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American Journal of Botany 85(7): 897–909. 1998.

INVITED SPECIAL PAPER

APPLICATIONS OF THE COMPENSATING PRESSURE

THEORY OF WATER TRANSPORT1

MARTIN J. CANNY

Biology Department, Carleton University, 1125 Colonel By Drive, Ottawa, Canada K1S 5B6

Some predictions of the recently proposed theory of long-distance water transport in plants (the Compensating PressureTheory) have been verified experimentally in sunflower leaves. The xylem sap cavitates early in the day under quite smallwater stress, and the compensating pressure P (applied as the tissue pressure of turgid cells) pushes water into embolizedvessels, refilling them during active transpiration. The water potential, as measured by the pressure chamber or psychrometer,is not a measure of the pressure in the xylem, but (as predicted by the theory) a measure of the compensating pressure P.As transpiration increases, P is increased to provide more rapid embolism repair. In many leaf petioles this increase in P isachieved by the hydrolysis of starch in the starch sheath to soluble sugars. At night P falls as starch is reformed. A hypothesisis proposed to explain these observations by pressure-driven reverse osmosis of water from the ground parenchyma of thepetiole. Similar processes occur in roots and are manifested as root pressure. The theory requires a pump to transfer waterfrom the soil into the root xylem. A mechanism is proposed by which this pump may function, in which the endodermisacts as a one-way valve and a pressure-confining barrier. Rays and xylem parenchyma of wood act like the xylem parenchymaof petioles and roots to repair embolisms in trees. The postulated root pump permits a re-appraisal of the work done byevaporation during transpiration, leading to the proposal that in tall trees there is no hydrostatic gradient to be overcome inlifting water. Some published observations are re-interpreted in terms of the theory: doubt is cast on the validity of mea-surements of hydraulic conductance of wood; vulnerability curves are found not to measure the cavitation threshold of waterin the xylem, but the osmotic pressure of the xylem parenchyma; if measures of xylem pressure and of hydraulic conductanceare both suspect, the accepted view of the hydraulic architecture of trees needs drastic revision; observations that xylemfeeding insects feed faster as the water potential becomes more negative are in accord with the theory; tyloses, which havebeen shown to form in vessels especially vulnerable to cavitation, are seen as necessary for the maintenance of P, and toconserve the supplementary refilling water. Far from being a metastable system on the edge of disaster, the water transportsystem of the xylem is ultrastable: robust and self-sustaining in response to many kinds of stress.

Key words: embolism refilling; hydraulic architecture; hydrostatic gradient; pressure chamber; reverse osmosis; rootpressure; starch sheath; tissue pressure; transpiration; tyloses; ultrastability; water pump; xylem-feeding insects.

This is an invitation to an adventure of exploration, anoffer of a new way to look at plants, a new way to in-terpret old data, a new way to plan investigations. It ismy purpose to persuade you, not that the way is whollyright, but that it connects previously unrelated facts andquickly leads to unexplored territory. The argument isinterrupted at several points to suggest exploratory ex-periments to test some of the proposed ideas.

I must assume that you have read the original state-ment of the theory (Canny, 1995) where full details aregiven of the reasons for presenting a new theory, and ofits scope and requirements as understood at that time. Ibegin with a brief statement of its main points.

STATEMENT

A plant organ is like a mass of osmometers (cells)confined in a box (epidermis, bark). When supplied with

1 Manuscript received 17 September 1997; revision accepted 5 March1998.

Symbol convention: Italic symbols are used for primary measuredquantities, plain text symbols for derived quantities.

The author thanks Margaret McCully and Steve Vogel for helpfuldiscussions and criticism of the manuscript, Adam Baker for makingthe plate, and the Natural Sciences and Engineering Research Councilof Canada for an operating grant.

water it generates a pressure inside the box because thecells are pressing against each other. The maximum avail-able pressure is P, the osmotic pressure of the cell sap.Some part of P is balanced by wall stretching, but somealso by mutual pressure of the cells (tissue pressure). Foreach cell, wall and tissue pressure together make up theturgor pressure. Through the organ, within this pressur-ized box, runs the xylem pipeline carrying water, and itspressure is coupled to the tissue pressure surrounding it.A first effect of pulling water through the xylem pipe isto reduce some of the tissue pressure in the box. Call thisreduction the compensating pressure (P). The harder thewater is pulled, the more the tissue pressure is reduced(i.e., P increases). Up to the limit of available P (,P)the pressure in the pipeline is kept near 0 to 1 bar (100kPa) absolute. The absolute pressure scale, on which at-mospheric pressure is 11 bar (1100 kPa), will be used,except in some published data. If the stretched water inthe pipeline breaks (to form an embolism), P providesthe force to push water out of static reservoirs and torefill the embolized space. A major source of this tissuepressure is the solute-rich phloem. A plant organ is ableto alter P both up and down as needed by osmoregulationof P in the sap of some of the cells. An easy way to dothis is by interconversion of starch and sugar.

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Figs. 1–4. Figs. 1–2. Preparations of a strand of xylem in the petiole of a sunflower leaf, frozen intact during active transpiration, and viewed(still frozen) in the cryo-scanning electron microscope. 1. Living cells are grey, containing white lines of solute crystals in a matrix of black ice.Some of the vessels contain black ice and were filled with sap when frozen, others contain gas and were embolized when frozen. Bar 5 100 mm.2. View inside an embolized vessel in a preparation like that in Fig. 1. The vessel was refilling with drops of water entering through pits fromadjacent parenchyma cells. Bar 5 10 mm. Figs. 3–4. Starch sheaths in the petiole of a hollyhock leaf. Transverse sections of petioles of adjacentleaves harvested on a day of bright sunshine. Iodine stain. 3. At 0645. 4. At 1930. Bars 5 100 mm.

DIRECT OBSERVATIONS OF EMBOLISMS

Deduction—Consideration of the phenomena and ex-perimental techniques of plant water relations from theviewpoint of the theory led me to propose that what isreferred to as the water potential (C) of the organ was infact a measure (as far as the limit near P) of the com-pensating pressure P, and that this was the quantity mea-sured by the customary techniques (the pressure chamberand the psychrometer). Beyond the limit P 5 P, C ismanifested as tension in the xylem water, as in the co-hesion theory. In Fig. 12 of Canny (1995) this argumentis traced in detail following the changes in water contentand pressure in various parts of a transpiring leaf whenit is cut off, and after its equilibration with gas pressurein a Scholander chamber. Because no one had ever fol-lowed the changes in water content of xylem conduitsfollowing excision of an organ, and because I had at hand

the means to do this, an experimental investigation wascarried out to test the predictions of Fig. 12 of Canny(1995).

Experiment 1. Changes on leaf excision—The instan-taneous content of the xylem conduits in a plant organcan be ascertained by snap freezing the organ, planing itflat in the desired section with a cryo-microtome, andstudying the planed face, still frozen, in the cryo-scan-ning electron microscope (CSEM) (Fig. 1). The trachearyelements are easily distinguished from surrounding pa-renchyma by their solute-poor sap (appearing black) andtheir thickened walls. Any tracheary element that is em-bolized shows empty space (also black, but often filledwith debris formed during the planing).

The percentages of embolized vessels were determinedby this technique in petioles and midribs of sunflower

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leaves, frozen intact on the plant, and at intervals aftercutting leaves off the plant (Canny, 1997a). The answerto the original question, that there was no significantmovement of water into or out of the vessels on cuttingexcept for a limited, slow efflux during an hour or so inthe middle of the day, was overshadowed by the unex-pected observations on the intact plants. As anticipated,the percentage of embolized vessels rose from a low val-ue in the morning to a maximum of 40% around noon.But then the percentage declined again throughout thetime of peak transpiration in the early afternoon, andreached near zero by 1600. Refilling of embolized vesselshas been recognized as a fact, but believed to occur onlyat night or in rainy weather when transpiration has ceasedand tension in the xylem has become a positive pressure.Its occurrence during active transpiration, implying apressure in the xylem at that time above 0.02 bar (20kPa) absolute (the vapor pressure of water), is so directlyopposed to the operation of the cohesion theory that itwas necessary to design a second experiment to verify ordisprove it.

