemistry. These volatile compounds3
react rapidly with hydroxyl radicals in the atmosphere and, in the presence4
of reactive nitrogen (NOx), lead to the formation of ozone and secondary5
organic aerosols (SOA) (Kulmala et al., 2004; Tsirgaridis et al., 2005). As SOA6
particles play a role in cloud formation the release of monoterpenes may change7
the radiative energy transfer or water availability, at least regionally which,8
in turn set constraints on carbon dioxide (CO2) uptake and monoterpene9
emission of the ecosystem. So far, the temporal patterns and dynamics of the10
biosynthesis and emission of biogenic volatile compounds (BVOC) is not taken11
into account in most of the larger scale model approaches (Arneth et al., 2007,12
2008). They employ, like many leaf level studies, empirical parameterizations13
(Guenther et al., 1993; Niinemets et al., 2002) that are only valid under steady14
state assumptions.15
∗ Corresponding author.
Email addresses: [email protected] (S.M. Noe), [email protected] (U.
Niinemets), [email protected] (J-P. Schnitzler).
2
On the cellular level, the incorporation of stable isotopes such as 13C into16
molecules have been widely used to investigate the metabolic pathways of17
plants by means of metabolic flux analysis (MFA) and metabolic control anal-18
ysis (MCA) (Morgan and Rhodes, 2002; Rios-Estepa and Lange, 2007). These19
labeling techniques are ”state of the art” methods in research on terpene20
(hemi-, mono-, and sesquiterpenes) emissions and the regulation of the terpene21
biosynthetic pathways (Tholl et al., 2006). Impact of environmental effects on22
the hemi- (isoprene) and monoterpene emission patterns have been intensively23
studied by means of labeling experiments (Loreto et al., 2000, 2006) on leaf24
level. The availability of fast online measurement systems such as proton trans-25
fer reaction mass spectrometry (PTR-MS) has further increased the number26
of 13C-labeling studies to investigate the origin and processing of carbon in27
the emitted isoprene molecules (Karl et al., 2002; Kreuzwieser et al., 2002;28
Hayward and Hewitt, 2003; Schnitzler et al., 2004; Brilli et al., 2007).29
Yet, all these studies had focused on isoprene (Schnitzler et al., 2004; Wolfertz30
et al., 2004) and none studied the incorporation dynamics of 13C during the31
light-dependent biosynthesis of monoterpenes. On leaf level, the temporal32
emission patterns are the result of an interplay of several transport, diffu-33
sion and biochemical reaction processes within the ”system” leaf, that are34
additionally altered by the molecules physico-chemical properties (Niinemets35
and Reichstein, 2002; Noe et al., 2006, 2008).36
In this work, we employed a mathematical model to describe the temporal37
dynamics of monoterpene emissions from leaves of Quercus ilex, a evergreen38
Mediterranean tree species that emit monoterpenes in a light-dependent pro-39
cess (Kesselmeier et al., 1997) closely linked to the availability of recently fixed40
carbon. We took the advantage of the availability of fast online analysis us-41
3
ing PTR-MS in connection with a leaf cuvette system. Using our model, we42
became able to apply ”easy” accessible 13C incorporation profiles to predict43
the temporal dynamics of underlying processes in monoterpene biosynthesis,44
diffusion and emission.45
2 Materials and Methods46
2.1 Model description47
To describe temporal patterns of Q. ilex monoterpene emissions on leaf level,48
in minimum, three processes have to be taken into account; (a) CO2 diffusion49
into the leaf, (b) biochemical incorporation of recently fixed carbon into pho-50
tosynthetic intermediates. The formation of monoterpene molecules via the51
plastidic methyl erythritol (MEP)-pathway from those intermediates, includ-52
ing ”old” carbon sources, and (c) diffusion of the monoterpene molecules to the53
atmosphere. These processes can be described by means of a box model where54
the fluxes into and out of the boxes are defined by the time constants of the55
underlying processes. Estimates of these time constants give a first criterion56
to define the structure of the model.57
Assumed leaves with open stomata, the timescale of CO2 diffusion into the leaf58
is in seconds given the published diffusion constants and path lengths (Aalto59
and Juurola, 2002; Aalto et al., 1999; Vesala et al., 1996; Parkhurst, 1994).60
Niinemets et al. (2005) reported leaf age depended mesophyll conductances61
for Q. ilex leaves, which are in the same range as found for other species.62
Time constants of photosynthetic carbon fixation dynamics are as well in the63
range of several minutes to reach steady state after changes in environmental64
4
parameters (Fridlyand and Scheibe, 1999) and due to changes in enzyme ac-65
tivities. The turnover time within the Calvin cycle can be estimated by means66
