On the mechanism of C4 photosynthesis intermediate exchange between Kranz mesophyll and bundle sheath cells in grasses
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Journal of Experimental Botany, Vol. 59, No. 6, pp. 1137–1147, 2008
doi:10.1093/jxb/ern054 Advance Access publication 28 March, 2008
OPINION PAPER
On the mechanism of C4 photosynthesis intermediate
exchange between Kranz mesophyll and bundle sheath
cells in grasses
Paweł Sowiński1,2,*, Jarosław Szczepanik1 and Peter E. H. Minchin3
1
University of Warsaw, Institute of Plant Experimental Biology, Department of Plant Growth and Development,
Miecznikowa 1, 02-096 Warszawa, Poland
2
Plant Breeding and Acclimatization Institute, Plant Biochemistry and Physiology
Department, Radzików, 05-870 Błonie, Poland
3
The Horticulture and Food Research Institute of New Zealand Ltd, 412 No 1 Road, RD 2 Te Puke 3182,
Downloaded from http://jxb.oxfordjournals.org/ by guest on September 16, 2015
New Zealand
Received 10 October 2007; Revised 4 February 2008; Accepted 5 February 2008
Abstract plasmodesmatal microchannels is not adequate to ex-
plain the C4 metabolite exchange during C4 photosyn-
C4 photosynthesis involves cell-to-cell exchange of
thesis. Alternative mechanisms are proposed, involving
photosynthetic intermediates between the Kranz meso-
the participation of desmotubule and/or active mech-
phyll (KMS) and bundle sheath (BS) cells. This was
anisms as either apoplasmic or vesicular transport.
believed to occur by simple diffusion through plentiful
plasmodesmatal (PD) connections between these cell Key words: C4 photosynthesis, grasses, modelling,
types. The model of C4 intermediates’ transport was plasmodesmata, symplasmic transport.
elaborated over 30 years ago and was based on
experimental data derived from measurements at the
time. The model assumed that plasmodesmata occu-
pied about 3% of the interface between the KMS and
C4 photosynthesis
BS cells and that the plasmodesmata structure did not
restrict metabolite movement. Recent advances in the The C4 carbon cycle involved in carbon dioxide trapping
knowledge of plasmodesmatal structure put these prior to photosynthesis has been well researched since its
assumptions into doubt, so a new model is presented discovery in the late 1960s. This process involves
here taking the new anatomical details into account. If morphological and physiological adaptations, so it has
one assumes simple diffusion as the sole driving been studied by anatomists, biochemists, and physiolo-
force, then calculations based on the experimental gists. This pathway enables carbon dioxide to be concen-
data obtained for C4 grasses show that the gradients trated at the site of Rubisco action, reducing
expected of C4 intermediates between KMS and BS photorespiration and enhancing water use efficiency.
cells are about three orders of magnitude higher than Primary carbon assimilation (PCA) takes place in the
experimentally estimated. In addition, if one takes into Kranz mesophyll (KMS) cells. The product of phospho-
account that the plasmodesmata microchannel diame- enolpyruvate (PEP) carboxylation, i.e. oxalacetate is
ter might constrict the movement of C4 intermediates converted to either malate or aspartate. C4 acids are
of comparable Stokes’ radii, the differences in concen- exported to the bundle sheath (BS) cells where they are
tration of photosynthetic intermediates between KMS decarboxylated. The released CO2 is incorporated into the
and BS cells should be further increased. We believe Calvin cycle for primary carbon reduction (PCR). The
that simple diffusion-driven transport of C4 inter- route of decarboxylation depends on the sub-type of C4
mediates between KMS and BS cells through the photosynthesis: NADP-malic enzyme (NADP-ME),
* To whom correspondence should be addressed. E-mail: pawes@biol.uw.edu.pl
ª The Author [2008]. Published by Oxford University Press [on behalf of the Society for Experimental Biology]. All rights reserved.
For Permissions, please e-mail: journals.permissions@oxfordjournals.org1138 Sowiński et al.
NAD-malic enzyme (NAD-ME), and PEP-carboxykinase Plasmodesmata linking KMS and BS cells in C4 grasses
(PEP-CK). After reduction, a fraction of the assimilated differ in ultrastructure and dimensions (Botha et al., 2005,
carbon moves back from the BS to the KMS cells as and literature cited herein). In some species, sphincters
pyruvate, where it is regenerated into PEP. Phospho- may occur on one or both cell sides (Evert et al., 1977;
glyceride (PGA) and triosephosphate (TP) are also Robinson-Beers and Evert, 1991; Botha et al., 2005).