Experiment 2. Vessel contents during transpiration—Note that this measure of percentage embolized vesselsis a direct measure of both water stress and tension inthe vessels. When you pull on something and it breaks,the extent of breaking is a measure of the pull. Here itmeasures both the evaporative stress and the transmissionof this stress through tension in the water in the vessels,the greater the tension, the more the breaks. Moreoverthe measure is an integrated one for the whole organbecause it is based on the state (water content or gas) ofall the individual vessels in the petiole.

The percentages of embolized vessels were measuredas before in petioles of sunflower leaves (Canny, 1997b),but this time all leaves were frozen while still attachedto the plant, and concurrent measurements were made ofirradiance, leaf temperature, transpiration rate, and leafwater potential (using a pressure chamber). The plantswere large, the days were longer, and additional waterstress was imposed by withholding water from the potsduring the day. Embolisms occurred earlier in the day(by 0900), but again were reduced during the day, andreached a minimum (4%) at 1500, which was the timeof peak transpiration and most negative water potential(highest balance pressure). Again embolized vessels werebeing refilled with water during vigorous transpiration.The images of the vessels revealed this refilling processat work: water being extruded through pits into emptyvessels from the neighboring cells, and vessels at allstages of partial filling (Fig. 2). X-ray microanalysis ofthe entering liquid showed that it contained no significantconcentrations of solutes, eliminating the osmotic pres-sure of the xylem sap as a possible filling force. The vigorof the refilling process increased as transpiration in-creased, keeping ahead of the increasing evaporative de-mand. Comparison of the time courses of percentage em-bolized vessels with those of balance pressure in the pres-sure chamber showed that the balance pressure was nota measure of water stress, and was certainly not a mea-sure of tension in the vessels. Just the opposite. Whenthe balance pressure was low, the tension was greatest,as shown by high or rising percentage embolisms. When

the balance pressure was at its maximum, the tension waslowest because the embolisms fell to a minimum. Whatthe balance pressure was strongly correlated with waswhat I have called the vigor of the refilling process, therate of reduction of embolisms. As explained above, theforce driving the refilling process is part of the tissuepressure of the cells surrounding the xylem, in fact thecompensating pressure P. Thus the second experimentdemonstrated practically the theoretical prediction inCanny (1995) that the chamber balance pressure is a mea-sure of the compensating pressure.

Hypothesis of vessel refilling—Given these new factsit is easy to construct a hypothesis to explain refilling.Just as a small overpressure in the pressure chamber forc-es water by reverse osmosis out of parenchyma cells andinto the vessels, so in the intact leaf the tissue pressurein the petiole pushes a small constant influx of water intoall the vessels. This influx is an insignificant part of themain transpiration flux through the vessels and dependsupon the magnitude of P and the hydraulic conductivityof the cell membranes (Lp). When the water cavitates ina vessel, it is replaced by gas, and the forward flow stops.The influx continues, the vessel refills over a short period(minutes), and forward flow through it resumes. The timeto refill is proportional to the vessel radius, and smallvessels both fill and empty faster than large ones. Hereinlies a major value of a population of small vessels in ablock of xylem. They spend little time out of action andprovide continuity of transpiration until the liquid con-tents are restored in large vessels. The source of water inthe petiole to supply the influx for the whole day’s tran-spiration is the mass of ground parenchyma cells, and theamount of water consumed in this repair function couldbe roughly estimated by the amount of petiole shrinkageduring the day. I will refer to this constant minor influxfor embolism repair as the supplementary water.

The regulation of increasing P in response to increasedtranspiration could be provided by changes in the osmoticpressure of a small population of petiole cells. The mainmass of water-supplying parenchyma needs to stay at itscustomary osmotic pressure so that water is still forcedout of them. The starch sheath cells were suggested (Can-ny, 1997b) as the source of the necessary extra pressure.Starch in the sheath cells would be converted into sugarswith increasing water stress. This is easily demonstratedexperimentally. On days of rapid transpiration there isextensive disappearance of petiole starch by the afternoon(Figs. 3–4). The starch polymer reforms overnight andthe pressure provided by the starch sheath drops. This isa necessary stage of the process, because it allows thewater storages of the ground parenchyma to be rechargedby water coming from the roots during the night. Thusthe petiole acts as a water pump on a 24-h cycle, squeez-ing water out of parenchyma cells into the vessels duringthe day at whatever rate is necessary to refill them, andrefilling the parenchyma cells at night via the vesselsfrom the supply below, ready for the next day’s repairs.

A prediction of this hypothesis is the existence of aflow of xylem water from roots into the shoot at nightwith zero transpiration. The water-deficient reservoirswould act as sinks for water, exert a small tension on thesap of the tracheary elements, and draw a slow flow of

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restoring water from the roots. The tension on the sapmight be sufficient to embolize tracheary elements, sothat a low percentage of embolisms would persist far intothe night.

The time scale of all these events depends critically onthe value of Lp for the petiole parenchyma cells, and thishas not yet been measured. The maximum rate of vesselemptying at greatest water stress in Experiment 1 was ;4min. Some sample calculations are done in Appendix 1using likely values for Lp and P, which show that a 5%shrinkage in diameter of the petiole would provide aday’s supply of supplementary water. The necessary sup-plementary water is ;1% of the transpiration water. Thisdoes not seem unreasonable, and could easily be tested.

Experiments: Investigate changes in xylem content after excisionin other plants and organs. Repeat the measurements of percentageembolized vessels during transpiration with as many other plantsas possible. Measure Lp of parenchyma cells adjacent to vessels.Look for the distribution of water channels in xylem parenchymacells. Measure organ shrinkage and compare with the required vol-ume of supplementary water. Look for changes in starch morningand evening in relation to transpiration rate (store tissues in 50%ethanol, cut hand sections, stain with I2/KI). Look for the signalsthat pass between the starch/sugar equilibrium and the rate of tran-spiration. Leave a xylem pressure probe inside a vessel after ob-serving a cavitation, and time the refilling process. Look for therestoring current of water at night with zero transpiration, and forthe slow disappearance of embolisms during the night.

Shift of emphasis—These observations and the in-duced hypothesis of refilling vessels change somewhatmy view of how the compensating pressure theory works.In the original formulation (Canny, 1995) the main focuswas on raising the pressure in the vessels to stop thewater threads breaking. Now a major effect of the com-pensating pressure appears also to be the provision of thesteady influx of supplementary water to the vessels froma water reservoir, refilling embolized vessels fairly quick-ly when the threads do break. This view of the xylemparenchyma, as providing a constant low-level supple-ment to the transpiration stream, stimulates useful in-sights into the operation of a number of other regions ofthe plant, some of which will be briefly discusssed.

ROOTS, ROOT EXUDATIONS, ANDROOT PRESSURE

There is good evidence that a process similar to thatfound in the leaves is operating also in roots. McCully,Huang, and Ling (1998) followed changes of embolismsin the vessels of transpiring corn roots, frozen intact inthe field. The technique used was the same cryo-scanningmicroscopy of the fully hydrated tissues and assessmentof the contents of the individual vessels. Early in the dayno root vessels were embolized. Embolisms appeared atsunrise, increased to a plateau (;75%) during the middleof the day, and fell during the afternoon or evening dur-ing active transpiration, to reach zero again by dusk. Inembolized vessels at all times water could be seen enter-ing through the pits in the vessel walls from the adjacentparenchyma and from branch roots (Fig. 2). Again, a re-verse osmosis of water squeezed from the xylem paren-chyma by the tissue pressure confined within the me-chanical barrier of the endodermis seems a likely expla-

nation. This is a manifestation of the well-known but in-adequately explained phenomenon of root pressure. Apossible source of the pressure, though not an explanationof the pressure-driven xylem flux of water, was identifiedin Canny (1995) as the tissue pressure generated by phlo-em and parenchyma cells confined within the stele. Theadditional hypothesis of the reverse osmosis of cellularwater into the vessels, which refills embolisms, is a steptowards explaining the water flux observed in excisedroots. We shall return to this question presently.