of metabolic control analysis tools (Fridlyand et al., 1999; Giersch et al., 1990)67
or alternatively by fitting analytical models to measured data (Noe and Gier-68
sch, 2004). Both, CO2 diffusion and carbon fixation, have short time ranges69
within some minutes, if compared to the time range needed for the diffusion70
of the monoterpene molecules through the leaf tissues back to the atmosphere71
(Niinemets and Reichstein, 2002; Noe et al., 2006), which can take several72
minutes up to hours. Beside these diffusion depending processes, the turnover73
time of the plastidic MEP-pathway (Lichtenthaler, 1999; Rohmer, 2003) for74
terpene synthesis also influences the temporal emission pattern. Analyzing the75
time constants of the enzymatic steps and steady state modeling studies with76
the biochemical part of the SIM-BIM (version 2) model as initially described77
by Zimmer et al. (2000), further developed and enhanced with the monoter-78
pene synthesis pathway by Grote et al. (2006), gives estimates for the time79
constants of that process, which was found to be around 15-20 minutes (see80
appendix A). Because of those findings, we haven’t implemented in the current81
model a specific diffusion term for the CO2 diffusion into the leaf, as the time82
scale of that process is a factor of one or more magnitudes smaller than of all83
other processes.84
It is known from several studies, that the incorporation of 13C into isoprene85
and monoterpenes never reaches 100%, due to the fact that alternative ”old”86
carbon sources within the leaf and the whole plant always provide unlabeled87
molecules (Delwiche and Sharkey, 1993; Loreto et al., 2000; Schnitzler et al.,88
2004; Wolfertz et al., 2004). Therefore, the model should include the possibility89
that a mixture of 12C and 13C containing molecules are present in the same90
5
time. Monoterpene isotopes are generally identified by their mass-to-charge91
ratio m/z which ranges for differently labeled monoterpenes, as seen from92
PTR-MS data, between 137 and 147.93
A box model approach, would need n+2 boxes to describe the temporal incor-94
poration pattern of 13CO2 into the leaf monoterpene pool, where n denotes the95
number of carbon atoms within the terpene molecule. In the case of monoter-96
penes, n = 10 and thus, the model will finally have 12 boxes, representing97
the state of the system which could be described textually as a ”volume that98
contains a leaf”. The state of these boxes and the fluxes between them are99
defined by several biochemical and diffusion processes, which may not neces-100
sarily map to one explicit process such as photosynthetic carbon fixation or101
the diffusion and non-specific storage of monoterpenes for instance.102
Figure 1 gives an overview of the model scheme for arbitrary numbers of C-103
atoms as it is developed in this work. We could combine the two boxes, denoted104
by their time integrated functions, y1(t) and y2(t) as one lumped box in which105
the process of photosynthetic carbon fixation, incorporation into the plastidic106
MEP pathway and monoterpene diffusion through the leaf tissues could take107
place. The split into two explicit boxes allow us to express a clear distinction108
between the labeled and unlabeled monoterpene fractions, even if y2(t) is a109
”virtual” construct due to mathematical abstraction. We further define the110
rate constant k1 that describes the temporal behaviour of the biochemical111
processes and d1 that describes the monoterpene diffusion in the unlabeled112
case. The additional rate constant α can be interpreted as the fraction of113
labeled carbon that is distributed into metabolic pathways other than the114
plastidic MEP-pathway and by that building up a pool of labeled carbon115
skeletons of all possible combinations which are used as labeled alternative116
6
carbon sources. We have not implemented an explicit dependency on that part117
of the labeled carbon sources as the measurement methodology does not allow118
to discriminate them. They should be an inherent part of the time constants119
described explicitly in the model. The inflow arrow enables the incorporation120
of carbon either from air or alternative sources into the system. Starting with121
y3(t) until yn+2(t), the boxes have the same set of processes denoted by their122
rate constants. For the biochemical part they are denoted by ki, and for the123
diffusion part by di. The remaining influence of the unlabeled isotope on each124
step is denoted by rate constants k1,i where i = 2...n + 1. All rate constants125
have the unit of a reciprocal time, in our case h−1. This model was formulated126
as a system of ordinary differential equations (ODE) as follows:127
d~y(t)
dt=
−k1 − d1 0
k1 −k2 − α
k1,2 k2 −d2
.... . . . . .
