Plant Physiol. (1968) 43, 1169-1184

Vol. 43 No. 8

PHYSIOLOGYGrowth Phvsics in Nitella: a Method for Continuous in Vivo Analysis

of Extensibility Based on a Micro-manometerTechnique for Turgor Pressure'

Paul B. GreenDepartment of Biology, University of Pennsylvania, Philadelphia. Pennsylvania 19104

Received Februarx 12, 1968.

Abstract. The view that the plant cell grows by the yielding of the cell wall to turgorpressure can be expressed in the equation: rate = cell extensibilitv X turgor. All growthrate responses can in principle be resolved into changes in the 2 latter variables. Extensibilitywill relate primarily to the yielding properties of the cell wall, turgor primarily tosolute uptake or production. Use of this simple relationship in vivo requires that at least2 of the 3 variables be measured in a growing cell. Extensibility is not amenable to directmeasurement. Data on rate and turgor for single Nitella cells can, however, be continuouslygathered to permit calculation of extensibility (rate/turgor). Rate is accurately obtained frommeasurements on time-lapse film. Turgor is estimated in the same cell, to within 0.1 atmor less, by measurement of the ability of the cell to compress gas trapped in the closed endof a capillary the open end of which is in the cell vacuole. The method is independent ofosmotic equilibrium. It operates continuously for several days, over a several fold increasein cell length, and has response time of less ithan one minute. Rapid changes in turgorbrought on by changes in tonicity of the medium. show that extensibility, as defined above,is not constant but has a value of zero unless the cell has about 80 %o of normal turgor.Because elastic ohanges are small, extensibility relates to growth. Over long periods oftreatment in a variety of osmotica the threshold value for extensibility and growth is seen tofall to lower values to permit resumption of growth at reduced turgor. A brief period ofrapid growth (5X normal) follows the return to normal turgor. All variables then becomenormal and the cycle can be repeated. The cell remains essentially at osmotic equilibrium,even while growing at 5X the normal rate. The method has potential for detailed in vivoanalyses of "wall softening."

The growvth of the plant cell may be regarded.instantaleoulslv at least, as the yielding of the cellwall to the stresses present in it. Tn the Nitellainternode and other cells not subject to tissuie ten-sions, the stresses can be assumiied to be prol)ortionalto turgor pressulre. This allows the rate of growtth(R) to be viewed simply as the lpro(luct of theyielding tendency of the cell (Ex, or gross exten-sibility) and turgor pressure ( T).

R (fraction/hr) -

Ex9 Efraction/hr)/atm] * T (atnm)All changes in growth rate then become resolv-

able into changes in one or both ternms. Suchchanges in inidividual terms, once clearly identified.can then be studied witlh rcgard to their origin instructuire or metabolism.

Supported by NatioInal Science Foundation GrantsGB 2575 and 6055X

Equationi ( 1). (lespite its brevity. is remarkablydifficult to solve in growing cells sinice onlyl therate term is rea(lil-v measuired while enlargemelnt isoccurring (21,22). Extensibility is not amenableto direct mlen sureimienlt because unilateral stretchlingof the grow-ing cell would alter the usuial stresspattern aind distuirb the growth process. Extensi-bility can be calculated using equation (1), providedinformation oln turgor can be combined with (lata onrate in the samle mlaterial.

Turgor estimiiates for the growing cell are oftenequivocal becauise eqjuilibriumn methods suIchl as pllas-molysis and plasmiometry give only anl upper linmitfor the valuie (luriig grow-th. In some tissues thevalue during enlargellment is estimated to be as muitichas 2 atmospheres below the equilibriumn figure (32).Even if near-equilibriuim conditions do obtain duringgrowth, as might be expected in single cells growingunder water, the growtth response of interest nmay berapid comp)aredl to the rate at which diffusion brinlgs

1169

PLANTAugust 1968

PLANT PHYSIOLOGY

concentrations to the neew equilibrium required fora mleasuirement (8, 32). Use of equation (I) toanalyze growth in tissues is made particularly diffi-cult by the possibility that the rarious cell types inthe tissue are not equivalent wvith regard to gen-erating pressure and yielding to it. For these rea-sonIs a mletlhod for turgor in single cells which israpid, contitnuous, independeint of osmotic equilibrium,and comipatible with growth is of some utility. Thisreport describes such a method based on measture-meint of a cell's capacity to compress gas trapped ina cap)illarv ( 16). Data on turgor, wheln combinedwith informNation on the growth rate of the samecell, permit the contintuous solving of equation (I)and the calculation of gross extensibility (Ex,).

Note that while turgor clearly can be affected bychanges in extensibility (e.g. increased extensibilityunder conditions of low permeability to water canredtuce turgor (21, 22), this does not miieani that the2 variables cannot be meastured independently. Thecell's ability to compress gas gives its internal pres-sure regardless of the many factors governing thispressure. Extensibility can thus be defined simnplyas the quotient of the existing rate and the existingturgor pressure.

EXr is given a subscript to distinguislh it fromrelated exp)ressions. Generally, extensibility relatesthe rate of yielding of a material to the appliedstress. For many materials the relationship can bewritten so that extensibility is a constant. Thisoften involves incorporatinig the complexity of yield-ing behavior into the stress term. For example. inquasi-plastic flow the stress above a certaini thresholdis raised to a power and then multiplied by a con-stant extensibility term to give the rate of yield(28). Because there is no a priori reason to expectthe extensibility of a growing cell to fall into one ofthe rheological relationships established for inertsubstanices, it seems reasonable here to keep thestress terml a simple pressure and to express complexyielding behavior, when it appears, in some elabora-tion of the extensibility term.

Plant cells typically show constant growth rateat constant turgor, so EX. will of necessity have thecharacteristics of a reciprocal viscosity. The simi-larity to viscous flow maxy well be only formalbecause, if metabolism is allowed to play a role, onecan envision a variety of complex yielding systemswhich show this kind of behavior (29).

Eq,, wheni measured over short periods of tinmeand over smlall deformations, will reflect the in-stantaneous yielding properties of the cell wall,properties which may be maintained by metabolismoccurring in, or at least acting on. the wall (30).The behavior of Ex9 in vivo therefore can be com-pared with the yielding properties of killed cells orisolated wall strips subjected to knovn artificialstresses. Provided the physical data on isolatedmaterial derive from small deformations at physio-logical rates, and provided correction can be madefor the fact that a unlilateral force instead of a

multi-lateral pressure is applied ill isolated material,differences in yielding properties froml those seenii izvio must reflect the absence of chemical ormetabolic factors normally present in the cell.

By the present method EX, can be evaluated afterrapid shifts in turgor to give informlation on thestress :strain-rate relationship in the growing cell.Continuation of the analvsis over longer perio(1sreveals sizable shifts in these properties.

Materials and Methods

Priinciple. \Vhen a fine glass capillary is fusedat one end and subimierged, air is trapped inside it.If the open end is then inserted into a cell and thewound sealed, the trapped gas is compressed inaccord with pressure inside the cell. Because ofthe constancy of pressure times volume, cell pressureis readily calculated. Turgor pressure is I atmos-phere less thani the pressure in the bubble. Thesmall tendency of capillarity to compress the gascan be measured beforehand and subtracted fromfinal turgor values. Adaptation of this principle foruse on the growing cell, under conditions where thegrowth rate of the same cell could be simultaneouslyfollowed, involved many problems. The major phys-ical one was that the trapped gas dissolved into tllecapillary fluid, at varying rates depending on turgor,so that volume changes over long periods of timewere not a reliable basis for pressure calculation.A slhort-termii vxolume change, brouglht on by avacuulml pump, was used for calibration.