Recent work has shown that there are at least two otherexudations produced by roots, which may be generatedby tissue-pressure-driven reverse osmosis, but operatingin the cortex, not the stele. The first of these to be pub-lished was the finding of liquid water (with varying con-centrations of solutes) in some of the intercellular spacesof the root cortex (Canny and Huang, 1993). The inter-cellular solutions were found at all times of the day, andin all ages of root, and were present even at times ofconsiderable water stress. Such accumulations of solutionoutside cells have been observed by us constantly since,in many hundreds of root samples examined with theCSEM (e.g., McCully, 1994) and come to be regarded asa normal component of root tissues. More recently, muchlarger accumulations of liquid water were recorded, fill-ing some of the large aerenchyma spaces in corn roots(Van der Weele, Canny, and McCully, 1996; Watt et al.,1996).

The second kind of expressed water is that found ex-uding from field-grown corn roots at night (McCully,1995). Convex drops of water were seen (again frozenpreparations in the CSEM) on the epidermis and roothairs and filling much of the space between soil particlesin the early morning. By midday the liquid had gone, andthe root–soil interface contained only air among the planttissues and the soil particles. Without attempting to for-mulate detailed mechanisms for these two kinds of exu-dation, it is tempting to couple them with the supple-mentary water as examples of pressure-driven reverse os-mosis from root cells. But if cortical cells may be con-sidered as confined and under pressure, the epidermalcells are certainly not so, and the source of pressure forthem is less clear (but see below).

Hypothesis of the root water pump—The logic deriv-ing from the compensating pressure theory demands thatthere must be a water pump in roots. The reasons for thisare several. First, with the pressure in the xylem conduitsnot far from zero bar absolute, a pump is needed to takewater from the soil where the water potential may beseveral bars negative, and transfer it to the conduits. Withthe simpler cohesion theory no such pump was necessary,and none was looked for. Pressures in the xylem werebelieved to be far enough negative to extract water fromeven quite dry soils. Without this comfortable simplicity,some role for the living cells of the root in extractingwater from the soil is required.

Second, the compensating pressure theory requires asupply of supplementary water to refill embolisms in theroots. In the stem and leaves this is stored locally, usedduring transpiration, and recharged at night from below.But in roots, though the cortex may act as a temporarystore, the ultimate source of the supplementary water for

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the whole plant is outside in the soil, and a pump isneeded to transfer the water to the empty vessels.

Third, though the compensating pressure theory ex-plains the origin of the pressure in root pressure, in orderto provide also the flow of xylem sap up through an ex-cised root, which constitutes the root-pressure-driven ex-udation from the cut stump, there must be a one-way fluxof water from outside the root to the xylem conduits, i.e.,a pump.

Fourth, the maintenance of the not-far-negative pres-sure in the xylem by the compensating pressure requiresvalves at the top and bottom of the conduits, so that thecompensating pressure is not dissipated while water flowsthrough them (Canny, 1995). As explained in that paper,the flows through the two valves must be independent ofpressure in the conduits. Taken with the first three points,this implies that the bottom gateway must be more thana valve—it must be a pump.

None of these root processes can be separate from themain activity of roots, the provision of the major flux oftranspiration water to supply evaporation from the leaves.The pump required in the four above points must haveall the properties consistent with the known attributes ofthe transpiration stream in roots. It must have the capacityto deliver water at the measured rates. It may respond toincreased demand by increasing throughput (Passioura,1988), but at the same time (point 4) it must be indepen-dent of pressure in the conduits. It would be an addedbonus if it were slowed down by low temperatures (sincemany plants wilt when their root systems are cooled), orif it could explain Rygol et al.’s (1993) observation ofincreased solute concentrations in the inner cortical cellsof transpiring roots, which dispersed in 20 min after tran-spiration stopped, or the finding of Schneider, Zhu, andZimmermann (1997) that transpiration induces a changein root radial reflection coefficients. How is it possible toconstruct a pump with all these properties from theknown hardware of cell membranes, osmotic vacuoles,cell walls, and plasmodesmata?

I propose the broad outlines of a hypothetical waterpump that satisfies these criteria. The pump is constructedfrom the whole mass of the endodermis and the tissuesit contains. One function of the endodermis is to act asthe mechanical barrier that confines pressure within it.The output of the pump is the reverse-osmotic flux fromstele parenchyma to the xylem conduits driven by thetissue pressure in the stele (Canny, 1995). The energydriving the pump is the difference in osmotic energy ofthe cells inside the stele relative to that in the cells of thecortex (see quantities and gradients measured by Mc-Cully, 1994). This energy is converted into a pressure todrive the reverse osmosis by the turgor pressure of thephloem and parenchyma cells of the stele (Canny, 1995).It is likely that the osmotic energy in roots is based, noton carbon compounds as in the stem and leaves, but onmineral ions, which are available close by in the soil.The input of the pump is a flux of water through theendodermis from the cortical cells, and via them from thesoil. The endodermis acts also as a one-way valve thatallows the influx of water to the stele and prevents theefflux of water from the stele. This valve is the essentialand novel element of the pump and deserves more de-tailed attention.

The operation of the valve depends on the distinctionbetween pressure flow and diffusion. Flow is driven bydifferences in pressure; diffusion is driven by differencesin concentration (activity). The valve takes advantage ofthe fact that at a septum with holes in it the two processesrespond differently to changes in the size of the holes. Inqualitative terms: smaller holes restrict pressure flowmuch more strongly than they restrict diffusion. By mak-ing the holes small enough it is possible to change theseptum into a valve that permits diffusion while pre-venting pressure flow. With high concentration on theoutside of the septum, diffusive influx can build up apositive pressure in the space inside the septum, and yetthis pressure cannot drive significant flow back throughthe holes. For a quantitative statement see Appendix 2.The principle has been shown to operate in the gaseousphase in leaves of water lilies by Dacey (1981). Therethe septum pores are ;1-mm-wide spaces between themesophyll cells of young, developing, floating leaves,which are small enough to generate gas pressures insidethe leaves when there are differences in gaseous com-position or temperature between inside and out. Thispressure drives a flow of gas down through the petiolesof the young leaves, along the rhizomes and back outthrough the stomata of older leaves. In the endodermisthe pump would operate in the liquid phase (water), andthe critical pores are the plasmodesmata through the innertangential wall between endodermis and pericycle. In or-der to confine the diffusion to these critical pores, alter-native apoplastic paths for flow or diffusion through thecell walls are blocked by thickenings, suberized lamellaeand the Casparian strip. In short, the endodermis, with itsknown structures, acts as a valve to allow diffusive waterinflux to the stele and to prevent pressure-driven effluxfrom the stele.

The driving force of the pump, the difference in waterconcentration between the cells of the cortex and thoseof the stele, is maintained in two ways. First, the solutesof the cortical and stelar cells are confined within vacu-oles and cannot easily diffuse through the plasmodesmatato equalize their concentrations (and hence the concen-tration of water). The water flux is from cell to cell, fromvacuole to vacuole in the cortex and stele, but, at theendodermal septum where the one-way valve operates,through the symplast only (Fig. 5). Second, as water iswithdrawn from the roots through the xylem by transpi-ration, the water concentration within the stelar vacuolesfalls. The gradient of water concentration from cortex tostele becomes steeper, and the diffusive flux increases.The pressure within the stele is higher than the pressurein the cortex, but never high enough to prevent the in-ward diffusion of water because it is relieved by the fluxof transpiration and supplementary water to the xylemoutlet, which the pressure drives. As we know from thebehavior of leaves in the pressure chamber, quite smalloverpressures are sufficient to express water from cells.An assessment of some of the quantitative requirementsof the valve is attempted in Appendix 2. The reader mustjudge whether they accord with acceptable limits. Theoperation of the valve depends on the balance betweenpore size and viscosity. For water the pore size is im-possibly small. But if the viscosity of the watery proto-plasm in the pores is as high as 20 Pa·s, the pore size is

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Fig. 5. Diagram of the features of a root required for the operation of the water pump. The thickened cell walls of the endodermis and thecentral xylem vessel are shown black; cytoplasm, pink; vacuoles and the sap of the central xylem vessel, blue. The solute concentration in thevacuoles increases progressively from the cortex (u, v), through the endodermis (w), the pericycle (x), and the xylem parenchyma (y). In otherwords, the water concentration in these vacuoles decreases along this path. The plasmodesmata between the endodermis and the pericycle constitutethe one-way valve that permits the inward diffusion of water (red arrows) down a concentration gradient of water, but restrict the outward (pressure-driven) flow of water. Pressure builds up in the stele, and drives water from the stelar cells into the vessel (black arrows). For details see Appendix3 and text.

