(American Journal of Botany. 2004;91:386-400.)
© 2004 Botanical Society of America, Inc.
Physiology and Development |
Analysis of circular bordered pit function II. Gymnosperm tracheids with torus-margo pit membranes1
Uwe G. Hacke2,
John S. Sperry and
Jarmila Pittermann
Biology Department, University of Utah, 257 South 1400 East, Salt Lake City, Utah 84112 USA
Received for publication July 1, 2003.
Accepted for publication October 21, 2003.
 |
ABSTRACT
|
|---|
A model of xylem conduit function was applied to gymnosperm tracheids with torus-margo pit membranes for comparison with angiosperm vessels. Tracheids from 17 gymnosperm tree species with circular bordered pits and air-seed pressures from 0.8 to 11.8 MPa were analyzed. Tracheids were more reinforced against implosion than vessels, consistent with their double function in transport and support. Tracheid pits were 3.3 to 44 times higher in hydraulic conductivity than vessel pits because of greater membrane conductivity of the torus-margo configuration. Tight scaling between torus and pit size maximized pit conductivity. Higher pit conductivity allowed tracheids to be 1.7–3.4 times shorter than vessels and still achieve 95% of their lumen-limited maximum conductivity. Predicted tracheid lengths were consistent with measured lengths. The torus-margo structure is important for maximizing the conductivity of the inherently length-limited tracheid: replacing the torus-margo membrane with a vessel membrane caused stem tracheid conductivity to drop by 41%. Tracheids were no less hydraulically efficient than vessels if they were long enough to reach their lumen-limiting conductivity. However, this may only be possible for lumen diameters below approximately 60–70 µm.
Key Words: functional wood anatomy • hydraulic architecture • plant biomechanics • plant water transport • tracheids • xylem cavitation • xylem hydraulic conductivity
|
INTRODUCTION
|
|---|
The secondary xylem of gymnosperms and angiosperms accomplishes the same functions of water transport and mechanical support, but with very different wood structure. This second of two papers completes a comparative analysis of water transport in these contrasting wood types.
Gymnosperm wood is superficially simple, composed mostly of the single-celled tracheid that functions both as a conduit for water flow and for providing mechanical strength to the axis. The intertracheid pits, however, are quite specialized. These are usually circular bordered pits with a torus-margo pit membrane (Bauch et al., 1972
). The torus-margo differentiation is a unique compromise to the conflict between allowing water flow between functional tracheids while preventing air flow from an embolized tracheid. The thin and porous margo provides passage for water (Fig. 1A), yet traps an air-water meniscus by capillary action. The capillary suction aspirates the membrane, and the thickened torus seals off the aperture to provide the final barrier to air movement (Fig. 1B). This valve is good up to a certain pressure difference, the "air-seed pressure," at which air leaks past and nucleates cavitation in the adjacent tracheid. The available evidence suggest that the torus is pulled through the aperture, exposing the margo (Sperry and Tyree, 1990
). Whether this happens by elastic stretching of the margo ("stretch-seeding") or by actual rupture of the margo ("rupture-seeding") is unknown (Fig. 1C). In latewood tracheids, in which the torus and margo can be less well differentiated, air seeding may occur through margo pores without membrane aspiration (Domec and Gartner, 2002
).
View larger version (59K):
[in this window]
[in a new window]
|
Fig. 1. Contrasting modes of interconduit pit function in angiosperm vessels (left) vs. gymnosperm tracheids with a torus-margo pit membrane (right). (A) Pits are open for water flow when surrounded by water. (B) Pits seal when an air–water meniscus is drawn into the membrane. Angiosperm pits seal by capillary forces in necessarily small membrane pores. Earlywood pits of gymnosperms seal by the aspiration of the essentially solid torus over the pit aperture after capillary forces at the margo pores have aspirated the membrane. (C) Air-seeding occurs when the pressure difference (Pa) between air (left) and water (right) across the pit membrane is high enough to force air through to nucleate cavitation. Vessel pits air-seed by capillary failure ("capillary-seeding") if the air is sucked through preexisting pores in the pit membrane. Vessel pits "rupture-seed" if air is sucked through pores created by structural failure in the membrane. Torus-margo pits air-seed by "stretch-seeding" if the margo is elastically stretched to the aperture, exposing margo pores large enough to allow air passage. Pits rupture-seed if structural failure of the margo allows the torus to be pulled through the aperture
|
|
Angiosperm wood, with its multicellular vessels for transport and fibers for mechanical strength, has more cell types than gymnosperm wood. However, its intervessel pitting is less specialized. The pit membrane is generally homogenous in thickness and porosity, and it is a much simpler valve. Water flows through the evenly distributed fine pores of the membrane (Fig. 1A), and these fine pores also trap an air–water interface. There is no torus, and the sealing of the pit depends entirely on the capillary forces generated at the same pores through which the water flows (Fig. 1B). Consequently, these pores must be much smaller than the pores of the gymnosperm margo. Air-seeding can occur either by the failure of the capillary forces in the preexisting membrane pores (capillary-seeding) or through pores created by structural failure of the membrane (rupture-seeding, Fig. 1C).
In the first paper of this series (Sperry and Hacke, 2004
), we showed that angiosperm pitting had relatively low hydraulic conductivity. However, this low conductivity could be overcome if vessels achieved a certain "saturating length." At this length, the vessel conductivity per unit length and per wall area is determined only by the lumen size and wall thickness, canceling out any direct effect of pit conductivity. Achieving the saturating conduit length may be no problem for the multicellular vessel. The optimal vessel length should be the saturating length because at this point conductivity has been maximized, and the disadvantages of excessive length (loss of conductivity by cavitation, damage, and vascular disease) is minimized (Comstock and Sperry, 2000
). In support of this hypothesis, predicted saturating lengths were consistent with observed lengths. Pit structure also came closest to achieving the maximum possible vessel conductivity for vessels at their saturating length.
We also showed that vessels maintained a fairly modest safety factor against wall collapse by negative pressure. Predicted implosion pressures were only about twice the air-seed pressure. The advantage of such modest safety factors may be in minimizing the wall thickness for a given cavitation pressure. Thin walls are more economical and achieve a greater vessel conductivity per unit wall area invested in transport.
