Journal of Experimental Botany, Vol. 52, No. 355, pp. 319-327,
February 2001
© 2001 Oxford University Press
Original Papers |
Xylem hydraulic conductivity related to conduit dimensions along chrysanthemum stems
1 Department of Plant Sciences, Wageningen University, Wageningen, The Netherlands
2 Plant Research International, Wageningen, The Netherlands
Received 12 June 2000; Accepted 12 October 2000
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Abstract |
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The stem xylem conduit dimensions and hydraulic conductivity of chrysanthemum plants (Dendranthemaxgrandiflorum Tzvelev cv. Cassa) were analysed and quantified. Simple exponential relations describe conduit length distribution, height dependency of conduit length distribution, and height dependency of stem hydraulic conductivity. These mathematical descriptions can be used to model the xylem water transport system. Within a chrysanthemum stem of 1.0 m, the conduit half-length (the length within which 50% of the conduits have their end) was 0.029 m at soil surface and decreased by half at a height of 0.6 m. With each 0.34 m increase in height up the stem, the hydraulic conductivity decreased by 50%. The resistance calculated from conduit lumen characteristics was 70% of the measured resistance. The remaining unexplained part of the hydraulic resistance is at least partly caused by inter-conduit connections.
Key words: Xylem conduit anatomy, hydraulic conductance, digital image analysis, Dendranthemaxgrandiflorum Tzvelev, vessel length distribution.
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Introduction |
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There are several quantitative studies of anatomical features of the xylem water transport system in plants (Fisher and Ewers, 1995
; Villar-Salvador et al., 1997; Ewers et al., 1997). In higher plants tracheary elements are the main conduits for water transport from roots to leaves. Dicotyledonous and monocotyledonous plants possess both tracheids and vessels. Tracheids are single tracheary cells while vessels are the product of longitudinally fused tracheary elements. Here both tracheids and vessels will be referred to as conduits. Bordered pit pairs connect neighbouring conduits. Conduits are of finite length and to pass from one conduit to another water must pass through bordered pit pairs.
The hydraulic conductivity of the xylem water transport system depends on the hydraulic conductivity within the conduit lumina and the hydraulic conductivity of the inter-conduit connections. Assuming the conduits as elliptic pipes arranged in parallel, it is possible to calculate the conductivity of the xylem conduit lumina in a stem segment from their cross-sectional dimensions (see Appendix). This calculated conductivity is higher than the measured conductivity since it does not include the inter-conduit resistance. Pickard (Pickard, 1981) stated that the resistance of conduit ends (i.e. bordered pits) may contribute significantly to the total resistance, but that a priori no accurate estimation of this resistance is possible due to the complex geometry of the system (see also Chiu and Ewers, 1993; Van Ieperen et al., 2000). However, it can be stated that bordered pits affect the resistance of stems with long conduits to a lesser extent than stems with short conduits. Thus diameter and length of the conduits and how they are interconnected determine the hydraulic properties of a vascular system.
The aim of the present study was to acquire a detailed but simple description of the hydraulic architecture in chrysanthemum stems in order to relate hydraulic conductivity to anatomical properties of xylem conduits, and to get a means to compare the hydraulic properties of different locations in one plant or phenotype, different cultivars or plants grown under different conditions. To understand the dynamics of water flow in plant stems (e.g. in case of induction and removal of embolisms), a proper knowledge of the hydraulic architecture of the stem is indispensable. In this study the anatomical basis of height dependency of hydraulic conductivity in chrysanthemum stems was investigated to test the method at various conductivities within one phenotype. Using digital image analysis, xylem conduit lengths and cross- sectional dimensions were quantified as a function of the height in the stem. Calculated cross-sectional hydraulic conductivities were integrated over the length of a stem segment and compared with the actually measured hydraulic conductivity.
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Materials and methods |
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Plant material
Dendranthemaxgrandiflorum Tzvelev (chrysanthemum) is a herbaceous perennial, originating from East Asia. It has pinnately lobed leaves spirally arranged around an erect stem. For the experiments (October 1998) chrysanthemum plants of the cultivar Cassa were propagated via stem cuttings. Rooted, 0.05 m long cuttings were transplanted into pots and grown in a greenhouse of Wageningen University (Van Meeteren and Van Gelder, 1999
). Total growth period from transplanting the cutting to harvest was about 12 weeks. Forty-four uniform flowering plants were collected early in the morning in the dark period (when they were fully turgid) and transported in their pots to the laboratory. A stem segment of 0.3 m in length was cut under water from each plant, using a new razor blade for each cut. The stem segments were cut off at 11 heights in four replicates. The 0.3 m stem segments began at the following heights above the soil surface: 0, 0.05, 0.10, 0.15, 0.20, 0.25, 0.30, 0.35, 0.40, 0.50, and 0.60 m. The cuts were always made in internodal regions of the stems. Leaves were removed from the stem segments with a razor blade, leaving 0.01 m of the petioles on the stem. No significant branches (and flowers) were present at the sampled heights. Hydraulic conductivity measurements and determination of the xylem conduit length distribution as well as light microscopic analysis on cross sections of the upper and lower end were carried out on the segments. The stem internode lengths were measured in all plants.