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in the range accepted for the gaps in the annulus aroundthe desmotubule (Terry and Robards, 1987).

It may seem paradoxical that a process transmittingsuch large volumes of water as the transpiration streamof a tree should depend at a critical step on diffusivetransfer. The traditional understanding of diffusion is thatit is a slow process, which indeed it is over distancesgreater than a few tens of micrometres. But diffusion overshort distances is very rapid. The limiting distance in themodel is the length of the endodermal plasmodesmata. InAppendix 3 a calculation is made from some simple as-sumptions, which shows that the model is not hopelesslyinadequate. It is sufficiently promising to stimulate thecollection of some real data about the two determiningvariables, the radius and number of the pores in the en-dodermal plasmosdesmata and the gradients of waterconcentration between cortex and stele.

Hypodermal pump—The same structures that blockthe apoplast and confine diffusive transfer to the symplastare found at the outer boundary of the root cortex in thehypodermis. That too could be the site of a valve andpump. The hypodermal pump could be responsible forthe elevated tissue pressure in the cortex to drive the ex-udations into the intercellular spaces. The whole root,cortex plus stele, would then be a two-stage pump withthe pressure rising in two steps. Note that this kind ofpump can be made to work in either direction by revers-ing the gradient of water concentration. The hypodermalpump might be reversed at night by solute uptake intothe epidermis reversing the water gradient between cortexand epidermis, and so drive the outward water flux ob-served into the soil.

Experiments: Work with branch roots of plants transpiring at dif-ferent rates during the day, and at night guttating with positivexylem pressures. Measure exclusion limits of endodermal/hypo-dermal plasmodesmata. Look for gradients of solute and water ac-tivities in vacuoles of inner cortex/stele and outer cortex/epidermiswith the CSEM. Measure the effects of low temperatures on ratesof refilling (percentage embolisms). Look at the distribution ofwater channels (aquaporins) in the critical boundaries: hypodermis/cortex; endodermis/pericycle; xylem parenchyma/vessel. Testwhether damage to the endodermis by herbivory or rot affects thepump.

STEMS, TREES, STATIC AND MOVING WATER,AND THE HYDROSTATIC GRADIENT

So far, the experiments on embolisms and supplemen-tary water have been done on petioles and roots, but thesame processes are at work in stems and the trunks oftrees. In trees the source of static water is water-filledfibers and tracheary elements of small diameter, or theelastic tissues of the inner bark. Static water in trees ismuch more voluminous and can supply transpiration aswell as the supplementary water (Waring, Whitehead, andJarvis, 1979). The source of pressure is the ray and par-atracheal parenchyma, and again the pressure is regulatedto provide higher pressures during rapid transpiration bythe conversion of starch to sugar. Again, the pressure isrelaxed at night when starch reforms. Determinations ofthe osmotic pressure of ray cells of wood are few, and Ihave found none published for different times of day.

Kny (1909) measured osmotic pressures of ray cells ofSalix, Populus, and Aesculus, and recorded some veryhigh values. The contact cells of Aesculus in early springhad osmotic pressures of 45 bar (4.5 MPa), and in latesummer, 50 bar (5.0 MPa). Ursprung and Blum (1916)record 35 bar (3.5 MPa) for the wood rays of Fagus.Pressures generated by such cells could drive large vol-umes of water from the static stores of the wood.

Experiments. Take cores from the outer xylem of trees at differenttimes of day, and different rates of evapotranspiration, and assessthe starch content by iodine staining; express the sap and measureits refractive index or freezing point. Measure P for ray and par-atracheal parenchyma by modern methods on a similar program.

The supplementary water is a more abundant and gen-eral manifestation of the water postulated (and rather de-viously demonstrated) by Munch (1930) to arise from thephloem. For Munch it was the superfluous water fromthe translocated sugar solution, left over after the sugarhad been used in a sink. This water would be returnedto the plant body and the source by transfer to the xylem.Milburn (1996) has revived the idea and proposed thatthis released water helps to repair embolisms.

The phloem was recognized as a likely source of pres-sure (Canny, 1995). A fairly direct measure of the tissuepressure that exists in the phloem, and which could drivesome of the reverse osmosis, was made by Buttery andBoatman (1966) in the bark of rubber trees. Manometersinserted into the bark were readily sealed into the poolof exuding latex and gave reproducible measures of thepressure driving the latex out of the laticifers. They rec-ord pressures in the range 19 to 113 bar (10.9 to 11.3MPa) morning and evening. The high values at dawn fellby ;4 bar (0.4 MPa) at times of high evaporative de-mand. This fall is a direct measure of the compensatingpressure P.

Experiments. Revive and exploit this system to investigate the be-havior of P.

The hydrostatic gradient—Once the possibility is ad-mitted of a water pump in roots, which might deliverwater into the xylem conduits against a pressure of sev-eral bars, it becomes possible to think in a new way aboutthe movement of water up trees. Since the first mentionof this question it has been a commonplace that the watermust be lifted up the tree against the force of gravity, that1 bar (0.1 MPa) of tension must be applied to lift thewater through each 10 m, or 10 bar (1 MPa) for the tallest(100 m) trees. I find no mention of the fact that the wateris already up the tree, that the tree is in fact a standingtank of static water surrounding a few conduits in whichwater moves. The static water, contained in living cells,fibers, intercellular spaces, and the smallest conduits,must be a continuum, even if it contains islands of drymaterial and gas. Isolated regions of static water cannotpersist. So the continuum of static water has a weight,and the force exerted by this weight is proportional tothe height. A standing tank of water with a pipe runningup it from bottom to top has a gradient of positive pres-sure increasing downwards, not a tension in the pipe in-creasing upwards. Everywhere the pressure in the pipeequals the pressure in the tank. To suck water from thetop of the pipe requires no more force than to suck water

904 [Vol. 85AMERICAN JOURNAL OF BOTANY

Fig. 6. Figure and legend reproduced by permission of the editorsof Nature from Fig. 1 of Pockman, Speery, and O’Leary (1995). ‘‘De-crease in hydraulic conductivity (kh) in xylem against xylem pressure(Cpx) generated by centrifuging (filled symbols) and air-drying (opensymbols) stems of a Populus fremontii, b, Salix gooddingii, c, Acernegundo and d, Abies lasiocarpa. Centrifuge data only are shown forJuniperus monosperma (d). Decrease of kh from air injection of xylem(a–c, open circles) is shown against the negative of the injection pres-sure for comparison.’’

through it when it is lying horizontal. The hydrostaticgradient is irrelevant to the flow through the pipe.

The tree differs from the tank and pipe in two respects.(1) The bottom of the xylem pipe is not open and con-tinuous with the static water. (2) The bottom of the tree,both the static water and the xylem pipe, ramifies intonarrowing branches (the roots), which are buried underanother weight (the soil). Because of (1), a pump is nec-essary to move water from the soil into the pipe againstthe positive pressure, and this is where the energy is ex-pended to lift the water up the tree. The pump describedabove, with an output pressure of 10 bar (1 MPa) (Ap-pendix 2), would transfer water into the conduits at thebase of the tallest trees. Because of (2), the pressure inthe root conduits will be less than at the bottom of thetank, but how much less is not easily assessed.

Experiments. It should not be difficult to distinguish a gradient ofincreasing pressure from top to bottom, from a gradient of increas-ing tension from bottom to top. At each level the living cells mustbe in balance with the prevailing pressure. Measure osmotic/turgorpressure of xylem/phloem parenchyma at different heights. Butteryand Boatman (1966), in the experiments already mentioned, founda gradient in their measured tissue pressures decreasing upwardsat about the rate of the gravity gradient.