k1,n+1 0 kn+1 −dn+1
~y(t),with n = 10, (1)128
in the case of monoterpenes. Solving equation 1 over an appropriate time129
interval lead to a vector function ~y(t) that describe the temporal dynamic of130
the n+ 2 boxes in the model.131
Equation 1 and Figure 1 describing a system in that the state of each 13CO2132
incorporation is dependent on it’s state before and the unlabeled state. Each133
dependency is defined by underlying, lumped processes, which should not be134
mistaken as ”real” processes such as photosynthetic carbon fixation or the135
7
plastidic MEP-pathway, which indeed are not pure sequential steps. Each136
state in the system is expressed as labeled or unlabeled emitted monoterpene137
molecule.138
All rate constants ρi are convertible into time constants τi and vice versa139
by the relation τi = ln(2)/ρi where ρ is a placeholder for k, d or α. A total140
pool turnover, in terms of the model as described above, is completed if the141
maximum of emitted monoterpene molecules is fully labeled, i.e. all carbon in142
the leaf is labeled except for the ”old” carbon coming from alternative sources143
within the plant. With that, we can calculate the total monoterpene pool144
turnover in the leaf according to the reciprocal sum of the time constants:145
1
τtotal=
m∑i=1
1
τi, (2)146
where m denote the number of boxes to be combined in the model.147
2.2 Plant Material and experimental design148
Two-year-old Mediterranean evergreen oak Q. ilex plants, grown from acorns149
in pots under natural light conditions within a greenhouse were used for the150
labeling experiment. The plants were grown on a sand/peat (1:1) soil mix-151
ture. They were irrigated daily and fertilized monthly according to standard152
procedures (Grote et al., 2006). The measurements were conducted in early153
spring, after transferring plants from outside into controlled climate chamber154
conditions (30◦C) and higher light intensity (1000 µmol quanta m−2 s−1). The155
analyses were performed on fully expanded mature leaves that had developed156
under the climate chamber conditions. A total of five plants out of twelve have157
been chosen for the labeling experiment.158
8
Unlabeled 12CO2 was added for the gas exchange analysis to purified artifi-159
cial air to reach an ambient CO2 concentration of 370 ppmv. The 13C isotope160
containing air has been readily mixed with a level of 370 ppm 13CO2 (Air161
Liquide, Griesheim, Germany). Change between labeled and unlabeled arti-162
ficial air was conducted by manually switching between both sources. The163
flow in the whole system was controlled by flow controllers and set to 800 ml164
min−1. As a cuvette system, the GFS-3000 portable IRGA system (Heinz Walz165
GmbH, Effeltrich, Germany) was used to control and monitor the plant gas166
exchange. The cuvette flow was set accordingly to the total flow. An aliquot167
(70 ml min−1) of cuvette outlet air was transferred to the PTR-MS (Ionicon168
Analytik, Innsbruck, Austria) for monoterpene emission analysis. The param-169
eters for the PTR-MS measurements have been throughout the experiments170
chosen as E/N = 110 Td, pdrift = 1.7375 mbar, V = 550, T = 43◦C and O2+171
and NO+ < 2% of H3O+.172
2.3 Determination of leaf gas exchange and monoterpene emissions173
Isotopic labeling is changing the infrared absorption bands of CO2 and due to174
that, a proper detection of CO2 is not possible during the labeling phase. We175
recorded the net CO2 assimilation rates before and after switching the inlet176
air to the labeled source. As the detection of water vapor is not affected by177
the change in the carbon source, we tracked the evaporation throughout the178
experiment. Together with the relative photosynthesis rate, these data help to179
assess the plants physiological state while labeling (Figure 4).180
Pilot experiments showed, that maximum monoterpene emissions from Q. ilex181
leaves were reached at 35◦C, so this temperature was chosen for the labeling182
9
experiments. Photosynthetic photon flux density (PPFD) was set to 1000 µmol183
quanta m−2 s−1 throughout the whole experiment and the time of labeling was184
chosen to be 12 hours, starting 1 hour after onset of light and stabilization185
of net CO2 assimilation and monoterpene emission. At the end of the 13C-186
labeling period gas exchange and monoterpene emission were recorded for an187
additional hour under 12CO2 atmosphere. The mean monoterpene flux and188
standard error prior to the labeling was 4.3 ± 0.7 nmol m−2 s−1 under the189
chosen settings.190
Online monoterpene measuring was conducted by the PTR-MS (Behnke et al.,191
2007), tracking the whole range of 13C labeled mass isomers, that are possible192