In this second paper, we subject the gymnosperm tracheid to the same scrutiny. Tracheids, being single-celled, are limited in length to less than approximately 7 mm in tree species such as we examined. Shorter lumen length means that pit conductivity could become much more limiting for the overall tracheid conductivity. Is the torus-margo pit structure more efficient hydraulically than the homogenous pit membranes of angiosperms as suggested by Lancashire and Ennos (2002)
? If so, it could compensate for shorter tracheid lengths. On the one hand, the much larger pores in the margo should increase membrane conductivity relative to the narrower pores of the angiosperm pit membrane. On the other hand, much of the membrane area is taken up by the nonconductive torus, and the pit aperture conductivity could be more important than the pit membrane for setting overall pit conductivity.
Another consideration is the role of tracheids in strengthening the axis—a role not required of vessels. This could require greater tracheid wall thickness than would be necessary just to resist implosion by negative pressure (Hacke et al., 2001a
). Thicker walls would compromise conducting efficiency per conduit investment relative to the vessel network of angiosperms.
In this paper, we extend our previously described model (Sperry and Hacke, 2004
) of xylem conduit function to gymnosperm tracheids with circular-bordered pit structure and torus-margo membranes. We employ a data set of 17 gymnosperm species (all conifers, except for one; Table 1) representing a wide range of air-seed pressure. We attempt to answer the following questions: (1) At the pit level, how does the torus-margo membrane compare with the angiosperm membrane in conductivity per air-seed pressure and per pit membrane area? (2) At the conduit level, how does the implosion resistance and hydraulic efficiency of tracheids compare with vessels? (3) How close does actual gymnosperm pit and tracheid structure come to achieving the maximum possible conducting efficiency?
View this table:
[in this window]
[in a new window]
|
Table 1. Study species and air-seed pressure of gymnosperms listed alphabetically by family. Habitats are Wasatch Mountains of Utah (WM), Piedmont of North Carolina (NC), Utah's Great Basin (GB), greenhouse-grown plants (GH), Sonoran Desert (SD), University of Utah campus (UU), Georgia (GA), and northern California (CA). In some species both stem (S) and root (R) organs were measured. The air-seed pressure (Pa) is the absolute value of the negative pressure required to eliminate 50% of the hydraulic conductivity of the xylem sample. When two Pa values are given, the second one refers to roots. Source of Pa data is given when not obtained specifically for this paper
|
|
|
MATERIALS AND METHODS
|
|---|
The data set
The data set (Table 1) on cavitation resistance and conduit anatomy included several species from previous studies (Hacke et al., 2001a
) studied with methods described in the first paper (Sperry and Hacke, 2004
). Cavitation resistance was represented by the air-seed pressure (Pa). This is the positive pressure difference required to force air into xylem conduits and cause cavitation. A species' air-seed pressure was the pressure required to cause a 50% loss of hydraulic conductivity by cavitation (the absolute value of P50 sensu Hacke et al., 2001a
). By including species from numerous diverse habitats, we were able to obtain a wide range of Pa from a minimum of 0.8 MPa in Taxodium distichum roots to a maximum of 11.8 MPa in Juniperus monosperma stems (Table 1).
We included species from four families, including the sole nonconifer, Ginkgo biloba. In addition, we also sampled root and stem xylem from many species. By sampling broadly across phylogeny and organ, we intended to include all sources of variation in tracheid structure, so as to have the broadest comparative basis for evaluating structure–function relationships. We included roots for two reasons. First, they tend to be more vulnerable to cavitation than stems (Sperry and Ikeda, 1997
; Linton et al., 1998
; Kavanagh et al., 1999
; Hacke et al., 2000
) as seen in the present data set, in which root Pa averaged 2.2 MPa less than stem Pa for the nine species where data for both organs was available (Table 1). Second, tracheids in roots are in a very different mechanical environment than tracheids in stems, with potential consequences for their wall structure.
The anatomical measurements were made on the same or similar xylem samples used to determine the Pa. The hydraulic mean conduit diameter (Dc) was measured as described in the companion paper (Sperry and Hacke, 2004
). The intertracheid wall thickness (tw; Fig. 2C) was measured on tracheids with diameters within approximately 2 µm of Dc. The width of the intertracheid wall (b, Fig. 2A) was calculated as the side of a square with an area equal to the area of the tracheid lumen. For the rectangular shape of tracheids, this was a better approximation than setting b = Dc as was done for the more circular geometry of vessels. Pit membrane (Dm), aperture (Da), and torus diameters (Dt) were estimated for tracheids of diameter Dc. In gymnosperms, these values were strongly correlated with tracheid diameter. After establishing this correlation for each organ and species, the pit dimensions corresponding to tracheid diameter Dc were calculated from the correlation. Measuring the torus required staining with toluidine blue. In Ginkgo biloba and Taxodium distichum, the torus did not stain strongly and its diameter was not determined. Relevant tracheid and pit parameters are summarized in Fig. 2. Symbols are defined in Table 2.
View larger version (46K):
[in this window]
[in a new window]
|
Fig. 2. Conduit wall structure. (A) Transverse view of two adjacent tracheids and pitted wall. Negative pressure in water-filled conduits (shaded) induces circumferential hoop stresses in the wall. Larger bending stresses are induced when the adjacent conduit is air-filled (nonshaded) and the common wall bends towards the water-filled side. b = width of the common wall. (B) Face view of pitted wall. Da = aperture diameter; Dm = membrane diameter; Dt = torus diameter; s = spacing between pits; Le = ligament efficiency (ratio of dimensions l/l'). (C) Transverse view of pitted wall showing pit aperture, border, and the torus-margo membrane: ry = radius of curvature of membrane deflected distance y from flat position; tw = double wall thickness; ta = thickness of single aperture
|
|
View this table:
[in this window]
[in a new window]
|
Table 2. List of parameters in the pit model with symbol, dimension (l, length; f, force; p, pressure [f · l–2]; t, time), definition, and for constants, the values employed
|
|
|
APPLICATION OF CONDUIT MODEL TO TRACHEIDS
|
|---|
The model was the same that was described in detail for angiosperm vessels by Sperry and Hacke (2004)
. Here we provide only the central equations, adding detail when modifications were required to apply it to gymnosperm tracheids.
Conduit implosion pressure (Pi)
The bending stresses that arise when an air-filled tracheid abuts a water-filled one under negative pressure are greater than the hoop stresses encircling the conducting tracheid (Fig. 2A). As such, bending stresses pose the greater threat to the collapse of the water-filled conduit. The implosion pressure (Pi) was defined as the pressure difference across the tracheid wall required to cause the bending stress to exceed the wall strength. Presumably, the Pi is at least equal to the air-seed pressure (Pa) so that the safety factor from implosion (Pi/Pa) is one or more. A safety factor less than one would seem unlikely because wall collapse itself might trigger air-seeding.