TazawsFa's cell compression method for turgor(34) and N'irgin's resonance frequency method (38)also do not require osmotic equilibrium. Arens (1)has described 2 methods to estimate turgor in Nitella.In one, the original compressibility of a cell wasrestored, after loss of turgor, by inflating the cellthrough a canula. The gas pressure required wasequal to the original pressure of the cell interior.In the other, the mid-portion of the cell was grippedand the position of one protruding cell-end (a) care-fully noted. The cell was allowed to wilt and gaspressure was theni applied to the space around theother cell-end (b) so as to restore the originalconfiguration at (a). Values of 3 to 10 atmos-pheres were obtained. Recently Villegas (37) hasused a capillary inserted in a Valonia cell to balanicecell pressure w\ith gas pressure. Pressure chanigesassociated With small volume changes could be esti-mated. Gutkneclht ( 17) has altered turgor inValontia bv connectinig a source of hydrostatic pres-sure to the cell interior by a capillary. Appareitlynone of these nmethods has been adapted for con-tinuouts use on growing material.

Detailed MIlethod. The following considerationsgoverned the adaptation of the capillary method tothe growving cell. All data necessary for determina-tion of both growth rate and cell pressure would bephotograplied (tinme-lapse). This meant that the

1170

GREEN-PHYSICS OF CELL GROWTH IN NITELLA

cell and capillary had to be in the same plane,

preferably side by side. Calibration was to be done

periodically and solution changing, over a period of

48 houirs, was to be automatic. Because calibration

involved a large drop below atmosphleric pressure,

the system, including automated valves, had to be

vacuum tight.The major biological problem involved the cell's

reaction to the presence of the capillary which, at

first, either resulted in failure of the cell to grow

or in failure of the capillary to function (due to

plugging). Success was obtained only after extreme

measures were taken to insure mechanical rigidity

of the cell and capillary both during insertion andthe protracted growth period.

a) Calibrationi of Cell Pressure. The pressure

in a bubble can be determined by its volume changein response to transitory changes in its pressure.

Normally 1 atm of the pressure on the bubble isfrom the atmosphere, the rest being due to turgor.

The former component can be altered by knownamounts by placing the entire system. plant andcapillary, in a strong vessel and applying a pump.

From the change in volume one obtains the pressure

(PB ) in the bubble.AP V.,

PB = (II)V1 - V..

We gave a decrement in pressure, AP, of minus

two-third atm for 3 minutes every half hour. V1

was taken as the mean of 2 volumes: 5 minutes

before and 5 minutes after the pulse. V. was the

maximum volume during the pulse.Turgor pressure, T, is:

T -_ [PB - C] 1 (III)

where C is capillarity, roughly 0.05 atm, measured

by the extent of water entry (gas compression)

when the capillary was submerged. Turgor was

computed from measurements punched on computer

cards. For pressure values between calibration

pulses, the volume of the bubble could be used

because the shrinkage was steady for a given turgor.

No variation in streaming rate or growth rate was

associated with pump action.The response of bubble length to pump action

and to the addition of osmoticum to the medium is

seen in figure 3 where length is measured at 2 minute

intervals. Upon a fall in turgor the bubble increasesboth its length and its response to the pump. The

bubble can accurately respond to a change in pres-

sure of two-third atm within 1 minute. Accuracy

of pressure drop was maintained by a Cartesiandiver type manostat (Greiner Science Companv,New York).

The Grozwth Vessel and Automated Solution

Changing. The plant grew in a continuously illu-

minated pressure vessel and was photographed

through a flat window. The vessel was made from

a large "0-ring" joint by glass-blowing. It was

clamped to a heavy lathe tool-holding device to

permit precise and stable adjustment of the vessel's

position. An outlet above the fluid level in thevessel went to a vacuumli pump, anl inlet was pro-vided below the 0-ring, and a drain was at the base(fig 1). Solutions were changed by draining andrefilling, all movements by gravity. Valves were

operated by air-driven linear actuators controlled bysolenoid valves. Automation of both calibration andsolution change involved combined use of a 1 rev/hrmultiple cam ("gang") timer and a stepping sxvitch.One cam activated a vacuum pump for 3 minutesevery half-hour for calibration (see above). Duringevery hour a second cam closed 1 of 2 gaps in a

circuit which could open the drain valve, and shortlythereafter a third cam closed a similar gap in an

inlet valve circuit for a few minutes. The valveswould actuallv open only during those hours whenthe stepper closed the second gap. The stepper was

advanced 1 step per hour by a fourth cam on thegang timer. Thus the major functions, being alltimed by the same rotating shaft, could not get outof phase. Typically, normal growtlh medium was

alternated with growth media of increased tonicity,using various osmotica such as sugar or polyethyleneglycols (,Carbowax). The Carbowax (Union Car-bide Company) had been passed througlh an ion-exchange column. Concentration of growth mediumwas kept constant, independent of osmoticium con-

centration. A large flask of normal medium was

repeatedly used to fill the growth vessel during 1run. Smaller flasks of altered medium (used once

each) were drained completely to fill the growthvessel. This arrangement permitted 7 or 8 solutionchanges with only 4 flasks and valves. Timing hadto be adjusted in advance to allow for variation inviscosity of the various solutions, particularly thosecontaining Carbowax.

Toxicity was avoided by using polyethylene fortubing, valves, and fittings and by making all gluejunctions with DeKhotinsky cement (Central Scien-tific Company, St. Louis). The 0-ring itself was

toxic so the solutions were kept from it.The Capillary. A fish-hook shaped capillary was

used in order to bring the compressed bubble along-side the growing cell surface for photography. Atfull turgor only about one-sixth of the capillary was

filled with gas. To have the length of the bubbleroughly correspond to the length of the young cellin order to maximize accuracy, the capillary was

made much longer than the cell, then bent. Aninternal diameter of about 40 ,u was found to makethe bubble readily visible on the film and to transferonly a modest volume of cell sap into the capillary.Cell diameter was about 200 ,u so the capillarycross-section was about 4 % that of the young cell.Initial sap dilution ran about 3 to 6 %. One mmdiameter thin-wall glass capillary (Corning GlassWorks, Corning, Nev York) was hand-drawn overa broad flame to give several cm of thin capillaryof essentially constant bore. The glass was thentreated with Siliclad!(Clay. Adams, Inc., New York,New York) to prevent later segmentation of the gas

1171

1172 PLANT PHYSIOLOGY

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FIG. 1. Genieral experimental set-up to permit continuous time-lapse photography (right) of the plant while it isgrowing in the pressure vessel. The vessel is held by a clamp (not slhown) fixed to a machinist's tool holder withscrew adjustments in 3 dimetnsions. The vacuum pump acts at one-half hour intervals for calibration of cell pressure(see text). Solution changiiwg was on a drain-and-refill basis, automated by circulating electric valves througlh agang timer and stepping switch. The mercury manometer was occasionally uised to check the leve! of vacuum deliveredby the pump.