to appear in a C10 skeleton of a monoterpene with a molecular mass at 136193
u. The proton transfer reaction, that takes place in the PTR-MS, leads to a194
molecule mass of m + 1, the tracked range was chosen to span over m/z 137195
to 147. As bigger molecules tend to fragment in the PTR-MS, we also tracked196
the masses starting at m/z 81 through to m/z 87 representing the fragments197
of labeled monoterpenes to control the labeling process. Even though the198
fragments provide a better signal, they are useless to assess the total labeling of199
the monoterpene molecule as they consist of only 6 C-atoms. As a robust, mass200
independent calibration of the system we diluted a 11 (including α-pinene)201
VOC mixture-standard in N2 (1 ppmv, Apel-Riemer Environmental, Denver,202
USA) into humidified cuvette air. Prior to each analysis the empty cuvette203
emissions were background corrected. The monoterpene emission rates were204
expressed as nmol m−2 s−1 based on the α-pinene signal from the standard205
gas.206
10
2.4 Model validation procedure207
To solve the model numerically we implemented the ODE system into the208
Mathematica software environment (Mathematica Version 5.1, Wolfram Re-209
search, Inc.,IL, USA) where also the fitting procedure to the measured PTR-210
MS data was conducted. As we were interested to describe the temporal dy-211
namics of the isotope emission pattern, we normalized and pooled the data212
from 3 out of 5 independent experiments into one data set. Normalization was213
conducted according to the 12C-emissions such that the average of the steady214
state monoterpene emission before the labeling was set to one for each mea-215
sured set of data. In addition, all data sets give the standard error of the 3216
minutes running average over the measurement time period. We selected one217
point each 6 minutes throughout the data set as validation points to simply218
reduce the amount of data for the fitting procedure.219
Fitting the model to data was done by means of minimizing the root mean220
squared distance (RMSD) between the modeled and measured data points:221
RMSD =ν∑j=1
√(fj,µ − fj,δ)2
ν, (3)222
where ν denote the size of the data set, fj,µ is the model result at point j223
and fj,δ is the value of the data set at that point. We calculated this fitting224
procedure for each mass isomer of the system as follows:225
min[RMSDi],with i = 1..12 (4)226
to obtain optimal values for the time constants, ki, k1,i and di.227
11
3 Results and Discussions228
3.1 Model validation229
To validate the model, we used the emission data obtained by PTR-MS mea-230
surements that track the release of 12C- and 13C-labeled monoterpene mass231
isomers online. As can be seen from Figure 2, monoterpene emissions decreased232
slightly over the course of the day, probably due to the long time where the233
leaves were kept under constant light and temperature within the cuvette.234
Analysis of net CO2 assimilation prior and after 13CO2 labeling showed a de-235
cline of photosynthesis by approximately 29% (Figure 4). It is known from236
the Mediterranean sclerophyllous oak Quercus suber L. e.g. that it declines237
photosynthesis in the afternoon even if there is no water stress due to in-238
creased light, temperature or leaf-to-air vapor pressure deficit (Faria et al.,239
1996; Chaves et al., 2002). To overcome this situation, we could handle the240
data as been overlaid by a systematic error and de-trend the data set or we241
could add an empirical term that mimics the decay. As it remains unsure, if242
the decay is only due to a systematic error which has been introduced by our243
experimental setup or a physiological response, we decided to use the data as244
they were measured and introduced an empirical function245
F (t) = σt, (5)246
where, σ equals to 0.02 h−1 and denotes an empirical factor that lowers the247
photosynthetic capacity by time. We linked that empirical function to the248
first equation in the differential equation system (Equation 1) as an additional249
12
outflow of the 12C carbon box and the first equation alters to250
y1(t)
dt= (−k1 − d1)y1(t) − F (t). (6)251
With that empirical extension, the model follows the decay within the mea-252
sured data as shown in Figure 2.253
3.2 Estimation of the time constants254
As the PTR-MS data have a high resolution in time but a low selectivity255
between molecules of the same molecular mass, it is not possible to distinct256
between several monoterpene species. Therefore, we considered an ”average257
monoterpene” in our calculation to obtain first guess values for the timescales258
of the leaf pool turnover. By applying the same light and temperature input we259