The implosion pressure was calculated exactly as for angiosperm vessels:
 | (1) |
where W is the strength of the solid wall material; and ß is a coefficient that depends on the ratio of the conduit width (b) to conduit length (L) and was set to 0.25 for b/L of 0.5 or less (Young, 1989
). The W was set to 80 MPa, the same as for angiosperm vessels (Hacke et al., 2001a
).
The (tw/b)2 term is the "thickness-to-span ratio," where tw is the double wall thickness (Fig. 2C): the thicker the wall relative to its width, the greater the implosion pressure. The Le is the "ligament efficiency," which quantifies the spacing of the pit apertures in the wall. The Le is equal to:
 | (2) |
where s is the spacing between adjacent pit membranes (Fig. 2B). When pits were nearly as wide as the tracheid, s was taken as the distance between the pit membrane and the edge of the tracheid wall. The bigger the apertures relative to the pit membrane and the more closely the apertures are spaced, the lower the Le and the weaker the wall. The (Ih/Is) is the "moment ratio." This ratio is the amount by which the second moment of area of a wall with pit chambers (Ih) is less than that for a solid wall perforated only by aperture-sized holes (Is). To the extent that the hollowed-out chambers reduce the second moment of area, the wall will be weakened.
Air-seed pressure (Pa)
We considered three modes of air-seeding for conifer pit membranes with a torus-margo organization (Fig. 1): stretch-seeding and rupture-seeding as defined earlier (Fig. 1C); and also capillary-seeding through pores in the margo prior to membrane aspiration (not shown in Fig. 1).
To predict the air-seed pressure, we calculated the pressure difference (Py) required to deflect the membrane a progressively greater distance y from its unstressed flat position (Fig. 2C):
 | (3) |
where the subscript "y" denotes a value at displacement y, and r is the radius of curvature of the membrane (Fig. 2C). The ns is the number of radial microfibril "spokes" assumed to bear the load on the membrane (Fig. 3), E is their elastic modulus, ey is their strain (at y), and Af their cross-sectional area (set to 707 nm2 as for vessel pit membranes; Petty, 1972
). When the membrane reached the pit chamber wall, aspiration occurred. The y at aspiration was calculated from an overall membrane strain (radial direction) at aspiration of 0.03, the same setting used for angiosperm pits.
View larger version (36K):
[in this window]
[in a new window]
|
Fig. 3. Representation of pit membrane. (A) A single sheet of parallel microfibrils, each spaced distance sf apart. One strand from each sheet formed a pair of radial spokes (numbered heavy line) assumed to bear the load on the stressed membrane. (B) A membrane composed of six sheets and ns = 12 radial spokes (numbered heavy lines) overlaid with a nonporous and nonstretchable torus. Dp = maximum pore diameter; Dpe = equivalent pore diameter giving same membrane conductivity if all pores were of equal size; Dm = membrane diameter; Dt = torus diameter; sf = spacing between strands of a single sheet
|
|
For deflection beyond aspiration, Eq. 3 was modified to account for the deflection of the membrane through the pit aperture:
 | (4) |
where Pasp is the pressure causing aspiration, Da is the aperture diameter, r is the radius of curvature of the membrane deflecting through the aperture, and 
e is the additional strain caused by deflection through the aperture.
Equations 3 and 4 were the same as those used for vessel pits with the exception that for conifer pits, the membrane strain was assumed to occur only within the thinner and presumably more extensible margo portion of the membrane. Thus, for an entire membrane strain (torus + margo) at aspiration of 0.03, the margo spoke strain at aspiration (ea) would be:
 | (5) |
Air-seeding occurred when the Py reached either the capillary-seed pressure, rupture-seed pressure, or stretch-seed pressure. Whichever of these three limiting pressures was lowest determined the mode of air-seeding. The capillary-seed pressure (Pc) was
 | (6) |
where 
is the surface tension of water, a is the contact angle between meniscus and wall, and Dp' is the stretched diameter of the membrane pores. The Dp' was calculated assuming for simplicity's sake that microfibril strands did not become thinner as the membrane deflected. The rupture-seed pressure was equal to the Py where spoke stress (Eey/Af) equaled the spoke strength (F). The stretch-seed pressure was the Py where the margo strain was sufficient to expose the margo pores at the pit aperture. The margo spoke strain at stretch-seeding (es) was:
 | (7) |
Stretch-seeding also required that the exposed margo pores be large enough to capillary-seed.
Membrane structure
The structure of the torus-margo membrane was represented in the same way as the vessel pit membrane, except that a torus was present (Fig. 3). The membrane was composed of ns/2 microfibril sheets superimposed on one another, with the microfibrils of each sheet spaced a constant distance sf apart. For such a membrane, the diameter of the largest circular pore (Dp) inscribed between microfibrils (Fig. 3B) was approximately:
 | (8) |
Petty's (1972)
measurements of Dp and ns give an sf of approximately 1.5 µm, which was used as the default value for both conifer and angiosperm membranes. As noted in the results section, we assessed the effect of varying the sf setting from the default over a range from 0.5 to 3.0 µm.
To match a given membrane structure with a specific air-seed pressure, we increased the number of spokes (ns) by increments of two (two spokes per microfibril sheet), and calculated the air-seed pressure for each spoke setting until the desired air-seed pressure was reached.
Pit and conduit hydraulic conductivity
The hydraulic resistance of the pit membrane (Rm) was:
 | (9) |
where npo is the number of pores in the membrane, 
is the viscosity of water, and f(h) is a function of the fraction of the membrane area occupied by pores (h), which accounts for the effect of pore spacing on pore conductivity (Tio and Sadhal, 1994
). The Dpe was the equivalent pore diameter (Fig. 3B) that gave the same membrane conductivity for the same number of pores as in the actual membrane. The equivalent pore diameter was approximately 63% of Dp. The pore number (npo) was estimated from the total membrane area divided by the area of a single circular pore (of diameter Dpe), including the surrounding microfibril strand.
The hydraulic resistance of the pit aperture (Ra) was (Dagan et al., 1982
):
 | (10) |
where ta is the length of one aperture (Fig. 2C). The ta was calculated from the double wall thickness (tw) and depth of the pit chamber. The total pit resistance (Rp) was equal to Ra and Rm in series: Rp = Ra + Rm. We expressed the pit resistance as a conductivity per membrane area (pit Ksp).
