TY - JOUR
AU - Xu, Liu‐Kang
AB - Abstract Water transport is an integral part of the process of growth by cell expansion and accounts for most of the increase in cell volume characterizing growth. Under water deficiency, growth is readily inhibited and growth of roots is favoured over that of leaves. The mechanisms underlying this differential response are examined in terms of Lockhart's equations and water transport. For roots, when water potential (Ψ) is suddenly reduced, osmotic adjustment occurs rapidly to allow partial turgor recovery and re‐establishment of Ψ gradient for water uptake, and the loosening ability of the cell wall increases as indicated by a rapid decline in yield‐threshold turgor. These adjustments permit roots to resume growth under low Ψ. In contrast, in leaves under reductions in Ψ of similar magnitude, osmotic adjustment occurs slowly and wall loosening ability either does not increase substantially or actually decreases, leading to marked growth inhibition. The growth region of both roots and leaves are hydraulically isolated from the vascular system. This isolation protects the root from low Ψ in the mature xylem and facilitates the continued growth into new moist soil volume. Simulations with a leaky cable model that includes a sink term for growth water uptake show that growth zone Ψ is barely affected by soil water removal through transpiration. On the other hand, hydraulic isolation dictates that Ψ of the leaf growth region would be low and subjected to further reduction by high evaporative demand. Thus, a combination of transport and changes in growth parameters is proposed as the mechanism co‐ordinating the growth of the two organs under conditions of soil moisture depletion. The model simulation also showed that roots behave as reversibly leaky cable in water uptake. Some field data on root water extraction and vertical profiles of Ψ in shoots are viewed as manifestations of these basic phenomena. Also discussed is the trade‐off between high xylem conductance and strong osmotic adjustment. Expansive growth, yield threshold, hydraulic isolation of growth zone, leaky cable model of root water uptake. Introduction A plant transports a huge amount of water—in the range of 200 to 1000 times the dry mass of its body over its life time. This is the result of having to keep the interior of its leaves open to the atmosphere for the adequate absorption and assimilation of carbon dioxide, with the inevitable consequence of water vapour escaping from the leaves. Water transport is closely intertwined with the myriad of plant processes, including photosynthesis, translocation, mineral nutrition, hormonal regulation, and numerous molecular and genetic facets. This paper will discuss a few selected aspects of water transport, mostly in relation to growth by cell expansion. The focus will be on the growth of roots relative to that of leaves in response to water stress, viewed mainly from a biophysical perspective, and the implications in the field in terms of adaptation to water‐limited environments. Also discussed is the link between osmotic adjustment and water transport in terms of hydraulic conductance of the plant. As made obvious by several other papers in this volume (Munns et al., 2000; Steudle, 2000; Tardieu et al., 2000), the literature on water transport and on growth as affected by water deficit is extensive and sometimes contradicting. The intent here is not to discuss the field as a whole, but to pull together selected ideas and results, much of them from our own group, some quite old and some new and not yet published, to provide an overview from a personal vantage point. One important facet not considered here is water transport as related to xylem embolism or cavitation under high tension (Milburn and Johnson, 1966; Boyer, 1971), an area of much research interest (Sperry et al., 1996; McCully et al., 1998; Tyree et al., 1999). Contrasting growth between roots and leaves under water stress—a biophysical perspective Leaf growth defines the canopy size of a plant for capturing sunlight and carrying out photosynthesis to gain carbon and energy. Root growth defines the extent to which a plant explores soil for water and mineral nutrients. Growth of the two organs, however, are in competition for assimilates produced by the leaves and for minerals and water taken up by roots. Yet growth of roots and leaves are co‐ordinated and their sizes relative to each other vary dynamically in response to environmental conditions, in a way that tends to optimize the utilization of assimilates and other resources (Wilson, 1988). How the co‐ordination is achieved remains unclear, in spite of recent progress made in the understanding of expansive growth. Discussed in this section are some of the recent advances in the study of more physical aspects of growth of roots and leaves. In the following sections the characteristics of water transport to the growth zone of roots and leaves are analysed, and a combination of transport and growth‐related processes and features is proposed as the mechanism co‐ordinating the growth of the two organs under conditions of soil moisture depletion. Equations of Lockhart Cells and organs expand and contract with changes in water content. To separate out elastic changes in size not associated with growth, it is necessary to define expansive growth as the irreversible enlargement of cells or organs. The enlargement refers particularly to the dimensions of the cell wall. The more physical aspects of expansive growth is usually examined in terms of the equations of Lockhart (Lockhart, 1965). The first Lockhart equation relates the relative rate of irreversible increase in volume of a cell to its turgor pressure (ψp):   \[\frac{dV}{Vdt}{=}m{(}\mathrm{{\psi}_{p}}{-}Y{)}\] 1 where V is the cell volume, t is time, m is volumetric extensibility, and Y is the yield threshold turgor pressure. Equation 1indicates that the growth rate, normalized for the size of the cell, is related by the coefficient m to the turgor pressure above a minimum threshold (ψp−Y), which is termed growth effective turgor. The loosening ability of the cell wall is reflected in both m and Y, which are measures of rheology of the cell wall (plastic properties). Because the chemical and structural properties of the growing cell wall are intimately linked to wall metabolism and growth regulators (Lockhart, 1965; Nakahori et al., 1991), m and Y are also (Bradford and Hsiao, 1982). Volumetric extensibility m is a three‐dimensional expression of plastic extensibility of the wall and incorporates the effects of cell geometry as well (Lockhart, 1965). Equation 1 emphasizes the fact that ψp must be above the threshold value of Y for the cell to grow. In addition to the implicit link of m and Y to metabolism, also implicit in equation (1) is the role of water potential (Ψ) and solute (osmotic) potential (ψs) in determining ψp (=Ψ−ψs). It is a mistake to view m and Y in the equation as constants, as often done. They have long been recognized to change with changes in cell water status (Green, 1968; Acevedo et al., 1971; Green and Cummins, 1974). These changes provide additional means for the plant to adjust growth of its organs to cope with water stress (Hsiao et al., 1976, 1998). With sustained growth, water must be transported continuously into the cell since most of the expansion in volume is due to added water. The common equation for water transport is to relate the water flow to the conductance of the path, C, and the difference in Ψ driving the transport. Lockhart combined the transport equation with equation 1 to obtain   \[\frac{dV}{Vdt}{=}\frac{mC}{m{+}C}{(}\mathrm{{\Psi}^{0}{-}{\psi}_{s}}{-}Y{)}\] 2 where C is the overall hydraulic conductance (including geometric effects) of the cell, Ψ° is Ψ of the medium surrounding the growing cell or of the source of water, and ψs is solute potential within the cell (Lockhart, 1965). It is seen in equation 2 that m has the same units as C. In the situation where C≫m, the denominator of the fraction on the right side of equation 2 becomes C and cancels the C in the numerator. Consequently equation 2 reverts to equation 1. An example of where the simpler equation 1 instead of the more complicated equation 2 is adequate to describe growth is the case of cells in maize roots bathed in a flowing aqueous solution (Frensch and Hsiao, 1995). There C was assessed to be large relative to m. On the other hand, studies have pointed to conductance as a major factor limiting growth of cells in the stem (hypocotyl) of soybean seedlings with roots in water‐deficient vermiculite (Nonami and Boyer, 1990). In that case, the low conductance of the radial path between the xylem and the growing cells was attributed to a layer of small cells about 200 μm thick separating the ring of xylem vessels from the cortical and epidermal cells (Nonami et al., 1997). In this paper, for simplicity, growth at the cellular scale will be discussed mostly in terms of the parameters in equation 1. The role of conductance and Ψ gradient will be assessed when water transport over longer distances to the growth zone is considered. Effects of water stress on expansive growth and dynamic responses Leaf growth has long been known to be very sensitive to inhibition by water stress (Boyer, 1968) whereas root growth is more resistant (Westgate and Boyer, 1985). This difference in sensitivity is illustrated for maize in Fig. 1. Elongation rate of the fifth leaf of maize was maximal when Ψ of the growth zone tissue was the highest (−0.75 MPa). Any reduction in growth zone Ψ reduced the elongation rate, to the extent that elongation stopped when Ψ was reduced to −1.1 MPa (Fig. 1A), a total reduction in growth zone Ψ of only 0.3 MPa. For maize roots growing in vermiculite, elongation was also reduced by small reductions in medium Ψ (Fig. 1B). Further reductions in Ψ, however, had less effect, and elongation continued at more than one‐third of the maximum rate even when medium Ψ was reduced to −1.9 MPa, 0.4 MPa below the permanent wilting point of −1.5 MPa. Ψ of the root growth zone must have been still lower, since a Ψ gradient is necessary for the root to absorb water from the medium to maintain growth. To gain an insight into the mechanism underlying the ability of roots to grow under such low medium Ψ, it is illuminating to examine the dynamic changes when water stress is imposed suddenly. In an early study, Acevedo et al. showed that when Ψ of the solution bathing roots of a maize seedling was suddenly reduce from zero to −0.2 MPa, leaf growth stopped momentarily, then slowly resumed after some adjustment, reaching a steady rate about only one‐third of the original (Acevedo et al., 1971). After the root medium Ψ was raised suddenly back to 0 MPa, there was a burst of rapid leaf elongation, lasting for about 1.5 h, followed by a return to the original rate. With a more marked reduction in root medium Ψ, to −0.3 MPa, leaf growth stopped for more than 2 h before resuming at a very slow rate. Kuzmanoff and Evans found that growth of lentil roots went through similar rate adjustments upon a stepwise reduction or increase in medium Ψ (Kuzmanoff and Evans, 1981). Growth recovery under reduced Ψ, however, was much stronger in those roots. Even after a 0.7 MPa stepping down of medium Ψ, lentil roots recovered to grow essentially at the full rate after 50 min of adjustment. How was this adjustment achieved in terms of the parameters in Lockhart equation? Osmotic adjustment and the maintenance of partial or full turgor under water stress was shown to play a role in early studies (Greacen and Oh, 1972; Meyers and Boyer, 1972; Hsiao et al., 1976). More details came from studies using the pressure microprobe to monitor changes in cell turgor pressure while growth was also monitored during stepwise changes in medium water status. Hsiao and Jing found that when the medium Ψ for the primary root of a germinating maize seedling was suddenly reduced from zero to −0.42 MPa by changing to an osmotic solution, turgor of cells in the root growth zone was reduced nearly proportionally, as quickly as could be measured (within a couple of minutes), and growth stopped (Hsiao and Jing, 1987). Growth restarted and turgor began to increase, however, in a few minutes. Initially the growth rate and turgor increased rapidly, then slowed with time. Growth recovered fully in 45 min in spite of the low Ψ. Turgor, on the other hand, recovered only to a level still 0.15 MPa below the value before the imposition of water stress. The results are consistent with the concept of yield threshold turgor and the need for turgor to rise above this threshold for growth to resume. The initial rapid turgor rise was the result of rapid osmotic adjustment. Also the fact that growth under the stress had recovered fully while turgor recovery was only partial showed that Y and probably m in the Lockhart equation must have adjusted to achieve the original growth rate. Other authors (Green, 1968; Green and Cummins, 1974) had emphasized the tendency of expansive growth to be self‐stabilizing as conditions varied by adjusting the loosening of the cell wall. It is desirable to separate out the contribution of any adjustment in Y from that in m in the maintenance of growth under water stress. Fig. 1. View largeDownload slide Growth of leaf (A) and root (B) of maize at 29 °C as affected by water potential (ψ). In (A), maize seedlings were