Hydraulic conductivity measurements
The upper end of each stem segment was connected to a silicone rubber tube with a pulling pressure difference of 25 kPa, created by a hanging water column. The lower end of the stem segment was placed in a container on a balance (Sartorius LC3200D), which contained an aqueous solution of sodium bicarbonate (1.5 mM), calcium chloride (0.7 mM) and copper sulphate (5 µM) at room temperature (20±2 °C; for details see also Van Meeteren et al., 2000). Water flow through the stem segment was calculated from weight changes measured with the balance, and recorded by a personal computer at 1 s-1 sampling rate and averaged over 30 s. Measured flow rates were corrected for evaporation at ambient pressure. Once the flow rate had remained stable for 10 min the hydraulic conductivity (CS) was calculated using the measured length of the stem segment (x), the applied pressure difference (
P) and the flow rate (q):
 | (1) |
Xylem conduit length distribution
Direct xylem conduit length measurements are hardly possible due to the enormous macroscopic lengths in combination with the microscopic diameters. A solution to this problem is to add a dye that cannot pass inter-vessel connections to a cut stem segment and to count how much vessels still continue at increasing distances from the plane of the cut. After the hydraulic conductivity measurements, and within 50 min after harvest, the stem segments were connected to a pumping system using the silicone rubber tubing attached for the conductivity measurement. With a pulling pressure difference of 50 kPa applied to the upper end of the segments, the lower end was placed in an aqueous 1% (w/w) suspension of red latex particles suspension (modification of the method of Zimmermann and Jeje, 1981). The latex suspension was prepared one day in advance to allow aggregates of particles to precipitate. Latex particles (<2 µm diameter) can easily enter an open conduit, but are too large to pass bordered pit pairs (Zimmermann, 1983). The particles are carried into the open conduits by the mass flow of water, eventually blocking them. Once water flow through the stem segments ceased, it was assumed that all cut open conduits were stained. The segments were removed, placed in plastic bags and stored in a refrigerator (4 °C) for at most 2 weeks before being subjected to further processing to determine xylem conduit length distribution. After storage, thick (2 mm) transversal sections were made with a razor blade. To distinguish the effect of nodes on conduit endings, two or more sections were cut out of every internode in order to have both nodal and internodal intervals. Images of the sections were made using a Sony 3CCD (DXC-950P) colour camera attached to a binocular microscope (Leica MZ8), giving a resolution of 13 µm per pixel. Earlier analyses of xylem conduit length distribution were based on counting individual filled conduits (Zimmermann and Jeje, 1981; Darlington and Dixon, 1991; Fisher and Ewers, 1995). In this study a technique based on measuring the total red-stained area of the stem using an image analysis programme (SCIL_Image 1.3, University of Amsterdam, Faculty of Mathematics and Computer Science, Amsterdam, The Netherlands) was adapted. This method enabled the analysis of hundreds of sections instead of just a few. The measured red area (amount of red pixels) of a section was divided by the average area of each conduit (see cross-sectional area analysis) to calculate the number of stained conduits in that section. For each stem segment the length distribution was described by its half-length (
c) as explained in the Appendix.
Cross-sectional area analysis
Portions of stem from just above and below the sampled stem segments were stored in 75% ethanol. Thin transverse sections were made with a slide microtome from the transverse planes that had faced to the upper and lower ends of the stem segments. The sections were embedded in Kayser's glycerol gelatine (Merck 9242, Darmstadt, Germany) on microscope slides. Digital images were made with the Sony 3CCD camera attached to a light microscope (Leitz Dialux) giving a resolution of 1.26 µm per pixel. More than 30 images were needed to acquire a detailed record of the entire xylem area of one transverse section. The number of conduits, (average) conduit cross-sectional area and the longest and shortest axis of an ellipse superimposed on the conduits were measured using the image analysis system. Conduits were distinguished from fibres by eye and marked with mouse clicks, using the presence of bordered pits as a criterion. Four sections (both ends of two 0.30 m segments sampled from heights of 0.10 m and 0.30 m above soil level) were analysed. Hydraulic conductivity of the sections was calculated assuming conduits as infinite, uniform elliptic, parallel arranged pipes. See Appendix for details on conductivity calculations.
