Hydraulics of plant growth

Transcription

1 CSIRO PUBLISHING Functional Plant Biology, 2004, 31, Review: Hydraulics of plant growth John S. Boyer A and Wendy K. Silk B A College of Marine Studies and College of Agriculture and Natural Resources, University of Delaware, Lewes, DE 19958, USA. Corresponding author; boyer@cms.udel.edu B Department of Land, Air, and Water Resources, University of California Davis, Davis, CA 95616, USA. Abstract. Multicellular plants rely on growth in localised regions that contain small, undifferentiated cells and may be many millimetres from the nearest differentiated xylem and phloem. Water and solutes must move to these small cells for their growth. Increasing evidence indicates that after exiting the xylem and phloem, water and solutes are driven to the growing cells by gradients in water potential and solute potential or concentration. The gradients are much steeper than in the vascular transport system and can change in magnitude or suffer local disruption with immediate consequences for growth. Their dynamics often obscure how turgor drives wall extension for growth, and different flow paths for roots and shoots have different dynamics. In this review, the origins of the gradients, their mode of action and their consequences are discussed, with emphasis on how their dynamics affect growth processes. Keywords: cell enlargement, growth-induced water potential, growth-sustaining water potential, osmotic potential, turgor. Introduction The enlargement of plant organs involves uptake of water by the cells and expansion of the cell walls because of the resulting turgor pressure (internal hydrostatic pressure). Nutrient and metabolite deposition accompany this process, causing the water uptake that creates the pressure and sustains the enlargement. For land plants, a vascular system carries these substrates for long distances, but growing cells often are located several cell lengths, and possibly several millimetres, from the nearest xylem or phloem element. After leaving the vascular system, the movement occurs through tissues anatomically unmodified for transport, but this last section of the path is an essential part of the supply chain for growth. Because both solutes and water are involved, factors affecting the movement of either type of molecule will alter the growth of the cells. This review provides an overview of some of the principles involved, with emphasis on water movement because of its requirement not only for metabolism but also for the cell expansion process. Attention also will be given to the kinematics of growth, since cellular water uptake is causally related to the spatial pattern of cell expansion. For readers requiring more details, we recommend related reviews by Boyer (1985, 1988), Silk (1994), Hsiao and Xu (2000), Pritchard et al. (2000) and Fricke (2002). A recent opinion paper on the role of aquaporins (Hill et al. 2004) is also relevant. For several years, we have studied what controls water and solute movement in growing tissue with our co-workers. Through this work we have found that the same forces that govern movement in the vascular system appear to be involved in movement afterward to the growing cells, but with a few differences. In this review we will consider the path of water and solute movement, flow rates, fluxes (flow rate per unit cross-sectional area), driving forces (potentials, as energy per unit volume, equivalent to a force per unit area or pressure) and the effects of these on growth. Path of water to growth zones in the root and shoot As water moves from the soil into the root and towards the shoot, some of it enters growing cells. It is distributed to each cell, and the tissue grows as a unit. In roots, cells in the tip absorb water from the root surface. The resulting elongation provides access to new soil volumes with their stores of water and nutrients. As the water moves radially inward, it encounters a progressively smaller circumference and thus, smaller number of cells, so that less water is needed to sustain Abbreviations used: G, water potential of enlarging cells of growth zone; M c, water potential of mature leaf tip; R, water potential of mature root; X, water potential of protoxylem in growth zone; w, water potential. CSIRO /FP /04/080761

2 762 Functional Plant Biology J. S. Boyer and W. K. Silk Fig. 1. Cross-sections of (A) the growth zone of soybean hypocotyls (stem), and (B) mature region of sunflower root, (C, D) corresponding directions for water flow during growth of the two organs, respectively, and (E) longitudinal section of root growth zone in maize. Note in (A) that protoxylem of stem has been stained red with safranin fed to cut stem base. Arrows show stained protoxylem vessels scattered inside a band of small, undifferentiated cells. Water must pass through this band in order to move outward. In (E), there is no functioning xylem (protoxylem is developing) and little functional phloem (mostly at top of section). Lines and arrows show likely path for water and / or solute after delivery by phloem (- ---)orfrom soil ( ). the growth of the root interior than the exterior (cross-section for a mature root is shown in Fig. 1B and a flow path for growth indicated in Fig. 1D). The uppermost adventitious roots in maize ( prop roots) can grow slowly through the air, and in this situation, they obtain all their water from distant xylem and phloem. Recent evidence indicates that the proximal end of the root growth zones may aquire water externally when surrounded by aqueous medium, while the tip (including the meristem) receives some water symplasmically, probably from the phloem that supplies solute and also some water (Bret-Harte and Silk 1994; Frensch and Hsiao 1995; Hukin et al. 2002; Gould et al. 2004). Phloem and xylem cells differentiate at a considerable distance behind the root tip (Fig. 1E). Solute must move several millimetres without phloem, and water moves more than a centimeter without xylem. Regardless of whether the water is delivered by xylem or phloem, its path after leaving these tissues takes it into the elongating tissues, and the forces and gradients will be similar for water from either source. Therefore, in ordinary circumstances, water probably enters from the soil for root growth, but some movement from the xylem and phloem is also involved. By contrast, in the shoot water moves from a few vessels, deep within the tissues, and the movement tends to be radially outward. The radial component spreads the water laterally from the internal, localised vascular system, although there may also be radial movement inward towards central parenchyma tissues. The contrasting properties for root and shoot are shown in Fig. 1 where water in soybean hypocotyls spreads radially outward to supply approximately 