Some Experimental and Theoretical Observations

Journal of Experimental Botany, Vol. 21, No. 67, pp. 304-24, May 1970

Some Experimental and Theoretical Observations Concerning Mass Flow in the Vascular Bundles of Heracleum M. T. TYREE 1 AND D. S. FENSOM Mount Allison University, Sackvilk, N.B., Canada Received 30 May 1969

INTRODUCTION In a recent paper Fensom and Spanner (1969) present a technique for measuring bioelectric potential gradients on intact vascular strands in Nymphoides, and suggest some ways in which the Onsager equations of irreversible thermodynamics could be used, in conjunction with the biopotential measurements, to analyse transport mechanisms in phloem tissue. While some qualitative statements could be made about the mechanisms at work, it was not possible to isolate the phloem strand of Nymphoides sufficiently to permit a more quantitative study to be made. This difficulty has been partly overcome by using the giant umbelhfer, Heracleum mantegazzianum, which has been studied previously in some detail by Zeigler (1958, 1960). Heracleum has discrete vascular bundles which are of appreciable size and can be isolated from the ground tissue and split at the cambial region into separate xylem and phloem while remaining attached to the plant at each end. Preliminary measurements of electro-osmosis and of hydraulic conductivity of H. mantegazzianum were made on excised phloem strands at Bedford College, University of London, by Fensom and Spanner in 1964. as were also bioelectric measurements on the phloem of growing plants. We have subsequently undertaken a more comprehensive study at Mt. Allison University. The results of this investigation 1

Present address: School of Botany, University of Cambridge.

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ABSTRACT The theory and practwe of applying the thermodynamics of irreversible processes to mass-flow theories is presented. Onsager coefficients were measured on cut and uncut phloem and cut xylem strands of Heracleum muntegazzitinum. In 0-3 N sucrose-)- 1 mN KC1 they are as followH. In phloem, LKE = o x 10~4 mho cm" 1 , LFE = 9 x 10~W+L**W'

( l a )

(lb)

where LPP is the hydraulic conductivity of the phloem tissue, LEE is the electrical conductivity, and LPE and LEP are electro-kinetic cross coefficients. The Onsager equations have two additional restrictions that are of importance. The first is the reciprocity relation (Staverman, 1952) LPE = LEP,

(2)

and the second is a basic theorem (Dainty, Croghan, and Fensom, 1963) L2PE < LPPLEE.

(3)

Since all the measurements in this paper are on whole pieces of phloem, it is essential to keep in mind that we are taking the fluxes J and / as theflowrate down the entire length of phloem per unit area of phloem tissue. J and / are assigned units


THEORY Two theories of electro-kinetic (or electro-osmotic) translocation in phloem have been proposed; these differ primarily in the pathway envisaged for the electric current. Fensom (1957 and 1959) proposed a continuous circulation of 'sap-carrying' ions down the entire length of the phloem tissue, or, at least, down the length of several sieve tubes. In contrast Spanner (1958) envisaged a 'micro-circulation' of 'sap-carrying' ions in which the ions followed a more or less circular pathway between the sieve plates and companion cells (which supply the motivating 'force'). The important distinction is that while the 'micro-circulation' pathway unavoidably includes part of the sieve tube lumen in the vicinity of the sieve plate, it does not necessarily envisage a current flow down the entire length of the sieve tube. The flow dynamics of both theories can be treated quantitatively by irreversible thermodynamics. However, we will deal with the flow dynamics of the first theory only since our experimental evidence is most relevant to this. A quantitative treatment of the second theory is advanced by Spanner (1970). The electro-kinetic theory of translocation in phloem is basically a mass-flow theory wherein the motivating 'force' for the flux of sap, J, is an electrical potential gradient, d-B/di. In mechanistic terms the electrical gradient is seen to induce a current flux, / , in the sap which causes an overall sap flux, J, as a result of the frictional drag between the current-carrying ions within the sap and the rest of the phloem sap. For completeness in writing the flow equations we allow for the contribution of water potential gradients, dP/dZ, to the fluxes J and / . The Onsager transport equations represent the flows as algebraic sums of the products of transport coefficients and the conjugated driving 'forces' (Staverman, 1952). d p d ^

