plant tissue. III. The role of the root cortex cells

Transcription

1 the Acta Bot. Neerl. 22(5), October 1973, p Diffusion and absorption of ions in plant tissue. III. The role of the root cortex cells 1 in ion absorption G.G.J. Bange Botanisch Laboratoriu, Leiden SUMMARY The theoretical aspects of diffusion of Rb + ions in the free space of young barley roots and their concoitant absorption by the epideral and cortical cells were studied on the basis of a siplified geoetrical odel. It is concluded that participation of the cortical cells in the process of Rb + uptake is irreconcilable with the kinetic features of this process as deterined experientally. Liitation ofuptake to the root surface is considered to pertain to other acronutrient ions and other objects as well. I. INTRODUCTION In the application of carrier kinetics to experiental data on ion absorption by plant roots, the absence of appreciable diffusion resistances between the outward solution and the absorbing cell surfaces is usually iplied. On the other hand, solutes are known to be able to penetrate into the cell walls and waterinjected intercellular spaces of roots by free diffusion. More specifically, therefore, ignoring effects of unstirred layers at the root surface tacit assuption is either that the diffusion resistance in the free space is too low to appreciably reduce the ion concentrations at the cell surfaces lining this space or, alternatively, that soehow these surfaces do not participate in the absorption process. Such an exclusion could occur if the diffusion resistance in the free space were too high to allow for effective penetration of the substance absorbed to the internal cell surfaces but could equally well be due to a lack of absorption capacity of the surfaces involved. These probles do not see to have been studied in any detail, and there does not see to be real any consensus about these atters. For instance, in his 1969 review Laties expresses doubt as to a considerable reduction of the ion concentration in the free space by absorbing cortex cells, to which he ascribes a gathering function. This opinion is endorsed by Epstein (1972). Bowling & Ansari (1972) also assign the cortical cells a role in ion absorption. But Vakhistrov (1967), basing hiselfon the results of shortter experients on 1 Parts I and II of this study were published in Acta Bot. Neerl. 10 (1961): ,

2 530 O. O. J. BANGE free space depletion, holds the view that the epideris is the only actively absorbing part of the root, the salt solution in the free space representing in a sense a ballast volue. The divergence of these opinions justifies an analysis of the theoretical aspects of the proble. It should be kept in ind that in this study we will consider the entrance of ions into the root free space to proceed exclusively by free diffusion fro the outside solution. An alternative possibility would be a radial polarity of the epideral and cortical cells such that uptake of ions fro the free space predoinates at the side facing outward and release of ions into the free space at the side facing inward. For justification of this view, we ay refer to the published evidence on syplasatic transportof ions in parenchyatous tissues (cf. Arisz 1960; Klepper & Green way 1968). Young barley roots served as testaterial, but the conclusions drawn are deeed to have a wider bearing. 2. SIMPLIFICATION OF THE FREE SPACE GEOMETRY For a quantitative treatent of diffusionin the root free space the coplicated geoetry of this space ust be caught in a siplified odel without loss of any essential features. We started with transverse and longitudinal sections of a barley root (speciens are illustrated in fig. I, A and B) grown in the usual way (cf. Bange & Fig. 1. Crosssection (A) and longitudinal section (B) fro the ature zone of ayoung barley root.

3 DIFFUSION AND ABSORPTIONOF lons IN PLANT TISSUE. 11l 531 Meijer 1966) and easured in the all the essential diensions except for the thickness of the cell walls, which was derived fro electron icrographs of the sae aterial. A transverse section of the odel used is shown in 2. Cells fig. are taken as having unliited extension in longitudinal direction. Table 1 copares the quantitative geoetrical characteristics of the root and the odel. The ost salient difference between the is that in the odel the thickness of the epideral + cortical layer is reduced fro 188 to 158 jj.. This reduction is connected with the fact that the natural curved layer was replaced by a non Fig. 2. Model of the diffusion volue (dotted) and absorbing surfaces (hatched) in the root cortex + epideris; diensions are in urn; ep epideris, en endoderis. Table 1. Coparison of the geoetrical characteristics of the root and the odel. Areas and volues are given per kg fresh weight of roots. Root Model Diaeter (total) 540 [x Diaeter of stele 165 x Thickness of epideral + cortical layer (x 158 (224 + ) [x Thickness of cell wall 0.50 (x (x Total volue of internal cell walls of epideris + cortex 36.2 x jx X (x 3 Total volue of intercellular spaces (lining cell walls excluded) 28.9 x 10' 2 jx 3 0 Total area of internal surfaces of epideris + cortex 145 x (x x [x of total volue of Percentage epideris + cortex occupied by: cell walls (total) intercellular spaces (lining cell walls excluded) free space after 1/2 ultiplication by a labyrinth factor of average value

