IV. Physiological Conditions Governing Uptake
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K. P. BARLEY
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,
t>O
(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
condition
f=-ac,
r = q, t > 0
(12)
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,
(13)
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 CONFIGURATION OF THE ROOT SYSTEM A N D NUTRIENT UPTAKE
173
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
cm
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),
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K. P. BARLEY
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,
v,,
to
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,
1965).
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
THE CONFIGURATION OF THE ROOT SYSTEM A N D NUTRIENT UPTAKE
175
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).
B.
VARIATION BETWEEN A N D ALONG
ROOTS
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
176
K. P. BARLEY
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
wetted.
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
5X
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.
THE CONFIGURATIONOF THE ROOT SYSTEM A N D NUTRIENT UPTAKE
0
SCALE
5
177
10cm
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
M
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.
V.
The Influence of Configuration on Uptake
A.
EFFECTIVE
RADIUS
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
:
178
K. P. BARLEY
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-