SUPPORTING INFORMATION
1
2
Text S1 Geometrical model of tomato leaf
3
We derived the anatomy of the tomato leaves from synchrotron computed laminography
4
experiments that were conducted at beam line ID19 of the European Synchrotron
5
Radiation Facility (ESRF, Grenoble, France), i.e., a long (150 m) imaging beam line
6
where the spatial coherence of the beam is particularly large (transverse coherence length
7
in the order of 100 m). This large coherence allows phase-contrast imaging where the
8
phase of the X-ray beam transmitted by the sample is shifted due to the interaction with
9
the electrons in the material. The tomographic reconstruction of a leaflet sample was
10
performed with a filtered back projection algorithm using the PyHST (ESRF) software
11
after
12
(http://www.gnu.org/software/octave/). We obtained volume renderings and the geometry
13
of the sample by 3-D image segmentation and isosurface representations with Avizo Fire
14
(Visualization Group Sciences, Merignac, FR). More details can be found in Verboven et
15
al. ( 2014).
16
The contrast in the laminography images was insufficient to distinguish cell organelles
17
such as chloroplasts and the vacuole. Chloroplasts appear as flat discs usually 2 to 10 µm
18
in diameter and 1 to 3 µm thick (Li et al., 2013). James et al. ( 2006) found that the
19
volume fraction of chloroplasts in the mesophyll cells was about 24% while Tholen &
20
Zhu (2011) proposed a chloroplast volume fraction of 26% for a single modeled
21
mesophyll cell. In our computational model, chloroplasts were modeled as a cluster with
22
a thickness of 2.6 µm and a diameter of 6 µm adhering to the mesophyll boundary and
23
occupying about 24% of the modeled mesophyll cell volume. Hereto, first we created in
24
every cell a layer of 2.6 µm thickness inside the cell wall / plasma membrane of the
25
mesophyll cell. We then segmented the layer into individual brick-like patches of similar
26
size (about 6 µm). We calculated the centroid of every patch, and created a sphere of 3
27
µm radius in such a way that its center coincided with this centroid. Finally we defined a
28
chloroplast as the intersection of this sphere and the patch. Note that this procedure may,
correction
for
sample
motion
1
using
GNU
Octave
software
29
incidentally, yield slightly overlapping chloroplasts as some patches were smaller than 6
30
µm (Supporting information Fig. S10).
31
The surface area of the chloroplast facing the intercellular space is expected to affect the
32
mesophyll conductance gm (Terashima et al., 2006). We described the chloroplast
33
distribution on the mesophyll air surface by the Sc/Sm ratio (Terashima et al., 2006),
34
where Sc and Sm are the chloroplast surface area exposed to intercellular air space and the
35
mesophyll surface area exposed to intercellular air space, respectively (Supporting
36
information Fig. S11). Tholen et al. ( 2008) showed that under saturated light intensity of
37
1200 µmol m-2 s-1, the Sc/Sm ratio was 0.63 to 0.75 in Arabidopsis thaliana leaves while
38
Tomás et al. ( 2013) indicated that Sc/Sm ratios ranged between 0.69 and 0.75 for leaves
39
of five different herb species. Galmés et al. (2013) reported a Sc/Sm ratio of 0.88 to 0.99
40
for different tomato leaves. For our simulations we calculated the Sc/Sm ratio by dividing
41
the number of mesophyll cell boundary voxels exposed to the internal airspace by the
42
number of voxels belonging to both chloroplasts and the mesophyll cell boundary. We
43
created specific spatial distributions of chloroplasts at high light level (profile distribution)
44
by removing chloroplasts around the periclinal cell walls of mesophyll cells. More or less
45
arbitrarily, we could impose intermediate and high Sc/Sm ratios (at about 0.7 and 0.9) by
46
positioning the chloroplasts artificially either along the boundary of the cells exposed to
47
the intercellular airspace or along the contact area between two neighboring cells, while
48
keeping the chloroplast fraction equal to 0.24 (Supporting information Fig. S6). We
49
generated a face distribution of chloroplasts at low light intensity (200 µmol m-2 s-1)
50
representing a low Sc/Sm ratio (0.36) with the chloroplast layers located along the
51
periclinal cell walls of mesophyll cells (Supporting information Fig. S6).
52
We modeled the vacuoles explicitly in the mesophyll cells by shrinking the cell by 70%
53
of its original size and considering the shrunk region to be vacuole. For the purpose of
54
this article, the layer between the chlorophyll clusters and the tonoplast was then defined
55
as cytoplasm (Supporting information Fig. S12).
2
56
We defined the epidermis as a continuous layer (see Fig. 1) without identifying individual
57
cells, as cell walls were difficult to detect on the reconstructed images. We assumed the
58
epidermis to have respiration but no photosynthesis. The size of the stomata was difficult
59
to assess. We, therefore, defined a cylindrical channel through the epidermis at the
60
position of the stoma with a radius that was chosen in such a way that the overall
61
stomatal conductance in the model was equal to the one determined from the gas
62
exchange measurements. The stomatal aperture is sensitive to environmental influences
63
(Damour et al., 2010). Our measurements indicated that the stomatal conductance gs
64
increased with increasing light intensity. The status of stomatal aperture to irradiation
65
level was adjusted by changing the diffusivity of the air within the stomatal aperture
66
(Supporting information Fig. S13). Simulation results indicated that the computed
67
stomatal conductance was mainly affected by the stomatal aperture. The stomatal
68
conductance was assumed to be proportional to the stomatal aperture. To model the
69
photosynthesis response to light intensity, we calibrated the status of stomatal aperture
70
based on the relationship between the stomatal conductance and light intensity level.
71
Text S2 Gas exchange and chlorophyll fluorescence measurements
72
We carried out simultaneous gas exchange and chlorophyll fluorescence measurements at
73
both 21% and 2% O2 at the beginning of the flowering stage, using an open gas exchange
74
system (Li-Cor 6400; Li-Cor Inc, Lincoln, NE, USA) and an integrated fluorescence
75
chamber head (LI-6400-40; Li-Cor Inc, Lincoln, NE, USA). We used four plants and
76
selected the distal-side leaflets from the top-most fully expanded leaf and from the fourth
77
leaf below the top-most fully grown leaf for measurements. These leaf types are denoted
78
by upper leaf and lower leaf, respectively. All measurements were done at a leaf
79
temperature of 25°C and a leaf-to-air vapor pressure difference of 1.0–1.6 kPa. For the
80
CO2 response curves we increased the ambient air CO2 concentration (Ca) step-wise: 50,
81
100, 150, 200, 250, 350, 500, 650, 1000, and 1500 μmol mol-1, while keeping incident
82
irradiance Iinc at 1000 μmol m-2 s-1. The time interval for the instrument to reach steady-
83
state was 4 min. For the light response curves, the leaf was first dark adapted for 15 min.
3
84
Then, the photon flux densities were in a series: 20, 65, 100, 150, 200, 500, 1000, 1500,
85
2000 μmol m-2 s-1, while keeping Ca at 380 μmol mol-1 for measurements at 21% O2, and
86
keeping Ca at 1000 μmol mol-1 for measurements at 2% O2 to ensure a non-
87
photorespiration condition. At each light level, we adjusted the time interval for
88
instrument to reach steady-state for stabilization to 6 min. The IRGA calibration was
89
adjusted for O2 composition of the gas mixture according to the manufacturer’s
90
instructions. All CO2 exchange data were corrected for CO2 leakage into and out of the
91
leaf cuvette, based on measurements on boiled leaves. We used the single rectangular
92
saturating light pulse method to measure chlorophyll fluorescence. The calibration
93
method used to derive potential electron transport rate J ensures that the error caused by
94
using this method - compared with the multiphase flash method - is minimal. We did
95
preliminary measurements using different orders of changing CO2 and Iinc levels and this
96
did not affect the shape of A versus Ci and A versus Iinc curves much. We estimated the
97
photosynthetic parameters of the FvCB model using the method described by Yin et al.
98
(2009); the estimates are given in Supporting information Table S3.
99
Chlorophyll fluorescence measurements assess the photosystem II (PSII) electron
100
'
'
'
transport efficiency as F / Fm = ( Fm - Fs ) / Fm , where Fs is the steady-state
101
'
fluorescence, Fm is the maximum fluorescence during a saturating light pulse (Genty et
102
'
al., 1989). We converted data for F / Fm into the flux of potential electron transport (J)
103
according to
104
J  sIinc F / Fm'
(S1)
105
where s is a calibration factor that was estimated as the slope of the empirical linear
106
'
relation between A and I inc (F / Fm ) / 4 using data of non-photorespiratory measurements
107
at 2% O2 combined with high CO2 levels (see Yin et al., 2009) for more details).
108
4
109
Text S3 Light penetration measurement
110
We used a double integrating sphere (DIS) measurement system (see Supporting
111
information Fig. S14) for measuring the total reflectance (Mr) and total transmittance (Mt)
112
in the wavelength range from 550 to 850 nm, with an interval step of 5 nm (Aernouts et
113
al., 2014). More details about the measurement system and the calibration procedure can
114
be found in Aernouts et al. (2014). We carried out replicate measurements on five leaves,
115
each from a different Admiro plant. Only lower leaves were used (details of leaf types are
116
discussed in the next section). The total reflectance (Mr) and total transmittance (Mt)
117
spectra of 5 leaves are shown in Supporting information Fig. S1. A clear absorption peak
118
can be observed at 680 nm as a dip in both the transmittance and reflectance spectra of
119
the tomato leaves. This corresponds to the absorption peak of photosystem II, also known
120
as P680 (Raszewski et al., 2008).
121
We obtained a good match between the measured and simulated values, for both
122
reflectance (RMSE = 0.015) and transmittance (RMSE = 0.0815) data (Supporting
123
information Fig. S1). Fig. S1 also shows that green light penetrates deeper into the leaf.
124
The transmittance increases even more strongly beyond the absorption peak of
125
chlorophyll around 680 nm. This is known as the ‘red edge’, which is often used in
126
remote sensing to quantify the chlorophyll content in plant material. It should be noted
127
that the absorption by chlorophyll in the blue region cannot be seen in Fig. S1 as the
128
double integrating spheres setup with its gold coated spheres does not provide good
129
quality measurements in that range.
130
Text S4 Models for light penetration, photosynthesis kinetics and CO2 diffusion
131
Monte Carlo photon transport method
132
The photon transport algorithm was based on the Monte Carlo method with free phase
133
function choice (fpf-MC) (Lux & Koblinger, 1991), which can handle any arbitrary phase
134
function. This is an adaptation from the well-known Monte Carlo code for multi-layered
135
tissues (MCML) (Wang et al., 1995). Instead of parallel layers of tissue the adapted
136
Monte Carlo code can account for arbitrary volume based geometries. Starting from
5
137
voxel based images, the Iso2mesh Matlab (The Mathworks, Inc., Natick, USA) toolbox
138
(Watte et al., 2012) was used for generating 3D tetrahedral meshes (Supporting
139
information Fig. S15). Tetrahedral meshes have the advantage of providing better
140
approximations of curved boundaries. We assigned appropriate optical properties
141
(refractive index n, absorption coefficient µa, scattering coefficient µs and anisotropy
142
factor g) to every tetrahedron (see further).
143
The computation was similar to the one applied in MCML (Wang et al., 1995) and based
144
on random walks of photons while traveling through tissues. These walks were defined
145
by random sampling from the probability distributions for step size and angular
146
deflection per scattering event (Wang et al., 1995). At each step, the fpf-MMC algorithm
147
checks whether a photon is still inside the same tetrahedral element. When the photon has
148
entered a new tetrahedron, the optical properties of that tetrahedron are used. When the
149
photon has not entered one of the four neighboring tetrahedra, implying that the photon is
150
outside of the boundaries of the mesh, the photon propagation is terminated. In order to
151
locate photons as efficiently as possible inside a tetrahedron, a barycentric coordinate
152
system was used. This allowed for a very fast evaluation of whether a photon could
153
continue its propagation inside the mesh. At interfaces of all the different tetrahedra, the
154
photons were assumed to obey the Fresnel and Snell equations (Lux & Koblinger, 1991).
155
The geometry acquired by X-ray micro-computer tomography (µ-CT) typically has quite
156
limited dimensions because of the fine spatial resolution. Using the meshes obtained from
157
the geometry directly in the Monte Carlo simulations can be problematic as many
158
photons might reach the boundaries. To get around this problem, a mirror is constructed
159
at the edges of the mesh to reflect photons reaching the boundary back into the tissue.
160
Other planes function as a perfect mirror, making sure the photons propagate inside the
161
volume. The idea is that the meshed structure is a representative subset of the entire tissue.
162
Photons exiting the structure, mirrored back into the tissue, are equivalent to photons
163
entering an identical, neighbouring mesh. This assumption is only valid for light sources
164
that display a radial symmetry with the mesh, as is the case for the uniform light source
165
covering the entire top layer of the mesh, used in the simulations for generating the
6
166
figures in this paper. Photons which are about to exit the tissue through either the top or
167
bottom surface are counted as transmission and reflection, respectively.
168
After a simulation was finished, the number of photons that had been absorbed in each
169
tetrahedral element was known and was represented as an absorption profile. The
170
expected value of a physical quantity (reflectance profile, absorption profile) is found by
171
running simulations many times over, each time applying the same probability density
172
functions, and eventually calculating the average of multiple independent samples. Each
173
simulation at a particular wavelength results in an absorption profile, defined as the
174
fraction of energy captured in each segment (either a voxel, or a mesh element) of the
175
leaf. As this allows the computation of this physical quantity locally, it can also be
176
computed at the chloroplast level to determine the photon absorbance in the chloroplasts.
177
Although the resolution of the applied methodology does not allow the differentiation
178
between the absorption profiles in the different structures of a chloroplast, it allows the
179
computation of the fraction absorbed by each chloroplast.
180
We re-voxelized the absorption profiles in the tetrahedral mesh to match with the voxel
181
based mesh used in the CO2 transport model. In this way, absorption profiles were
182
constructed.
183
The light source used during gas exchange measurement was artificial light from blue
184
and red LEDs. We assigned to 10% of the simulated photons the properties of blue light
185
(470 nm), and to 90% those of red light (665 nm). We generated two independent optical
186
simulations, with each a different set of optical properties (Supporting information Table
187
S4) and combined both into one single absorption profile.
188
The meshed Monte Carlo methodology has been validated by comparing the simulation
189
results for a tissue consisting of four homogeneous layers with those obtained with
190
MCML (Wang et al., 1995). The MCML algorithm is considered to be the standard for
191
light propagation modeling in turbid multi-layer systems (Wang et al., 1995; Tuchin,
192
2007; Tuchin, 2008). It assumes the tissue to be a slab, a geometric shape that can be
193
meshed and thus used for simulations with the meshed Monte Carlo methodology.
7
194
A varying range of optical properties has been simulated with both methodologies, and
195
the resulting total reflectance, transmittance and absorbance values were almost identical.
196
197
FvCB model
198
We used the Farquhar, von Caemmerer & Berry (FvCB) model to describe the rate of
199
RuBP carboxylation w* in the chloroplasts of C3 plants (Farquhar et al., 1980; Yin et al.,
200
2009; von Caemmerer, 2013). Briefly,
201
w*  min  wc , w j , wp 
(S2)
202
with wc the RuBisCo limited carboxylation rate, wj the RuBP-regeneration or electron
203
transport limited rate, and wp the triose phosphate utilization limited rate. They were
204
calculated from
[CO2 ] Vc*,max
205
wc 
206
[CO2 ]  j *
wj 
4[CO2 ]  8 Γ *
207
wp 
(S3)
[CO2 ]  K m,C (1  [O 2 ] / K m,O )
(S4)
3Tp*
(S5)
1  Γ *


