Journal of Experimental Botany, Vol. 48, No. 315, pp. 1753-1765, October 1997Journal ofExperimentalBotany

REVIEW ARTICLE

The Cohesion-Tension theory of sap ascent: currentcontroversies

Melvin T. Tyree1

USDA Forest Service, Aiken Forestry Sciences Laboratory, PO Box 968, S. Burlington, VT 05402, USA

Received 12 February 1997; Accepted 21 May 1997

AbstractIn recent years, the Cohesion-Tension (C-T) theory ofsap ascent in plants has come under question becauseof work published by Professor Ulrich Zimmermannand colleagues at the University of Wurzburg,Germany. The purpose of this review is to (1) state theessential and testable elements of the C-T theory, (2)summarize the negative evidence for the C-T theory,and (3) review critically the positive evidence for theC-T theory and the evidence that the Scholander-Hammel pressure bomb measures xylem pressurepotential (Px) correctly, because much of the evidencefor the C-T theory depends on pressure bomb data.

Much of the current evidence negates the conclu-sions drawn by Zimmermann from studies using thexylem pressure probe (XPP), but it is not yet clear inevery instance why the XPP results disagree withthose of other methods for estimating xylem pressure.There is no reason to reject the XPP as a useful newtool for studying xylem tensions in the range of 0 to-0 .6 MPa. Additional research is needed to test theC-T theory with both the XPP and traditional methods.

Key words: Cohesion-Tension theory, cavitation, embol-ism, xylem pressure probe, pressure bomb.

IntroductionTwo other reviews of the current controversy over theCohesion-Tension (C-T) theory have been written(Canny, 1995; Milburn, 1996). The first concentrates ona number of strange and unproven ideas. The secondprovides an interesting, although limited, historical over-view of some of the current questions. The present reviewis intended to put the Cohesion-Tension theory in aquantitative and biophysical context and reviews what I

believe to be the strongest, quantitative evidence availablefor the C-T theory.

Essential elements of the C-T theoryThe C-T theory was proposed 103 years ago by Dixonand Joly (1894), and some aspects of the C-T theorywere put on a quantitative basis by van den Honert(1948) with the introduction of the Ohm's law analogueof sap flow in the soil-plant-atmosphere continuum.

According to the C-T theory, water ascends plants ina metastable state under tension, i.e. with xylem pressure(Px) more negative than that of the vapour pressure ofwater. The driving force is generated by surface tensionat the evaporating surfaces of the leaf. The tension istransmitted through a continuous water column from theleaves to the root apices and throughout all parts of theapoplast in every organ of the plant. Evaporation occurspredominantly from the cell walls of the substomatalchambers due to the much lower water potential of thewater vapour in air. The evaporation creates a curvaturein the water menisci of apoplastic water within thecellulosic microfibril pores of cell walls. Surface tensionforces lower Px in the liquid directly behind the menisci(the air-water interfaces). This creates a lower waterpotential, tp, in adjacent regions, including adjoining cellwalls and cell protoplasts. The lowering of tf> is a directconsequence of Px being one of the two major componentsof water potential in plants, the other component beingosmotic pressure, -n\

<l> = P*-ir (1)

The energy for the evaporation process ultimately comesfrom the sun, which provides the energy to overcome thelatent heat of evaporation of the water molecules; i.e. theenergy to break hydrogen bonds at the menisci.

1 To whom correspondence should be addressed. Fax: + 1 802 9516368. E-mail: MelTyree@ AOL.COM

1754 Tyree

Water in xylem conduits is said to be in a metastablecondition when Px is below the vapour pressure of water(/*'), because the continuity of the water column, oncebroken, will not rejoin until Px rises to values above thatof P'. Metastable conditions are maintained by the cohe-sion of water to water and by adhesion of water to wallsof xylem conduits. Both cohesion and adhesion of waterare manifestations of hydrogen bonding. Althoughair/water interfaces can exist anywhere along the path ofwater movement, the small diameter of pores in cell wallsand the capillary forces produced by surface tensionwithin such pores prevent the passage of air into conduitsunder normal circumstances. However, when Px becomessufficiently negative, air bubbles can be sucked into xylemconduits through porous walls.

The tension (negative Px) at the evaporating surface ofleaves is ultimately transferred to the roots where it lowers>fi of the roots below the </< of the soil water. This causeswater uptake from the soil to the roots and from theroots to the leaves to replace water evaporated at thesurface of the leaves.

Van den Honert (1948) quantified the C-T theory in aclassic paper in which he viewed the flow of water in theplant as a catenary process, where each catena element isviewed as a hydraulic conductance (analogous to anelectrical conductance) across which water (analogous toelectric current) flows. Thus, van den Honert proposedan Ohm's law analogue for water flow in plants. TheOhm's analogue leads to the following predictions: (1)the driving force of sap ascent is a continuous decreasein Px in the direction of sap flow, (2) evaporative fluxdensity from leaves (E) is proportional to negative of thepressure gradient (—dPJdx) at any point (cross-section)along the transpiration stream. Thus at any given pointof a root, stem, or leaf vein,

branched model

- dPJdx = AE/Kh + (fg dh/dx) (2a)where A = leaf area supplied water by a stem segmentwith hydraulic conductivity A h and pg dh/dx is the gravita-tional potential gradient where p = density of water, g =acceleration due to gravity and dh/dx = height gained, dh,per unit distance, dx, travelled by water in the stemsegment.