The total tracheid resistance (Rc) was computed from the lumen resistance (Rl) and the pit resistance (Rw) in series (Rc = Rw + Rl) according to Lancashire and Ennos (2002)
. This calculation assumes that water on average traverses just half of a conduit's total length. The lumen resistance is estimated as half of the Hagen-Poiseuille resistance for a tracheid of length L:
 | (11) |
The pit resistance is the resistance of just half of the tracheid's pits:
 | (12) |
where npi is the number of pits per tracheid. This was given by
 | (13) |
where int[number] returns the largest integer of the number, s is the minimum horizontal or vertical distance between pit edges (Fig. 2B), and LX is the cumulative length of pitted walls, with the "pitting coefficient" X being the proportionality factor between the tracheid length (L) and the cumulative pitted length. For example, if a tracheid had pitted walls on two sides for all of its length, X = 2. The npi' is the number of pits (an integer) fitting side-by-side across the conduit wall of width b in an opposite pitting arrangement (Fig. 2). The npi' was usually 1 for tracheids in stems, but could be higher in roots. Tracheid length (L) and pitting coefficient (X) were not measured, and we present a sensitivity analysis of these variables in the results.
To express the hydraulic efficiency of a conduit, we converted Rc to the hydraulic conductivity of a single tracheid on a per conduit length and per unit cross-sectional wall area basis (vessel Ksc):
 | (14) |
where Aw is the cross-sectional area of the conduit wall. To account for the wall investment in the conduit over its entire length, the Aw was calculated from the total wall volume of the conduit (V) divided by the conduit length (Aw = V/L). Volume calculations were identical to those used for angiosperm vessels.
|
RESULTS
|
|---|
Wall implosion pressure (Pi) and tracheid dimensions
The predicted implosion pressure exceeded the air-seed pressure across the full range (Fig. 4A). The two pressures were tightly correlated, but with different intercepts in root vs. stem tracheids. Root tracheids had an intercept no different than zero, implying a constant safety factor from implosion (Pi/Pa), which averaged 2.4 ± 0.3. Stem tracheids had a substantially positive intercept of 8.1 MPa, indicating additional wall reinforcement that was independent of air-seed pressure. The average safety factor for stem tracheids was 4.8 ± 0.4, double that in roots. Tracheids from both stems and roots had higher safety factors against implosion than angiosperm vessels as reported in the first paper (Fig. 4A, dashed "vessel" line).
View larger version (27K):
[in this window]
[in a new window]
|
Fig. 4. (A) Implosion pressure (Pi) vs. air-seed pressure (Pa) for stem (circles) and root (triangles) tracheids. Lowest solid line is 1 : 1; dashed line is for vessels (from Sperry and Hacke, 2004
). (B) Components of implosion pressure vs. air-seed pressure. Left ordinate and solid symbols (circles = stems; triangles = roots) are the thickness-to-span ratios (tw/b)2. Right ordinate is the ligament efficiency (Le; open circles for stems, triangles for roots) or the moment ratio (Ih/Is; dotted circles stems, dotted triangles for roots)
|
|
The increase in implosion pressure with air-seed pressure was entirely the result of increased thickness-to-span ratio (tw/b)2 (Fig. 4B, solid symbols). The ligament efficiency (Le) did not increase with air-seed pressure, remaining constant at 0.75 ± 0.01 (Fig. 4B, open symbols). The spacing between pits or between pits and the edge of the tracheid (Fig. 2B; s) was generally negligible, meaning the Le was chiefly a function of the diameter of the pit aperture and membrane (Le 
1 – Da/Dm). The moment ratio (Ih/Is) did not change with air-seed pressure and averaged 0.94 ± 0.01 (Fig. 4B, dotted symbols). Thus, the presence of pits lowered the implosion pressure by about 30% relative to a solid wall of the same dimensions, with apertures causing 25% and chambers causing 5% of the effect.
Tracheid pits were essentially as wide as the tracheid up to tracheid diameters of approximately 20 µm (Fig. 5A) and greatly exceeded the diameter range reported in the first paper for vessel pits (Fig. 5B, dashed line). The Da was correlated with Dm (Fig. 5B, circles), keeping Le relatively constant with pit size. The torus diameter also increased linearly with pit membrane size (Fig. 5B, squares), staying at about 49% of the pit diameter.
View larger version (22K):
[in this window]
[in a new window]
|
Fig. 5. (A) Hydraulic mean tracheid diameter (Dc) vs. pit membrane diameter (Dm) for stem (circles) and root (triangles) tracheids. Curve is a quadratic fit to pooled data (r2 = 0.60). (B) Pit aperture diameter (Da; circles) or torus diameter (Dt; squares) vs. pit membrane diameter (Dm) for pooled root and stem tracheid data. Dashed line shows linear correlation for vessels from Sperry and Hacke (2004)
|
|
Tracheid pit membranes and apertures were significantly smaller in diameter for greater air-seed pressures (Fig. 6A). This was consistent with a decline in tracheid diameter with air-seed pressure (Fig. 6B) and the fact that pit membrane and tracheid diameter were correlated (Fig. 5A).
View larger version (23K):
[in this window]
[in a new window]
|
Fig. 6. (A) Pit membrane (Dm; circles) or pit aperture (Da; squares) diameter vs. air-seed pressure (Pa) for pooled root and stem tracheids. (B) Hydraulic mean conduit diameter (Dc) vs. air-seed pressure (Pa) for root (triangles) and stem (circles) tracheids from the data set (r2 = 0.47 for pooled data, fit by a two-parameter power function). Crosses show vessel data from Sperry and Hacke (2004)
|
|
The scaling relationships in Figs. 4–6 allowed us to define what we hereafter refer to as the "average" tracheid for the data set. The average tracheid had the mean Pa = 4.8 MPa for the data set, which corresponded to a mean hydraulic diameter of Dc = 19 µm from the curve fit in Fig. 6B, a Dm = 12.9 µm and Da = 3.6 µm from the correlations in 6A, and Dt = 6.15 from the correlation in Fig. 5B. The corresponding thickness-to-span ratio (hence setting the tw) was 0.1 from the stem tracheid regression Fig. 4B.
Mode of air-seeding and the mechanical properties of membrane microfibrils (E, F)
As shown for vessel pits in the first paper (Sperry and Hacke, 2004
), the mode of air-seeding depended on the settings for membrane spoke strength (F) and elastic modulus (E; Fig. 7). The actual values for these properties are ambiguous, conceivably ranging from theoretical values for cellulose microfibrils to experimental values for primary cell walls (F = 25 to F < 1 GPa; E = 250 to E < 3 GPa; (Mark, 1967
; Petty, 1972
; Jeronimidis, 1980
; Ashby et al., 1995
; Hepworth and Vincent, 1998a
, b
). A sensitivity analysis predicted four types of pit function depending on the F and E settings (Fig. 7).