grown in a potting mixture in a controlled environment chamber until the fifth leaf emerged, then watering was withheld and elongation rate of the fifth leaf was monitored with a position transducer (linear variable differential transformer). When elongation rate slowed to the indicated level, segments 50 mm long encompassing the growth zone were excised from the base of the leaf and measured for Ψ at 5 °C by the Shardakov method (modified from Hsiao and Jing, 1987). In (B), after germination, maize seedlings were planted in well moistened vermiculite and transferred to vermiculite wetted to the indicated Ψ in a dark controlled temperature chamber 30 h after planting. The elongation rate of primary roots were measured later (ranging from 15 h for Ψ=−0.03 MPa to 48 h for Ψ=−1.7 MPa) after growth had become steady. Ψ of vermiculite was measured at 29 °C by isopiestic thermocouple psychrometry (modified from Sharp et al., 1988). Fig. 1. View largeDownload slide Growth of leaf (A) and root (B) of maize at 29 °C as affected by water potential (ψ). In (A), maize seedlings were grown in a potting mixture in a controlled environment chamber until the fifth leaf emerged, then watering was withheld and elongation rate of the fifth leaf was monitored with a position transducer (linear variable differential transformer). When elongation rate slowed to the indicated level, segments 50 mm long encompassing the growth zone were excised from the base of the leaf and measured for Ψ at 5 °C by the Shardakov method (modified from Hsiao and Jing, 1987). In (B), after germination, maize seedlings were planted in well moistened vermiculite and transferred to vermiculite wetted to the indicated Ψ in a dark controlled temperature chamber 30 h after planting. The elongation rate of primary roots were measured later (ranging from 15 h for Ψ=−0.03 MPa to 48 h for Ψ=−1.7 MPa) after growth had become steady. Ψ of vermiculite was measured at 29 °C by isopiestic thermocouple psychrometry (modified from Sharp et al., 1988). Differentiating changes in Y from changes in m and other methodological problems Analysing growth in terms of the parameters in Lockhart's equations, especially at the whole organ level, can involve a number of uncertainties, particularly difficult is how to distinguish changes in m from changes in Y when growth is altered by changes in conditions. This difficulty is further aggravated by the loose use of the term ‘extensibility’. Lockhart originally termed m ‘gross extensibility’, to differentiate it from the physically better defined extensibility used in the one‐dimensional stress–strain relationship, on which his equations were based. For decades, extensibility has also been used to denote the relative or absolute uniaxial extension of pieces of excised tissue per unit of uniaxial force, applied externally to the tissue, without consideration of a force threshold. Clearly, that is distinct from the Lockhart m, because Y is not accounted for and the force is acting in one dimension, instead of in three dimensions as exerted by turgor pressure. Extensibility has also been used in the literature in a general and non‐quantitative sense to denote the ability of the cell wall to extend. To avoid confusion, in this paper volumetric extensibility, denoted by the coefficient m, is used only in the sense defined by the Lockhart equation, and the ability of the cell wall to extend in a general sense is referred to as wall loosening ability. Separating out changes in Y from those in m is not simple. It is pertinent to summarize here the various methods used. In early studies, Y and m were evaluated from approximately linear plots of growth rate versus ψp. Growth rate and ψp were varied by varying tissue water status and ψp was calculated as the difference between measured Ψ and ψs of the tissue. Under the assumption that Y and m remained the same for different growth rates, the slope of the plot was taken as m, and the intercept with the x‐axis, as Y. Obviously, if Y or m changed as the result of water status differences, the method would not yield definitive results (Frensch and Hsiao, 1994). Later, a stress or turgor relaxation technique (Cosgrove, 1985) was used to evaluate Y and m. Growing organ or tissue was monitored for its expansion after it was excised and deprived of a water source. The cell wall continued to relax (irreversibly) under high turgor and the organ continued to expand as long as its ψp was greater than Y. Turgor declined with time because of wall relaxation and expansion stopped when turgor dropped to the level where ψp=Y. Y then was obtained by measuring ψp at that point (Cosgrove, 1985) or by calculating ψp from measured Ψ and ψs. Once Y was obtained, m was calculated from Y and the growth rate. A variation of this technique is the pressure block method (Cosgrove, 1987). Expansion of the excised tissue was monitored inside a pressure chamber and pressure was applied and raised in the chamber until expansion just stopped. At that point the applied pressure is a measure of how much ψp exceeds Y, or the growth effective turgor (ψp−Y). By measuring ψp, Y was then calculated. Underlying these methods was the assumption that Y did not change during the stress relaxation or the time it took to block expansion by pressure. Should Y change with time to some lower limit, then these techniques determine the lower limit of Y, not the Y at the moment of tissue excision or at the start of the pressure blocking. The underestimation of Y in turn would lead to calculated m being too low. Green showed decades ago that Y was reduced rather quickly under low ψp in Nitella (Green, 1968). The pressure block data (Cosgrove, 1987), obtained on higher plants, in fact suggested that Y might have decreased during the determination. The initial stoppage of expansion by pressure did not last and the pressure had to be increased several times before expansion was prevented for good. The tendency of walls of growing cells to continue to relax when ψp>Y causes Ψ measured by thermocouple psychrometry on excised tissue to be too low because the required equilibration of several hours provides ample time for wall relaxation. Consequently, the turgor calculated would be lower than that at the time of excision and would closely reflect the lower limit value of Y. Some of the early results indicating that Y did not change with water status were based on calculations using Ψ measured in psychrometers and the conclusion is questionable. The problem of wall relaxation could be minimized if tissue Ψ is measured at a low temperature (e.g. 5 °C) using a method that requires only a short time for equilibration. The Shardakov dye method (Slavik, 1974) has been used for that purpose (Hsiao and Jing, 1987). To keep the time of measurements short and thus minimizing changes in Y and m, Okamoto et al. developed the pressure jump method for the study of the growth of excised hypocotyl segments of Vigna (Okamoto et al., 1989). Pressure is increased stepwise by a small amount (e.g. 0.02 MPa) in the xylem and maintained for only a very short time (e.g. 3 min) while elongation of the segment is continuously monitored. Extensibility m is calculated as the ratio of increase in relative growth rate to the increase in ψp, which is approximated by the applied pressure if hydraulic conductance of the cells (C) is large relative to m. The underlying assumption is that the small and very brief increase in pressure does not alter m and Y. By subjecting the growing segment intermittently to several pressure steps of different magnitudes, Y can be determined by linear extrapolation. Another way to determine Y is by tracking cell ψp with a pressure microprobe and determining at what ψp growth just stops as ψp falls, and at what ψp growth resumes as ψp increases (Frensch and Hsiao, 1994). This will be described in more detail in the next section. With rapid perturbations in turgor and growth measured over a short time interval, there is a concern that changes in rates of measured growth may be confounded by elastic changes in the cell or organ volume or length. Proseus et al. have shown that elastic changes of growing Chara internodal cells, determined at a cold temperature that eliminated growth, may be subtracted from the total length change to obtain changes in the true growth rate at a warm temperature (Proseus et al., 1999). The pressure jump technique (Okamoto et al., 1989) appears to be free from the problem of elastic changes because ψp is altered only by small amounts and growth rates are based on steady‐state measurements. Dynamic adjustments in yield threshold and volumetric extensibility Recent evidence indicates that as water stress develops, Y and m may change within minutes in the direction that aids in the maintenance of growth. Skilful use of the pressure microprobe have enabled Frensch and Hsiao to determine instantaneous Y of maize roots during the transitional period from the time of stress imposition to the recovery in growth under the same stress (Frensch and Hsiao, 1994). An example of the data is shown in Fig. 2. When the nutrient solution bathing the root was switched suddenly to one containing mannitol at ψs=−0.29 MPa, turgor decreased instantly and growth stopped (Fig. 2A). Within 5 min or so, turgor began to recover at a fast rate via osmotic adjustment and growth started again slowly after 10 min (Fig. 2B). The rate of turgor increase had slowed by then but growth rate continued to increase with the further small increases in turgor. After 25 min, growth recovered to a steady rate that was about two‐thirds of that before stress and turgor reached a value that was 0.12 MPa lower than before stress (Fig. 2A). By recording growth without interruption and monitoring ψp continuously in the same cell (curves of solid lines, Fig. 2B) when medium Ψ was stepped down or up, it was possible to determine the turgor at which growth stopped (left large circle, Fig. 2B) or resumed (right large circle, Fig. 2B). By definition these ψp values are the values of yield threshold Y. In Fig. 2B it is seen that the first Y (Y1), where growth stopped, was more than 0.1 MPa higher than the second Y (Y2), where growth resumed. That is, Y decreased substantially during the initial 10 min of stress, and this decrease in Y enable growth to start again at a lower ψp. Frensch and Hsiao determined the first and second Y by exposing roots to ψ reductions of different magnitudes (Frensch and Hsiao, 1995). When these Y values are plotted against the time it took to reach them after the downstep in Ψ (Fig. 3), it is seen that the reduction in Y began early, a few minutes after the imposition of water stress. It appears that less than 20 min was required to achieved the maximal reduction in Y. The data also show that the larger the downstep in Ψ, the greater was the reduction in Y when growth resumed (Frensch and Hsiao, 1995). There is a limit to the reduction, however, and the data suggest that the minimal Y reachable was around 0.35 MPa (under a reduction in medium Ψ of 0.6 MPa), in agreement with the range of Y measured by the turgor relaxation (Cosgrove, 1985; Matyssek et al., 1988) or pressure block (Cosgrove, 1987) technique on other crop species. For maize roots, Y did not decline when medium Ψ was lowered by 0.1 MPa and growth recovered quickly and fully, effected only by osmotic adjustment (Frensch and Hsiao, 1995). Only with further lowering in medium Ψ was Y reduced. The problem of elastic changes confounding the Y determined for maize roots appears to be minimal, as Frensch and Hsiao elaborated on earlier (Frensch and Hsiao, 1995). Other evidence of quick change in Y came from the data on turgor and growth after Ψ of the medium was raised suddenly to the original value. As shown in Fig. 2A, there was a burst of growth and a jump in turgor as soon as medium Ψ was stepped up to the original level. A few minutes after the step the very high growth rate declined, to a rate slightly lower than the original after another 10 min. In contrast, turgor remained nearly 0.1 MPa higher than the original. Similar results were obtained by Hsiao and Jing (Hsiao and Jing, 1987). The slower growth at a higher turgor after the growth burst is indicative of raised values of Y. The possibility of a greatly reduced m accounting for all of the reduction in growth per unit of turgor without the elevation of Y seems unlikely. Fig. 2. View largeDownload slide Responses of root growth and turgor to the addition (↓) and withdrawal (↑) of −0.29 MPa mannitol and the determination of yield threshold turgor Y. (A) Time course of 5 min mean elongation rate (•‐‐•) measured with an LVDT and of cell turgor (ψp) measured with a pressure microprobe in the region of maximum growth (4–5 mm from apex). Open points (○) represents ψp of different cells and solid line with open point at the end (—○) represents continuous measurements of ψp in a single cell. (B) Details plotted on a larger time scale for the period when medium Ψ was stepped down to the time after growth had resumed, showing how Y was determined. Left large circle indicates the region of turgor when growth just stopped or the first Y. Right large circle indicates the region of turgor when growth just resumed or the second Y. The primary root was 175 mm long and was bathed continuously by flowing nutrient solution either with or without mannitol added to −0.29 MPa (modified from Frensch and Hsiao, 1994). Fig. 2. View