bubble. The 40 u bore was ideal for the readingpart, but was too large for insertion. A special tipwas fashioned with a DeFonbrune microforge (AloeScience Company, St. Louis). The platinum fila-ment was coated with glass to prevent toxic vapors

from being deposited oni the capillary. The capillarywas fused at 2 points 12 mm apart and a regionjust above the lower fusion was heated to form an

extremely thin-walled (3 2u) swelling. A weightwas added below and tlle swelling stretched, byheating, into a delicate, and thin-walled extension.After bending into a hook slhape, the capillary was

glued to a cover-glass chip. The tip was broken

with tweezers to give a roughly oblique cut tip ofdiameter 20 ,u. The mounted capillary was thenreturned to the forge and the broken tip touclhed tothe filament and stretched and smoothed to a formlike that of a syringe needle. Just before insertionit was dipped in water, then 20 % "Bio-nox" de-tergent (Triton X-100, Rohm and Haas ChemicalCorporation, Philadelphia, Pa.) to minimize thecell's reaction to insertion.

The Holder. A complex holder was tised forboth the insertion, carried out in a large Petri dishtinder a dissection microscope, and for prolongedobservation in the pressure vessel. See figture 2.

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GREEN-PHYSICS OF CELL GROWTH IN NITELLA

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1173

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FIG. 2. A glass holder, assembled from a slide and cover glass pieces, uised to hold the cell during insertion ofthe capillarx- and during prolonged grow-th in the pressure vessel. Adjustment of the position of the cell and the sleeveguide pernmitted advance alignment of the capillary tip with the central axis of the cell. The celi was firmly com-pressed at full turgor as showxn; further compression upon reduction of turgor was prevented by the safety rod.When the holder and plant were in the vessel (fig 1), the field of the camera included the region of the cell showingtlhe marking heads (on cell, left of bubble) and the adjacent part of the capillary containiing the bubble. The structureat the base aids in the straightness of growth of the cell.

PLANT PHYSIOLOGY

It hooked onto a horizontal bar glued inside thepressure vessel. The holder gripped the plant byvisibly compressing the upper end of the cell ofinterest. It also served to hold an adjustablesleeve-guide by which the capillary tip was alignedprecisely with the axis of rotation of the cell. Inthe horizontal plane the alignment was made byplacing the cell in the proper position before com-pressing. The vertical alignment was made by ad-justing the elevation of the sleeve guide with asmall rod (fig 2) while observing through a 450mirror which was part of the holder. The mirrorwas made by evaporating chromium onto a cover-glass chip.

The Cell. A plant with an upper internode about5 mm long was chosen. The shoot tip and lateralsat both ends of the chosen cell were removed witha glass needle. This bare upper end (node) wascompressed and accepted the capillary. A smallweight was attached to keep the cell vertical duringgrowth. Curiously, this eliminated the "twisting"component of growth and facilitated analysis.

Insertion. The capillary-bearing chip was posi-tioned so it could slide along the holder on a layerof stopcock grease. The capillary tip was directedinto the sleeve guide by pushing the chip withforceps (fig 2). A protection bar was put underthe cell-compressing lever to prevent any furthercompression upon reduced turgor and the capillarytip was pushed several hundred microns into thecell. In about one-fourth of the cases cytoplasmicstreaminig did not stop during insertion. In theothers it resumed within 30 seconds. Good align-ment, complete rigidity throughout insertion andgrowth, and a well-fashioned capillary tip wereessential. Otherwise the cytoplasm built up at thewound region and gradually covered the capillarytip. Often it would lay down a cell wall (found tobe birefringent) over all the glass inside the cell.rendering the capillary topologically outside (anduseless). Cell grovth rate was not optimal duringsuch cytoplasmic reaction.

Cell Alarking and the Growth Rate. The exten-sion of the cell surface can be measured by followingthe separation of anv 2 points on the cell surfacebecause growth is uniformly distributed (12). Thefractional increase in length, per unit time, is therelative rate. It is measured as the slope on a curverelating the natural logarithm of separation to time.For marks, small anion-exchange resin beads in thehydroxyl form 1(15) are ideal optically. Marks wereapplied by hand with a hair, the cell being in ion-freewater. The use of a defined salt medium (in whichchloride competed with the wall for the beads'binding groups) along with periodic draining andfilling of vessel, lead to frequent loss of marks.An excess had to be applied initially. Those beadsthat remained on throughout were seen in the movieto remain firmly fixed to the wall during growth.The camera took 1 frame per minute, recordingbehavior of the cell surface and the bubble. Key

dimensions on the developed film (Kodachrome II,16 mm) were measured on a Vanguard MotionAnalyzer (Vanguard Instrument Corporation, Mel-ville, New York). L was the distance between thecenters of 2 widely separated resin beads. A com-puter averaged measurements for 1 frame and pro-vided ln L.

Elasticity and the Measuremiient of Growth.Total elongation, as measured on the film, is thesum of elastic and permanent (irreversible) exten-sion. There is considerable evidence that the elasticchanges in Nitella are small enough to be ignored inall but the most severe shifts in turgor. Kamiyaet al. (18) have shown that the total shrinkage inlength of a live Nitella cell is about 0.8 % and theshrinkage upon a fall in turgor of 2.4 atm, nearly

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FIG. 3. Analysis at 2 minute intervals of capillary-bubble length (above) and in cell length (below). Theintermittent expansion of the bubble, due to the actionof a vacuum pump, is shown by vertical dashed lines.This permits calculation of the pressure inside thebubble (see text). (These calibration values, convertedto turgor pressure, are plotted in fig 5, middle treatment).After a change to a medium of higher tonicity (2410min, vertical solid lines), there is an initial delav of atleast 2 minutes before the response of the bubble is seen.There is a further lag of at least 10 minutes before astable bubble length is reached. That these delays are dueto slow establishment of the new trans-membrane con-centration gradient is indicated by the fact that thev arelong compared to the response time of the bubble tohydrostatic pressure change. A similar delay is seenupon return to higher turgor (2590 min). Growth haltsfor a brief period (x) at the start of inhibition, butthen normal rate is rapidly restored. Upon return toessentially full turgor, a growth burst (GB) ensues, lead-ing to a net increase in cell length over that anticipatedin the absence of inhibition (long arrow). Duration ofthe burst (y) is about equal to the initial lag (x).

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1174

11

GREEN-PHYSICS OF CELL GROWTH IN NITELLA

equal to the largest drop imposed by us, is only0.1 %. Elastic changes took about 2 to 3 minutesto be three-fourths complete. In our material shrink-age could not be detected upon a fall in turgor of0.8 atm (fig 3). A fall in turgor of about 3 atmdid lead to about 0.4 % shrinkage over about 10minutes on some trials, but to no shrinkage onothers (fig 6). These shrinkages are small com-pared to length changes used to determine rates andare ignored unless otherwise specified.