306

Tyree and Fensom—Observations Concerning 3

1

2

of cm s" cm" and A cm"2 ( = C s~x cm~2) respectively. The electrical gradient, dE/dl, has units of V cm"1 ( = J C - 1 cm"1) and, for consistency, the pressure gradient has units of (J cm"3) cm-1. (One J cm- 3 equals about 10 atm.) There are a number of important concepts relating to the above equations which will be used throughout the remainder of this paper. They are (a) The coefficient £ / J p is the hydraulic conductivity of the phloem. It is a measure of the 'permeability' or ' openness' of the phloem tissue to sap movement. It should be clearly understood that LPP is a sum of the hydraulic conductivities of a number of parallel pathways, for example, the sieve cells (lumina and sieve plates), L*tp, all the cell walls of the phloem tissue, Lx°p, the phloem parenchyma, LftJ), and the companion cells, Lyp. In symbols we have (4)

where a8, aw, a,p, and ac are the relative areas occupied by sieve cells, cell walls, phloem parenchyma, and companion cells respectively in the phloem. If the sieve plate is assumed to offer the greatest resistance to sapflowin the sieve cells, then clearly L8PP will be largely dependent upon the physiological state of the sieve plate. It is generally agreed that the LPP of a sieve cell free of slirne plugging ought to be greater than with slime plugging. At times it is helpful to speak of the measured value of LPP as if the only major contribution were that of the sieve cells. Clearly if this assumption is to be reasonable then it must be true that «s L%, > K L%+ar L%p+ac Lcpp).

(5)

On the basis of calculations by Tyree (1969) it is probably reasonable to assume that

but whether or not, aaLPP > awLf,P depends upon the degree of plugging in the sieve plates. If the Munch (or any) pressure-flow mechanism is to work then LPP must be sufficiently large to accommodate the observed sap flux rates, J, at physiologically reasonable pressures. LPP has units of cm3 s - 1 cm- 2 (J cm- 3 )- 1 cm. (b) The coefficient LEE is the electrical conductivity of the phloem. It is a measure of the concentration and mobility of the current carrying ions in solution. As with LPP, LEE is a sum of the conductivities of several parallel pathways, i.e. LEE = aaLEB+awVl:E+apLEE+aeLEE.

(6)

Since most plant cell membranes exhibit low ionic permeabilities LEE and LEE are probably very much smaller than L'%E (Hayden, Moyse, Calder, GYawford, and Fensom, 1969). The magnitude of L'EE depends upon the degree to which the sieve plates are covered with membranes. The units of LEE are ohm- 1 cm- 1 ( = mho cm- 1 ). (c) LPE ( = LEP) is the electro-kinetic coefficient and can be taken as a measure (or index) of the degree of ion-sap interaction in the phloem. The plausibility of the


Lpp = aa L*jp+aw L%,+ap L»p+ae Lpp,

Mass Flow in the Vascular Bundles of Heracleum

307

electro-kinetic theory of the first type (Fensorn, 1957, 1959) rests upon the magnitude of LFE in the same way as the plausibility of a pressure-flow theory rests upon the magnitude of LPP. Furthermore, as before LPE

= LEP = a8 LPE+aw 3

1

2

Lf,E+ap

1

LpE+ac

LCPE.

(7) 2

3

The units of LPE are cm s~ crn~ V~ cm, and £ £ P h a s units of A cm" (J cm" )" 1 cm. These two units can be shown to be equal, i.e. one cm3 s"1 cm~2 V" 1 cm equals one A cm~2 (J cm- 3 )- 1 cm.

(e) A parameter frequently referred to in the literature is the electro-osmotic efficiency (e-o efficiency). It is a favoured term because it gives the easily measured ratio of the observed volume flux, J, to the applied current flux, I, when dP/dZ is zero. That is, from equations (1 a) and (1 b), J I

LrE LEE

dP dl

. .

A high e-o efficiency is favourable to an electro-kinetic (E-K) theory because it could correspond to a high value of LPE. However, a high e-o efficiency does not necessarily imply a large LPE; for example, Tyree and Spanner (1969) have shown that in Nitella cell walls J\I increases as the saline concentration decreases despite the fact that LPE is concurrently decreasing because LEE decreases even more rapidly. The units of Jjl are cm3 C"1. Frequently J/I is expressed in moles Faraday" 1 (the moles of water carried per Faraday of charge) or, equivalently, as water molecules per ionic charge. The latter is usually calculated assuming that all the J is due to the flux of water; this is a reasonable approximation for values of Jjl exceeding about 30 or 40 moles Faraday- 1 (I cm3 C"1 = 5-36x 103 mole Faraday- 1 ). (/) It is apparent from equation (1 a) that the pressure-flow term is LPP(dP\dl) while the electro-kinetic term is LPE(dEldl). When this last term assists the normal flow dEldl is positive, and the term represents the electro-osmotic component of flow. On the other hand when the flow has an electrical component acting against it, dE/dl is negative. We can solve for the electrical potential gradient inside the phloem directly from equation (1 b): dl