View larger version (21K):
[in this window]
[in a new window]
|
Fig. 7. Influence of microfibril spoke strength (F) and elastic modulus (E) on pit aspiration and mode of air-seeding for the average tracheid as defined in text. Type 1 pits stretch-seeded after aspiration. Type 3 pits rupture-seeded without aspiration. Type 4 pits rupture-seeded after aspiration. Not shown are type 2 pits that capillary-seeded without aspirating. The solid "rupture boundary" divides rupture-seed pits (below) from capillary-seed pits (above). The dashed "aspiration boundary" divides aspirating pits (above and to left) from nonaspirating pits (below and to right). Increasing the torus diameter relative to the rest of the pit caused the rupture and aspiration boundaries to steepen (dash-dotted lines for Dt = 60% of Dm vs. normal 49%) and vice versa
|
|
Type 1 pits showed aspiration and stretch-seeding. These pits had high F and low E—strong, flexible membranes (Fig. 7, upper left).
Type 2 pits showed no aspiration and capillary-seeding through margo pores. These were associated with high F and high E—strong, stiff membranes. These pits occurred for F and E outside of the range shown in Fig. 7.
Type 3 pits showed no aspiration and rupture-seeding. These were associated with relatively low F and high E—weak, stiff membranes (Fig. 7, lower right).
Type 4 pits showed aspiration and rupture-seeding. These pits occupied a wedge between type 1 and 3 pits (Fig. 7).
The aspiration boundary between types 3 and 4 (Fig. 7, dashed diagonal) is the F/E ratio that equals the margo strain at aspiration (ea) because no pit can aspirate if in doing so it must stretch past the rupture point. The margo strain at aspiration depends on the torus diameter relative to the membrane diameter (Eq. 5). For a torus diameter 49% of the pit diameter (Fig. 5B), the margo strain at aspiration was approximately 0.06, which also gives the slope of the aspiration boundary. Increasing the torus diameter relative to the pit membrane diameter resulted in a higher margo strain at aspiration and a steeper slope for the aspiration boundary (Fig. 7, dash-dotted line above aspiration boundary for Dt = 60% of Dm).
The rupture boundary between pit types 1 and 4 (Fig. 7, solid diagonal) is the F/E ratio that equals the margo strain at stretch-seeding (es) because no pit can stretch-seed if to do so it must stretch beyond the rupture point. The margo strain at stretch-seeding depends on the torus and aperture diameters relative to the membrane diameter (Eq. 7). The aperture diameter averaged 29% of the pit membrane diameter (Fig. 5B), which together with the scaling of the torus gives an approximate margo strain at stretch-seeding of 0.45, which was just steeper than the slope of the rupture boundary (Fig. 7; slope = 0.40). Increasing the torus diameter relative to pit membrane and aperture diameters caused a higher margo strain at stretch-seeding and a steeper rupture boundary (Fig. 7, dash-dotted line above rupture boundary for Dt = 60% of Dm).
The boundaries between pit types 1, 3, and 4 for the F and E range shown in Fig. 7 were essentially independent of the air-seed pressure and microfibril spacing (sf) because neither of these influenced the margo strain at aspiration or at stretch-seeding. The boundaries were also insensitive to changes in pit size as long as the torus and aperture diameters scaled with pit membrane diameters as observed (Fig. 5B). This suggests that the observed scaling of pit dimensions may be necessary to maintain the same mode of air-seeding across a range of pit sizes.
If we assume that pits do aspirate as has been observed (Petty, 1972
) and that they do not rupture-seed—because this would cause irreversible damage to the membrane—we can narrow down the range of F and E values for the microfibril spokes to what results in type 1 pits (Fig. 7). For pits of average torus proportions, the F/E must exceed approximately 0.40. Except where noted, the default setting for all subsequent analyses was F = 2.2 and E = 5 GPa, which insured type 1 pits for observed pit dimensions. These settings are intentionally the same that we used for the membrane spokes of vessel pits in the first paper of this series (Sperry and Hacke, 2004
).
Pit conductivity (pit Ksp) vs. air-seed pressure (Pa)
There was a slight, but significant decline in tracheid pit Ksp with increasing Pa (Fig. 8A, r2 = 0.19). Pit Ksp dropped by a factor of 1.7 for a 10-fold increase in Pa from 1 to 10 MPa. These calculations were for pits and tracheids of measured diameters and of a wall thickness giving the Pi predicted from the root and stem regressions in Fig. 4A.
The decline in tracheid pit Ksp was considerably less than the 30-fold decline we found for vessel pit Ksp over the same 1–10 MPa Pa range in the companion paper (Sperry and Hacke, 2004
) (Fig. 8A, dashed line). In addition, conifer pit Ksp was considerably greater than vessel Ksp—by a factor of 3.3 at Pa = 1 MPa, increasing to a factor of 43 at Pa = 10 MPa.
Torus-margo pit Ksp was limited by aperture conductivity rather than membrane conductivity, because the former was consistently less than the latter across the Pa range (Fig. 8B, compare open vs. solid symbols). The decline in tracheid pit Ksp with Pa was attributable to a statistically nonsignificant trend for decreasing membrane conductivity and aperture conductivity with Pa (Fig. 8B). Membrane conductivity tended to decline because of the higher number of microfibril spokes (and hence smaller margo pores) required to hold the membrane against greater pressures. Aperture conductivity tended to decline because of the thicker walls (and hence larger aperture depth ta) required to keep Pi equal to Pa and because of the decline in aperture diameter with increasing Pa (Fig. 6A).
In contrast, the vessel analysis in the companion paper (Sperry and Hacke, 2004
) showed that vessel pits were generally membrane-limited except at low Pa (Fig. 8B, compare vessel aperture vs. membrane lines). The steeper decline in vessel pit Ksp with air-seed pressure was primarily a result of a much more pronounced decline in membrane conductivity compared with the torus-margo pit membrane. The low membrane conductivity of the intervessel pit was the main reason why vessel pits analyzed in the first paper had a much lower Ksp than tracheid pits. In addition, vessel pits had a slightly narrower aperture diameter for a given pit membrane diameter than tracheid pits (Fig. 5B), causing the vessel pit aperture conductivity to be lower in vessels vs. tracheids (Fig. 8B).
