It is clear that the fine porosity of pit membranes is vital in preventing the spread of vascular pathogens and embolism throughout the xylem. However, because of the powerful relationship between pore diameter and conductivity (Vogel, 1994), the increased safety afforded by pit membranes comes at a substantial cost in terms of increased hydraulic resistance (Box 1). It has long been recognized that the hydraulic conductivity of wood is less than the theoretical conductivity calculated from the diameter of xylem conduits (Ewart, 1906; Riedl, 1937; Münch, 1943). Zimmermann & Brown (1971) asserted that limitations in vessel length, and therefore an increase in the number of pit crossings, was the most important factor in the reduction of hydraulic conductivity from its theoretical maximum. More recent studies have indicated that pit resistance can play a major role in determining the efficiency of water transport through the xylem, accounting for > 50% of the total xylem hydraulic resistance in many species (Schulte & Gibson, 1988; Sperry et al., 2005; Wheeler et al., 2005; Choat et al., 2006; Pittermann et al., 2006). As such, it was hypothesized that a trade-off should occur between hydraulic efficiency of the xylem and the safety from embolism, both of which are strongly influenced by pit membrane porosity. Next, we will next examine the potential for trade-offs at the individual pit level: how much do changes in pit geometry, and pit membrane porosity and thickness influence the relationship between vulnerability to embolism and hydraulic conductivity?
1. The influence of pit-level hydraulic parameters
Measurement of hydraulic characteristics at the individual pit level is extremely difficult because of the small size of pits. Likewise, mathematical modeling of pit membrane hydraulics is inherently difficult because of their spatially complex nature. In homogeneous pit membranes, pores are not likely to be straight paths through the membrane, but rather tortuous pathways through the interstices of multiple microfibril layers (Schmid & Machado, 1968). Mathematical models of angiosperm pit membrane hydraulic resistance based on pore sizes predicted from vulnerability to embolism of each species yielded values from 0.1–30.0 MPa s m−1 for rp of homogeneous membranes (Sperry & Hacke, 2004) and 0.14–0.50 MPa s m−1 for species with torus–margo membranes (Hacke et al., 2004). However, empirical measurements of rp from a variety of methods are generally much greater than modeled values (Fig. 5a).
Figure 5. Pit membrane resistance per area (a, note log scale) and proportion of total resistance attributed to pits (b) across taxa and according to different techniques. Box and whisker plot shows median (symbols), first and third quartiles (boxes), minimum and maximum (vertical lines). Method indicated by symbols: circles, subtraction; squares, single-vessel; triangles, membrane digestion; dashed lines, modeling. Subtraction: conifers, Pittermann et al. (2006); diffuse-porous angiosperms, Wheeler et al. (2005); ring-porous angiosperms, Hacke et al. (2006). Single-vessel: Choat et al. (2006). Membrane digestion: Schulte & Gibson (1988). Modeling: conifers, Hacke et al. (2004); angiosperms, Sperry & Hacke (2004). Sample size of species is given for each group.
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The largest body of data for rp in homogeneous pit membranes comes from the work of Wheeler et al. (2005) and Hacke et al. (2006), who estimated rp by subtracting lumen resistance from total resistance. These experiments yielded values of 30–2040 MPa s m−1 across 29 angiosperm species. Slightly higher values (2.56–5.32 × 103 MPa s m−1) were obtained by Choat et al. (2006) by measurements on individual vessels in two ring-porous species. Schulte & Gibson (1988) estimated rp in stems and petioles of several species by measuring hydraulic resistance before and after pit membranes had been dissolved with cellulase. These measurements gave a relatively low range of rp between 1.0 and 28.8 MPa s m−1. The only value available for roots comes from Peterson & Steudle (1993), who estimated an rp of 8.33 × 104 MPa s m−1 from root pressure probe measurements of pit membranes in maize. Thus values of rp have shown a large range both within a single study and between studies using different techniques.