Culturing. Stock cultures were maintained byalternate growth (2 wk periods) in autoclaved soilextract (100 ml garden soil in 6 1 distilled waterautoclaved 20 min) and in a modified Forsberg(10) medium. It contained, per liter, Ca (NO.)280 mg; MgSiO4 * 7 Ho0, 100 mg; NaHCO3, 60 mg;KNO3, 100 mg; NH4CI, 20 mg; Na2SiO3, 12.5 mg;KCI, 100 mg; K,HPO4, 1 mg. The tris buffer usedby Forsberg was omitted because it supported bac-terial growth. Because the plants grew in largevolumes which were replaced every 6 hours or less,buffering was not important. pH was adjusted to6.5 with HCI. Trace elements, individually chael-ated with sodium nitrilotriacetate were added, at1 ml/l from stock solutions: FeSO4, 2.5 g/l; ZnClI,526 mgt'l; MnCl9, 1.15 mg/I; CuCl, 21.3 mg/l;H3B03, 295 mg/l; Na,MoO,, 60 mg/l; Co(N03)2,30 mg/l. The modified Forsberg medium supportedgrowth for 2 weeks and was used for experiments.It did not sustain good growth indefinitely as didsoil. The Forsberg solution did not support growthof any of the visible contaminants, including Oedo-goniumnt, so by innoculating soil medium with theterminal 10 cm tips of Forsberg medium plants, thecultures were kept free of visible contamination.

Osmiiotica. To alter turgor it is desired to adda solute whose sole action is to lower the waterpotential of the medium. There is alwavs the pos-sibility that anv soluble organic molecule will enterthe metabolism of the cell to either stimulate or

inhibit growth. In non-sterile systems such as thepresent one, effects mediated by bacterial activityare hard to exclude. The traditional osmotica,mannitol and polyethylene glycols, were used in thepresent study and it was found that when incor-porated into growth medium they could supportbacterial growth after days of standing.

Certain inorganic molecules cannot serve as

energy sources but may have other disadvantages.KCI would be expected to effect the resting potentialof the membrane. Further, potassium and calciumions are known to have direct "loosening" and"hardening" effects on Nitella cell walls (27).None-the-less, the cell response to KCI does notdiffer markedly from that to organic osmotica.(KCl does not enter unusually rapidly to alterturgor).

Lintitations. The method is capable of resolvingany growth response into turgor and extensibilitycomponents. The major limitation is that thegrowth response caused by the presence of an osmo-

ticum may be due to changes other than the simplechange in the colligative properties of the medium.The most striking example of this was found withCarbowax 400 (A low mol wt polyethylene glycol,Union Carbide Company, New York). Presence ofthis compound reduced turgor and initially stoppedgrowth. The cell then not only recovered its orig-inal rate but exceeded it by 80 %, still at reducedturgor! The data to be presented will thereforeprimarily illustrate the method and only tentativelycharacterize the response of the cell to turgor change.Some confidence is justified in the immediate aspectsof a response and in those slower aspects that arecommon to osmotica of diverse chemical nature.

Results

Possible Departutre Fromt Osmotic Equilibrium-Delays in, Mixing. A rough test for whether thegrowing cell is in osmotic equilibrium is whether adecrease in tonicity of the medium surrounding anon-growing cell is fully matched by an increase inturgor inside the cell as it resumes growth. A dis-crepancy would show a departure from equilibrium.In figure 6, below, the length of the vertical arrowsgives the change in tonicity of medium, the verticalshift in the large dots, the shift in cell turgor. Thedifferences are small fractions of an atmosphere and,after considerable growth has occurred, could be dueto rapid sap dilution. It was thought possible thatdetailed study of bubble length might detect finitedepartures from osmotic equilibrium during thebursts of rapid growth after the end of inhibition.The detailed record in figure 3 does show slightlyreduced pressure (by 0.08 atm) during the growthburst compared to values for steady elongation.This discrepancy apparently has its origin howeverin the delay required for the establishment of a newconcentration gradient across the cell membrane.This general problem is discussed by Dainty (8).There is a roughly 20 minute delay in fully estab-lishing a new turgor pressure when osmoticum isadded and growth stops (fig 3, 2412-2432 min).This delay exists despite the presence of considerabledifferences in density of the solutions being changed;these differences would promote mixing by convec-tion. Here the pressure is "too high" to roughlythe same extent for about the same amount of timeas it was "too low" above. Part of the slightlyreduced pressure during the gro-wth burst could bethe result of rapid sap dilution during the growthburst (see fig 6, third treatment). It is concludedthat departure from osmotic equilibrium is certainlyless than 0.08 atm and probably infinitesimal. Thisresult is not unexpected in light of the high waterpermeability (7-12 u/min/atm) of mature Nitellacells (35).

Growth Response. In all experiments a growingcell was alternately placed in normal medium and innormal medium supplemented with osmoticum. Theperiods in normal medium were 4 to 6 hours.

1175)

PLANT PHYSIOLOGY

The data are presented with the 2 directly meas-ured variables, ln L and turgor pressure, plottedagainst time. This gives an Lover-all view of thecourse of the experiment, the magnitude of thegrowth response, etc. The growth rate is the slopeon the ln L curve and is given at representativepoints as r. Cell extensibility, Exg, is the quotient:rate/turgor and is given at the same points as e.In figure 6 the variable ln diameter is also given.

Initially a detailed study using one osmoticumwas planned. Concern with the potential side ef-

159

In

fects of all osmotica has lead, however, to a broaderand less intensive effort. The response to variousosmotica will be briefly described and the commonfeatures summarized.

In figure 4 a cell is periodically subjected toincreasing concentrations of Carbowax 4000 in Fors-berg medium, reducing its turgor by 0.3, 1.0, and1.8 atm respectively. In all cases the cell's initialresponse is to stop elongating. Then, after periodsof time which increase with larger loss of tugor,growth resumes. This recovery is primarily due to

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' 5HOURS 500min TIME 1000 min 1500FIG. 4. Time course of an experiment with periods of osmotic inhibition of constant duration but increasing

severity. The natural logarithm of length (between 2 marks) is given at 10 minute intervals, by the small dots.Use the upper vertical scale. The large dots and the small inserted scales give the turgor of the same cell at thesame time. Tihe relative rate of growth is the slope of the ln length curve and is given as r at various points. Thegross extensibility (e) of the cell is also given. Descending arrows show start of osmotic inhibition, ascending arrows,its release. Note slight sensitivity to a small drop in turgor, resumption of normal growth rate upon moderate re-

duction of turgor (2nd inhibition) which is followed by a growth burst. A greater drop in turgor (3rd inhibition)almost totally inhibits growth, but is followed by a growth burst. Osmoticum: Carbowax 4000. Small x's showresumption of growth.

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1176

GREEN-PHYSICS OF CELL GROWTH IN NITELLA

a change in Ex., not turgor. After the 2 smallerlosses in turgor the normal rate is regained but aftera loss of 1.8 atm only partial recovery is seen duringthe time available. In all cases a rapid elongationfollows the return to osmoticum-free medium. Thewall is seen to be highly extensible. The maximumrate attained and the amount of added lengthachieved during these "growth bursts" appear toincrease as a function of the time the cell has spentat reduced (or zero) growth rate. A similar recordis seen in figure 5 where the osmoticum was thesame but the medium was soil extract. Here apronounced net increase in length, due to inhibitionplus recovery, is seen after the second inhibition.The over-shoot was very striking in runs withCarbowax 400, where a bacterial bloom eventuallyappeared, so its origin may be in extraneous meta-bolic factors combined with the change in turgor.