used during the measurements to the biochemical part of the SIM-BIM (ver-260
sion 2) model, we obtained estimates for the turnover of the MEP-pathway261
(Appendix A). In the case of monoterpenes, the half-life for the formation262
obtained was τMT = 16 minutes. Combining this result with the time scales263
for the turnover of the photosynthesis process, the half-life of carbon in the264
described Q. ilex system against biochemical processing to form a monoter-265
pene should be around 20 minutes. Indeed, the time constant found by fitting266
to data for the biochemical processing of the non-labeled isotope τbio,1 = 26267
minutes (0.43 hours). Table 1 summarizes the optimized time constants for268
the biochemical and diffusion processes. For the diffusion process, we found as269
maximum time scale τdif,11 = 3 hours and 9 minutes (3.15 hours). Compared270
with the values given in Niinemets and Reichstein (2002) for Q. ilex, the time271
constants in the present work matched the range of time constants reported272
13
there.273
The optimization procedure for the reaction rate α gave a value of 3.3 h−1.274
This parameter reflects the fact that the distribution of the recently fixed275
carbon to several metabolic pathways has to be considered in the model to276
maintain the homeostatic balance of the organism. In the present case with277
Q. ilex leaves we estimated a 1.5% carbon use by the MEP-pathway related278
to total carbon flow within the leaf system. This value is in the same range of279
an earlier observation of Kesselmeier et al. (2002) who determined that under280
non-stressed situations about 1.2% of the carbon gained by Q. ilex leaves can281
be emitted back as monoterpenes.282
3.3 Model performance283
Overall, the model fits very well to the measured data (Figure 2). We obtained284
r2 = 0.953 for the sum of labeled monoterpenes and r2 = 0.978 for the unla-285
beled monoterpene. The model slightly overestimated the measured values of286
the sum of 13C labeled monoterpene emissions, but well within the boundaries287
of the standard errors. The unlabeled monoterpene emission was in the first288
half of the time course slightly underestimated by the model and after 7 hours289
the model overestimated again slightly the measured values.290
Figure 3 shows the comparison of the model data and the measurements for291
each mass-to-charge ratio. As the monoterpene molecules consist of 10 carbon292
atoms, we should have the range from unlabeled to fully labeled, m/z 137293
until 147, to exchange all carbon atoms available in the molecule with a 13C294
isotopic carbon atom, because the measured data for m/z 147 (fully 13C-295
14
labeled) were often below the detection limit of the measurement system, we296
did not use them for model fitting. The model itself calculates m/z 147 and297
therefore, the molecule was included in the calculations of the pool turnover298
times. For m/z 138, the isotope molecule with one 13C atom, the model does299
not followed the steep initial slope in the measurement but after the first 2300
hours it agrees to the measurement with a slight overestimation. It is likely,301
that due to the simplification introduced by the model the temporal dynamics302
over the first hours show some uncertainty. On the other hand, we might have303
missed other processes in the model, that are important on that stage of the304
incorporation of 13C into the monoterpene molecule. Possible candidates for305
such processes have been recently proposed (Monson et al., 2007; Wilkinson306
et al., 2009), such as cellular regulation mechanisms of the MEP-pathway307
by phosphoenolpyruvate carboxylase (PEPC) as dependent on atmospheric308
carbon dioxide levels. All other isotope masses fitted well to the initial slopes309
of the inclusion dynamics and the higher the masses become, the better was310
the fit of the model to the measured data. The r2 values ranged between 0.969311
and 0.997 and by that, each fit to a single m/z ratio showed a higher accuracy312
as the value obtained for the sum of labeled monoterpene emission.313
3.4 Temporal dynamics of 13C isotope incorporation into the monoterpene314
molecules315
We investigated the temporal behavior of the labeling process as affected by316
the processes described before and the possibility to develop a model tool to317
estimate and study time scales and dynamics of these underlying processes on318
the leaf level. Table 1 compiles together the time constants for the biochemical319
15
τbio and the diffusion τdif processes. In both cases, we found an increase in the320
half-life times against these processes with rising masses. While the biochemi-321