shuttled to the KMS (Furbank and Foyer, 1988). KMS/BS plasmodesmata diameter is of approximately
The architectural arrangement of the cells involved in 100 nm, however, if suberin lamellae are present
photosynthesis and photosynthate export optimizes this plasmodesmata diameter might be restricted down to
cell-to-cell exchange. According to Gamalei’s (1991) approximately 40 nm (Robinson-Beers and Evert, 1991;
classification based upon the route of phloem loading, the Botha et al., 2005). Even if plasmodesmata do not cross
veins in C4 plants represent a type 2c ultrastructure, suberin lamellae (NAD-ME sub-type), they show con-
specific for many C4 and crassulacean acid plants. In striction at the neck regions down to approximately 40 nm
plants with this vein ultrastructure type, Kranz mesophyll (Valle et al., 1989; Sowiński et al., 2007). The diameter
layer(s) surround the bundle sheath layer, and are inter- of plasmodesmata at the KMS/BS interface in the di-
connected by numerous plasmodesmata, while the number cotyledonous C4 plant Salsola kali L. was approximately
of plasmodesmata between companion cell/sieve tube 50 nm (Olesen, 1975).
complex and adjoining cells is limited.
In C4 grasses, symplasmic continuity exists between the Mechanism of C4 intermediate transport between
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Kranz mesophyll, the bundle sheath, and the vascular KMS and BS cells
parenchyma (VP). In some species (Botha, 1992) or sub- It has been proposed that C4 photosynthesis intermediates
species (Sowiński et al., 2001), symplasmic continuity were transported between KMS and BS cells by means of
occurs between bundle sheath cells and companion cells, diffusion, driven by a concentration gradient (Leegood,
but this is rare. In grasses, sieve tubes in small and 2000, and citations therein). This was supported by
intermediate vascular bundles are of two types: thin- estimations of concentration differences of the main
walled sieve tubes connected to companion cells, and photosynthetic metabolites in maize (Leegood, 1985; Stitt
thick-walled sieve tubes connected to vascular paren- and Heldt, 1985) that were in agreement with values
chyma cells. The role of the thick-walled sieve tubes is obtained by modelling transport of the C4 intermediates
still unknown, while the companion cell/thin-walled sieve (Osmond, 1970; Hatch and Osmond, 1976). The model,
tube complex is responsible for phloem loading (Fritz elaborated over 30 years ago, was based on the experi-
et al., 1983). There are some anatomical differences mental data of Tyree (1970). Authors assumed that
among C4 photosynthesis sub-types, manifested mostly in plasmodesmata occupied about 3% of the interface
the distribution of BS chloroplasts, located centrifugally in between the KMS and BS cells and that the plasmodes-
NADP-ME, PEP-CK, and PCK-like NAD-ME species mata structure did not constrict metabolite movement.
and centripetally in the classical NAD-ME species Recent advances in knowledge of plasmodesmatal struc-
(Ohsugi and Murata, 1986; Dengler et al., 1994; Giussani ture throw doubt on these assumptions, so these are
et al., 2001; Ueno et al., 2006). There is general revised, taking into account the new anatomical details.
agreement that exchange of C4 photosynthetic intermedi- The number of plasmodesmata linking KMS and BS
ates between KMS and BS cells is solely through cells in C4 plants is well documented (Botha, 1992; Cooke
plasmodesmata (Hattersley and Browning, 1981; Hattersley, et al., 1996; Sowiński et al., 2007) and it is agreed that
1987, but see Eastman et al., 1988a, b). The role of this number is higher in C4 than in C3 plants (Botha,
plasmodesmata in C4 photosynthesis is supported by the 1992; Cooke et al., 1996), with C4 plants having
positive correlation between the number of plasmodes- approximately 6 plasmodesmata lm2 of KMS/BS in-
mata and the net photosynthesis rate found in several C4 terface (Table 1). With a plasmodesma diameter of 40 nm,
grasses (Botha, 1992; Sowiński et al., 2007). In species the total plasmodesmatal cross-section occupies approxi-
that synthesize sucrose in KMS, it is symplastically mately 0.8% of the cellular interfaces. However, accord-
transported through at least three cells: KMS–BSC–VP, ing to present knowledge of plasmodesmata ultrastructure,
before being loaded into the phloem. The crucial role of part of the cross-section is occupied by the desmotubule
plasmodesmata in the export of photosynthates from and transport takes place within the 7–9 microchannels
leaves finds strong support in studies of a maize mutant, (Overall et al., 1982; Ding et al., 1992), each with
SXD-1 (Russin et al., 1996), in which plasmodesmata at a diameter of 2.5–4 nm (Overall et al., 1982; Roberts and
the BSC/VP interface were occluded by callose (Botha Oparka, 2003). Therefore the cross-section open for
et al., 2000), resulting in the arrest of sucrose export. All transport would constitute only ;0.07% of total KMS/BS
these data support the conclusion that the rates of C4 interface area, i.e. two orders of magnitude less than is