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Results |
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Description of the plants
From 0.10–0.90 m along the stem, the internode length was more or less constant at between 34 and 41 mm (Fig. 1
). Below 0.10 m and above 0.90 m the internodes were shorter. The lowest 0.10 m of the stem developed before and during propagation and the part higher than 0.90 m developed during the generative phase; this may explain the shorter internode lengths at both ends of the stem. The plants had about seven flowers, originating from nodes higher on the stem than 0.60 m. The stems had one leaf at each node and apart from the flower branches the stems had no side shoots.
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Hydraulic conductivity
Figure 2 shows the results of the hydraulic conductivity measurements on the 0.30 m stem segments. Hydraulic conductivity decreased with height up the stem and this conductivity/height relationship could be described by an exponential function:
 | (2) |
=-2.09±0.16. In other experiments (not shown) it was found that conductivity was independent on the applied pressure.
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Conduit length distribution
An example of the red pixel counts (Y) on sections with increasing distances from the lower cut surface of the stem segment is shown in Fig. 3 and it is evident that there are many more short conduits than long ones. The log-scale plot shows the same data with a logarithmic Y-axis, revealing a decreasing exponential relation. Nodes (locations indicated with bars at the top of the graph) seem to have no effect on the distribution of conduit ends, because no slope differences are visible between adjacent pixel counts over nodal and inter-nodal intervals. By calculating the value of the conduit half-length (c), the length distribution of the conduit parts above the cut surface is completely described. For all 44 stem segments this half-length was determined. Red pixel counts lower than 15 were not taken into account for the analysis to prevent a rise of the signal-to-noise ratio close to zero. During storage the latex suspension filling the conduits occasionally showed some shrinkage close to the end of the stem segment. Red pixel counts from that regions were discarded. The mean values of c for the different heights in the stem are shown in Fig. 4. The value of c as function of the height in the stem was fitted with an exponential function:
 | (3) |
in metres and with c,0=0.029±0.001 and =-1.18±0.12.
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According to this function the estimated value of
c is 0.029 m at soil level, and halves with every 0.59 m higher up the stem. The correction of the pixel counts for average conduit area caused only a small change in the c,h function.
Cross-sectional area
Within the four analysed sections the number of conduits (more than 2000) was sufficient to determine the histograms of cross-sectional conduit dimensions. Estimations of whole stem conductivity based on only four sections need to be treated with caution. Figure 5a–c show the histograms for the major and minor axes and the areas of the conduits at 0.10, 0.30, 0.40, and 0.60 m height in the stem. The distributions of the major and minor axes have their highest frequency at, respectively, 14 and 8 µm. The areas vary from very small (less than 100 µm2) up to more than 1500 µm2. The frequency of occurrence of conduits within different area classes decreases with increasing area. More than 35% of all conduits lie within the smallest area class (0–100 µm2) used. The influence of the height in the stem on the distribution of conduit areas seems to be small. However, there are relatively more large conduits in the lower parts of the stem.
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The average cross-sectional conduit area (
) in the four sections is shown in Fig. 6a, and its dependency on height up the stem is given by:
 | (4) |
in µm2 and h in metres. This h-function was used in the conduit length determinations.
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The height dependency of total cross-sectional conduit number is given by (Fig. 6b
):
 | (5) |
The hydraulic conductivities calculated from cross-sectional dimensions of all conduits of the four sections are shown in Fig. 7. The hydraulic conductivity as a function of height in the plant (CSh) was estimated by (Fig. 7, curve 1):
 | (6) |
, curve 2, see Appendix for calculation):
 | (7) |
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Curve 3 in Fig. 7
shows the measured conductivity as determined in Fig. 2. Closed symbols indicate the measured conductivity in the segments that were used for anatomical analysis. The measured conductivity is for all heights in the stem about 30% lower than the calculated conductivity. This means that the calculated resistivity (reciprocal of the conductivity) in the stem segments is 30% lower than the measured resistivity of the stem segments. The data used to calculate hydraulic conductivity from sections also yielded the conductivity of the individual conduits. In Fig. 5d a histogram of the conductivity of the four sections per area class is shown. From Fig. 5c and Fig. 5d can be derived that the largest 5% of the conduits make 50% of the total conductivity.