cal time constants start at 26 and 30 minutes for τ1 and τ2, they reach up to 4322
hours and 38 minutes for τ11. Using Equation 2, they sum up to 21 hours and323
42 minutes for the total biochemical processes turnover half-life. The diffusion324
process was the time-limiting process only in the case of the unlabeled and325
the molecule with one 13C carbon atom included. For the higher masses, the326
diffusion process was found to be faster than the biochemical process. The327
diffusional time constants ranged from 32 minutes for d1 to 3 hours and 9328
minutes for d11. We summed up these time constants and reached 16 hours329
and 30 minutes for the half-life of the total diffusional process turnover.330
It is not surprising, that the time constants changed as the mass of the331
monoterpene molecule rises, because it is well known that due to the change in332
molecular mass, both, the chemical and the physical properties are changing.333
Especially for research on enzymatic pathways the ”kinetic isotope effect” was334
used to get insight into the enzymatic networks (Cleland, 2003). Furthermore,335
the stable isotope analysis is based on the fact that biochemical and physical336
processes are discriminating between stable isotopes. Due to that fact, one can337
use accumulation or depletion information on stable isotopes within probes to338
discriminate the processes which lead to the formation of that probe (Farquhar339
et al., 1989; Ehleringer et al., 2000; Ekblad and Hogberg, 2001; Eglin et al.,340
2009). It has been already described by Ekblad and Hogberg (2001), that341
the photosynthetic intermediates of leaves are depleted in 13C due to assim-342
ilation and respiration processes that prefer the more abundant 12C isotope.343
The MEP-pathway itself is also discriminating against 13C and the emitted344
isoprene was found to be further depleted in 13C than the assimilated car-345
16
bon (Sharkey et al., 1991; Affek and Yakir, 2003). Within the MEP pathway,346
deoxyxylulose-5-phosphate synthase (DXP) is likely to discriminate against347
13C and it has been also reported by Melzer and Schmidt (1987) that the348
pyruvate dehydrogenase (PYRDH) reaction is depleting 13C on the stage of349
the major precursors (pyruvate and acetyl-CoA) of the MEP-pathway. This350
was assumed to cause at least a portion of the observed depletion in the351
emitted BVOC compounds. However, the present model was not designed to352
address these changes in the isotopic composition but the rise in the time con-353
stants may reflect these changes in the compounds physico-chemical properties354
and possible regulatory steps preferring 12C which are not explicitly addressed355
here.356
In Table 1, we also show the values for the influence of the 12C carbon on the357
emitted labeled compound, k1,n. This numbers are descending from 0.95 h−1358
to 0.001 h−1, demonstrating that the influence of the unlabeled carbon, origi-359
nated from alternative sources (Kreuzwieser et al., 2002; Schnitzler et al., 2004)360
within the plant, only marginally effected the almost fully labeled monoter-361
penes but played a role in the determination of the timely behavior of the362
monoterpene emissions. Thus, the temporal dynamics were mostly determined363
by the biochemical and diffusional processes but the alternative carbon sources364
and the distribution of the labeled and unlabeled molecules within the leaf lead365
to a kind of additional memory effect of the system.366
3.5 The model as a predictive tool367
The present model can be used to predict the labeling and emission patterns368
and changes in those patterns for molecules of arbitrary length. Due to the369
17
abstraction, the time constants can be issued to more or less lumped processes370
of same kind, such as biochemical processing or diffusion through tissues. This371
allows insight into the temporal pattern of the underlying processes or let one372
gain information about the lumped processes dynamics as well. In that sense,373
the model can be seen as a tool to predict such temporal dynamic behavior of374
biochemical or diffusional processes. The inclusion of process-based method-375
ology into larger scale models has recently been proposed (e.g. Arneth et al.,376
2007). However, moving from smaller to larger scales is usually connected to a377
loss of information due to fact that the measured signal therein is further pro-378
cessed as the measured signal on the smaller scale. To circumvent that scaling379
problem, one can either try to put in more details but, this is usually limited380
by the available information, or, build an abstraction layer where the smaller381