largeDownload slide Responses of root growth and turgor to the addition (↓) and withdrawal (↑) of −0.29 MPa mannitol and the determination of yield threshold turgor Y. (A) Time course of 5 min mean elongation rate (•‐‐•) measured with an LVDT and of cell turgor (ψp) measured with a pressure microprobe in the region of maximum growth (4–5 mm from apex). Open points (○) represents ψp of different cells and solid line with open point at the end (—○) represents continuous measurements of ψp in a single cell. (B) Details plotted on a larger time scale for the period when medium Ψ was stepped down to the time after growth had resumed, showing how Y was determined. Left large circle indicates the region of turgor when growth just stopped or the first Y. Right large circle indicates the region of turgor when growth just resumed or the second Y. The primary root was 175 mm long and was bathed continuously by flowing nutrient solution either with or without mannitol added to −0.29 MPa (modified from Frensch and Hsiao, 1994). Fig. 3. View largeDownload slide Yield threshold turgor (Y) of cells in roots of maize seedlings as affected by change in ψ of the bathing medium (A) and the time required to reach its new lower value after the down step in medium Ψ (B). Values of Y were determined as shown in Fig. 2B by exposing primary roots 110–180 mm long of 5–7‐d‐old seedlings to an osmotic solution within the range of −0.1 to −0.6 MPa and measuring cell turgor with a pressure microprobe. In (B) data are plotted as a function of the time interval from the sudden reduction in medium Ψ to the time when Y reached its minimal value (right large circle in Fig. 2B). Open circles (○) represent Y1 for roots in nutrient solution without added osmotica, and closed circles (•), new and second Y (Y2) after reduction in medium Ψ (B). Lines were fitted by eye (from Frensch and Hsiao, 1995). Fig. 3. View largeDownload slide Yield threshold turgor (Y) of cells in roots of maize seedlings as affected by change in ψ of the bathing medium (A) and the time required to reach its new lower value after the down step in medium Ψ (B). Values of Y were determined as shown in Fig. 2B by exposing primary roots 110–180 mm long of 5–7‐d‐old seedlings to an osmotic solution within the range of −0.1 to −0.6 MPa and measuring cell turgor with a pressure microprobe. In (B) data are plotted as a function of the time interval from the sudden reduction in medium Ψ to the time when Y reached its minimal value (right large circle in Fig. 2B). Open circles (○) represent Y1 for roots in nutrient solution without added osmotica, and closed circles (•), new and second Y (Y2) after reduction in medium Ψ (B). Lines were fitted by eye (from Frensch and Hsiao, 1995). Comparing leaf and root growth under water stress in terms of Lockhart's equation Detailed time‐courses of changes in turgor and growth rate upon stepwise changes in water status for leaves are very few. For the situation of water stress developing slowly over days, growth zone turgor was reported to be completely maintained by osmotic adjustment initially (Michelena and Boyer, 1982; Van Volkenburgh and Boyer, 1985) but the growth rate slowed. Eventually growth dropped to zero as water stress became more severe. Turgor, however, was nearly as high as before the onset of stress. Compared to leaves of recently watered plants, stressed leaves acidified their growth zone apoplast more slowly and had a higher surface pH (Van Volkenburgh and Boyer, 1985). Wall extension, measured in vitro with an extensometer on methanol‐boiled leaf segments, was lower for the water stress leaves compared to the control. Turgor was calculated as the difference between Ψ and ψs measured by thermocouple psychrometry, raising the question of whether the reported constant ψp might have been an artefact of wall relaxation during the Ψ measurements. However, Hsiao and Jing also found that growth of leaves was reduced by mild water stress in spite of turgor maintenance in a field study on sorghum (Hsiao and Jing, 1987). They measured Ψ of the growth zone with the Shardkov dye method at 5 °C using an equilibration time of less than 10 min. The cold temperature and short measurement time should have essentially eliminated wall relaxation. The slower growth in spite of the full maintenance of turgor was due at least partly to a shortening of the leaf growth zone under water stress (Walker and Hsiao, 1993). Growth zone is also shortened in roots under water stress (Sharp et al., 1989; Spollen and Sharp, 1991). As for effects of stepwise changes in medium Ψ on growth and turgor in leaves, it was already mentioned that the early data (Acevedo et al., 1971) showed the kinetic of growth responses of maize leaves to be similar to that of roots, but recovery in growth after the down‐step was much weaker. In that study, turgor was not measured. Later Hsiao and Jing, also using the Shardkov method at cold temperature, investigated changes in maize leaf growth and turgor at 15 min intervals upon a stepping down in medium Ψ of 0.25 MPa (Hsiao and Jing, 1987). Growth stopped for about 15 min, then began to recover slowly as ψp began to recover through osmotic adjustment. This is in contrast to the recovery in turgor and growth within minutes after the 0.29 MPa down‐step for roots (Fig. 2). After 75 min, turgor had recovered to the level prior to stress imposition, but growth of the leaf remained partly inhibited. These results indicate that under water stress, wall loosening ability in the leaves was reduced (an increase in Y or a reduction in m), in contrast to the enhanced wall loosening ability in roots as evinced by the reduction in Y (Fig. 3). Leaves of the Gramineae are often chosen for studies because their growth is predominantly one‐dimensional with clear gradients in the longitudinal direction. On the other hand, their growth zone is wrapped in older leaves and difficult to reach with a pressure microprobe. It is not surprising that the initial studies of turgor and growth using a pressure microprobe were on leaves of dicots (Shackel et al., 1987, on grape leaves). A more detailed study with the microprobe on leaf growth in relation to water stress was on another dicot, Begonia argenteo‐guttata L. (Serpe and Matthews, 1992). Turgor was measured in the epidermal cells near the central midvein. With a down‐step in root medium Ψ of 0.2 or 0.3 MPa, growth stopped and turgor dropped. Growth remained zero for 25 min or more and then recovered gradually to reach a slower but steady rate. Turgor, however, did not recover measurably and remained reduced over the 2 h stress period. Hence, there was no osmotic adjustment in Begonia leaves and the resumption in growth under water stress was the result of an enhanced loosening ability of the cell wall. A similar study was carried out on maize leaves with somewhat similar results (A Thomas and TC Hsiao, unpublished results). A window was carefully cut in the coleoptile sheathing the first leaf of seedlings to expose the growth zone of the leaf for the measurement of turgor with the pressure microprobe. Upon a 0.4 MPa down‐step of root medium Ψ, growth was stopped within minutes and remained virtually zero for approximately 1 h, before resuming at a very slow rate. Turgor in the growth zone of the leaf declined by nearly 0.3 MPa over a 30 min period, then increased very slowly thereafter. Overall, it may be said that there is a sharp contrast in the responses to reductions in tissue Ψ between the root and the leaf. The root adjusts osmotically and its turgor recovers quickly but only partially under water stress. With the quick lowering of Y and possibly increases in m, root elongation can recover fully under mild water stress, at reduced turgor. Root growth is maintained partially even down to the permanent wilting point and beyond. The leaf osmotically adjusts either slowly or not at all (Serpe and Matthews, 1992). The loosening ability of its cell wall is either reduced (increase in Y as reported by Hsiao and Jing, 1987) or at least not markedly enhanced under water stress. Consequently, leaf growth is much more inhibited by a given reduction in medium or tissue Ψ compared to the root. The discussion on the contrasts between roots and leaves in their growth responses to water stress has emphasized the more biophysical aspects and changes. Obviously these are underlain by physiological and biochemical changes. Of particular relevance is the role of ABA in altering the growth responses of roots versus leaves. Under water stress ABA increases both in leaves and roots (reviewed by Hsiao, 1973) and more ABA is transported from roots to leaves (Zhang and Davies, 1990; Davies and Zhang, 1991). Convincing evidence was obtained by Sharp and coworkers (Spollen et al., 1993; Sharp et al., 1994) in long‐term experiments indicating that ABA maintains root growth while inhibiting shoot growth in maize at low Ψ. Inhibition of ABA synthesis by the chemical fluridone depressed root elongation and promoted shoot elongation of etiolated maize seedlings at low Ψ, but had little effect on root or shoot elongation at high Ψ (Saab et al., 1990). A maize mutant deficient in ABA maintained better shoot growth but suffered more inhibition of root growth at low Ψ compared to the wild type. Under water stress ABA concentration was the highest at the apical 3 mm of root where the relative elongation rate was fully maintained (Saab et al., 1992). Exogenous ABA at the right concentration overcomes the effect of ABA synthesis inhibitor on the growth of root and shoot at low ψ, and at low ψ modified the growth of ABA‐deficient mutant to resemble that of the wild type (Sharp et al., 1994). Interestingly, recent evidence (Sharp et al., 2000) indicates that ABA at the normal endogenous level is also needed in maintaining good shoot and leaf growth in ABA‐deficient mutants of tomato. Without adequate ABA the production of excessive ethylene apparently reduced shoot growth. Taken together, these results provide strong evidence that ABA plays a central role in orchestrating the differential long‐term growth responses to water stress of root and shoot. What is unclear is whether ABA is similarly involved in the rapid changes in the growth parameters of the Lockhart equation in the two organs. Those changes were very rapid, taking place within minutes or a fraction of an hour after a down‐step in Ψ. The increase in tissue ABA effected by water stress and the increased transport of ABA from root to shoot may take considerably longer (Hsiao and Bradford, 1983), and cannot be easily invoked to explain the early responses. Some recent exciting developments in molecular biology are very pertinent to expansive growth. Evidence is accumulating implicating expansin proteins in the effects of water stress on expansive growth. As discussed in the paper by Wu and Cosgrove in this volume, expansins promote wall loosening and acid induced growth (Wu and Cosgrove, 2000). Both the amount of expansins in the cell wall and the responsiveness of the wall to expansins were altered by water stress in a way that facilitates root growth at low Ψ. As yet there appears to be no study on the effects of water stress on expansins in leaves. It would be important to know whether at low Ψ expansins undergo changes in direction in leaves opposite to that in roots, and whether the level of expansins may change fast enough to account for the fast changes in wall loosening ability, such as that indicated by the rapid reduction in Y in Fig. 3. The other exciting development is the recent isolation of two types of proteins from the growth zone of Vigna hypocotyls, one apparently functioning specifically to change the yield threshold Y, and the other, the extensibility m (Okamoto‐Nakazato et al., 2000). So far these proteins have only been tested on killed and reconstituted Vigna growth tissue and the effects of water stress have yet to be determined. Hydraulic isolation of root apex, water transport, and root growth in drying soil The particular anatomical and hydraulic feature of the root apex must also be considered when examining the mechanism for the preferential growth of roots over leaves under water stress. In maize roots, the xylem cells differentiate very slowly and do not mature until they are displaced a substantial distance from the growth zone (Wang et al., 1991; McCulley, 1995). Consequently, the apical region of the root is hydraulically largely isolated from the more basal part (Frensch and Steudle, 1989; Frensch and Hsiao, 1993) with developed xylem vessels, which supply water to the shoot. This can be seen in the half‐time of pressure relaxation of the xylem cells or elements. As shown in Fig. 4, the half‐time was much longer for xylem elements located in the apical 35 mm, a reflection of the high resistance to water movement in this region. As the root grows, the apical growing region moves continuously into new soil volume containing yet‐to‐be‐used water. Therefore, Ψ of the growth zone should remain high and remote from the influence of tension in the xylem generated by leaf transpiration. To examine this effect in quantitative terms requires model simulation because the root acts as a leaky conduit and Ψ in the stele and water uptake at any point along the root are the result of complex interactions among the radial and axial conductances, external Ψ, and Ψ at the basal end of the root (Landsberg and Fowkes, 1978). As mentioned