70% of the cells and inward to supply 30% (compare shoots in Fig. 1A, C with roots in Fig. 1B, D). For shoots, the outward movement involves a larger circumference and thus, greater number of cells along the radius, and the cells next to the vessels must transmit water not only for their own growth but also for this increasing number of outlying cells. As a consequence, the growth fluxes through cells near the vessels are quite large compared with those through cells at the surface. In the leaf, water is also supplied to other growing cells by an internal protoxylem. Note that for sorghum in Fig. 2, water must pass from protoxylem through some densely packed cells to enter and inflate both parenchymal and epidermal cells. The water relations of growth of a similar tissue, the maize leaf, are discussed in a later section (Relation between growth-sustaining and transpirationsustaining water potentials). Growth-sustaining water potentials There is substantial evidence that water moves from cell to cell driven by gradients in water potential or its components (Kramer and Boyer 1995). Potential gradients indicate the

3 Hydraulics of plant growth Functional Plant Biology 763 Fig. 2. Cross-sections of growth zones in sorghum leaves. (Left) Fluorescent dye supplied to the base of the shoot is absorbed by functional protoxylem, but not by developing metaxylem. (Right, A and B) The sixth leaf encloses the younger seventh leaf (scale bar = 300 µm). (Right, C and D) Enlarged images of the vascular bundle (scale bar = 25 µm) are displayed below the cross-sections of a control (A) and a salt-affected (B) leaf. Taken from Baum et al. (2000) with permission from Blackwell Publishing. change in potential per unit distance and, in the xylem, the gradients consist mostly of tensions (negative pressures per unit distance along the xylem). In the phloem, bulk-solute flow is driven long distances by positive hydrostatic pressure gradients. Where water must cross membranes, it is the sum of osmotic and hydrostatic potentials, i.e. the water potential, that drives flow (Kramer and Boyer 1995). Therefore, outside of the xylem and phloem in growing tissues, the implication is that gradients in potential should also exist. Because gradients provide the driving forces for flow, their shape and steepness give important information about flow. One can tell whether or not flow is occurring and if so, in which direction. Gradients can reverse and cause the flow direction to reverse. Occasionally, gradients give a clue about how much flow is occurring, provided something is known about the conductivity of the flow path. As a result, measuring potentials in particular positions in enlarging tissues allows a potential distribution to be drawn. Its slope, d / dx, at a particular place gives the gradient at that location in the distribution. Gradients often have different values in different parts of a growth zone. They also change with time and environmental conditions. Much of the evidence for growth hydraulics comes from this type of gradient information. The first gradients reported by Boyer (1968) were followed by many examples in a range of species (Cavalieri and Boyer 1982; Barlow 1986; Nonami and Boyer 1993; Fricke et al. 1997; Fricke and Flowers 1998; Martre et al. 1999) and different growth zones from individual plants (Westgate and Boyer 1984, 1985). Molz and Boyer (1978) developed the theoretical basis for the radial flux in one dimension in the intercalary meristem of soybean hypocotyls (later developing into stems), while Silk and Wagner (1980) provided the theoretical framework for a 3-dimensional treatment of the corresponding gradients in maize roots. These treatments did not require any special features of growing cells and assumed only that they transmitted water as readily as other cells. The gradients developed as water moved through many cell wall / plasma membrane barriers. Considering only the water potentials in the gradients, in shoots the nearby xylem with high water potential (X) supplied growing tissues of lower water potential (G), and the growth-sustaining water potentials (X G) were surprisingly large. In maize leaves and stems, (X G) was MPa (Westgate and Boyer 1984; Tang and Boyer 2002). It was reported that the potential G was an artefact of excision (Cosgrove et al. 1984), but it was observed in completely intact plants (Boyer 1968; Cavalieri and

4 764 Functional Plant Biology J. S. Boyer and W. K. Silk Diffusivity (10 10 m 2 s 1 ) Ψ w (MPa) A B Pith Xy Cortex Radius (µm) Fig. 3. Diffusivity (A) and water potential (B) for water moving from cell to cell across the radius of the growth zone in a soybean hypocotyl. Note that in (A) the band of small, undifferentiated cells has a low diffusivity for water (shown between the vertical dashed lines). Water must move to the right through this band to reach the outlying cells. As water moves outward, its water potential ( w ) becomes lower (B) and it encounters larger volumes of tissues to which water must be supplied. Diffusivity was determined from the kinetics of cellular water flow with a pressure probe. w was determined as the sum of cellular turgor pressures measured with a pressure probe and osmotic potentials from the same cell measured with a nanolitre osmometer. In (B),, uncorrected for dilution in the pressure probe;, corrected for this effect. Adapted from Nonami and Boyer (1993) and Nonami et al. (1997). Boyer 1982; Westgate and Boyer 1984; Boyer et al. 1985). Other evidence indicated only slight changes in G with excision (Boyer 1968; Boyer et al. 1985; Matyssek et al. 1991; Tang and Boyer 2002). G appeared to be low because water needed to be extracted from the distant xylem at a rate sufficient to meet the demand of the enlarging shoot tissues. Another feature of fundamental importance was the location of the shoot vascular supply relative to the growing cells. In intercalary meristems, such as those in grass leaves and stems or hypocotyls of dicotyledonous plants, a few xylem strands run right through the growth zone and are located inside a sheath of small, undifferentiated cells (Fig. 1A). The small cells place many cell wall / plasma membrane barriers in the path for flow from the protoxylem to the outlying growing cells. Nonami et al. (1997) measured the diffusivity for water in these cells in soybean hypocotyls and found that it was low, only approximately 10% of that in the cortical cells farther outside (Fig. 3A). Much of the low diffusivity comes from the size of the cells, which are small, and it occurs despite the particularly abundant expression of aquaporin mrna in the cells close to the vascular system (see references cited in Hukin et al. 2002). This illustrates the effect of small, tightly-packed cells on water flow. When the water potential