[CO 2 ] 

208
with [CO 2 ] and [O2 ] the CO2 and O2 concentrations in the chloroplast, respectively; j*
209
the volumetric potential rate of electron transport; T p* the maximum volumetric rate of
210
triose phosphate export from the chloroplast; Γ *  0.5[O2 ] / Sc / o the CO2 compensation
211
point in the absence of normal respiration; and S c / o the relative CO2/O2 specificity factor
212
for RuBisCo. K m,C and K m,O are constants. Vc*,max and T p* are derived from the partitioning
213
of photosynthetic capacity inside the leaf (see further in Supporting information Text S5).
8
214
The meaning and units of all symbols are given in Supporting information Tables S1-2.
215
The potential electron transport rates are further described in the text.
216
We calculated the volumetric rate of photorespiration R*p in a mesophyll cell k according
217
to the model of Farquhar et al. ( 1980) as:
218
R*p 

Vchl ,k
w* 
Γ*
dV
[CO 2 ]
(S6)
Vcyt ,k
219
where the numerator indicates the total photorespiration over the chloroplast volume Vchl,k
220
in the mesophyll cell; Vcyt,k is the volume of the cytoplasm of the mesophyll cell. Note
221
that our model did not explicitly model mitochondria as a separate compartment because
222
this would require a very fine computational mesh and thus an excessive amount of
223
computer time to solve the equations. Eq. S6 implicitly assumes that the photorespiratory
224
CO2 release occurs in the cytoplasm.
225
Potential electron transport rate
226
In the FvCB model (Farquhar et al., 1980), the potential PSII electron transport rate j* at
227
a certain position inside the leaf can be described in terms of limiting values including ji ,
228
the light limited rate of PSII electron transport, and jm, the light saturated PSII electron
229
transport rate (Buckley & Farquhar, 2004). In practice, we modeled j as the hyperbolic
230
minimum of ji and jm (Buckley & Farquhar, 2004):
231
j  min h  ji , jm  
*
ji  jm 
 ji  jm 
2i
2
 4i  ji  jm
(S7)
232
where  i is a measure of co-limitation of electron transport by light and capacity
233
(Buckley & Farquhar, 2004). jm was derived from the partitioning of photosynthetic
234
capacity inside the leaf (see further in Supporting information Text S5). ji was calculated
9
235
from the rate of absorbed photon iabs and the maximum quantum yield of electron
236
transport m :
ji  m  f II  iabs
237
(S8)
238
where fII is the fraction of absorbed photons driving PSII electron transport (normally
239
assumed to be 0.5 (Pons et al., 2009)). The rate of photon absorption iabs is the product of
240
actinic irradiance and the fraction of that irradiance absorbed by the chloroplasts. We
241
computed the absorbed light profile in the leaf by means of the Monte Carlo photon
242
transport method (see above).
243
244
Model parameters
245
Scattering of photons in the leaf tissue is dominated by the cell organelles which are of
246
similar size as the photon wavelength. In order to obtain realistic scattering properties,
247
the particle size distribution of organelles and nuclei in the epidermis and cytoplasm, as
248
well as the grana in the chloroplast layers were translated into scattering coefficients and
249
phase functions through simulations based on Mie theory(Di Vittorio, 2009).
250
We used literature values of particle sizes of mitochondria, peroxisomes, nuclei, Golgi
251
stacks and ribosomes to compute the scattering coefficient and phase function of the
252
cytoplasm; for chloroplasts we used typical particle sizes of grana (Supporting
253
information Table S6). We assumed the volumetric particle size distribution PSDV  r  of
254
an organelle to follow a normal probability density function with an equivalent particle
255
radius r.
256

 r r
1
PSDV  r  
exp  
 2 r2
 r 2

10

2




(S9)
257
As we did not have experimental data on the sizes of the organelles, we estimated the
258
mean r and standard deviation  r by setting the 5th and 95th percentile of the distribution
259
equal to the lowest (rLB) and highest (rUB) value we found in the literature (Supporting
260
information Table S6), so that
261
r
rUB  rLB
2
(S10)
262
r 
rUB  rLB
4
(S11)
263
in which the symmetry of the normal distribution was used.
264
Using transformation theory (Hertog et al., 2009) and assuming spherical organelles, it
265
can be shown that the particle size distribution PSDN(r) is equal to:


