Annals of Botany 81 : 225–232, 1998
Modelling of the Hydraulic Architecture of Root Systems : An Integrated
Approach to Water Absorption—Distribution of Axial and Radial Conductances in
Maize
C L A U D E D O U S S AN*†, G I L L E S V E R C A M B R E‡ and L O I$ C P A G E' S‡
* INRA, UniteU de Science du Sol, Domaine Saint Paul, Site Agroparc, 84914 AŠignon Cedex 9, France and
‡ INRA, UniteU de Recherche en Ecophysiologie et Horticulture, Domaine Saint Paul, Site Agroparc,
84914 AŠignon Cedex 9, France
Received : 14 July 1997
Returned for revision : 25 August 1997
Accepted : 21 September 1997
The ‘ Hydraulic Tree Model ’ of the root system simulates water uptake through root systems by coupling a root
architecture model with laws for water flow into and along roots (Doussan, Page' s and Vercambre, Annals of Botany
81 : 213–223, 1998). A detailed picture of water absorption in all roots comprising the root system is thus provided.
Moreover, the influence of different distributions of radial and axial hydraulic conductances in the root system on the
patterns of water uptake can be analysed. Use of the model with Varney and Canny’s data (1993) for flow along maize
roots demonstrated that a constant conductance in the root system cannot reproduce the observed water flux profiles.
Taking into account the existing data on hydraulic conductances in maize roots, we fitted the distribution of
conductances in the root system to the observed flux data. The result is that, during root tissue maturation, the radial
conductivity decreases by one order of magnitude while the axial conductance increases by about three orders of
magnitude. Both types of conductance exhibit abrupt changes in their evolution. Due to the conductance distribution
in the root system, appreciable water potential gradients may develop in the roots, in both the branch roots and main
axes. An important point is that the conductance distribution in the branch roots described by the model should be
related to the age of the tissue (and not the distance from the branch root tip) and is therefore closely related to the
development process. Thus for branch roots, which represent about 90 % of the calculated total water uptake in
43-d-old maize, water absorption will depend on the opening of the metaxylem in the axes, and on the time dependent
variation of the conductances in the branch roots.
# 1998 Annals of Botany Company
Key words : Water, absorption, root system, architecture, model, hydraulic conductance, Zea mays L.
INTRODUCTION
In an accompanying article (Doussan et al., 1998), we
presented a model for the simulation of water uptake by
root systems. This model (the ‘ Hydraulic Tree Model ’ of
the root system) simulates water transfer into and along
roots by coupling a model of root system architecture
(Page' s, Jordan and Picard, 1989) with laws describing flow
in roots. By combining local information on axial conductance and radial root hydraulic conductivity with data
on root system architecture, water uptake and transfer can
be investigated at the level of the single root and the root
system.
When applied to maize architecture using the values of
axial conductance and radial conductivity measured by
Frensch and Steudle (1989), the model showed that only the
upper part of the root system is active in water uptake, even
if immersed in a solution with a high water potential. This
example emphasized the limit to the maximum water flow
through the xylem in primary roots, but it contradicted the
experimental data of Varney and Canny (1993) for maize.
Indeed, they showed that the entire length of primary roots
is active in water uptake. Thus, an improved analysis of the
† For correspondence.
Fax (33) 4 90 31 62 44, e-mail doussan!avignon.inra.fr
0305-7364}98}020225­08 $25.00}0
spatial variation of hydraulic conductance in the root
system is required.
In fact, it is well recognized that radial conductivity and
axial conductance are not constant throughout the root
system and that differentiation of root tissues becomes more
marked with distance from the apex. Xylem vessels open at
various distances from the root apex, increasing longitudinal
flow capacity, while the endodermis develops thick and
lignified cellular walls, thought to be relatively impervious
to water (Lu$ ttge, Kluge and Bauer, 1992). This led to the
classical view that most of the water is absorbed in the
vicinity of the tip. However, numerous studies have shown
that the older proximal parts, even suberized, also absorb
water, but generally at a reduced rate (Graham, Clarkson
and Sanderson, 1974 ; Sanderson, 1983 ; Varney and Canny,
1993 ; Kramer and Bullock, 1996). Absorption may be even
higher in proximal than distal parts (Maertens, 1971). The
influence of endodermis differentiation on water transport
depends on the water pathway in root tissues. If the radial
pathway is essentially apoplasmic, the lignified endodermis
may control the water flow. Conversely, if water transport
is largely symplasmic (i.e. water enters cells in the epidermis
or in the cortex), the influence of the endodermis should be
considerably reduced (Varney, McCully and Canny, 1993).
