Plant Physiol. (1970) 45, 133-138

Active and Passive Transport of Potassium in Cells of ExcisedPea Epicotyls1

Received for publication June 24, 1969

A. E. S. MACKLON2 AND N. HIGINBOTHAMDepartment of Botany, Washington State University, Piullman, Washington 99163

ABSTRACT

The Ussing-Theorell equation, which provides a funda-mental test for the independent passive movement of ionsunder conditions of nonequilibrium, has been used to assessthe active and passive components of K+ uptake by segmentsof pea epicotyl (Pisum sativum L. cultivar Alaska), incu-bated for 24 hours in both 1-fold and 10-fold concentrationsof a complete nutrient solution. Mleasurements of the ratesat which 41K diffused out of the segments provided data fromwhich were estimated the K+ content of, and the fluxes toand from, the nonfree space compartments, interpreted asbeing cytoplasm and vacuole. For this analysis the serialmodel of IacRobbie and Dainty and Pitman for thespatial arrangement of cell compartments was used. On thebasis of these values, and measurements of electrical poten-tial across the cell membranes, the vacuolar K+ concentra-tion was found to be fairly close to that expected as a resultof passive diffusion between the cytoplasm and vacuoleprovided that no potential exists across the tonoplast.Cytoplasmic K+ concentration, however, was much too highin both treatments to be accounted for in passive terms. Itwas concluded, therefore, that, on the basis of the model,the high ratio of influx to efflux was maintained in the cellsby an active K+ pump located at the plasmalemma. There issome reason to question the applicability of this model forflux analysis to the conditions of high net influx as en-countered here; nonetheless, it provides a first approach toan over-all flux analysis in pea stem tissue.

The most straightforward situation in which to assess the sig-nificance of cell electropotential, E (=PD), in determining thetransmembrane concentration gradient of an ion is one in whichthe cells under study are at ionic equilibrium. In these circum-stances the relationship between E and the concentration gradientof an ion resulting from passive diffusion is described by theNernst equation:

E =-ln ]zjF Cj' (1)

where E is the electrical potential difference between the inside

1 This work was supported by National Science Foundation GrantGB 5117X and by funds provided for biological and medical researchby the State of Washington Initiative Measure 171.

2 On leave of absence (September, 1966, to September, 1967) fromthe Macaulay Institute for Soil Research, Aberdeen, Scotland.

and outside of the cell; zj is the valance of ion j; R is the gas con-stant; T, the absolute temperature; and F, the faraday. Cjo andCji are the external and internal concentrations of the ionj.

In a study of the mineral ion contents and cell transmembraneelectrical potentials of pea and oat seedlings, Higinbotham et al.(6) found little net change in the content of most ions during theincubation of excised root segments in the same nutrient solutionas that in which the plants had been grown. Thus, for these tissues,a comparison between observed ionic concentration gradientsand the gradients predicted by the Nernst equation, on the basisof observed PD, gave a good indication of how far passive diffu-sion accounted for the ionic distribution observed.

In contrast to root segments, segments of shoot tissue fromthese seedlings were found to be far removed from ionic equilib-rium when immersed in the nutrient solution, there being con-siderable uptake of several ions. This is most notable for K+ con-tent in pea epicotyl segments, the time course of which has beenfurther examined by Macklon and Higinbotham (8). In an ac-cumulating system such as this, the Nernst equation alone is nota sufficient criterion for evaluating the active or passive nature ofion transport. Where there is a net flux across a membrane, abetter test for the independent passive movement of an ion isgiven by the following expression, deduced by both Ussing (16)and Teorell (15):

Ji CjO A)joJo C.z exp (zjFEIRT) H/i (2)

where Ji is the flux of the ion j from outside to inside the mem-brane and Jo is the flux from inside to outside the membrane;Aji is the electrochemical activity of ion j outside (where E, byconvention, is zero) and uji (= Cji exp [zj FE/RT]) is the electro-chemical activity inside.

In order to test whether or not an ion moves in accord with theUssing flux ratio equation in plant cells, it is necessary to have in-formation on the fluxes, concentration gradients, and electropo-tential gradients across both the plasmalemma and tonoplast.