earlier, the Ψ gradient necessary for water uptake in the growth zone to maintain growth has been modelled with spatial details (Molz and Boyer, 1978; Silk and Wagner, 1980), but only for non‐transpiring conditions. Water uptake along a root to supply water to the shoot has also been modelled with spatial details (Landsberg and Fowkes, 1978; Frensch and Steudle, 1987), but without considering the growth zone and growth‐induced water uptake. To define the role of hydraulic isolation of the growth zone in maintaining root growth under drying conditions, it is necessary to simulate growth zone Ψ under transpiring conditions. For the simulation, radial and axial hydraulic conductances must be known or estimated. Radial and axial hydraulic conductances of maize roots Frensch and Steudle measured axial (Rx) and radial (Rr) hydraulic resistance of maize primary roots along the length between 20 and 130 mm from the apex and found Rr to be essentially constant over this length, with an average value of 4×106 MPa s m−1 (Frensch and Steudle, 1989). Using a different technique based on pressure kinetics of single cells at different depths within the root cylinder measured with a pressure microprobe, radial hydraulic conductivity (m2 s−1 MPa−1) of the growing region of maize root has been determined by Frensch and Hsiao (Frensch and Hsiao, 1995). Their value corresponded to an Rr of 2.5×106 MPa s m−1. Rx was found to remain essentially constant between 70 and 130 mm, but to increase markedly from 60 mm toward the apex, to the extent that Rx at 20 mm was almost three orders of magnitude higher than that at 60 mm (Frensch and Steudle, 1989). There is no direct measurement to indicate that Rx would continue to increase from 20 mm toward the apex. Anatomical data (Frensch and Steudle, 1989), however, suggest that this is the case. They found only two mature early metaxylem elements per cross‐section at 20 mm, but none at 10 mm. Early metaxylem vessels of maize roots, with a diameter more than four times that of protoxylem vessels (Frensch and Steudle, 1989), should be much more conductive. This points to the likelihood of still higher Rx at 10 mm. Fig. 4. View largeDownload slide Half time (t1/2) of pressure relaxation in the early metaxylem (EMX) and late metaxylem (LMX) at various locations along the length of excised maize primary roots after a step‐wise change in pressure in the xylem at the base (cut end) of the root. Pressure (ψp) in the xylem elements, monitored with a pressure microprobe, changed from the initial pressure at the time of pressure step to the new steady pressure after some time. Half time was the time it took for one half of the change in ψp to take place and was always faster in the EMX than in the LMX. Dashed line (–––) indicates the shortest t1/2 (0.3 s) the pressure microprobe was able to measure. 175 mm of the primary root was excised from 5‐d‐old seedlings for the measurements. Values are means±SD (from Frensch and Hsiao, 1993). Fig. 4. View largeDownload slide Half time (t1/2) of pressure relaxation in the early metaxylem (EMX) and late metaxylem (LMX) at various locations along the length of excised maize primary roots after a step‐wise change in pressure in the xylem at the base (cut end) of the root. Pressure (ψp) in the xylem elements, monitored with a pressure microprobe, changed from the initial pressure at the time of pressure step to the new steady pressure after some time. Half time was the time it took for one half of the change in ψp to take place and was always faster in the EMX than in the LMX. Dashed line (–––) indicates the shortest t1/2 (0.3 s) the pressure microprobe was able to measure. 175 mm of the primary root was excised from 5‐d‐old seedlings for the measurements. Values are means±SD (from Frensch and Hsiao, 1993). Simulation of single root water uptake and growth zone water potential The model of Landberg and Fowkes (Landberg and Fowkes, 1978) as used by Frensch and Steudle (Frensch and Steudle, 1989) can be traced to the leaky cable theory dealing with electrical flow in nerve fibres (Taylor, 1963). Starting with that model, a sink term is added to account for water uptake and transport in the growth zone. That made it possible to calculate the Ψ gradients and water fluxes along both the non‐growing part and the growth zone of a root from known hydraulic resistances and external Ψ. The basic equations are those for radial water uptake and axial water transport. For radial water flux Jr (flow per unit root surface area per unit time, m3 m−2 s−1),   \[J_{\mathrm{r}}{=}\frac{\mathrm{{\Psi}_{s}{-}{\Psi}_{x}}}{R_{\mathrm{r}}}\] 3 The subscripts of Ψ denote the beginning and the end of the radial path, s for surface of the root and x for the xylem or centre of the root. Rr (MPa s m−1) is the radial total resistance from the root surface to the xylem or centre of the root per unit root surface area. The inverse of Rr is radial conductance, which is distinct from radial conductivity. For total axial flow Qx (m3 s−1) at any particular point along the length of a root,   \[Q_{\mathrm{x}}{=}{-}\frac{\mathrm{1}}{R_{\mathrm{x}}}\frac{d\mathrm{{\Psi}_{x}}}{dz}\] 4 where Rx (MPa s m−4) is axial resistance per unit of root length. Distance along the root measured from the apex is denoted by z. In the mature part of the root, xylem tracheary elements determine the size of Rx since their resistances are several orders of magnitude lower than that of the parenchyma cells which constitutes the alternative parallel path for water transport. In the growth and adjacent zones, conduction of water presumably takes place axially in all cells, since the lumens of vessels are yet to form. The inverse of Rx is axial conductance. Qx changes from one point to the next along the length of the root because of water uptake from the medium or water deposited in the enlarging cells in the growth zone. An equation of continuity may be written to account for this change, linking radial flux to axial flow. Combining these equations and adding a sink term for water consumed by the growth zone, the equation describing changes in xylem Ψ gradient along the length of the root may be derived:   \[\frac{d^{\mathrm{2}}\mathrm{{\Psi}_{x}}}{dz^{\mathrm{2}}}{=}\mathrm{2{\pi}}r\frac{R_{\mathrm{x}}}{R_{\mathrm{r}}}{[}\mathrm{{\Psi}_{x}}{-}\mathrm{{\Psi}_{s}}{]}{+}\frac{d\mathrm{{\Psi}_{x}}}{dz}\frac{dR_{\mathrm{x}}}{R_{\mathrm{x}}dz}{+}SR_{\mathrm{x}}\] 5 where r is radius of the root, and S, the sink term, is the rate of water gain per unit length of root (m3 m−1 s−1) due to local growth. The equation is applicable at each point along the root (each value of z) but local values of Ψ, R, and S must be used since they may vary with location along the root. Where Rx remains constant along the root, the middle term on the right side drops out of equation 5. For the mature part of the root where there is no growth, the sink term (SRx) is set to zero. The spatial pattern of local water gain due to growth (water deposition rate) has been measured by a number of investigators. The local rates for maize root (Sharp et al., 1990) were fitted with a second degree polynomial and used as input for the sink term in equation 5. The Appendix provides more details on the derivation of equation 5 and its use in simulation, including the model inputs and the techniques used to solve equation 5 to obtain the changes in xylem Ψ gradient along the root. With changes in Ψx gradient along the root calculated using equation 5 and Ψx at the basal end of the root and soil Ψ along the root as boundary conditions, the gradients in Ψx were calculated. Radial and axial flux of water were then computed using equations 3 and 4. Simulated patterns of root Ψ and water uptake The simulation was run for several situations. The first case is where soil is at field capacity (approximated by Ψs=−0.03 MPa) all along the root, a likely situation after a good rain or irrigation. The root was assumed to be 120 mm long with Ψx=−0.25 MPa at 120 mm. The results (Fig. 5A) show that there is a steep Ψx gradient along the root, with Ψx rising to nearly Ψ of the soil as the growth zone is approached (Fig. 5A, upper). The steep axial gradient in Ψ exists not only because of the high axial resistance in the region where xylem is not yet developed, but also because of the leaky cable behaviour of the root. The low Ψ at the basal end of the root is quickly dissipated along the root by fast radial water uptake (Jr, Fig. 5A, lower) driven by the large ΔΨ between the xylem and soil. This, together with the high axial resistance near the apex, enabled the growing apex to maintain its Ψ near to that of the surrounding soil. The difference in Ψ between the soil and the centre of the root in the growth zone at the apex is the result of growth induced depression in Ψ (Molz and Boyer, 1978; Silk and Wagner, 1980). It should be noted that in Fig. 5 the radial transport (Jr) is in terms of flux density at a particular point along the length of the root whereas the axial flow is cumulative and represents the sum of all upstream radial fluxes, minus the water used for growth from the apex up to the point in question along the root. It is informative to examine the flux and flow in the growth and adjacent region, enlarged in the inset of the lower figures. Where axial flow (Qx) is positive, the net flow along the root is directed toward the base of the root. Where axial flow is negative, the net flow is in the reverse direction, directed toward the zone of high growth rate. In the inset of Fig. 5A, it is seen that axial flow was directed toward the growth zone up to 15 mm from the apex, although the growth zone ended at 10 mm in the simulation. With the much faster water uptake (Jr) at the basal portion of the root in Fig. 5A, the soil surrounding the older part of the root will dry faster, leading in time to a gradient in soil Ψ (and hence Ψs) along the root. The shape of this gradient is not obvious and depends on hydraulic properties of the soil and the root, as well as transpiration rate and root elongation rate, and the duration of soil water depletion. Opting for simplicity, a simulation was run for the situation where Ψs decreased linearly from −0.03 MPa at the apex to −0.21 MPa at 120 mm, but Ψx remained at −0.25 MPa at 120 mm as in Fig. 5A. The result (Fig. 5B) shows interesting contrasts with Fig. 5A. As might be expected, the total uptake (Qx at 120 mm) is reduced by almost 50%, as a consequence of the reduction in soil Ψ at the basal end. Radial uptake was much reduced in the basal portion, but was maintained almost the same in the portion younger than 30 mm, in spite of the fact that the overall soil Ψ for the younger portion is substantially lower than that simulated in Fig. 5A. This occurred because the tension in the xylem (as negative Ψx) was better transmitted to the younger portion (Fig. 5B, upper) compared to the situation depicted in Fig. 5A, creating the radial Ψ gradient needed to maintain the uptake rates of the younger part of the root. Note that Ψx was set to be the same at 120 mm in both situations (Fig. 5A, B). In the uniformly wet soil situation (Fig. 5A), however, more tension was dissipated by the high radial uptake rates in the basal portion, so less tension was transmitted to the xylem in the younger portion. For a situation of drying soil (Fig. 5B), it could be said that the cable acted as if it partly sealed itself in the drier part of the soil. That is, the root is really a ‘reversibly leaky cable’. Because the profiles of Ψ for the growth zone (0–10 mm) are very similar for the two situations (Fig. 5A versus B), the growth rate as a function of location along the root was assumed to be unchanged and the same sink function (last term of equation 5) was used in the simulation of the two situations. The most important result overall in comparing the two simulations is that Ψx of the growth zone was barely reduced in the case of the drying soil (Fig. 5B) in comparison with the case of wet soil (Fig. 5A), showing the advantage of the slow maturation of xylem vessels close to the growth zone. A simulation was also run for the case of a longer root, 180 mm, in a soil at field capacity, and under the same boundary conditions as in Fig. 5A. The results (Fig. 5C) show that the longer root increased the total water uptake only by a small amount (8.6%) and the radial uptake was confined even more to the basal portion. This may be said to be the result of more dissipation of xylem tension along the longer root length before the younger part was reached. Consequently, Ψ of the growth zone and the adjacent newly mature zone was very slightly higher and the axial flow was directed toward the growth zone for a slightly longer distance (changed from 15 mm to 17.2 mm, insets of Fig. 5A and C) basal to the growth zone. The simulated results in Fig. 5 involved a number of simplifications. Most important was the fact that the impact of soil hydraulic conductivity was omitted by assuming that Ψ at the root surface was the same as Ψ of the soil. To be more realistic, the simulation should include the segment of water transport path from the bulk soil to the root surface, which is jointly determined by the Ψ gradient, geometric of the soil–root interface, and hydraulic conductivity of the soil. Because hydraulic conductivity of the soil decreases approximately exponentially with decreases in soil water content (Hillel, 1982), the effect of