 r r 2 

exp  
2

2 r 


PSDN  r  
 rr 2 

1
 dr
r 3  3 exp  
2

r
2 r 

o


266


(S12)
267
We calculated the number of organelles per unit volume having an equivalent radius r
268
from:
269
f  r   ftot  PSDN  r 
(S13)
270
where ftot is the total number of the organelle per unit volume.
271
We computed the bulk optical properties of the different optical media inside the leaf
272
from f ( r ) (Aernouts et al., 2012). In the cytoplasmic domain, the contribution of each
273
organelle to the bulk optical properties was computed separately; the final bulk optical
274
properties of the domain were then calculated from the contributions of each organelle
275
(Aernouts et al., 2012):
11
276
s,bulk   s,i
(S14)
277
a,bulk  a,med   a,i
(S15)
278
p     s,i  pi  
(S16)
279
where µs and µa are the scattering and absorption coefficients, respectively, and p   the
280
phase function. The subscripts bulk and med of the symbols indicate the properties of
281
medium with and without particles, respectively, while the subscript i indicates
282
mitochondria, peroxisomes, nucleus, Golgi stack and ribosome-like complexes
283
(epidermis and cytosol), or grana (chloroplasts). In Eq. S15 it is assumed that the total
284
volume of the organelles is small compared to the volume of the medium in which they
285
are suspended. The effect of the particle size distribution on the phase function is
286
illustrated in Supporting information Fig. S16 for the epidermis and the chloroplast layer.
287
Supporting information Fig. S17 shows the resulting anisotropy factor and scattering
288
coefficient. The optical properties in Supporting information Table S4 are the result of
289
applying Eqs. S14 – S16 for two specific wavelengths. Note that we modeled the vacuole
290
explicitly in the mesophyll cells, but not as such in the epidermis cells. We assumed that
291
the total number of organelles per cell volume in both the epidermis and mesophyll cells
292
was the same. The scattering phase function for both was, therefore, identical; the
293
scattering coefficient of the epidermis was then equal to that of the cytoplasm times its
294
volume fraction.
295
We calculated the absorption coefficient of the chloroplasts at 680 nm from the specific
296
absorption coefficient of chlorophyll. We assumed that the chlorophyll content of tomato
297
leaves was 40 µg cm-2 (Haardt & Maske, 1987; Di Vittorio, 2009; Aernouts et al., 2012),
298
and the specific absorption coefficient to be 0.1 cm2 µg-1 (Haardt & Maske, 1987; Feret et
299
al., 2008; Steele et al., 2008; Di Vittorio, 2009; Féret et al., 2011; Watte et al., 2012). We
300
calculated the absorption coefficients at other wavelengths relative to the aforementioned
301
values based on the absorption spectrum of chlorophyll a and b (Feret et al., 2008; Féret
302
et al., 2011). The absorption coefficients of the epidermis, vacuole and cytosol were set
12
303
to 100 m-1 for all wavelengths to account for absorption by cell constituents such as other
304
organelles, proteins and metabolites. This value was based on the specific absorption
305
coefficient of dry matter (~10-3 cm2 g-1) that is almost constant in the wavelength range of
306
interest (Jacquemoud, 2000) and the mass fraction of dry matter that we assumed to be
307
equal to 5%. The absorption coefficient of air was set to 0 m-1 since air is a non-absorbing
308
medium. An overview of the different optical properties attributed to the different
309
compartments is given in Supporting information Table S4.
310
We determined the photosynthetic parameters of the FvCB model for different cultivars
311
and leaf ages experimentally from combined gas exchange and chlorophyll fluorescence
312
measurements (Supporting information Table S3), using the method of Yin et al. (2009).
313
We calculated the simulated potential electron transport rate ( J ) at the whole leaf level
314
from

315
J
j *dV
Vleaf
(S17)
Sleaf
316
where Sleaf is the area of a cross section of the computational domain, j* is the local
317
volumetric rate of electron transport, and Vleaf is the total leaf volume.
318
The maximum quantum yield of electron transport m was set at 0.85 mol e- mol-1 photon.
319
This value corresponds to the maximum efficiency of PSII in healthy dark adapted leaves
320
(Hendrickson et al., 2004). We determined the maximal electron transport rate of chloroplasts by
321
fitting the modeled potential electron transport to the calculated J from the chlorophyll
322
fluorescence measurements at different light intensity levels using a nonlinear least square
323
estimation procedure in Matlab (The Mathworks, Inc., Natick, USA) (See Supporting information
324
Fig. S18).
325
We obtained gas transport properties from the literature (Supporting information Table
326
S5). The diffusion coefficient of gas through the liquid phase has often been considered
327
to be close to that through water (Aalto & Juurola, 2002; Ho et al., 2012). However,
328
Kohler et al. (2000) observed that the diffusion of green fluorescent protein (GFP)
13
329
through the cytosol of tobacco cells was two to three times slower than through an
330
aqueous solution, presumably due to microstructural features such as the cytoskeleton or
331
the presence of proteins and solutes. Proteins and solutes increase the viscosity of the
332
cytosol; diffusion in the liquid phase is inversely related to the kinematic viscosity of the
333
solvent (Einstein, 1905). Tholen & Zhu (2011) assumed that the viscosity of the cytosol
334
was twice that of pure water. Likewise, Dieteren et al. (2011) showed that the viscosity
335
inside organelles such as the mitochondrial matrix was 1.5-fold to twofold higher than
336
that of pure water. We, therefore, assumed here that the viscosity of the intracellular
337
liquid phase was equal to twice that of water.
338
Nobel (1991) assumed that the apparent diffusivity of CO2 in the mesophyll cell wall was
339
around 30% that of CO2 in pure water. A similar result was found by Kamiya et al.
340
(1962). Richter & Ehwald (1983) estimated that the cell wall diffusivity of radiolabeled
341
sucrose in parenchyma from sugar beet (Beta vulgaris L.) tissue was between 0.11 to
342
0.16 times that of sucrose in an aqueous solution. Fanta et al. (2012) found that the
343
apparent diffusivity of water in artificial cell walls was 0.18 to 0.21 times the
344
autodiffusivity of free water. For these reasons we assumed here that the apparent
345
diffusivity of CO2 in the mesophyll cell wall was 20% of its diffusivity in pure water. The
346
cell wall thickness of a leaf typically ranges from 0.05 to 0.4 µm (Evans et al., 2009). We
347
assumed a cell wall thickness of 0.2 µm in this study.
348
CA has been considered to facilitate CO2 diffusion within the choloroplast (Makino et al.,
349
1992; Price et al., 1994; Williams et al., 1996). It is predominantly located in the stroma
350
of chloroplasts of C3 leaves (Jacobsen et al., 1975; Tsuzuki et al., 1985) where a high pH
351
of 8 favors its enzyme activity (Donaldson & Quinnt, 1974). We assumed CA to be
352
present in the chloroplasts but not in the cytoplasm and the vacuole. The CA
353
concentration in the stroma of tomato leaf was assumed to be equal to that of tobacco
354
(Nicotiana tabacum) as described by Gillon & Yakir ( 2000) (0.27 mol m-3). The kinetic
355
parameters of the CA hydration reaction are shown in Supporting information Table S5.
356
14
357
Model implementation details
358
The model for CO2 diffusion was solved on the 3-D geometrical model using the finite
359
volume method (Ho et al., 2011). 3-D tomographic images of leaf tissue samples (127.5
360
µm × 127.5 µm × 195 µm) were discretized into 7.514×106 cubical elements with edges
361
of 0.75 µm. At the top and bottom sides of the geometrical domain, we applied the
362
external CO2 concentration as a Dirichlet boundary condition while we assumed the other
363
sides to be impermeable. The model equations were discretized over the finite volume
364
grid to yield a system of algebraic equations for the unknown concentrations at the nodes.
365
The nonlinear equations were linearized using Newton iteration method. For each
366
iteration, the resulting linear system of equations was solved by the preconditioned
367
conjugate gradient procedure available in Matlab (The Mathworks). We solved the model
368
equations on a 16-GB RAM node of the High-Performance Computer in the VSC –
369
Flemish Supercomputer Center, Belgium. We visualized the simulation results with
370
isosurface representations using Avizo Fire software. (Visualization Group Sciences,
371
Merignac, FR).
372
Definition of macroscale variables
373
The microscale model predicts local variables which may depend on the position inside
374
the leaf, whereas the gas exchange and chlorophyll fluorescence experiments measure
375
lumped, macroscale variables of the whole leaf. In order to compare both measurements
376
and simulations, equivalent macroscale variables have to be calculated from the
377
microscale simulation results (Ho et al., 2012). We will use the following convention for
378
symbols: macroscopic variables which we estimated from gas exchange and chlorophyll
379
fluorescence experiments are denoted by a ‘^’ symbol. Volume averaged variables
380
calculated from the micro-scale model are overlined).
381
The volume averaged CO2 concentration of the chloroplasts ( C c ) predicted by the
382
micro-scale model was computed as
15

383
Cc 
[CO 2 ]dV
Vchl ,leaf
(S18)
Vchl ,leaf
384
The integration domain Vchl,leaf in Eq. S18 is the volume of all chloroplast clusters in the
385
3-D microstructural leaf tissue.
386
The volume averaged intercellular CO2 concentration C i is computed from the
387
microscale model according to a similar expression as in Eq. S18. For the whole leaf
388
photosynthesis rate A we integrated the CO2 flux over both the adaxial and abaxial leaf
389
surface and then expressed it per unit leaf projected area.
390
Text S5 Partitioning of photosynthesis capacity along the leaf depth
391
We wanted to test whether scaling of photosynthesis capacity with light absorption was
392
optimal for nitrogen use in a leaf using the microscale model. We assumed three
393
scenarios of distribution of photosynthesis capacity:
394
(I) Uniform distribution: chloroplasts irrespective of their position inside the leaf were
395
assumed to have the same photosynthetic capacity. The volumetric photosynthetic
396
capacity P m ,c (jm , Vc*,max and Tp* ) of chloroplasts is calculated from
397
P m ,c 
Pm ,leaf
(S19)
Vchl ,leaf
398
where Pm ,leaf and Vchl ,leaf are the total photosynthetic capacity and the total volume of the
399
chloroplasts in the leaf.
400
(II) Optimal distribution: Farquhar (1989) proposed that photosynthetic capacity should
401
scale with light absorption for the optimal use of nitrogen in the leaf. Note that the
16
402
properties of all the chloroplasts in a single cell are identical as the coordinating
403
message/signal is presumably the same for all the chloroplasts in a mesophyll cell.
404
Therefore, the ratio of averaged photosynthetic capacity P m , k of the chloroplasts in a
405
particular mesophyll cell k to that of the leaf Pm , leaf is assumed to be:
406
P m, k
i abs , k