In the context of stem segments of length (L) with finitepressure drops across ends of the segment,

APx = LAE/Kh + pgAh (2b)Figure 1 illustrates water flow through a plant representedby a linear catena of conductance elements near the centreand a branched catena of conductance elements on theleft. The number and arrangement of catena elements isdictated primarily by the spatial precision desired in therepresentation of water flow through a plant; a plant canbe represented by anywhere from one to thousands ofconductance elements.

Vsoil =- 0 0 5 MPa

Absorption

Fig. 1. The Ohm's law analogy The total conductance is seen asresultant conductance (K) of the root, stem, and leaf in series andparallel. Water flow is driven by the differences in water potentialbetween the soil </isoll and the water potential at the evaporating surface,i/>evap. On the right is the simplest Ohm's law analogy with conductancesin series. On the left is a more complex conductance catena where someconductance elements are in series and some in parallel.

The Scholander-Hammel pressure bomb (Scholanderet al., 1965) is one of the most frequently used tools forestimating Px. The C-T theory does not depend on theaccuracy of the pressure bomb, but much of what isknown about the range of Px tolerated by different speciesof plants depends on the pressure bomb. Typically, Pxcan be as low as —2 MPa (in crop plants) or to —4 MPa(species in arid zones) or even —10 MPa (Californiachaparral species). How the pressure bomb functions isdiscussed later.

Negative evidence for C-T theory summarizedUsing a xylem pressure probe (XPP), Balling andZimmermann (1990) demonstrated that the Scholander-Hammel pressure bomb (Scholander el al., 1965) doesnot measure xylem water tension correctly under manycircumstances. The pressure bomb functions properlyonly if there is direct pressure transmission from the airin the bomb to the xylem fluid. For example, when sapefflux from the cut end of a leaf is blocked by a fluid-filled pressure transducer on a leaf at i/> = 0, there shouldbe a 1:1 relationship between gas pressure in the bomband PK measured by the transducer. But a 1:1 relationshipwas not found (Balling and Zimmermann, 1990) intobacco leaves, and this finding has been confirmedindependently in Tsuga canadensis by C Wei and MTTyree (unpublished results). The failure of pressure trans-

mission in the positive pressure range in T. canadensis isrelated to the elasticity of woody stems and the compres-sion of air bubbles in embolized tracheids and does notinvalidate the theoretical functioning of the pressurebomb in the normal mode of operation when Px<0.

More worrisome is an apparent failure of pressuretransmission in the negative pressure range, i.e. Px meas-ured with the XPP in individual vessels did not increaseas expected with an increase of air pressure in the pressurebomb. Professor Zimmermann concluded that the pres-sure bomb overestimates tension (gives a Px that is toonegative).

He has also shown that xylem tension exceeding0.6 MPa is rarely observed with the XPP (Zimmermannet al., 19936). For example, the XPP has been insertedinto vessels of many species in the morning and Px valuesusually are positive (on an absolute pressure scale wherea vacuum is 0 MPa). As the day progresses and transpir-ation increases, Px falls to —0.2 to —0.6 MPa. Then thevessel punctured by the XPP cavitates and Px returns topositive values consistent with embolized lumens filledwith water vapour and air. When many plants are probedat midday, most vessels are found to be embolized,i.e. the XPP records absolute pressures >0MPa .Zimmermann and colleagues have proposed a number ofmechanisms of sap transport in plants that are consistentwith sap flow around embolized vessels, which they believeis the normal state in plants (Zimmermann et al., 1993a,b). Zimmermann does not reject the C-T theory outright;he acknowledges that tension-driven water movement isoccurring when he measures Px values in the range of 0to - 0 . 6 MPa with the XPP, but he also postulates thatother mechanisms must be at work when tp values dropmuch below —0.6 MPa.

Important questions can be raised and answered byexamining the current literature in the next section dealingwith positive evidence for the C-T theory.

(1) Does normal water transport occur while vessels areembolized? If plants normally transpire with mostvessels embolized then this condition ought to beidentifiable by measuring the hydraulic conductanceof stems in their native state and by quantitative testsof the Ohm's law analogue (Equations 2a, b).

(2) Do most intact xylem conduits embolize at Px

> —0.6 MPa or do they embolize only because thexylem wall has been damaged by insertion of theXPP? This question can be answered by looking atthe mechanism of cavitation events and by usingclever ways of inducing xylem tension.

(3) Is there independent evidence of the expected pressuretransmission in a pressure bomb when Px<0 MPa?One way to answer this question is to use a temper-ature corrected stem hygrometer on woody plants.

Cohesion-Tension theory 1755

Evidence in support of the pressure bomb and theC-T theory

The Scholander-Hammel pressure bomb

The Scholander-Hammel pressure bomb is a device usedto measure the equilibrium xylem pressure, Px. Forexample, a cut leaf is placed inside a pressure vessel withthe petiole protruding through a rubble seal to the outsideair. When compressed gas is admitted into the pressurechamber, the gas pressure is presumed to be transmitteddirectly to the xylem fluid raising Px. When Px reaches avalue slightly above zero (= atmospheric pressure) thenwater begins to flow out of the vessels at the cut end ofthe petiole. The gas pressure when water first emerges iscalled the balance pressure, PB. The negative of PB isequated to Px prior to admitting compressed gas to thechamber.