photosynthesis and photosynthate export depend on the assumed for models postulated 30 years ago. With this
number and conductivity of plasmodesmata. limitation on the area available for exchange, simpleMechanism of C4 photosynthesis transport 1139
Table 1. Properties of plasmodesmata (PD) at the Kranz mesophyll (KMS) and bundle sheath (BS) interface and assumptions for the
model on symplasmic transport between photosynthetic cells in C4 grasses
Feature Values or phenomenon reported Value or phenomenon Implications of assumed value
by other authors or possible assumed in the current
in vivo situation model
Length of a PD between 150–250 nma 150 nm The shorter transport channel, the more
KMS and BS cells efficient diffusion
Diameter of single microchannel 2.5–4.0 nmb 4.0 nm The wider transport channel, the more
efficient diffusion
Tortuousity of a microchannel Tortuousb Straight High tortuousity factor lowers diffusion
coefficient inside a transport channel
Number of microchannels per PD 7–9b 9 The higher number of channels, the more
efficient diffusion
PD shape in longitudinal view Constriction at neck regions or at A cylinder of equal thickness Neck regions act as bottlenecks, limiting
crossing of suberin lamella diffusion coefficient
BS circumference KMS/BS interface contributes to KMS/BS interface contributes Shorter cell interface raises the volume
20–50% of the BS circumference to 50% of the BS fraction of plasmodesmatal transport channels,
circumference that, in turn, raises the diffusion coefficient
Molecules transported Various types of small molecules Only C4 metabolites, triose The presence of other molecules inside
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through KMS/BS PD and probably proteins and RNAs phosphates and sucrose microchannels could affect diffusion of C4
metabolites
Interactions between Bidirectional transport of molecules Absent Interactions between transported molecules
transported molecules lower diffusion coefficients of the molecules
Interactions between transported Transport of molecules of size Absent Interactions between transported molecules
molecules and microchannel compared to microchannel and the channel wall lower diffusion
diameter coefficients of the molecules
Molecule shape Transported molecules differ Each transported molecule is
in shape a rigid sphere of radius rST,
equal to the Stokes’ radius
Polarity of transported Negatively charged molecules Molecules have no Charged molecules interact with structural
metabolites electric charge proteins of PD and other molecules
transported through microchannelsc
Hydration spheres around Present Absent Hydration spheres raise molecular radii of
transported molecules transported metabolites that results in a
decreased diffusion coefficient
a
Botha et al. (2005); Botha et al. (1993); Botha et al. (1982); Botha and Evert (1988); Robinson-Beers and Evert (1990); Sowiński et al. (2007).
b
Ding et al. (1992); Overall et al. (1982).
c
For details, see Tyree (1970) and Woermann (1976).
diffusion would not seem to be sufficient to account for membrane, with microchannels acting as the pores. Then,
the volume of metabolites being transported. This problem the transport rate through such membranes will be affected
has led us to propose new calculations. Our calculations in two ways: by the frequency of pores in a membrane and
are based on the experimental data obtained for C4 by the pore size. The importance of the porosity factor on
grasses, representing all three C4 sub-types (Botha et al., the diffusion coefficient is rather obvious—the more pores
1982; Ohsugi and Murata, 1986; Botha and Evert, 1988; within a membrane, the larger the space for diffusion
Valle et al., 1989; Botha, 1992; Soros and Dengler, 1998; (Bret-Harte and Silk, 1994; Patrick, 1997).
Ueno et al., 2006; Sowiński et al., 2007) and show that We are aware that plasmodesmatal microchannels are
the expected gradients between KMS and BS cells of C4 not simple tubes, but complex and irregular structures
intermediates are much higher than experimentally esti- with many fjord-like structures branching out from the
mated. These calculations confirm that diffusion-driven channel’s lumen. Such channel architecture might be
transport of C4 intermediates between KMS and BS cells thought to impede metabolite flux. However, while
through the plasmodesmatal microchannels is not ade- surface roughness does affect diffusivity of a single mole-
quate to explain the observed concentration differences. cule, it has no effect on transport diffusivity. This differ-
An alternative mechanism is proposed. ence is of great significance when the channel is rough
even at the molecular level (Malek and Coppens, 2003),
as in plasmodesmatal microchannels, which have diam-
Simple diffusion: first approximation
eters similar to the size of the transported metabolites (the
Diffusion through the plasmodesmatal microchannels in diameters of photosynthesis intermediates are calculated
the cell wall can be treated as diffusion within a porous further).1140 Sowiński et al.