scale dynamics are mapped into the larger scale. Our present model is build382
in the latter sense. We used data from the whole leaf level and described the383
dynamics of processes that take place on a smaller organizational scale within384
the leaf itself.385
In the case of the inclusion of 13C into the monoterpene pools of Q. ilex, the386
model predicted time scales for all isotopic combinations that can be found387
within the monoterpene molecule that is emitted and, as well gives estimates388
of the half-live for the total pool turnover times. In case of Q. ilex leaves these389
times were rather long summing up in the ”worst case” to almost 38 hours390
and in the ”best case” to just one hour. Such long term dynamic changes can391
indeed influence the set up of recent larger scale models as many of them run392
based on daily time steps (Cramer et al., 2001; Guenther et al., 2006; Sitch393
et al., 2003). So far, the emission processes have been considered to be fast394
enough to be already in steady state and the daily step is large compared to395
18
their dynamic, but for Q. ilex, with no specific terpene storage structure, this396
seems not always to be the case. As a consequence, the use of an empirical,397
steady state algorithm (e.g. Guenther et al., 1993) seems not always to fit best398
to describe emissions with daily time steps.399
Another implication of the present study relates to the question posed by Ar-400
neth et al. (2008). They showed that the variation in the results of several401
monoterpene emission models are almost freely diverging while that is not the402
case for isoprene emission models. Maybe the fact, that monoterpene emis-403
sions are possibly still in a transient state, even on daily time scale, while404
the isoprene emissions are not is partly explaining the difference. Isoprene405
formation should have a shorter time scale in the biochemical processing as406
it has a ”shorter” formation pathway, and it has lower diffusional constraints407
compared to the longer and structural more complex monoterpene molecule.408
Because of that, it is likely that the isoprene emissions temporal dynamics409
have already reached a steady state within the often used daily time step of410
larger scale models. Thus, the selection of an empirical steady state parame-411
terization algorithm for isoprene is less critical but this is not always the case412
for monoterpenes.413
4 Conclusions414
We observed the possibility that the turnover of the monoterpene pool in Q.415
ilex leaves can exceed one day. Due to that finding, the use of empirical steady416
state algorithms in connection with daily monoterpene emission estimates417
which employ still a transient emission pattern in that time scale might be418
the wrong choice. Indeed, the present model exercise supports the need of an419
19
inclusion of process-based methods into larger scale models as a beneficial step420
in increasing their prediction accuracy.421
The present work demonstrates, that the use of a model that is located on a422
higher integrated level of organization (”volume with a leaf”) can very well423
predict the temporal behavior of processes that are located on a lower inte-424
grated level (”biochemical processes or diffusion within the leaf tissues”). The425
prerequisite for such an application is the ability to describe the time constants426
of those processes in a single or lumped manner. Our modeling exercise can,427
as well, be seen as a step towards a possible solution to tackle with the prob-428
lem of the upscaling procedure by solving an inverse problem on the higher429
integrated level with information input from the lower integrated level.430
Acknowledgements431
Financial support from the Human Frontier Science Program (http://www.hfsp.org),432
the Estonian Academy of Sciences, the Estonian Science Foundation (Grants433
7645, 8110), the Estonian Ministry of Education and Science (Grant SF1090065s07)434
is gratefully acknowledged. We would like to thank Dr. Almut Arneth and An-435
drea Ghirardo for their cooperation and fruitful discussions.436
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27
Tables613
Table 1
m/z
constant 137 138 139 140 141 142 143 144 145 146 147 sum
τbioa 0.43 0.50 0.89 0.98 1.26 1.98 2.10 2.31 2.77 3.85 4.63 21.7
τdifa 0.53 0.55 0.63 0.79 1.02 1.73 1.87 1.93 1.98 2.31 3.15 16.5
k1,nb - 0.95 0.8 0.45 0.25 0.08 0.02 0.008 0.005 0.003 0.001 2.567
n 1 2 3 4 5 6 7 8 9 10 11
a unit in hours
b unit in h−1
28
Figures614
12C
13C1
13Cn
k1
k1,2
d1
d2
y1(t)12
y3(t)
yn+2(t)dn+1k1,n+1
k3
kn+1
k2
y2(t)13
13C
!
Fig. 1.
29
0 2 4 6 8 10 120
0.2
0.4
0.6
0.8
1
1.2
1.4
Time in hours
norm
aliz
ed m
onot
erpe
ne e
mis
sion
Fig. 2.