4 . Thus, ± 532 G. O. J. BANOE curved layer in the odel. This was done because atheaticaltreatent ofthe diffusionabsorption interaction in a curved layer is very coplicated. The effect of the curvature is to reduce the average distance of the cells fro the root surface as copared with a noncurved layer of the sae thickness. We therefore coputed an equivalent thickness for a noncurved layer (see Appendix, /) and ultiplied it by a labyrinth factor equal to 2 1/2 to take into account the eandering shape of the diffusion path in the root cell walls. In this way we arrived at a final thickness of 225 for the cortical p, layer of the odel. Another point of difference is that in the odel the natural syste of relatively wide intercellular and narrow cell walls was spaces replaced by a cell wall of unifor but slightly greater thickness chosen so as to give the sae diffusion resistance as in the original syste. At the sae tie, the total diffusion volue decreased fro 7.18 to 4.22%. To clarify this iportant point, let us represent the network of cell walls and intercellular spaces in the root by a syste consisting of pieces of flat cell wall alternating with intercellular spaces in the shape of parallel square tubes oriented perpendicular to the direction of diffusion {fig. 3). The sall extension of the intercellular in the spaces direction of the diffusion path (radialtangential) justifies this representation (cf. fig. I). The diensions indicated in fig. 3 approxiate the actual ean diensions and volue ratio of both free space coponents. The diffusion resistance in this syste is approxiately proportional to (146/0.50) + (8.7/8.7) 293 at a volue of 146 X ± 149 (i 3. If the cell wall did not widen into intercellular spaces, the diffusion resistance of the syste at equal total length would be proportional to ( )/ Therefore, as far as the diffusion resistance is concerned, the syste of intercellular spaces and cell walls in the root be ay replaced by an equivalent cell wall of equal total length but slightly larger thickness, viz. (309/293) X 0.50 ± 0.53 pun, occupying a volueof only ( ) x ± 82 pun despite their relatively large volue, the intercellular spaces do not effectively reduce the resistance to radial diffusive penetration into the root. An uncertainty is introduced by the unknown valueof the diffusion coefficient Fig. 3. Siplified odel of a cell wall with intercellular spaces (crosssection); diensions are in p..

5 DIFFUSION AND ABSORPTIONOF lons IN PLANT TISSUE. 11l 533 of RbCl in cell wall aterial. Reduction of the water volue and a labyrinth factor will tend to lower this value with respect to free water. Therefore, we started fro a value slightly lower than in water (1.5 x 10 5 c 2 1.sec instead of 1.9 x 10 5 c 2.see 1 at 25 C) and investigated the effect of deviating values. 3. MATHEMATICAL PROCEDURE The following sybols will be used; a, b paraeters (c.sec 1 and oles.c 2.sec 1, respectively) a b, paraeters valid within the concentration interval fro c 1( 2 c concentration (oles.c 3 ) to c 2 D diffusion coefficient in water (c 2.sec 1 ) D' diffusion coefficient in cell wall aterial (c 2 1.sec ) D apparent diffusion coefficient in the tissue (c 1) 2.sec a K MichaelisMenten constant (oles.c 3 ) 1 total length of diffusion path in the odel (c) thickness of cell wall in the odel (c) O c O e total crosssectional area of cell walls in the odel (c 2.kg 1 ) total area external surface of the root (c 2.kg 1 ) p concentration expressed in ters of K (diensionless) q proportionality factor (sec.c 3) r radius of root (c) Tj radius of stele (c) v absorption rate per unit area of absorbing surface (oles.c 2.sec 1 ) Y V' v t x the value of v at saturation (oles.c 2 1.sec ) axial absorption rate per of tissue c3 (oles.c 3.sec overall absorption rate of the root (oles.kg 1.h 1 ) distance fro inner boundary 1 ) Subscripts indicate the following: i o x at inner boundary (endoderis) at outer boundary (root surface) at distance x for inner boundary 1,2 at distance x ls x 2 fro inner boundary s h at saturation at half saturation A detailed discussion of the diffusion of a substance into and its concoitant absorption by a layer of plant tissue has been given by Briggs & Robertson (1948). The basic equation for the steady state (dc/dt 0) is d 2 c/dx 2 q.v. (1) In general, v will be a function of c. For our special case we suppose that a MichaelisMentenrelationexists between c and v. In other words, in the absence of any diffusive restraints the relation between rate of ion absorption by the cell surface and ion concentration is assued to be given by v V.c/(K + c). (2)