soil water depletion at the basal end of the root in shifting water uptake to the more apical region would be substantially more pronounced than that seen by comparing Fig. 5A with 5B. Because the model does not yet take soil hydraulic conductivity into account, no attempt is made to simulate a drought situation when soil Ψ could fall to much below −0.21 MPa and soil hydraulic conductivity becomes the major factor limiting water uptake. Fig. 5. View largeDownload slide Simulated inside water potential (Ψx) (upper figures) and simulated radial water flux (Jr) and axial water flow (Qx) (lower figures) along the length of a maize primary root. Insets depict values of Qx plotted on an enlarged scale and Jr plotted on the same scale for the apical 20 mm of each root. Inside water potential refers to xylem water potential for the mature portion of the root, and to water potential at the centre of the root for the growing and undifferentiated portion. Note that in each inset a substantial portion of Qx is negative, indicating water flow toward the apex induced by growth. The boundary conditions for the simulations are: (A) soil at the root surface is at field capacity (−0.03 MPa); root is 120 mm in length; and Ψx at the basal end of the root is −0.25 MPa. (B) Soil water potential at the root surface is −0.03 MPa at the root apex and declines linearly with distance toward the basal end and is −0.21 MPa at the basal end; root is 120 mm in length; and Ψx at the basal end of the root is −0.25 MPa. (C) Soil at the root surface is at field capacity (−0.03 MPa); root is 180 mm long; and Ψx at the basal end of the root is −0.25 MPa. Fig. 5. View largeDownload slide Simulated inside water potential (Ψx) (upper figures) and simulated radial water flux (Jr) and axial water flow (Qx) (lower figures) along the length of a maize primary root. Insets depict values of Qx plotted on an enlarged scale and Jr plotted on the same scale for the apical 20 mm of each root. Inside water potential refers to xylem water potential for the mature portion of the root, and to water potential at the centre of the root for the growing and undifferentiated portion. Note that in each inset a substantial portion of Qx is negative, indicating water flow toward the apex induced by growth. The boundary conditions for the simulations are: (A) soil at the root surface is at field capacity (−0.03 MPa); root is 120 mm in length; and Ψx at the basal end of the root is −0.25 MPa. (B) Soil water potential at the root surface is −0.03 MPa at the root apex and declines linearly with distance toward the basal end and is −0.21 MPa at the basal end; root is 120 mm in length; and Ψx at the basal end of the root is −0.25 MPa. (C) Soil at the root surface is at field capacity (−0.03 MPa); root is 180 mm long; and Ψx at the basal end of the root is −0.25 MPa. Relevance of simulation results to field behaviour of roots So far the discussion concerns laboratory studies and simulations and can be considered largely theoretical. How are these concepts manifested in the field? One manifestation is that for plants relying on soil‐stored water without rain or irrigation, roots grow more into new and yet unexplored soil where there is moisture. Figure 6 compares the profile of root distribution at the end of the season of a maize crop that was not irrigated and growing virtually only on water stored in the soil at planting with one that was regularly irrigated. Roots of the well‐irrigated treatment proliferated mostly in the upper 0.5 m of the soil. Below 1.0 m root length density dropped to less than 1 cm root cm−3 soil. Without irrigation, but starting with a soil profile at field capacity, roots of the unirrigated treatment depleted the soil water deeper and deeper over the season, and roots proliferated much more in the lower depth layers, where the root length densities were more than twice those of the well‐irrigated treatment (Fig. 6). As the simulations (Fig. 5B) made clear, hydraulic isolation of the growth zone of the root coupled with the leaky‐cable characteristics of the mature portion of the root ensures that root growth has the first call on the water contained in the newly intercepted soil volume, largely in disregard of the demand for water from the shoot manifested as increased xylem tension. The maintenance of root growth as water stress develops and the shifting of growth to the deeper soil layers where there is remaining water (Fig. 6) are also aided by two other factors. One is the enhancement in cell wall loosening and rapid osmotic adjustment which sustains root growth in the face of declining Ψ, as discussed in an earlier section. The other is the fact that leaf growth is inhibited by even very mild water stress while leaf photosynthesis continues unabated (Boyer, 1970; Acevedo et al., 1971; Bradford and Hsiao, 1982). This reduction in the strength of sink for assimilates above‐ground should make more assimilates available for root growth. As the outcome, not only is root growth favoured relative to shoot growth in order to explore the soil more thoroughly for water, the distribution of roots is also shifted to the wetter soil to make more effective use of each mm of root length for water uptake and transport to the top. Another field observation that may be explained in terms of the fundamental understanding is the pattern of water extraction of an annual crop from a drying soil profile and after a heavy rain or irrigation. When there is no rain and the crop grows on water stored in the soil, the extraction front moves downward with the growth of roots and the depletion of water in the depth where the roots have resided for some duration (Fig. 7). The rapid deepening of the roots in the drying soil was presumably facilitated by the high Ψ at the growing tips maintained by their hydraulic isolation and continuous movement into the wet and yet to be exploited soil. At the same time, the leaky cable characteristics of the roots also plays a critical role. The ‘cable’ is leaky as long as there is substantial water uptake along its length, which dissipates the Ψ gradient initiated at the proximal end and minimizes uptake at the distal end (Fig. 5A). As the water depletes in the upper part of the soil profile, however, uptake at the proximal part of roots becomes minimal and the Ψ gradient is transmitted more fully to the distal end, enabling more effective water removal from the deeper part of the soil. As mentioned earlier, the root is really a ‘reversibly leaky cable’ and acts as if it seals itself in the parts where there is little or no water to be taken up. This notion applies not only to single long roots, but in principle also to root systems with branches. Hence, the removal of water from the deeper layers of a depleting soil profile does not require a huge drop in Ψ at the proximal end of the root system. For the crop depicted in Fig. 8, around 70 DAP (days after planting) when the maximum water extraction rate occurred at the depth of 1.8 m and very little water was extracted from the dry soil above the depth of 1.0 m, leaf Ψ of the crop was only 0.2–0.3 MPa lower than that for the well‐watered control (Fereres et al., 1978) and transpiration was nearly as high, as can be deduced from the sum of extraction rates for all depth layers in Fig. 7. The leaky cable behaviour also appears to be applicable to water extraction by roots after a heavy rain or irrigation following a prolonged period of drying. Figure 8 shows that the extraction from the deep part of the soil before the irrigation changed quickly to extraction mostly from the upper layers, with the heaviest extraction taking place at the proximal portion of the root system after the irrigation. Although the situation was complicated by the root length density being higher in the upper layers and the possibility of the soil Ψ also being slightly higher, the leaky cable behaviour of the root system must have played a role. With the soil wet and uptake high at the proximal end of the root system, the Ψ gradient dissipated quickly going down the root system. This then aided in confining uptake to the upper soil after the soil profile was rewetted. The basic principle is illustrated by the simulations shown in Fig. 5, although the simulations were for highly simplified situations in comparison with the soil–root system described by the data in Fig. 8. Fig. 6. View largeDownload slide Effects of irrigation on maize root distribution at crop maturity in various depth layers of a Yolo clay loam soil in Davis, California. The crop was planted after a deep irrigation and received virtually no rain during the growing cycle. One treatment was irrigated weekly and the other was left unirrigated. Lines are fitted by eye. Original data of JD Vega and DW Henderson (from Hsiao and Acevedo, 1974). Fig. 6. View largeDownload slide Effects of irrigation on maize root distribution at crop maturity in various depth layers of a Yolo clay loam soil in Davis, California. The crop was planted after a deep irrigation and received virtually no rain during the growing cycle. One treatment was irrigated weekly and the other was left unirrigated. Lines are fitted by eye. Original data of JD Vega and DW Henderson (from Hsiao and Acevedo, 1974). Fig. 7. View largeDownload slide Estimated rooting depth (A) and computed root water absorption rate in each 300 mm soil depth layer (B) at different times after planting of a maize crop on a Yolo clay loam soil in Davis, California. Number on the curves denotes number of days after planting (DAP). Rooting depth was estimated by combining soil water content data in this experiment with root length density measured by the line interception method on soil core samples in this and another experiment. Water absorption was calculated by water balance with soil water content measured by a neutron probe. The crop was grown without irrigation on a Yolo clay loam soil in Davis, California. The soil was well wetted to 3 m at planting time and received only about 1 cm of water as rain during the growing cycle (from Acevedo, 1975; Hsiao et al., 1976). Fig. 7. View largeDownload slide Estimated rooting depth (A) and computed root water absorption rate in each 300 mm soil depth layer (B) at different times after planting of a maize crop on a Yolo clay loam soil in Davis, California. Number on the curves denotes number of days after planting (DAP). Rooting depth was estimated by combining soil water content data in this experiment with root length density measured by the line interception method on soil core samples in this and another experiment. Water absorption was calculated by water balance with soil water content measured by a neutron probe. The crop was grown without irrigation on a Yolo clay loam soil in Davis, California. The soil was well wetted to 3 m at planting time and received only about 1 cm of water as rain during the growing cycle (from Acevedo, 1975; Hsiao et al., 1976). Fig. 8. View largeDownload slide Water extraction from various depths of the soil by roots of a sorghum crop 2 d before and 4 d after an irrigation. The crop was growing in Davis, California on a soil with high water holding capacity (Yolo clay loam) and well‐watered at planting. The irrigation was applied 55 d after planting and there was no effective rain. Soil water content at the various depths were measured by a neutron probe and extraction was calculated by water balance (from Fereres, 1983). Fig. 8. View largeDownload slide Water extraction from various depths of the soil by roots of a sorghum crop 2 d before and 4 d after an irrigation. The crop was growing in Davis, California on a soil with high water holding capacity (Yolo clay loam) and well‐watered at planting. The irrigation was applied 55 d after planting and there was no effective rain. Soil water content at the various depths were measured by a neutron probe and extraction was calculated by water balance (from Fereres, 1983). Water transport through the stem to leaves and growth implications Xylem conduits, conductances, and depression in ψ of leaf growth zone By delaying the maturation of xylem cells, roots do not act as a source of water for the shoot until its own growth requirement for water is satisfied. Leaves, on the other hand, must acquire the water for growth through still developing xylem or yet‐to‐develop xylem cells. Equation 2, though derived for the growth of cells, may be used to conceptualize how water transport from selected points along the soil–stem–leaf catena affects the growth of leaves. If Ψo is taken to be the base of the stem, then C represents the overall conductance of the path consisting of the stem and the petiole supporting the growing leaf. If m≫C, the denominator of the fraction on the right side of equation 2 is approximated by m, which cancels the m in the numerator, leaving C as the coefficient ahead of the parenthesis, and with a major role in determining the rate of leaf growth. Of the many studies of conductances of the stem and petioles, most focus on water movement to mature leaves and do not consider the supply to growing leaves. Two that included the path to growing leaves, the immature internodes and petioles, are selected for discussion here. Dimond painstakingly measured the diameters of functioning vessels in all the internode and petiole xylem bundles in tomato plants with the 16th leaf just unfolding (Dimond, 1966). In each stem internode there were six bundles, and