The other factor concerning plasmodesma architecture is Dengler, 1998; Ogle, 2003; Ueno et al., 2006; Sowiński
its possible helical arrangement (Overall et al., 1982; Ding et al., 2007).
et al., 1992; Roberts, 2005). Diffusion will be most The area of KMS/BS cell walls (SW) mm2 of leaf area
efficient, if transport channels are straight cylinders. If was calculated as:
they are tortuous, the diffusion pathway inside a channel
will increase. This may be the case of plasmodesmatal SW ¼ 1000IBS CBS nV ð2Þ
microchannels. Anyway, without detailed knowledge on where 1000 is a conversion factor, since 1 mm ¼ 1000
plasmodesmata ultrastructure, a helical arrangement of lm, IBS is equal to 0.5 and allows for the contribution of
microchannels could not be taken into account. intercellular spaces to BS circumference (Table 1), CBS is
a circumference of BS cells (Table 2), nV gives the
Assumptions for the model number of veins in leaf segment of 1 mm2 (Table 3).
Assuming that diffusion is the only mechanism involved Total cross-sectional area of microchannels (TSK) is
in transport of metabolites between KMS and BS cells and given by:
that this is through the microchannels of the plasmodes-
mata, then there must be a sufficient concentration TSK ¼ 9fPD SK ð3Þ
gradient of each metabolite to sustain diffusion flow given
for nine microchannels per plasmodesma (Table 1), fPD is
by Fick’s law:
the number of plasmodesmata mm2 of leaf area (Table 3),
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J ¼ D=c ð1Þ and SK is the cross-sectional area of a single microchannel
(SK¼12.56 nm2).
@c
where =c ¼ @x denotes concentration gradient, and D is On the basis of equations (2) and (3), u¼TSK/SW is
the diffusion coefficient for the specific metabolite. defined as the surface fraction of plasmodesmatal micro-
To calculate the concentration gradient necessary to channels in the KMS/BS cell walls mm2 of leaf area.
sustain diffusion between KMS and BS cells, we start The results of calculations of u made for different C4
with several assumptions, most of them intentionally photosynthesis sub-types are shown in Table 3. The
chosen as favourable for diffusion. The assumptions are surface fraction of microchannels in NADP-ME and PCK
shown in Table 1. sub-types is just about 0.06% and in NAD-ME species
having the highest u values, it is only 0.3%.
Biometric data and cross-section of transport channels
To calculate the symplasmic flow of photosynthates Diffusion coefficients for transported metabolites
between KMS and BS cells, experimental data of six C4
Diffusion coefficients in water for each metabolite were
grasses have been considered: Zea mays (NADP-ME),
calculated using the Stokes–Einstein formula:
Digitaria sanguinalis (NADP-ME), Themeda triandra
(NADP-ME), Panicum miliaceum (classical NAD-ME), kT
Eragrostis plana (classical NAD-ME), and Panicum DðiÞ ¼ ð4Þ
6pgrST
maximum (PEP-CK). Panicum miliaceum and Eragrostis
plana will be further referred to as NAD-ME species. All where D(i) is the diffusion coefficient for metabolite i of
biometric and carbon flux data (Table 2) have been taken, Stokes’ radius rST in solution of viscosity g and
or calculated, from published data (Botha et al., 1982; temperature T¼298.15 K and k¼Boltzman’s constant
Oshugi and Murata, 1986; Botha, 1992; Soros and (1.3831023 J K1).
Table 2. CO2 assimilation rates and biometric parameters for different C4 photosynthetic sub-types in grasses
Mean values are shown in parenthesis. PD, plasmodesmata; KMS, Kranz mesophyll cell(s); BS, bundle sheath cell(s).
Photosynthetic sub-type NADP-MEa NAD-MEa PEPCKa
CO2 assimilation (lmol m2 s1) 13.00–23.00 23.00–27.00 22.00–23.00
(19.30) a, b (25.00) a, b (22.50) a, b
IVD, Interveinal distance (lm) 86.30–123.60 149.79–213.60 116. 61–148.20
(109.88) a, b, c, d, e, f, g (171.76) a, b, c, d, e, f (131.75) a, b, c, d, e
CBS, Circumference of BS cells (lm) 153.20–211.50 240.40–246.70 263.80–292.70
(182.29) a, b, g (243.55) a, b (278.25) a, b
nPD, number of PD per lm of vein (lm1) 284.92–559.00 2587.35–3045.00 574.00–857.41
(440.31) a, b (2816.17) a, b (715.70) a, b
PD per lm2 KMS/BS interface (lm2) 3.13–6.23 20.97–25.33 3.92–6.53
(4.74) a, b, h (23.13) a, b (5.22) a, b
a
(a) Data from Sowiński et al. (2007); (b) data from Botha (1992); (c) calculated from Ogle (2003); (d) values from Ohsugi and Murata (1986);
(e) data from Ueno et al. (2006); (f) data from Soros and Dengler (1998); (g) calculated from Botha et al. (1982); (h) data from Cooke et al. (1996).Mechanism of C4 photosynthesis transport 1141
Stokes’ radii for transported metabolites (Table 2) were be built into triose phosphates (C3-P), which in turn were
determined using HyperChem 7.5 Student software completely used for sucrose synthesis. It was assumed that
(www.HyperChem.com), with all metabolites assumed to for NADP-ME species sucrose was synthesized in KMS
have no hydration spheres around them. The results of cells only, while for NAD-ME and PEP-CK species only
calculations are shown in Table 4 half the sucrose was produced in KMS cells (Ohsugi and
There is no agreement on the viscosity of the cytoplasm. Huber, 1987; Usuda and Edwards, 1980). For all species
The mobility of BCECF (fluorescein derivate, MW 520) examined, 60% of synthesized sucrose was assumed to be
in cytoplasm using spot photobleaching was a quarter of exported to the phloem (Sowiński et al., 2007).