VULNERABILITY CURVES

As explained in Canny (1995) the results of almost allexperiments are interpretable equally by the cohesion the-ory and the compensating pressure theory. As an exampleof alternative explanation I take the experiments of Pock-man, Sperry, and O’Leary (1995) who tried to show thatthe pressure chamber did indeed measure tension in thexylem by inducing known amounts of water stress inbranches. They compared the effects of the centrifugalstress generated by spinning branches with two otherstress treatments, drying in air and external air pressureapplied around the branch. They measured the effects ofthese stresses by estimating the hydraulic conductancesof the branches. Their argument is that the hydraulic con-ductance gives a measure of the cavitations produced inthe conduits by the stresses. The stresses of centrifugationand drying act by moving or extracting water, and airpressure acts by forcing air into the conduits throughpores in pit membranes. The results are displayed in theform of ‘‘vulnerability curves,’’ plots of the percentageloss of conductance against the stress (Fig. 6). The threestresses are measured as pressures in MPa, centrifugalstress calculated from the angular velocity, drying stressmeasured by the pressure chamber on leaves taken fromthe branches, and pressure stress by the air pressure ap-plied in a jacket around the branch.

To understand the procedure it is necessary to consultan earlier paper (Sperry and Saliendra, 1994) describingthe apparatus (Fig. 7). Air pressure was applied in a jack-et around the body of the branch, while one end wasconnected to a reservoir supplying solution for the con-ductance measurement under small pressure determinedby the elevation of the reservoir. Note the air vent, whichallowed escape of bubbles driven through the branch bythe air pressure, and the notches that admitted air to thebranch. An initial flow measurement was made with anair pressure of 11 bar (1100 kPa) . The pressure was

raised to the desired level (up to 40 bar [4 MPa]), heldfor 10 min, depressurized to 11 bar (1100 kPa), and theflow measured again. This measurement was expressedas a percentage of the initial flow. The curves of Fig. 6were constructed from measurements at increasing valuesof air pressure and the two other stresses. All three stress-es induced an abrupt change in conductance from highto low values over a narrow range of stress, and the stresslevel at which this happened was characteristic of thespecies. The authors argue that they have demonstratedthat the water in the conduits withstands negative pres-sure (generated by any of the three stresses) up to athreshold value which varies from 215 bar (1.5 MPa) toaround 240 bar (4 MPa). This is the cohesion-theoryinterpretation.

The compensating pressure theory proposes that the x-axis of Fig. 6 should be labelled, not as negative waterpressure, but as the compensating pressure applied to theconduits to protect them from cavitation in response todrying, and to refill them when they do cavitate. The

July 1998] 905CANNY—APPLICATIONS OF A THEORY OF WATER TRANSPORT

Figs. 7–8. Figures from Sperry and Saliendra (1994) reproduced bypermission of the editors of Plant, Cell and Environment. 7. ‘‘Apparatusfor measuring vulnerability curves on single hydrated stems using airpressure. The stem (SEGMENT) was sealed in a double-ended steelbomb with both ends protruding.’’ From their Fig. 1. 8. The correlationbetween compensating pressure (P) applied to the vessels (reducingcavitation and refilling embolized vessels) and the mean hydraulic ves-sel diameter for individual root, trunk, and twig segments from a singleindividual of Betula occidentalis. Redrawn, with the y-axis relabelled,and omitting the data on hydraulic conductances, from their Fig. 4.

centrifuging is a drying stress, just like the air drying.The pressurization technique will also dry the branch. Airwas being forced through it at up to 40 bar (4 MPa)pressure for 10 min. The amount of drying will be rough-ly proportional to the applied air pressure. From what isnow known about the capacity of living cells to pushwater back into empty vessels, the whole concept of avulnerability curve becomes suspect. The apparatusshown in Fig. 7 pushes water through a dehydrated tissue.While the xylem parenchyma is able to function as shownin Fig. 2, embolized vessels will be refilled in a few min-utes, and the conductance will rise during the act of mea-surement. What the graphs tell us is that up to a thresholdvalue of drying stress there is little or no effect on thehydraulic conductance, that is, that the compensatingpressure of the living cells is able to restore the dryingdamage and refill any cavitated vessels during the con-ductance measurement when the branch is supplied withwater. Beyond the threshold of stress the living cells havebeen irreversibly damaged, they cannot repair the cavi-tations, and the conductance stays at zero.

Note the consequences of this interpretation and thepredictions that may be made to test it. First, the maxi-

mum pressure that can be applied to refill the conduits isthe osmotic pressure of the ray cells and xylem paren-chyma, so the cavitation threshold for each speciesshould correspond approximately with the osmotic pres-sure of the ray cells. The rays of poplar, willow, andmaple with sharp thresholds should have fairly uniformosmotic pressures, while in those of the two conifers (Fig.6d) they would be expected to be high and variable. Sec-ond, the high conductance in the part of the curve up tothe threshold is maintained by refilling of conduits cav-itated at low stress levels when water is supplied to thedehydrated wood from the solution used to measure con-ductance. Third, the activity of living cells is necessary.

Experiments. Prediction 1: Check by measurements on fresh handsections of the wood. The high values of osmotic pressure deducedfor these ray cells accord with the determinations by Kny (1909)and Ursprung and Blum (1916) already noted. Note also, the cor-respondence of the cavitation threshold with the osmotic pressureof the living cells, in the data of Sperry and Saliendra (1994, theirFig. 5) showing that the turgor pressure of the leaf cells of birchfalls to zero at just that value of P where the threshold change inconductance occurs. Prediction 2: Check by varying the osmoticpressure of the conductance-measuring solution; the higher thisosmotic pressure, the lower the expected threshold of critical stress.Prediction 3: Check by adding a poison to the conductance solu-tion, which should shift the cavitation threshold to its unprotectedlevel of around 23 bar (2300 kPa) and prevent refilling. Also,follow the changes in percentage of embolized vessels during aconductance measurement by direct observation in the CSEM.

HYDRAULIC ARCHITECTURE

Just as the pressure chamber does not measure tensionin the xylem, so the traditional way of measuring hy-draulic conductance does not measure conductance be-cause the activity of the living cells alters the conduc-tance during the measurement. If all the measurementswe have of pressure gradients are wrong, and all the mea-surements of hydraulic conductance are wrong, what towe truly know about the hydraulic architecture of trees?

Measurements of C throughout the canopies of treeswith the pressure chamber have produced the broad gen-eralization that C becomes more negative along the out-ward path from the trunks through branches of smallerdiameters to twigs and leaves (e.g., Borchert, 1994). Thegradient of C is seen as a manifestation of the pressuregradient needed to drive the water flow along the outwardpath. It agrees well with Zimmermann’s demonstrationthat the leaf specific conductance (i.e., the flow througha portion of the wood pathway divided by the area of theleaves it supplies) decreases along the same path, and sodoes the diameter of the largest vessels (Zimmermann,1983). This concept of tree hydraulic architecture hasbeen elaborated to map the pressure gradients necessaryto account for the distribution of leaf specific conduc-tances in a number of different tree types (e.g., Tyree andEwers, 1991). The orthodox explanation of the gradientof C is that there are ‘‘junction constrictions’’ where eachbranch or twig joins a larger one, which would generatean increase in the pressure gradient across the junction,and negative pressure would increase outwards in thecanopy (Tyree and Ewers, 1991).

On the compensating pressure theory the gradients of

906 [Vol. 85AMERICAN JOURNAL OF BOTANY

pressure are much smaller than the gradients of C sincea major part of the measured C is the compensating pres-sure protecting the conduits. The gradient of C is rathera gradient of compensating pressure applied to protectthe conduits as they decrease in diameter along the out-ward path. The junction constriction becomes, on thisview, a nonexistent entity, a piece of plumbing postulatedto explain a gradient that has another purpose. Checks ofthe reality of junction constrictions by conductance mea-surements across the junctions seem to have been incon-clusive (Tyree and Ewers, 1991; Tyree and Alexander,1993).