in each petiole, three. Dimond calculated the conductance of each bundle for the given internode or petiole length using the Poiseuille equation (Nobel, 1974) and tabulated the results. He also measured water flow for a given pressure difference across each mature internode and petiole, and stem segments consisting of several internodes, and found that the pressure difference driving a particular flow was generally in agreement with those predicted by the application of Poiseuille's equation and resistance network analysis. For the purpose of this paper, his bundle conductances were summed to obtain the conductance of each internode and petiole. The results show that for the mature leaves, conductance of the internode was at least two orders of magnitude greater than conductances of the petiole attached to the node above the internode, and for the growing leaves, one order of magnitude greater. The vessel diameter measurements (Dimond, 1966) indicates that going upward from the internode supporting the most recently fully enlarged leaf, axial conductance per internode length declined markedly, to less than a half for the rapidly enlarging leaves and to less than a few per cent for the just unfolding leaves. This marked change is shown in the plot of Rx versus internode number in Fig. 9. Petiole conductance, on the other hand, was much lower only for the unfolding leaf. The results suggest that generally, Ψ must drop substantially across the immature internodes and petioles to supply water to the growing leaves. Another detailed study combining conductance measurements with a comprehensive evaluation of xylem conduits is that of Schultz and Matthews, on current‐year shoots of grape (Schultz and Matthews, 1993). They used the leaf plastochron index (LPI) to characterize the development stage of the conducting segments associated with each leaf. Maximum growth rate was between an LPI of 1 and 2 for leaves, and between an LPI of −1 and zero for internodes; and leaves reached full size at an LPI between 8 and 9, and internodes, at an LPI between 4 and 5 (Schultz and Matthews, 1988). Axial conductance per unit length was more than one order of magnitude higher for internodes than for petioles of similar LPI. Going from an LPI of 10 to that of zero (the latter corresponded to a growing leaf 30 mm long), conductance decreased by about two orders of magnitude for both internodes and petioles. Conductance was measured in two different ways, by the rates of water flow through excised internodes and petioles under a range of applied pressure gradients, and by measuring transpiration and water potential of exposed and enclosed leaves of the shoot of intact plants. Conductance was also calculated from the measured vessel and tracheid diameters with Poiseuille's equation. Calculated conductances were about an order of magnitude higher than these measured. The calculated order of differences between internodes and petioles, and among internodes of different LPI, however, were similar to the order of differences measured. Schultz and Matthews measured all tracheary elements and assumed that all were functional in their calculation of conductance (Schultz and Matthews, 1993). Dimond tested the functionality of the vessels by dye uptake and included only the elements judged to be functional in his calculations (Dimond, 1966). It is quite common that calculated conductance turned out to be higher than measured ones, even when elements judged to be non‐functional were excluded (Frensch and Steudle, 1989). One possible cause is the narrowing of vessel elements and tracheids at their ends in some species. Its impact cannot be adequately accounted for by applying the Poiseuille equation in a simple way (Calkin et al., 1986). These data (Dimond, 1966; Schultz and Matthews, 1993) show clearly that there is notable resistance to water transport between the just matured end of the stem and the growing leaves because of the lack of functioning tracheary elements in the young and still developing stem and petiole. At a still smaller scale, resistance may be even more prominent in and adjacent to the growth zone. As already mentioned, Boyer and colleagues (Nonami and Boyer, 1990) have emphasized the depression in water potential induced by growth in general. In particular, the growth of soybean hypocotyls with roots in water‐deficient medium is thought to be limited by low conductance of the radial path between the xylem and the growing cells. For growing leaves, literature data also indicate a growth‐induced depression in ψ of the growth zone. This is more obvious for Gramineae because of the concentration of growth at the base of the leaf, in contrast to dicots with growth distributed more evenly over much of the leaf. In early studies of maize leaf growth, Ψ was found to be about 0.2 MPa (Michelena and Boyer, 1982) to 0.4 MPa (Westgate and Boyer, 1984) lower in the growth zone relative to the mature zone of the same leaf. It is possible that the magnitude of growth induced depression in Ψ was exaggerated because of wall relaxation error in the Ψ measured by thermocouple psychrometry (Cosgrove, 1985; Matyssek et al., 1988). Jing and Hsiao (unpublished results) found that Ψ of the growth zone of rapidly elongating maize leaves decreased by as much as 0.25 MPa during equilibration in the psychrometer. In any event, there is little question that growth zone Ψ of leaves of grasses is lower than that of the mature zone of the same leaf, even if a part of the difference might have been the result of wall relaxation. Limited measurements with pressure microprobes have also been made on turgor pressure and solute potential in the parenchyma cells of the growth zone, making it possible to calculate Ψ as the sum of its component potentials. Inference from these results is that relative to Ψ of the adjacent xylem, cell Ψ in the growth zone of leaves, no more than 10–25 cells away, may be 0.17 MPa lower in maize (Fricke and Flowers, 1998) and 0.3 MPa lower in fescue (Martre et al., 1999). After the growing leaf of grasses emerges from the whorl of older leaves, its apical portion is approaching maturity and actively transpiring, and must obtain water from the basal portion. At first glance, the finding that Ψ of the apical portion of leaves is higher instead of lower than that of the growth zone at the base of the leaf under transpiring conditions (Westgate and Boyer, 1984) appears intriguing. The explanation is that the measured growth zone Ψ is not representative of Ψ of the xylem, but Ψ of the parenchyma cells at the leaf base. Ψ of parenchyma cells must be considerably lower than xylem Ψ in the growth zone because radial conductance from the xylem to the growing cells is low, as indicated by calculations based on half‐time of pressure relaxation of cells in the growth zone (Fricke and Flowers, 1998). Since Ψ measured on a tissue is the volume‐averaged value; the measured growth zone Ψ should be dominated by Ψ of the parenchyma cells as water in the functioning xylem is a very minor part of the total water volume in the growth zone. In other words, the reason for the apparent reversal of Ψ gradient is the high axial conductance to the mature portion of the leaf coupled with a low radial conductance in the growing zone from the xylem to the enlarging cells, as well as the fact that the measured Ψ is a volume averaged value. Also intriguing is how good axial conductance is maintained in the basal growth zone to supply water to the mature and actively transpiring apical portion of grass leaves. It has long been known that the rapid elongation at the base ruptures the protoxylem vessels (Sharman, 1942; Evert et al., 1996) while the metaxylem vessels have not yet differentiated fully to conduct water. A recent anatomical study (Paolillo, 1995) indicates that although mature protoxylems in the growth zone are destroyed continuously by elongation, new protoxylems also form and mature continuously, such that there are always a few protoxylems present for conduction. Overall, it seem clear that even after water is moved to the distal end of the fully developed xylem in the stem, much additional resistance is still to be overcome to transport it to the actively growing cells in leaves. In contrast to roots, where the time it takes to develop the vascular system protects the growing cells from low Ψ, in the shoot the time it takes to develop the vascular system does just the opposite, being actually a major cause of the low Ψ of the growing cells. Fig. 9. View largeDownload slide Calculated axial hydraulic resistance per unit of stem internodes length (Rx) as related to internode number in tomato plants with 16 leaves. Leaf attached to node 16 was the youngest leaf and size of its petiole (Dimond, 1966) indicated that the leaf was just unfolding. Rx was calculated from the conductances of single xylem bundles (reported by Dimond, 1966) as described in the text. Fig. 9. View largeDownload slide Calculated axial hydraulic resistance per unit of stem internodes length (Rx) as related to internode number in tomato plants with 16 leaves. Leaf attached to node 16 was the youngest leaf and size of its petiole (Dimond, 1966) indicated that the leaf was just unfolding. Rx was calculated from the conductances of single xylem bundles (reported by Dimond, 1966) as described in the text. Field observations of Ψ gradients in the shoot In considering water transport in the root–stem–leaf catena, the hydraulic conductivity at the locations along the way as well as the distance of transport is important in determining the drop in water potential necessary along the transport path to sustain a given water flow. Roots have long been thought to be the site of high resistance to water transport. Substantial data also point to high resistance in leaves, as made clear in the preceding discussion on resistances of petioles and in the growing leaves. Resistance in the stem is often low in comparison, at least for many annual plants not subjected to excessive xylem cavitation. The relative size of resistance in stems and leaves are evident in the drop in water potential along the stem–leaf transport path. Stem xylem Ψ may be estimated from Ψ of leaves which have been covered to prevent transpiration and allowing the equilibration in Ψ between the leaf and stem xylem. One of the first data sets using this technique to compare leaf Ψ with stem xylem Ψ, obtained by Begg and Turner on tobacco plants in the field, is reproduced in Fig. 10A (Begg and Turner, 1970). As a reference, stem xylem Ψ was also measured on a plant which was completely covered to prevent transpiration. The pattern of Ψ was determined on a clear sunny day during the period of 12.00 h to 13.30 h, a time of high transpiration and fast water transport. It is seen (Fig. 10A) that leaves at the top of the plant had the lowest Ψ and there was a relatively large drop (by 0.2 MPa or more) in Ψ from the stem xylem to the leaf, even for leaves low on the stem and substantially shaded. This indicates that resistance of the petiole–midrib–lamina path was large. The drop in xylem Ψ from the stem base to the top of the plant was also large, more than 0.5 MPa. So resistance of the stem xylem was large in this species. With water flow reduced to a minimum in the fully covered plant, its stem xylem Ψ was nearly in equilibrium at the various heights and much higher than that of the plant with most leaves uncovered (Fig. 10A), and reflected the Ψ of the soil. Using a similar approach, the pattern of stem xylem Ψ and leaf Ψ of cotton, including that of an actively growing leaf in the field on a clear day during the period of high transpiration, were assessed. The results are given in Fig. 10B. Water potential was about 0.3 MPa lower in the upper leaves, and about 0.2 MPa lower in the lower leaves, than Ψ of the stem xylem to which the leaves were attached. In contrast to tobacco (Fig. 10A), Ψ of stem xylem in cotton did not show a substantial gradient with height under transpiration rates similar to that of the tobacco. Thus, xylem resistance was very low in the mature stem of cotton. The xylem near the stem base may be an exception. At the node where the lowest leaf was attached, stem xylem Ψ (large solid triangle, Fig. 10B) was considerably higher than at the higher nodes. This suggests that the lowest part of the stem may be considerably higher in resistance. The measured actively growing leaf at the top of the cotton plant exhibited a Ψ lower than that of the stem xylem, but higher than that of the more mature leaves below (Fig. 10B). This meets expectations since the growing leaves are at the terminus of the stem water transport path and must maintain their Ψ lower than that of the stem xylem to obtain water for growth. At the same time, actively enlarging leaves have not yet fully developed their potential for photosynthesis and stomatal opening (Field, 1987; Bolaños and Hsiao, 1991) and therefore should have a slower rate of transpiration per unit leaf area as well as smaller leaf area compared to the more basal mature leaves. Consequently, Ψ of the enlarging leaves may be higher than Ψ of the more mature leaves below. This was in spite of the immature and yet to be developed vascular system in the apical internodes and petioles. One may infer from the results of Dimond on tomato and Schultz and Matthews on grape that going upward from the internode supporting the most recently fully enlarged