In this paper we present data from such an analysis ofK+ in peaepicotyls in complete nutrient solutions. The compartmentalanalysis scheme of MacRobbie and Dainty (10), Pitman (11),MacRobbie (9), and Cram (1) was utilized. The results suggestthat another model may be required for a system such as thatencountered here in which high net uptake occurs.

MATERIALS AND METHODSPea seedlings (Pisum sativum L. cultivar Alaska) were grown,

and samples of etiolated epicotyl segments 1 cm long (except asnoted) were taken in the manner described in an earlier paper(8).The nutrient solution used for growing the seedlings and incu-

bating the segments, and for the efflux experiments, was of thefollowing composition in mM: KCI, 1.0; Ca(NO3)2, 1.0; MgSO4,

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MACKLON AND HIGINBOTHAM

0.25; NaH2PO4, 0.904; Na2HPO4, 0.048; pH between 5.5 and5.8. Used at this concentration, the solution is referred to as 1 X.Experiments were also performed with nutrient solutions of 10times this strength (10X).

Samples of segments, amounting to about 0.6 g, which were tobe used for efflux measurements, were pretreated in nutrient solu-tion for 12 hr and then transferred to a similar solution contain-ing the radioisotope 4K for a 12-hr loading period. Parallel sam-ples were used to follow influx of labeled K+ at intervals up to 24hr, and these samples were also used for chemical assay of K+.Details of the assay procedures are given in a previous paper (8).All experiments were carried out in a constant temperature roomat 200.At the end of the 12-hr tracer-loading period, the samples to be

used for efflux measurements were drained and placed in a cylin-drical filter tube having a chamber 29 mm in diameter by 70 mmhigh, fitted with a drainage tap 8 mm in diameter. The tubes were

c 6.080 *

CC

E._,0cr_

6.0750

o 0

oFoI-0J 6.070

0 2 4 6 8 l0Time in Hours

FIG. 1 (left). Time course of the reduction in the total amount of42K in a sample of segments during washing in unlabeled 1X solution.Data for tissue grown and incubated in 1 X solution.

4.5

0

E0.

3cco

0,, 4.0 -

CP

0'

CP0a3.5\

o 1 2 3

Time in Hours

estimated to be in cytoplasm, free space and cut cells of a sample dur-ing washing in unlabeled 1 X solution.

E

) r0. Wall a Surface Film

0 ;;0 Surface Film Only

14.0

3.0

C

E

0)

2.0

0

n ~ ~~~6lo0 15 20

Time in M inutes

FIG. 3. Time course of the reduction in the amount of 42K estimatedto be in free wall space plus surface film (including cut cells), and inthe surface Mim only of a sample during washing in unlabeled 1Xsolution.

mounted on a reciprocating shaker to simulate as closely aspossible the conditions of incubation used in the uptake studies(8). A small polyethylene partition was inserted vertically in theneck of each tube to prevent escape of the segments during drain-ing. Each sample was then immersed in 10-ml aliquots of the ap-propriate unlabeled nutrient solution for various periods of timepermitting efflux of tracer. Each washing aliquot was collected ina beaker and then evaporated to dryness in a stainless steelplanchet on a hotplate at 80° prior to counting. Initially solutionchanges were frequent, but thereafter the frequency was pro-gressively reduced (see the time scale and experimental points inFigs. I to 3) to obtain adequate activity in each wash-out sample.

Efflux measurements were also made using freshly cut tissuefrom intact seedlings which had been preloaded for 16 hr with42K by flushing the vermiculite growing medium with labeled nu-trient solution.