The basic hypothesis of the pressure bomb can bestated as follows: When a transpiring shoot is excisedfrom a plant, the negative Px prior to excision is main-tained after excision in the xylem by surface tension atpit membranes in vessel walls. The actual situation isslightly more complicated because a transpiring shootwill have gradients of Px whereas the pressure bombmeasures an equilibrium Px after the gradients of P% havedisappeared. Let us focus on how Px changes near thepoint of excision, i.e. within one vessel length of the cutsurface. Immediately after cutting, Px temporarilybecomes zero in all severed vessels. Then Px becomesnegative again as water is sucked into dehydrated cells inleaves by osmosis draining the vessels until a meniscus isre-established on pit membranes at the ends of remainingintact vessels. As water flows into the living cells their >pbecomes slightly more positive. At equilibrium two thingshappen: (1) Any gradients in Px originally between thecut surface of the stem or petiole and the evaporatingsurface of the leaves disappears. (2) An equilibrium isestablished between the <p of all living cells and the </> ofxylem fluid (=Px—rrx). So the equilibrium Px could bemore negative than originally present at the point ofcutting if there was a large pressure gradient from the cutpoint of the stem to the leaves, because the more dehyd-rated leaf cells will tend to draw water from the lessdehydrated petiole or stem cells until the gradient disap-pears. Or the equilibrium Px could be less negative, ifthere was substantial rehydration of living cells when thecut vessels were drained of water and only some of thevessels refill when the balance pressure, PB, is established.Thus, equilibrium Px in the xylem does not return to thePx in the xylem at the time of cutting.

Regardless of how much the equilibrium Px differsfrom the steady-state Px in the transpiring shoot, thepressure-bomb hypothesis can be stated as follows:

When the shoot is placed in a pressure bomb with thecut end protruding though a pressure seal to the outside

1756 Tyreeair, the value of Px can be changed by applying airpressure Pa to the entire shoot surfaces within the bomb.For every unit increase in Pa, Px will become less negativeby one unit until the balance pressure (PB) is reachedwhen P* = 0 and water is 'balanced' on the cut end. Thiscan be expressed as:

P, = Pa-PB (3a)/>x = i/,x + 77x (3b)

The second equality states that Px can be expressed interms of tfiK (=the xylem water potential) minus TTX ( =the xylem osmotic pressure). Equating Equation 3a to 3byields:

li =P —77 — P (3c)

In an enclosed air space adjacent to xylem water, thewater potential of the vapour phase (tpv) should equal t/ixprovided equilibrium of temperature and water-vapourpressure is obtained. Thus we have:

ill =P —TT —PB (4)

Equation 4 and thus the validity of the pressure bombhave been confirmed on Thuja occidentalis shoots overthe range of 0 to —2.1 MPa using temperature-correctedstem psychrometers to measure I/IV under rigorously docu-mented conditions of vapour equilibrium (Dixon andTyree, 1984). In these experiments, a large T. occidentalisshoot was enclosed in a pressure bomb and dehydratedto a Pg = 2.1 MPa. A temperature-corrected stem hygro-meter was attached to the cut basal surface of the shootoutside the pressure bomb. Dixon and Tyree demon-strated that vapour equilibrium occurred with a half-timeof 19 s. Thermal equilibrium never was obtained sincethe wood surface always was cooler than the thermo-couple in the hygrometer used to sense i/>v, but temperaturestability was reached with a half-time of 27 s. A thermo-couple touching the surface of the wood was used tomeasure the stable temperature difference between thewood surface and the sensing thermocouple. This differ-ence could be used to make thermodynamic correctionsto i/iv. Without thermal corrections, the data resembledFig. 2a, and Fig. 2b after correction.

These data provide strong evidence for the validity ofthe pressure bomb hypothesis. More recently, Holbrooket al. (1995) have used an elegant method to create xylemtension mechanically and further test the pressure-bombhypothesis. Unfortunately, the experiment has causedconfusion because Holbrook et al. (1995) did not discussthe underlying physics in sufficient detail due to spacelimitations in the original publication. They excised stemsegments with a single leaf at the midpoint of the segment,and mounted the midpoint of the stem on the rotatingaxis of a motor-driven shaft (Fig. 3). The rotation of thestem segment will produce a centrifugal tension at the

a ' B. MPa

Fig. 2. Experimental demonstration of how air pressure in a pressurebomb controls the />„ in the xylem of an excised shoot of Thujaoccidentalis. The _v-axis is the predicted Px based on the current airpressure (/>a = the variable) and the balance pressure (PB = a constant inthis experiment). The j'-axis is the water potential of the vapour phaseabove the cut end of the shoot. A temperature-corrected stemhygrometer was attached to the cut end and the hygrometer chamberapproached vapour equilibrium with a half-time of 27 s and temperaturestability was reached with a half-time of 19 s. (A) The relationshipbefore correction for the steady-state temperature difference betweenthe cut surface of the stem and the measuring thermocouple of thehygrometer. (B) the relationship after correction for the influence ofthe measured temperature differences on i/rv. The dashed line shows the1: 1 relation.

H ydrophilic V inylPolysiloxane ImpressionM aterial(D ental ImpresssionP olymer)

Attached Leaf

C ontrol Leaf

Q .

s§(A

Q .