leaf, axial conductance in cotton must have declined markedly (Dimond, 1966; Schultz and Matthews, 1993). These field results support the earlier conclusion that, generally, Ψ must drop substantially across the immature internodes and petioles to supply water to the growing leaves. Similar to tobacco, stands of cereals in the field also exhibit significant vertical gradient in water potential of exposed leaves, as exemplified in Fig. 11. Near noon on a sunny day leaves at the top of the canopy of both maize (Fig. 11A) and sorghum (Fig. 11B) were about 1 MPa lower in Ψ than leaves at the low part of the canopy where the mean photosynthetic photon flux density (PPFD) was only about 10% of the incident due to shading by leaves above. Measurements of PPFD at various strata of the canopy (Acevedo, 1975; Fereres, 1976) indicated the common exponential decline in radiation with canopy depth. So the higher the leaves were in the canopy, the greater should have been the transpiration because of the greater radiative energy supply. The crops were at their full heights with the stems fully elongated. Unfortunately, Ψ was not measured on covered leafs to estimate stem xylem Ψ. Turner compared, in the field, Ψ of upper leaves of sorghum covered the day before to prevent transpiration with those not covered over a daily cycle (Turner, 1981). His results indicated that the upper leaves were some 0.3 MPa lower in Ψ than the stem xylem at midday. Stem xylem Ψ declined by some 0.4 MPa from dawn to midday (Turner, 1981) suggesting high resistance in the stem xylem or roots. Hence, the reduction in leaf Ψ with height in maize and sorghum at midday depicted in Fig. 11, totalling about 0.9 MPa, was probably the result of considerable resistance to water transport in the leaf sheath, midrib and blade, as well as in the stem xylem or roots. In these studies Ψ of the leaf growth zone was not measured. In a separate study, where it was measured in well‐irrigated sorghum in the field over a diurnal cycle on a clear day (Hsiao and Jing, 1987), Ψ of the growth zone at midday fell to around −0.75 MPa, in spite of the fact that the zone was well enclosed in the sheath of the older leaves. Thus, resistance for transport to the growing part of the leaf was also substantial. Considering water transport and growth adjustment characteristics of the roots and leaves together, some generalization may be made regarding growth and adaptation to water stress. Growing leaves are at or near the end of the water transport line, and worse yet, they are connected by pathways of extremely high resistance to the water supplied by the mature portion of the stem. With their cell Ψ already low, any reduction in soil Ψ or increase in transpiration may cause a slowing down in their growth. The slower leaf growth leads to a smaller canopy and less water requirement by the plant. Photosynthesis of the mature or more mature portion of the leaves, however, are usually not affected by such small reductions in Ψ (Boyer, 1968; Hsiao et al., 1971; Bradford and Hsiao 1982), but photosynthesis per plant is reduced because of the smaller plant size. The growing portion of the root, on the other hand, is protected by the high axial resistance from low Ψ generated by high transpiration rates or soil water depletion by the mature portion of the root. With its quick but partial osmotic adjustment and enhanced loosening ability of its cell wall, aided by the enhanced assimilate supply as a result of reduced leaf growth, growth of the root is maintained, at least partially. The continuous growth of roots requires a continuous assimilate supply and minimizes assimilate accumulation and ‘feedback inhibition’ of photosynthesis (Stitt and Schulze, 1994; Van Oosten and Besford, 1994). Most importantly, it makes possible the continuous exploration of new soil volume for water and the partial amelioration of water stress. Thus, effects of water stress on the plant are partly ameliorated by this improvement in water supply, and partly by the reduction in canopy size and transpiration. It is possible over the long term for the plant to adjust its canopy size to its water supply as determined by the root system in a way that nearly matches the supply to the transpiration loss, provided that the soil water storage capacity is high (Hsiao et al., 1976). Fig. 10. View largeDownload slide Water potential of stem xylem and leaves at midday for (A) a tobacco crop in relation to height and (B) a cotton crop in relation to node number of the main stem. Data were obtained on clear days in the field. Measurement of Ψ was made on leaves with a pressure chamber. Selected leaves were covered in the early morning to prevent transpiration. Their Ψ was measured 6 h or longer later and taken to be Ψ of the stem xylem under the assumption that Ψ of the covered leaves was in equilibrium with Ψ of the stem xylem. In (A) solid triangles represent Ψ of leaves of a plant with all leaves covered so there was no transpiration. In (B), data were taken on two dates, 20 September (circles) and 30 September (triangles) in Davis, California. Open symbols represent Ψ of leaves and closed symbols represent Ψ of stem xylem. Ψ of the xylem of the basal most node is shown as a large solid triangle (from Begg and Turner, 1970 (A) and original data of the authors (B)). Fig. 10. View largeDownload slide Water potential of stem xylem and leaves at midday for (A) a tobacco crop in relation to height and (B) a cotton crop in relation to node number of the main stem. Data were obtained on clear days in the field. Measurement of Ψ was made on leaves with a pressure chamber. Selected leaves were covered in the early morning to prevent transpiration. Their Ψ was measured 6 h or longer later and taken to be Ψ of the stem xylem under the assumption that Ψ of the covered leaves was in equilibrium with Ψ of the stem xylem. In (A) solid triangles represent Ψ of leaves of a plant with all leaves covered so there was no transpiration. In (B), data were taken on two dates, 20 September (circles) and 30 September (triangles) in Davis, California. Open symbols represent Ψ of leaves and closed symbols represent Ψ of stem xylem. Ψ of the xylem of the basal most node is shown as a large solid triangle (from Begg and Turner, 1970 (A) and original data of the authors (B)). Fig. 11. View largeDownload slide Water potential (Ψ) and solute potential (ψs) of leaves at midday for a well irrigated (A) maize crop and (B) sorghum crop in relation to height of the leaves. Data were obtained on clear days in the field in Davis, California. Isopiestic thermocouple psychrometer was used to measure Ψ of the leaf sample first, then ψs after freezing and thawing of the sample (maize data are from Hsiao et al., 1976, and sorghum data, from Fereres, 1976). Fig. 11. View largeDownload slide Water potential (Ψ) and solute potential (ψs) of leaves at midday for a well irrigated (A) maize crop and (B) sorghum crop in relation to height of the leaves. Data were obtained on clear days in the field in Davis, California. Isopiestic thermocouple psychrometer was used to measure Ψ of the leaf sample first, then ψs after freezing and thawing of the sample (maize data are from Hsiao et al., 1976, and sorghum data, from Fereres, 1976). Osmotic adjustment in relation to water transport With water potential in the plant at less than zero all the time, positive turgor is possible in cells only in the presence of solutes and the delineating semipermeable membrane backed by the mechanically strong wall. Turgor in cells can be maintained within a reasonable limit in the face of variation in Ψ by adjusting osmotic solute content in the cells. A substantial gradient in Ψ with height was shown in Fig. 10A for transpiring tobacco plants. Similarly, marked vertical gradient in Ψ was also observed in maize and sorghum in the field. As shown in Fig. 11, these gradients are accompanied by gradients in solute potential (ψs). The magnitude of the ψs gradient was such that turgor, the difference between Ψ and ψs, was maintained at a similar level regardless of the height of the leaf within the crop canopy (Fig. 11). The frequent exception is the older leaves near the bottom of the canopy, which are usually shaded and have a lower turgor. Much of the vertical osmotic adjustment may be the result of accumulation of soluble sugars, as soluble carbohydrates showed a vertical gradient very similar in shape to that of the gradient in ψs (Hsiao et al., 1976). If a plant has a more conductive xylem system, its vertical gradient in Ψ would be less steep for a given transpiration rate. Consequently, in theory, it would not have to adjust osmotically as much at the downstream part of the root–stem–leaf flow path. The same may be said for plants with a more extensive or conductive root system, resulting in a lower overall root resistance. Since the formation of more xylem vessels or a more extensive root system is costly in terms of carbon and energy, and enlarging the diameter of vessels may expose the plant to greater risk of xylem cavitation, it should be asked what is the optimal root and stem conductance for a plant? There are species differences in whether to favour high conductance of the root–stem–leaf pathway or high concentration of osmotica in cells distal to the source of water. This is seen in the contrast in leaf Ψ among different species under similar evaporative demand. An example is given in Fig. 12, where midday leaf Ψ over most of the crop life cycle are plotted for a tomato, cotton and sorghum crop growing in Davis, California, on the same soil and field area. Although the crops were grown in different years, the weather was similar and the sky was nearly always sunny, and the crops were all irrigated nearly weekly to maintain the soil Ψ within the root zone around field capacity. In spite of the very similar environmental conditions, it is obvious that midday Ψ of exposed fully mature upper leaves was always higher in tomato than in cotton, by about 0.6 MPa. The value for sorghum fell between that for tomato and cotton. Solute potential was measured on the sorghum leaves after their Ψ was measured. The general trend shows that Ψ and ψs changed in near unison over the season and turgor appeared to remain almost constant with time (Fig. 12B). Solute potential was not measured regularly and with adequate sampling on the leaves of tomato and cotton, but their complete moisture release curves were determined. These curves (Fig. 13) show that at full saturation (leaf Ψ=0 MPa), ψs of the tomato leaf was −0.98 MPa, and of the cotton leaf, −1.23 MPa. At saturation ψs of the sorghum leaf was −1.2 MPa on day 45 after emergence (Acevedo et al., 1979). Hence, compared to cotton, tomato allocated less carbon and energy for making and maintaining solutes in the cells, but presumably more carbon and energy for making a more conductive system to ensure that leaf Ψ remained high enough to maintain good leaf turgor in spite of the more dilute solute content in its cells. Sorghum appears to fall between tomato and cotton in terms of the investment in solutes and in making the conductive system. Fig. 12. View largeDownload slide Midday leaf Ψ of a well irrigated tomato and cotton crop (A) and midday leaf Ψ and ψs of a well irrigated sorghum crop (B) over the season in Davis, California. Measurements were made on the upper exposed and most recently matured leaves with a pressure chamber in (A) and by isopiestic thermocouple psychrometry in (B). (Data were from Bolaños, 1988, for tomato, Puech‐Suanzes, 1988, for cotton, and Fereres et al., 1978, for sorghum.) Fig. 12. View largeDownload slide Midday leaf Ψ of a well irrigated tomato and cotton crop (A) and midday leaf Ψ and ψs of a well irrigated sorghum crop (B) over the season in Davis, California. Measurements were made on the upper exposed and most recently matured leaves with a pressure chamber in (A) and by isopiestic thermocouple psychrometry in (B). (Data were from Bolaños, 1988, for tomato, Puech‐Suanzes, 1988, for cotton, and Fereres et al., 1978, for sorghum.) Fig. 13. View largeDownload slide Curves of water potential (—) and solute potential (–––) versus relative water content (RWC) for the upper exposed and most recently matured leaves of a tomato and cotton crop in the field in Davis, California. Each symbol represents a leaf from a different plant. Data were obtained by dewatering the leaves in a pressure chamber with incremental pressure and collecting and weighing the amount of water removed to calculate RWC. The inverse of Ψ was plotted versus RWC in accordance with Morse's equation (Hsiao and Bradford, 1983); the linear portion of the plot was fitted with a linear equation and the equation was used to calculate the curve of ψs. (Data were from Bolaños, 1988, for tomato and Oliveira, 1982, for cotton.) Fig. 13. View largeDownload slide Curves of water potential (—) and solute potential (–––) versus relative water content (RWC) for the upper exposed and most recently matured leaves of a tomato and cotton crop in the field in Davis, California. Each symbol represents a leaf from a different plant. Data were obtained by dewatering the leaves in a pressure chamber with incremental pressure and collecting and weighing the amount of water removed to calculate RWC. The inverse of Ψ was plotted versus RWC in accordance with Morse's equation (Hsiao and Bradford, 1983); the linear portion of the plot was fitted with a