distribution was plotted as a function of position in the growth zone, gradients were apparent (Fig. 3B). Those extending outside through the cortex were steeper than those extending inward to the central pith, partly because of the barrier of small cells (Fig. 3B), which will later differentiate into vascular cells. These small cells will not enlarge until most elongation growth is completed, at which time thick, relatively nondeformable walls can be built. The result during elongation is a low number of vessels close to the enlarging cells, with many small undifferentiated cells creating a flow barrier. In three dimensions, the gradient in water potential appears as a downwardly-directed potential field in the growth zone (the gradient is rotated around the centre of the stem to form the field shown in Fig. 4A). The downward direction is indicated by the slope of the field. It is steepest close to the xylem and shallowest in the outer regions of the stem and in the centre. The shallowness occurs because water is needed only for the growth of the cells in these locations. This is in contrast with cells near the xylem vessels, which must move water for their own growth and for all the outlying cortical cells (and in-lying pith cells). When tensions develop in the vascular system, the potential falls and reverses the potential field near the xylem (Fig. 4B). The reversal of the field immediately prevents water from moving out of the xylem. Indeed, water tends to move back into the xylem from the surrounding cells. Because water must enter all the cells in order for them to grow as a tissue, a lack of water movement out of the xylem stops growth immediately. Growth does not resume until the field

5 Hydraulics of plant growth Functional Plant Biology 765 Pith Xylem Cortex Pith Xylem Cortex ψ w (MPa) ψ w (MPa) Radius (µm) Radius (µm) A B Hydrated soil Dehydrated soil (3 h) Fig. 4. Three-dimensional field of w in the growth zone of a soybean hypocotyl (A) during rapid plant growth in hydrated soil and (B) 3 h after tension develops in the xylem in dehydrated soil. Downward slope of the field indicates direction of water movement. Adapted from Nonami et al. (1997) and reproduced with permission from the Annual Reivew of Phytopathology, volume 33(c) 1995 by Annual Riviews, moves downward and the water potential again decreases radially from the xylem. Nonami et al. (1997) found that re-establishing the gradient may take several hours, during which growth is inhibited. This finding has proven to be one of the most important features of growth hydraulics. It is based on slow water transmission by the growing tissue, allowing local gradients to change without immediately altering the rest of the gradient as in Fig. 4B. Growth is affected for the entire organ because these gradients are responsible for moving water into the enlarging cells, and a local change can disrupt the entire supply. Such local changes in gradients tend to occur in and around the xylem (Nonami et al. 1997) since xylem tensions can change rapidly. However, they are also found in small groups of cells such as differentiating callus in tissue culture (Ikeda et al. 1999). In shoots, the local changes may occur near the xylem without detectable turgor changes in the outer layers of growing cells such as the epidermis (Nonami and Boyer 1989), which seems to control extension rate (Passioura and Boyer 2003). Passioura and Boyer (2003) constructed a mathematical model relating these spatial aspects of water potentials, water uptake and turgor-driven growth in soybean hypocotyls, then used measured growth properties, tissue dimensions, and diffusivities to test whether a local change in the potential field next to the xylem could rapidly affect growth. With the diffusivities from Fig. 3A, the w measured in Fig. 3B could be predicted from observed growth rates. The field in the model could be changed by altering the w in the xylem, and a local change developed in the cells next to the xylem similar to that shown in Fig. 4B. Importantly, growth rates responded immediately for the entire tissue without detectable changes in turgor or water potential of the epidermis, confirming the experimental behaviour of the hypocotyls reported by Nonami et al. (1997). This model was the first to link the rheological properties of the growing cell walls to the transport of water in a growing tissue. Lockhart (1965a, b) considered cell enlargement to be driven largely by turgor pressure, which irreversibly deformed the cell wall as the cell compartment expanded. The expansion required turgor above a minimum before irreversible deformation began. Using this relation, it would be expected that the larger the turgor, the faster the growth. However, because of the hydraulics of growth, water needs to enter the cells simultaneously. As a consequence, a lower turgor creates a lower water potential and enhances water uptake. It is this balance of the higher turgor for wall deformation and lower turgor for water uptake that is the central feature of the growth model of Passioura and Boyer (2003). Where do potential fields come from, and how do they extend to the xylem? There is evidence that they originate from the yielding of the cell wall, which prevents turgor pressure from becoming as high as it otherwise would (Boyer 1968, 2001). In order to demonstrate this, the hypocotyl of soybean was allowed to grow into a high-pressure vessel

6 766 Functional Plant Biology J. S. Boyer and W. K. Silk while the roots were in water held outside the vessel (Boyer 2001). Applying pressure decreased wall yielding of the growing cells and made the growth-sustaining potential field smaller. Eventually wall yielding was prevented as pressures increased. The growth-sustaining potential disappeared (Boyer 2001), establishing wall yielding as the inducer of the potential field. Consequently, the growth-sustaining potentials are often called growth-induced potentials (Molz and Boyer 1978). When the wall yields, the low turgor contributes to the maintenance of cell water potential below that of the water source, that is, below the potential of the soil or xylem and creates (X G). Thus, wall yielding is essential to the thermodynamics of growth, and is induced by the action of metabolism on the cell walls, allowing them to extend with the force of turgor. Growth regulators such as auxin mediate the softening of the walls that allows this yielding, and auxin-responsive tissues show larger growth-sustaining water potentials when auxin is present and growth is rapid than when auxin is depleted and growth is slow (Maruyama and Boyer 1994; Ikeda et al. 1999). Therefore, regulation of the fields in growth-sustaining water potentials depends partly on those factors that enhance wall yielding and may include