160

In-1.5

In LENGTH1.4

-1.3

r o.c10% e o10

-1.2 rO0.02 .e 0.004

r 0.0180

..---5atm .....

TURGOR 3

5 hours

An increase in size of the growth burst withincreasing time of growth inhibition (but no over-shoot) is seen in figure 6 where the osmoticum wasmannitol and where the duration, not the severity,of osmotic inhibition was varied. Recovery of rateappears only after about 4 hours into the longestinhibition. During this long inhibition an increasein turgor pressure is clearly seen. This increase isabout that expected if solute increase had continuedundiminished during the inhibition of volume in-crease. Extremely high rate and extensibility arenoted upon return to normal medium. A fourtlhperiod of inhibition (at 2200 min) shows that thegrowth burst does not increase as a function of thenumber of inhibitory periods (a possibility nototherwise excluded) and that the rapid increase inlength of the large growth burst is inelastic. atleast after several hours.

r 0.012

ru.v.JJ/

r 0.136e 0.027 */

D22005--..,

0.001

0.152!0.034

. a X - - 0.

TIMEFIG. 5. Legenid and experimental procedure the same as in figure 4. The second inhibitioni led to a pronounce(d

nlet increase inl cell length over that which wvould have been reached if the cell lhad beeni uniidisturbed. Note that thegrowth burst of the third inhibition gives a cell extensibilitv about 10 times that t fpia for the steady growth pe-riods hefore and after the inhibition. Osmoticum: Carbowax 4000.

-

a I

1177

PLANT PHYSIOLOGY

In

-1.7In DIAMETER

r O.031.0.0055

In LENGTHr0.03*0.0056

r Q..053*U01

r 0.02e 0.004

t6atm;e~ jLi**',JRGOR 4

E --2bhr-- 500 min

r0.14*0.0254

.................

r 0.00200.0008

\r0.0025.0.0004

r 0.009.0.0015

-,r 0.3200.055

- Bubbler0.0515IS4 length

1I,

i..16

V.4- - -

1000

-2

1500

FIG. 6. Symbols and scales as in figure 4 and 5. An experiment wlhere durationi, niot severity, of osmotic inhibitionis varied. Here 1, 3, 9, and 1 hour of the same osmotic inhibition is given, -swith 6 hours of growth in normal mediumletween treatments. Note the progressive increase in size of the growtlh burst wx ith increasing time of inhibition. Themaximiium slope at the start of each burst also increases. The turgor slowly increases throughouit, but muclh more

rapidly during inhibition. The turgor increases as if solute accumulation were continuing at the normal rate whilevoluime increase was inhibited. Note partial recovery of growlth rate after 4 hours of the third inhibitioni. In

Diameter is plotted above. Note the sharp increase du ring the largest growth burst (1800 min). Normally theincrease in ln diameter is about 0.2 that of In length. Over the first 40 minutes of the growxth burst, it is about 0.5.The length of the vertical arrows corresponds to the change in turgor predicted by change in the tonicity of themedium (mannitol). That the change in cell turgor nearly corresponds to this, after a period at osmotic equilibriumduring inhibition, indicates that a near-equilibrium condition persists even during the growth bursts. Bubble lengthmeasurements show lag in attainment of the steady trans-membrane concenitrationi gradient after a change of solution.

Figure 7 shows the response to turgor changeswhere the osmoticum was KCI. The typical initialhalt in growth, the eventual recovery of much ofthe previous growth rate, and the rapid elongationfollowing an increase in turgor are evident.

The similarity of response among ionic anduncharged osmotica is somewhat unexpected, particu-larly if the resting potential of the cell membrane issignificant in the growth process. This is not im-probable since membrane fusions, particularly of

Golgi vesicles, are implicated in the growtlh response.A fairly direct demonstration of this is found ingeotropic response of the rhizoids of Chara (33).The concentration of KCI used would virtuallyabolish the resting potential if artificial pond waterwere the normal medium (19, 20). Because our

normal medium contained KCI in sizeable anmount.the resting potential would be reduced by rouglhlyhalf, according to a simplified equation for restingpotential given by Giese (11). Relatively non-ipolar

- 1.6

- 1.5

-1.4

-1.3 t- 10 %

-1.2 l

-I.I

-1.0

TIM0

26

2

i24 _

1i22

T .1

2000I I I I

1178

GREEN-PHYSICS OF CELL GROWTH IN NITELLA

223

0.1InL

....~ ~ ~ .. I. ," II

T, irnnr, IIUr yvi I\ I o0 o

@6 011

0-5 0 0 000 0

4-3

at

Time

100 200 300 400 500 600minFIG. 7. Course of growth response to a single period

of osmotic inhibition where the osmoticum is KCI. Thetime re(quired for resumption of growth is somewhatlonger than typical for other osmotica and the growthburst is somewhat reduced. Otherwise the response issimilar to uncharged osmotica.

solutes, even ethanol, can also lower the restingpotential. Because KCl and Polyethylene glycol,(a fat solvent) give a response similar to thatelicited by mannitol, it appears that the value of theresting potential may not be a highly significantfactor in the growth process. This could be con-

firmed by adapting the micro-manometer to serve

as a micro-electrode to monitor resting potentialconcurrently with pressure, but this modification hasnot yet been tried.

The well-known "wall loosening" properties ofpotassium are not evident in the comparison ofresponses, perhaps because our normal medium con-

tained sufficient KCl to saturate those wall com-

ponents responsible for the effect.In light of the similarity of response to various

added solutes, there is some justification in con-

cluding that the typical growth reactions reflect thecell's adjustment to a change in turgor per se ratherthan to various chemical and electrical properties ofthe osmotica. The adjustments, which tend to re-

store normal growth rate after shifts in turgor ineither direction, are made primarily in extensibility,not turgor.

The Directed Character of Expansion. In Nitellathe ratio of relative rate of increase in length to thatin diameter is normally about 4.5 (13). During thelargest growth burst observed (fig 6) changes indiameter were also measured. The ratio temporarilyfell to about 2.0, so it appears that high Exg correlateswith reduced physical anisotropy of yield in thewall. That extension occurring far above the mini-mum yield stress should show reduced anisotropywas predicted in the model for Nitella wall growthdeveloped by Probine and Barber (28).

Inhibitiont of Helical Growth. The extension ofthe Nitella cell is normally accompanied by a pro-nounced rotation of the top of the cell relative to itsbase (12). In the present experiments a smallweight (0.07 g when submerged) was tied to thebase of the plant to keep it vertical. Because thecell wras gripped at its top, this tension spanned theobserved cell. This vertical tension, small com-pared to the 3.5 g exerted by turgor on the end wallsof the growing cell, virtually eliminated the rota-tional component. This facilitated the following ofindividual marks. That such a small weight iseffective is remarkable because it acts at a smallangle (about 150) to the direction of helical growth.One of the osmotica tested, 1,2 di-methoxy ethane,when present at 0.1 m, virtually eliminated twistingin unclamped cells.