RESULTS AND DISCUSSION

Fitsof Compartments and Fluxes. Efflux of labeled K+from epicotyl segments was measured over a period of about 10hr using duplicate samples of tissue grown and incubated in eachstrength of nutrient solution (1 X and IO0X). From counts of theactivity remaining in the tissue at the end of the elution and fromthe activity in each of the washings an efflux curve for each samplewas constructed, as in Figure 1. This can be considered as a com-pound curve, made up of first order rate losses from each of sev-eral compartments in the tissue; it is amenable to the method ofanalysis used by others (1, 2, 9-11). This yields a series of straightlines (from semilogarithmic plots) each characteristic of a particu-lar phase. The contribution ofthe slowest compartment, asssumedhere to be the vacuole, to the efflux is indicated by the final, linearpart of the curve in Figure 1. The line resulting has a slope whichis the rate constant, k,, (In cpm/time), for loss from the vacuole;the intercept at zero time (start of efflux) gives the amount ofradioactivity in the vacuole. Subtraction of the vacuolar com-ponent from the activity of the total tissue at each time intervalyields the efflux curve representing loss from compartments otherthan the vacuole, with the final linear phase being attributed tothe cytoplasm (Fig. 2). Extrapolation of this line to zero time givesan intercept which is the amount of activity initially in the cyto-plasm: its slove is the loss constant from the cytoplasm, kc

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ACTIVE AND PASSIVE TRANSPORT OFK1

Table I. Antalysis of Efflux from Immersed Epicotyl Segments and Apparent Influx to VacuoleSegments were immersed for 24 hr (12 hr of pretreatment in nonlabeled nutrient solution followed by 12 hr of loading in 42K-labeled

solution, then washed out in aliquots of nonlabeled nutrient solution for a total period of over 10 hrs [see text]).

SampleCompartment k ~~~~~~~~~~~~~~~SpecificRadio- ESample Compartmentt k t peiil.Rdi >ppatrent Equilibration Apparent Influxsactivity' Conteqnt bato ApretInlx

min?F' min cpm 'Aeq K+ ueq K+/g fresh wt N peq K+/g min1 (iX) Vacuole 1.56 X 10-5 737 X 60 22,900 51.6 33.7 2.42 X 10-2

Cytoplasm 1.00 X 10-2 69 68,000 0.108 100Free space 2.74 X 10-1 2.53 68,000 0.107 100 ...

Surface film 2.12 0.33 68,000 0.273 100 ...

2 (iX) Vacuole 1.63 X 10-1 711 X 60 i 24,900 51.5 36.6 2.62 X 10-2Cytoplasm 0.88 X 10-1 79 68,000 0.100 100Free space 2.08 X 10-' 3.34 68,000 0.131 100 ...

Surface film 1.84 0.38 68,000 0.339 100 ...

3 (IOX) Vacuole 1.04 X 107 5 1114 X 60 8,960 70.7 32.5 3.19 X 10-2Cytoplasm 1.02 X 10-2 68 27,600 0.091 100 ...

Free space 1.14 X 10-1 6.09 27,600 0.201 100Surface film 1.27 0.55 27,600 1.199 100 ...

4 (lOX) Vacuole 1.01 X 10-5 1140 X 60 9,100 70.7 33.0 3.24 X 10-2Cytoplasm 1.13 X 10-2 61 27,600 0.102 100 ...

Free space 1.15 X 10-1 6.02 27,600 0.257 100 ...

Surface film 1.28 0.54 27,600 1.156 100 ..

1 At an arbitrary zero time, here designated at the start of incubation in labeled solution.2 Estimated from the amount of 42K accumulated in the vacuole

time).

Further analysis in this manner reveals two additional phases(Fig. 3) which we consider to relate to the free space-possiblythe Donnan space-in the tissue, and finally, the surface film ofsolution on the segments (perhaps including the water-free space).The interpretation which is put on such flux data depends upon

the spatial relationships which are considered to exist between thevarious cell compartments. They may be arranged in the series:wall, cytoplasm, and vacuole, so that ions moving between theoutside solution and the vacuole necessarily traverse the cyto-plasm. Alternatively, the cytoplasm and vacuole may each be ac-cessible directly to the free space, in a parallel arrangement. Theserial model is the one generally accepted for giant algal cells (2,9, 10), and that this model is relevant to higher plant cells hasbeen demonstrated convincingly by Pitman (11) with beet roottissue and Cram (1) with carrot root tissue. It is the serial model,therefore, which we have adopted as the basis for the interpreta-tion of the present data.From the graphical analysis of the results (Figs. 1-3) the efflux