growth regulators transported between roots and shoots (Passioura 1988; Gowing et al. 1990; Davies and Zhang 1991; Sharp and LeNoble 2002; Liu et al. 2003). As a result, roots and shoots may communicate conditions that accelerate or retard the development of growth-sustaining potentials and growth in the relevant organ. There is increasing evidence that low cell water potentials are transmitted to the xylem as a tension in the cell walls, measurable with a pressure chamber (Nonami and Boyer 1987; Boyer 2001) or isopiestic psychrometer (Boyer et al. 1985). The pressure chamber measures the tensions in the xylem extending into the apoplast of the surrounding tissues (Boyer 1967a, b), and the isopiestic psychrometer measures the vapour pressure of water directly in the apoplast (Boyer 1995). For several reasons (Boyer 1995), psychrometers other than isopiestic ones often have difficulty operating within the range of (X G) that sustains growth. Solutes in the apoplast were initially thought to accumulate and account for most of the growth-sustaining potential (Cosgrove and Cleland 1983), but later work found only low concentrations of solutes in the stems (Nonami and Boyer 1987; Boyer 1993) and detected sizeable tensions instead (Nonami and Boyer 1987). Similarly low concentrations occur in the apoplast of leaves (Scholander et al. 1965, 1966; Boyer 1967a; De Roo 1969; Jachetta et al. 1986) but fruits often have high concentrations where the phloem unloads solute into the apoplast around the developing embryo (Maness and McBee 1986; Bradford 1994). As a consequence, the sequence of events appears to be that wall yielding often mediated by plant growth regulators prevents turgor from reaching its maximum, a low water potential is generated, the potential is transmitted to the cell walls as a tension, and the tension draws water out of the xylem for the growth process. Solute deposition inside the cells is necessary to provide the substrates for the growth process, and to prevent osmotic forces from being diluted by the incoming water. Solute deposition rates in growing tissue are synchronised with growth to maintain solute potentials as low as (Silk et al. 1986; Martre et al. 1999; Pritchard et al. 2000) or lower than (Cavalieri and Boyer 1982; Michelena and Boyer 1982; Westgate and Boyer 1985; Nonami and Boyer 1993) those found in the mature tissue. Relation between growth-sustaining and transpiration-sustaining water potentials In comparison with growth, larger amounts of water move through the plant for transpiration. In effect, growth competes with transpiration for water in the xylem, and the forces causing water to move to the evaporative surfaces are important for the forces that supply water for growth. The xylem is constructed to move large amounts of water with small forces, but water for growth must be extracted against these forces. By contrast, the pathway for growth involves cells mechanically undifferentiated for transport, and comparatively large forces need to be generated. Figure 5A compares the water potentials for transpiration and growth in a maize plant, and illustrates that the protoxylem running through the basal growth zone supplies water to an exposed leaf blade with only a modest gradient, i.e. (R M c ) for the distance between mature root and leaf tip. Water for the growth zone is removed from the transpiration stream rushing upward, and (X G) is larger than (R M c ) despite the small distances the growth water must move. At first, it may seem surprising that water moving out of the protoxylem in the growth zone of a leaf should encounter a high resistance to flow. However, anatomically, the growth zone resembles the vascular architecture of the soybean hypocotyl (compare Fig. 6 with Fig. 3, also note the radial character of tissues around the vessels in growing sorghum leaves, Fig. 2). The protoxylem is enclosed by a sheath of small, undifferentiated cells that later enlarge and become vessels and vessel-associated tissues. Water moving radially out of the xylem must pass through the large number of cell walls and plasma membranes of these small cells before it reaches the bulk of the growing tissues. A slice through the probable water potential field is shown below the anatomical section in Fig. 6, and indicates that the steepest part of the field is likely to be in the sheath of undifferentiated cells that will differentiate into vascular bundles, although the distribution of aquaporins could alter the shape. The higher potentials in the leaf growth zone are confined to the xylem and nearby cells, and most of the growing cells have low water potentials. This may account for

7 Hydraulics of plant growth Functional Plant Biology 767 M A B M - - M - G R S Fig. 5. Forces required to move water for leaf growth and transpiration in maize. The growth zone for the labelled leaf is in the basal 10 cm, G. Above the growth zone are the mature tissues of the exposed leaf (M a, M b, M c ). Below the growth zone are the soil, S, and mature tissues of the roots, R. For a growing leaf (A), water potentials for each of these positions are shown during the daytime ( ) and at night ( ). Transpiration rates are low at night but growth takes place and the growing tissues exhibit a growth-sustaining (growth-induced) water potential (G is located to left of S, R, M a, M b, M c ). The vertical dashed line is the water potential in the protoxylem of the growth zone, defined in the text as potential X, inferred by connecting the points above and below the growth zone. During the day, the xylem develops a transpiration-induced tension that moves the dashed line left towards lower potentials. Growth must extract water under this tension and G moves left. A transpiration-induced water potential is evident throughout the shoot. Note that the growth-induced potential (X G) is larger than the transpiration one (R M c ), reflecting the difficulty water encounters when it moves radially outward into the growing tissues compared with its upward movement in the xylem. When the leaf matures (B), the growth-induced potential is absent but the transpiration-induced potential remains. Adapted from Tang and Boyer (2002). the low water potentials in the growth zone when measured by isopiestic psychrometry, because the psychrometer indicates the vapour pressure of water in the cell walls of the entire region (G in Fig. 5). Martre et al. (2000) observed that in fescue leaves, which have parallel veins, the longitudinal pattern of local growth rates, and associated water deposition rates, parallels the pattern of size of the radius of the protoxylem elements. This observation is consistent with the leaky pipe model of monocot-leaf growth. Larger water sources (wider veins), leaking in response to the radial water potential gradients, are