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IV. Physiological Conditions Governing Uptake

IV. Physiological Conditions Governing Uptake

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uptake found in experiments with stirred solutions, Epstein and Hagen

(1952) showed that one function of basic interest is

where T (moles c m P sec-') is the steady rate of uptake observed at

sufficiently large times, V (moles cmP2sec-I) is the maximum rate of uptake when supply is nonlimiting, and p (moles ~ m - is

~ a) plant parameter.

Equation (lo), which is analogous to the Michaelis-Menten equation of

enzyme kinetics, may be used to describe the uptake of ion species either

in the absence or in the presence of a given concentration of competing

ions. The parameter p may be treated as constant for a given class of roots

at a given temperature, provided that the plant does not begin to approach

salt saturation, and that the internal demand does not change significantly

as a result of shifts in the phase of plant development. The ordinary range

of values of V and p are shown in Table 11. Equation (8) can be solved

numerically using finite difference methods subject to a variety of nonlinear boundary conditions governing uptake. Kautsky et al. ( 1 968) give a

numerical solution for the case v = 0, subject to the modified EpsteinHagen condition,

f = - v,,c/o, + c ) ,

r = q,


(1 1)

where V,, is the maximum rate of uptake analogous to that defined by Eq.

(lo), but expressed per unit area of the surface of a root zone of radius q.

They show also that, provided the initial concentration c, < p, a good

approximation may be obtained by substituting the linear boundary



r = q, t > 0


where a (cm sec-I) is the apparent surface conductance of the root

(analogous to the surface conductance in the theory of heat conduction),

and is defined by

T,,= aC,

when C

= c,


Strictly, neither condition ( 1 1 ) nor the linear approximation (12) hold at

extremely low concentrations, since there is a limit below which the plant

cannot achieve any net uptake. The limits are of the order lo-' M for

nitrate (C. Olsen, 1950), and

M for phosphate and potassium

(Asher and Loneragan, 1967; Williams, 196 1).



The values of V , p , a, etc., given in the physiological literature have

usually been found by measuring the uptake of ions by sets of excised

roots, when the uptake time is limited to a few hours, or by the root systems of whole seedlings or young plants, when the uptake time may be

several days. We need to know whether such values apply over longer

periods of time. Care needs to be taken when averaging uptake values for

a set of roots. From transfer theory we know that components of the ion

flux are influenced by the product aq. For reasons given below the values

of a and q for the set of root zones comprising a root system are likely to

be correlated, so that, statistically (Yq # (1! (for zero correlationFy i = 0). Yet physiologists conventionally find the value of a (or more

sophisticated alternatives) by expressing the uptake as uptake per unit

root abundance and relating this to solution concentration. For present

purposes we can avoid this difficulty and define 7,by

where Q (moles cm-’) is the uptake per unit length of root. Over a period

of weeks the continuation of uptake clearly depends upon the growth of

the plant, and, as shown by Nye and Tinker (1969),

where W (8) is the weight of the plant, L (cm) is the length of root per

plant, and u (moles g-’) is the gravimetric concentration of the absorbed

element in the plant. Note that when u is constant Cur, depends upon

dWldt. Equations ( 14) and ( 15) suggest one possible approach by which

nutrient uptake models of the kind described in this review may be linked

with models of photosynthesis. Values of 7,derived from Eq. (14) do

not depend upon hypotheses about uptake mechanisms. If 7) is assumed

to be constant, Eq. (14) may be used to derive 6 from data of Loneragan

and Asher (1967) for the steady uptake of phosphate by a number of

species from continuous flow cultures over 4 weeks. For a constant

radius of 0.02 cm the estimated values of CU are of the order of


sec-’, and this is within the range found in short-term experiments with

low-salt plants.