rate constant (k) and the half-time for exchange (t½) can be esti-mated for each phase. In calculating the apparent amount of K+in each compartment at the start of the washing procedure, it isassumed that the cytoplasm and free space reach a steady state ofspecific activity well before the end of the 12-hr incubation in thelabeling solution and that the "apparent" amount of K+ in thecompartment can in each case be taken as equal to the counts perminute at the intercept divided by the specific activity of the ex-ternal solution. The amount of K+ in the vacuole, Qw, is thenrepresented by the difference between total K+ estimated chemi-cally on parallel samples and the sum ofK+ in the other compart-ments estimated by specific radioactivity. Finally, apparent influx,I, /t.P across the tonoplast is estimated from the amount of traceraccumulated in the vacuole during the 12-hr loading period, inwhich net influx is linear (8). The experimental values for eachcompartment are given in Table I.

In general, the results shown in Figures 1 to 3 and Table Iagree with similar wash-out data on other plants (10, 11) and areconsistent with the concept that ions traverse compartments inthe series: wall, cytoplasm, and vacuole. The rate constants forloss from each of these compartments show sharp differences from

(apparent content X fractional equilibration divided by the uptake

Table II. Real Values of K+ Iniflux, Efflux, and Content for Cyto-plasm and Vacuole Estimated from Serial Compartmental Model(1, 9, 11) from Apparent Values (Table I) Measured on Pea Epi-cotyl Segments

Sample Extenal Cell Compartment Jin' Jou 1 KR4 ContentSolution matel

pIeqig fresh wm1 IX Cytoplasm 25.3 1.8 4.3

Vacuole 40.8 17.3 47.42 1 x Cytoplasm 27.0 1.6 5.8

Vacuole 48.2 22.8 45.53 lOX Cytoplasm 32.8 1.6 5.4

Vacuole 55.1 23.9 65.24 lox Cytoplasm 33.6 1.8 4.8

Vacuole 51.2 19.4 66.0

X Flux in units of 1l-i3 eq/(g, fresh wt, X min).

one another, thus providing a reasonable basis for such a graphi-cal analysis.The efflux and content values in Table I are apparent values,

i.e., values not corrected for concurrent opposing fluxes. Theyconsiderably underestimate cytoplasmic content in particular,since, in basing them on data for the appearance of tracer in thewashing medium, no account is taken of the concomitant transferof ions between the cytoplasm and the vacuole. Nevertheless,Table I contains all the data required to estimate real values forthe fluxes and for K+ content of cytoplasm and vacuole. Theseare given in Table II. For the derivation of the equations per-mitting these calculations, the articles of MacRobbie (9), Mac-Robbie and Dainty (10), Cram (1), and Pitman (11) should beconsulted. The equations are (9):

dQc J= - (JCV + Jco) * + Jrc *dt Q(3)

Qc*d Joc- (Jcr + Jco) _Sc +Jvc * Sdt

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MACKLON AND HIGINBOTHAM

where Q* is the amount of isotope in the compartment as desig-nated by the subscript; likewise, Q is the amount of the stablespecies; o, c, and v designate, respectively, the outer solution, cyto-plasm, and vacuole; t is time; J is the ion flux in the direction in-dicated by the subscripts; S, is the specific activity in the cyto-plasm as a fraction of that outside; and S, is the specific activityin the vacuole as a fraction of that outside. Calculations of com-partmental amounts and fluxes may be made using the relation-ships given as follows:

Ji,, (for cytoplasm) = Joc = kIc +-Itlup

where kc is the loss rate constant for the second slowest phase be-lieved to be cytoplasmic; lI is the apparent content of this phase,i.e., the cpm at the intercept (at the start of efflux) divided by thespecific activity of the external solution; Iv /t,,p is the apparentinflux (tracer-labeled) to the vacuole (which, of course, must passthrough the cytoplasm).