associated with greater growth rates. Martre et al. (2001) and Tang and Boyer (2002) found similarly steep radial water potential gradients in growth zones of fescue and maize leaves. In comparing droughted and control leaves of sorghum, Baum et al. (2000) found that the water deposition rates associated with growth were proportional to the square of the protoxylem radius. They hypothesised that the closer spacing of veins in the droughted leaves also influenced the hydraulics of growth. Most recently, Zwieniecki et al. (2003) showed that the ratio of axial and radial hydraulic resistance is a major design parameter influencing the distribution of water uptake from a porous pipe. All of these analyses draw attention to the importance of tissue geometry in regulating water delivery for growth. Hsiao et al. (1998) found that pressure applied to a root system would alter rates of leaf growth if the water status of the shoot was not too high. They ascribed the effect to changes in turgor pressure of the growing cells, which also implies that the growth-sustaining w field could have changed. Tang and Boyer (2003) measured (X G) in leaves of plants growing in moderately water deficient soil and found that a similar pressurisation increased xylem w and thus (X G). Leaf growth increased. This gives good support for the implications from Hsiao et al. (1998). However, in severely dehydrated soils, the pressure application did not drive water into the roots rapidly enough to increase (X G), and growth did not respond. This suggests that the ability to hydrate the xylem is a key to the growth response to pressure (Tang and Boyer 2003). Tang and Boyer (2003) found that the xylem w responded not only to the amount of water absorbed from the soil but also to the need to hydrate mature tissues and satisfy the losses caused by transpiration. The amount of water needed to satisfy these latter demands is large compared with the amount needed for growth. Consequently, low rates of root water absorption can limit the growth response because

8 768 Functional Plant Biology J. S. Boyer and W. K. Silk J 2 J 1 2 J J = K Ψ µm J 1 g 1 = K Ψ 1 J 2 g 2 = K Ψ 2 w X VB M Fig. 6. Anatomy and likely distribution of water potential in the elongating region of a growing maize leaf. The distribution is hypothesised from (X G) measured with an isopiestic psychrometer in Fig. 5. Distance is shown by the scale bar = 100 µm. The anatomical structure suggests that the slope of the w distribution (gradient) will be steepest in cells close to the protoxylem. Note the small, undifferentiated cells enclosing the protoxylem, which is stained red with safranin moved into the leaf by transpiration. The small cells will later enlarge and differentiate into xylem elements, sieve elements, and associated tissues in the mature blade. X, protoxylem; VB, vascular bundle; M, mesophyll. Adapted from Tang and Boyer (2002). a favourable (X G) fails to form when the mature shoot tissues use large amounts of water. A continuum model for growth-sustaining water potential A general description of the relationship between water potential and growth in a non-compartmented continuum was formulated by Silk and Wagner (1980) for roots, generalising from ideas of Molz and Boyer (1978) in stems. The approach led to an equation in three dimensions for any non-compartmented continuum. For the corn root, the boundary conditions and 2-D geometry specific for the root were added. The other addition was the distinction between spatial and material visualisations. The 2-D spatial solution could be combined with the growth trajectory to infer water potential of a material element (very small segment of root) during its displacement in time and space. Using the numerical methods available at the time, the equation was solved. The spatially varying diffusivities implied by the anatomy were unknown, and neither the Molz and Boyer (1978) nor the Silk and Wagner (1980) theory included the X VB Fig. 7. Diagram of a cell embedded in a file of contiguous, expanding cells. J, water flux; K, hydraulic conductivity. Only water moving faster than the cell wall will cross the wall to inflate the cell. The water potential causing growth is related to the difference in growth displacement velocity, g, between the apical and basal ends of the cell. Adapted from Silk and Wagner (1980). bulk flow of water from the phloem. Growing tissue was seen as a distributed sink for water. The driving force for water movement in the plant, as in other porous media, was the gradient in total water potential w. To take growth into account, we recognise that only water moving faster than a cell wall (with a displacement velocity due to growth of other cells) will cross the cell wall. Figure 7 is a diagram of a cell file showing water fluxes at an apical wall (labelled 1 ) and a basal wall (labelled 2 ). The difference equations show the differential in water potential driving the movement of water across the walls. Since cell elongation is the difference between apical and basal displacement velocities, the difference in water potential differences is related to the cell elongation rate. This 1-D formulation can be generalised to a 3-D treatment, as shown in the derivation below. Here, hydraulic conductivity is considered to be a tensor, i.e. it has different values in different directions. Water flux and growth are vectors, i.e. they have components in different directions that are summed to give a quantity with both magnitude and direction. We begin with the Reynolds transport theorem for flux across the surface of a moving element: (j g ) n ds = s (K ϕ) n ds. (1) s Flux across surface = conductivity driving force. By the divergence theorem, (j g )dv = v ( K ϕ)dv. (2) v

9 Hydraulics of plant growth Functional Plant Biology 769 Since water is incompressible, j 0, (3) and we see that the fundamental relationship between growth and water potential in a non-compartmented medium is given by: L = (K ϕ), (4) where L = g is recognised as the relative elemental growth rate and the scalar ϕ is w in the notation of this article. Solutions for the maize root Some simplifying assumptions can be used to make the basic eqn (4) more tractable. For a primary maize root one can assume that the tissue is cylindrical, with radius r, and growing only in the direction of its long axis, z. The distribution w is axially symmetric. Conductivities in the radial direction are independent of conductivities in the longitudinal direction so that radial flow is not modified by longitudinal flow. The growth pattern is steady, so that the equation may be treated as a timeindependent problem with coordinate origin at the root tip. It is recognised that the frame of reference is moving at constant velocity, and one is solving for spatial values of