Pm ,leaf iabs ,leaf
(S20)
407
where i abs , k is the average rate of absorbed photons of the chloroplast in mesophyll cell k,
408
and iabs , leaf is the total rate of absorbed photons of chloroplasts in the leaf. From the light
409
penetration simulation, iabs , leaf is calculated as follows:
410

iabs ,leaf 
(S21)
iabs dV
Vchl ,leaf
411
The average rate of absorption of photons by the chloroplast of mesophyll cell k is
412
calculated as:
413
i abs , k 

iabs dV
Vchl ,k
(S22)
Vchl ,meso
414
where Vchl , k is the volume of the chloroplasts in mesophyll cell k.
415
The averaged photosynthetic capacity P m , k of the chloroplasts in mesophyll cell k was
416
calculated from S20.
17
P m, k 
417
i abs , k
iabs ,leaf
(S23)
Pm,leaf
418
(III) Distinct photosynthetic capacity of the palisade and spongy chloroplasts. The
419
photosynthetic capacity of the palisade chloroplast was found to be larger than that of the
420
spongy chloroplast. In this case, the photosynthetic capacity of the spongy chloroplast
421
P m, S is calculated as
422
P m, S 
Pm ,leaf
(S24)
rP / S  Vchl , P  Vchl , S
423
where Vchl , P and Vchl , S are the total volume of palisade and spongy chloroplasts,
424
respectively; rP/S is the ratio of the photosynthetic capacity of the palisade chloroplast to
425
that of the spongy chloroplast. The photosynthetic capacity of the palisade chloroplast
426
P m, P is
427
Pm, P  rP / S  Pm, S
(S25)
428
At saturating light, the activities of overall electron transport and CO2 fixation in palisade
429
chloroplasts were respectively 1.6 ̶ 2.0 and 2.5 ̶ 3.0 fold higher than those in spongy
430
chloroplasts (Terashima & Inoue, 1985). We assumed that the maximum RuBisCo
431
carboxylation rate and the maximum rate of triose phosphate utilisation of palisade
432
chloroplasts were twice those of spongy chloroplasts while the maximal potential
433
electron transport rate of palisade chloroplasts was three times that of spongy chloroplasts.
434
Pm ,leaf is meant for the total maximum potential electron transport rate, the total
435
maximum rate of RuBisCo activity-limited carboxylation and the total rate of triose
436
phosphate which are calculated from Table S3. Partitioning of photosynthetic capacity
437
(jm , Vc*,max and Tp* ) for three assumed scenarios was calculated from Eqs. S19, S23, S24 ̶
438
25. The potential electron transport rate (j*) was calculated from jm and iabs using Eqs. S7 ̶
18
439
8. The parameters j*, Vc*,max and Tp* were incorporated into Eqs S2 ̶ 5 of the FvCB model.
440
The combined model of the CO2 diffusion and the FvCB model was used to calculate
441
photosynthesis in the 3D leaf.
442
To calculate relative photosynthetic capacity along the leaf depth, a volumetric slice
443
V (l ) of the leaf with a thickness Δl and cross section area Sleaf (l) at the depth l was
444
defined (see Eq. 6, main text). The thickness Δl was set to 0.75 µm (voxel thickness of
445
the laminography images). The distribution of the relative photosynthetic capacity Pc
446
along the depth l of the leaf was calculated as the amount of photosynthetic capacity in a
447
layer with a thickness Δl at depth l normalized by the total photosynthetic capacity of the
448
leaf:
449
Pc (l ) 

Pm dV

Pm dV
V ( l )


Pm dV
V ( l )
(S26)
Pm,leaf
Vleaf
450
where the numerator is the integration of photosynthetic capacity Pm over the volumetric
451
slice V (l ) ; the denominator is the total photosynthetic capacity of the leaf. Partitioning
452
of Pm is described by Eq. S19, Eq. S23 and Eqs. S24 ̶ 25 for scenarios (I), (II) and (III),
453
respectively.
454
The fraction of absorbed photons fabs was calculated on a particular small volume dV as
455
f abs 