LEE

LEE dl'

M

Equation (9) clearly demonstrates that a water potential gradient will always produce a component of electrical potential gradient with a proportionality factor of —L E P jL E E . Equation (9) affords the theoretical basis by which we can


(d) In order to avoid confusion in sign conventions we should note that dP/dZ is taken in the positive sense if the pressure is decreasing in the direction of increasing distance. Similarly, dE/dl is taken as positive if the direction of increasing distance is the direction of decreasing voltage. Strictly this is in the opposite sense to what should be adopted in a Cartesian frame of reference; however, since the nonCartesian sense for the sign of dEjdl and dP/dZ has been used in nearly all the literature of the biological applications of irreversible thermodynamics we will retain the above convention.

308

Tyree and Fensom—Observations Concerning

In brief, we had two main objectives in our work at Mt. Allison University. First, we hoped to measure LPP, LHE, LEP, LEE to see if these coefficients are indeed constant over reasonable ranges of dP/dl and dE/dl and to see if Eqns. (2) and (3) hold as theory predicts. Second, we hoped to measure dEjdl on conducting but laterally detached phloem bundles in order to gain some insight into the possible translocation mechanism by following the reasoning of section (/). MATERIALS AND METHODS Plant material Seeds of Heracleum mantegazzianum (Somrn. et Lev.) were obtained from Bedford College, London, and were successfully gorminated in 1965. The plants do not develop to full maturity the first year and therefore, seedlings were planted both in the greenhouse garden and in ] 2 in (30-5 cm) clay pots indoors for study in or after the second summer. The vascular bundles are exceptionally large in this plant (up to 3 mm diam.) and easily isolated. However, the smaller species, Heracleum spkondylium (L.), which now grows naturally in eastern North America is suitable also. Preparation of excised phloem strands for Onsager measurements Twenty-cm portions of mature petiole of H. manlegazzumitm were cut in the field and immediately placed in 0-3 molar sucrose solution. After a lapse of about half an hour the individual phloem strands were separated out under the sucrose solution and in .some cases were allowed to remain 24 h in this solution to relieve internal turgor. Two-cm lengths were cut from the centre of each strand. These lengths were placed in the split rubber stopper of an electro-osinometer (for procedure see Fensom and Dainty, 1963: Fensom, Meylan. and Pilet, ]965; Fensom anrl Wanless, 1967). The following measurements were then made in order: electro-osmotic efficiency, hydraulic conductivity, electrical resistance and cross-sectional area. The first two measurements were made as soon as possible after mounting ui the apparatus —usually requiring 2 to 3 h to complete the measurements. The last two measurements were made outside the osmometer after blotting. Resistance was measured using short pulse D.C. with a WTieatstone bridge. Low pressures were maintained by adding columns of water to one side of the apparatus, and high pressures by using a piston which gave pressures up to 0-8 atm.


distinguish between the E-K and pressure-flow theories of translocation. If an E-K mechanism of the first type is dominant, and if the positive sense of distance is downstream, then clearly the dEjdl measured in phloem in situ must be positive, i.e. decreasing voltages downstream (cf. Eqn. 1 a). On the other hand, if a pressure-flow mechanism is dominant then we can expect to measure a dEjdl in situ that is negative (i.e. increasing voltages downstream) provided that we can be reasonably sure that I is equal to zero. This latter proviso must be established by independent observations. (It is important to keep in mind that we are speaking of a current flux, /, down the entire length of the phloem. Spanner (1970) treats the E-K mechanism of the second type and demonstrates how a finite micro-circulation of current can exist while dEjdl is negative. Since we wish to confine ourselves mainly to the plausibility of E-K mechanisms of the first type we shall ignore this possibility.) In the limiting case where / = 0 in Eqn. (9) the observed dE/dl is called a streaming potential gradient. However, this definition is not universally held since some people refer to dEjdl as a streaming potential whenever