6 and the approxiation used (B); concentration plotted as ultiples of K. 534 O. G. J. BANGE This assuption sees justified because, within a liited range of concentrations, overall root absorption shows saturation kinetics and consequently the basic relation ust also show this behaviour. Furtherore, this type of relation is characteristic for a great nuber of absorption processes in all sorts of aterial. Thus, we have d 2 c/dx 2 q.v.c/(k + c), (3) the value of q in the odel being given by q 2/(D'.). (4) Equation (4) iplies that no diffusion gradients are assued to exist in a direction perpendicular to the cell wall plane. Integration of equation (3) between the liits (dc/dx) x, (dc/dx)i O, c and x c, yields (dc/dx) 2 x 4V.[c x c, K.log(K + c x )/(K + c,)]/(d'.). (5) Further integration at constant value of C would give a relation between c and x x fro which, with the aid of the known length of the total diffusion path, the corresponding value of c e couldbe calculated. Overall internal absorption being proportional to (dc/dx) could then be coputed with the aid of equation (5). Unfortunately, further integration of equation (5) is ipossible, so an approxiation has to be used. For that purpose we represented the Michaelis Menten relation by a syste of five straight lines, each valid within a definite concentration interval (see fig. 4, A and B, and table 2). The basic equation then becoes d 2 c/dx 2 q.(a.c + b). (6) Fig. 4. The MichaelisMenten relation (A)

7 [at.q.(c cf) For siplicity, it is convenient to express all concentrations in ters of K 3600.[D'.O cj < II < 3 v V surface ( V ) can be calculated to equal X 10 8 oles.c 2.sec 1. DIFFUSION AND ABSORPTION OF lons IN PLANT TISSUE. 11l 535 Table 2. Paraeters of the straight lines used to approxiatethe MichaelisMenten relation and their p and v intervals. Line nuber a b p and v intervals 1 V /K 0 p 0 P 1/3 v 0 v VJ3 2 V /4K 3 V /16K V /4 P 1/3 P 5/3 v V /3 v 2V /3 9V /16 P 5/3 P 33/7 v 2V /3 v 6V /7 4 V /100K 81VJ100 P 33/7 p 19 v 6V /7 v V 5 0 v p 19 p CO By integration between the liits (dc/dx) 1; (dc/dx) 2, c lt c 2, x x and x 2 we obtain (dc/dx) 2 + 2b,.q.(c2 + (dc/dx)?] 1/2 (7) and x 2 x, (a,.q) 1/2.log{[af. (c 2 cf) + 2a 1.b,.(c 2 c x) + a 1.(dc/dx)f/q] 1/2 + a!.c 2 + bj (a,.q) 1/2.log[(a 1 /q) 1/2.(dc/dx) (8) according to c p.k. (9) The further procedure is as follows. For any arbitrarily chosen value of p^ with the aid of equations (7) and (8), the distance fro the inner boundary can be calculated at which the concentrationattains the lower liit of the next concentration interval. With new values for a and b the procedure is repeated so that for each concentration interval a value for the corresponding interval on the diffusion pathway is obtained. The length of the last interval is calculated by subtracting the su of the lengths ofall preceding intervals fro the total length of the pathway. Substitution of this value in equation (8) gives the value of p corresponding to the chosen value of pj. The overall rate of root absorption is then expressed by the equation v t c.(dc/dx) + O.V.c /(K o e 0 + c )]. (10) 0 4. RESULTS AND DISCUSSION The rate of Rb + absorption by lowsalt excised barley roots in the initial rapid phase lasting about 2 hours has a saturation level of approxiately 8.5 oles, kg Mi 1 (Bange & Meijer 1966), which is attained at an external concentration of about 0.15 M. When it is assued that this absorption capacity is distributed uniforly over the whole external and internal surface of the epideral and cortical cells, the axial absorption rate per unit area of absorbing For any chosen value of K the relation between external concentration and

8 536 G. O. J. BANGE overall absorption rate can then be calculated. Fig. 5 A shows the relation for a K valueof M andfig. 5 B for the25ties higher value of0.005 M. The corresponding values of Cj are also given. Despite the appreciable disparity of the underlying K values, the quantitative differences between both lines appear to be very sall. Their shape deviates considerably fro the MichaelisMenten type of curve, especially with respect to a rather abrupt transition to saturation, which is due to the liited depth of the absorbing layer. This effect is the ore pronounced the lower the K value Fig. 5. Theoretical relation between the overall rate of Rb + absorption ( v,) and external concentration ( c ) for the case that the absorption capacity observed at 0.15 M (Bange & Meuer 1966) is distributed uniforly over the surface of all epideral and cortical cells and is characterized by a K value of M (A) or M (B), respectively; the dashed line represents the concentration at the inner boundary ( c,; ordinate on the right).