that in water (Verkman, 2002), while in vivo measure- Metabolite fluxes (J) were expressed here as a number
ments of GFP (27 kDa) movement in Escherichia coli was of a given metabolite molecules [nM, (moles)] transported
one-tenth of that in water (Sear, 2005, and references through 1 nm2 of single channel’s cross-section
therein). However, in our calculations, the lowest reported (SK¼12.56 nm2) in 1 s, using the following equation:
value (1.2 mPa s) was used for the viscosity of the nM
cytoplasm’s aqueous phase (Fushimi and Verkman, 1991). J¼ ð5Þ
9fPD SK
The calculated diffusion coefficients for all considered
metabolites are given in Table 4. The calculated data are Calculated metabolite fluxes are given in Table 5.
comparable to values assumed by other authors (Hatch The required concentration differences (@c) between
and Osmond, 1976).
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KMS and BS cells to give the estimated flow rates for
each metabolite was calculated using the transformed
Metabolite fluxes and concentration differences equation (1):
required to sustain diffusion between KMS and BS
@x
cells @c ¼ J ð6Þ
D
The stoichiometry between carbon assimilation and C4
metabolites transported between KMS and BS cells is where J is given by equation (5), @x equals length of
shown in Fig. 1. All the assimilated CO2 was assumed to plasmodesma (150 nm, Table 1), and D is the
Table 3. Biometric parameters used in the model, calculated on the basis of mean values from Table 2
NADP-ME NAD-ME PEPCK Calculation formula
2 2
nV, number of veins in 1 mm of leaf blade (mm ) 9.10 5.82 7.59 nv¼ 1000
IVD
2 2 6 6 6
fPD, number of KMS/BS PD in 1 mm of leaf blade (mm ) 4.01310 16.39310 5.43310 fPD¼1000nVnPD
TSK, total cross-sectional area of plasmodesmatal microchannels 0.453109 1.853109 0.613109 TSK¼9fPDSKa
in cell walls between Kranz mesophyll (KMS) and bundle
sheath (BS) cells (nm2)
SW, total area of KMS/BS cell walls (nm2) 0.8331012 0.7131012 1.0631012 SW¼1000IBSCBSnVb
3 3 3
u, surface fraction of microchannels in KMS/BS cell 0.55310 2.62310 0.58310 u ¼ TS
Sw
K
walls of 1 mm2 leaf blade
a
SK area of single microchannel’s cross-section (12.56 nm2).
b
See text for details.
Table 4. Molecular size, diffusion coefficients and confinement factors for metabolites transported between Kranz mesophyll and
bundle sheath cells
Metabolite rST: Stokes’ D, diffusion Dcyt, diffusion Confinement factor inside Confinement factor (Kc) inside
radius (nm) coefficient in coefficient in microchannel with desmotubule of diameter
water (m2 s1) cytoplasma (m2 s1) diameter of 4 nm (Kc)
15 nm 25 nm 35 nm
Malate 0.27 8.1231010 6.7731010 0.56 0.86 0.92 0.94
Pyruvate 0.26 8.4031010 7.0031010 0.57 0.87 0.92 0.94
Alanine 0.26 8.4031010 7.0031010 0.57 0.87 0.92 0.94
Aspartate 0.34 6.4031010 5.3331010 0.47 0.83 0.89 0.92
PEP 0.35 6.3031010 5.2531010 0.47 0.83 0.89 0.92
C3-P 0.35 6.3031010 5.2531010 0.47 0.82 0.89 0.92
Sucrose 0.44 5.0031010 4.1731010 0.38 0.78 0.87 0.90
a
Assuming 1.2 times higher viscosity for cytoplasm than for water (Fushimi and Verkman, 1991).1142 Sowiński et al.