8c

JSrom

0.5 10 1.5

Rotational Tension, MPa2.0

Fig. 3. The Holbrook experiment. (A) The experimental method. Astem segment was mounted on a centrifuge motor. Centrifugation ofthe segment induced a Px as given in Equation 5. The strobe light wasused to measure angular velocity. (B) Results show that the rotationaltension was transmitted to the attached leaf; the *-axis is the calculatedrotation tension = PX in Equation 5 and the y-axis is the balancepressure of the attached leaf at the end of the experiment.

midpoint of the segment which in pressure units will beequal to:

Px = -0.5oa>2r2 (5)

where a = the fluid density, w = the angular velocity ofrotation, and r = distance between the axis of rotationand the end of the stem segment. The negative Px at themidpoint of the segment will cause a dehydration of theliving cells in the attached leaf, and the water drawn outof the leaf will travel to the ends of the rotating segmentwhere the centrifugal forces on the water will cause it to

Cohesion-Tension theory 1757

fly off ends in a fine spray. When the motor is turned offthe Px in the midpoint will be preserved by the </. of thedehydrated leaf cells. After centrifugation, the balancepressure of the excised leaves correlated well with theexpected Px (Fig. 3). This experiment demonstrated thatxylem tensions created by centrifugation of shoots aretransmitted to leaves and measured correctly with thepressure bomb. This experiment also proved that Pxvalues down to —1.8 MPa could be sustained withoutcavitation because Equation 5 correctly predicts Px onlyif the water columns are continuous in the centrifugedstem. The centripetal force of the rotating mass of watermolecules near the ends of the column are transmittedtoward the axis of rotation by the cohesion of water. Thevalue of Px is most negative at the axis of rotation andrises continuously to atmospheric pressure at the ends ofthe stem segment. If the water columns had broken, someof the mass toward the ends would have been lost fromthe rotating system and Px would have been less negativethan predicted by Equation 5.

Hydraulic architecture and the Ohm's lawanalogueRecent studies of the hydraulic architecture of woodyplants have provided strong support for the C-T theory.The basic approach has been to obtain independentmeasurements of Px (usually with a pressure bomb), E(via weight loss or gas exchange method), and Kh (witha conductivity apparatus) and then test the validity of theOhm's law analogue, Equation 2a, b. Testing the Ohm'slaw analogue on a large plant (tree or liana) requires thefollowing steps:

(1) Estimate the regression of Kh versus stem diameterover the range of diameters on the tree.

(2) Make a hydraulic map of the tree in which eachbranch is made up of discrete segments, the segmentsbeing delineated by nodes (branch insertion points)so that Equation 2b can be applied to each segment.Keep a record of segment length (L) and diameter sothat Kh can be estimated from the regression in (1),and keep a record of leaf area attached to eachsegment.

(3) Measure E for representative leaves.(4) Compute APX for each segment using Equation 2b.

Then, using the map, add the APX values from thebase of the tree to any shoot apex.

Benkert et al. (1995) measured Px at the apex of severalbranches at different heights, h, in a large liana duringthe day when £ > 0 . They argued that the pressure gradi-ent, dP/dh, should be <—pgdh/dx (Equation 2a), i.e. Pxshould decline more than —0.01 MPa m - 1 gain in heightin vertical stems where dh/dx=\. Benkert et al. (1995)also argued that the Ohm's law analogue was incorrect

1758 Tyree

Q_

CO

10

LO G S tem D iam., mm

100

Fig. 4. Hydraulic conductivity of stems per unit pressure gradient, Kh, plotted versus diameter of the stem (excluding bark, x-axis). Speciesrepresented are Thuja occidentalis, Acer saccarum, and Schefflera morototoni. Both axes are logarithmic Adapted from Tyree el al. (1991).

because the pressure gradient was > -pg dh/dx. Theypointed to similar examples of Px (measured with apressure bomb) versus height in tall trees failing to satisfyEquation 2a. The implication of this argument wouldappear to be that water transport must be driven by aforce in addition to dP/dx. It will be seen later that suchreasoning is invalid because Equation 2a correctly predictsdP/dx along the pathway of water transport, i.e. alongthe axis of stems. The error made by Benkert et al. (1995)is in using Equation 2a to predict the pressure gradientbetween apices at different heights with no knowledge ofKh along the pathway of water flow. It is erroneous toassume dP/dh at shoot apices can be predicted by dP/dxwithout knowing the functional dependence of Khversus x.

Zimmermann would predict that the left side ofEquation 2a should be larger than first term of the rightside (AE/Kh). He suggested that xylem conduits usuallyare embolized when Px is more negative than -0.6 MPa.So Kh should be lower at times of maximum E. Valuesof Kh are measured in a conductivity apparatus underpositive Px, so few conduits will be embolized and henceKh should be maximal (reducing the estimated AE/Kh).

Zimmermann also stated that the pressure bomb under-estimates Px, i.e. gives values that are too negative (inflat-ing — dP/dx). But studies have confirmed equality inEquation 2a, suggesting that both measures of Kh and ofPx (measured with the pressure bomb) are correct (Tyree,1988; Ewers et al, 1989).

An examination of case studies will prove the pointsjust raised. Figure 4 shows Kh versus stem diameter for agymnosperm, a temperate angiosperm, and a tropicalangiosperm. Kh varies over several orders of magnitudefor a given species because large-diameter stems cantransport more water and hence are more conductivethan small-diameter stems. The species variation is evenmore remarkable; e.g. a Schefflera stem can be as muchas 100 times more conductive than a Thuja stem of thesame diameter.

