For single-vessel flow measurements, stems were cut under water to 0.5–2 cm lengths. A standard glass microcapillary (1 mm outer diameter, 0.58 mm inner diameter, World Precision Instruments, Inc., Sarasota, FL, USA) was pulled to create tips of varying size corresponding to vessel size in each species. The large end of the microcapillary was connected to a pressurized water source that was purified (Barnstead International, Dubuque IA, USA) and filtered (0.2 µm). Delivery pressure was measured on a gauge inserted along the tubing between the water source and the capillary tube. The hydraulic resistance of the microcapillary and tubing (rcapillary) was determined by dividing the delivery pressure by the volume flow rate of water. Volume flow rate was measured by timing the travel of a meniscus through a graduated pipette. The capillary tip was then inserted into one end of a vessel using a micromanipulator. Lengths of stem and microcapillary were measured individually prior to insertion and compared with total length of stem and microcapillary after insertion to account for insertion depth. Microcapillaries were secured to the stem with superglue (Loctite 409 and 712, Loctite Corp., Rocky Hill, CT, USA). Only vessels which did not include end walls were measured (see below). After letting the glue harden for 1–2 min, water was flushed through the vessel lumen at 130 kPa to remove air bubbles. Estimated bubble pressures for scalariform perforation plates are generally below 50 kPa (Bolton & Robson 1988). Following this, pressure was reduced to 60–80 kPa and resistance of the capillary plus vessel lumen (rtotal) was measured. We used pure water instead of a KCl solution because in the absence of any vessel ends and intact pit membranes, resistivity would not be influenced by ionic strength or composition of the measuring solution. Although pit membrane remnants have been observed in some of the species (Table 2), ionic effects were assumed to be unlikely because remnant openings are much larger than in intact membranes.
Table 2. Perforation plate morphology and % added resistivity for single-vessel measurements
|Species||Angle (deg)||# of openings||Slit width (µm)||Bar thick (µm)||Le (µm)||% added resistivity|
|CW||20.2 (0.3)||16.1 (0.6)||5.07 (0.29)||3.41 (0.08)||452 (26)||140 (38)|
|CA*||12.7 (1.6)||56.5 (2.6)||2.80 (0.21)||1.23 (0.05)||535 (25)||100 (11)|
|CR||15.2 (0.8)||44.0 (8.0)||2.48 (0.04)||1.49 (0.04)||425 (25)||80 (55)|
|DI||7.9 (0.6)||66.4 (2.3)||2.58 (0.07)||1.37 (0.05)||583 (28)||57 (4)|
|IF*||5.3 (0.5)||84.0 (6.4)||2.84 (0.12)||2.10 (0.01)||648 (29)||96 (18)|
|IP*||10.7 (0.3)||33.1 (1.2)||3.16 (0.13)||1.55 (0.07)||530 (32)||71 (17)|
|IV||8.9 (0.4)||65.0 (5.4)||2.28 (0.09)||1.38 (0.06)||430 (20)||220 (50)|
|LS||19.2 (0.3)||20.3 (0.6)||4.26 (0.16)||1.52 (0.05)||550 (37)||110 (41)|
|LT||20.3 (1.4)||6.6 (0.3)||11.90 (0.70)||2.60 (0.09)||580 (40)||130 (45)|
|MF||23.2 (1.4)||6.1 (0.3)||13.80 (0.33)||3.04 (0.10)||438 (19)||44 (n = 1)|
|RP||24.0 (0.7)||6.0 (0.4)||9.06 (0.22)||4.88 (0.29)||422 (3)||44 (15)|
|ST||16.0 (1.0)||20.6 (0.7)||4.00 (0.24)||1.71 (0.06)||550 (49)||58 (15)|
|SY||11.4 (0.6)||39.0 (5.1)||2.96 (0.07)||1.53 (0.06)||530 (67)||130 (69)|
The resistance of the vessel lumen (rvessel) was solved by subtracting rcapillary from rtotal based on the equation for two resistances in series:
where P is the pressure difference across lumen and capillary, and V/t is the volume flow rate. The resistivity of the vessel lumen (Rv) was calculated by dividing rvessel by the vessel lumen length (Lv = stem length minus capillary insertion depth).