2. Torus–margo vs homogeneous pit membranes
One of the most obvious differences in pit membrane hydraulic characteristics across species is between homogeneous membranes and torus–margo membranes. As with homogeneous pit membranes, the resistance of torus–margo membranes estimated from physical and mathematical models falls at the low end of values obtained empirically. Using physical models, Lancashire & Ennos (2002) calculated the rp of torus–margo pits of Tsuga canadensis at 0.4 MPa s m−1, which would contribute 29% of total resistance for a ‘typical’ tracheid. Mathematical models of torus–margo pits predicted very similar values (0.14–0.5 MPa s m−1) for a range of gymnosperm species (Hacke et al., 2004). However, empirical measurements indicated that rp values were much higher than this, ranging from 0.2–20 MPa s m−1, with a mean of 5.7 MPa s m−1 (Pittermann et al., 2006). Once again, the difference in modeled and measured values could be attributed to the complex geometry of the flow pathway through pit membranes. However, measured values of rp for torus–margo membranes are still far below measured values for angiosperm membranes (Pittermann et al., 2005). The much lower resistance of torus–margo pits results from the very porous margo region, and provides gymnosperms with a large advantage in pit hydraulic efficiency over species with homogeneous pit membranes. Pittermann et al. (2005) proposed that the development of torus–margo membranes in gymnosperms may be analogous to the development of vessels in angiosperms (analogous to the development of perforation plates). Thus, while the evolution of vessels in angiosperms species greatly increased efficiency by reducing the frequency of pit crossings, the torus–margo pit membrane provides an increase in efficiency in the xylem tissue of gymnosperms, which is composed entirely of much shorter tracheids (Pittermann et al., 2005).
3. Influence of pit chamber and pit membrane dimensions
The dimensions of the pit canal and pit chamber are quite variable: species with thick secondary conduit walls have much longer pit canals than those with thin walls. However, for both homogeneous and torus–margo membranes, the measured pit resistances are much larger than resistances calculated for the pit canal. When resistance is calculated on the individual pit level (Rind), the pit canal resistance typically represents < 5% of total resistance (Gibson et al., 1985; Wheeler et al., 2005; Choat et al., 2006; Pittermann et al., 2006). For instance, the resistance of a single pit of F. americana is 4.26 × 1014 MPa s m−3 compared with calculated resistance of a pit canal of 3.68 × 1011 MPa s m−3, more than 1000 times smaller (Choat et al., 2006). Therefore it appears that the hydraulic efficiency of pits is governed primarily by the structure of the pit membrane. This makes sense given the very small-diameter pores found in pit membranes compared with the size of the pit aperture and pit canal. The hydraulic resistance of individual pits is therefore dictated primarily by the average porosity and thickness of the membrane. The findings of Choat et al. (2006) show that rp appears to scale with pit membrane thickness; however, data were obtained for only two species, and a larger data set is required to test this hypothesis. Careful comparison of anatomical observations and measurement of rp will be required to elucidate how pit-level changes in structure influence hydraulic characteristics.
4. The balance of pit and lumen resistance
Thus far we have focused on structural and functional variation at the pit level. However, when examining functional relationships at the individual pit level, the impact of tissue-level differences in structure are neglected; the total xylem hydraulic resistance (Rtot) is determined by the dimensions and arrangement of conduits as well as the area-specific resistance of pits (Fig. 6). The total resistance can be broken into separate terms for lumen and pit resistances, which are additive in series by Ohm's law analogy. Given the length (L) and diameter (D) of a conduit, the resistance of the lumen (Rlum) can be calculated using the Hagen–Poiseuille equation:
Figure 6. Simplified model explaining the division of xylem hydraulic resistance. As water moves through the xylem, it will encounter two principal resistances. Lumen resistance (Rlum) can be approximated by the Hagen–Poiseuille equation from the length (L) and diameter (D) of conduits. The contribution of pit resistance (Rpit) can be calculated from the area-specific resistance of pits (rp) divided by the average area of pits connecting conduits (Apit).
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- (Eqn 2)
where η is the viscosity of water at 20°C (1.002 × 10−9 MPa s). Thus Rlum is particularly sensitive to changes in the diameter of conduits, with resistance decreasing with the fourth power of diameter. The Hagen–Poiseuille equation has been shown to provide a close approximation of the resistance in open vessels with simple perforation plates (Zwieniecki et al., 2001a). However, irregularities in the shape and sculpturing of vessels such as scalariform perforation plates and tapering at vessel ends may contribute to the often substantial deviations of empirical measurements from theoretical estimates (Schulte et al., 1989; Lewis & Boose, 1995).