So far we have considered the physiological conditions governing

nutrient uptake without reference to effects of the concomitant uptake of

water by the root. As indicated in Section 111 the water flux density Y,, at

the root surface r = q depends not only on the transpiration E , but also on

the abundance of the roots. If by analogy with the well known Leaf Area

Index (LAI) we term the product 27r$ LAthe “Root Area Index” (RAI),



then, as LA is of the order of lo2cm-' under crops, and may be as high as

lo3 cm-' under grasses (Newman, 1969), and as is commonly about

0.02 cm, the RAI is likely to be of the order 10' or lo2. Since E rarely

exceeds 1 cm day-' (1 x loe5cm sec-I), provided a reasonably high

proportion of the root surface is operative, v,, is unlikely to exceed

cm sec-', and will more commonly be of the order of lo-' cm sec-'.

Assuming for the present that at ordinary values of v,, effects of water

uptake on the conductance a are small, then, when v,, > a , ions accumulate

at the root surface and diffusion is away from the root; when, as is usual,


cm sec-' for readily absorbed nutrients-the root depletes the soil locally and diffusion occurs toward the

root. Marriott and Nye (1968) show that, when v,, < a and providing

~ , f / $ > I , the rate of uptake increases linearly with v,,; moreover the relative increase is almost independent of a. In dry soils y,, is unlikely to

exceed I x lo-' cm sec-', and, for this value, and for 6, = 0. I , k, = I X I OPfi

cm2 sec-',j = 10, 7) = 0.02 cm, at t = lo5 sec the relative increase in the

rate of uptake due to transpiration, predicted by the theory of Marriott

and Nye, is 5%. In moist soils v,, may rise to 1 X lop6cm sec-I when E is

cm sec-I

at its peak and all the roots are operating, or even to 5 X

when only a fifth of the roots are operating. For the last value of v,,, and

8 = 0.4, k, = 5 X I 0-6 cm' sec-',j = 10, = 0.02 cm, at t = lo5 sec the predicted increase in uptake is 17%. Marriott and Nye give an example that

magnifies the effect of transpiration, but the circumstances are improbable

as the transpiration is very rapid, yet the soil is dry.

While the theory outlined by Marriott and Nye is valuable as a first

attempt, it begs the question insofar as a is taken to be independent of v.

Although the rates of ion and water uptake from stirred solution can be

varied independently in experiments with respiration inhibitors or

osmotica (Brouwer, 1954), and although the two rates are nearly independent in extremely dilute solutions, correlations are often found when

C > 1-10 mM. As the rate of transpiration rises, the selectivity of the

root tends to decline (Pitman, 19651, and passive uptake to the shoot

tends to increase, the most straightforward example being the positive

effect of transpiration on the uptake of Si by oats (Jones and Handreck,


In experiments with well stirred solutions when u is expressed per unit

area of root surface, we can generally disregard the area of the root hairs.

This is because ions from the ambient solution pervade the free space of

the root, uptake through the plasmalemma can occur throughout the

cortex, and the hairs add little to the area of the interface between free

space and plasmalemma. Provided c, = co this is likely to hold in the soil



also. When this is so the uptake per unit length Q is correlated with q P

(volume per unit length) (see, for example, Fig. 4 of Russell and Newbould, 1968). But in the soil, when c,,/co+ 1 , and particularly if the soil is

relatively dry, most of the uptake is likely to occur via the root hairs

(Section V). Since ions tend to accumulate in the hairs (Lauchli, 1967),

the chief regulating barrier then resides in the plasmalemma lining the

inner tangential wall of the epiderm and/or in the plasmalemma of the

outermost file of the cortex. When this is so Q will be correlated with r )

(surface area per unit length). As we shall see below this description is too

simple, but it serves to show that the microscopic flow path followed by

ions within the root may not be the same when the root is in a stirred

solution as when it is in the soil. This raises doubts about the utility of

determining plant parameters such as a by measuring uptake from stirred

solutions; at least we need to compare conventional values with those

found by measuring Q in soils of known properties, and fitting transfer

equations such as Eq. (8) (Clarke and Barley, 1968).