A parameter of more interest is leaf specific conduct-ance, KL = KJA. This parameter is useful because dPJdxin a stem segment is inversely proportional to KL at agiven E if gravity is ignored in Equation 2a:

-dPJdx = E/Kh (6)Ranges of values of KL versus stem diameter are shown

in Fig. 5. Again, KL can differ by up to two orders ofmagnitude between species for stems at a given diameter.Also, KL increases as a function of diameter, so —dPJd.xis steepest in the smallest diameter branches. In somecases — dPJdx can be as much as 1 MPa m ~' as in Thujawhere KL= 10~5 kg s"1 m"1 M P a 1 for stem segments2-4 mm in diameter and £ '=10~ 5 kgs~ 1 m"2 at noon.The consequence of this pattern of KL versus diametercan be seen in Px profiles predicted by the Ohm's lawanalogue and the hydraulic map of representative trees.Figure 6 shows plots of Px versus path length, x, fromthe base of the tree to representative branch apices. The

Cohesion-Tension theory 1759

Px profiles were calculated using values of E at midday,KL, and the hydraulic maps.

Looking at the pattern of PK at branch apices in theThuja profile, it can be seen that there is no consistentpattern in declining Px with height up the tree. The apicesmark with '*' are at heights 4.1 and 7.5 m in the hydraulicmap, but have Px values of —1.0 and -0 .9 MPa, respect-ively, giving a dPJdh= +0.071 MPa m" 1 rather than therequired value of -0.01 MPam~' needed to lift wateragainst the force of gravity. Tyree (1988) computed themean Px of all small-diameter branches versus h in Thujaand concluded that there is no consistent decline of P.

10"1

COQ .

CDO

-10-4

10-5

10"6

S che ffle ra ->

Acer— >

. , . , i

0.1 1 10 100

Log S tem D iam , mm

Fig. S. Leaf specific hydraulic conductance KL = KJA, where A = leaf area apical of the stem segment on which Kb was measured plotted versusdiameter of the stem (excluding bark). Species are as in Fig. 5; both axes are logarithmic. Adapted from Tyree et al. (1991).

1760 Tyree

-1.6

-1.8

-2.0 -

i 1 1 1 i 1

Acer E = 6X 10 5

Thuja E = 2X 10 s

0 2 4 6 8 10 12 14 16 18 20 22

P ath le ngth, m

Fig. 6. Profiles of xylem pressure potential, P*, versus distance watermust travel from the base of the tree to a stem apex. All values includethe gravitational potential gradient required to lift water up the tree.The curves were calculated from the hydraulic maps and the representat-ive midday evaporative flux densities (E) indicated for each species inthe graph. Adapted from Tyree et al. (1991).

versus h (Tyree, 1988; Fig. 3). Nevertheless, Px declinedwith increasing distance along every pathway such thatdPJdx always was <-0 .01 MPam"1 in all stem seg-ments. Tyree (1988; Fig. 5) also found that the Ohm'slaw analogue combined with diurnal measurements of Eprovided good predictors of actual diurnal changes in Pxmeasured with a pressure bomb. The agreement betweenmeasurement and theory suggests that three conditionswere met simultaneously: (1) the pressure bomb providesa correct estimate of Px; (2) the method of measuring Khyields valid results; and (3) the Ohm's law analogueis correct.

Other studies have confirmed the correctness of theOhm's law analogue. Ewers et al. (1989) studied thehydraulic architecture of a large woody vine (>20mlong) growing along the ground to avoid the effects ofgravity on Px. They measured KL, E, and constructedhydraulic maps. They used the Ohm's law analogue tocompare predicted values of — dPJdx with values meas-ured on bagged leaves using a pressure bomb. Thepredicted gradients (0.083±0.033 MPam"1) agreed withthe gradients measured during midday with a pressurechamber (0.076 + 0.016 MPa m"1). Measured and pre-dicted gradients also agreed when E=0. Tsuda and Tyree(unpublished results) compared the predicted drop in Pxfrom soil to leaf (based on gravimetric measures of Eand whole shoot and root hydraulic conductances) tovalues of Px measured with a pressure bomb. They found

good agreement in young Acer saccharinum plants(Fig. 7).

The stark contrast between these examples andZimmermann's predictions should be noted. In every casecited, KL, was measured with positive pressures, so accord-ing to Zimmermann, all KL values would be overestimatesof the values that apply during midday when he believesvessels are embolized. Zimmermann also suggested thatthe pressure bomb underestimates Px. Hence, the Ohm'slaw analogue (Equation 2b) should be violated if he iscorrect. Since Equation 2b is quantitatively correct,Zimmerman's observations must not represent the normalstatus of plants, and the pressure bomb must be presumedmore reliable than suggested by his studies.

The mechanism of cavitation and the tensions thatseed cavitationsFinally, recent studies on the mechanism of cavitation inxylem conduits have confirmed that cavitations are air-seeded. The air-seeding hypothesis provides strong evid-ence for the existence of large negative Px values prior tocavitation events.