Discussion

The results permit preliminary examination ofthe working relationship: relative growth rate =extensibility X turgor, as set forth in equation (I).The equation implies that shifts in turgor shouldlead to proportional shifts in growth rate. Thisclearly does not happen because the cell responds toa small drop in turgor by cessation of growth thena gradual resumption of the normal rate. This andother behavior shows that the variables in equation(I) are interdependent. The observed behavior couldbe the result of complexity in either extensibility orturgor (or both). Fortunately, the variation inturgor, beyond that brought on by changes in tonicityof the external medium, is relatively small. A minorincrease in turgor (due to continued solute uptakeor production) can be seen during the resumption ofgrowth after a turgor drop (fig 6). A small de-crease in turgor due to rapid sap dilution during agrowth burst probably contributes to the decline tonormal growth rate. These changes, however, aresmall compared to the concurrent ones in extensi-bility. It will develop that the value of the exten-sibilitv term is a function of turgor, growth rate,and time.

Cell Extensibility anid the Cell Wall. Extensi-bilitv of a cell has been shown by Lockhart (21, 22)to be a function of several variables. It is inverselyproportional to wall thickness, and proportional tocell radius and cell wall extensibility. WTall thick-ness in Nitella is known to increase comparativelyslowly (40 %/day) during mechanical inhibition ofgrowth (14). Cell extensibility may change severalfold in an hour. Since cell extensibility increasesduring inhibition in the present experiments, wallthickness change is actually in the wrong directionto explain the extensibility changes. It is thereforenot considered a primary factor. Cell radius can bemeasured and its total variation over 2 days (in-crease of about 15 %) is very small compared tochanges in cell extensibility. It is concluded that

1179

PLANT PHYSIOLOGY

cell extensibility is primarily a fulnctionl of extensi-bility of the cell wall.

Two Stages of Growth Respontse to Turgor Shift.The first step in an effort to modify equation (I)to permit prediction of growth behavior is to lookfor broad characteristics common to all or almostall the responses observed. Study of the reaction ofthe grox-ing Nitella cell to sudden shifts in turgor(fig 3, 4. 5, 6, 7) reveals that its growtlh rate can becharacterized by 2 stages of response. The immedi-ate change in rate following a shift in turgor ineither direction appears as an exaggeration of theeffect that would be predicted by equation (I).That is, a moderate (25 %) drop in turgor leads tomuch larger (100 %) drop in growth rate; a mod-erate increase in turgor (33 %) in a growing cell(fig 4, 5, imiddle) temporarily leads to a muchgreater (up to several hundred percent) increase ingrowtl rate. This rapid response is followed by aslowN-er comipensatory adjustment wNhich tends to re-store the normal rate: normal growtlh mav beresumled after being stopped by reduced turgor; thehighi rates of growth seen immediately after anupward shift in turgor are gradually restored tonormiial (fig 8A).

Somew-hat similar rate changes, but witlhout raterecovery at reduced turgor, are found in non auxin-treated Aveiia coleoptile sections temporarily ex-posed to osmoticum (29). A transient reduction inrate, a return to normal, and a brief recovery periodat a rapid rate are associated with the temporaryexposure of growing Phycomnyces sporangiophores tolongitudiinal stretch (9). The same general kineticsare founcd upon exposure of a light-grown sporangio-phore to a period of darkness (3). This sort ofrate patterin, seen here in the response of Nitella totransitory osmotic inhibition, can be analyzed interm.s of turgor and extensibility.

A Prelimiiiary, Model. The immediate rate re-sponlse (either decrease or increase) seen uponchange in turgor could be based on a single relation-ship betwseen EX.r (or rate) and turgor wlhiclh has athreslhold value and, above this, has a positive slope.See figture 8B. The slow- response cotuld involve atransposition of this relation. Durinig the tvpicalexxperimental cycle the rapid and slow responsesalterinate. A normally growing cell w-ould be atpositioIn 1 in figure 8A, B, With a turgor of 5 atm.Upon a rapid loss of turgor to 3 atn position 2)growth Nould stop because this turgor is below thethreslhold. One assumption sufficient to give re-s'ored growth at reduced turgor involves a lateraldisplacement of the original curve. to the left. untilthe normlal rate is resumed (position 3 ). This isonie aspect of the slow response. The sudden returnto 5 atm of turgor would give, temlporarilv. a veryhiglh rate of growth (position 4) aid theil the slowVresponise w\ould shift the curve to the riglht tintilnor-miial rate -and extensibility wvere restor-ed (posi-tioiin s).

The major aspects of this scllemiie that seemii

N ITELLA

LENGTH 5

A.4

,,/-LOW TURGOR

TIME

TURGOR TURGOR

FIG. 8. A diagram to il,lustrate 2 types of grom-,thresponse and their possible origin in different kinds of"wall softening." As a simplification, rate is consideredroughly proportional to extensibility, Exg. A shows thetypical sequence of length change in Nitella through atemporary reduction in turgor. This is accounted for inthe model B where ordinary growth finds Exr near thebase of an arbitrarily linear curve relating Exg to turgor(postion 1). A drop in turgor, position 2, reduces EX,and rate to zero. A shifting of the original curve to theleft supports normal growth at position 3. Restorationof the original turgor causes very high extensibility andrate (position 4). A shift of the curve to its originalposition ultimately restores the normal growth rate (po-sition 5). In C a transient stimulation of growth inhigher plants by auxin is diagrammed. Its possible ex-planation, in terms of Ex, and turgor, as inferred fromthe literature, is shown in D. The mechanism here is achange in slope of the curve without shifting thethreshold. Note that the variation of rate and Ex, isidentical along the dashed lines in B and D but theunderlying mechaniislm of rate change would be differentThe present method has the potential of describing therelation between Erx and turgor pressure through variousgrowth responses.

Note added in proof: The wsork of Evans (Plh.D.Thesis, University of California, Santa Cruz, 1967)shows that auxin-grown Avena sections have a solutecontent of 8.2 atm compared to 10.1 atm for n-on-treatedmaterial. The thresholid turgor for growth, hoxN ever,was 3.4 atm and 7.8 atm respectively. Because tlhe treat-ments were prolonged it is not known whether thisre(luction in imiinimiium yield stress (and an apparent lateralslhifting of the extensibilitv-zs-turgor relation) is theimimediate action of IAA on wall properties or is theresult of considerable elongation in auxin. Only in thelatter case could diagrams C and D apply to Avenacoleoptiles. The 2 model growth responises conitrastedhere never-the-less illustrate the potential utilitv of invivo anaIN-sis of the extensibility-turgor relation in thestudy of x-wall softeniing.

establishe-d are the disproportionate shift in rate uponchange in turgol- (in both dlirectionls) anid theresulmption of growth at low turgor. Data areinsufficient to show that relationslhip between ELx.,or rate) and turgor is of any specific forlmi (suIch1

as the linear onie in the diagram) and that this formlis unchanged as the thrleshold value is displaced

1180

GREEN-PHYSICS OF CELL GROW'TH IN- NITELLA

along the turgor axis. This can be tested by break-ing up the large turgor shifts into smiall steps. Thevarious components of this tentative model can beexamined for their generality and, where possible,for their physical or metabolic basis.

a) A Threshold Value of Turgor for Growth andExtensibility. All osmotica tested show that inNitella a small drop in turgor leads to a cessation ofgrowth and thus a reduction of Ex, to zero. Asseen at the left in figure 4 a drop in turgor ofabout 0.4 atm is sufficient. Since turgor was 4 atmthe threshold value is roughly 90 % of full turgor.A threshold concentration (above the plasmolvticvalue) of osmoticum sufficient to stop growth, hasoften been reported for other material. Cleland (4)found that 0.25 M mannitol inhibited almost allgrowth in Avena coleoptile sections while 0.12 Minhibited almost all of the auxin-stimulated com-ponent of growth. Ray and Ruesink (32) showedthat mannitol of 0.2 to 0.3 mI stopped growth intissues whose cell contents were about 0.4 osmolal.Bennet-Clark (2) found that KCl at a concentrationof about 5.4 atm was sufficient to halt growth inmaterial with an internal solute concentration ofabout 13 atm. While more dilute solutions maymomentarily halt growth, this is not pertinent be-cause the effect is probably a rapid elastic responsewhich briefly compensates the extension accom-plished by growth.