309

Resistance of strands in situ After the parameters of flow had been obtained on cut segments attempts were made to measure the resistance of strands in situ. Impedance measurements were made by resting the freshly separated strand across two Ag/AgCl needles, 5 or 10 mm apart, and measuring the resistance between them at both 60 and 100 Hz. The diameter of the strand was then measured as before. (We found the electrode resistance to be negligible compared to the tissue resistance.) Preparation of phloem strands for biopotential studies


From the p3tiole of a mature leaf of Heracleum a 10-20 cm length of vascular bundle was rapidly separated so that the bundle was still connected to the petiole at its ends as shown in Fig. 1. The parenchyma sheath, if present, was carefully removed and the xylern separated from the phloem (it separates quite readily by gentle pressure) so that the Isolated phloem strand was free of parenchyma, schlerenchyma (except for a few strands in the phloem itself) and xylem. Care was taken to prevent the phloem strand from drying out; at Bedford College this was accomplished by wrapping it in polythene after spraying gently with water; at Mt. Allison University this was done either by spreading Vaseline over the entire bundle or by laterally slipping it into a split length of polythene tubing of about the same internal diameter as the strand, the tube being then vaselined externally. Meanwhile, the cut region of the petiole was wrapped with polythene sheeting held in place with Vaseline. Sometimas at Bedford College the cut strand was inserted after electrical isolation into the hollow of the cut petiole to keep it moist. Preparations were examined after the experiments to ensure that the strand was still in good condition. Two main types of electrode application were employed. In the first year at Mt. Allison, small vials, 45 mm x 7 mm diam., were filled with 0-25 N KC1 and attached to the petiole with grafting wax. Cotton wicks saturated with 0-25 N KC1 were threaded through polythene tubing and used as bridges between the strand and the vials from which Ag—AgCl wires were connected via coaxial cables to a sensitive VOM recorder. Three of these salt wick bridges were used, placed 5 cm apart on the strand. A similar cotton wick reference electrode was placed on the same strand, 5 cm below the third electrode on the dissected portion. This reference electrode was earthed. An automatic switch permitted a recorder (input impedance 10' ohms) to register successively three biopotentials at about ten second intervals. This electrode arrangement, or modifications of it, was also used in the second year although after several days of continuous recording the vials and wicks tended to dry out. Therefore, in the third year, ways of getting closer contact between the silver wire and the phloem bundle were tried. The following technique was found to be reproducible and reasonably satisfactory. Phloem bundles were dissected fre3 from the petiole for 10 cm and after removal of xylem and parenchyma were quickly slipped into a narrow polythene tube 9-5 cm long, Kpht along one side. Fine chloridized silver wires were inserted through the split in the polythene tube and hooked around the phloem strand. A drop of warm 0-25 N KC1 in agar was then injected into the tube at each electrode hook. Three electrodes were used 4-0 cm apart with a reference Ag/AgCl electrode in the base of the petiole (see Fig. 1). The exposed tissue at either end of the polythene tube was covered with Vaseline to prevent drying. In some cases, regions of petiole were cooled down to near 0 °C; all these experiments were done on petioles using the set-up just described. For these experiments air was drawn through a CaCl, desiccator and then forced through copper tubes surrounded by methanol and dry ice. Two tubes carried the cold air to about 2 cm from the intact petiole about 5 cm above the dissected phloem strand. This provided a cross current of dry cold air from two directions on to the petiole immediately external to the strand under study. A thermocouple was embedded in the petiole less than 2 mm distant from the vascular bundle. Temperatures were recorded with a precision of ^0 - 5 CC. In this third year, all biopotentials were measured by electrometer pre-amplifier (input impedance 1010 ohms) which was then connected to the recorder. All experiments were done inside a Faraday cage in a windowless ventilated interior room. The temperature varied from 23 to 27 °C from day to day, when the fluorescent lighting was on. The light intensity from base to top of plant varied from 16000 to 48 500 lx.

Tyree and Fensom—Observations

310

Concerning


FIG. 1. A drawing of a Heradeum petiole preparation showing an isolated phloem bundle passing through ft polythene tube with Ag/AgCI electrodes making three contacts with the bundle and one with the bulk parenchyma of the petiole.

RESULTS Onsager coefficients of phloem

We measured the Onsager coefficients of phloem first at Bedford College and later at Mt. Allison University. We determined the values of LPP, LPE, LEE, and Jjl, of excised pieces of Heradeum phloem kept in various bathing media and at various dates.