The resistance of pits (Rpit) is determined by rp and the surface area of overlap between vessels (Apit):
- (Eqn 3)
The total resistance is then calculated as:
- (Eqn 4)
Thus Rlum will increase with increasing conduit length; however, the total resistivity (Rtot/L) should decrease because there will be fewer end-wall crossings per unit length. For Rpit, resistance will decrease with thinner, more porous pit membranes (low rp) and as the surface area of pit membrane connecting vessels increases. Thus xylem tissue with a high degree of connectivity between vessels will minimize the resistance caused by pit membranes.
The contribution of pit resistance to total resistivity has been estimated in a range of angiosperm, conifer and fern species using a variety of techniques (Fig. 5). From these experiments, it appears that the contribution of pit resistance is highly variable across species, ranging from 12–91% of total xylem resistivity. Because of this variation, the principal methods used to measure pit resistance bear further discussion. The most common method of estimating the contribution of pits to xylem resistivity is simple subtraction: Rlum is estimated from conduit diameters using the Poiseuille equation, the resistance through the xylem is measured empirically, and the difference is ascribed to the pit membranes (Sperry et al., 2005; Wheeler et al., 2005; Hacke et al., 2006; Pittermann et al., 2006). This technique should provide robust estimates of tissue-level parameters provided that resistance components other than pit and lumen resistance (irregularity of vessel form) are not a large factor. This method also requires working through many averages to scale down to the pit-level parameters. Another technique involves the digestion of pit membranes by perfusing cellulase through xylem tissue (Calkin et al., 1986; Schulte & Gibson, 1988). This technique offers the advantage that all components of resistance are taken into account, that is, anything additional to theoretical lumen resistance. Thus the true pit resistivity can be estimated as long as all pit membranes are dissolved properly. Finally, measurements on individual vessels provide a direct estimate of pit resistance, but require scaling up through many averages to arrive at tissue-level parameters (Zwieniecki et al., 2001a; Choat et al., 2006).
Although the contribution of pits to total resistivity varies considerably, the average across species is 58% for angiosperms and 64% for conifers (Fig. 5b). The largest data sets for cross-species comparisons of pit resistance using a standard technique come from Hacke et al. (2006); Pittermann et al. (2006) for angiosperms and conifers, respectively. These studies both indicate that there is a significant linear correlation between lumen and pit resistivity: species with high lumen resistivity also tend to have high pit resistivity. The fact that pit resistivity does not become dominant in species with wide vessels suggests that the tendency of wide vessels to be longer may allow lumen resistivity to keep pace with pit resistivity (Fig. 7; Schulte & Gibson, 1988; Lancashire & Ennos, 2002).
Figure 7. Conduit conductivity (1/resistivity) vs diameter and length according to equation 15 of Lancashire & Ennos (2002). (a) Indicates increasing total conduit conductivity (including lumen and pit components) with diameter if pit density is assumed constant at 5.06 × 108 m−2 and pit resistance is 1.7 × 109 MPa s m−3. For a fixed conduit length of 8 mm, total conductivity of the conduit is maximized at a diameter of 69 µm. Diameters greater than this would lead to lower total conductivity because the pitted area increases with the diameter while the lumen area increases with the diameter squared. (b) For a fixed conduit diameter of 69 µm, conductivity is always higher with a longer conduit because of the reduced contribution of pits (fewer end-wall crossings per length).
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Lancashire & Ennos (2002) demonstrated that tracheid resistance per length normalized by cross-sectional area is minimized when diameter increases with 2/3 power of the length if the density of pitting (pits per area) remains constant (Fig. 7). Thus a greater proportional increase in tracheid length relative to diameter across species could conserve the proportion of resistance contributed by pit membranes. At these optimal dimensions, pits should account for 67% of the total resistivity. This is very close to the species average for conifers of 64% found by Pittermann et al. (2006). The model of Lancashire & Ennos (2002) also suggests that the optimization of conduit dimensions places an upper limit on tracheid diameter because of the developmental constraints on tracheid length: tracheids are unicellular and appear to be limited to < 10 mm long by the cambial initials.