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Discussion |
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In this study a mathematical description has been developed for both hydraulic conductivity and conduit length distribution as functions of height in a chrysanthemum stem. The authors prefer to describe the anatomical relations as exponential functions, even in cases where linear functions gave as good a fit. This preference for exponential functions was for several reasons. First, exponential functions can represent first order stochastic underlying processes. Secondly, exponential functions are independent upon a starting value (e.g. where you choose the h=0 point). Lastly, simple exponential functions do not generate negative values as results (e.g. negative conduit lengths).
With increasing distance from the cut end where the red latex was introduced, a greater percentage of red latex containing conduits come close to their upper end. Zimmermann suggested that conduits would show some tapering at the ends (Zimmermann, 1983), so it is not certain whether the ends of long conduits have the same average area as the average of all conduits in the cross-section. End tapering of the conduits makes the red pixel count per conduit less, and thus the estimated conduit half-length becomes lower than the real conduit half-length. On the other hand, the wide conduits have greater impact on pixel counts than the small conduits. If the wide conduits are longer than the small ones, the conduit half-length is overestimated. However, if there was a difference between the half-length determined by counts of red pixels and the real conduit half-length, this would be rather consistent throughout the stem. Thus the absolute half-length could have been under- or overestimated, but the estimation of half-length changes as a function of height in the stem is not altered. The alternative, counting the number of red conduits, can also cause uncertainties. Neighbouring conduits can be counted as one conduit, and the further from the cut surface, the fewer conduits are coloured red and relatively more individual conduits will be distinguished. This effect would result in an overestimation of the half-length.
Assuming that conduits are randomly located in the longitudinal direction, the length distribution of the entire conduits can be calculated using the double-difference algorithm (DD-algorithm; Zimmermann and Jeje, 1981; Zimmermann, 1983). This DD-algorithm has serious problems with non-random conduit ends (Tyree, 1993) and with stochastic fluctuations of the conduit counts. Therefore, in this paper, an alternative way to describe conduit lengths was used (Darlington and Dixon, 1991). In this method the part of the conduits below the plane of the cut is not taken into account and the length distribution of the parts of the conduits above the cut is directly analysed. In case of an exponential length distribution, as in these results, the entire conduit length distribution is simply described by the exponential length distribution function multiplied by the height above the cut surface. Description of the conduit length by one number (the half-length) provides an opportunity to compare different conduit length distributions. However, plants growing under (seasonal) changing conditions may show non-exponential conduit length distributions. In oak xylem very large conduits are formed in spring, differing in all dimensions from conduits formed in summer. Consequently, the conduit length distribution for oak therefore appears to be irregular (Zimmermann and Jeje, 1981). Thus, comparing single half-lengths is not applicable for all plants. A decrease of conduit length was found when going higher up the stem, which is also found in other plant species (Zimmermann and Potter, 1982). In contrast to the findings in some other diffuse-porous species (Salleo et al., 1984), conduit length in chrysanthemum stems decreases gradually and there are no special regions where conduits end. No relation was found between internode length and conduit length.
The number of conduits in the small-area classes were nearly the same throughout the stem, but the presence of a relatively small number of wide conduits caused the considerably higher conductivity in the lower stem. The presence of wider conduits in the lower stem is frequently encountered (Zimmermann and Potter, 1982; Zimmermann, 1978; Altus et al., 1985) and may be explained by lower auxin gradients further from the leaves (the six-point hypothesis from Aloni and Zimmermann, 1983).
The calculated resistivity in the studied chrysanthemum stems was about 70% of the measured resistivity. It is tempting to attribute the extra 30% of resistivity to that of the bordered pits, whose resistance is not included in this study's analysis. This step, however reasonable, needs to be considered critically. As in most estimations of conductivity based on anatomical studies so far undertaken (Ewers et al., 1997; Lovisolo and Schubert, 1998) the hydraulic conductivity was calculated from cross-sectional diameters of the conduits. However, slight errors in the measured diameter are amplified by the fourth power when the diameter is used to estimate the conduit hydraulic conductivity (Mapfumo, 1994). Additionally, the calculation of the hydraulic conductivity is based on the assumption that the conduits are all pipes arranged in parallel, whereas in reality the conduit system is a complex bundled network of conduits with finite length. In the studied stem segments, the leaf traces extended for four internodes before the connection with the other vascular bundles. It was calculated that probably 10% of the calculated conductivity was not effective during the conductivity measurements due to isolated bundles (J Nijsse, unpublished data). Other factors that can cause a lower conductivity than calculated are: non-laminar flow, changing of diameter within conduits, and the perforation plates of the conduit members (Chiu and Ewers, 1992). In chrysanthemum the perforation plates are wide and simple and therefore not thought to cause any significant additional hydraulic resistance. It cannot, therefore, be said exactly what percentage of the measured resistivity is caused by resistance of the conduit lumina, but if these cross-sectional area measurements are correct, the resistivity due to the properties of the vessel lumina is higher than 70%. Interestingly, this fraction is rather constant throughout the stem and seems, therefore, to be independent of conduit dimensions. In other words: higher in the stem the resistivity of conduit lumina is larger, but the resistivity due to inter-conduit passages is also larger. The increase of the inter-conduit resistivity is explained by the finding that higher in the stem the conduits are shorter. Thus higher in the stem the water flux has to cross more inter-conduit passages per unit of stem length. The dimensions of bordered pit pairs can also vary within one plant (Van Alfen et al., 1983; Tyree and Sperry, 1989), resulting in different resistances.