The Rv of a lumen composed of repeating vessel elements is identical to the average resistivity of an individual vessel element (lumen + one perforation plate). Element resistivity in turn is composed of a lumen resistivity (RL) and a plate resistivity (Rp) in series, such that
We used the Hagen–Poiseuille (HP) equation for the resistivity through cylindrical capillaries to calculate RL from the measured vessel diameter, allowing us to determine Rp from Eqn 3.
The Rp in Eqn 3 is the plate resistance (rp) divided by the average spacing between perforation plates (Le). The Le is shorter than the vessel element length which includes the full extent of two perforation plates. Measurements of Le from macerated material taken from the same stem piece (see below) allowed us to calculate rp:
The analogous equation was used to calculate the lumen resistance of the element rL (rL = RLLe). To quantify the additional resistance or resistivity associated with the perforation plate, we calculated the ‘% added resistivity’ as:
which represents the plate resistivity (or resistance) as a percentage of the HP lumen resistivity (or resistance).
During measurements of open capillaries, which was when the highest flow rates were achieved, the dimensionless Reynolds number, Re (Vogel 1994), calculated as Re = UD/v, where D is the diameter of the pipe, U is mean fluid velocity and v is the kinematic viscosity of the fluid, was approximately 0.02, indicating flow was laminar and viscosity dominated. The Re was even lower in the xylem vessel lumen. The typical upper range in Reynolds number for xylem vessels is 0.01–0.1 (Ellerby & Ennos 1998). Thus, we were confident that our measurements represent laminar flow conditions.
After measurement, the microcapillary was detached from the water source and a small amount of safranin dye (0.1% w/w) was injected with a syringe into the capillary. Pressure was reduced to 10 kPa and the microcapillary was attached to the tubing until the dye was observed to pass through the other end of the stem. As soon as dye was observed at the other end, the microcapillary was reattached to the water source and the dye was flushed out of the lumen of the vessel. Finally, the microcapillary was connected to an air source to confirm that the vessel lumen was open at both ends. Air pressure was slowly raised until approximately 300 kPa, which corresponds to an opening of approximately 1 µm diameter. We used a cut-off pressure of 300 kPa to allow for air penetration through perforation plates with pit membrane remnants, as has been reported for some of our species (Table 2). Most vessels showed air passing through under 150 kPa. Vessels that did not pass air below 300 kPa were assumed to end within the segment and the measurements were not used.
Stems were sectioned to obtain the diameter of the dye-stained vessel lumen. Sections were photographed at 400 times magnification and the cross-sectional area of the stained lumen was measured with Image-Pro software (Image-Pro Plus, Media Cybernetics, Inc., Bethesda, MD, USA). Approximately 4–6 pictures were analysed per vessel. In preliminary experiments with simple-plated species, the vessel diameter was measured in one of four ways. Firstly, transverse vessel areas were measured and diameters were calculated based on an equivalent circle's diameter:
where A is the lumen area. Three additional methods of calculating vessel diameter were used following options presented in Lewis (1992). Firstly, an equation for determining the hydraulic diameter of an inscribed ellipse,
where a and b are the major and minor axes, respectively. Secondly, an abbreviated equation for hydraulic diameters of elliptical openings,
and thirdly, an equation based on the ratio of transverse sectional area to wetted perimeter (P):
Results obtained from each of these calculations were plotted against the calculated HP diameter corresponding to the lumen flow resistance for simple-plated vessels. We assumed that the best method for representing vessel diameter would be the one showing the strongest correlation with the HP diameter.
Longitudinal strands of xylem split from the measured stem were macerated to measure Le, and other features of perforation plate and vessel element anatomy (Table 2). Because the safranin dye used to identify the vessel for diameter measurements was not apparent after maceration, it was not possible to identify the exact vessel elements involved in the single-vessel measurement. Plate characteristics (plate length, plate width, bar number, size of openings between bars, and bar thickness) were measured on several plates for each stem and averaged to obtain a species mean. Plate angle was calculated from the length and width of the plates. Vessel element length and spacing distance between plates (Le) was also measured in these macerations. The Le corresponding to the vessel diameter of the single-measured vessel was determined from the average ratio of Le to element diameter obtained from the macerated sample.