In angiosperms, the length of vessels is not constrained by unicellularity. Vessels are also largely free from biomechanical constraints because fibers bear much of the mechanical stress of self-support in angiosperms. In this case, xylem resistivity could be minimized by attaining vessel lengths that saturate resistivity at the Poiseuille limit, where pit resistivity becomes negligible (Fig. 7b). Pit resistivity could also be decreased by having the maximum possible overlap area between vessels. The fact that vessels have not reached these saturating lengths in plants is suggestive of a powerful constraint on vessel dimensions and connectivity. Because water is transported through the xylem under tension, it is constantly vulnerable to dysfunction. A vascular system in which there is little partitioning between vessels is also most vulnerable to dysfunction via embolism or pathogens. Recent studies have shed further light on how scaling in conduit dimensions and connectivity influences the balance between safety and efficiency in xylem structure (Choat et al., 2005; Wheeler et al., 2005; Pittermann et al., 2006; Loepfe et al., 2007).
5. Trade-offs in safety and efficiency: pit level vs tissue level
The air-seeding hypothesis states that vulnerability to water stress-induced cavitation should be related to the porosity of intervessel pit membranes. Because of the large proportion of hydraulic resistance attributed to pit membranes, one would expect a tight trade-off in the porosity of pit membranes driven by the competing requirements to reduce hydraulic resistance and to reduce the potential for air seeding between vessels. Therefore species that are vulnerable to embolism should have more porous membranes and lower pit hydraulic resistance (Sperry & Hacke, 2004). However, this relationship relies on a link between the average diameter of pores in the pit membrane, which will dictate pit membrane resistance, and the air-seeding threshold of the vessel. In fact, some studies have shown that the average porosity of pit membranes does not appear to be linked to the air-seeding threshold (Choat et al., 2003, 2004). Instead, vulnerability to embolism may be related to rare, large pores that occurred in only a few membranes. Because hydraulic resistance would be less affected by the presence of a few large pores, no trade-off would be expected between vulnerability to embolism and hydraulic resistance of pits.
Wheeler et al. (2005) provided empirical evidence for this theory, showing that rp was not correlated with average cavitation pressure across 16 vessel-bearing species. Instead, vulnerability to embolism was correlated with the average area of pit membrane per vessel. Wheeler et al. (2005) hypothesized that the chance of having a large pore between two vessels increases stochastically with increasing pit membrane area per vessel. In contrast, the average porosity, and therefore rp, would not necessarily change with increasing area. This theory, the ‘pit-area hypothesis’, was later extended to 29 vessel-bearing species with a wide range of xylem anatomies (Hacke et al., 2006).
Hydraulic resistance at the tissue level is strongly influenced by the area of pit membrane between two vessels: as the area of overlap increases, pit resistance falls (equation 4). Because the area of overlap tends to be larger in vessels of greater size (diameter and length), this provides a basis for the relationship between vessel diameter and vulnerability to embolism observed within a single plant (Lo Gullo & Salleo, 1991; Hargrave et al., 1994), and also for the weak relationship between vessel diameter and vulnerability to embolism across species (Tyree & Zimmermann, 2002). However, it is important to emphasize that the relationship between vessel size and vulnerability is not sufficient to make predictions across species: a species with narrow vessels may still be vulnerable to embolism if the overlap between vessels is large. Another, simpler link between vessel dimensions and vulnerability to embolism is that species with larger vessels will suffer a greater proportional loss of conductivity for each vessel lost. Therefore increases in conduit dimensions may worsen both the probability of air seeding between vessels, because of the increased pit area, and the consequences of each air-seeding event.
One prediction of the pit-area hypothesis is that pit membrane porosity is ‘generic’ among vessel-bearing species (Sperry et al., 2006). However, recent anatomical studies have revealed significant variation in the thickness and porosity of pit membranes (Sano, 2005; Jansen et al., 2007; Schmitz et al., 2007; Choat et al., unpublished). The order of magnitude variation in pit membrane thickness observed could translate to a significant difference in rp, although changes in resistance could be less than proportional to thickness in very thin pit membranes (see Loudon & McCulloh, 1999). Additionally, while it is not certain that pore sizes observed with SEM represent the pores of hydrated membranes, it is easy to imagine that differences in porosity may be indicative of the propensity for large pores to develop under natural conditions. Thus species with thinner membranes probably have lower hydraulic resistance and a greater chance of developing a large pore or rupture for a given membrane area. This raises the question as to how much variation in pit structure may influence the safety vs efficiency trade-off. Although pit area is well correlated with cavitation pressure, there is a large range of cavitation pressures for a given average pit area (see Fig. 7 in Hacke et al., 2006). This spread of values for a given pit area may be caused by differences in pit membrane structure: for a given average pit area, a species with thinner or more porous membranes will have a lower cavitation threshold.
It is worth noting that, mechanistically, both the intrinsic characteristics of pit membranes and the pit area between conduits must play a role in susceptibility to embolism, so the pit-area and pit-resistance hypotheses are not mutually exclusive alternatives. Instead, the question is to what extent variation in vulnerability across taxa can be attributed to variation in pit-level vs tissue-level properties. These hypotheses can be seen as addressing the underlying question of why or how different species achieve different vulnerabilities to cavitation. The results of Wheeler et al. (2005); Hacke et al. (2006) indicate that, in general, the selective pressures that act to match the vulnerability of angiosperm species to their environment have been satisfied mostly by shifts in pit area, rather than microscopic pit structure. However, further measurements that provide finer detail of pit membrane function and the connectivity between vessels are necessary to confirm this.
In gymnosperms, it appears that the average pit area is a less important factor (Pittermann et al., 2006; Sperry et al., 2006). Instead, Pittermann et al. (2006) showed a correlation between pit hydraulic resistance and cavitation pressure for northern hemisphere conifers, although the relationship was obscured when southern hemisphere conifers were included. Domec et al. (2006) found a strong relationship between P50 and pit resistance within a single Douglas fir tree. These results indicate that the trade-off between safety and efficiency is much stronger at the pit level in margo–torus membranes than in homogeneous membranes. A denser margo meshwork would provide greater protection against stretching and rupture of the pit membrane, but would also increase pit hydraulic resistance. It is clear that the relationship between margo porosity and cavitation pressure is complicated by other factors, such as depth of pit chamber (distance that the margo is stretched), pit aperture diameter and thickness of microfibril strands. Further anatomical work is required to confirm the importance of various factors involved in this relationship.
6. Three-dimensional analysis of xylem network
Thus far, the vast majority of analyses and models have examined xylem structure in two dimensions. While these analyses are useful in understanding partitioning of the xylem resistances, they overlook the complex and convoluted nature of many xylem networks (Zimmermann & Tomlinson, 1966; Burggraaf, 1972; Kitin et al., 2004) and the effects of the three-dimensional arrangement of xylem conduits on the transport of water and the propagation of embolism (Loepfe et al., 2007). In a simulation of a 3D xylem vessel network, Loepfe et al. (2007) found that hydraulic conductivity was lower than would be predicted from the sum of pit and lumen resistance. This suggests that some network-level properties are also contributing to the overall resistance of the vascular system, consistent with the results of Calkin et al. (1986), who found that conductance of the fern Pteris vittata was still only 69% of theoretical conductance for lumens and pit cavities even after pit membranes were dissolved. The discrepancy could have arisen from the only partial degradation of some pit membranes, but also from the effects of vessel topology. Consistent with the pit-area hypothesis, Loepfe et al. (2007) nominated connectivity of the system (over area of pits) as one of the most important factors determining vascular efficiency and safety. The influence of connectivity can also be seen in work on the sectoriality of plants showing that plants with highly sectored xylem are more tolerant to drought (Zanne et al., 2006). The topology of vessels is also important in terms of the propagation of embolism: vessels with large pit pores will not air seed unless neighboring vessels are air-filled.