In a study of the gradual "creep" of excisedNitella cell wall strips Probine and Preston (27)found a threshold for extension at about 35 % ofthe stress normally experienced by the wall in. vivo.Our data indicate a considerablv higher threshold.It would be interesting to know if the in vivo shiftin minimum yield stress would be reflected inthe properties of wall strips from cells killed beforeand after adjustment to osmotic inhibition.

b) Extensibility Above tihe Threshold. The invivo quantitative relation between increase in turgorand increase in Exg, above the threshold, cannot bedescribed by the data presently available. Upwardshifts in turgor of varying amount, all starting froma given low turgor at which growtlh was occurring,could be used to discover the relation between in-creased turgor and increased extensibility, from thatgiven turgor. Perhaps the curves would be similarfor various turgors. At present no in vivo data isavailable. Probine and Preston, however, (27)have studied the mechanical properties of excisedlongitudinal strips of Nitella cell wall and foundthat, after a variable amount of "set" followingapplication of a weight, the strips slowly yielded tothe weight. Their data correlated well qualitativelywith the normal growth process in that strips fromrapidly growing cells crept relatively rapidly. Inabsolute terms the strips yielded more rapidly to theapplied stress than they had been yielding to theequivalent longitudinal component of turgor stress.[E.g., a 9 % yield at normal stress over 99 minwas observed in a strip from cell that had grown

9.5 % over 1 day (1,440 min))]. The differencemay reflect the fact that the strip could decrease itslateral dimiiension while the intact growing wallcontinuously increases its lateral dimension. A rolefor creep in the normal growth process was alsosupported by their finding that transverse stripsshowed negligible creep, correlating with the smallincrease in this direction in zivo.

Their data were scattered above the thresholdbut a plot of percent extension (ordinate) vs. loadgave curves which rose roughly linearly. As alreadynoted the threshold value was considerably lowerthan that seen in zivo. Such a relation, if reversiblyshifted as in figure 8B, could give the typical re-sponse (fig 8A). Their data were later used in atheoretical model for Nitella wall growth that gavea linear increase in rate of movement of individualmicrofibrils, with stress, above a threshold stress(28).

The rapid "exaggerating" growth response to ashift in turgor in Nitella appears to have a counter-part in Avenia coleoptile tissue. In auxin grownmaterial, above a certain value for turgor, a shift inturgor will vield a relatively larger shift in growthrate. E.q., a 14 % increase in apparent turgor(8.4-9.6 atm) gives a 39 % increase in rate over4 hours as calculated from data of Cleland (4).Exg would also increase over this range. Unlikethe data from NTitella there is growth below thebreak in the curve. This may reflect osmoregulationduring the 4 hours. In osmotic inhibition of coleop-tile section growth there appears to be little growthrecovery bv lowering of the yield threshold of thewall. In aLixin-free medium, however. some actionon the wall during inhibition is indicated bv therapid elongation that occurs upon restoration of fullturgor (29). Because the yield point does not seemto be lowered, this softening may take the form seenin figure 8D. Here the increased extensibilitywould be due to a change in slope of the E.r,-turgorrelation rather than to a shift in the curve withconstant slope as in figure 8B. In Avena the elasticcomponent of elongation is greater than in Nitella;it would be included in Ex,

c) MlIovemnen,.t of the Yield 7Threshold. lMovementof mininmim yield stress to lower values of turgoris a widespread process. It undoubtedly occurs inmanv cases of initiation of expansion such as thebranching of hyphae, rhizoid formation in the Ftucutszygote, etc. Presumably the lowering involves achemical breaking of cross-links in the wall so as toconcentrate stress on the remaining links, causingthem to give. If this process is reversible, a reduc-tion in the concentration of the lytic agent wouldraise the yield value. An alternate mlechaniislmi isavailable, however, for the raising of the vield value.Higher plant tissues (and many inert materials)show "strain hardening", an increase in yield valuecoupled to the amount of stretch the material hasundergone (5, 24). The metabolic nature of thelowering and the physical (or metabolic) nature of

1 181

PLANT PHYSIOLOGY

the raising of the yvield poinlt is not known forNitella. A rough similarity in the durationi of thereduction and raising of the vield point in figure 3suggests both might be metabolic.

Few Ihiglher plant tissue display yield pointlowering, as evidenced in resumed growth at reducedturgor. In Azrena, full restoration of growth rateat reduced tiirgor appears not to occur. Aftercomplete cessation, the amount of subsequent elonga-tion1 ox-er several hours is not much more than arecovery of elastic shrinkage (2, 26). The smallanmoutnt of rate recover- after growtth cessation,weakly enhanced b- auxin at 5 ppm but not at 1 ppm

(2 )- nma- be due to osmoregulation ratlher thani to a

change in wx-all properties because deplasmolysis isobserved in strongly' inhibited sections (26 ). Su-crose p)ronlotes increase in internal solutte contentand recov-erx-.

Recovery- of the full normal growth rate in a

solutioni of osmoticum (0.49 M) stronlg eInoughl toinitially halt growtlh has been reported for potato byThimnanni et al. (their table I) (36). This recovery

onlx- took place in the presence of auxin and ap-

peared to require 2 davs. Data on internal soluteconcentratioin wvere Inot giveIn so it is not knowxn ifrecovery was due to recovery of turgor and IAA-increased extensibility or a lowering of a thresholdfor extensibility (or a combination).

Twe,o .lodes of Wall Softening. Oile caIn recog-

nize, ex-en at the present abstract level of analysis,2 extremle kinds of "softening." In terms of growth

rate and turgor alone a shift from position 1 to

positioIn 4 in figure 8B would be indistinguishablefrom the shift from position 1 to 2 in figure 8D.The basis of the rate change in terms of the whole

Ex-r-turgor relation could be quite different. Com-binations of these 2 extremes can readily be imag-ined.