There is a satisfying explanation of the need for thisgreater protection as the diameter decreases, in terms ofthe fluid mechanics of the system. The volume flow in aconduit varies with the pressure gradient and the fourthpower of the diameter. So for a given perturbation in flowrate the consequent change in the pressure gradient (andhence the compensating pressure to protect against it)will vary inversely as the fourth power of the diameter.As the conduits decrease in diameter along the outwardpath the compensating pressure necessary to protect themwill increase. But it will not increase as fast as the fourthpower of the diameter, because the number of conduitsincreases along the outward path, and the perturbation offlow is dispersed among a larger number of smaller con-duits. This dispersal can be estimated from Murray’s law,a generalization about branching pipelines known to ap-ply to such diverse systems as blood veins and capillaries,tracheae and bronchi of the lungs, and vein systems ofleaves (see Murray, 1926; La Barbera, 1990; Canny,1993). Murray’s law says that the number of pipes in-creases as the cube of the ratio of diameters (i.e., theproduct [number of pipes 3 diameter3] is a constant).Therefore, the size of the fluctuation is reduced as thecube of the decreasing diameters, and the necessary com-pensating pressure varies inversely only as the fourth mi-nus the third, equals the first power of the diameter.

An elegant confirmation of this linear dependence ofcompensating pressure on conduit diameter can be de-rived from the birch vulnerability curves of Sperry andSaliendra (1994). What they interpret as ‘‘cavitation ten-sions’’ are interpreted on the new theory as maximumcompensating pressures. Reproducing their report withthis single alteration and omitting the figures not repro-duced here, we have:

‘‘The within tree variation in vulnerability . . . was cor-related with the vessel diameters of the same axes ... .Vessels were widest in roots, narrowest in twigs, and in-termediate in trunks ... . Furthermore, the breadth of thedistributions corresponded to the shape of the vulnera-bility curves. Cavitation in roots occurred over a widerange of ‘compensating pressures,’ and the vesselsshowed a similarly wide range of diameters. Vulnerabilitycurves in trunks and twigs were steep and associated withrelatively narrow vessel diameter distributions. Finally,the correlation between mean ‘maximum compensatingpressure’ and mean hydraulic diameter was highly sig-nificant with an r2 of 0.87 (Fig. 4)’’ (Sperry and Salien-dra, 1974, p. 1237). Their Fig. 4 has been redrawn withthe relabelled y-axis as Fig. 8.

XYLEM-FEEDING INSECTS

As emphasized previously (Canny, 1995; Crews et al.,1998), one of the strongest arguments against large neg-ative xylem pressures is the extraction of xylem sap bymany species of insect. Mittler (1967) calculated the pres-sure that a leafhopper generated to suck sap through itsstylets at the rate it was excreted as 23 bar (2300 kPa),and Raven (1983) estimated from the dimensions andproperties of the muscles of the cibarial pumps, a maxi-mum suction of 3 bar (300 kPa). A detailed study of thefeeding of the leafhopper Homalodiscus on four plantspecies (Andersen, Brodbeck, and Mizell, 1992) pro-duced results that the authors have great difficulty in rec-onciling with the cohesion theory. These leafhopperssucked and exuded sap at the rate of up to 0.7 cm3/hthrough stylet canals 12 mm wide, implying a velocity of43 cm/sec and a pressure gradient along the 2 mm ofstylet of 0.48 bar (48 kPa). Feeding rates were stronglycorrelated with the organic nitrogen in the sap, whichvaried on a diurnal cycle, and was highest in the after-noon. The authors were puzzled to find that the feedingrate increased at this time, just when the pressure cham-ber required the strongest balancing pressure. Feedingrate increased as C became more negative down to218 bar (21.8 MPa). In plants stressed beyond 218 bar(21.8 MPa), when C reached values down to 232 bar(23.2 MPa), the feeding rate was reduced.

By now, the reader will easily make the translation tothe alternative interpretation, that down to C valuesequivalent to the threshold of xylem parenchyma osmoticpressure (.18 bar[1.8 MPa]) the pressure in the conduitsis kept close to zero, any embolisms are quickly refilled,and the leafhoppers are easily able to pump the sap withits enhanced organic nitrogen at maximum rates. In thestressed plants, as the compensating pressure runs out andsap pressures fall to 23 bar (2300 kPa) and beyond, therate of extraction slows, embolisms cannot be refilled,and excretion stops.

TYLOSES, TERMINATING VESSEL FUNCTION

In the frozen preparations of sunflower petioles, whichprovided the data for the embolism studies (Canny,1997a, b), tyloses were frequently observed. A full ac-count of them is given in Canny (1997c). They wereforming in, and filling, the oldest, thick-walled vessels atthe inner ends of the xylem arcs, farthest from the phlo-em. These were just those vessels that were shown to bemost vulnerable to embolism during the first water stressimposed by transpiration early in the day. In terms of thecompensating pressure theory these tyloses are readilyinterpretable as a device to preserve tissue pressure, pre-vent its dissipation in compressible gas spaces, and con-serve supplementary water by eliminating superfluoussinks for it. Those vessels farthest from the pressurizingphloem would be the most vulnerable to embolism. Thestrategy to put them out of action, replace them with in-compressible parenchyma, and form new ones near to thephloem from the cambium, is entirely consistent with therequirements of the theory and with the tactics of meetingthese requirements by pressurizing and supplying supple-mentary water with the available tissues.

July 1998] 907CANNY—APPLICATIONS OF A THEORY OF WATER TRANSPORT

THE SELF-SUSTAINING PIPELINE,ULTRASTABILITY

Looked at in these ways, the xylem is not a vulnerablepipeline on the edge of disaster exerting large forces onstrong threads of metastable water liable to breakage. Itis a self-sustaining pipeline that controls the flow of weakwater under varying evaporative demands, using at leastfive levels of homeostatic response and adjustment. Atthe first level, by applying the compensating tissue pres-sure P, and working downwards from a positive pressure,it keeps the tension in the water threads in a range wherecavitation is restricted. At the second level, it maintainsa flow of supplementary water to refill embolisms whenthey occur. At the third level, it responds to increasedevaporative demand by osmoregulating the available Pupwards, to raise the xylem pressure and to provide moresupplementary water. At the fourth level it maintains apopulation of conduits of small diameter, which will refillquickly, to ensure continuity of some water threads untila rapid flux can be restored in the larger conduits. At thefifth level, it works to eliminate gas spaces, conserve sup-plementary water, and preserve the hydrostatic pressurewithin the organ, by terminating the activity of the con-duits most vulnerable to cavitation and filling them withliving parenchyma cells. It is in fact what Ashby (1960)distinguished as an ultrastable system, a system that isnot just a homeostat, but one that responds to environ-mental changes outside its previous operating experienceby changing the parameters of its operation and regainingstability (Appendix 4). Living systems are ultrastable. Forexample, a population of bacteria responds to an antibi-otic that it has never encountered before and transformsitself into a resistant strain. Plant water transport hasjoined the living world.

LITERATURE CITED

ANDERSEN, P. C., B. V. BRODBECK, AND R. F. MIZELL III. 1992. Feedingby the leafhopper, Homalodisca coagulata, in relation to xylemfluid chemistry and tension. Journal of Insect Physiology 38: 611–622.

ASHBY, W. R. 1960. Design for a brain, 2d ed. Wiley, London.BORCHERT, R. 1994. Water status and development of tropical trees dur-

ing seasonal drought. Trees 8: 115–125.BUTTERY, R. G., AND S. G. BOATMAN. 1966. Manometric measurements

of turgor pressures in laticiferous phloem tissues. Journal of Ex-perimental Botany 17: 283–296.

CANNY, M. J. 1993. The transpiration stream in the leaf apoplast—waterand solutes. Philosophical Transactions of the Royal Society ofLondon B 341: 87–100.

. 1995. A new theory for the ascent of sap. Cohesion supportedby tissue pressure. Annals of Botany 75: 343–357.

. 1997a. Vessel contents of leaves after excision—a test of Scho-lander’s assumption. American Journal of Botany 84: 1217–1222.