Jout (of vacuole) = J, c = Joc kvQi

QV, the amount of K+ in the vacuole, is the amount determinedfor the total tissue less the amounts found in the cytoplasm andwalls at the start of efflux.

Jou.t (of cytoplasm) = Jco = kcIc + kvQv

where k,, is the loss constant of the slowest phase, the vacuole,and the other notations are as above. Here it is assumed that theK+ content is steady so that Joc -Jco Jc, - JL. Thus, Ji,,(for vacuole) = Jcv = Jgc + Jc -Jco .

Ic(Jco + JCQC =SCJCSc Jco

Sc, the specific activity (as a fraction of So) of the cytoplasm atthe start of efflux is J,c,'(Jc, + Jco). The estimates of K+ contentfound here for pea epicotyl cells (Table II) are reasonably close tothose found previously for red beet root tissue (11) and for barleyroots (12). However, estimates of K+ concentration in the cyto-plasm seem high relative to vacuolar concentration (Table V);they exceed the values reported for beet (11) and also the concen-trations in pea root cells measured by Etherton (3) with a K+-specific microelectrode.

Efflux of Freshly Cut Tissues. In a recent paper (8) we reportedthe occurrence of a lag phase in K+ uptake by freshly excised peaepicotyl segments. One possible explanation would be that duringthe lag period K+ efflux exceeds influx as reported for beet roottissue (14). Consequently an experiment was designed in whichintact seedlings were allowed to take up 4'K from nutrient solu-tion added to the vermiculite substrate and then epicotyl segmentswere excised for efflux measurements during the initial immersionperiod. The data are reported in Table III. Under these conditionsthe external concentration and specific activity in neither the sub-strate nor the wall space surrounding the absorbing protoplastswere known exactly; therefore, only the rate constant and half-times are given and amounts in each compartment and the fluxeswere not estimated. In addition, in this experiment the effect ofsegment length, 1 cm vs. 2 cm long, was tested.The efflux rate constants and half-times of exchange for vacuole

and cytoplasm in freshly cut tissue (Table III) indicate that effluxfrom these compartments is a little higher than from tissue incu-bated 24 hr. Examination of the efflux curve for each sampleshowed that the rate constant for efflux from the vacuole changedabout 5 hr after excision, and so two values (for zero time and 7hr) are shown in Table III. However, even the initial efflux wouldbe small compared with subsequent influx, and these data provide

Table III. Anialysis of Efflux from Epicotyl Segmenits Cut fromn 42K-labeled Seedlitigs

Sample Compartment k

inin-l t'l,1. 1-cm segments Vacuole (zero 10.44 X 10- 110 X

(I X) j time)Vacuole (7 hr) 6.85 X 10-5 169 XCvtr)nlq,m 7: in \v 1(-2 I I3%-y LUPIW5111

Free spaceCut cells

2. 2-cm segments(lX)

3. 1-cm segments(lOX)

4. 2-cm segments(lOX)

Vacuole (zerotime)

Vacuole (7 hr)CytoplasmFree spaceCut cells

Vacuole (zerotime)

Vacuole (7 hr)CytoplasmFree spaceCut cells

Vacuole (zerotime)

Vacuole (7 hr)CytoplasmFree spaceCut cells

'-.I1V A- IV -

2.04 X 10-12.34

60

60

3.40.30

6.36 X 10-5 181 X 60

4.51 X 10-5 256 X 602.69 X 10-2 262.11 X 10-' 3.31.86 0.37

3.99 X 10-1 290 X 60

2.57 X 10-s 449 X 602.14 X 10-2 321.97 X 10-1 3.52.17 0.32

3.19 X 10-5 362 X 60

1.93 X 10-s 1 597 X 602.08 X 10-2 331.95 X 10-1 3.62.27 0.31

additional evidence for the view that the lag in net K+ uptake byepicotyl segments, reported earlier (8), is the result of a delayedinflux and not an initially high efflux.The effect of segment length on efflux is not impressively large.