Gro.ewth Physics in Higher Planit Tisstues. Incomparison to the situation in Nitella the phy-sicalproperties of higher plant tissues, manifested intheir resistanice to imposed stretch, appear less ade-quate to explain, in themselves, the it vivo responses

to sli fts in turgor. There are major mechanicaldifferences between growth and imposed stretch,

especially in killed tissue. A decrease in -olumeand surface area may accompany- stretclh (24). Atany esent, the high threshold of turgor needed forrapid growth inl Vivo is not matched by a highmniimum ield stress in the artificiallN- stretchedtissue (25). The minimum yield force for increasein area in nearly plasmolysed mung beain is onl-about 5 grams (wvith IAA) to about 30 grams

(xwithout previous incubation in IAA ). The hypo-cotyl's longitudinal component of norimial ttirgor was

calculated to be 235 g (24). Furthler, the iwi rivo

relation between rate and turgor, wlhiclh might beexpected to correspond to a straini-rate v's. stress

relation found in imposed stretch, does not obtain.Strain-rate and stress are almost independeint.Starting at a rate 15 X the normal onie for .4Aenia,

an increase in rate of imposed extension of 100-foldis accompanied by rouglhly a 15 % decrease in theyielding tendency of coleoptile tissue not previouslygrown in auxin (6. fig 8). WNith previous growtlhin auxin the decrease is roughly 25 %. Lockhart(23) found onix small viscous properties in mungbeani. A 5 X increase in rate of stretch gave onlya 50 % inicrease in the Nwork of deformation. Tem-perature effects wrere minimal. The failure to findprominent viscous properties in stretch tissue haslead Cleland (personial commun.) to the view thatgrowth occurs in a series of pulses statisticallyspread throughout the wall.

A pulse is started bv the metabolic lowering ofthe yield threslhold of the wall. \NVhenl this fallsbelowv the existing stresses generated by turgor, thexvall yields. The process of yielding however iscoupled to an increase in the yield threshold, theplheiionoenon of straini-lhardeninig. This ultimatelyraises the threslhold above existing stresses to endthe pulse. This process is called strain-hardeningplastic defornmatioin (SHPD) (5, 6). The action ofauxin, which could potentially increase rate in manyways (c.g. increasing the frequenicy of pulses, rateof lowering of yield threshold. etc.), may be tochange the coupling between extension (not rate ofextension) and increase in the vield threshold of thew all. In stretched tissues it is found that thiscoupling is changed by auxin treatment so as togive more extension per unit increase in the yieldthreshlold. Eveen below its threshold value forgrowtth, increased turgor promotes the increase incomllpliance brought oIn by incubation in auxin (7).The present method cannot distinguish betweenviscous flow and either SHPD or a chemorheologicalmode of wall yielding (29, 31). The major com-ponent of the pulse growth mechanism that is ob-viously present in Nitella is a capacity to lower theyield threshold. This is seen in the resumption ofgrowth at reduced turgor, a phenomenon not promi-nent in Avenia. In the coleoptile it is thereforeassumed that yield point lowering can occur onlyabove a very high threshold value of turgor (Cleland,personal commun.).

In summary, there appears to be a high turgorthreshold for growth and Eyg in many plant systems,including Nitella. The physical nature of yieldingabove this threslhold is not clear but stretchingexperiments on Nitella cell walls indicate it couldbe a viscous process while stretch studies on higherplant tissues find little viscosity and inappropriatelysmiall auxini effects on it. The prominent auxineffect in stretch experiments is a reduction in strain-hardening, a process essentially- independent of rate.To incorporate strain-hardening as a rate limitingstep int zizo a pulsed metabolic lowering of thewall's yield threshold during pulses of growth mustbe assumed. This lowering is, curiously, a strikingfeature of Nitella's slow in vizo response to reducedturgor but it is not notewvorthy in the response ofgrowing higher plant tisstues to reduced turgor. It

1182

GREEN-PHYSICS OF CELL GROWTH IN NITELLA

is suggested that further in vivo characterization ofthe extensibility-turgor relationship, in the manner

diagrammed in figure 8, can resolve "wall softening"into sub-processes and thereby promote understand-ing of the growth process in terms of structure andmetabolism.

Acknowledgment

Conceptual and technical advice from Dr. Peter M.Ray (University of California, Santa Cruz), Dr. AlbertList (Drexel Institute of Technology, Philadelphia), andDr. Gordon Ellis (University of Pennsvlvania), wasincorporated into the present project. The technicalassistance of Mrs. Shirley Serota, Mr. James Buggy,and Mr. Edward Jahn is gratefully acknowledged.

Literature Cited

1. ARE-NS, K. 1939. Bestimmung des Turgordruckesan einer Einzelzelle mit dem Manometer. Planta30: 113-17.

2. BENNET-CLARK, T. A. 1956. Salt accumulationand mode of action of auxin. A preliminary hy-potthesis. In: Chemistry and Mode of Action ofPlant Growth Substances. R. L. Wain and F.Wightman, eds. Butterworth and Company, Lon-don.

3. CASTLE, E. S. 1966. Light responses of Phvcomy-ces. Science 154: 1416-20.

4. CLELAND, R. 1959. Effect of osmotic concentra-tion on auxin-action and on irreversible and re-

versible expansion of the Avena coleoptile. Physiol.Plantarum 12: 809-25.

5. CLELAND, R. 1967. Extensibility of isolated cellwalls: measurement and changes during cell elon-gation. Planta 74: 197-209.

6. CLELAND, R. 1967. Auxin and the mechanicalproperties of the cell wall. Ann. N. Y. Acad. Sci.144: 3-18.

7. CLELAND, R. 1967. A dual role of turgor pressure

in auxin-induced cell elongation in Avena coleop-tiles. Planta 77: 182-91.

8. DAINTY, J. 1963. The polar permeability of plantcell membranes to water. Protoplasma 57: 220-28.

9. DENNISON, D. S. AND C. ROTH. 1967. Phycomycessporangiophores: fungal stretch receptors. Science156: 1386-88.

10. FORSBERG, C. 1965. Axenic culture of Clhara glob-ularis Thuill. and Chara zevlanica Wild. LifeSciences 4: 225-26.

11. GIESE, A. C. 1962. Cell Physiology. W. B. Saun-ders Company, Philadelphia, Pennsylvania.

12. GREEN, P. B. 1954. The spiral growth pattern ofthe cell wall in Nitella axillaris. Am. J. Botany41: 403-09.

13. GREEN, P. B. 1963. Cell walls and the geometryof plant growth. In: Meristems and Differentiation.Brookhaven Symp. Biol. 16: 203-17.

14. GREEN, P. B. 1963. On mechanisms of elongation.In: Cytodifferentiation and Macromolecular Syn-thesis. M. Locke, ed. Academic Press, New York.

15. GREEN, P. B. 1965. Anion-exchange resin spheresas marking material for wet cell surfaces. Expti.Cell Res. 40: 195-96.

16. GRFEN, P. B. AND F. W. STANTON. 1967. Turgorpressure: direct manometric measurement in singlecells of Nitella. Science 155: 1675-76.

17. GUTKNECHT, J. 1968. Salt transport in Valonia:inhibition of potassium uptake by small hydrostaticpressure. Science 160: 68-70.

18. KAMIYA, N., M. TAZAWA, AND T. TAKATA. 1963.The relation of turgor pressure to cell volume inNl'itella with special reference to mechanical prop-erties of the cell wall. Protoplasma 57: 501-21.

19. KISHIMorO, U. 1959. Electrical characteristics ofChara corallina. Ann. Rep. Sci. Works Fac. Sci.Osaka Univ. 7: 115-46.

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