linear equation and the equation was used to calculate the curve of ψs. (Data were from Bolaños, 1988, for tomato and Oliveira, 1982, for cotton.) Concluding discussion Roots are capable of growing at low Ψ, down to −1.5 MPa and lower, albeit more slowly. Leaf growth, on the other hand, is very sensitive to water stress, and may stop with a reduction in tissue Ψ of only a fraction of a MPa (Fig. 1). Differences in responses to reductions in tissue water status apparently account for a part of the contrasting growth behaviour of the two organs under water stress. In terms of the parameters in the Lockhart equation, the growth zone of root adjusts osmotically to sudden reductions in Ψ and its turgor recovers within minutes, but only partially (Fig. 2A). Simultaneously, the yield threshold turgor (Y) declines (Fig. 3B). With the quick recovery in ψp and lowering of Y, and possibly increases in volumetric extensibility (m), growth recovers in spite of the low Ψ. In contrast, the leaf osmotically adjusts slowly or not at all upon stepwise reductions in Ψ, and the loosening ability of its cell wall is either reduced, as suggested by limited indication of an increase in Y (Hsiao and Jing, 1987), or at least not greatly enhanced. Hence, leaf growth is much more inhibited by a given reduction in tissue Ψ compared to the root. Beyond the biophysical aspects, strong evidence obtained by Sharp and colleagues (Saab et al., 1990, 1992; Spollen et al., 1993; Sharp et al., 1994) indicate that the accumulation of ABA under water stress plays a pivotal role in inhibiting shoot growth while maintaining root growth. On the other hand, the evidence is based on experiments involving prolonged water stress. It is not clear whether the increase in ABA is fast enough to be consistent with the fast manifestation of the differences in root and leaf growth at the onset of water stress, in terms of the parameters in the Lockhart equation. The literature indicates that in the root–stem–leaf pathway for water transport the major resistances lie in the parts across parenchyma cells, and also in the differentiated xylary system of some species, especially when the axial pathway is long. Resistance per unit cross‐sectional area is high when water moves radially or laterally to and from xylems and through growing or mature parenchyma cells, or axially through the undifferentiated portions of roots, stems and petioles. These high resistances are in the apical portion of roots and stems, leaving the growth zone of roots and leaves largely isolated hydraulically. This isolation also plays an important role in the differential effect of water stress on root and leaf growth. To quantify, a sink term for water to account for root growth is added to the leaky cable model of Landsberg and Fowkes (Landsberg and Fowkes, 1978) as used by Frensch and Steudle (Frensch and Steudle, 1989) for water transport in roots. Results of simulations with the model show that as the root grows into new soil volume, the apical growing region has the first call on the water in the newly intercepted soil, largely disregarding the transpirational demand for water manifested as high xylem tension in the mature part of the root, and largely irrespective of the soil water status enveloping the mature part. Thus, the late maturation of xylary elements in roots ensure that Ψ of the growth zone is maintained high and close to Ψ of the adjacent newly entered soil. In contrast, late maturation of the xylem and the consequent hydraulic isolation of the growth zone of leaves have the opposite effect, being a major cause of the low Ψ of the leaf growth zone. The combination of the different responses in the growth parameters such as the reduction in Y and the hydraulic isolation effects apparently underlies the co‐ordinated preferential growth of roots relative to leaves under water stress. Aquaporins are the subject of much current research (Maurel, 1997; Chrispeels et al., 1999; Tyerman et al., 1999). There is the potential to manipulate aquaporin genes to alter membrane water permeability in the developing xylem cells and growing parenchyma cells in the shoot. From the forgoing discussion it is obvious that the manipulation has to be well targeted to a particular location and ontogenetic stage of the cells. Even then, it is not at all clear whether the aim should be to enhance or reduce water permeability and hydraulic conductance. Excessive leaf growth resulting from raised hydraulic conductance and leaf water status when water is not plentiful is likely to be detrimental. On the other hand, reduced hydraulic conductance may shift growth too much in favour of roots and limit productivity markedly by reducing photosynthetic surface area. An indirect way to overcome low hydraulic conductance is to accumulate more solutes in tissue distal to the source of water by osmotic adjustment. Limited field data on leaf Ψ under similar climatic and soil water regimes indicate that species might have evolved differently, some contain more solutes but with apparently lower overall conductance for water transport to the leaves, and others contain less solutes, but with high overall conductance. Presumably there is a trade off, in the cost of carbon and energy, between maintaining more solutes or more xylary tissue. Simulation with the model for root water uptake and transport also shows that the root behaves as a ‘reversibly leaky cable’. When soil adjacent to the root contains ample water, the cable is ‘leaky’ and uptake is confined more to the proximal end. That uptake dissipates the Ψ gradient along the root so that uptake at the distal end is minimal. This contributes to the observed preferential extraction of water from the upper soil layers in the field when the soil profile is fully wet. As water is depleted in the proximal part, uptake is greatly reduced there and the Ψ gradient is transmitted more fully to the distal part. In that case the cable acts more as if it is sealed and the soil water adjacent the distal portion of the root system can be absorbed without an inordinately large drop in Ψ of the plant. Appendix Simulation of local water potential, uptake and transport by the root As explained in the main text, water status and transport are location specific, and therefore equations 3 and 4 of the text are rewritten with location along the length of the root specified by i;   \[J_{\mathrm{r}}{(}i{)}{=}\frac{\mathrm{{\Psi}_{s}}{(}i{)}{-}\mathrm{{\Psi}_{x}}{(}i{)}}{R_{\mathrm{r}}{(}}\] A1  \[Q_{\mathrm{x}}{(}i{)}{=}{-}\frac{1}{R_{\mathrm{x}}{(}}\frac{d\mathrm{{\Psi}_{x}}{(}i{)}}{dz}\] A2 For steady‐state conditions, Qx(i) can be related to Jr(i) in term of the conservation equation for mass,   \[\frac{Q_{\mathrm{x}}{(}i{)}}{dz}{=}\mathrm{2{\pi}}rJ_{\mathrm{r}}{(}i{)}\] A3 where r (m) is the radius of the root. For the growth region, radial water uptake (Jr) may be retained by the growing cells and not contribute to the axial flow (Qx). So a sink term S(i), rate of water gain per unit length of the root (m3 m−1 s−1) due to the local growth, must be added. Replacing Qx and Jr in equation A3 with equations A1 and A2, and incorporating the sink term yields   \[\frac{d}{dz}\left[{-}\frac{1}{R_{\mathrm{x}}{(}i{)}}\frac{d\mathrm{{\Psi}_{x}}{(}i{)}}{dz}\right]{=}\mathrm{2{\pi}}r{[}\frac{\mathrm{{\Psi}_{s}}{(}i{)}{-}\mathrm{{\Psi}_{x}}{(}i{)}}{R\mathrm{_{r}}{(}i{)}}{-}S{(}i{)}\] Taking the derivative of the left side of the equation, transforming and combining terms, the following differential equation is obtained:   \[\frac{d^{\mathrm{2}}\mathrm{{\Psi}_{x}}{(}i{)}}{dz^{\mathrm{2}}}{=}\mathrm{2{\pi}}r\frac{R_{\mathrm{x}}{(}i{)}}{R_{\mathrm{r}}{(}i{)}}{[}\mathrm{{\Psi}_{x}}{(}i{)}{-}\mathrm{{\Psi}_{s}}{(}i{)}{]}{+}\frac{d\mathrm{{\Psi}_{x}}{(}i{)}}{dz}\frac{1}{R\mathrm{_{x}}{(}i{)}}\frac{dR_{\mathrm{x}}{(}i{)}}{dz}{+}S{(}i{)}R_{\mathrm{x}}{(}i{)}\] A4 The differential equations can be solved numerically with the information on Rr(i), Rx(i) and growth water uptake S(i) along the root under the following boundary conditions: (a) At the root apex where z=0, xylem water potential Ψx(0) equals soil water potential Ψs(0). (b) At the zone of maximum growth 6 mm from the apex, there is no axial water flow. (c) Length of the root, Ψx at the basal end of the root, and Ψs are as specified in the main text. (d) The axial resistance Rx along the root is based on a polynomial fitted to the data of Fig. 5 of French and Steudle (French and Steudle, 1989), which did not span the portion of the root younger than 20 mm. For locations apical to 20 mm, Rx was assumed to be the same as Rx at 20 mm. Rr is taken to be 2.46×106 MPa s m−1 (converted from hydraulic conductivity of French and Hsiao, 1995) for the 0–10 mm segment, and 4.0×106 MPa s m−1 for the 20–120 mm segment (French and Steudle, 1989). For the segment between 10 and 20 mm, Rr is assumed to increase linearly from 2.46×106 to 4.0×106 MPa s m−1. (e) The values for the sink term S(i) are from Fig. 7. of Sharp et al. (Sharp et al., 1990), for the well‐watered roots. (f) For numerical calculations, dz to solve the differential equation is set to 0.1 mm. That is, each i represents a 0.1 mm segment along the root. Root radius is set to 0.5 mm. The method to solve equation A4 for the growth region is briefly described as an example. Since Rx is assumed to be constant in the growth region, the second term on the right side of the equation A4 drops out. Staring from i=1 at the root apex, equation A4 written in finite differential form is   \[\frac{\mathrm{{\Psi}_{x}{(}2{)}{-}2{\Psi}_{x}{(}1{)}{+}{\Psi}_{x}{(}0{)}}}{dz^{\mathrm{2}}}{=}2\mathrm{{\pi}}r\frac{R\mathrm{_{x}{(}1{)}}}{R\mathrm{_{r}{(}1{)}}}{[}\mathrm{{\Psi}_{x}{(}1{)}}{-}\mathrm{{\Psi}_{s}{(}1{)}}{]}{+}S{(}\mathrm{1}{)}R_{\mathrm{x}}{(}\mathrm{1}{)}\] According to the first boundary condition that Ψx(0)=Ψs(0) and after rearranging, equation A5 may be written in an abbreviated form for ease of representation:   \[F\mathrm{{(}1{)}{\Psi}_{x}{(}1{)}}{+}G\mathrm{{(}1{)}{\Psi}{(}2{)}}{=}H\mathrm{{(}1{)}}\] A6 with the definitions of:   \[F{(}\mathrm{1}{)}{=}{-}\mathrm{2{-}2{\pi}}r\frac{R\mathrm{_{x}{(}1{)}}}{R\mathrm{_{r}{(}1{)}}}dz^{\mathrm{2}}\ G\mathrm{{(}1{)}}{=}1.0\ H\mathrm{{(}1{)}}{=}{-}\mathrm{2{\pi}}r\frac{R\mathrm{_{x}{(}1{)}}}{R\mathrm{_{r}{(}1{)}}}\mathrm{{\Psi}_{s}{(}1{)}}dz^{\mathrm{2}}{+}S\mathrm{{(}1{)}}R\mathrm{_{x}{(}1{)}}dz^{\mathrm{2}}{-}\mathrm{{\Psi}_{s}{(}0{)}}\] For, 2≤i≤59, the finite form of the differential equation would be   \[\frac{\mathrm{{\Psi}_{x}{(}}i{+}\mathrm{1{)}{-}2{\Psi}_{x}}{(}i{)}{+}\mathrm{{\Psi}_{x}{(}}i{-}1{)}}{dz^{\mathrm{2}}}{=}\mathrm{2{\pi}}r\frac{R\mathrm{_{x}{(}}i{)}}{R\mathrm{_{r}{(}}i{)}}\mathrm{{[}{\Psi}_{x}{(}}i{)}{-}\mathrm{{\Psi}_{s}{(}}i{)}{]}{+}S{(}i{)}R\mathrm{_{x}{(}}i{)}\] Rearranging, the abbreviation form of the equation would be   \[E{(}i{)}\mathrm{{\Psi}_{x}{(}}i{-}\mathrm{1{)}}{+}F{(}i{)}{+}G{(}i{)}\mathrm{{\Psi}_{x}{(}}i{+}\mathrm{1}{)}{=}H{(}i{)}\] A7 with the definition of E(i)=1.0,   \[F{(}i{)}{=}{[}{-}\mathrm{2{-}2{\pi}}r\frac{R_{\mathrm{x}}{(}i{)}}{R_{\mathrm{r}}{(}i{)}}dz^{\mathrm{2}}{]}G{(}i{)}{=}1.0\ H{(}i{)}{=}{-}\mathrm{2{\pi}}r\frac{R\mathrm{_{x}{(}}i{)}}{R\mathrm{_{r}{(}}i{)}}\mathrm{{\Psi}_{s}{(}}i{)}dz^{\mathrm{2}}{+}S{(}i{)}R\mathrm{_{x}{(}}i{)}dz^{\mathrm{2}}\] For i=60, at the centre of the growth zone, according to boundary condition b, there is no axial water flow, so Ψx(59)=Ψx(61), and   \[\frac{{-}\mathrm{2{\Psi}_{x}{(}60{)}{+}2{\Psi}_{x}{(}59{)}}}{dz^{\mathrm{2}}}{=}\mathrm{2{\pi}}r\frac{R\mathrm{_{x}{(}60{)}}}{R\mathrm{_{r}{(}60{)}}}{[}\mathrm{{\Psi}_{x}{(}60{)}}{-}\mathrm{{\Psi}_{s}{(}60{)}{]}}{+}S\mathrm{{(}60{)}}R\mathrm{_{x}{(}60{)}}\] Rearranging, the abbreviation form of the equation is   \[E\mathrm{{(}60{)}{\Psi}_{x}{(}59{)}}{+}F\mathrm{{(}60{)}{\Psi}_{x}{(}60{)}}{=}H\mathrm{{(}60{)}}\] A8 with the definition of E(60)=2.0,   \[F\mathrm{{(}60{)}}{=}{[}{-}\mathrm{2{-}2{\pi}}r\frac{R\mathrm{_{x}{(}60{)}}}{R\mathrm{_{r}{(}60{)}}}dz^{\mathrm{2}}{]}\ H\mathrm{{(}60{)}}{=}{-}\mathrm{2{\pi}}r\frac{R\mathrm{_{x}{(}60{)}}}{R\mathrm{_{r}{(}60{)}}}\mathrm{{\Psi}_{s}{(}60{)}}dz^{\mathrm{2}}{+}S\mathrm{{(}60{)}}R\mathrm{_{x}{(}60{)}}dz^{\mathrm{2}}\] Taking equations A6, A7 and A8 together, there are 60 linear equations with 60 unknowns, and they can be written in the following matrix form:   \[\left[\begin{array}{lllllll}F{(}1{)}&G{(}1{)}&0&.&.&.&0\\E{(}2{)}&F{(}2{)}&G{(}2{)}&0&.&.&0\\0&0&.&.&.&.&0\\0&.&E{(}i{)}&F{(}i{)}&G{(}i{)}&.&0\\0&.&.&.&.&.&0\\0&.&.&.&E{(}59{)}&F{(}59{)}&G{(}59{)}\\0&.&.&.&0&E{(}60{)}&F{(}60{)}\end{array}\right]{\times}\left[\begin{array}{lllllll}\mathrm{{\Psi}_{x}}{(}1{)}&\mathrm{{\Psi}_{x}}{(}2{)}&.&\mathrm{{\Psi}_{x}}{(}i{)}&.&\mathrm{{\Psi}_{x}}{(}59{)}&\mathrm{{\Psi}_{x}}{(}60{)}\end{array}\right]\ =\left[\begin{array}{lllllll}H{(}1{)}&H{(}2{)}&.&H{(}i{)}&.&H{(}59{)}&H{(}60{)}\end{array}\right]\] Note that the coefficient matrix is in tridiagonal linear form, which can be solved by Crout Factorization method (Burden and Faries, 1993). 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TI - Sensitivity of growth of roots versus leaves to water stress: biophysical analysis and relation to water transport
JF - Journal of Experimental Botany
DO - 10.1093/jexbot/51.350.1595
DA - 2000-09-01
UR - https://www.deepdyve.com/lp/oxford-university-press/sensitivity-of-growth-of-roots-versus-leaves-to-water-stress-FIhCmy4zJj
SP - 1595
EP - 1616
VL - 51
IS - 350
DP - DeepDyve
ER -