Although 1-cm segments have twice the area of cut surface pergram, the efflux rate constant does not show this magnitude ofdifference in loss rates from any compartment; in fact, the fastercompartments show little difference due to segment length. It canbe concluded that diffusion is not restricted to the cut surfacearea and that the length of segments-or distance of diffusionfrom innermost tissue-is not very significant in the isotope wash-out method of compartmental analysis.

Estimates of Compartment Volumes. Although the data ofTable II provide information on the amounts of K+ in the cyto-plasm and vacuole, they do not reveal concentrations without in-formation on the volumes of these compartments. Measurementswere made to provide some estimates of these volumes. Fromestimates of the relative volumes of cortex and vascular tissue itwas concluded previously (8) that experimental results from epi-cotyl segments reflect, predominantly, the behavior of the corticalparenchyma. Further examination of fresh hand-cut sections ofepicotyl segments was undertaken to establish the dimensions ofan average cortical cell and the relative volumes of cytoplasm andvacuole. It proved to be difficult to distinguish the cytoplasm inthese cells, which at this level in the epicotyl (more than 1.5 cmfrom the apex) are fully vacuolated and approaching the limits oftheir final extension. Even at a magnification of 1000 X, the cyto-plasm was of measurable thickness only where it enclosed thenucleus, which was in every instance appressed to the cell wall.There the cytoplasm appeared as a layer less than 1 ,u thick. Aminimum volume for the cytoplasm in fully vacuolated cells canbe approximated by measuring the mean volume of cytoplasm incells at the early stages of vacuolation (where the cytoplasm is

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ACTIVE AND PASSIVE TRANSPORT OFK1

easily seen) and calculating the percentage of the cell volume thatthis represents after final enlargement (Table IV). This figure is0.6%0 of the protoplast, and this would appear to set a lowermostlimit for cytoplasm volume (Table IV). As an upper limit to thecytoplasm volume, allowing for the probability of an increase inthe absolute volume of the cytoplasm during cell expansion, amean thickness of 0.5 ,u can be taken; this gives a value of 3.4%of the total protoplast. The limits arrived at in this way are shownin Table IV, in which other cell measurements are also presented.For the calculation of volumes, the cells were considered to ap-proximate the form of a right cylinder; 1 g, fresh weight, wastaken as 1 cm3; wall and air space were each estimated to consti-tute 5 of the volume and cut cells 3% of the volume. Thus 87%of the volume is occupied by protoplasts.

Fit to Ussing Flux Ratio Equation. Both in 1 X and 10 X solu-tion, cortical cells of pea epicotyl exhibit a considerable electro-potential difference, of negative polarity, between the bathingmedium and the vacuole. The available information in higherplants (4) indicates that most or all of this potential resides acrossthe plasmalemma, and that there is presently no clear evidencethat a significant potential difference occurs across the tonoplast.Thus, it is here assumed to be zero.

With the information on fluxes and amounts of ions in the cyto-plasm and vacuole (Table II) and the estimate of compartmentvolumes, together with data for electropotentials from previouswork (8), it is now possible to apply the Ussing flux ratioequation, equation 2, as a test for the independent passive move-ment of K+. Table V summarizes the results. The serial modelused describes the ions as moving from the external solutionacross the plasmalemma to the cytoplasm, then across the tono-plast to the vacuole. As may be seen in Table V, for each sample,in both concentrations of external solution, the electrochemicalactivity ratio between the outer solution and the cytoplasm ismuch smaller than the flux ratio; thus, the influx of K+ to thecytoplasm is against a strong energy gradient suggesting an activeinward transport at the plasmalemma. However, in the case of thecytoplasm to vacuole relationship the flux ratio approximates theelectrochemical activity ratio as predicted by the Ussing equationfor a passive diffusion process.The cytoplasmic K+ concentrations in Table V are those ob-

tained if the cytoplasmic volume is taken at its upper limit (3.4%of the protoplast). If the cytoplasmic volume were taken at itslower limit (0.6% of the protoplast, Table IV), much higher con-centration values would be obtained, but the general conclusionswould be unaltered. Active transport at the plasmalemma (against

Table IV. Dimensions of Cortical Parenchyma Cells in ThirdInternode Segmenits of Etiolated Epicotyls1

Fully Vacuo- Newly Vacue-Dimension lated Cells lated Cells

(Mean of 28)1 (Mean of 4)1

Cell length, mm 0.318 0.016Cell volume, mm3 (X 104) 8.99 ...