Not all roots are concerned primarily with the absorption of water or

nutrients, and root form often shows adaptation for the performance

of functions other than absorption. The fleshy roots of many perennial and biennial dictotyledons, for example, act as organs of storage, as

does the cortex of the main roots of many monocotyledons; even laterals

may be modified to form storage organs in certain species. The prop-roots

of tall grasses show mechanical adaptation; for example the proproots of maize have thick double rings of fibers. The roots of plants

adapted to wet places frequently have abundant aerenchyma; and, while

aerenchyma is most conspicuous in the marsh plants, it is by no means

confined to them. The various adaptations may give rise to obvious dior trimorphism within a root system (Kokkonen, 1931; Jacques, 1937;

Barley, 1953). Dimorphism may also result from the presence of mycorrhizal roots, and mycorrhizal associations are common in grasses including the cereals, clovers, and horticultural plants. It has been shown that

mycorrhizal roots can sustain their ability to absorb phosphate for much

longer periods than uninfected roots (Bowen, 1968), and the possible

role of mycorrhizas in the nutrition of crop and pasture plants deserves

more attention.

Along the length of a root characteristic differences in form and structure are found corresponding with the various stages in development and



degeneration. Close behind the elongating tip root hairs arise, and in the

hair zone the root is “glued” to the soil by its mucilage (Section V);

elsewhere it separates easily from the soil; in older zones, owing to exfoliation of the outer cells, the central cylinder is often left within a wider

air-filled channel (see Fig. 2b of Head, 1968). When the outer cells degenerate, the outermost intact cortical layer generally becomes suberized,

when it is termed an exodermis. Although water and solutes penetrate the

exodermis when the root is immersed (Kramer and Bullock, 1966), this

is less likely when the root is in the soil, as the suberized zones are poorly


Given the known differences in form and structure between and along

the roots of a plant, it is obvious that simple relations between Q and r) of

the kind mentioned in Section IV, A are unlikely to account for more than

part of the variation in physiological uptake ability within a root system.

Using a series of potometers, Grasmanis and Barley (1969) found, for

example, that in stirred solution QNon/r)or QNo3/q2varied by a factor of

4 or 5 along the length of the pea radicle, most of the variation being

associated with differences in protein content between the zones. Recently the study of uptake and translocation along the root has been expedited by the technique of scanning the root after uptake from radioactive solutions (Bowen and Rovira, 1967). The technique also lends itself to the study of uptake by different members of the root system

(Bowen and Rovira, 1969). In either case careful account must be taken

of the influence of isotopic exchange. An example of the results is given

for seminal roots of wheat in Fig. 2. After the roots had been treated with


M p h o ~ p h a t e - ~ in

~ , calcium

~ ~ P sulfate solution for 15 minutes,

some of the plants were removed for scanning, and the remainder were

transferred to phosphate-:”P in calcium sulfate for a further 210 minutes

to allow translocation of the 32P.The scan at 15 minutes (Fig. 2) shows

the usual subapical peak (see also Brown and Cartwright, 1953; Grasmanis and Barley, 1969) and a second peak in the zone where laterals

were developing. Much of the absorbed %&P

was retained in the growing

tip (see also Kramer and Wiebe, 1952), but it was translocated readily to

the tops from zones proximate to the tip and from the laterals. Finally

it is known that the various members of the root system differ in their

relative rates of absorption of different nutrients. For example, Russell

and Sanderson (1967) showed with small potometers that the ratio

QP/Qsrfor first-order laterals of barley was twice that for the main root

axes. We conclude that, while form may be important, the pattern of

nutrient uptake depends also on physiological differences and gradients

in the root system.







FIG.2. Distribution of 32Pin a wheat seedling (Bowen and Rovira, 1969). Top: After 15

minutes in 5 x 10-RMph~sphate-~l.~*P.

Bottorn:After a further 210 minutes in 5 x


p h ~ s p h a t e - ~ ~Only

P . one of five seminal roots is shown. The radioactivity of laterals is included, and the position of the most distal lateral is shown by the arrow.