9 . DIFFUSION AND ABSORPTION OF lons IN PLANT TISSUE. 11l 537 chosen and reflects the abrupt increase of the concentration at the inner boundary to saturating levels when the outside concentration attains a certain value (cf. fig. 5). The lower the K value chosen, the saller in general the outside concentration at which overall absorption saturates. Nevertheless, it can be shown easily (see Appendix, 2) that however low the value of K, overall absorption in the syste described will not saturate below a liiting external concentrationof 1.04 M Rb +. This value is 7 ties higher than the actual saturating concentration of about 0.15 M Rb +. By the sae token the halfvalue for overall internal absorption can be shown (see Appendix, 2) to have a liiting lower value of about 0.25 MRb + or about 20 ties higher than the value actually observed. Both these inial values are proportional to 1 2 /D'.. So only ifthe value of this factor were 7 or 20 ties lower, respectively, than assued, could theory and experient be brought into line. Underestiationof the part played by the intercellular spaces ay lead to a value that is too high, but in view of the considerations in Chapter 2 (cf. fig. 3) it would see extreely unlikely that the error would be so large. If considerable accuulation of the cation in the Donnanphase of the cell wall diffusion will be enhanced occurs, as a result of steeper gradients. In the exaple chosen, 5 M was present CaS04 in the solution. Even so, calculation shows that there is sufficient accuulation of the onovalent cationin the DFS to enhance diffusion appreciably. On theother hand, Rb + absorption at 0.1 M is alost insensitive to a 50fold excess of Ca + + (Bange & Hooyans 1967), so apparently diffusion in a Donnanphase is not at all involved in the process of Rb + uptake by excised barley roots. Therefore, it ust be concluded that a unifor distribution of the observed absorption capacity over theexternal and internal surfaces of all epideral and cortical cells would result in a kinetic pattern deviating irreconcilably fro the actual findings, and ust consequently be rejected. This does not iply that the internal cell surfaces show a lack of absorption capacity. There is still the alternative possibility to be exained, that in the range of low Rb + concentrations (below 0.5 M) the observed absorption takes place ainly at the external root surface, although an absorption density ( absorption capacity per c 2 ) siilar to that of the external surface extends over all internal epideral and cortical surfaces as well. The area of the external root surface being about 5 % of the area of the internal surfaces, the value of V will be about 20 ties higher in this case than under the assuption elaborated above, and equal to 3.38 oles.c 2.sec 1 In this situation the contribution to overall absorption by the external relative to the internal surface will be uch higher in the range of low concentrations than under the previous hypothesis, because, unlike external absorption, internal uptake at a given value of c increases proportionally not to V but to 0 V 1^2 (equation 5). Consequently, the overall concentrationisother in this range ay be expected to deviate less fro the basic relation between concentration and uptake as expressed by equation (2). This feature is deonstrated

10 538 O. G. J. BANGE Fig. 6. Theoretical relation between the overall rate of Rb + absorption ( v t ) and external concentration ( c ) for the case that the absorption capacity observed at 0.15 M (Bange& Meuer 1966) is located at the external root surface and is characterized by the halfvalue found experientally, viz M; the dashed line represents the sae relation for a diffusion resistance 100 ties larger; the dotted line is based on the absorption data ebodied in fig. 2 A of the work cited above. by the curve in fig. 6, which was calculated for a K valueof 0.012M(cf. fig. 2 A in Bange & Meijer 1966). In this case equation (5) could be used, the concentration at the inner boundary being negligible in the range of concentrations studied (cf. fig. 5). Despite this shift in the relative contributions of the external and internal coponent to overall absorption, it appears fro fig. 6that in coparison with the epirical relation the theoretical curve reains far fro saturation. It can be shown that its rise continues until the outward concentrationattains a value of about 24 M and internal absorption exceeds external uptake by a factor of 20. This discrepancy could be due to an overestiationof the value of the diffusion coefficient for RbCl in the cell wall aterial. However, internal absorption being proportional to D' 1/2, even in the unlikely case that the value of D' were 100 ties saller, the theoretical and epirical curve would not coincide (fig. 6). In the case of Cs + absorption by the sae aterial the discrepancy is even larger. Using the absorption data of Bange & Overstreet (1960), we worked out the theoretical curves for Cs + absorption (fig. 7) to be expected under the prevailing assuption in the sae way as for Rb + absorption in + fig. 6. For Cs absorption, the concentrationsaturated region extends fro 0.1 to 2 ram. Hence, even if the diffusionresistance were as uch as 900 ties larger than assued in Chapter 2, theory and experient would not be reconciled in this case (fig. 7). Still, it ay be argued that a secondary rise in the concentrationisother is ore rule than exception in ion uptake by roots. But it is equally true that quite frequently such a rise sets in sharply as the concentration is increased, the re