Protoplast volume, mm3 (X 104) 8.46 0.09Cytoplasm volume, mm3 (X 104) 0.29, 0.05Cytoplasm as % of protoplast 3.42 55Cytoplasm of newly vacuolated cell as 0.6 ...

% of protoplast after enlargementNo of intact cells per g of tissue 32,000 ...

Surface area of plasmalemma, cm2/g 707tissue

1 Segments, as used in experiments, taken 1.5 cm from apex ofseedlings grown 7 days. Newly vacuolated cells were observed insections taken from the apical hook.

2 Taking cytoplasm as a 0.5-is layer lining the cell wall.

Table V. Test of Ussing Flux Ratio Equation: Data from Experi-mentally Determined 42K Fluxes, Chemical Concentrations,

and Electropotentials in Pea Epicotyl Segments

Sample External Cnel' uin2Solution Compartment Joua Kin~

jieqiml mn

1 1X Cytoplasm 14.0 145 -128 1.13Vacuole 2.4 56 0 2.64

2 1 X Cytoplasm 16.9 193 -128 0.83Vacuole 2.1 54 0 3.64

3 lox Cytoplasm 20.5 180 -108 4.03Vacuole 2.3 78 0 2.34

4 lOX Cytoplasm 18.7 160 -108 4.53Vacuole 2.6 79 O° 2.04

1 Assuming cytoplasm occupies 3.0% of total tissue volume(=3.6% of protoplast) and vacuole occupies 84% of total tissuevolume (excluding air space).

2 From Macklon and Higinbotham (8).3 The electrochemical activity ratio across the plasmalemma.4 The electrochemical activity ratio across the tonoplast.

an even stronger energy gradient) would be implied, and passivediffusion would be sufficient to account for influx into the vacuole.The only additional indication would be the possibility of a Kefflux pump at the tonoplast effecting transport from the vacuoleto the cytoplasm.Assuming reasonable accuracy in measurements of electropo-

tentials, compartmental concentrations, and fluxes, we must con-clude from the present data that, during the period of substantialion accumulation by pea epicotyl segments, K+ is actively trans-ported into the cytoplasm and then diffuses passively into thevacuole. The site of the K+ pump must be at the plasmalemma.These conclusions, of course, are based upon the model used forcompartmental and flux analysis. Regardless of the compart-mental values the cells must be pumping K+ at some site on thebasis of the Ussing equation.

Permeability Coefficient. The permeability coefficient, PK, forK+ across the plasmalemma can be calculated from the data pro-vided. Since K+ appears to be actively transported into the cyto-plasm, it is assumed to be passively leaking outward. The unidi-rectional flux equation based on the Goldman (5) model is:

zjFE Cj, exp zj FE/RTJCO = PAR

RT I1-exp Zj FEIRT(4)

where Cji is the estimated concentration of K+ in the cytoplasmand with other notations having the same meaning as given be-fore. Here Cji was multiplied by the activity coefficient. The aver-age PK of the two experiments at an external concentration of 1 Xwas 1.02 X 10-8 cm sec-', and, of lOX, 1.01 x 10-8 cm sec-1.These values are about 20-fold less than those reported for broadbean roots by Scott et al. (13) based on a unidirectional flux in-ward. As noted by Scott et al., the flux of water through the rootscould influence K+ influx; this would lead to an overestimate ofPK .

Critique of Results. There are some reasons to question the ac-curacy of these initial attempts to test the flux ratio equation inhigher plant cells undergoing rapid uptake. The primary difficultylies in the fact that the method is best adapted to cases in whichlittle or no net influx occurs, i.e., when only the specific activityin the compartments change with no net mass transfer. Theamount of isotope removed in a typical wash-out experiment of10-hr duration is about 3.7% of the amount taken up (with 12-hrloading). Of this the loss from the surface film and wall spaceamounts to about 2.1 % and from the vacuole to approximately

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MACKLON AND HIGINBOTHAM

1.0%; the amount thought to come from the cytoplasm is only0.6%. Obviously small errors in the graphic derivation of slopeand intercept in the slow phase of the wash-out curve can lead tolarger errors in estimates of slopes and of cytoplasmic content.The calculated amount of K+ in the cytoplasm is 40 to 60 timesthe apparent content of the cytoplasm.