311

These coefficients are tabulated in Table 1; the values are presented individually whenever there are less than four samples; otherwise means and standard deviation of the mean are presented. The e-o efficiency. The e-o efficiency at any one stage of growth appears to decrease as the saline concentration of the bathing medium increases. Also, the e-o efficiency seems to have a seasonal dependence, i.e. it decreases at any one concentration as the growth season proceeds. The e-o efficiency is observed to be somewhat dependent

-

6

I3 10-

0-5

10 1-5 20 dP/dl (J cm"3) c m - ' x l O 3

2-5

30

FIG. 2. A plot of the observed mass flow, J, of solution (1 mN KCl-f 0-3 N sucrose) through a 2 cm length of phloem bundle vs. the applied pressure gradient, dP/d/. The second ordinate represents the calculated mean sap velocity when the relative area occupied by the sieve lumina, at, is 0-2.

on the current density, decreasing to about half at higher current densities (maximum current about 0-07 A cm- 2 ); this indicates that LPEjLEE is not quite constant in any one bathing medium. The hydraulic conductivity. LPP appears to have a seasonal dependence. It ranged from a maximum of 016 cm3 s - 1 cm~2 (J cm- 3 )- 1 cm in June to about 0-02 in August with the July reading of 0-05 (Bedford College, 1964) lying reasonably between the two Mt. Allison readings. Fig. 2 shows the observed J as a function of the applied dP/dZ for five different samples of phloem in June 1967. It appears that LPP is not quite constant over the range of recorded pressures. (The maximum applied pressure gradient was 3x 10"3 (J cm-3) cm- 1 ~ 3 atm m-1.) The value of as of Heracleum is about 0-2. From this we can calculate the mean sap velocity corresponding to each J assuming that a8 L'PP = LPP by the relation mean velocity (cm h -1 ) =

= 1-8 X 104 J.

(10)


7

Observer and location

D.S.F. (A) ditto

ditto ditto

M.T.T. (B)

ditto

P.I.

M.T.T. (B) P.I. (B)

M.T.T. (B)

M.B.A. (B)

M.T.T. (B) ditto

Date of work

1-10 July 1964 ditto

July J964 ditto

3 July 1967

19-23 June 1967

8-15 Aug. 1967

21 Aug. 1967 24-31 Aug. 1967

22 Aug. 1967

Aug. 1968

5-8 Sept. 1967 June 1967

OlNNaCl+0-1 N sucrose, 22 °C, excised phloem 0-1 NNaCl + O05N sucrose, 22 °C, excised phloem Fresh strand in situ (uncut) no bathing medium 2 mN KC1, excised xylem 2mNKCl+2mNNaCl, excised xylem

0-lmNKCl, 22°-23°C, excised phloem 10m N KC1 +0-3 N sucrose 22-23 °C, excised phloem ditto 0-1 mN KC1, 22-23 °C excised phloem Freshly excised strands 2 cm long, no bathing medium 1 mN KC1 + 0-3N sucrose, 22 °C, excised phloem lmNKCl+0-3N sucrose, 22 °C, excised phloem ditto

Solution and conditions

6-2±M

0-56

0-64

1-7 + 0-3

0-59 + 0-04 1-2, 1-8

0-62 + 0-04

1-34 + 0-12

(J//)XlO a cm8 Coul"1 1

1

X 10*

0-5, 1-8, 2-3

3-5+1-5

1-9 + 0-7

16±2

4-5 + 0-7* 4-1, 8-2

cm s" cm" (Jem" 3 )" 1 cm

3

1. Thermodynamic coefficients of flow in Heracleum vascular bundles 3

3•6 + 0-6

0 •9 + 0-2

7-1 ± 1-6

7-5 + 0-6

0-77 + 0-09

0-92 + 0-1

0-52±0-05

5-0 + 0-5

5-8±l-7 0-9, 3-0

mho cm"1

23±8

3-1 + 0-8

0-59 + 0-12

0-90 + 0-15

4-0+1-2 1-1, 51

2-4±O6

0-57 + 0-13

LpEx^0 apLpP-\-acLPP by at least a factor of 20 (Tyree, 1969). If we estimate aw at 0-05 and if we assume that slime plugging completely blocked our sieve tubes then from Eqn. (4) we have

320

Tyree and Fensom—Observations Concerning

Croghan, and Fensom, 1963). However, we can put an upper limit on LrE by the relation in Eqn. (3). ,f , _,,,,T u, n u \1JI>E\