11 DIFFUSION AND ABSORPTION OF lons IN PLANT TISSUE. 11l 539 Fig. 7. Theoretical relation between the overall rate of Cs + absorption ( v,) and external concentration ( c ) for the case that the absorption capacity observed at 0.1 M (Bange & Overstreet 1960) is located at the external root surface and is characterized by the halfvalue found experientally, viz M; the dashed line (ordinate on the right) represents the sae relation for a diffusion resistance 900 lies larger; the dotted line (ordinateon the right) is drawn through the experiental points found by the authors cited above. suiting inflection point being preceded by a region in which the rise is negligible as in the case of Cs + absorption quoted above (cf. Bange & Overstreet I960). It sees inconceivable that an interplay between diffusion and absorption as visualized here could bring about such a discontinuous behaviour. Besides, a coparable secondary rise has also been described for a unicellular organis (K ANNAN 1971). These considerations see to rule the out possibility that a latent absorption density as high as calculated for the external root surface extends over all internal epideral and cortical surfaces as well. Therefore, our arguents adit of no other final conclusion than that the cell surfaces lining the root free space show a lack of absorption capacity for Rb + ions and, presuably, for other acronutrient ions aswell.lt is not only extreely unlikely that the internal surfaces would discriinate between ion species in a copletely different way than the outer root surface, but also arguentationsiilar that to presented above, albeit quantitatively soewhat different, can be given for other acronutrient ions. The argin of the theoretical considerations on which this conclusion is based, is sufficiently aple to allow for any iperfections in the geoetry of the odel and uncertainties as to the true value of the diffusion resistance in the cell wall. Nor will it be of any consequence whether, in the basic relation between rate of absorption and concentration, saturation is attained in strict accordance with MichaelisMenten kinetics or, for instance, after a sigoid initial part of the curve. For as the external concentration rises, the contribution to overall

12 540 G. G. J. BANGE uptake by cells absorbing at nonsaturating concentrations becoes less and less iportant. 5. CONCLUDING REMARKS In Part I of this series van den Honert & Hooyans (1961) described striking differences in the relation between NHJ uptake and external concentration in aize roots on the one hand and potato discs on theother. Their suggestion that the difference ight be due to a restriction of the absorptive capacity to the root surface is borne out by the present study provided a generalization of our inferences to other types of roots is not too bold. Thus, the divergent behaviour of these two types of tissue reflects not a quantitative difference in diffusionabsorption relations but a ore fundaental qualitative distinction. The developent of an absorption capacity in discs of storage tissue is a phenoenon closely linked to the abandonentof a dorant state and as such ay be expected to extend over the whole surface of the reactivated cells. On the other hand, a root is an organ adapted to water and salt absorption and therefore it would not be surprising if the absorption capacity were concentrated in the region where it can be used ost effectively, viz. the outer surface. One copelling reason fur such a concentration could be the fact that under natural conditions the soil solution ay be very diluteand consequently its diffusion pressure low. Expansion of this surface by root hairs would also see to have ore effect when the absorption capacity at the root surface is high than when its contribution represents only a sall percentage of the overall absorption capacity. Nevertheless, even though our conclusion can be understood fro this teleological point of view, there is still the theoretical possibility that the lack of absorption capacity of the internal surfaces is due not to the absence of an absorbing echanis but to soe kind of repression of the activity of such a echanis. At any rate it is noteworthy that the cortical cells are able to accuulate considerable aounts of ions in their vacuoles, as shown by the direct easureents of Dunlop & Bowling (1971) and Bowling (1972). So apparently in these cells transport at the tonoplast can occur quite independently of transport at the plasalea. As to the role of the root free space in the absorption of acronutrient ions, this study endorses the stateent by Vakhistrov referred to in the introduction, i.e. that it represents just a ballast volue without further significance. APPENDIX 1. Calculation of the equivalent thickness of a noncurved cortical layer. The aount of salt diffusing through a cylindrical plane of radius r t + x and unit length between the outer and inner boundary is given by D.27r.(r, + x).dc/dx. a In the steady state this aount equals the aount of salt absorbed by the part