The Influence of Configuration on Uptake




1. The Axial Part of the Root

As noted in Section IV, when cq co, uptake occurs throughout the

cortex and we can disregard the root hairs; also, for purposes of illustration we can treat the problem deterministically and assume that T and

hence a are likely to be related to q2.Provided the roots do not interact,

the influence of r) on uptake per unit surface area can be found by making

the appropriate adjustment to a, and referring to solutions of Eq. (8)

subject to Eq. (12). Carslaw and Jaeger [( 1959, p. 337, Eq. (IS)] provide a solution for the case v = 0, from which it can be seen that, when

t is of the order of days, as 7 decreases, the influence of the parameter qalk,8 outweighs that of KLt/r)*,so that the rate of uptake per unit

surface area increases. For the ordinary range of values of other variables, q has an appreciable influence when (Y =s

cm sec-l. Furthermore, the surface area of a given weight of roots varies inversely with r).

Nye ( I 966) borrows likewise from Carslaw and Jaeger, but he underestimates the effect of r) through assuming that a is independent of r). This

, that Q is likely to be directly prois appropriate only when c , , ~ ~ , ,so

portional to q. But when this is so the root hairs are influential, and r) no

longer determines the effective radius of the root.

Steady state solutions of Eq. (5) for v > 0 and subject to various

boundary conditions are given by S. R . Olsen and Kemper ( 1968, p. 13 l ) ,

from which it can be seen that r) appears in a logarithmic term.





2. The Irlfluence of Root Hairs

As noted in Section IV, when c,, 4 co, most of the uptake is likely to

occur via the root hairs. Before evaluating the role of the hairs in uptake,

we need to know the time for which they continue to absorb nutrients.

Unfortunately such information is meager. Hairs may persist for long

periods in many species, but they do not necessarily continue to absorb

ions, as the walls of persistent hairs may thicken or even become lignified (McDougall, 1921). Root hairs generally collapse after a few days or

weeks, but in the Gramineae, and in the cereals in particular, the hairs

tend to persist, thin-walled hairs being found on all parts of the root

system. A recent report that the root hairs of barley, Hordeum vulgare

L., live for only 2 days (McElgunn and Harrison, 1969) should be discounted, as the roots were illuminated brightly and stained at hourly

intervals with neutral red, and this treatment kills cells in the barley root

(Patterson, 1941). In dicotyledons having roots that show extensive

secondary thickening -and these include the common pasture legumes

(Soper, 1959)-the root hair cells are lost together with the rest of the

epiderm as thickening proceeds, but in other dicotyledons the hairs may

persist for weeks or even months (Whitaker, 1923).

a . Qualitative Efects. The most important function of root hairs may

well be the maintenance of liquid continuity between water in the cell

wall and pore water in the soil. Main roots and laterals are far too wide to

occupy the narrow voids into which water menisci retreat as the soil

dries. Even those voids that can just be entered by hairs (radius = 5 p )

drain at a suction of only 0.3 bar. However, the hairs are more effective

than this value would indicate, as their walls secrete mucilage, and the

mucilage infiltrates into finer pores. The author has observed that more

mucilage is secreted when the soil is dry than when it is moist. Although

the existence of 3 “junction resistance” has not yet been established for

hairless roots grown in situ, a resistance of this kind has to be invoked to

explain the low ion uptake observed when roots are disturbed and pressed

back onto the soil (Clarke and Barley, 1968; see particularly their Fig. 7).

In addition to any effect that root hairs may have on junction resistance,

the significance of local alteration of the soil around the hairs needs to be

considered. Local changes in sorption characteristics resulting, for example, from pH shifts, or complexing with diffusible exudates or rhizosphere products, can set up diffusion gradients either toward or away from

the root. Wilkinson et al. (1 968) show how such effects can lead to local

jepletion of calcium independently of uptake.

b. Geometrical Efects. The geometrical effects of root hairs on nutri-

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IV. Physiological Conditions Governing Uptake

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