The scatter in the relationship between tracheid pit Ksp with Pa was related to variation in tracheid and pit membrane size. Narrower tracheids had narrower pit membranes (Fig. 5A) and also greater pit Ksp than wider tracheids (Fig. 8A, narrow line vs. wide line). The greater hydraulic conductivity of pits in narrow tracheids was due to both higher membrane conductivity and aperture conductivity. Membrane conductivity was higher in pits of narrow tracheids because the smaller pit membranes required fewer spokes to support the same air-seed pressure vs. wide pit membranes. Fewer spokes translated into larger margo pores and higher conductivity. The large variation in membrane conductivity (Fig. 8B, solid symbols) was attributable to variation in pit membrane diameter. Aperture conductivity was higher in pits of narrow tracheids because the wall thickness was less for the same thickness-to-span ratio compared to the walls of wide tracheids. The variation in aperture conductivity (Fig. 8B, open symbols) was thus linked to variation in wall thickness with tracheid diameter.
The tight scaling of torus diameter with membrane and aperture diameter (Fig. 5A) was consistent with the torus size required to maximize the pit Ksp (Fig. 9). We defined the "torus overlap" as the fraction of the pit border width that was covered by the torus [(Dt – Da)/(Dm – Da)]. The scaling in Fig. 5B corresponded with a torus overlap between 0.21 and 0.38 (Fig. 9, horizontal bar above abscissa). This narrow range of overlap corresponded with values that maximized the calculated pit Ksp when the torus diameter was varied while keeping Dm and Da constant at the observed ratio (Fig. 9). Although a torus narrower than the optimum allowed for greater margo area, it also reduced the amount the margo stretched before air-seeding. Thus, to maintain an air-seed pressure, more margo spokes were required, which reduced membrane pore size and conductivity. A torus wider than the optimum reduced the margo area, countering the advantage of larger margo pore size. A wider torus also led to rupture-seeding, because the margo could not be stretched to the aperture without exceeding its point of failure. Rupture-seeding occurred at an overlap of between 0.31 and 0.34 for the default settings of F (2.2 GPa) and E (5.0 GPa; Fig. 9, vertical dash-dotted line). The optimal torus overlap was insensitive to pit size (not shown), but became much broader at low air-seed pressure (Fig. 9, compare average Pa = 4.8 MPa with Pa = 1.0 MPa). The optimum also increased slightly with large increases in the F/E ratio (not shown).
View larger version (22K):
[in this window]
[in a new window]
|
Fig. 9. Pit conductivity per membrane area (Ksp) vs. torus overlap [(Dt – Da)/(Dm – Da)] for the average tracheid as defined in text. The line with symbols is for the average air-seed pressure (Pa = 4.8 MPa). The upper dashed curve is for a Pa of 1.0 MPa near the minimum, and the lower dashed curve is for a Pa of 10 MPa near the maximum. Regardless of air-seed pressure, maximum pit Ks occurred for a torus overlap of between 0.24 and 0.30—within the observed range (horizontal bar above abcissa; mean and range). Rupture-seeding (vertical dashed line) occurred for an overlap of between 0.31 and 0.34 for the default settings of F = 2.2 GPa, E = 5 GPa
|
|
Tracheid conductivity (Ksc) vs. air-seed pressure
The tracheid Ksc incorporated both the pit and lumen components of the overall tracheid conductivity. It was expressed per conduit length and per wall area allocated to conduit construction. A greater tracheid Ksc means the plant can move more water with less drop in water potential per unit length and less investment in wall material per unit length.
As was shown for vessel Ksc in the companion paper (Sperry and Hacke, 2004
), the tracheid Ksc increased in sigmoidal fashion with increasing tracheid length (L; Fig. 10). Tracheid lengths were not measured, and the curves in Fig. 10 are for the average tracheid in the data set as a function of increasing L. All other dimensions equal, a short tracheid has low conductivity because it is limited by the low conductivity of the pitted tracheid walls (Fig. 10, pit-limited). Lengthening the same tracheid causes the conductivity to increase as the relatively high conductivity of the lumen becomes significant. When long enough, the tracheid achieves a maximum "saturated" conductivity that is limited by the lumen diameter and conduit wall area (Fig. 10, lumen-limited). This saturated conductivity was calculated directly by the model, but a summary equation indicates its dependency on tracheid size and wall thickness:
 | (15) |
where the proportionality depends in part on how much of the wall is occupied by pits.
View larger version (20K):
[in this window]
[in a new window]
|
Fig. 10. Tracheid Ksc vs. tracheid length (L) for average tracheids as defined in text. Symbols represent the default setting for pits on 50% of the tracheid wall. Dashed lines indicate 10% and 100% pitting as indicated. Short tracheids were limited by pit conductivity and had low Ksc; longer tracheids were limited by lumen conductivity and had a maximum saturated Ksc given by Eq. 15. The "saturating length" (asterisked point at L = 0.002 m) was defined as the tracheid length required to achieve 95% of the saturated tracheid Ksc
|
|
The "saturating length" is the tracheid length required to achieve 95% of the saturated tracheid Ksc. It may represent the optimal tracheid length: shorter tracheids cost the plant conductivity, and longer tracheids provide little benefit in conductivity when water-filled, yet cause a greater drop in conductivity when embolized.
The saturating tracheid length decreased with increasing length of pitted wall (LX; Eq. 13): the fewer pits, the more limiting was the pit conductivity and hence the longer the tracheid must be to reach its saturated conductivity. The saturated tracheid length increased from 1.3 mm when all sides of the tracheid were completely pitted (Fig. 10; 100% pitting, X = 4) to 4.6 mm when only 10% of the wall space was pitted (Fig. 10; 10% pitting, X = 0.4). Tracheids are generally pitted only on their radial walls. Assuming the two radial walls were completely pitted and the two tangential walls were not pitted, we adopted a pitting percentage of 50% (X = 2) as the default for subsequent analysis. This also matched the default used in the vessel analysis in the companion paper (Sperry and Hacke, 2004
). A 50% pitting percentage yielded a saturating tracheid length of 2 mm (Fig. 10, asterisk by 50% pitting curve).
The saturating length also depended on tracheid diameter. The wider the tracheid, the less limiting the lumen conductivity compared to the pit conductivity, and the longer the lumen must be to achieve the maximum tracheid Ksc. The saturating lengths predicted for tracheids in the data set (50% pitting) agreed well with length vs. diameter data from a literature data set of 37 species (Fig. 11A, compare solid vs. open symbols; data from Panshin and de Zeeuw, 1970
, tables 4–4, 4–5). Maximum average tracheid length in the literature data set for conifers was 5.6 mm, with a maximum average diameter of 56 µm.
Compared to vessels, tracheids had a much shorter saturating length (Fig. 11A, compare dashed vessel line with modeled symbols). The shorter saturating length of tracheids was because of their considerably greater pit Ksp compared with vessels (Fig. 8A). A higher pit conductivity for tracheids means the tracheid lumen does not have to be as long to limit the conduit conductivity.