. 1997b. Vessel contents during transpiration—embolisms andrefilling. American Journal of Botany 84: 1223–1230.

. 1997c. Tyloses and the maintenance of transpiration. Annals ofBotany 80: 565–570.

, AND C. X. HUANG. 1993. What is in the intercellular spaces ofroots? Evidence from the cryo-scanning electron microscope. Phy-siologia Plantarum 87: 561–568.

CREWS, L. J., M. E. MCCULLY, M. J. CANNY, C. X. HUANG, AND L. E.C. LING. 1998. Xylem feeding by spittlebug nymphs: some obser-vations by optical and cryo-scanning microscopy. American Jour-nal of Botany 85: 449–460.

DACEY, J. W. H. 1981. Pressurized ventilation in the yellow waterlily.Ecology 62: 1137–1147.

HAKE, S., AND B. R. CHAR. 1997. Cell-cell interactions during plantdevelopment. Genes and Development 11: 1087–1097.

KNY, L. 1909. Der Turgor der Markstrahlzellen. LandwirtschaftlicheJahrbucher 38: 375–394.

KRAGLER, F., W. J. LUCAS, AND J. MONZER. 1998. Plasmodesmata: dy-namics, domains and patterning. Annals of Botany 81: 1–10.

LA BARBERA, M. 1990. Principles of design of fluid transport systemsin zoology. Science 249: 992–1000.

MCCULLY, M. E. 1994. Accumulation of high levels of potassium inthe developing xylem elements in roots of soybean and some otherdicotyledons. Protoplasma 183: 116–125.

. 1995. Water efflux from the surface of field-grown grass roots.Observations by cryo-scanning electron microscopy. PhysiologiaPlantarum 95: 217–224.

, C. X, HUANG, AND L. E. C. LING. 1998. Daily embolism andrefilling of xylem vessels in the roots of field-grown maize. NewPhytologist 138: 327–342.

MILBURN, J. A. 1996. Sap ascent in vascular plants: challengers to thecohesion theory ignore the significance of immature xylem and therecycling of Munch water. Annals of Botany 78: 399–407.

MITTLER, T. E. 1967. Flow relationships for hemipterous stylets. Annalsof the Entomological Society of America 60: 1112–1114.

MUNCH, E. 1930. Die Stoffbewegungen in der Pflanze. Fischer, Jena.MURRAY, C. D. 1926. The physiological principle of minimum work. I.

The vascular system and the cost of blood volume. Proceedings ofthe National Academy of Sciences, USA 12: 207–214.

PASSIOURA, J. B. 1988. Water transport in and to roots. Annual Reviewof Plant Physiology and Plant Molecular Biology 39: 245–265.

POCKMAN, W. T., J. S. SPERRY, AND J. W. O’LEARY. 1995. Sustained andsignificant negative water pressure in xylem. Nature 378: 715–716.

RAVEN, J. A. 1983. Phytophages of xylem and phloem: a comparisonof animal and plant sap feeders. Advances in Ecological Research13: 135–234.

ROBARDS, A. W., AND W. J. LUCAS. 1990. Plasmodesmata. Annual Re-view of Plant Physiology and Plant Molecular Biology 41: 369–419.

RYGOL, J., J. PRITCHARD, J. J. ZHU, A. D. TOMOS, AND U. ZIMMERMANN.1993. Transpiration induces radial turgor pressure gradients inwheat and maize roots. Plant Physiology 103: 493–500.

SCHNEIDER, H., J. J. ZHU, AND U. ZIMMERMANN. 1997. Xylem cell turgorpressure probe measurements in intact roots of glycophytes: tran-spiration induces a change in the radial and cellular reflection co-efficients. Plant, Cell and Environment 20: 221–229.

SPERRY, J. S., AND N. Z. SALIENDRA. 1994. Intra-plant and inter-plantvariation in xylem cavitation in Betula occidentalis. Plant, Cell andEnvironment 17: 1233–1241.

TERRY, B. R., AND A. W. ROBARDS. 1987. Hydrodynamic radius alonegoverns the mobility of molecules through plasmodesmata. Planta171: 145–157.

TYREE, M. T. 1970. The symplast concept: a general theory of sym-plastic transport according to the thermodynamics of irreversibleprocesses. Journal of Theoretical Biology 26: 181–214.

, AND J. D. ALEXANDER. 1993. Hydraulic conductivity of branchjunctions in three temperate tree species. Trees 7: 156–159.

, AND F. W. EWERS. 1991. The hydraulic architecture of trees andother woody plants. New Phytologist 119: 345–360.

URSPRUNG, A., AND G. BLUM. 1916. Uber die Verteilung des osmotisch-en Wertes in der Pflanze. Berichte der deutschen botanischen Ge-sellschaft 34: 88–104.

VALBERG, P. A., AND D. F. ALBERTINI. 1985. Cytoplasmic motions, rhe-ology and structure probed by a novel magnetic pole method. Jour-nal of Cell Biology 101: 130–140.

VAN DER WEELE, C. M., M. J. CANNY, AND M. E. MCCULLY. 1996.Water in aerenchyma spaces in roots. A fast diffusion path forsolutes. Plant and Soil 182: 492–501.

VARNEY, G. T., AND M. J. CANNY. 1993. Rates of water uptake into themature root system of maize plants. New Phytologist 123: 775–786.

WANG, X.-L., M. E. MCCULLY, AND M. J. CANNY. 1995. The branchroots of Zea. V. Structural features that may influence water andnutrient transport. Botanica Acta 108: 209–219.

WARING, R. H., D. WHITEHEAD, AND P. G. JARVIS. 1979. The contribution

908 [Vol. 85AMERICAN JOURNAL OF BOTANY

of stored water to transpiration in Scots pine. Plant, Cell and En-vironment 2: 309–317.

WATT, M., C. M. VAN DER WEELE, M. E. MCCULLY, AND M. J. CANNY.1996. Effects of local variations in soil moisture on hydrophobicdeposits and dye diffusion in maize roots. Botanica Acta 109: 492–501.

WESTGATE, M. E., AND E. STEUDLE. 1985. Water transport in the midribtissue of maize leaves. Plant Physiology 78: 183–191.

WHITE, P. R. 1938. ‘‘Root pressure’’—an unappreciated force in sapmovement. American Journal of Botany 25: 223–227.

ZIMMERMANN, M. H. 1983. Xylem structure and the ascent of sap.Springer, Berlin.

APPENDIX 1

THE PETIOLE AS A SOURCE OF SUPPLEMENTARY WATER

Consider a petiole of one of the sunflower leaves used in Canny(1997a), with radius 4 mm and ;150 vessels whose median diameteris 40 mm. The question is: what volume of water must be provided tomaintain a supplementary water supply for the day, and is it reasonableto suppose that the petiole parenchyma can supply it by a modest vol-ume shrinkage? If DP is the pressure difference between the parenchy-ma and the vessel lumen, and Lp is the hydraulic conductivity of theplasma membranes of the cells surrounding a vessel, the volume neededfor unit length is

Lp 3 total vessel surface 3 DP 3 time.

We must select likely values for Lp and DP. In Canny (1997a) the valuechosen for the former was from the midrange of those measured formidrib tissue of corn leaves by Westgate and Steudle (1985), Lp 5 1027

m3·m22·s21·bar21 [1026 m3·m22·s21·MPa21]. The value of DP must begreater than the vapor pressure of water but need not be very large. Inthe middle of the day the difference is reversed, because water flowedout of the vessels. Suppose an average of 1/10 bar (10 kPa). Then for1 m of petiole with 150 vessels of diameter of 40 mm and an 8-h daythe volume becomes,

1027 3 150p 3 40 3 1026 3 28 800 3 0.1 5 5.4 3 1026 m3.

This would require a 5% shrinkage in the diameter of the petiole.Assuming a transpiration of 100 g/d from a leaf with 1 dm2 of lamina

and 20 cm of petiole, the supplementary water would be ;1% of thetranspiration flow.