Fig. 1. Schematic diagram of transport processes during C4 photosynthesis. (A) NADP-ME sub-type, (B) NAD-ME sub-type, (C) PEP-CK sub-type.
Abbreviations: BS, bundle sheath cell; KMS, Kranz mesophyll cell; PD, plasmodesmata; C3-P, triose phosphates. Numbers in parentheses show how
many molecules of C4 metabolites must be transported through PD for each one molecule of CO2 assimilated. For amounts of C3-P and sucrose being
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transported, see ‘Metabolite fluxes’. PD are drawn without desmotobules, since microchannels in cytoplasmatic sleeve were assumed to be the only
transport pathway.
plasmodesmatal diffusion coefficient (DPD) taken to species, characterized by similar values of @c. These
be proportional to the surface fraction of microchannels discrepancies reflect different plasmodesmatal frequency
(u, Table 3) in KMS/BS cell walls for a leaf segment of (Table 2).
1 mm2 and cytoplasmatic diffusion coefficient (Dcyt,
Table 4): Conclusions to the simple diffusion approximation
DPD ðiÞ ¼ Dcyt ðiÞu ð7Þ The estimated concentration differences required assum-
ing transport by diffusion through microchannels, were
The values of @c obtained in our model are shown in very high. These concentration differences, being tens of
Table 5. The calculated data have been compared with moles, seem unrealistic given that in the species studied to
experimental data obtained by Stitt and Heldt (1985). date, concentrations of C4 metabolites and triose phos-
Their data concerned concentrations of C4 intermediates phates were in the order of a few tens of millimoles
in KMS and BS cells of maize. These authors obtained (Hatch and Osmond, 1976; Leegood, 1985, 2000; Stitt
concentrations of C4 metabolites as high as a few and Heldt, 1985). Similar discrepancies were noticed by
hundreds of nanomoles per mg of chlorophyll (mg Chl). Bret-Harte and Silk (1994), when they estimated solute
They assumed that the chlorophyll was equally distributed deposition rates and corresponding fluxes in growing root
between KMS and BS cells and that the combined volume of Zea mays, assuming that diffusion was the only
of chloroplasts and cytoplasm was 40 ll per mg Chl. As mechanism for metabolite transport. Diffusion coefficients
a result, the estimated concentration of each metabolite and concentration gradients calculated by these authors
between KMS and BS cells was a few nanomoles per ll, were a few orders of magnitude higher than expected. Our
equal to a few milimoles per litre. Comparison of the data calculations of DPD and @c made using Bret-Harte and
of Stitt and Heldt (1985) with the values of @c we Silk’s model gave values similar to the approach assuming
calculated using the different approaches, are shown in transport through microchannels (data not shown).
Table 3.
In addition, the values of @c proposed by Weiner et al.
(1988) are shown in Table 5. Authors assumed a concen-
Simple diffusion: second approximation
tration gradient of 1 mM to describe the rate of diffusion
of particular photosynthetic metabolite into BS cells. All C4 metabolites considered were of similar size and
Calculated concentration differences of metabolites therefore had similar diffusion coefficients (Table 4). All
required to sustain diffusion are higher by about three had low molecular weight, compared with the plasmodes-
orders of magnitude, as compared to experimental data mata exclusion limit of about 0.9 kDa, but their Stokes’
(Stitt and Heldt, 1985; Weiner et al., 1988). Moreover, radii (rST) were quite high compared with the micro-
differences between photosynthetic types were observed: channel radius (rK¼2 nm). This observation raises queries
in NAD-ME species, concentration differences were about of our assumption (Table 1) that microchannel diameter
three times lower than in NADP-ME and PEP-CK does not affect metabolite movement.Mechanism of C4 photosynthesis transport 1143
Table 5. Metabolite fluxes (mol nm s ) and concentration differences of photosynthetic metabolites (mol dm3) between Kranz
2 1
mesophyll and bundle sheath cells in C4 grasses
Photosynthetic C4 metabolite Metabolite fluxes Concentration differencies of metabolites between Kranz mesophyll and bundle sheath cells
sub-type through single
microchannel) Experimental No constrictions Constrictions from Metabolites passing
data from channel size, all channel size present, from KMS to BS
metabolites move all metabolites move move inside
through palsmodesmatal through plasmodesmatal desmotubule of diameter
microchannels microchannels
15 nm 25 nm 35 nm
NADP-ME Malate 4.2631020 0.018a 17.16 30.64 8.20 1.00 0.26
Pyruvate 4.2631020 0.005a 17.16 30.10 30.10
C3-P 1.4231020 0.010a 7.51 15.98 15.98
Sucrose 0.2131020 1.40 3.68 0.73 0.09 0.02
NAD-ME Alanine 1.3531020 0.001b 1.10 1.93 1.93
Aspartate 1.3531020 0.001b 1.45 3.08 0.72 0.09 0.02
C3-P 0.2231020 0.001b 0.25 0.53 0.53
Sucrose 0.0331020 0.001b 0.05 0.13 0.02 0.003 0.001
PEP-CK Malate 1.8331020 – 6.99 12.48 3.33 0.40 0.10
Pyruvate 1.8331020 – 6.76 11.85 11.85
Aspartate 1.8331020 – 8.88 18.89 4.38 0.52 0.13
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PEP 1.8331020 – 9.01 19.17 19.17
C3-P 0.6131020 3.00 6.38 6.38
Sucrose 0.0931020 0.56 1.47 0.30 0.03 0.01
a
Data from Hatch and Osmond (1976).