Assuming that tracheid length was equal to the saturating length and that tracheids were 50% pitted, we predicted the relationship between tracheid Ksc and tracheid diameter (Fig. 11B). Tracheid Ksc increased as a power function in accordance with Eq. 15. The scatter was due to variation in air-seed pressure (and hence tw in Eq. 15) that was independent of conduit diameter. Notably, tracheids and vessels were predicted to be similar in their Ksc (Fig. 11B, compare symbols with crosses)—the only difference was attributable to variation in tw, depending on the safety factors from conduit implosion (Fig. 4A). Although tracheids are usually considered to be inherently less efficient than vessels, the model suggests that this is not true if both conduits are at their saturating lengths and they have equal pitting volumes and thickness-to-span ratios.
Tracheids did become less efficient than vessels when the tracheid diameter was increased while holding tracheid length constant at the near maximum obtained from the literature data set (L = 5.0 mm). At large diameters, tracheid Ksc plateaued at an approximately constant value (Fig. 11B, dashed line). Any advantage of increased lumen diameter was offset by the limitation of pit conductivity as wider tracheids became too short to achieve the saturated Ksc.
Continuing to assume tracheids at their saturating length, we predicted the relationship between tracheid Ksc and air-seed pressure (Fig. 12). There was a significant negative relationship between this tracheid Ksc and increasing air-seed pressure (r2 = 0.57). The scatter was related to independent variation in tracheid diameter. Wider tracheids had much higher tracheid Ksc than narrow ones (Fig. 12, compare wide vs. narrow lines) as expected from Eq. 15 for saturated Ksc. Although the pits in wide conduits are less conductive due to greater wall thickness (Fig. 8A), in long tracheids where pit conductivity is not limiting this disadvantage is masked by the much greater conductivity of a wide lumen. The decline in tracheid Ksc for constant tracheid diameter (e.g., wide and narrow lines) was due to increasing wall thickness required to maintain the necessary implosion pressure as air-seed pressure increased.
View larger version (19K):
[in this window]
[in a new window]
|
Fig. 12. Tracheid Ksc vs. air-seed pressure (Pa) for stem (circles) and root (triangles) xylem samples in the data set (r2 = 0.57 for linear correlation of pooled data). The tracheids were at their saturating length. The dash-dotted "vessel" line is the correlation for vessel data from Sperry and Hacke (2004)
. Solid "wide" line is for maximum tracheid diameter in the data set (Dc = 51 µm) with its pit dimensions held constant (Dm = 19.8; Da = 5.2; Dt = 8.6 µm) and L at the saturating length. Solid "wide-short" line is the same, except L was capped at a maximum of 5 mm. Dashed "narrow" line is for the minimum tracheid diameter in the data set (Dc = 7.2 µm) with its pit dimensions held constant (Dm = 6.2; Da = 1.9; Dt = 3.0 µm) and L of the saturating length
|
|
Tracheids were less conductive than vessels, especially at high Pa (Fig. 12, compare symbols with dashed "vessel" line). However, as pointed out before, this was not because tracheids were inherently less efficient than vessels of the same diameter and Pa. Instead, it was because tracheids were generally much narrower than vessels (Fig. 6A). The largest tracheid was 51 µm in diameter (Pinus palustris roots), which approximated the average vessel diameter in the angiosperm data set (49 µm). When the tracheid Ksc was calculated for 51 µm diameter across all Pa (Fig. 12, solid wide line), it approximated or even exceeded the vessel Ksc—indicating that the only factor preventing tracheids from achieving a higher Ksc was maintaining a wider diameter.
One explanation for the lack of wide tracheids at high Pa is that they cannot achieve their saturating length (and maximum Ksc) because of the higher pit resistance at high Pa and an inherent limit to tracheid length. To test this, we set L to 5 mm, which was the observed length for tracheids of the maximum 51 µm diameter (Fig. 11A). As expected, these length-limited tracheids lost more conductivity as Pa increased, because they become progressively shorter than their saturating length (Fig. 12, compare wide–short line with wide line). However, this cannot be the only reason for the observed trend for narrower tracheids with increasing Pa (Fig. 6B), because even if wide tracheids were shorter than their saturating length, they were still substantially more efficient than narrow ones at their saturating length (Fig. 12).
Maximum possible tracheid Ksc
To find the pit dimensions that maximized tracheid Ksc, we computed the Ksc for a wide range of pit diameters from a minimum of 3 µm to a maximum equal to Dc. For each Dm setting, we varied the aperture diameter from a minimum of Da = 1 µm to a maximum of (Dm – 1 µm). The torus diameter (Dt) was calculated from the average torus overlap for the data set of 0.28 (Fig. 9). All other parameters were kept constant at the value for the average tracheid. The optimal combination of pit dimensions maximized the tracheid Ksc. We repeated this analysis independently at each tracheid length setting (Fig. 13A; open symbols). The maximum Ksc was then compared with the "actual" tracheid Ksc for average tracheids (Fig. 13A; solid symbols).
View larger version (21K):
[in this window]
[in a new window]
|
Fig. 13. (A) Tracheid Ksc vs. tracheid length (L). "Actual" values (solid symbols) are from Fig. 10
for average tracheids from the data set with 50% pitting. Open symbols show the maximum possible Ksc achieved by allowing pit dimensions (Dm, Da, Dt) to vary for each length setting. (B) The percentage of the maximum possible Ksc achieved by actual tracheids for each length (L). Actual Ksc achieved 95% of the maximum (arrows in panels B and A) near the saturating tracheid length
|
|
The maximum tracheid Ksc exceeded the actual Ksc across all length settings (Fig. 13A, compare open vs. closed symbols). However, the actual Ksc rose to within 95% of the maximum near the saturating tracheid length (Fig. 13B, arrow). Thus, actual pit dimensions most closely matched the optimum at what one would assume to be the optimal length setting—the saturated length. The optimum pit membrane diameter for the saturated length of 2 mm was 18.5 µm with Da = 3.5 µm. Actual pits had a similar aperture diameter (Da = 3.6 µm), but smaller membrane size (Dm = 12.9 µm).