iabs dV
Vleaf
(S27)
iabs dV
456
Text S6 Recycling of CO2
457
An in silico simulation with air containing
458
CO2 recycling. We assumed that the tomato leaf was initially exposed to ambient air
459
containing 350 μmol mol-1 12CO2, 21% O2, Iinc = 1000 μmol m-2 s-1 at 25°C. Therefore, the
13
19
C labeled CO2 was carried out to quantify
460
carbon in the leaf was fully 12C. Then, we imposed an instantaneous replacement of the
461
12
462
information Fig. S19). We assumed that the contribution of (photo)respiration by
463
was negligible in the simulation and only 12CO2 was produced by the mitochondria. The
464
gas transport model included transport equations for both
465
for 13CO2 and H13CO3 . We assumed further for this simulation analysis that RuBisCo has
466
no preference for either labeled or unlabeled CO2. The ratio of 12CO2 assimilation rate wr*
467
to 13CO2 assimilation rate w13* C in chloroplasts is considered to be equal to the ratio of the
468
chloroplast concentration of 12CO2 and 13CO2.
CO2 in the air by the same concentration of
wr*  w13* C
469
CO2 (350 μmol mol-1) (See Supporting
13
12
13
CO2
CO2 and H12 CO3 as well as
[CO2 ]
[ CO2 ]
(S28)
13
12
13
470
where [CO 2 ] and [ 13 CO 2 ] are the chloroplast
471
respectively. The CO2 evolved from (photo)respiration cycles in the leaf was released as
472
12
473
RuBisCo, frecycle then as:
474
f recycle 
CO2 and
CO2 concentrations,
CO2. We then calculated the fraction of (photo)respiration CO2 flux reassimilated by
wr*
Rd*  R*p
(S29)
12
475
where Rd* , R*p and wr* are the respired, photorespired and re-assimilated
476
respectively. We assumed that after imposing an instantaneous replacement of the
477
unlabeled 12CO2 in the air by the same concentration of labeled 13CO2, a quasi steady state
478
would be established quickly.
479
Supporting information figures
20
CO2 flux,
480
481
Figure S1. Comparison of measured (solid lines) and simulated (stars) transmittance (Mt)
482
and reflectance (Mr) spectra for five tomato leaves (cv. Growdena). The two bundles of
483
red lines are likely due to the presence of vascular bundles in the leaf that change its
484
scattering properties.
21
485
486
Figure S2 Simulated distribution of relative CO2 fixation rate along the depth (a) and A-
487
Ci curves (b) of three different geometries of Admiro leaves. Panel (a) Simulations were
488
carried out at 350 µmol mol-1 CO2, 21% O2, Iinc of 1000 µmol m-2 s-1 and T=25°C. The
489
definition of relative CO2 fixation rate is provided in Supporting information Text S5.
490
The arrow (1) indicates the transition from palisade parenchyma to spongy parenchyma.
491
Panels (b) Simulated A-Ci curves with different scenarios at 21% O2, I inc =1000 μmol m-2
492
s-1 and T=25°C. The symbols (o) indicate the measured data while and the lines represent
493
model predictions of three different geometries. The error bars represent the standard
494
error (n = 4).
22
495
496
Figure S3. Relative photosynthetic capacity along the depth and intracellular CO2
497
distribution of different tomato leaves. a, b and c show the relative photosynthetic
498
capacity as a function of depth from the adaxial surface in lower leaves of Admiro,
499
Doloress and Growdena, respectively. The corresponding geometrical models had an
500
Sc/Sm ratio of 0.76, 0.71 and 0.71, respectively; the light intensity (Iinc) was set to 1000
501
µmol m-2 s-1. The arrows in the panels indicate the transitions between the palisade and
502
spongy mesophyll. d, e and f show the computed intracellular CO2 distribution in a
503
tomato leaf for the aforementioned cultivars. The ambient conditions were 350 μmol mol-
504
1
505
mol-1. Optimal distribution of photosynthetic capacity inside the leaf is assumed for the
506
simulations.
CO2, 21% O2, Iinc of 1000 μmol m-2 s-1 and 25°C. Concentrations are expressed in µmol
23
507
508
509
Figure S4. CO2 distributions in the air phase (a) and mesophyll cells (b) of Admiro lower
510
leaf. The air phase includes external boundary air and intercellular spaces inside the leaf.
511
The ambient condition is Ca = 350 μmol mol-1, Iinc = 1000 μmol m-2 s-1 and T = 25°C,
512
O2=21%. The ambient condition was 350 μmol mol-1 CO2, 21% O2, Iinc of 1000 μmol m-2
513
s-1 and 25°C. Concentrations are expressed in µmol mol-1. Eas, external air space; Ias,
514
intercellular air space. Optimal distribution of photosynthetic capacity inside the leaf was
515
assumed for the simulations.
24
516
517
Figure S5 Simulations of the net rate of whole-leaf photosynthesis A with and without
518
CA facilitation of different leaves at different CO2 levels at 21% O2, I inc =1000 μmol m-2
519
s-1 and T=25°C. The symbols (o) represent the measured data. The solid (―) lines and
520
dashed ( ̶ ̶ ) lines represent model predictions with and without CA facilitation. Panels
521
(a), (b) and (c) represent the results of Admiro, Doloress and Growdena lower leaves,
522
respectively. Optimal distribution of the photosynthetic capacity inside the leaf was
523
assumed in the simulations. The corresponding geometrical models had an Sc/Sm ratio of
524
0.76, 0.71 and 0.71, respectively. The error bars represent the standard error (n = 4).
525
25
526
527
528
Figure S6. Microscale geometry of Admiro lower leaf generated with different
529
chloroplast distributions. (a) Sc/Sm = 0.36 (face distribution). (b) Sc/Sm = 0.76 (profile
530
distribution). (c) Sc/Sm = 0.9 (profile distribution). Chl, chloroplast cluster; Cyt, cytosol; E,
531
epidermis; Vac, vacuole.
532
26
533
534
Figure S7. Simulated CO2 distribution in response to different levels of incident light in
535
lower leaves (cv. Admiro). a, b, and c show the predicted intracellular CO2 distribution
536
for Iinc=65, 1000 and 2000 μmol m-2 s-1, respectively, at 380 μmol mol-1 CO2, 21% O2,
537
and 25°C. Details of the chloroplast distribution are given in the Supporting information
538
Fig. S4. The color bar indicates the CO2 concentration (µmol mol-1). Optimal distribution
539
of photosynthetic capacity inside the leaf was assumed for the simulations.
27
540
541
Figure S8. Simulated 12CO2 (a) and 13CO2 (b) distribution in a tomato leaf (cv. Admiro).
542
In the simulation, the tomato leaf was assumed to be exposed to ambient air containing
543
350 μmol mol-1
544
(photo)respiration by 13CO2 was negligible. The color bar indicates the CO2 concentration
545
(µmol mol-1). Optimal distribution of photosynthetic capacity inside the leaf was assumed
546
for the simulations.
13
CO2, 21% O2, Iinc = 1000 μmol m-2 s-1 at 25°C. The contribution of
547
28
548
549
Figure S9. 2D model versus 3D model. (a) and (c) CO2 distribution profiles obtained
550
from simulations on 2-D vertical cross-sections of tomato leaf. (b) and (d) CO2
551
distribution profiles of corresponding vertical cross-sections obtained from simulation on
552
3D geometry of tomato leaf. The color bar indicates the CO2 concentration (µmol mol-1).
553
554
29
555
556
Figure S10. Modeled profile distribution of chloroplasts in a mesophyll cell. (a) a
557
mesophyll cell; (b) modeled centroids of chloroplasts on the boundary layer of the
558
mesophyll cell; (c) chloroplasts clusters created from the centroids; (d) profile
559
distribution of chloroplasts obtained by removing chloroplasts around the periclinal cell
560
walls of the mesophyll cell.
561
30
562
563
564
Figure S11. Schematic representation of the mesophyll surface areas exposed to the
565
intercellular air space, and chloroplasts facing the outer surfaces of exposed mesophyll
566
cells in a leaf. Chl: Chloroplasts; E: Epidermis; Meso: Mesophyll cell; Int: Intercellular
567
air space. Mesophyll surface areas (Sm) and chloroplast surface areas (Sc) exposed to
568
intercellular air spaces are represented by dark blue solid ( — ) and red solid (— )
569
boundaries, respectively.
31
570
571
572
Figure S12. Microscale geometry of tomato leaf. (a) Reconstructed microscale geometry
573
based on synchrotron X-ray laminography images of Admiro lower leaf; (b) Mesophyll
574
cell with modeled vacuole; (c) Profile distribution of chloroplasts at high light intensities
575
generated from mesophyll cell; (d) detailed modeled mesophyll cell with profile
576
distribution of chloroplasts. Chl, chloroplast clusters; Cyt, cytosol; E, epidermis; Vac,
577
vacuole.
578
579
32
580
581
582
Figure S13. Measured (a) stomatal conductance ( g s ) to CO2 as a function of I inc of
583
tomato lower leaves (cv. Admiro). (b) The relation between degree of stomata opening
584
and stomata conductance computed from the microscale model.
33
585
Rdiff
Tdiff
Light source
Tcol
Sample
586
587
Figure S14. Schematic representation of the DIS set-up, with collimated transmittance Tc,
588
diffuse reflectance Rdiff and diffuse transmittance Tdiff.
589
34
590
591
Figure S15. Geometrical model of a lower Admiro leaf. (a) Original voxel-based; (b)
592
tetrahedral mesh for Monte Carlo photon transport simulations. Chl, chloroplast clusters;
593
Cyt, cytosol; E, epidermis; Vac, vacuole.
594
35
595
596
Figure S16. Particle size distribution f(r) of the different cell organelles in the epidermis domain (top panels), with resulting
597
phase function (bottom panels) at 680 nm, expressed in a logarithmic scale. (a), (b), (c), (d), (e) and (f) correspond to
598
mitochondria, peroxisomes, nuclei, Golgi stacks, ribosomes in the epidermis domain, and grana in the chloroplast domain,
599
respectively.
36
600
601
Figure S17. Resulting scattering coefficient (a, c) and anisotropy factor (b, d), caused by
602
the scattering of a specific cell organelle in the epidermis (a, b) and chloroplast (c, d).