b
Values based on Weiner et al. (1988).
The dependence of diffusion coefficient on pore di- correspondingly in approximately twice higher concentra-
ameter is not simple. If the pore diameter is over ten times tion differences of photosynthetic intermediates between
that of the transported molecule, then diffusion through KMS and BS cells necessary to sustain the transport of
the pore will equal that of the bulk fluid, while with a pore photosynthates between KMS and BS cells, as compared
diameter smaller than two molecular diameters, single file to the data obtained in the first approximation (Table 5).
diffusion will occur (Cui, 2005). For a ratio of pore width
to molecular diameter of 2–10 (relevant to the metabolites
we considered, where this was 4.54 to 7.69) pore
diffusivity falls between those two extremes (Liu et al., Simple diffusion model: the need for the
2005). Taking this into account, transport through a micro- third approximation?
channel is the result of at least three types of diffusion: The model presented here is a highly simplified version of
continuous diffusion (diffusion in bulk fluid), Knudsen’s the situation encountered in planta. However, it shows,
diffusion, and surface diffusion, the latter two reducing that even under assumptions favouring diffusion, the
transport (Gudmundsson, 2003; Valiullin et al., 2004; Liu concentration differences of transported metabolites be-
et al., 2005). However, for the simplicity of current tween KMS and BS cells necessary for maintaining the
approximation, the diffusion through the microchannels current net photosynthetic rates are high and hardly
was assumed to be continuous, and to vary with the ratio possible in living cells. If this model is to be valid in
of the channel’s diameter to the molecular size, according describing transport processes in vivo, several additional
to the confinement factor (Kc), defined as: assumptions, neglected here, must be taken into consider-
ation. The most important constriction to the model is that
rst 4 C4 photosynthesis, because of its nature, needs exchange
Kc ¼ 1 ð8Þ
rK of metabolites between cells, i.e. simultaneous movement
of some intermediates from KMS to BS, and others from
which is a simplification of Renkin’s (1954) approach, BS to KMS. As it is stated above, Stokes’ radii of
valid for rST/rK > 0.01. Equation (7) is now generalized photosynthetic metabolites are comparable to the micro-
to: channel radius. So the assumption (Table 1), that two
DPD ðiÞ ¼ Dcyt ðiÞuKc ð9Þ streams of molecules moving in opposite directions in
narrow channels do not disturb each other, is improbable.
The confinement factor varied from 0.38 to 0.54 (Table In addition, transport of other compounds simultaneously
4), results in a 2–3-fold slow down of diffusion inside the with the transport of photosynthetic intermediates; the
microchannel in relation to bulk fluid conditions, and existence of hydration spheres around polar molecules1144 Sowiński et al.
increasing the Stokes’ radius of a molecule; the specificity experimentally. For other C4 sub-types, these values were
of diffusion inside micropores cannot be disregarded. higher, but the difference was reduced to one order of
Therefore, one must be aware that taking these processes magnitude only.
into consideration will result in further increase of the Participation of desmotubules in cell-to-cell transport
concentration differences required to sustain diffusion. was postulated by Waigmann et al. (1997) for cotton
Clearly C4 plants do transport a large amount of extrafloral nectary trichomes expelling large amounts of
photosynthates. Photosynthesis in C4 plants, which might nectar. Desmotubules have also been postulated as a trans-
even excess 40 lmol CO2 m2 s1, produces a significant port route in the symplasmic phloem loading mechanism
amount of assimilates exchanged between KMS and BS (Gamalei et al., 1994). This sort of phloem-loading
cells symplasmically. Thus: (i) other diffusion pathways mechanism is related to so-called open (type 1) vein
apart from the plasmodesmal microchannels are involved; ultrastructure (Gamalei, 1991), where companion cells are
and (ii) another transport mechanism is involved in connected to adjoining mesophyll cells by numerous
metabolic exchange between KMS and BS cells. These plasmodesmata (more than 10 PD per lm2 of the cell
possibilities are considered below. interface). Symplasmic phloem loading was postulated to
be powered by polymer trapping mechanism (Turgeon,
1996), however, even in plants showing abundant plas-
Simple diffusion model: combined two-way metabolite modesmata linking companion cells and mesophyll
exchange utilizing desmotubule and microchannels cells, for the transport of carbohydrates from photosyn-
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of plasmadesmata thetic cells to companion cells/sieve tube complex other
If combined two-way metabolic exchange is assumed, mechanisms have been postulated as mass flow (Voitse-
then the second route remains to be found. This would khovskaja et al., 2006) or even apoplasmic transport
result in spatial separation of the transport from KMS to (Turgeon and Medville, 2004).