APPENDIX 2

THE POROUS SEPTUM AS A ONE-WAY VALVE

A classic analysis by Tyree (1970) of transport in the symplastthrough plasmodesmata, comparing diffusion and pressure flow, pro-vides the notation (differing from that in the rest of this paper), basicequations, and values for many of the variables used here.

For N pores of radius r and length l, pressure flux (JvP) of a liquid of

viscosity h with a pressure difference DP is

JvP 5 Np r4 DP/8h. (1)

For the same pores, and concentration (strictly activity) difference DCof substance whose diffusivity is D, diffusive flux (Jv

D) is

JvD 5 Npr2 D DC/l. (2)

It is likely that Eqs. 1 and 2 are not applicable in very small spaces.(1) must overestimate the flow in spaces so narrow that some of thevolume is occupied with vicinal water. Poiseuille flow develops in pipes100 times longer than their diameter, which is roughly the ratio in thedesmotubule channels (below).

We are seeking the pore size that will effectively restrict JvP relative

to JvD. Suppose we choose to set Jv

D 5 100 JvP. Most of the variables

on the two sides cancel, and we are left with

r2 5 8hD DC/100 DP. (3)

Before proceeding we must get the units right. The units of JvP are

volume flow units, m3/sec, while those of JvD are mass transfer units,

e.g., moles/sec. To equate the two fluxes they must be measured in thesame units, which can be achieved by multiplying Jv

P by the number ofmoles of water in a cubic metre, 5.5 3 104. With this change, Eq. 3becomes

r2 5 8hD DC/5.5 3 106 DP. (4)

Values of the variables—Self diffusion coefficient of water (D)—Eisenberg and Kauzmann (1969) give values over a range of tempera-tures. At 258C, D 5 2.5 3 1029 m2/s. D is somewhat influenced byviscosity, as considered by Tyree (1970). For small uncharged solutesthe effect is small, and their diffusivities in agar gel are little less thanin water. For water molecules the effect will be even less.

Difference of pressure (DP)—As mentioned in the text, small over-pressures of the order of 1 bar (100 kPa) would be sufficient to expresswater into the xylem, and would suffice for most plants most of thetime. A moderate maximum value for the pressure which might be builtup within the endodermis by the osmotic energy of the living cells ofthe stele relative to those in the cortex would be 10 bar (1 MPa). Thiswas the minimum pressure estimated by White (1938) to be generatedby his cultured tomato roots. This overpressure would push the fluxthrough into the xylem conduits in plants working under considerablestress and probably satisfy most of the requirements of the pump. Inthe SI units used for this calculation this is 106 Pa.

Difference of water concentration (DC)—This is the reduction in wa-ter concentration (mole fraction) in the pericycle vacuoles comparedwith that in the inner cortical vacuoles due to the difference in soluteconcentration. The difference of 10 bar (1 MPa) in DP generated os-motically would require a difference in the mole fraction of water of0.007, which is equivalent to a difference of water concentration, of400 moles/m3.

Viscosity (h)—This is the most uncertain of the variables, but maynot be relevant. The viscosity of water at 208C is 0.001 Pa·s. Cytoplasmcan vary from being very fluid to being a strong gel. Valberg and Al-bertini (1985) list a dozen published values that range from 0.001 to105 Pa·s. Tyree (1970) mentions the range 5 3 1022 to 2 Pa·s, and alsorecognizes that ‘‘it is quite possible that the cytoplasm in the pores ofthe plasmodesmata is completely gelled; in this case h would be infi-nite.’’ If this were so pressure flow is zero and h is irrelevant. Thesensible choice is a value of h that gives a value of r comfortably largerthan the plasmodesmatal pores, so that the choice is not critical. Sucha value is h 5 20 Pa·s.

Calculation—Entering these values in Eq. 4, we have2 29 6 6r 5 8 3 20(2.5 3 10 ) 3 400/(5.5 3 10 3 10 )

r ø 5 nm,

while for water,

r ø 0.04 nm.

Comparison with experimentally determined pore sizes—The detailedstructure of plasmodesmata and the sizes of the pores in them havebeen the subject of much experiment and debate (Robards and Lucas,1990). An extensive study by Terry and Robards (1987) measured therates of diffusion of fluorescent probes of various molecular sizesthrough plasmodesmata of Abutilon nectary trichomes. They concludedthat the annulus around the desmotubule is probably divided into 10–20 cylindrical channels, each of radius ;1.5 nm. It is also clear (Hakeand Char, 1997; Kragler, Lucas, and Monzer, 1998) that the size of poresin plasmodesmata is under cellular control, and the exclusion limit formolecules can vary from ,1000 Da to at least 40 000 Da.

APPENDIX 3

WATER FLUX THROUGH THE ENDODERMAL VALVE

Measured water flux through plasmodesmata—A fairly complete setof data exists on water flux through the endodermis of the branch rootsof corn. Wang, McCully, and Canny (1995) combined their measure-ments of the number of plasmodesmata through the endodermis, withthe rates of water uptake by the branch roots measured by Varney andCanny (1993), to express the flux through the endodermis per plasmo-desma (plasmo). From Table 3 of Wang, McCully, and Canny (1995),the water flux was 0.1 to 0.4 pL·h21·plasmo21. Converting this to molesof water we have

July 1998] 909CANNY—APPLICATIONS OF A THEORY OF WATER TRANSPORT

5–22 pmol·h21·plasmo21.

This may be compared with a calculated possible diffusive flux.

Calculated water flux through the endodermal valve—From Eq. 2 inAppendix 2 and continuing with the notation used there

JvD 5 Npr2 D DC/l.

Values of the variables—We have already (Appendix 2) settled onvalues for D 5 2.5 3 1029 m2/s, and DC 5 400 mol /m3. The value forl was not needed in Appendix 2, but can be taken from Tyree (1970)as 5 3 1027 m. For the pore radius r, the argument of Appendix 2 wasthat values of r less than 5 nm would turn the endodermal plasmodes-mata into the one-way valve for water movement. The value of Jv

D

depends very critically on the value of r. The estimate of Terry andRobards (1987) for the Abutilon nectary trichomes was that in eachplasmodesma there was an annulus of 10–20 cylindrical pores each withr 5 1.5 nm.

Calculation—Inserting these values in Eq. 2 gives a flux of

JvD 5 1 pmol·h21·plasmo21

while the generous maximum value of r 5 5 nm gives

J 5 10 pmol·h21·plasmo21.

Conclusion—The proposed mechanism is at the threshold of possi-bility and deserves more detailed consideration. If the endodermal plas-modesmata have channels somewhat larger than 1.5 nm, the diffusiveflux with the assumed values for the other variables would comfortablysupply water at the middle range of measured rates. To achieve fluxes

at the higher end of the range wider channels, a steeper gradient ofwater concentration or some other modification of the conditions wouldbe needed.

APPENDIX 4

ULTRASTABLE SYSTEMS

A complex example of an ultrastable system is your blood tempera-ture. The internal homeostats that regulate blood flow through capillar-ies, sweating, rates of heat production by respiration, etc., have evolvedto accommodate a large range of temperature conditions. You havelearned to extend these conditions almost indefinitely by (for exampleon the cold side) putting on more clothes, seeking or constructing shel-ters and insulation, lighting fires, constructing elaborate heating sys-tems, migrating to warmer climes. Each of these steps provides a changeof the parameters within which the basic bodily thermostats work.

Ashby (1960) defines an ultrastable system as follows: ‘‘Two systemsof continuous variables (that we called ‘environment’ and ‘reactingpart’) interact, so that a primary feedback (through complex sensoryand motor channels) exists between them. Another feedback, workingintermittently and at a much slower order of speed, goes from the en-vironment to certain continuous variables which in their turn affectsome step-mechanisms, the effect being that the step-mechanismschange value when and only when these variables pass outside givenlimits. The step-mechanisms affect the reacting part; by acting as pa-rameters to it they determine how it shall react to the environment’’ (p.136).

In the xylem system the four levels of regulation above the basiccompensating pressure homeostat correspond with four sets of Ashby’sstep mechanisms, whose parameters may be changed over longer timescales to sustain the flow of water.