13 & c, 2r 2r DIFFUSION AND ABSORPTION OF lons IN PLANT TISSUE. 11l 541 of the tissue between this plane and the stele. Thus, when uptake is independent of concentrationand equals V', we have D.27i.(r, + x).dc/dx n. [(r, + x) 2 2 r a,].v' ) fro which c q (V' /4D a ).[r 2 r 0 2, 2,.Iog(r 0 /ri)]. For a noncurved layer of thickness y and width b, we have under the sae conditions D.b.dc/dx b.x.v' a, fro which follows c (V'J4D a ). 2y 2. In order for c, to be identical in both cases at equal c 0, we ust have 2y 2 r 2 r 2, 2 i.log(r 0 /r i ), fro which for our case a value of y 158 p can be calculated. 2. Calculation of the inial value of the saturating concentration and of the halfvalue. At sufficiently high values of c the rate of internal absorption will saturate 0 up to the inner boundary. In that case equation (3) is reduced to d 2 c/dx 2 q.v, fro which by integration (dc/dx) (2q.V.K ) 1/2. x ( Px Pi ) 1/2 and 1 (D'..K /V ) 1/2.(p 0 p,) 1' 2. Consequently, the saturating concentration is given by c os l2.v /(D'.rn) + 19K, fro which follows a inial value (K y 0) of 1.04 M. By the sae token we have at halfsaturation i(dc/dx) os (iq.v.k ) 1/2.(p os Pi S ) 1/2 l.v /(D'.rn) (dc/dx) oh (2q.V.K ) 1/2.[p oh So for the value of c oh we copute p lh log(l + p oh )/(l + p,,.)] 1' 2. c h l2.v /(4D'.rn) + c ih + K.log[(l + p oh )/(l + pih )]. Consequently, the inial value of c oh (K >0) is J ties the inial value of the saturating concentration, or 0.26 M. For overall absorption the halfvalue will be only slightly lower because of the additionof the uptake by the external surface. REFERENCES Arisz, W. H. (1960):Syplasatischer Salztransport in VallisneriaBlattern. Protoplasa 52: Bange, G. G. J. & J. J. M. Hoovans (1967): Transport of onovalent cations into, through and out of barleyroots: anexperiental theory. Isotopes in Plant Nutrition and Physiology International Atoic Energy Agency, Vienna. C. L. C. Meijer (1966); The alkali cation carrier of barley roots: a acroolecular structure? Acta Bot. Neerl. 15:

14 & 542 O. G. J. BANGE Bange, G. G.J. & R. Overstreet (1960): Soe observations on absorption of caesiu by excised barley roots. Plant Physiol. 35: Bowling, D. J. F. (1972): Measureent of profiles of potassiu activity and electrical potential in the intact root. Planta 108; A. Q. Ansari (1972): Control of sodiu transport in sunflower roots. J. Exp. Bot. 23: Briggs, G. E. & R. N. Robertson (1948): Diffusion and absorption in disks of plant tissue. New Phytol. 47: Dunlop, J. & D. J. F. Bowling (1971): The oveent of ions to the xyle exudate of aize roots. I. Profile of ebrane potential and vacuolar potassiu activity across the root. J. Exp. Bot. 22: Epstein, E. (1972): Mineral nutrition of plants: principles and perspectives. J. Wiley and Sons, New York. Honert, T. H. van den & J. J. M. Hooyans (1961): Diffusion and absorption of ions in plant tissue. I. Observations on the absorption of aoniu by cut discs of potato tuber as copared to aize roots. Acta Bot. Neerl. 10; Kannan, S. (1971): Plasalea: the seat of dual echaniss of ion absorption in Chlorella pyrenoidosa. Science 173: Klepper, B. & H. Greenway (1968): Effects of water stress on phosphorus transport to the xyle. Planta 80: Laties, G. G. (1969): Dual echaniss of salt uptake in relation to copartentationand longdistance Ann. transport. Rev. Plant Physiol. 20: Vakhistrov, D. B. (1967): On the function of apparent free space in plant roots. A study of the absorbing power ofepideral and cortical cells in barley roots. Sov. Plant Physiol. 14: