Modeling fluid flow in Medullosa, an anatomically unusual Carboniferous seed plant

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1 Paleobiology, 34(4), 2008, pp Modeling fluid flow in Medullosa, an anatomically unusual Carboniferous seed plant Jonathan P. Wilson, Andrew H. Knoll, N. Michele Holbrook, and Charles R. Marshall Abstract. Medullosa stands apart from most Paleozoic seed plants in its combination of large leaf area, complex vascular structure, and extremely large water-conducting cells. To investigate the hydraulic consequences of these anatomical features and to compare them with other seed plants, we have adapted a model of water transport in xylem cells that accounts for resistance to flow from the lumen, pits, and pit membranes, and that can be used to compare extinct and extant plants in a quantitative way. Application of this model to Medullosa, the Paleozoic coniferophyte Cordaites, and the extant conifer Pinus shows that medullosan tracheids had the capacity to transport water at volume flow rates more comparable to those of angiosperm vessels than to those characteristic of ancient and modern coniferophyte tracheids. Tracheid structure in Medullosa, including the large pit membrane area per tracheid and the high ratio of tracheid diameter to wall thickness, suggests that its xylem cells operated at significant risk of embolism and implosion, making this plant unlikely to survive significant water stress These features further suggest that tracheids could not have furnished significant structural support, requiring either that other tissues supported these plants or that at least some medullosans were vines. In combination with high tracheid conductivity, distinctive anatomical characters of Medullosa such as the anomalous growth of vascular cambium and the large number of leaf traces that enter each petiole base suggest vascular adaptations to meet the evapotranspiration demands of its large leaves. The evolution of highly efficient conducting cells dictates a need to supply structural support via other tissues, both in tracheid-based stem seed plants and in vessel-bearing angiosperms. Jonathan P. Wilson. Department of Earth and Planetary Sciences, Harvard University Cambridge, Massachusetts jpwilson@fas.harvard.edu Andrew H. Knoll, N. Michele Holbrook, and Charles R. Marshall. Department of Organismic and Evolutionary Biology, Harvard University Cambridge, Massachusetts Accepted: 21 July 2008 Introduction Fluid flow in plants is governed by the physical properties of conducting cells. Because of this close relationship between anatomical structure and function, fossilized xylem tissues permit inferences to be drawn about fundamental physiological properties of ancient plants. Cichan (1986a) pioneered the estimation of transport rates through fossil stems, but progress in biophysical modeling now allows more accurate quantification of fossil plant function in ways that are readily understood and easily compared with that of modern plants (Tyree and Sperry 1989; Comstock and Sperry 2000; Roth-Nebelsick et al. 2000; Hacke et al. 2001, 2004; Roth-Nebelsick and Konrad 2003; Sperry and Hacke 2004). In this paper, we develop a model of water transport in the late Paleozoic seed fern Medullosa, a plant that was widely distributed in tropical ever-wet lowlands of North America and Europe, and compare it with modeled transport rates through the late Paleozoic coniferophyte Cordaites and the living pine, Pinus. Medullosa s unusual anatomy has attracted paleobotanical attention for many years. Our conclusion that Medullosa s tracheids enabled high-throughput fluid transport similar to that of angiosperm vines has important consequences for interpreting its anatomy, vascular development, and paleoecological distribution. Water Transport in Plants Photosynthesis and water transport have fundamental and far-reaching impacts on plant form and function. More than 95% of the water drawn upward from roots into the plant stem evaporates from actively photosynthesizing surfaces (Taiz and Zeiger 2002). Plants 2008 The Paleontological Society. All rights reserved /08/ /$1.00

2 FLUID FLOW IN MEDULLOSA 473 open their stomata in response to a variety of biochemical cues, allowing carbon dioxide to diffuse into the stomatal aperture, where it is ultimately dissolved in water and transported into the internal cells of leaves or other sites of photosynthetic carbon fixation. Open stomata, however, expose well-hydrated interior tissues of plants to the drying power of the atmosphere, resulting in water loss by evaporation. Water supply indirectly determines the amount of photosynthesis that can occur by limiting stomatal opening and, hence, rates of carbon assimilation; water supply can also limit cell expansion in developing leaves (Kramer and Boyer 1995; Taiz and Zeiger 2002). Evaporation of water from leaves generates a tension that causes water to move via bulk flow from the soil into roots. Water is transported to the leaves through a network of dead cells, the xylem, which in many plants also provides significant structural support. For water to ascend through the xylem, the water column must remain continuous from root to leaf; this is made possible by strong hydrogen bonding between water molecules. Gas bubbles called embolisms can develop within conducting cells when air is pulled in through the relatively porous wall regions that allow interconduit water movement, breaking the stream and jeopardizing water transport. Photosynthetically produced sugars and other solutes move down the plant from their synthesis sites through a second network, consisting of highly modified living cells called phloem. Flow of photosynthate within the phloem may be coupled to water transport through the xylem (Thompson and Holbrook 2003), but unlike xylem, phloem cells provide little, if any, structural support in most terrestrial plants and rarely preserve in the fossil record. Water flows through the lumen of xylem conduits approximately at Poiseuille flow, a rate proportional to the fourth power of the radius of the conducting cell, so a small increase in tracheid or vessel diameter can have a large effect on the amount of water transported through the xylem (Tyree and Zimmermann 1983; Sperry 1989; Comstock and Sperry 2000). Water flows between xylem conduits through pits, regions where the secondary cell wall is not deposited, such that water need only pass through the remaining primary cell wall, called the pit membrane (Pesacreta et al. 2005). Pit morphology and density have a strong effect on xylem flow rates and thus whole-plant hydraulics (Zimmermann 1983; Carlquist 2001). It has been known for decades that in seed plants xylem cell morphology reflects optimization for two mutually exclusive tasks: transport and mechanical support (Esau 1977; Mosbrugger 1990; Rowe and Speck 2004). Xylem cells optimized for maximum water transport are wide, open-ended, and covered with numerous pits, for example, vessel elements in angiosperms. In contrast, xylem cells optimized for support are long and thin, with walls that are thick relative to lumen diameter, e.g., conifer tracheids. This dichotomy extends even to the chemistry of xylem cell walls. Heavily lignified cells provide support, but this is hypothesized to reduce the ability to modulate fluid flow (Boyce et al. 2004). In contrast, lightly lignified xylem cells may be able to regulate the rate of water flow on a minuteby-minute basis, owing to the presence of pectins in the compound middle lamella that act as hydrogels, expanding and contracting in response to changes in sap ion concentration (Zwieniecki et al. 2001; Boyce et al. 2004). These cells, however, may be compromised in their ability to provide structural support. Other recent research has shown that the ability of xylem cells to resist implosion at high tensions is related to wood density and the thickness-to-span ratio of individual xylem cells (Hacke et al. 2001). Because of these wellunderstood and well-quantified relationships between structure and function, water transport and tracheid strength in ancient plants can be reconstructed by using models of xylem hydraulic and mechanical function (Esau 1977; Carlquist 2001; Sperry and Hacke 2004). Medullosa Medullosans are stem-group seed plants, sister to the clade that includes cycads, Ginkgo, conifers, Gnetales, and angiosperms (Crane et al. 2004). Ecologically, medullosans became important constituents of floodplain communities beginning in the Late Mississippian (Stewart and Delevoryas 1952; Phillips 1981;

3 474 JONATHAN P. WILSON ET AL. Dunn et al. 2003) and expanded into coal swamp environments following a mid-pennsylvanian drying event (Phillips et al. 1974; Phillips 1981; DiMichele et al. 2001). Both permineralized and compressed medullosan remains occur widely in deposits from the United States, Europe, and northwest Africa (Stidd 1981; Wnuk and Pfefferkorn 1984; Galtier et al. 1986; Galtier 1997). Reasonable whole-plant reconstructions are available (Andrews 1940; Pfefferkorn et al. 1984), although debate about thehabitofmedullosa persists (Pfefferkorn et al. 1984; Wnuk and Pfefferkorn 1984; Hamer and Rothwell 1988; Mosbrugger 1990; Dunn et al. 2003). In fact, there is little reason to believe that all medullosans had the same habit, but they all exhibit the same unusual morphology, with massive, pinnately compound leaf systems attached to slender stems characterized by a distinctive vascular system (Andrews 1940; Delevoryas 1955; Pfefferkorn et al. 1984; Wnuk and Pfefferkorn 1984; Arens 1997). Medullosans have several characters found individually in other plant groups, both extinct and extant (e.g., Calamopityales, gigantopterids, cycads), but their overall architecture is unique. Four genera of stems are recognized on the basis of morphological characters: Medullosa, Sutcliffia, Quaestora, andcolpoxylon. The vegetative structure of Medullosa species is best known, so we concentrate on them here. The 11 described species of North American medullosans range in age from Late Mississippian to Early Permian. Morphology and Anatomy. It has been noted for almost two centuries that medullosans had an unusual vascular system (Cotta 1832; Brongniart 1849; Solms-Laubach 1891; Scott 1899). Like many other seed plants, the primary xylem of medullosans developed as a eustele (Basinger et al. 1974). Secondary vascular development, however, was striking: multiple cylinders of vascular cambium developed around one or more procambia, resulting in stems that, at the completion of secondary growth, contained what look like multiple vascular segments surrounded by abundant parenchyma, rather than the solid cylinder of secondary xylem typical of extant seed plants (Fig. 1). This anatomical arrangement was originally thought to form through fusion of separate stems (Delevoryas 1955), but is now understood to reflect anomalous cambial development (Basinger et al. 1974). Cambial development in Medullosa placed each secondary xylem cell in close contact with living cells of axial parenchyma, with large, multiseriate xylem rays, or with both. Vascular segments anastomose throughout the stem of a typical Medullosa, generally separating below a petiole insertion point and reconnecting above it (Stewart and Delevoryas 1952). The degree of anastomosis and number of segments varies along the length of individual stems as well as among species. In general, stems contain two to four segments, but as many as 23 have been documented in M. primaeva. One specimen of this species has two segments near its base, divides apically into six, and then 23, following which the xylem fuses back to two segments within less than 7 cm of distance along the stem (Stewart and Delevoryas 1952). No other known plant displays this amount of variability in the distribution and activity of its vascular cambium. In medullosans, each petiole is vascularized by multiple leaf traces that arise from several segments within the stem (Basinger et al. 1974). Thus, each frond is connected to many separate but well-connected paths of water throughout the stem. Leaf traces depart from the primary xylem at the center of each segment, dichotomizing repeatedly near the point of petiole insertion to form ten to more than 100 individual vascular strands within the petiole base. This pattern of leaf trace development appears to extend, as well, to protostelic representatives of the family; in the Late Mississippian medullosan Quaestora amplecta, leaf traces that depart from multiple primary xylem points across the stem all lead into a single petiole (Mapes and Rothwell 1980). Quaestora has been interpreted as ancestral to eustelar medullosans (Mapes and Rothwell 1980), but new finds in Arkansas show that it coexisted with at least one species of Medullosa that contained a eustele, which therefore might represent the plesiomorphic morphology (Dunn et al. 2003). In any event, this distinctive pattern of petiole vascularization constitutes a synapomorphy for the Med-

4 FLUID FLOW IN MEDULLOSA 475 FIGURE 1. Morphology and anatomy of the Paleozoic seed plant Medullosa. A, Reconstruction of Medullosa thompsonii, from Andrews (1940), reprinted with permission. Because of the need to fit the drawing on one page, the fronds in this reconstruction are drawn as if the plant were wilting. For an alternative reconstruction, see Pfefferkorn et al. (1984). B, A cross-section of Medullosa sp. from the Harvard University Paleobotanical Collections, with important anatomical features labeled. ullosaceae (Mapes and Rothwell 1980; Dunn et al. 2003). Cycads exhibit a similar pattern of leaf vascularization, but their stems have concentric vascular cylinders instead of multiple vascular segments (Norstog and Nichols 1997). Medullosan plants had narrow stems (generally a few centimeters in diameter, but with axes of one species reaching 0.5 m across) but massive petioles (up to 5 m long) (Wnuk and Pfefferkorn 1984). Most Medullosa species are thought to have grown as trees (Pfefferkorn et al. 1984; Stewart and Rothwell 1993; Taylor and Taylor 1993); however, buttressing large petioles with a narrow stem presents a biomechanical problem: what supported the plant in an upright position? A number of extant plants have large petioles borne on relatively narrow stems, including tree ferns, cycads, palms and some other monocots, and the dicot Gunnera. Each of these groups has a dedicated, low-resistance pathway for water as its vascular system and differentiates loadbearing tissue elsewhere (Mosbrugger 1990, Rowe and Speck 2004). In cycads, xeromorphic and fire-resistant leaf bases support the large petioles (Norstog and Nichols 1997). A dense cortex and fibers scattered throughout the stem provide mechanical support in palms, whereas tree ferns such as Angiopteris have bands of sclerenchyma near the stem periphery, as well as armored leaf bases. Determining the role of vascular tissue in the structural support of Medullosa will help determine the best comparative model to use in efforts to understand its mechanical properties. Although briefly noted by others (Andrews 1940; Cichan 1986a,b), little attention has been paid to the fact that tracheids found in Medullosa are among the widest and longest ever reported from seed plants, living or extinct. Andrews (1940) measured 17.5 and 24.0 mm long tracheids in Medullosa, noting that the cells were so long it was difficult to find a complete cell shorter than a thin section and suggesting that his measurements, thus, underestimated the tracheids true lengths. Secondary xylem tracheids commonly exceed 200

5 476 JONATHAN P. WILSON ET AL. FIGURE 2. A, Light micrograph of Medullosa sp. tracheid; scale bar is approximately 130 m. B, Surface view of a torus-margo pit from Tsuga canadensis (Lancashire and Ennos 2002). C, Surface view of homogeneous pit membrane of Fraxinus (modified from Choat et al. 2006). D, Diagram of idealized water flow through tracheids, showing the location and simplified cross-sectional view of torus-margo and homogeneous pit membranes. m in diameter, wider than those of any extant gymnosperm (Schopf 1939; Andrews and Mamay 1953). In addition to their large size, medullosan tracheids have a high density of pits covering their walls (Fig. 2). Increased pit density decreases total resistance in the tracheid; pits are analogous to parallel resistors in a circuit. Pinus and Cordaites We chose to compare Medullosa with two other seed plants, the Carboniferous coniferophyte Cordaites and the living conifer Pinus. Cordaites contains xylem cells that are morphologically similar to those of many other extinct seed plants, including the dominant tree of Gondwana, Glossopteris. Pinus tracheids typify those of conifers and several other gymnosperms in their size, shape, and type of pits. Medullosan tracheids, in their extreme size and number of pits, represent a third type of xylem found in a small number of Paleozoic seed plants, including the Late Permian gigantopterids (Li and Taylor 1998). These three taxa are, thus, representative of the wide range of tracheid diversity evolved throughout the history of vascular plants. Pinus evolved during the middle Mesozoic and currently forms extensive boreal forests that appear to have expanded since the Oligocene Epoch (Axelrod 1986; Millar 1993). Pinus trees are characterized by crowns of needlelike foliage atop trunks of dense wood composed of short tracheids with torus-margo pits an arrangement characteristic of extant conifers in general (Bannan 1965; Bauch et al. 1972; Greguss and Balkay 1972; Judd et al. 2007). Torus-margo pits allow for high porosity in pit membranes and provide some cavitation protection, endowing conifers with a conducting efficiency comparable to that of small-vesseled angiosperms (Sperry and Tyree 1990; Pittermann et al. 2005; Pittermann et al. 2006). The cordaites are a group of woody plants considered to be stem-group conifers on the basis of ovulate branches aggregated into loose, conelike structures and saccate pollen (Florin 1950, 1951; Crane 1985; Stewart and Rothwell 1993; Taylor and Taylor 1993; Falcon- Lang and Scott 2000). In North America, cordaites were widely distributed in mire and dryland environments from the Late Mississippian through the Early Permian. Cordaites can generally be described as a group of small shrubs to tall ( 30 m) trees bearing strap-

6 FLUID FLOW IN MEDULLOSA 477 shaped leaves 10 cm to 1 m long that were attached to stems bearing broadly conifer-like wood. Unlike extant conifers, cordaite tracheids did not contain a single row of torusmargo pits; instead they contained two or three rows of pits bearing homogeneous pit membranes. In this paper, we use the leaf genus Cordaites to represent tracheid morphology for the whole plant. Methods Early models of water transport in plants focused on the nature of individual xylem cells as hollow tubes and used the Hagen-Poiseuille equation to estimate flow rates (Zimmermann 1983; Cichan 1986a). These models treated xylem in the stem as a single set of unobstructed pipes extending from roots to leaves and thus overestimated flow volumes through stems. In vivo, fluids flowing through the xylem are impeded by resistance associated with the movement between cells. A more accurate model of water transport in xylem cells, based on an Ohm s Law analogy (van den Honert 1948) that takes into account the structures that link xylem cells, allows a quantitative and anatomically accurate evaluation of xylem hydraulic properties (Hacke et al. 2004; Sperry and Hacke 2004). We have used this approach to model tracheid-level hydraulic capacity of medullosan hydraulic architecture by adapting a more generalized model of single-cell hydraulics that was developed and described in detail by John Sperry, Uwe Hacke, and colleagues (Hacke et al. 2004; Sperry and Hacke 2004). This model is based upon Hagen-Poiseuille flow through tubes (Vogel 1994) that have a finite length and are closed at the ends (Comstock and Sperry 2000), and which contain pits through which water moves from one cell to another (Hacke et al. 2004; Sperry and Hacke 2004). Two versions of the tracheid model were implementedinmatlab, onefor xylem cells with homogeneous pit membranes (Medullosa, Cordaites) and another for those with torus-margo pit membranes (Pinus). Ohm s Law models are based on the analogy between the flow of current through a circuit and water flow through the conductive tissue of a plant (Comstock and Sperry 2000; Hacke et al. 2004; Sperry and Hacke 2004). Tracheids are modeled as resistors in a circuit with total resistance (R), with flow rate (Q) analogous to current (I) and pressure drop ( P) to voltage drop ( V) (eqs. 1 and 2): V I (1) R P Q (2) R Conductance (K) is the inverse of resistance in an individual tracheid (eq. 3) andspecificconductivity, K sp K normalized by tracheid length and wall area is calculated in the model by dividing cell length (L) by the product of the cell wall area (A wall ) and total resistance (R tot ) (eq. 4). 1 K (3) R L Ksp (4) R A tot wall Measuring flow in terms of conductance, rather than flow rate, allows quantitative comparisons of different plants independent of the pressure gradient within each plant. Pressure gradient reflects the ambient environmentand can vary widely, depending on temperature, time of day, soil moisture, and other factors. Wall area is found by dividing the cell wall volume (V) by the tracheid length (eq. 5). For the cell wall volume, we modeled the tracheid as two concentric cylinders, with the same length and different radii corresponding to the outer wall and lumen, wall volume being the difference between the two. A wall equals the amount of wall material per unit length; normalizing conductance to this term gives a measurement of cell wall invested per tracheid. This is a nonstandard normalization, but it has been used in previous modeling studies (Hacke et al. 2004; Sperry and Hacke 2004). A more standard normalization is conduit conductivity per cross-sectional area (K sc, eq. 6), calculated by substituting cross-sectional area of the tracheid, including both the cell wall and the lumen, into equation (4). Conduit area (A conduit ) is calculated from the

7 478 JONATHAN P. WILSON ET AL. area of a circle with radius equal to the sum of the lumen radius and wall thickness. V Awall (5) L L Ksc (6) R A tot conduit There are two components to resistance in the tracheid (eq. 7), onederivedfromresistanceto flow through the tracheid, which is mathematically equivalent to resistance to flow in a tube (R lumen ), and the other from resistance to water flow through the pits from one tracheid to another, where (R pit ) is equal to resistance through one pit. Because water will pass through two sets of pits when moving from the lumen of one tracheid to the lumen of another, the resistance component from pits is doubled. R pit N pits R R 2 (7) tot lumen Individual pits are modeled as resistors in parallel, so that the total resistance from pits is inversely proportional to their number (N pits ). Conifers often have a single row of pits in each tracheid, usually between ten and 30, whereas Medullosa has large numbers of pits, commonly more than 200 per tracheid. To compensate, conifer pits are usually large, with a torus-margo structure that increases flow but may impede refilling after embolism (Sperry and Tyree 1990). R lumen (eq. 8) is the inverse of the Hagen-Poiseuille equation for flow across half of a tube s length. Half-tube length is used because it represents the mean distance that water flows through any given tracheid, given that tracheids have closed ends with water flowing in and out via the pits; this reduces the numerator by a factor of two. As noted above, resistance to flow is inversely proportional to the diameter of a conducting tube (here, D tracheid ) to the fourth power. Therefore, a small increase in the dimensions of a xylem cell results in a dramatic improvement in fluid flow. In addition, if all other variables are held constant, an increase in the length of a conducting tube (L) will decrease flow, albeit at a slower rate than any change in diameter. As others have pointed out (Comstock and Sperry 2000), this is not necessarily held constant in living plants, because water will pass through fewer sets of pits over a given distance when conducting cells are longer. Viscosity of water flowing through the tracheid ( HO 2 ) will vary slightly depending on environmental factors such as temperature; we used the viscosity of waterat25 C for all our calculations. 64 HO 2 L R lumen 4 (8) (D ) tracheid R pit, the pit resistance (eq. 9), consists of the resistance from the two apertures (R aperture ) through which water flows at a given viscosity (eq. 10) plus resistance from flow through the pit membrane (R membrane ; eq. 11). We modified the pit membrane resistance by a constant ( ), described in detail below. The pit aperture has a measurable thickness (t ap ) and diameter (D ap ) and opens to the pit membrane (Fig. 2D). The pit membrane is modeled as a thin sheet with a number of pores (N pore ) in it, each with a given diameter (D pore ). The pores are also modeled as individual resistors in parallel, with the consequence that membrane itself can vary; in equation (11), we used a term to modify the number of active pores per pit; F[porosity] varies from 0 to 1. Our default value of 0.7 is based on literature estimates, recognizing the possibility that some pit membrane pores may be obstructed by macromolecular gel-like compounds (Hacke et al. 2004; Sperry and Hacke 2004). R R 2R (9) pit membrane aperture 128tap H O 24 2 H2O Raperture (10) 4 3 D D ap 24 HO R 2 membrane 3 (11) N D pore pore We calculated the number of pores in the pit membrane (eq. 12) by dividing the area of the pit membrane (the square of the pit membrane diameter [D membrane ]) by the square of the sum of a single pore s diameter (D pore )plustheaverage thickness of a cellulose microfibril (t f ). We chose 15 nm as our microfibril thickness (Taiz and Zeiger 2002) and simulated a range of pore sizes, from 5 to 65 nm, consistent with ap

8 FLUID FLOW IN MEDULLOSA 479 estimates in the literature based on vulnerability curves and direct measurement (Choat et al. 2003, 2004, 2006; Pesacreta et al. 2005). (D membrane) 2 Npore F[porosity] (12) 2 (D t ) pore Value of. To adjust for discrepancies between theoretical models and experimental data from fluid flow experiments (Brodribb et al. 2003, 2005; Brodribb and Holbrook 2004; Hacke et al. 2004; Sperry and Hacke 2004; Pittermann et al. 2005; Sperry et al. 2005), the pit membrane resistance (eq. 11) was modified by a constant to allow the membrane resistance to vary (, resistivity constant ). Measurements on living angiosperms suggest that pit membranes may have up to three orders of magnitude higher resistance than models predict on the basis of first principles (Choat et al. 2006). This may be due to uncertainty about the role of pectins hypothesized to function as hydrogels in the overall retardation of fluid flow between adjacent xylem cells (Zwieniecki et al. 2001). Because the phylogenetic pattern of pit membranes contribution to overall tracheid resistance is uncertain in living plants, this constant allows for more flexibility in interpreting the functional space of tracheid conductivity. We varied between 0.1 and 1000 for Cordaites and Medullosa, but our default values were 1 and 16, respectively. These values preserved the proportionality of lumen to pit resistances at 67% and 77% respectively for tracheids of average dimensions (Fig. 3). Although neontological in its formulation, the approach outlined in the preceding paragraphs is valuable to paleobotanists because many of its stated parameters are constants or vary within well-defined environmental limits, and those that are not constants can be determined either from comparative biology of living plants and environmental data, or from anatomical study of fossil plants. Measurements and Sensitivity Analyses To calculate medullosan tracheid conductivity, we measured tracheid width, tracheid length, pit density, and pit dimensions on specimens from two species: M. anglica (Harvard Paleobotanical Collection #24474), and an unnamed species (Medullosa sp. Harvard f FIGURE 3. Proportion of tracheid resistance from cell wall (pits) as a function of diameter and length. Proportion of resistance from tracheid lumen is the reciprocal of the data shown. For tracheids as large as those in Medullosa, most of the hydraulic resistance comes from pits. Black stars indicate proportions of wall resistance that were used as default values for the three taxa and were used to calibrate values for and D pore. Tracheid dimensions: Medullosa, 142 m, 25 mm; Cordaites, 25 m, 3.3 mm; and Pinus, 39 m, 3.8 mm. Paleobotanical Collection #7791). We made measurements by using light microscopy for Cordaites (Harvard Paleobotanical Collection #53824 and #7878) and SEM imaging of macerated tracheids from Medullosa. Further measurements of tracheid diameter were made from figures of two species described in the literature to determine if dimensions were significantly different: M. noei (Delevoryas 1955; Cichan 1986b) and M. primaeva (Delevoryas 1955) (see Table 1). For comparison, measurements were also taken from Andrews (1940) and Bannan (1965) of the same parameters for Cordaites (Mesoxylon) andpinus. The tracheids of Cordaites and Pinusaresimilar in length and diameter, but they differ in

9 480 JONATHAN P. WILSON ET AL. TABLE 1. Measurements of tracheid length and diameter for fossil Medullosa and Cordaites specimens. Mean, standard deviation, and maximum and minimum dimensions are given for six taxa. Because complete tracheid length in Medullosa is difficult to observe in thin section, the numbers are based on five measured xylem cells. Diameter ( m) Mean SD Max Min n Length (mm) Mean SD Max Min n Medullosa noei Medullosa primaeva Medullosa sp Medullosa anglica Cordaites sp Cordaites sp pit morphology. Cordaite pits are ellipsoidal apertures bounded by a thin permeable membrane, whereas Pinus has circular-bordered pits that are differentiated into a porous mesh of fibers, the margo, that surrounds a thick, non-porous primary wall segment, the torus. Because of this distinctive pit structure, we used a different set of values for D pore in equations (11) and (12) for Pinus to account for the torus-margo pit membrane s increased porosity (Sperry and Tyree 1990; Pittermann et al. 2005), as described by Hacke et al. (2004). Briefly, the margo was modeled as a mesh containing large pores up to 1 m in diameter, and the torus was modeled as a nonconducting cylinder in the center of the pit membrane. Pinus stem tracheids appear to have asinglerow of torus-margo pits regardless of the tracheid s diameter, whereas Cordaites tracheids add a second or third row of pits as tracheid diameter increases. Extant conifer roots may contain wider tracheids that have a second row of pits, but this condition is rare in stems. We substituted anatomical values, as well as parameters based on estimations from extant material, into the equations and then varied length and diameter as sensitivity analyses, both to approximate the ranges of anatomical measurements found in the fossils and to study the parameter space (Table 2). In particular, the pore size (D pore ) in fossil plant pit membranes is unknown, so we substituted a value derived from analysis of cavitation vulnerability in vessel-bearing angiosperm rain forest trees for Medullosa and Cordaites (40 nm; Choat et al. 2003). There is considerable variation in pit membrane pore size; direct measurements of pore diameter via gold bead perfusion (5 20 nm; Choat et al. 2004) differ from estimates made on the analysis of vulnerability curves through application of the capillarity equation ( nm; Choat et al. 2003, 2004, 2006). We chose our value because it falls within the range bounded by the two estimates, although it increased the proportion of medullosan tracheid resistance from pits above the 40 60% threshold found in analysis of tracheids and vessels (Sperry et al. 2005, 2006; Wheeler et al. 2005). Pit Area Resistance. To assess our model of pit membrane porosity and our values for D pore and, we calculated the flow resistance per tracheid normalized on a pit membrane surface area basis. The pit area resistance (r p ) is equal to the product of the cell wall resistance (R wall ) and one-half the pit area, which is the product of the area of a single pit (A pit )and one-half the number of pits in a tracheid (N pits ) (eq. 13). Rwall Npits rp A pit (13) 2 2 Wall resistance (eq. 14) is found by subtracting the lumen resistance (R lumen ) from the total resistance (R tot ). R R R wall tot lumen (14) We compared pit area resistance calculations for Cordaites and Medullosa with recent analyses showing that tracheids of conifers and vesselless angiosperms and eudicot vessels form two statistically distinct populations with low and high pit area resistances, respectively (Hacke et al. 2007). We calculated r p for a range of pit membrane pore diameters, from 5 to 65 nm, and plotted the results against data from Hacke et al. (2007) both to compare our model

10 FLUID FLOW IN MEDULLOSA 481 TABLE 2. A comparison of the major terms in the tracheid model across the three species surveyed. The term in the equation appears at the top, followed by how the term varies across the three taxa. Anatomical measurements and literature data were used to determine ranges in the model. Calculations that varied length and diameter (Figs. 3, 6, 7, 8) also varied the number of pits (N pits ) to keep pit fraction (F pit ) within a range found in anatomical measurements and literature data. Calculations on a single tracheid morphology to determine pit area resistance and conduit specific conductivity (r p and K sc ; Figs. 4, 5) varied pit morphology and membrane parameters (D ap, D membrane, t wall, t ap, N pore ) but held diameter, length, pit fraction, and number constant. See figure captions for details. Term: D tracheid L N pits D ap D membrane t wall t ap F pit D pore N pores F[porosity] Resistivity constant Fraction of pores that are functional Number of pores in pit membrane Pore diameter (mm) Fraction of tracheid walls containing pits Pit aperture thickness ( m) Wall thickness ( m) Pit membrane diameter ( m) Pit aperture opening diameter ( m) Pit type Pit number Tracheid length (mm) Meaning: Tracheid width ,000 63, Medullosa Circularbordered , Pinus Torusmargo Cordaites Circularbordered FIGURE 4. Pit area resistance for Cordaites, Medullosa, and three types of xylem from Hacke et al. (2007): conifer tracheids, vesselless angiosperm tracheids, and eudicot vessels. Ranges for the two fossil taxa represent sensitivity analyses, with D pore increasing from 5 to 65 nm with a 1 nm step size. Horizontal lines represent medians, box ranges represent 25th through 75th percentile range, vertical lines represent 10th to 90th percentiles, and symbols are outliers. Black stars indicate values that matched expected proportions of wall and lumen resistances and were used to calibrate default values for and r p when calculating conductance. The value used for Medullosa overlaps with vesselless angiosperms, and Cordaites overlaps with conifers. with experimental data and to place Paleozoic seed plants in this context (Fig. 4). Estimating Cavitation Vulnerability. The physical structure that accounts for the wide variability in cavitation resistance observed in xylem cells remains unknown. Two hypotheses that describe the relationship between cavitation vulnerability and vessel size are the capillarity hypothesis and the pit area hypothesis. In both, the size of the largest pore in the pit membrane determines resistance to cavitation of the entire tracheid, operating under the assumption that given a pressure gradient imposed across a xylem cell, the largest pore will be the likeliest place for air-seeding to occur. In the former, the size of the largest pore is a function of interspecific variation in pit membrane pore size and cannot necessarily be predicted from first principles alone; each plant species has its own distribution of pore sizes within membranes, and this governs the plant s tradeoff between conductivity and vulnerability to cavitation. Such a view is supported by calculated values of pore sizes that can vary tenfold among species (Choat et al. 2003). In contrast, the pit area hypothesis is based on an observed correlation between increasing pit area in a xylem cell and more pos-

11 482 JONATHAN P. WILSON ET AL. itive cavitation pressure, suggesting that xylem cells with a larger proportion of their cell wall dedicated to pits will cavitate at more modest pressures than cells with lower pit areas. It has been hypothesized that the size distribution of pit membrane pores is close to uniform across all seed plants and that the probability of an anomalously large pit membrane pore in contact with a neighboring airfilled tracheid or vessel element is what determines cavitation pressure, and this latter property increases with increasing pit area. We investigated the functional consequences of Medullosa s pit area according to both of these scenarios. First, using our estimated pore size, we used the capillarity equation (eq. 15) to estimate the pressure drop ( P) required to pull air through a pit membrane with a single pore of this size, which is a function of pore diameter (D pore ), the surface tension of water ( ; 0.07 Nm 1 HO 2 ), and the contact angle between air and the lignocellulosic membrane ( ; 0 ): [ ] HO 2 (cos ) P 4 (15) D pore Second, we used the pit area from an average medullosan tracheid with diameter 142 m and length 25.4 mm to compare with Sperry et al. s (2006) correlation between pit area and cavitation pressure, to estimate a cavitation threshold. To compare the effect of pit area on cavitation vulnerability among the three taxa, we used a tracheid 41 m in diameter and 5 mm in length for both Pinus and Cordaites. To assess the structural stability of tracheids under extreme tensions, we used the observed relationship between tracheid wall thicknessto-span ratio and resistance to implosion found in Hacke et al. (2001) to determine the threshold at which tracheids in each of our taxa would implode. Others have observed that the ratio of the thickness of xylem cell walls to the span of the lumen is correlated with the ability to resist implosion. Cells with large lumens and thin cell walls are subject to implosion under strong pressure gradients, whereas cells with thick walls and short lumen diameters are not (Hacke et al. 2001), a relationship that holds across vessel elements and tracheids, albeit with slightly different within-group trends, reflecting different safety margins between the groups. We measured xylem cell wall thicknesses from Medullosa, Cordaites, and Pinus, calculated their thickness-to-span ratio for a given diameter, and plotted this value against tracheid diameter in order to determine the size at which tracheids would have been vulnerable to implosion at 2 MPa. We chose this value because 2MPa, which can be reached at moderate environmental conditions, such as a temperate forest on a summer day, is a tension at which large vessels can be vulnerable to implosion but tracheids are not. Results Anatomical Measurements. Light microscope examination of tracheids macerated from Medullosa specimens in coal balls and measurements from published figures show that these cells have large diameters, ranging from 74 to more than 200 m (see Table 1), in agreement with other published measurements of medullosan tracheid diameter (Cichan 1986a,b). In contrast, measurements of secondary xylem in two Cordaites specimens yielded average diameters of 25 and 30 m (n 21). Because flow rate is proportional to the radius of the conducting cell to the fourth power, and tracheids of Medullosa are two to five times as wide as those of contemporaneous coniferophytes, they should yield a pertracheid flow rate times higher. Medullosan tracheids macerated from coal balls had pits that covered approximately onehalf of the cell s surface and contained up to six rows of 20- m-diameter circular-bordered pits (Table 2). Cordaite tracheids macerated from coal balls contained up to three rows of circular-bordered pits that covered slightly less than one-fifth of the cell s surface. Pinus tracheids normally contained a single row of torus-margo pits along the radial wall, but rare specimens have a second row. Pit fractions ranged from a maximum of 0.5 in Medullosa to a minimum of 0.05 in Pinus. Hydraulic Conductivity. Our model produces two principal results, the first dealing with water transport capacity and the second dealing with biomechanical tradeoffs resulting

12 FLUID FLOW IN MEDULLOSA 483 from tracheid structure. First, at diameters and lengths common to both taxa in the fossil record, an individual tracheid of Medullosa would move far more water per pressure gradient and unit time than a coniferophyte tracheid, with or without torus-margo pits (Figs. 5, 6). Conduit specific conductivity (K sc ) for a medullosan tracheid of average dimensions 142 m in diameter and 25.4 mm long is approximately 0.3 m 2 /MPa s. A large Pinus strobus tracheid, 39 m in diameter and 3.8 mm long,wouldhaveak sc of approximately 0.02 m 2 /MPa s, whereas a tracheid from Cordaites of average dimensions (25.4 m in diameter, 3.3 mm long) would conduct at approximately 0.01 m 2 /MPa s. For size ranges simulated in our tests, even small medullosan tracheids have higher K sc than tracheids from Pinus and Cordaites (Fig. 6). Simulated conductivity and resistivity values compare favorably with measurements made on living angiosperms and gymnosperms (Figs. 4, 5). Resistance measurements made on conifer tracheids and angiosperm vessels are broadly consistent with this model s predictions of conductivity in Cordaites and Pinus and in Medullosa, respectively, when the dimensions are comparable between the fossil and living taxa (Choat et al. 2003; Sperry 2003; Hacke et al. 2004, 2007; Sperry and Hacke 2004; Pittermann et al. 2005). In terms of conductivity, then, medullosan tracheids are more similar to angiosperm vessels than they are to conifer tracheids, despite originating from a tracheid-like developmental program. The anatomy of medullosan tracheids alone also puts to rest the suggestion that there are developmental limits to tracheid size that prevent them from reaching sizes comparable to some vessels (Lancashire and Ennos 2002). For a Medullosa noei tracheid 142 m in diameter and 25 mm long, conductivity normalized to cross-sectional wall investment (K sp ) is approximately 9.5 m 2 /MPa s (Fig. 7). A large Pinus tracheid 40 m in diameter and 4 mm long could conduct at approximately 0.11 m 2 /MPa s. Tracheids of Cordaites, with circular-bordered pits, conduct water nearly at values comparable to Pinus tracheids because of the increased area of pits on each tracheid, but have a lower conductivity than tracheids of Medullosa (data not shown). When the size ranges of medullosan and pine tracheids are overlain andconductivityis compared, it becomes clear that even the largest pine tracheids have a lower conductivity per cross-sectional wall investment than the smallest medullosan xylem cells (Fig. 7). The largest medullosan tracheids conduct nearly two orders of magnitude more water than the largest conifer tracheids, independent of pitting style, when normalized to cross-sectional wall thickness. The hydraulic conductivity of medullosan xylem per unit area is high. It is difficult to make quantitative comparisons with experimental values for living plants, because of the different methods in reporting data (Tyree and Ewers 1991); however, virtually half of the cross-sectional area of a medullosan stem is composed of large tracheids, whereas angiosperm xylem combines relatively few large, long vessels with numerous fibers. In this way, medullosan stems are constructed like conifer stems, except they contain tracheids with high conductivity rather than numerous low-conductivity tracheids. Given the large amount of stem cross-sectional area devoted to medullosan tracheids, we would expect per-area conductivity to be comparable between a vessel-bearing eudicot and a tracheid-bearing Medullosa. Pit Membrane Porosity and Morphology Varying pit membrane porosity over three orders of magnitude affects the magnitude of our results but not the rank order of the differences between medullosan and coniferophyte tracheids. Making individual pits less porous in the model by increasing the resistance of the pit membranes had a stronger effect on tracheids that have fewer pits than on those that have many (Fig. 5). However, because the resistance component from pits models them as resistors in parallel, with a higher number of pits lowering the total resistance, the porosity of the membrane is only one of many important considerations. Pit area resistance measurements for Cordaites and Medullosa yielded values of 1.5 and 23.2 MPa s/m 1 for pit membrane pores 40