w. With these assumptions the basic eqn (4) can be expanded as 2 [ ϕ 2 K z z 2 + K ϕ r r 2 1 ] ϕ + K z ϕ r r z z + K r ϕ r r = L (z). (5) Equation (5) shows that the relative elemental growth rate is related to radial and longitudinal hydraulic conductivities and their gradients, and to the second derivative of the water potential with respect to position (i.e. the difference in the water potential gradient with respect to position). This equation can be solved with measured values of growthrate (Erickson and Sax 1956; Silk et al. 1986) and hydraulic conductivity (Bret-Harte and Silk 1994; Frensch and Hsiao 1994) in roots to find the spatial pattern of water potential sustaining the observed growth-rate pattern. The boundary values are to assume that the root is growing in pure water or saturated air, i.e. w = 0 in the non-growing region and outside the root boundary. Then a solution can be found in terms of the water flux that sustains the observed growth-rate pattern (Fig. 8A). Consistent with Fig. 1, the solution implies that the root absorbs water mostly in a radial direction from the soil solution or saturated air. Flux decreases in magnitude as the water moves inward. To obtain a solution for growth-sustaining water potential we made the simplifying assumption that hydraulic conductivity, while different in radial and longitudinal directions, was uniform in the longisection (see Fig. 1E). The solution uses a measured value of radial conductivity, Distance from root tip (z, mm) A B Distance from root axis (r, mm) Fig. 8. Fields of water flux (A) and water potential (B) that could sustain growth of a primary maize root absorbing water from its outer surface. The eqn (5) is solved for flux (as K w ) assuming measured values for local growth rates. Lengths of the arrows (A) correspond to magnitudes of the local water flux, and the direction of the arrow represents the flux direction. Then empirical values for radial and longitudinal conductivities are used to infer the local water potentials. The darkness of the shading (B) represents the magnitude of the water potential. Adapted from Silk and Wagner (1980) and Silk (1994). K r = m 2 MPa 1 s 1. The root median longisection has egg-shaped isopotential regions (Fig. 8B) The most negative water potential is found longitudinally at the location of greatest growth rate and radially in the root centre. The darkest region has the most negative water potential needed to sustain growth, w = MPa. As suggested in earlier papers, the growth-sustaining water potentials for roots are smaller in magnitude than those for shoots. However, to understand the hydraulics of growth, we must recognise that individual tissue elements are displaced through the growth zone and experience in a temporal sequence the water potential shown as a function of position. Because the tissue element accelerates through the growth zone, a growth trajectory (plot of position of tissue element v. time) can be used to map the spatial pattern into the time course of water potential acquired by the cellular

10 770 Functional Plant Biology J. S. Boyer and W. K. Silk elements. From further development of eqn 5, the material specification for a cell initially located 1 mm from the root tip shows that the cell water potential becomes progressively more negative for 16 h and then rapidly (over a 3-h period) rises to the level of the non-growing zone as growth ceases. Experiments suggest an extension of the growth theory for roots The growth sustaining fluxes and water potentials shown in Figs 1, 4, and 8 are inferred from the hypothesis of osmotically-driven water flux. The water source is protoxylem for the stem, and mostly soil for the root. If osmosis is indeed the major process driving water movement, then physiologists should be able to find the predicted patterns of water potential that are providing the driving force. For stem tissue, particularly hypocotyls, there is evidence that radial gradients in solute potential exist to drive the water flux. The association of sucrose import with stem growth is consistent with an important role for solute potential in sustaining stem growth (Schmalstig and Cosgrove 1990). Using a nanolitre osmometer, Nonami and Boyer (1993) found that solute potential was least negative near the xylem and decreased in both directions from the water supply, as suggested by the theory. Turgor pressure was mostly uniform, with a slight drop in the outer cortex that may help to drive the flux. Thus, in stems, osmotically-driven water fluxes produced by radial patterns of solute accumulation are empirically detectable and theoretically reasonable. For roots the empirical studies raise some questions about the adequacy of the theory. In the 1990s, refinement of the pressure probe enabled resolution of the spatial patterns of turgor pressure within the growth zone of roots (Spollen and Sharp 1991; Rygol et al. 1993; Frensch and Hsiao 1994, 1995; Pritchard et al. 2000). The distribution of turgor pressure appears to be fairly uniform during steady growth, although slightly higher pressures can sometimes be detected in the root centre and at the apex of the growth zone. Although the comparatively low turgor pressures in the growth zone are essential for growth, the distribution of turgor pressure within the growth zone would not drive a growth-sustaining influx of water. Thus, in roots as in stems, the prime candidate to produce the growth-sustaining water potential pattern is a radial gradient in solute potential. In roots, solute potential may decrease with distance from the root surface (Rygol et al. 1993; Frensch and Hsiao 1994). However, a radial gradient in solute potential is not always found (Rygol et al. 1993). In fact, no studies have yet demonstrated a radial gradient in total water potential in root growth zones. The possibility that water potential differences may be so small they cannot be detected is supported by the large radial hydraulic conductivities calculated theoretically (Bret-Harte and Silk 1994) and found with pressure-probe experiments (Frensch and Hsiao 1995). Another possibility is that the theory needs to be extended to consider pressure-driven flow from the phloem. Several investigators (Bret-Harte and Silk 1994; Pritchard 1996; Hukin et al. 2002; Gould et al., 2004) have proposed that some of the water for root growth may come from the phloem. Frensch and Hsiao (1994, 1995) found that when external water potential is lowered, turgor recovery (presumably mostly through solute import) occurs fastest in the cells deep in the root cortex and slowest in cells near the surface. Turgor recovery is also fastest and most complete in the youngest cells, 3 4 mm from the tip. This suggests that importation of solutes from deep within the root (the phloem) underlies the