37
603
604
Figure S18. The response of potential electron transport rate (J) to incident irradiation
605
(Iinc) under photorespiratory conditions of Admiro (a) and Growdena (b) lower leaves.
606
The symbols (o) and solid line (―) represent measurements and model predictions,
607
respectively.
608
38
609
610
Figure S19. Schematic representation of different CO2 fluxes in a leaf with an ambient
611
air containing labeled 13CO2. The CO2 fixation flux (Wr) of unlabeled 12CO2 is assumed
612
to be produced from photorespiration (Rp) and respiration (Rd) of unlabeled 12CO2. For a
613
short time imposing instantaneous replacement of the
614
concentration of
615
assumed to be negligible (Haupt-Herting et al., 2001). A13 CO is the CO2 fixation flux of
13
12
CO2 in the air by the same
CO2, the contribution of (photo)respiration by labeled
13
CO2 was
2
616
labeled 13CO2 and L is the CO2 flux of the unlabeled 12CO2 releasing from the mesophyll
617
cell to the atmosphere after imposing instantaneous replacement of the unlabeled
618
in the air by the same concentration of labeled
619
Mitochondria.
620
13
12
[CO2] and
13
13
12
CO2
CO2. Chl: Chloroplasts; Mito:
[CO2] are concentrations of unlabeled
12
CO2 and labeled
CO2. The subscript indices a, i indicate ambient and intercellular air space, respectively.
39
621
Supporting information tables
622
Table S1. List of model variables, their symbols, definitions and units
Variable
Definition
A
Net photosynthesis rate (mol CO2 m-2 s-1)
CO2 fixation flux of labeled 13CO2 (mol 13CO2 m-2 s-1)
A13 CO
2
A
B
Ca
Cc
Ci
Cc
Ci
[CA]
[CO 2 ]
Mean net photosynthesis rate computed from microscale model (mol
CO2 m-2 s-1)
Net hydration of CO2 to HCO3 (μmol m-3 s-1)
Ambient air CO2 concentration (mol mol-1)
Mean chloroplast CO2 concentration (mol mol-1)
Mean intercellular CO2 concentration (mol mol-1)
Mean chloroplast CO2 concentration computed from microscale model
(mol mol-1)
Mean intercellular CO2 concentration computed from microscale model
(mol mol-1)
Carbonic anhydrase concentration (µmol m-3)
CO2 concentration (µmol m-3)
[13 CO2 ]
13
[CO 2 ]*m
f r 
Equivalent liquid CO2 concentration at the outer cell wall of the
mesophyll cell (µmol m-3)
Number of particles per unit volume (µm-3)
f recycle
Fraction of (photo) respiration CO2 flux refixed by RuBisCo
gs
Stomatal conductance (mol m-2 s-1)
[HCO3- ]
HCO3- concentration of the mesophyll (μmol m-3)
I inc
iabs
Photon flux density incident to leaves (mol photon m-2 s-1)
i abs ,k
iabs ,leaf
J
J
J
CO2 concentration (µmol m-3)
Rate of absorbed photons per unit volume (mol photon m-3 s-1)
Average rate of absorbed photons of the chloroplast in a particular
mesophyll cell (mol photon m-3 s-1)
Total rate of absorbed photons of chloroplasts in the leaf (mol photon
s-1)
Rate of potential electron transport (mol electron m-2 s-1)
Rate of potential electron transport calculated from chlorophyll
fluorescence measurements (mol electron m-2 s-1)
Rate of potential electron transport computed from microscale model
(mol electron m-2 s-1)
40
j*
ji
L
Mr
Mt
[O2]
Pc (l )
P
PSDV  r 
Potential electron transport rate at a certain position inside the leaf
(mol electron m-3 s-1)
The electron transport rate supplied by photo-oxidation of water at PSII
(mol electron m-3 s-1)
The CO2 flux of the unlabeled 12CO2 releasing from the mesophyll cell
to the atmosphere after imposing instantaneous replacement of the
unlabeled 12CO2 in the air by the same concentration of labeled 13CO2
(see Supporting information Fig. S19) (mol CO2 m-2 s-1)
Reflectance of the leaf
Transmittance of the leaf
Oxygen concentration (mbar)
Relative photosynthetic capacity at a depth l inside the leaf
Total pressure of the ambient air (kPa)
Volume frequency of particles distribution of an organelle (µm-1)
PSDN  r 
p(θ)
pi(θ)
Rd*
r
Rw (l )
Sleaf (l )
Number frequency of particles distribution of an organelle (µm-1)
T
*
w
wr*
Temperature (K)
Volumetric CO2 assimilation rate in chloroplast (mol CO2 m-3 s-1)
Volumetric 12CO2 reassimilation rate in chloroplast (mol CO2 m-3 s-1)
w13* C
Volumetric 13CO2 reassimilation rate in chloroplast (mol CO2 m-3 s-1)
wc
wj
Rate of RuBisCo activity-limited carboxylation (mol m-3 s-1)
wp
Rate of TPU-limited carboxylation (mol m-3 s-1)
 V (l )
a ,bulk
Volumetric slice of the leaf with a thickness Δl and cross section area
Sleaf (l) at the depth l (m3)
Thickness of the slice at leaf depth l. The thickness dl was set to 0.75
µm
Rate of CO2 transport through the boundary of the mesophyll cell (mol
m-2 s-1)
Absorption coefficient of medium with particles (m-1)
a ,med
Absorption coefficient of medium without particles (m-1)
 a ,i
Absorption coefficient of particles (m-1)
Δl
b
Phase function
Phase function of particle i
Volumetric photorespiration rate (mol CO2 m-3 s-1)
Radius of an organelles (m)
Relative CO2 fixation at a depth l inside the leaf
Cross section area of the leaf at the depth l (m2)
Rate of electron transport-limited carboxylation (mol m-3 s-1)
41
 s ,bulk
Scattering coefficient of medium with particles (m-1)
 s ,i
Scattering coefficient of particles (m-1)
i
Convexity coefficient
Subscripts
a
bulk
chl
cw
cyt
g
k
l
med
Ambient air
Bulk properties
Chloroplasts
Cytosols
Gas phase
Mesophyll cell
Liquid phase
Medium
623
The unit µmol mol-1 for CO2 concentration (often used in the FvCB model) was converted to
624
µmol m-3 for use in the gas diffusion model by multiplying with a factor P( R  T )
625
or P  H ( R  T ) (mesophyll).
1
42
1
(gas phase)
626
Table S2. List of model parameters, their symbols, definitions and units
Variable
Definition
Notes
DCO2
Diffusivity of CO2 (m2 s-1)
Table S5
DCO2 , g
Diffusivity of CO2 in the gas phase (m2 s-1)
Table S5
2 -1
DCO2 ,l
Diffusivity of CO2 in liquid phase (m s )
Table S5
DCO2 , w
CO2 diffusivity of cell wall (m2 s-1)
Table S5
DHCO
Diffusivity of HCO3- in the mesophyll (m2 s-1)
Table S5
ftot
Total number of an organelle per unit volume (number Table S6
µm-3)
Volumetric fraction of chloroplasts of the leaf
Calculated from
leaf geometry
Volumetric fraction of cytosol of the leaf
Calculated from
leaf geometry
Fraction of absorbed photons that is partitioned to
Photosystem II (=0.5)
Henry’s constant for CO2 (µmol m-3 liquid) (µmol m-3 Table S5
gas)-1
H+ concentration (µmol m-3)
Table S5
3
fc
f cyt
f II
H
[H ]
Jm
Whole-leaf maximal potential electron transport rate Table S3
(mol electron m-2 s-1)
Light saturated maximum potential electron transport Text S5
rate (mol electron m-3 s-1)
CO2 hydration rate constant (s-1)
Table S5
jm
k1
k2
K
CO2 dehydration rate constant (s-1)
Table S5
-3
Acid dissociation constant for H2CO3 (µmol m )
Michaelis-Menten constant of CA hydration (µmol m-3)
K CA,CO2
Table S5
Table S5
K eq
Michaelis-Menten constant of CA dehydration (µmol m- Table S5
3
)
Michaelis-Menten constant of RuBisCo for CO2 (mol Table S5
mol-1 or bar)
CO2 equilibrium constant (µmol m-3)
Table S5
K m ,O
Michaelis-Menten constant of RuBisCo for O2 (mbar)
KCA, HCO
3
K m ,C
-1
kCA
CA turnover rate (s )
Lleaf
Average thickness of tissue (m)
Pcut
Pcw
Table S3
Table S5
Calculated from
leaf geometry
Cuticular membrane permeability (m s-1)
Table S5
Effective permeability of the membrane and the cell Table S5
43
Pmem
Pm
P m ,c
P m, k
P m, P
P m,S
Pm ,leaf
wall (m s-1)
CO2 permeability of membrane (m s-1)
Photosynthetic capacity (See Supporting information
Text S5)
Average photosynthetic capacity of the chloroplast in
scenario I (mol m-3 s-1)
Average photosynthetic capacity of the chloroplast in a
particular mesophyll cell k in scenario II (mol m-3 s-1)
Photosynthetic capacity of the palisade chloroplast in
scenario III (mol m-3 s-1)
Photosynthetic capacity of the spongy chloroplast in
scenario III (mol m-3 s-1)
Total photosynthetic capacity of the leaf (mol s-1)
Table S5
Eq. S19
Eq. S23
Eq. S25
Eq. S24
Table S3
Rd*
Universal gas constant (8.314 J mol-1 K-1)
Day respiration (i.e., respiratory CO2 release other than Table S3
by photorespiration) (mol CO2 m-2 s-1)
Table S3
Volumetric respiration rate (mol CO2 m-3 s-1)
rLB
Lowest radius (m)
Table S6
rUB
Highest radius (m)
Table S6
r
rP/S
Mean equivalent radius of an organelle (µm)
Ratio of the photosynthetic capacity of the palisade
chloroplast to that of the spongy chloroplast. Defined in
scenario III
Calibration factor
Chloroplast surface area that faces the intercellular
spaces on a leaf area basis (m2 m-2)
Relative CO2/O2 specificity factor for RuBisCo (mbar
bar-1)
Area of a cross section of the computational domain
(m2)
Mesophyll surface area that faces the intercellular
spaces on a leaf area basis (m2 m-2)
Rate of triose phosphate export from the chloroplast
(mol m-2 s-1)
Volumetric production rate of triose phosphate export
from the chloroplast (mol m-3 s-1)
Maximum
rate
of
RuBisCo
activity-limited
carboxylation (mol m-2 s-1)
Volumetric maximum rate of RuBisCo activity-limited
carboxylation (mol m-3 s-1)
Table S6
Text S5
R
Rd
s
Sc
Sc / o
Sleaf
Sm
Tp
Tp*
Vc ,max
Vc*,max
44
Table S3
Calculated from
leaf geometry
Table S3
Calculated from
leaf geometry
Calculated from
leaf geometry
Table S3
Text S5
Table S3
Text S5
Vcyt ,k
Volume of the cytosol of a mesophyll cell k (m3)
Vchl ,leaf
Volume of chloroplasts in the leaf(m3)
Vchl ,k
Volume of chloroplasts in a mesophyll cell k (m3)
Vchl,P
Total volume of palisade chloroplasts (m3)
Vchl,S
Total volume of spongy chloroplasts (m3)
Vleaf
Volume of the leaf (m3)
m
Maximum quantum yield of Photosystem II electron
transport (mol e- mol-1 photon) (0.85 mol e- mol-1
photon, Hendrickson et al., (2004))
Anisotropy factor
Table S4
-1
Absorption coefficient (m )
Table S4