A cavitation event in xylem conduits ultimately resultsin dysfunction. A cavitation occurs when a void ofsufficient radius forms in water under tension. The voidis gas filled (water vapour and some air) and is inherently

-0 .3 -

-0 .6 -

-0.9 -

-1.2-1 .2 -0 .9 -0.6

P redicted (P L

-0.3 0.0

, ) , M Pa

Fig. 7. Computed versus measured APx = P1.-P,ol] for Acer saccarmumplants growing in pots. Each point represents a different plant.Evaporative flux density (£) was estimated from weight of water lostfrom the potted plants and leaf area measured at the end of theexperiment. E was varied by controlling light intensity. Once a steady-state E was reached, the balance pressure of a transpiring leaf wasestimated (PL). Soil-water potential (/>so,i) was estimated by the balancepressure of nontranspiring plants. So the >>-axis is the measured pressuredrop from soil to leaf. At the end of the experiment, the entire plantwas harvested and the hydraulic conductance of the root (KR), thestems (Ks) and the leaves (KL) was estimated with a high pressureflowmeter. The predicted J/>, on the .r-axis was computed by applyingEquation 2b to each conductance element (root, stem, and leaf).Unpublished data of Makoto Tsuda and Melvin T Tyree.

unstable, i.e. surface-tension forces will make it collapsespontaneously unless the water is under sufficient tension(negative pressure) to make it expand. A digressionfollows to explain why this is true.

The chemical force driving the collapse is the energystored in hydrogen bonds, the intermolecular forcebetween adjacent water molecules. In ice, water is boundto adjacent water molecules by 4 hydrogen bonds. In theliquid state, each water molecule is bound by an averageof 3.8 hydrogen bonds at room temperature. In the liquidstate, hydrogen bonds are forming and breaking all thetime permitting more motion of molecules than in ice(Slatyer, 1968). However, when an interface betweenwater and air is formed, some of those hydrogen bondsare broken and the water molecules at the surface are ata higher energy state because of the broken bonds. Theforce (N = Newtons) exerted at the interface as hydrogenbonds break and reform can be expressed in pressureunits (Pa), because pressure is dimensionally equal toenergy (J = Joules) per unit volume of molecules, i.e.J m~3 = Nm m~3 = N m ~ 2 = Pa. Stable voids in watertend to form spheres because spheres have the leastsurface area per unit volume; and thus, a spherical voidhas the minimum number of broken hydrogen bonds perunit volume of void. The pressure tending to make a voidcollapse is given by 2r/r, where r is the radius of thespherical void and T is the surface tension of water (=0.072 Pa m at 25 °C).

For a void to be stable, its collapse pressure (2r/r) mustbe balanced by a pressure difference across its surface ormeniscus = Pv — Pw, where Pw is the absolute pressure (=Px + the atmospheric pressure) of the water and Pv is theabsolute pressure of the void.

P —P =2r/r (7)

Pv always is above absolute zero pressure (= perfectvacuum) since the void usually is filled with water vapourand some air. Relatively stable voids are common in dailylife, e.g. the air bubbles that form in a cold glass of waterfreshly drawn from a tap. An entrapped air bubble istemporarily stable in a glass of water because Pw is arelatively constant 0.1 MPa and Pv is determined by theideal gas law, Pv = nRT/V, where « = the number of molesof air in the bubble, R = gas constant, T= absolute tem-perature, and K=the volume of the bubble. So thetendency of the void to collapse (2-r/r) makes V decreasewhich causes Pv to increase according to the ideal gaslaw because Pv is inversely proportional to V. The rise inPv provides the restoring force across the meniscus neededfor stability. But an air bubble in a glass of water is stableonly temporarily because according to Henry's law, thesolubility of a gas in water increases with the pressure ofthe gas. So the increased pressure exerted by 2-r/r makesthe gas in the bubble more soluble in water and it slowlycollapses as the air dissolves, i.e. as n decreases.

Cohesion-Tension theory 1761

Air bubbles are rarely stable in xylem conduits becausetranspiration can draw Pw to values <0. As Pw fallstowards zero the air bubble expands according to theideal gas law, but V can never grow larger than thevolume of the conduit, so Pv can never fall low enoughto allow Pv — Pw to balance 2r/r without a decline in Pw.Once the bubble has expanded to fill the lumen, theconduit is dysfunctional and no longer capable of trans-porting water. Fortunately for the plant, a dynamicbalance at the meniscus in cell walls ultimately is achieved.This stability will be discussed first in the context of avessel and its pit membranes.

As the air bubble is drawn up to the surface of the pitmembrane in vessel cell walls, the pores in the pit mem-brane break the meniscus into may small menisci at theopening of each pore. As the meniscus is drawn throughthe pores, the radius of curvature of the meniscus, rm,falls toward the radius of the pores, rp. Again, as long asrm exceeds rp, the necessary conditions for stability areachieved, i.e.

Pv-Pvl = 2r/rm (8)

Usually, a dysfunctional conduit eventually will fillwith air at atmospheric pressure (as demanded by Henry'slaw), so Pv eventually approaches 0.1 MPa as gas diffusesthrough water to the lumen and comes out of solution.When Pv equals 0.1 MPa, the conduit is said to be fullyembolized. As Pw rises and falls as dictated by thedemands of transpiration, rm adjusts at the pit-membranepores to achieve stability. When the conduit is fullyembolized, both sides of Equation 8 can be expressed interms of xylem pressure potential,

The minimum Px that can be balanced by the meniscusis given when rm equals the radius of the largest pit-membrane pore bordering the embolized conduit. If thelargest pore is 0.1 or 0.05 ^m, the minimum stable Px is— 1.44 or —2.88 MPa, respectively. So the porosity ofthe pit-membrane is critical to preventing dysfunction ofvessels adjacent to embolized vessels (Sperry and Tyree,1988). When Px falls below the critical value, the airbubble is sucked into an adjacent vessel, seeding a newcavitation.