BS cells from that of the flux in the opposite direction. In C4 plants, metabolite concentration differences
The desmotubule seems to be an ideal candidate. The role between KMS and BS cells obtained when desmotubular
of desmotubules as a transport pathway was postulated transport was assumed to occur were more realistic than
many years ago, also in C4 plants (Evert et al., 1977). those from other approximations. Thus, desmotubule
Recently, this idea has been restated (Waigmann et al., involvement as a transport pathway in C4 photosynthesis
1997; Cantrill et al., 1999). One should underline, seems reasonable. However, it has been assumed that this
however, that there are strong arguments for the opinion pathway is available only for metabolites moving in one
that the desmotubule is a static, appressed structure at the direction (i.e. from KMS to BS cells). Transport in the
centre of PD, not available for transport processes and opposite direction remains a problem as there are only the
acting as a structural component, often referred to as microchannels available, and these require high values of
a central rod (Gunning and Overall, 1983; Tilney et al., @c (Table 5). This implies the involvement of transport
1991; Botha et al., 1993, Overall and Blackmann, 1996; mechanisms other than simple diffusion.
Ding, 1998).
In this approach, it is assumed that metabolites moving
from the KMS to the BS cells are transported inside Alternative mechanisms
desmotubules, while photosynthetic intermediates move Apoplasmic transport is an alternative to symplasmic
from BS to KMS in plasmodesmatal microchannels. transport. However, in the case of exchange of metabolites
Various possible desmotubule sizes (15, 25, and 35 nm in between KMS and BS cells, apoplasmic transport may be
diameter) have been considered, with the resulting questioned for two reasons. One is the suberin lamella
confinement factors (see Table 4) taken into consideration. within the KMS/BS walls of many C4 plants, which nearly
The metabolite fluxes and the desmotubule diffusion precludes apoplasmic transport of solutes (Hattersley, 1987;
coefficients were calculated as described in the section on Hatterlsey and Browning, 1981). It has also been shown
‘Metabolite fluxes and concentration differences required that PCMBS, an inhibitor of the proton pump, has no
to sustain diffusion between KMS and BS cells’ and the distinct effect on photosynthesis in maize, a C4 plant
concentration differences between photosynthetic cells, (Bourquin et al., 1990; Sowiński 1998), which clearly
necessary to maintain the current net photosynthesis rates, demonstrates that apoplasmic transport is not involved in
were estimated (Table 5). the photosynthate transport in that species. Unfortunately,
With the desmotubule assumed to be the additional such studies have not been performed with other C4
transport pathway for diffusion, the required concentration plants.
differences between KMS and BS cells decreased signif- There are two possible alternatives to simple diffusion,
icantly (Table 5). For NAD-ME species, when the widest the first being mass flow, postulated as an efficient means
desmotubule was taken into account, the differences of cell-to-cell transport (Anisimov and Egorov, 2002;
were similar to the metabolite concentrations estimated Voitsekhovskaja et al., 2006), and the second beingMechanism of C4 photosynthesis transport 1145
vesicular transport (Bil’ et al., 1976; Karpilov et al., 1976; SW total area of KMS/BS cell walls in leaf segment of 1 mm2
Evert et al., 1977), similar to that postulated for proteins (nm2)
T temperature (K)
and other high molecular weight molecules and viruses TSK total area of plasmodesmatal microchannels cross-section
(Chen and Kim, 2006). Vesicles could accumulate solutes in KMS/BS cell walls in leaf segment of 1 mm2 (nm2)
to very high concentrations, using transporters located in x diffusion pathway [nm]
the vesicle membrane. Vesicles could be unloaded at the
plasmodesma neck region in a manner similar to the
Acknowledgements
vesicle-mediated secreting transport system involving the
vacuole and plasmalemma (Echeveria, 2000). The idea of The authors wish to thank anonymous reviewers for suggestions
a vacuole–desmotubule–vacuole continuum (Gamalei, that have greatly improved the clarity of the paper.
1996; Rinne et al., 2001) is intriguing in this context.
However, we await experimental data to support these References
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