turgor recovery; solutes and water move readily in the radial direction from cell to cell in the growth zone; and the youngest portion of the root is most effective in importing solutes. These conclusions are supported by a recent direct demonstration of symplasmic conductivity between sieve cells and root growing cells in the apical third of the root growth zone, but not in proximal regions (e.g. Patrick and Offler 1996; Hukin et al. 2002). The model should be extended to include a pressure-driven bulk flow of water through the phloem to the region where phloem is beginning to be functional (3 4 mm from the apex). Radial water movement could occur from both the surrounding soil (inward flux) and the functional phloem (radial and longitudinal flux) in response to both water potential gradients and a pressure driven conductive flow. For several species, the availability of empirical data with good spatial resolution within growth zones suggests an improved theory of the physiology of root growth could be derived. This theory could include consideration of symplasmic and apoplastic pathways, coupling of solute and water flows, and integration of phloem function with water relations of growth. Interactions between growth zones and their rhizospheres As we have seen, water flows radially from the soil into the growth zone of roots, at least in the proximal part of the growth zone. A steady but spatially varying flux across the root surface can lead to a steady field of water and solute in the soil next to the moving root tip (Kim et al. 1999; Nichol and Silk 2001). The model developed and tested for ph patterns related to hydrogen ion fluxes also gives insight into water extraction patterns in the rhizosphere of the growth zone. Growth-rate patterns are often quasi-steady, particularly in monocot roots in a homogeneous soil. This implies a steady field of water flux, such as that shown in Fig. 8, and a resulting steady field of water content around the moving growth zone. The implication is that growing root tips are surrounded with a micro-environment of soil moisture as they penetrate the soil. Consistent with this idea, several recent studies have emphasised the hydraulic isolation of the root growth zone from the transpirational pulls of the mature tissue (Hsiao

11 Hydraulics of plant growth Functional Plant Biology 771 C D C B A Intensity (water) A B C D mm from root tip C Fig. 9. Neutron radiography of corn seedling roots in sandy soil. Digitised image reveals drainage water (A); little extraction around root tip (B), progressively greater water extraction (C) and horizontal root segment (D). and Xu 2000; Zwieniecki et al. 2003). The growth zone may be somewhat protected from the transpiration-induced dryness in soil surrounding the mature part of the root because water for transpiration is absorbed well behind the growth zone. To study the absorption of water from soil during root growth, R-A Bartlett and WK Silk grew a corn seedling for several days in moist sand and then subjected the seedling to the powerful technology of neutron beam radiography at the McClellan UC Davis nuclear reactor (unpublished data). The energy in the neutron beam is absorbed by water, but not by the silica of the soil or the aluminum of the root chamber. Thus, the brightness of the image is related to the amount of water present in the corresponding horizontal slice through the object. A vertical line was drawn through the centre of the image of the growth chamber, and image intensity was digitised along the line. Distance was measured from the root tip. Preliminary results (Fig. 9) indicate at the bottom of the chamber that water appears to have collected, presumably due to soil drainage. Below the root tip was a region of uniform water content. Above the tip was a region of increasingly dry sand that we attribute to progressively greater water extraction. (The very bright region is the root itself, where a horizontal root segment crosses the vertical line that was digitised.) The neutron radiography may illuminate questions such as: how does the size of the shoot affect the moisture content of the rhizosphere around the growth zone; can the rhizosphere of the growth zone have a steady pattern of water content over a prolonged period of growth; and what part of the growth zone perceives the signal of drying soil? We hope to extend this study to quantify interactions between the growth zone and the water content of its rhizosphere. Conclusion It is apparent from this discussion that the hydraulics of growth zones originate from their inherent structure involving many small cells. Multiple cell walls and membrane barriers must be crossed in order for water and solutes to enter all of the cells in a coordinated fashion. Gradients develop to move these substances, and the gradient steepness depends on the distances and particular anatomical architectures encountered along the way. Compared with vascular tissues, the gradients are steep because of the barrier-strewn flow path, but they consist of forces similar to those in both kinds of vascular tissues. These properties produce several consequences, perhaps the most obvious being that growing tissues must have turgor pressures low enough to form the required growthsustaining w gradients but high enough to enlarge the cells. Factors that alter the rate of growth thus affect the steepness of the gradient. Examples such as decreasing growth with cold (Boyer 1993), auxin deprivation (Maruyama and Boyer 1994) or cell maturation (Westgate and Boyer 1985) cause turgor to increase when the growth-sustaining gradients decrease. These opposing relationships between growth rates and turgor obscure the underlying effects of turgor on wall extension, making them difficult to discern experimentally. At a practical level, we see these increasing turgors with slower growth in the form of crisper salads when they are chilled, or tissues that stiffen as they mature (wall strengthening also contributes). Another consequence is that growth-sustaining w gradients provide multiple sources of water for the growth process. If external water is unavailable, the growthsustaining w can move water from surrounding mature tissues having a higher w (Matyssek et al. 1991). This assists sprouts to form on potatoes and onions while in storage, and leaves to develop ephemerally in spring on a tree felled the previous winter. Because these gradients extend over considerable distances, it is logical that altering them in only a few cells can disrupt the overall flow. A decrease in the w of water in the xylem of a stem or leaf can reverse the gradient in a few cells next to the xylem, which immediately blocks water flow to all the outlying cells and inhibits growth. These local effects probably underlie many experiences with excised plant parts, such as cut flowers, where an immediate deceleration of growth occurs when the flowers are cut but the water content of the tissues scarcely changes. In roots, the uptake geometry differs from that in shoots and tends to involve gradients in growth-sustaining w that are not as steep as in shoots. But, as in shoots, solute delivery to the growth zone is essential to develop the osmotic force for elongation and the amount of water brought with the solute might contribute significantly to the elongation. Acknowledgments We thank Missy Holbrook and Maciej Zwieniecki who organised the Harvard Forest Workshop on Long Distance Transport Processes in Plants where this review was