Consequently, the genetics that determines pit morpho-logy and pit-membrane porosity must be under strongselective pressure. A safe pit-membrane will be one withvery narrow pores and one thick enough and thus strongenough to sustain substantial pressure differences withoutrupturing.

The situation for tracheids of conifers is differentbecause air movement from an embolized tracheid to anadjacent tracheid is prevented by the sealing (aspiration)of the torus against the overarching border of the pit. Inmost cases, the porosity of the margo that supports the

1762 Tyree

INCREASING TENSION

H I WALL [ H I AIR i H WATER

Air Seeding through pore

4n 1Air S eeding through hydrophobic crack

D

H omogeneous nucleation

O

H ydrophobic adhesion fa ilure

oFig. 8. Four possible mechanisms of cavitation induction. ( I ) Air-seeding through a pore occurs when the pressure differential across themeniscus is enough to allow the meniscus to overcome surface tensionand pass through the pore. (2) Air-seeding through a hydrophobiccrack occurs when a stable air bubble resides at the base of ahydrophobic crack in the wall of a xylem conduit. When the Pxbecomes negative enough the bubble is sucked out of the crack. (3)Homogeneous nucleation involves the spontaneous generation of a voidin a fluid. It is a random process requiring thermal motion of the watermolecules. The hydrogen bonds at a specific locus are broken when allwater molecules randomly move away from any locus at the sameinstant with sufficient energy to break all hydrogen bonds betweenwater molecules. As the tension in the water increases the hydrogenbonds are stretched and weakened so the energy needed to break thebonds decreases making a homogeneous nucleation more likely. (4)Hydrophobic adhesion failure is similar to homogeneous nucleationexcept that hydrogen bonds are broken between water and ahydrophobic patch in the wall where the energy of binding betweenwater and wall is reduced.

torus is too large to prevent meniscus passage at pressuredifferences exceeding 0.1 MPa (Sperry and Tyree, 1990).But the margo is elastic, so a pressure difference of only0.03 MPa is sufficient to deflect the torus into the sealedposition. Air bubbles pass between tracheids when thepressure difference becomes large enough to rip out thetorus from its sealed position (Sperry and Tyree, 1990).

A biophysical understanding now exists of the stabilityof emboli and how they can be sucked into a water-filledconduit from a neighbouring embolized conduit. Plantsalways will have some embolized conduits to seed embol-

C otton collector — >H

Pressure Chamber

100

W ater potentia l, M Pa

-2 -1

OQ_

3 2 1Applied P ressure, M Pa

Fig. 9. The first experimental test of the air-seeding hypothesis. (A)The experimental apparatus. A willow branch is bent around in a largepressure bomb so that both cut surfaces are outside the bomb. Watercontinually passes through the stem segment under positive pressurefrom a water column to a cotton collector. Flow rate is estimated bymeasuring the weight change of the cotton collector over known timeintervals. (B) The results are shown as a vulnerability curve where thei»-axis is the per cent loss of hydraulic conductivity (PLC) and the .v-axis is the negative Px or the air pressure in the bomb needed to causethe plotted PLC. Open symbols are for PLC induced by negative P%and closed symbols are induced by positive pressure applied in thepressure bomb. See text for more details.

ism into other conduits. Embolisms are the natural con-sequence of foliar abscission, herbivory, wind damage,and other mechanical fates that might befall a plant. Itis now appropriate to question whether all emboli areseeded from adjacent conduits or whether another mech-anism occurs in some or most of the cases.

Four mechanisms for the nucleation of cavitations inplants have been proposed. These are illustrated in Fig. 8,which shows for each mechanism the sequence of eventsthat might occur as Px declines in the lumen of a conduit.See Zimmermann (1983), Tyree et al. (1994), and Pickard(1981) for a detailed discussion of the four mechanisms.Other air-seeding mechanisms have been proposed thatapply to SCUBA divers (Yount, 1989). Such mechanismsalso might occur in plants when gas solubility decreasesin xylem water as it warms, but little is known about theimportance of this mechanism in plants. This study is

concerned only about which mechanism occurs mostfrequently in plants.

Experiments can discriminate between the air-seedingmechanism and the other three in Fig. 8 and Yount(1989). All mechanisms predict cavitation when xylemfluid is under tension, but the air-seeding mechanismpredicts that air can be blown into vessels while the fluidis under positive pressure. The air-seeding mechanismrequires only a pressure differential (P^ — Pw), where Pais the air pressure outside and Pw is the fluid pressureinside (Fig. 9a). It makes no difference if P& is 0.1 andPw is —3.0 or if ^ is 3.1 and Pw is 0.1. Experiments haveshown that the same vulnerability curve results whetherPw is reduced by air dehydration or Pa is increased in apressure bomb (Cochard et al., 1992). A vulnerabilitycurve is a plot of per cent loss hydraulic conductivity(PLC) versus the Px required to cause the PLC bycavitation events. The results of this experiment are shownin Fig. 9b (see also Jarbeau et al., 1995).