30
0
0.5
1
0
0.5
0
0.25
norm
aliz
ed m
onot
erpe
ne e
mis
sion
s
0
0.25
0 2 4 6 8 10 120
0.15
Time in hours2 4 6 8 10 12
m/z 137r2 = 0.978
m/z 139r2 = 0.979
m/z 140r2 = 0.987
m/z 142r2 = 0.989
m/z 141r2 = 0.983
m/z 143r2 = 0.993
m/z 144r2 = 0.995
m/z 145r2 = 0.995
m/z 146r2 = 0.997
m/z 138r2 = 0.969
Fig. 3.
31
0 2 4 6 8 10 120.8
1
1.2
1.4Ev
apor
atio
n m
mol
m−2
s−1
0 2 4 6 8 10 120.6
0.8
1
1.2
Time in hours
rel.
phot
osyn
thes
isA
B
Fig. 4.
32
Captions615
Table 1. Time constants used in the model for stable isotope 13C incorpora-616
tion into the emitted monoterpene molecules. τbio is calculated from the rate617
constant as τn = ln(2)/kn for different mass isomers (n). τdif denote the similar618
time constants for the diffusion in the system. k1,n is the rate constant of the619
influence from the unlabeled fractions on the monoterpene emission denoting620
”old” carbon inflow, for instance from sources in the leaf. n is the number of621
carbon atoms in the monoterpene molecule.622
Fig. 1. Scheme of the defined boxes and the flows between them. The rate con-623
stants ki, i = 1...n + 1 describe the dynamics of the incorporation of the 13C624
atoms by the biochemical pathways, k1,i, i = 2...n+ 1 the influence of the re-625
maining 12C isotopes and the di, i = 1...n+1 the diffusion of the monoterpenes626
through the leaf tissues. α denotes the fraction of labeled carbon skeletons that627
is distributed within the leaf biochemical pathways. n equals the number of628
carbon atoms in the monoterpene molecule.629
Fig. 2. Modeled (lines) and measured (dots) normalized values of the emission630
of the 12C monoterpene (dashed) and the sum of 13C labeled mass isomer631
monoterpene (solid) over the course of the experiment. The grey areas denote632
the upper and lower bounds of the standard errors of the measurements. The633
data of three independent experiments were normalized with respect to the634
12C isomer in the non-labeled leaves under steady-state photosynthesis and635
monoterpene emission.636
Fig. 3. Modeled (solid line) and measured (dots) normalized values for the637
12C (m/z 137) and the 13C (m/z 138 - 146) mass isomers of the monoterpene638
33
emission. Standard errors of the measurements are given as grey areas. r2639
values have been calculated according to equations 3 and 4.640
Fig. 4. Mean and standard error of the measured evaporation (A) and relative641
photosynthesis (B) during the labeling experiment. Within the 12 hours of642
labeling, where the leaf was kept in constant light and temperature, a decline643
in the photosynthetic capacity occurred.644
34
Appendix645
A Estimation of the MEP pathway time constants from steady-646
state simulations647
To estimate the time constants of the MEP pathway we used a typical ”dose-648
effect” simulation experiment. We implemented the biochemical part (BIM)649
of the SIM-BIM (version 2) model including the synthetic steps until geranyl-650
diphosphate (GDP) into a compartment model. This model consist of a total651
of 10 compartments representing the intermediates within the MEP pathway,652
including pools for isoprene and monoterpenes. Time constants have been653
taken either from Zimmer et al. (2000) and Grote et al. (2006) or by personal654
communication. Additionally, the system includes a photosynthesis module,655
providing triose phosphates as input to the MEP pathway. Assumed a steady656
state and non stressed situation, changes in the biochemical intermediate pools657
can be initiated by changes in the precursors (3-phosphoglyceric acid, PGA658
and glyceraldehyde-3-phosphate, GAP) while energy supply and temperature659
are held constant.660
Analyzing the recovery time of the steady-state in the products (isoprene and661
monoterpene pools) leaded to an average half-life for the isoprene pool of 5662
minutes which is in accordance to Delwiche and Sharkey (1993) showing that663
the half-life to label isoprene molecules was 4.78 minutes. Furthermore, they664
showed, that the time to label 80% of the isoprene pool took 18 minutes. In665
the case of the monoterpene pool, additional steps to reach to GDP and to666
form the monoterpene molecule, leaded to 15-20 minutes for the lifetime of667
carbon in the intermediate pools leading to monoterpenes.668
35
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