12 772 Functional Plant Biology J. S. Boyer and W. K. Silk originally presented. We also thank An-Ching Tang for help with the artwork. This work was supported by DOE grant DE-FG02 87ER13776 to JSB and NRI Competitive Grants Program/USDA grant to WKS. References Barlow EWR (1986) Water relations of expanding leaves. Australian Journal of Plant Physiology 13, Baum SF, Tran PN, Silk WK (2000) Effects of salinity on xylem structure and water use in growing leaves of sorghum. New Phytologist 146, doi: /J X Boyer JS (1967a) Leaf water potentials measured with a pressure chamber. Plant Physiology 42, Boyer JS (1967b) Matric potentials of leaves. Plant Physiology 42, Boyer JS (1968) Relationship of water potential to growth of leaves. Plant Physiology 43, Boyer JS (1985) Water transport. Annual Review of Plant Physiology 36, doi: /ANNUREV.PP Boyer JS (1988) Cell enlargement and growth-induced water potentials. Physiologia Plantarum 73, Boyer JS (1993) Temperature and growth-induced water potential. Plant, Cell and Environment 16, Boyer JS (1995) Measuring the water status of plants and soils. (Academic Press: San Diego) Boyer JS (2001) Growth-induced water potentials originate from wall yielding during growth. Journal of Experimental Botany 52, doi: /JEXBOT/ Boyer JS, Cavalieri AJ, Schulze E-D (1985) Control of cell enlargement: effects of excision, wall relaxation, and growth-induced water potentials. Planta 163, Bradford KJ (1994) Water stress and the water relations of seed development: a critical review. Crop Science 34, Bret-Harte MS, Silk WK (1994) Nonvascular, symplasmic diffusion of sucrose cannot satisfy the carbon demands of growth in the primary root tip of Zea mays L. Plant Physiology 105, Cavalieri AJ, Boyer JS (1982) Water potentials induced by growth in soybean hypocotyls. Plant Physiology 69, Cosgrove DJ, Cleland RE (1983) Solutes in the free space of growing stem tissues. Plant Physiology 72, Cosgrove DJ, Van Volkenburgh E, Cleland RE (1984) Stress relaxation of cell walls and the yield threshold for growth: demonstration and measurement by micropressure probe and psychrometer techniques. Planta 162, Davies WJ, Zhang J (1991) Root signals and the regulation of growth and development of plants in drying soil. Annual Review of Plant Physiology and Plant Molecular Biology 42, doi: /ANNUREV.PP De Roo HC (1969) Leaf water potentials of sorghum and corn, estimated with the pressure bomb. Agronomy Journal 61, Erickson RO, Sax KB (1956) Rates of cell division and cell elongation in the growth of the primary root of Zea mays. Proceedings of the American Philosophical Society 100, Frensch J, Hsiao TC (1994) Transient responses of cell turgor and growth of maize roots as affected by changes in water potential. Plant Physiology 104, Frensch J, Hsiao TC (1995) Rapid response of the yield threshold and turgor regulation during adjustment of root growth to water stress in Zea mays. Plant Physiology 108, Fricke W (2002) Biophysical limitation of cell elongation in cereal leaves. Annals of Botany 90, doi: /AOB/MCF180 Fricke W, Flowers TJ (1998) Control of leaf cell elongation in barley. Generation rates of osmotic pressure and turgor, and growth-associated water potential gradients. Planta 206, doi: /S Fricke W, McDonald AJS, Mattson-Djos L (1997) Why do leaves and leaf cells of N-limited barley elongate at reduced rates? Planta 202, doi: /S Gowing DJG, Davies WJ, Jones HG (1990) A positive root-sourced signal as an indicator of soil drying in apple, Malus domestica Borkh. Journal of Experimental Botany 41, Gould N, Thorpe MR, Minchin PEH, Pritchard J, White PJ (2004) Solute is imported to elongating root cells of barley as a pressure driven-flow of solution. Functional Plant Biology 31, doi: /FP03231 Hill AE, Schachar-Hill B, Schachar-Hill Y (2004) What are aquaporins for? Journal of Membrane Biology 197, doi: /S Hsiao TC, Frensch J, Rojas-Lara BA (1998) The pressure-jump technique shows maize leaf growth to be enhanced by increases in turgor only when water status is not too high. Plant, Cell and Environment 21, doi: /J X Hsiao TC, Xu L-K (2000) Sensitivity of growth of roots versus leaves to water stress: biophysical analysis and relation to water transport. Journal of Experimental Botany 51, doi: /JEXBOT/ Hukin D, Doering-Saad C, Thomas CR, Pritchard J (2002) Sensitivity of cell hydraulic conductivity to mercury is coincident with symplasmic isolation and expression of plasmalemma aquaporin genes in growing maize roots. Planta 215, doi: /S Ikeda T, Nonami H, Fukuyama T, Hashimoto Y (1999) Hydraulic contribution in cell elongation of tissue-cultured plants: growth retardation induced by osmotic and temperature stresses and addition of 2,4-dichlorophenoxyacetic acid and benzylaminopurine. Plant, Cell and Environment 22, doi: /J X Jachetta JJ, Appleby AP, Boersma L (1986) Use of the pressure vessel to measure concentrations of solutes in apoplastic and membranefiltered symplastic sap in sunflower leaves. Plant Physiology 82, Kim TK, Silk WK, Cheer AY (1999) A mathematical model for ph patterns in the rhizospheres of growth zones. Plant, Cell and Environment 22, doi: /J X Kramer PJ, Boyer JS (1995) Water relations of plants and soils. (Academic Press: San Diego) Liu F, Jensen CR, Andersen MN (2003) Hydraulic and chemical signals in the control of leaf expansion and stomatal conductance in soybean exposed to drought stress. Functional Plant Biology 30, doi: /FP02185 Lockhart JA (1965a) An analysis of irreversible plant cell elongation. Journal of Theoretical Biology 8, Lockhart JA (1965b) Cell extension. In Plant biochemistry. (Eds J Bonner and JE Varner) pp (Academic Press: New York) Maness NO, McBee GG (1986) Role of placental sac in endosperm carbohydrate import in sorghum caryopses. Crop Science 26, Martre P, Bogeat-Triboulot MB, Durand JL (1999) Measurement of a growth-induced water potential gradient in tall fescue leaves. New Phytologist 142, doi: /J X Martre P, Cochard H, Durand JL (2001) Hydraulic architecture and water flow in growing grass tillers (Festuca arundinacea Schreb.). Plant, Cell and Environment 24, doi: /J X