Although not all anatomical properties of the xylem conduit system have been revealed here, this study shows how a simple and accurate description of hydraulic-anatomical properties of plant stems can be achieved. The approach used in this study allows the comparison of conduit lumen characteristics and hydraulic properties at different locations in one plant, or between cultivars or between different species. Three-dimensional imaging techniques (Lewis, 1995) will be needed to explore the detailed shape of individual conduits (diameter and roundness fluctuations) and the conduit connection patterns. In the near future the mathematical description of anatomical properties will enable proper 3D-modelling of the hydraulic architecture of plant stems (for a recent general model see West et al., 1999). Besides providing a better (mechanistic) understanding of plant vascular development and functioning, 3D-models can predict the consequences of disruptions of parts of the system caused by, for example, cavitation, mechanical damage or infections.
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Appendix |
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TopAbstractIntroductionMaterials and methodsResultsDiscussionAppendixReferences |
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Conduit length distribution
The number of red pixels (Y) as a function of the distance from the plane of the cut in chrysanthemum stems can be described by an exponential function as follows:
 | (8) |
y is the exponential factor from which the half-length (y; analogous to half-time of radioactive isotopes) can be calculated:
 | (9) |
y is of particular interest, because for every value of x the following is true:
 | (10) |
y is the distance along the stem over which the number of red pixels halves or doubles.
The number of red conduits as a function of distance from the plane of the cut (Nx) can be calculated from the red area divided by the average cross-sectional conduit area (x).
 | (11) |
x is calculated from the cross-sectional area measurements (see Fig. 6b), and N0 is the number of all conduits at the plane of the cut. From this equation, the conduit half-length (c), can be derived:
 | (12) |
 | (13) |
Hydraulic conductivity
The hydraulic conductance (C) of a water transport system can be described as:
 | (14) |
P is the pressure difference. The hydraulic conductance is dependent on the length of the transport system. The longer the system (e.g. stem segment), the lower the conductance of the system. The hydraulic conductivity (CS) is the hydraulic conductance per unit of length (x):
 | (15) |
In his review on the ascent of sap in plants, Pickard (Pickard, 1981) gave a theoretical, mathematical description of the water transport within xylem conduits. Assuming the conduits as uniform, infinite and elliptic pipes, the conductivity per conduit (CSc) is given by (Pickard, 1981):
 | (16) |
is the viscosity of the liquid (1.00x10-3 Pa s for water at 20 °C). This formula is a more general form of the Hagen–Poiseuille formula for circular capillaries where a>=a<=radius. Thus, the conductivity of a conduit lumen can be calculated from the major and the minor axes of an ellipse superimposed on its cross-sectional area.
The conductivity in a cross-section (CSh) of the combination of all conduits (j) at a certain height above soil surface (h) in the stem is calculated by:
 | (17) |
 | (18) |
 | (19) |
 | (20) |
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Acknowledgments |
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We thank Annie van Gelder, Joke Oosterkamp and Belén Uriz for their practical assistance. We thank Jeremy Harbinson, Olaf van Kooten, Rob den Outer, Rob Schouten, and Michiel Willemse for helpful advice and critical reading. This research is financially supported in part by the Technology Foundation, STW, applied science division of NWO.
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Notes |
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3 To whom correspondence should be addressed at: Horticultural Production Chains Group/Laboratory of Plant Cell Biology, Wageningen University, Marijkeweg 22, 6709 PG Wageningen, The Netherlands. Fax: +31 317 484709. E-mail: jaap.nijsse{at}hpc.dpw.wau.nl
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