The same conclusion was reached in our analysis of vessels, except that tracheids came 7% closer to the optimum at their saturated length. In both conduit types, the optimal pit size was relatively large, because large pits mean higher ligament efficiencies and thinner walls, leading to less wall area for a given implosion resistance and lumen conductivity. The larger size of tracheid vs. vessel pits (Fig. 5B) resulted in tracheids coming closer to the maximum possible conduit Ksc.
|
DISCUSSION
|
|---|
The results provided theoretical answers to our three questions of the introduction, the first being whether the torus-margo membrane of gymnosperm tracheids is more or less conductive than the homogenous pit membranes of vessels. The torus-margo membrane has 3.3 to 43 times higher conductivity per membrane area than the homogenous pit membrane (Fig. 8A). The reason was primarily in the much greater membrane conductivity per area, which also showed relatively little decrease with increasing air-seed pressure as compared to the vessel pit membrane (Fig. 8B). This result supports the intuition of Lancashire and Ennos (2002)
, who, after measuring the hydraulic conductivity of physical models of the conifer pit membrane, speculated that it must be more conductive than the vessel type.
The efficiency of the torus-margo membrane is the direct consequence of the larger pores possible in the margo compared to the homogenous vessel pit membrane. Capillary forces at these pores are only required to aspirate the membrane so that the torus can seal the aperture (Petty, 1972
). They do not have to provide the ultimate seal against air entry as they must in the vessel membrane (Fig. 1B). Being larger, the pores are much more conductive, there being a roughly third-power relationship between pore diameter and conductivity (Vogel, 1994
). Even though there are fewer membrane pores because of a torus, this was more than made up by the greater pore size. In fact, the torus must become much wider than it was to cause a significant decrease in membrane conductivity (Fig. 9).
Interestingly, narrowing the torus also caused the membrane conductivity to decrease—even though a smaller torus created relatively more margo area (Fig. 9). The reason was that a greater number of margo strands were required to hold the narrower torus in sealing position. More margo strands mean smaller pores and lower membrane conductivity. The observed torus size relative to the rest of the pit appeared to optimize the membrane conductivity by maximizing the size and number of margo pores.
The torus width also has implications for the mode of air-seeding. A relatively narrow torus is more likely to stretch the margo to the aperture without breaking it, causing stretch-seeding. Conversely, a wide torus is more likely to break the margo and cause rupture-seeding (Figs. 7, 9). Based on our mechanical model, we predicted that the ratio of the membrane spoke strength to elastic modulus (F/E) must exceed 0.4 for stretch-seeding to occur for observed torus dimensions. The corresponding ratio for vessel pits from the companion paper (Sperry and Hacke, 2004
) was only approximately 0.1, meaning that the gymnosperm pit must have about four times greater microfibril strength than the vessel pit to avoid rupture-seeding for the same elastic modulus. The higher value for gymnosperm pits is because we assumed all membrane strain was located in the margo and the gymnosperm pits were so much larger in size than the vessel pit.
Unfortunately, we know little about the actual mechanical properties of the pit membrane. We also know little about whether the actual mode of air-seeding is by elastic stretching or by rupture-seeding. It seems likely that the air-seeding may occur beyond the elastic limit, because Petty (1972)
concluded that because cellulose microfibril creep can occur at a strain of 0.01, the typical aspiration strain of approximately 0.03 should cause at least temporarily irreversible stretching. This may be why pits can become stuck in an aspirated condition, particularly when the xylem is subjected to prolonged or severe water stress (Petty, 1972
). However, pits briefly aspirated by hydraulic pressure can rebound (Sperry and Tyree, 1990
). It seems unlikely that the margo strands are completely broken in half during air-seeding, because conifers in nature appear to go through embolism and refilling cycles (Sperry et al., 1994
; Mayr et al., 2002
). We do not know whether the phenomenon of "cavitation fatigue" (Hacke et al., 2001b
) extends to the torus-margo type of pit membrane. Although for lack of other information we assumed the same F and E values for both torus-margo and homogenous membranes, the analysis suggests that at least the F/E ratios are probably much lower for the vessel type of membrane. If so, this could be one reason for the generally smaller size of vessel pits (Fig. 5B).
The second question from the introduction concerned how the tracheids and vessels compared with respect to resistance to implosion by negative pressure and hydraulic efficiency. Tracheids, especially stem tracheids, had higher safety factors (average Pi/Pa = 4.8 for stems) from implosion than vessels (average Pi/Pa = 1.8; Fig. 4A). Vessels are presumably buffered to some extent against extra mechanical stress by fibers. The extra reinforcement of tracheids was expected, given that tracheids must transport water and strengthen the axis. The greater reinforcement of stem vs. root tracheids was also expected, given the greater structural demands of gravity and wind on the freestanding stem in comparison to roots that are supported by the surrounding soil. Without such reinforcement, negative xylem pressures could significantly weaken the stem against breakage by wind. It is an interesting question if drought stress could lead to greater vulnerability to stem breakage by increasing the stress in tracheid walls, even given their added wall thickness.
As for vessels, the scaling between implosion and air-seed pressures in tracheids was achieved by an increase in thickness-to-span ratio of the tracheid with air-seed pressure (Fig. 4B, solid symbols). Tracheid pits weakened the wall by an average of 30%. This is similar to the 20–40% figure for vessel pits, the only difference being that the larger pit chambers of tracheid pits accounted for 5% of the weakening vs. having no effect in the smaller vessel pits. Our model did not account for the typical bulge of the pit border toward the tracheid lumen of gymnosperm pits. Such a bulge could make the pits stronger than our analysis predicted by moving the pit border farther from the neutral axis of bending. The relatively thicker walls of tracheids mean that they are potentially less efficient conductors of water on a wall area basis than vessels. However, if the considerable wall area devoted to fibers is considered, water transport in gymnosperms is actually cheaper in terms of wood density and the metabolic cost of wood production (Hacke et al., 2001a
).
The tracheids of pine needles appear to behave quite differently from what our analysis suggests for those in stems and roots. Needle tracheids appear to undergo a controlled and reversible wall collapse without causing cavitation (Cochard et al., 2004). The collapse is not initiated by the bending stresses we analyzed, but by hoop stresses in water-filled tracheids that seem to trigger folding at thin areas in the wall. This interesting phenomenon may be adaptive in shutting down water transport and initiating stomatal closure without cavitation. The tracheids in pine stems behaved as expected from our results, cavitating before showing any signs of collapse (Cochard et al., 2004). Collapsing conduits may be a special adaptation limited to tissues not involved in mechanical support and to a conduit structure that can accommodate wall folding without disrupting vascular continuity.
An important prediction of the model is that, aside from differences in thickness-to-span ratio, tracheids and vessels should be of equal hydraulic conductivity—as long as they are of equal diameter and as long as they can achieve their saturated length (Fig. 11B). The conductivity of conduits at the saturated <
TOP
ABSTRACT
INTRODUCTION