Six stems per species (Table 1) of approximately 10 mm diameter were trimmed under water to 27.5 cm length and bark was removed from each end. Stems were then flushed with 20 mm KCl at 69 kPa to remove reversible embolism. Branch resistivity was made with the standard ‘gravity’ method using 20 mm KCl as a measuring solution to control for ionic effects on vessel end-wall resistance. A pressure head of approximately 4–6 kPa was used (Pockman, Sperry & O'Leary 1995; Li et al. 2008).
Safranin dye (0.1% w/w) was perfused through the stems following the resistivity measurement. The cross-sectional area of dye-stained xylem was measured at the centre of the branch segment. Branch resistivity multiplied by sapwood area gave the sapwood-specific resistivity. Transverse sections of the segments were also made and the number of vessels per wood area was determined on three to four radial sectors of the functional xylem. Sapwood-specific resistivity was multiplied by the number of vessels per sapwood area to give the mean vessel resistivity.
Vulnerability curves showing the percentage loss in hydraulic conductivity (PLC) versus xylem pressure were obtained for a subset of whole-branch species using either the flow centrifugation (Cochard 2002; Cochard et al. 2005; Li et al. 2008) or static centrifugation methods (Alder et al. 1997). Despite generally good agreement with the traditional static centrifugation or ‘gravity’ method (Li et al. 2008), the flow centrifugation method sometimes results in higher conductivities (reciprocal of resistivity) at the initial (0.25 or 0.5 MPa) spin pressures relative to the initial gravity method. When this occurred, PLC was calculated relative to the highest conductivity measured (i.e. at the 0.25 or 0.5 MPa spin pressure).
Branch conductivity of six stems per species was measured as described above. Stems were then spun in a Sorvall RC-5C centrifuge (Thermo Fisher Scientific, Waltham, MA, USA) using a custom-built rotor (Li et al. 2008). Conductivity was measured either during spinning (flow centrifugation) or between bouts of spinning with a gravimetric head (static centrifugation). Spin speed was increased until >95% loss of conductivity was detected. The pressure at which there was 50% loss of conductivity (P50) and the mean cavitation pressure (MCP) were calculated from a Weibull function fit to the percent loss of conductivity data for each stem and averaged for each species.
Additional anatomical measurements
Vessel lengths were also measured for species on which branch resistivity measurements were made. We followed the silicone injection procedure of Hacke et al. (2007). Six stems per species were flushed with 20 mm KCl at 69 kPa to remove reversible embolism and were injected basipetally under 50–75 kPa pressure overnight with a 10:1 silicone/hardener mix (RTV-141, Rhodia, Cranbury, NJ, USA). A fluorescent optical brightener (Ciba Uvitex OB, Ciba Specialty Chemicals, Tarrytown, NY, USA) was mixed with chloroform (1% w/w) and added to the silicone (1 drop g−1) to enable detection of silicone-filled vessels in stem sections under fluorescent microscopy. After allowing the silicone to harden for several days, stems were sectioned at five places beginning 6 mm from the injection end and ending 8–12 cm back from the cut end. The fraction of silicone-filled vessels at each length was counted and the data were fitted with a Weibull function. The best fit was then used to estimate the vessel length distribution. A full description of the procedure and equations used is presented in Christman, Sperry & Adler (2009).
Average inter-vessel pit area and number per vessel was obtained by methods detailed in Sperry et al. (2007). The fraction of inter-vessel walls occupied by pits was measured on longitudinal sections. The fraction of the vessel wall area in contact with adjacent vessels was estimated from cross-sections as the fraction of total vessel perimeter contacting adjacent vessels. The two fractions (pit area per inter-vessel wall, inter-vessel wall area per vessel wall area) multiplied gave the fraction of vessel wall area occupied by inter-vessel pits. This value in turn was multiplied by the average vessel wall area to give the average area of inter-vessel pits per vessel. The average vessel wall area was computed from the mean vessel length and mean diameter, assuming a cylindrical shape.