Secondly, it may well be that in the tissues here, which show astrong net accumulation, the loss rates may not be first order. Thisis suggested by some experimental data and by theoretical con-siderations. As noted above, the loss from the slow phase(vacuole) is quite slow, and the fit to a straight line is somewhatarbitrary (Fig. 1). In practice the slope chosen is that which givesthe best fit to the points of the second slowest phase (Fig. 2).From a theoretical standpoint there are several possible reasonsfor a deviation from a first order rate process. The premise onwhich such a rate is based is that it is diffusion-controlled (i.e., afunction of the permeability coefficient) whereas much evidence,including that presented here, suggests that in part, at least, fluxesare pump-controlled and thus probably second order or nth order.An isotope effect has not been ruled out here or in other suchanalyses. With increasing internal K+ concentrations membraneresistance may be altered, thus resulting in changes in permea-bility coefficients; there is evidence that increasing K+ concentra-tion, externally at least, lowers electrical resistance (7).

It should be made clear that the criticisms of the serial modelcompartmental analysis are not a denial of the series aspect andare restricted to questioning the degree of accuracy in the case inwhich a strong net influx occurs. In previous analyses on giant-celled algae the cells were in flux equilibrium (or nearly so) withthe external solution (2, 9, 10) or subjected to low temperature,thus avoiding large net changes (11, 12). However, Cram (1)measured the Cl- fluxes of carrot root disks at 200; he concludedthat the influx to the cytoplasm was the most reliable of the sev-eral estimates. In his work it is not clear whether a strong net ac-cumulation occurred during the experiments.

Acknowledgments-The authors thank Robert B. James, James S. Graves, andKaren M. Johnson for technical assistance; Dr. Enid A. C. MacRobbie for aid inthe mathematical analysis of results; and Dr. Alan Koch for suggestions on the manu-script.

LITERATURE CITED

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2. DIAMOND, J. M. AND A. K. SOLOMON. 1959. Intracellular potassium compartmentsin Nitella axilsaris. J. Gen. Physiol. 42: 1105-1121.

3. ETHERTON, B. 1968. Vacuolar and cytoplasmic potassium concentrations in pearoots in relation to cell-to-medium electrical potentials. Plant Physiol. 43:838-840.

4. ETHERTON, B. AND N. HIGINBOTHAM. 1960. Transmembrane potential measure-ments of cells of higher plants as related to salt uptake. Science 131: 409-410.

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9. MAcRosBBE, E. A. C. 1964. Factors affecting the fluxes of potassium and chlorideions in Nitella translucenis. J. Gen. Physiol. 47: 859-877.

10. MAcROBBIE, E. A. C. AND J. DAINTY. 1958. Ion transport in Nitellopsis obtusa.J. Gen. Physiol. 42: 335-353.

11. PITMAN, M. G. 1963. The determination of the salt relations of the cytoplasmicphase in cells of beetroot tissue. Aust. J. Biol. Sci. 16: 647-668.

12. PITMAN, M. G. AND H. D. W. SADDLER. 1967. Active sodium and potassiumtransport in cells of barley roots. Proc. Nat. Acad. Sci. U. S. A. 57: 44-49.

13. Scorr, B. I. H., H. GULLINE, AND C. K. PALLAGHY. 1968. The electrochemicalstate of cells of broad bean roots. I. Investigations of elongating roots of youngseedlings. Aust. J. Biol. Sci. 21: 185-200.

14. VAN STEVENINCK, R. F. M. 1962. Potassium fluxes in red beet tissue during its"lag-phase." Physiol. Plant. 15: 211-215.

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138 Plant Physiol. Vol. 45, 1970

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