13 484 JONATHAN P. WILSON ET AL. FIGURE 5. Conduit specific conductivity (K sc ) for Medullosa (asterisks), Cordaites (stars), and Pinus (open triangles) for given pit area resistivities (r p ). Comparison is made with vesselless angiosperm and conifer tracheids with comparable diameters for the two coniferophytes, and for a eudicot vessel with comparable diameter to Medullosa. Bolded characters identify values used as per-taxon standard throughout the paper. Values for vesselless angiosperm tracheids, conifer tracheids, and a eudicot vessel are from Hacke et al. (2007). Vesselless angiosperm and conifer tracheid diameters are presented next to crosses and squares. Owing to the lack of data for vessels with diameters comparable to Medullosa, 142 m vessel value is extrapolated from 67% optimum line in their Figure 1B. Bolded value for Medullosa K sc yields 77% of total hydraulic resistance from pits; bolded value for Cordaites has 67% of hydraulic resistance in pits. Because tracheid resistivity is highly variable with respect to diameter, two values are shown for vesselless angiosperm and conifer tracheids. nm in diameter (Fig. 4). These values place Cordaites within the group of living conifers and Medullosa between the vesselless angiosperms and vessel-bearing eudicots (Hacke et al. 2007). Smaller pore sizes increase pit area resistance for both taxa but do not change this association. Except for tracheids of extremely low diameters and lengths (less than 20 m and1 mm, respectively), medullosan tracheids could conduct higher volumes of water than conifer tracheids, with or without torus-margo pits (Fig. 6). Tracheids of these sizes are absent in our specimens of Medullosa (Table 1). The large number of pits in each medullosan tracheid, compared with conifer tracheids (Table 2, Fig. 2), dramatically reduces the resistance to water flow through a xylem cell by greatly increasing pit membrane area. This increase in pit area, in turn, decreases the total resistance to fluid flow through the xylem cell. Large pit diameters in Medullosa further decrease resistance in any individual pit. Resistance to Implosion and Cavitation. The second result concerns the biomechanical functionality of medullosan tracheids. The advantages these cells confer in conductivity come at a physiological cost, making Medullosa more vulnerable than pycnoxylic seed plants to implosion and cavitation induced by water stress. Wood density, expressed as the thickness-to-span ratio of xylem cells, has been shown to correlate positively with resistance to implosion under tension (Hacke et al. 2001). Calculating this ratio for Medullosa and Pinus while varying the diameter of the tracheids shows that medullosan tracheids would suffer irreversible damage at modest negative pressures (Fig. 8). Experimentally derived lines of implosion found by Hacke et al. (2001) suggest

14 FLUID FLOW IN MEDULLOSA 485 FIGURE 6. Conduit specific conductivity (K sc )inmedullosa, Pinus, andcordaites tracheids versus diameter and length. Note differences in scales in the three graphs. Color (z-axis values) is consistent across the three plots. that the largest tracheids in Medullosa would have imploded at tensions less than 2 MPa, a tension that can be reached in a temperate forest on a dry, sunny day. Indeed, medullosan tracheids would probably have embolized at lesser tensions. The thicker, narrower tracheids of Pinus and Cordaites are unlikely to implode at these tensions; their thickness-to-

15 486 JONATHAN P. WILSON ET AL. FIGURE 7. Conductance normalized to cross-sectional wall thickness (K sp )inmedullosa and Pinus tracheids versus diameter and length. Contours show lines of equal conductance (K sp )inm 2 /MPa s, and boxes outline size ranges possible in extant plants (for Pinus) or the fossil record (for Medullosa). Conductance in medullosan tracheids always exceeds that of pine tracheids. span ratio lies far from the line of implosion. In fact, in some Pinus species, excised branches do not experience any loss of conductivity under tensions greater than 2 MPa (Pittermann et al. 2006). The thickness-to-span ratio of medullosan tracheids also suggests that the vascular system could not have been an important source of structural support, as it was always at risk of cavitation, embolism, and subsequent implosion. As described above, our model also predicts that most of the hydraulic resistance in a medullosan tracheid should come from the pits, rather than approximately 35% and 65% from the lumen and the tracheid wall, respectively, as experimental data suggest for both conifers and woody angiosperms in the Rosaceae (Wheeler et al. 2005; Sperry et al. 2006). To investigate the cavitation resistance of a medullosan tracheid that, according to the capillarity hypothesis, had 65% of its flow resistance coming from pits, we imposed an increase in the size of the pores in pit membranes of an average medullosan tracheid (diameter 142 m, length 25.4 mm) until the pits accounted for 65% of the tracheid resistance, rather than 87%. We used this pore diameter to predict the pressure gradient that would have caused 50% loss of conductivity FIGURE 8. Medullosa (thick line), Cordaites (dotted line), and Pinus (thin line) thickness-to-span ratios versus tracheid diameter. Ranges are based on tracheid diameters and thicknesses found in fossils and the literature (Bannan 1965; Greguss and Balkay 1972). The hashed zone is where given thickness-to-span ratios cause irreversible implosion at 2 MPa (from Hacke et al. 2001). from cavitation (P 50 ) in medullosan wood, using the capillarity equation (eq. 15). Pores 100 nm in diameter caused pits to account for 65% of medullosan tracheid resistance, and this value substituted into equation (15) suggests that a pressure gradient of 3 MPa could cause air-seeding in medullosan tracheids. It is possible that there are rare occurrences of pores this size in medullosan pit membranes; they occasionally occur in vesselless angiosperms (Hacke et al. 2007) but are rare in angiosperm and fern pits (Carlquist 2001). To estimate cavitation vulnerability in Pinus, Cordaites, andmedullosa according to the pit area hypothesis, we also calculated the pit area of a tracheid from each of our three taxa. A medullosan tracheid of average diameter and length would contain pit area of approximately 3.3 mm 2, whereas Pinus and Cordaites are two to three orders of magnitude smaller: and mm 2, respectively. We plotted these estimates of pit area against the experimentally derived correlations of pit area and cavitation resistance found by Sperry et al. (2006). Tracheids from Medullosa fell within the ranges of pit area per tracheid found within angiosperm vessels and yielded a cavitation pressure of 0.88 MPa. Cordaites and Pinus fell within the range of conifer stem tracheids, and yielded a cavitation pressure between 2and 7.5 MPa, with uncertainty due to a poor r 2 value for conifer tracheids (r ). These values are consistent with cavitation pressures found in experimental analyses of conifer and