a
s

r
*
Scattering coefficient (m-1)
Calculated from
leaf geometry
Calculated from
leaf geometry
Calculated from
leaf geometry
Calculated from
leaf geometry
Calculated from
leaf geometry
Calculated from
leaf geometry
Table S4
Viscosity relative to that of water
Table 4
Standard deviation of equivalent radius of the organelle Table S6
(µm)
Cc-based CO2 compensation point in the absence of Rd Table S3
(mol mol-1 or bar)
*
627
The respiratory CO2 release from mitochondria Rd was assumed constant. The volumetric Rd was
628
calculated from Rd*  Rd /  Lleaf  f cyt  , with Lleaf the average thickness of the leaf.
45
629
Table S3. Estimated photosynthetic parameters (± standard error if applicable) of leaves of different tomato cultivars and leaf
630
ages.
631
Vc,max (µmol m
s-1)
Growdena
Lower leaves
Upper leaves
Admiro
Lower leaves
75.56 (4.42)
110.2 (7.45)
69.53 (3.70)
133.6 (13.68)
89.94 (5.8)
147.70(15.53)
-
8.87 (0.32)
-
9.04 (0.3)
-
0.690
1.386
136.79 (3.75)
104.01 (3.69)
1.937
1.693
162.76 (4.3)
118.0 (3.89)
0.976
0.891
116.52 (5.71)
92.20 (5.01)
1.453
2.106
205.97 (6.69)
139.1 (5.84)
0.836
1.395
162.77 (4.32)
118.0 (3.89)
9.51 (0.22)
1.741
1.733
0.473
0.478
0.429
0.473
0.491
Upper leaves
Doloress
Lower leaves
Upper leaves
-2
Tp (µmol m-2 s-1)
-2 -1
Rd (µmol m s ) PR
NPR
-2 -1
Jm (µmol m s ) PR
NPR
s
Sc/o (mbar µbar1
)
θi(*)
Km,C (µmol mol1 ( )
) **
K m ,O
(mmol
-1 ( )
mol ) **
3.320 (0.325)
3.174 (0.267)
0.97
3.300 (0.256)
267
164
632
633
634
*Assumed value
**Bernacchi et al. ( 2002).
PR and NPR denote photorespiration (21% O2) and non-photorespiration (2% O2) conditions.
635
*, Cc-based CO2 compensation point in the absence of Rd, is calculated by: * 
46
0.476
0.5  [O2 ]
Sc / O .
636
637
638
The total maximum potential electron transport rate, the total maximum rate of RuBisCo activity-limited carboxylation and the
total rate of triose phosphate are calculated by multiplying Jm, Vc,max and Tp with the cross section Sleaf of the computational
domain, respectively.
47
639
Table S4. Computed optical properties of the different compartments of the leaf model.
640
The absorption profile is the result of averaging the absorption profile at 470 nm (10%)
641
and at 665 nm (90%). Two independent optical simulations were needed, with each a
642
different set of optical properties.
a ( m 1 )
0
 s ( m 1 )
0
 ()
1
Cytosol
Vacuole
Chloroplast
100
100
18216
39600
0.915624
0. 915624
100
465300
0
295915
1
0.96260
665 nm
Air
Epidermis
Cytosol
Vacuole
Chloroplast
0
100
100
100
229000
0
9275
19893
0
159690
1
0.884978
0.884978
1
0.93340
470 nm
Air
Epidermis
643
48
644
Table S5. Physical parameters of the microscale gas exchange model. Diffusion in the
645
liquid phase was assumed to follow the Stokes-Einstein law (Einstein, 1905),
646
DCO2 ,l  DCO2 , water /  .
647
Model parameters
Diffusivity
- Air
Symbol
Values
DCO2 , g
1.60×10-5 m2 s-1 at 20°C (1)
- Water
DCO2 , water
1.67×10-9 m2 s-1 at 20°C
DHCO , water
1.17×10-9 m2 s-1 (2)
Cuticular membrane
permeability
Cell wall thickness
Henry’s constant
Pcuti
7×10-6 m s-1 (3)
lw
H
CO2 hydration rate constants
CO2 dehydration rate constants
Acid dissociation constant
CO2 equilibrium constant
CA turnover rate
CA concentration in stroma
CA hydration constant
k1
k2
K
Keq
kCA
[CA]
K CA,CO2
0.2×10-6 m (assumed)
0.83 (µmol m-3 liquid)(µmol m-3
gas)-1 at 25°C (1)
0.039 s-1 (4)
23 s-1(4)
2.5×10-4 mol L-1 (4)
5.6×10-7 mol L-1 (5)
3×105 s-1 (5)
0.27 mol mol-3 (6)
1.5 mol m-3(6)
CA dehydration constant
KCA, HCO
(1)
3
34 mol m-3(6)
3
pH
-Cytosol
-Chloroplast
-Vacuole
Cytosol viscosity
 log10 [H + ]
7 (assumed)
8 (assumed)
5 (assumed)
2 (relative to water) (7)
ηcyt
Stroma viscosity
ηc
Cellular membrane permeability Pmem
2 (relative to water)
3.5×10-3 m s-1 (2,8)
Cell wall diffusivity
Dw  0.2  DCO2 , water
Effective permeability of the
membrane and the cell wall
 1
l 
Pcw  
 w  1.13×10-3 m s-1
 Pmem Dw 
Assumed
1
Stomatal radius (µm)
2.01
49
648
(1)
649
1985)
650
(8)
(Lide, 1999);
(2)
(Geers & Gros, 2000) ;
(5)
(Pocker & Ng, 1973);
(3)
(Frost-Christensen & Floto, 2007) ;
(6)
(Tholen & Zhu, 2011) ;
(Evans et al., 2009).
50
(7)
(4)
(Jolly,
(Dieteren et al., 2011);
651
Table S6. Organelles and their sizes for computing optical properties in tomato leaf
652
domain.
Organelle
Description
type
Mean
Standard
ftot
equivalent
deviation
(number
 r (µm)
µm-3)
0.059
0.00585
0.025
0.0025018
0.0899
0.000201
0.0917
0.002518
radius
r
(µm)
Mitochondria
Cylindrical shape with radius 0.60
of 0.27±0.035 µm, length of 4
±0.035 µm (Dieteren et al.,
2011),
volume
fraction
=0.05% (Winter et al., 1994).
Peroxisomes
Spherical
shape
with
a 0.25
diameter between 0.4 and 0.6
μm
(Furt
number=25
et
al.,
2012),
(Lingard et al.,
2008). The calculated total
number of peroxisomes per
unit volume is about (1.55)×10-3 µm-3.
Nuclei
Spherical shape with volume 2.57
of
about
72.4±7.5
µm3
(Dittmer et al., 2007).
Golgi stacks
Disk shape with diameter of 0.42
0.5 to 2.0 µm and height of
0.3 µm (Dupree & Sherrier,
1998), number=25 (Dupree &
51
Sherrier,
1998).
The
calculated total number of
Golgi stacks per unit volume
is about (1.5-5)×10-3 µm-3.
Ribosome-
Spherical shape with diameter 0.0137
like
of 25-30 nm (Verschoor et al.,
complexes
1998). There were about 1250
0.000625
445.44
0.0558
0.68
ribosome-like complexes in an
Ostreococcus tauri cell with
volume
about
2.8
µm3
(Henderson et al., 2007).
Grana (*)
Cylindrical stack (about 4 to 0.472
17
stacks)
(Austin
and
Staehelin, 2011), diameter of
about 1 µm, stack height
about 0.25 to 1 µm (derived
from
Austin
&
Staehelin
(2011)). Mature chloroplasts
could contain 40 to 60 grana
stacks (Staehelin, 2003).
1/3
654
 3V organelle 
The equivalent radius of an organelle was defined from its volume V organelle as r  
 4 