Willow stem segments with leaves were enclosed in apressure chamber with cut ends protruding into the openair. Water was passed continually through the xylemunder positive pressure. While stem conductance wasbeing monitored, the gas pressure, Pa, in the pressurechamber was increased gradually. Initially, the hydraulicconductance of the stem segment did not decrease untila critical pressure of 1 MPa was applied. (Each solidcircle in Fig. 9b represents the application of pressure for

Cohesion-Tension theory 1763

30-40 min.) When /*„ was increased gradually beyond thecritical value the stem conductance began to fall(increased PLC). When Pa was gradually decreased, thePLC stopped decreasing. The vulnerability curve fromthis experiment was identical to that found for similarbranches dehydrated in the air.

This is the strongest evidence presented to date thatthe air-seeding mechanism explains how cavitations occur,though there is other circumstantial evidence (Crombieet al., 1985; Sperry and Tyree, 1988). The air-seedinghypothesis can be viewed as providing strong evidencefor the existence of large negative Px values prior tocavitation events. The aspiration of the meniscus into acavitating vessel is driven by a pressure difference =Pa-Pw. If the pressure difference is, say, 8 MPa whenPw = 0.\ and />a = 8.1 MPa, it follows that />w must equal- 8 . 1 MPa (Px= - 8 .0 ) when Pa = 0.\ MPa. Sperry et al.(1996) compared the vulnerability curves of numerousspecies measured by the application of positive air pres-sure versus curves measured by bench-top dehydrationwhere Px values were measured by the pressure bombmethod. A 1:1 agreement was found for — Px or /*a from1.0 to 9.5 MPa (Fig. 10). For this agreement to exist, twothings have to be true: (1) The air-seeding hypothesismust be the mechanism of cavitation and (2) the pressurebomb must measure values of Px correctly. For readerswho still may doubt the accuracy of the pressure bomb,after all the arguments in this paper, one other elegant

Fig. 10. Vulnerability curves were generated in two ways. (1) Cavitations induced by negative Px in which the pressure bomb was used to estimatePX=-PB measured on leaves attached to the dehydrated stems. (2) Cavitations induced by positive pressure, />., in an experiment like that inFig. 9. The vulnerability curves were examined in the range of 40-60 PLC and for each PLC value corresponding values of — Pa and — PB wererecorded and plotted on the x- and _c-axis, respectively. These data were compiled from vulnerability-curve data on 12 species, (modified fromSperry et al., 1996). The slope is not significantly different from 1.0 (Student's ( test, ;s = 0.30l, P>0.5) indicating that negative pressures aremeasured correctly by the pressure bomb and that cavitations occurred by air-seeding.

1764 Tyree

100

8 0

60

4 0

20

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100

80

60

4 0

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80

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Fig. 11. Comparison of vulnerability curves obtained by different methods. The )>-axis is per cent loss hydraulic conductivity (PLC) induced by a'pressure' on the x-axis: solid symbols, negative pressure induced by centrifugation; open symbols, negative pressure induced by air-dehydrationand measured on excised leaves with a pressure bomb; dotted symbols, PLC induced by positive pressure as in Fig. 9.

experiment can be presented to show that xylem conduitscan sustain substantial tensions without cavitation.Tension can be controlled independently and induced instems by centrifugation (Holbrook et al., 1995), so itfollows that centrifugation can be used to induce cavita-tions and measurable loss of hydraulic conductivity. Ithas been shown that vulnerability curves produced bycentrifugation are the same as those produced by bench-top dehydration (Pockman et al., 1995, Alder et al., 1997)(Fig. 11).

ConclusionsThe Scholander—Hammel pressure bomb seems to meas-ure Px correctly. This has been confirmed by two direct

and two indirect pieces of evidence. The pressure bombagrees with xylem tension measured directly with a tem-perature-corrected thermocouple hygrometer and withtensions created by centrifugation. The pressure bomb isvalidated indirectly because it has been used to confirmtwo hypotheses: (1) the air-seeding hypothesis and (2)the hypothesis that water flow can be treated as an Ohm'slaw analogue. Both hypotheses make quantitative predic-tions about Px and the pressure bomb measurements havebeen used to confirm both hypotheses. The followingmust be true for the confirmation to occur: (1) thehypothesis must be true and (2) the pressure bomb mustmeasure Px correctly. More experiments of the typedescribed above must be repeated to confirm the accuracyof the pressure bomb with other plant species. This

study's tentative conclusion is that the XPP must beincorrect if it does not agree with the pressure bomb. TheXPP does not measure PK< —0.6 MPa in plants; the mostlikely explanation is that the XPP induces embolisms byair seeding when P < — 0.6 MPa. It is less clear why theXPP disagrees with the pressure bomb in direct compar-isons made by Balling and Zimmermann (1990), so thiswork should be repeated in other laboratories and withadditional species. There is no reason to reject the XPPoutright as a useful method to measure xylem-fluid pres-sure in the range of 0 to —0.6 MPa. Further advances inXPP technology may even extend the useful range tomore negative pressures.

Studies of xylem dysfunction due to cavitation providesthe best evidence that water is transported in plants in ametastable state as proposed by the C-T theory. Muchof what is now known about xylem anatomy and evolu-tion is best explained in terms of the function of xylemstructures in the avoidance of cavitations and readersmay consult Tyree et al. (1994) for details. Recent studiesof the Ohm's law analogue for sap flow in plants haveprovided strong quantitative support for the C-T theory.

AcknowledgementsI thank the following for their critical review of an earlier draftof this manuscript: Peter Becker, Stephen Davis, FrederickMeinzer, John Sperry, and David Yount.

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