The standard deviation  r was determined from the lowest and highest value observed from
655
literature (See Supporting information Text S4).
656
*Calculated for the chloroplast domain.
657
ftot was determined from the volume fraction or the number of organelles per unit volume
653
658
52
659
Supporting information References
660
661
Aalto T., Juurola E. (2002) A three-dimensional model of CO2 transport in airspaces and
mesophyll cells of a silver birch leaf. Plant, Cell and Environment 1399–1409
662
663
664
Aernouts B., Van Beers R., Watté R., Lammertyn J., Saeys W. (2014) Dependent
scattering in Intralipid® phantoms in the 600-1850 nm range. Optics Express
22,6086
665
666
667
668
669
670
671
Aernouts B., Watte R., Lammertyn J., Saeys W. (2012) A flexible tool for simulating the
bulk optical properties of polydisperse suspensions of spherical particles in an
absorbing host medium. In Y Wyrowski, F and Sheridan, JT and Tervo, J and
Meuret, ed, A flexible tool for simulating the bulk optical properties of polydisperse
suspensions of spherical particles in an absorbing host medium. Proceedings of the
Society of Photo-Optical Instrumentation Engineers: Vol. 8429. SPIE Photonics
Europe. Brussels, pp 1–12
672
673
674
Austin J.R., Staehelin L.A. (2011) Three-dimensional architecture of grana and stroma
thylakoids of higher plants as determined by electron tomography. Plant Physiology
155,1601–1611
675
676
677
678
Bernacchi C.J., Portis A.R., Nakano H., von Caemmerer S., Long S.P. (2002)
Temperature response of mesophyll conductance. Implications for the determination
of Rubisco enzyme kinetics and for limitations to photosynthesis in vivo. Plant
Physiology 130,1992–1998
679
680
Buckley T.N., Farquhar G.D. (2004) A new analytical model for whole-leaf potential
electron transport rate. Plant, Cell and Environment 27,1487–1502
681
682
Von Caemmerer S. (2013) Steady-state models of photosynthesis. Plant, Cell and
Environment 36,1617–1630
683
684
Damour G., Simonneau T., Cochard H., Urban L. (2010) An overview of models of
stomatal conductance at the leaf level. Plant, Cell and Environment 33,1419–1438
685
686
687
688
Dieteren C.E.J., Gielen S.C.A.M., Nijtmans L.G.J., Smeitink J.A.M., Swarts H.G., Brock
R., Willems P.H.G.M., Koopman W.J.H. (2011) Solute diffusion is hindered in the
mitochondrial matrix. Proceedings of the National Academy of Sciences of the
United States of America 108,8657–8662
689
690
Dittmer T. a, Stacey N.J., Sugimoto-Shirasu K., Richards E.J. (2007) Little nucleic genes
affecting nuclear morphology in Arabidopsis thaliana. The Plant Cell 19,2793–2803
53
691
692
693
694
Donaldson T.L., Quinnt J.A. (1974) Kinetic constants determined from membrane
transport measurements: carbonic anhydrase activity at high concentrations.
Proceedings of the National Academy of Sciences of the United States of America
71,4995–4999
695
696
Dupree P., Sherrier D.J. (1998) The plant Golgi apparatus. Biochimica et biophysica acta
1404,259–270
697
698
Einstein A. (1905) On the movement of small particles suspended in stationary liquids
required by the molecular-kinetic theory of heat. Annalen der Physik 17,549–560
699
700
Evans J.R., Kaldenhoff R., Genty B., Terashima I. (2009) Resistances along the CO2
diffusion pathway inside leaves. Journal of Experimental Botany 60,2235–2248
701
702
703
Fanta S.W., Vanderlinden W., Abera M.K., Verboven P., Karki R., Ho Q.T., De Feyter
S., Carmeliet J., Nicolaï B.M. (2012) Water transport properties of artificial cell
walls. Journal of Food Engineering 108,393–402
704
705
Farquhar G.D. (1989) Models of integrated photosynthesis of cells and leaves.
Philosophical Transactions of the Royal Society B 323,357–367
706
707
Farquhar G.D., Caemmerer S., Berry J.A. (1980) A biochemical model of photosynthetic
CO2 assimilation in leaves of C3 species. Planta 149,78–90
708
709
710
711
Feret J.-B., François C., Asner G.P., Gitelson A.A., Martin R.E., Bidel L.P.R., Ustin S.L.,
le Maire G., Jacquemoud S. (2008) PROSPECT-4 and 5: Advances in the leaf
optical properties model separating photosynthetic pigments. Remote Sensing of
Environment 112,3030–3043
712
713
714
715
Féret J.-B., François C., Gitelson A., Asner G.P., Barry K.M., Panigada C., Richardson
A.D., Jacquemoud S. (2011) Optimizing spectral indices and chemometric analysis
of leaf chemical properties using radiative transfer modeling. Remote Sensing of
Environment 115,2742–2750
716
717
718
Frost-Christensen H., Floto F. (2007) Resistance to CO2 diffusion in cuticular membranes
of amphibious plants and the implication for CO2 acquisition. Plant, Cell and
Environment 30,12–18
719
720
721
Furt F., Lemoi K., Tüzel E., Vidali L. (2012) Quantitative analysis of organelle
distribution and dynamics in Physcomitrella patens protonemal cells. BMC Plant
Biology 12,70
722
723
Galmés J., Ochogavía J.M., Gago J., Roldán E.J., Cifre J., Conesa M.À. (2013) Leaf
responses to drought stress in Mediterranean accessions of Solanum lycopersicum:
54
724
725
anatomical adaptations in relation to gas exchange parameters. Plant, Cell and
Environment 36,920–935
726
727
Geers C., Gros G. (2000) Carbon dioxide transport and carbonic anhydrase in blood and
muscle. Physiological Reviews 80,681–715
728
729
730
Genty B., Briantais J., Baker N. (1989) The relationship between the quantum yield of
photosynthetic electron-transport and quenching of chlorophyll fluorescence.
Biochimica et Biophysica Acta 990,87–92
731
732
Gillon J.S., Yakir D. (2000) Internal Conductance to CO2 Diffusion and C18OO
Discrimination in C3 Leaves. Plant Physiology 123,201–214
733
734
Haardt H., Maske H. (1987) Specific in vivo absorption coefficient of chlorophyll a at
675 nm. Limnology and Oceanography 32,608–619
735
736
737
738
Haupt-Herting S., Klug K., Fock H.P. (2001) A new approach to measure gross CO2
fluxes in leaves. Gross CO2 assimilation, photorespiration, and mitochondrial
respiration in the light in tomato under drought stress. Plant Physiology 126,388–
396
739
740
Henderson G.P., Gan L., Jensen G.J. (2007) 3-D ultrastructure of O. tauri: electron
cryotomography of an entire eukaryotic cell. PloS One 2,e749
741
742
743
Hendrickson L., Furbank R.T., Chow W.S. (2004) A simple alternative approach to
assessing the fate of absorbed light energy using chlorophyll fluorescence.
Photosynthesis Research 82,73–81
744
745
746
Hertog M.L.A.T.M., Scheerlinck N., Nicolaï B.M. (2009) Monte Carlo evaluation of
biological variation: Random generation of correlated non-Gaussian model
parameters. Journal of Computational and Applied Mathematics 223,1–14
747
748
749
Ho Q.T., Verboven P., Verlinden B.E., Herremans E., Wevers M., Carmeliet J., Nicolaï
B.M. (2011) A three-dimensional multiscale model for gas exchange in fruit. Plant
Physiology 155,1158–1168
750
751
Ho Q.T., Verboven P., Yin X., Struik P.C., Nicolaï B.M. (2012) A microscale model for
combined CO2 diffusion and photosynthesis in leaves. PloS One 7,e48376
752
753
Jacobsen B.S., Fong F., Heath R.L. (1975) Carbonic anhydrase of spinach. Studies on its
location, inhibition and physiological function. Plant Physiology 55,468–474
55
754
755
756
Jacquemoud S. (2000) Comparison of four radiative transfer models to simulate plant
canopies reflectance direct and inverse mode. Remote Sensing of Environment
74,471–481
757
758
759
760
James R.A., Munns R., von Caemmerer S., Trejo C., Miller C., Condon T.A.G. (2006)
Photosynthetic capacity is related to the cellular and subcellular partitioning of Na+,
K+ and Cl- in salt-affected barley and durum wheat. Plant, Cell and Environment
29,2185–2197
761
Jolly W.L. (1985) Modern inorganic chemistry. McGraw-Hill, New York
762
763
Kamiya N., Tazawa M., Takata T. (1962) Water permeability of the cell wall in Nitella.
Plant and Cell Physiology 3,285–292
764
765
766
Kohler, RH, Schwille, P, Webb, WW (2000) Active protein transport through plastid
tubules: velocity quantified by fluorescence correlation spectroscopy. Journal of
Cell Science 113,3921–3930
767
768
Li Y., Ren B., Ding L., Shen Q., Peng S., Guo S. (2013) Does chloroplast size influence
photosynthetic nitrogen use efficiency? PloS One 8,e62036
769
Lide D.R. (1999) Handbook of Chemistry and Physics. CRC Press, New York
770
771
772
Lingard M.J., Gidda S.K., Bingham S., Rothstein S.J., Mullen R.T., Trelease R.N. (2008)
Arabidopsis Peroxin11c-e, Fission1b, and Dynamin-related protein3A cooperate in
cell cycle-associated replication of peroxisomes. The Plant Cell 20,1567–1585
773
774
Lux I., Koblinger L.I. (1991) Monte Carlo particle transport methods: Neutron and
photon calculations. CRC Press
775
776
777
778
Makino A, Sakashita H, Hidema J, Mae T, Ojima K, Osmond B (1992) Distinctive
responses of ribulose-1,5-bisphosphate carboxylase and carbonic anhydrase in wheat
leaves to nitrogen nutrition and their possible relationship to CO2 transfer resistance.
Plant Physiology 100,1737–1743
779
780
Nobel P.S. (1991) Physicochemical and environmental plant physiology. Academic
Press, San Diego
781
782
Pocker Y., Ng S.Y. (1973) Plant carbonic anhydrase: properties and carbon dioxide
hydration kinetics. Biochemistry 12,5127–5134
783
784
785
Pons T.L., Flexas J., von Caemmerer S., Evans J.R., Genty B., Ribas-Carbo M., Brugnoli
E. (2009) Estimating mesophyll conductance to CO2: methodology, potential errors,
and recommendations. Journal of Experimental Botany 60,2217–2234
56
786
787
788
789
Price D., von Caemmerer S., Evans J.R., Yu J.W., Lloyd J., Oja V., Kell P., Harrison K.,
Gallagher A., Badger M. (1994) Specific reduction of chloroplast carbonicanhydrase activity by antisense rna in transgenic tobacco plants has a minor effect
on photosynthetic CO2 assimilation. Planta 193,331–340
790
791
792
Raszewski G., Diner B.A., Schlodder E., Renger T. (2008) Spectroscopic properties of
reaction center pigments in photosystem II core complexes: revision of the multimer
model. Biophysical Journal 95,105–119
793
794
Richter E., Ehwald R. (1983) Apoplastic mobility of sucrose in storage parenchyma of
sugar beet. Physiologia Plantarum 58,263–268
795
796
797
Staehelin L.A. (2003) Chloroplast structure: from chlorophyll granules to supramolecular architecture of thylakoid membranes. Photosynthesis Research 76,185–
196
798
799
800
Steele, Mark, Gitelson, A. A., Rundquist, Donald (2008) Nondestructive estimation of
leaf chlorophyll content in grapes. American Journal of Enology and Viticulture
59,299–305
801
802
803
Terashima I., Hanba Y.T., Tazoe Y., Vyas P., Yano S. (2006) Irradiance and phenotype:
comparative eco-development of sun and shade leaves in relation to photosynthetic
CO2 diffusion. Journal of Experimental Botany 57,343–354
804
805
Terashima I., Inoue Y. (1985) Palisade tissue chloroplasts and spongy tissue chloroplasts
in spinach: Biochemical and ultrastructural differences. Plant Cell Physiol 26,63–75
806
807
808
Tholen D., Boom C., Noguchi K., Ueda S., Katase T., Terashima I. (2008) The
chloroplast avoidance response decreases internal conductance to CO2 diffusion in
Arabidopsis thaliana leaves. Plant, Cell and Environment 31,1688–1700
809
810
811
Tholen D., Zhu X.-G. (2011) The mechanistic basis of internal conductance: a theoretical
analysis of mesophyll cell photosynthesis and CO2 diffusion. Plant Physiology
156,90–105
812
813
814
815
816
Tomás M., Flexas J., Copolovici L., Galmés J., Hallik L., Medrano H., Ribas-Carbó M.,
Tosens T., Vislap V., Niinemets Ü. (2013) Importance of leaf anatomy in
determining mesophyll diffusion conductance to CO2 across species: quantitative
limitations and scaling up by models. Journal of Experimental Botany 64,2269–
2281
817
818
819
Tsuzuki M., Miyachi S., Edwards G. (1985) Localization of carbonic anhydrase in
mesophyll cells of terrestrial C3 plants in relation to CO2 assimilation. Plant Cell
Physiology 26,881 – 891
57
820
821
Tuchin V.V. (2007) Tissue Optics: Light scattering methods and instruments for medical
diagnosis, 2nd ed. 840
822
823
Tuchin V.V. (2008) Handbook of optical sensing of glucose in biological fluids and
Tissues. CRC Press
824
825
826
Verboven P., Herremans E., Helfen L., Ho Q.T., Abera M., Baumbach T., Wevers M.,
Nicolaï B.M. (2015) Synchrotron X-ray computed laminography of the 3-D anatomy
of tomato leaves. The Plant Journal 81,169–182
827
828
Verschoor A., Warner J.R., Srivastava S., Grassucci R. a, Frank J. (1998) Threedimensional structure of the yeast ribosome. Nucleic acids research 26,655–661
829
830
831
832
Di Vittorio A. V. (2009) Enhancing a leaf radiative transfer model to estimate
concentrations and in vivo specific absorption coefficients of total carotenoids and
chlorophylls a and b from single-needle reflectance and transmittance. Remote
Sensing of Environment 113,1948–1966
833
834
835
Wang L.H., Jacques S.L., Zheng L.Q. (1995) MCML - Monte Carlo modeling of photon
transport in multi-layered tissues. Computer Methods and Programs in Biomedicine
47,131–146
836
837
838
Watte R., Aernouts B., Saeys W. (2012) A multilayer Monte Carlo method with free
phase function choice. Proceedings of the Society of Photo-Optical Instrumentation
Engineers: Vol. 8429. SPIE Photonics Europe. Brussels, pp 1–12
839
840
841
842
Williams T.G., Flanagan L.B., Coleman J.R. (1996) Photosynthetic gas exchange and
discrimination against 13CO2 and C18O16O in tobacco plants modified by an
antisense construct to have low chloroplastic carbonic anhydrase. Plant Physiology
112,319–326
843
844
Winter H., Robinson D.G., Heldt H.W. (1994) Subcellular volumes and metabolite
concentrations in spinach leaves. Planta 193,530–535
845
846
847
848
849
Yin X., Struik P.C., Romero P., Harbinson J., Evers J.B., Van Der Putten P.E.L., Vos J.
(2009) Using combined measurements of gas exchange and chlorophyll
fluorescence to estimate parameters of a biochemical C3 photosynthesis model: a
critical appraisal and a new integrated approach applied to leaves in a wheat
(Triticum aestivum) canopy. Plant, Cell and Environment 32,448–464
58