Moreover, late metaxylem differentiation can be slow, the
opening of the large vessels starting 20–30 cm from the tip
bo970541
# 1998 Annals of Botany Company
Doussan et al.—Modelling of the Hydraulic Architecture of Root Systems
WATER ABSORPTION ALONG A ROOT :
EXPERIMENTAL DATA AND MODEL
RESULTS FOR A CONSTANT
CONDUCTANCE IN THE ROOT SYSTEM
Radial water inflow (cm3 cm–2 s–1 × 106)
Varney and Canny (1993) designed an elegant experiment
using a fluorescent dye (sulphorhodamine G) to examine
water fluxes in roots of aeroponically grown maize. The
results of their measurements of fluxes into main axes and
branch roots with distance from the tip of the main axis are
shown in Fig. 1 (redrawn from their Fig. 6). The same type
2.5
2.0
Main axis
Branch roots
1.5
1.0
0.5
0
20
40
60
80
Distance from the main axis tip (cm)
100
F. 1. Experimental data of Varney and Canny (1993) for water fluxes
into main axes and branch roots of a maize root system (aeroponically
grown maize) as a function of distance from the main axis root tip
(redrawn from their Fig. 6). The branch root water flux is the mean
water flux from all the branch roots on a 2 cm piece of main axis.
0
3
2
Water Water
potential flux
Kh = 5 × 10–11 m4 s–1 MPa–1
Kh = 4.2 × 10–10 m4 s–1 MPa–1
Kh = 1 × 10–8 m4 s–1 MPa–1
–0.05
–0.10
1
–0.15
0
20
40
60
80
Distance from root tip (cm)
Xylem water potential (MPa)
(St Aubin, Canny and McCully, 1986). As a consequence,
the longitudinal water transport can be notably hindered in
this zone.
Experimental data on root hydraulic conductance are
available in the literature. Usually, total conductance of the
root system is measured (Kolb, Sperry and Lamont, 1996 ;
Yang and Grantz, 1996). Nevertheless, some measurements
at the level of the root segment are also available : evolution
of axial conductance and radial conductivity as a function
of distance from the root tip (Frensch and Steudle, 1989 ;
Nobel and Alm, 1993), of root age (Nobel, Huang and
Garcia-Moya, 1993) or of branching order (Moreshet,
Huang and Huck, 1996). Anatomical observations also
provide information on evolution of hydraulic conductance
at the single root level. However, this scattered information
does not lead to an integrated quantitative view of water
absorption and transfer in the whole root system from the
soil to the shoot.
In this article, while reviewing certain measured hydraulic
data of roots (flux, conductance), we attempt to analyse the
consistency of this data with the ontogenic development of
roots with the help of the model. Some of the consequences
for water uptake and transfer at the root system level will be
presented. Throughout this article, we often use Varney and
Canny’s (1993) data for fluxes of water absorption in the
maize root system.
Radial water inflow (cm3 cm–2 s–1 × 106)
226
100
F. 2. Calculated xylem water potential and water flux using the
‘ Hydraulic Tree Model ’ of the root system (Doussan et al., 1998) for
a main axis and its branch roots in a 43-d-old maize root system as a
function of the distance from the main axis tip. The radial conductivity
is the same in the whole root system (2±2¬10−( m s−" MPa−" for main
axes as well for branch roots). Results are shown for three simulations
with different axial conductances (Kh ¯ 5¬10−"", 4±2¬10−"! and
1¬10−) m% s−" MPa−") which are considered to be the same in the
whole root system. Results for branch roots fluxes are confounded with
those for the main axes in the figure.
of profile for water absorption along main axes has also
been shown experimentally in potometric measurements on
barley (Hordeum Šulgare, Sanderson, 1983 ; Graham et al.,
1974), pumpkin (Cucurbita pepo, Graham et al., 1974),
broad bean (Vicia faba, Brouwer, 1965) and onion (Allium
cepa, Rosene, 1941). The main advantage of Varney and
Canny’s data is that they simultaneously measured water
fluxes into main axes and branch roots. They demonstrated
a maximum uptake in the distal part of the main axes, as
well as a maximum uptake 30–60 cm behind the tip of the
mother root for branch roots.
Some results produced by the ‘ Hydraulic Tree Model ’ of
the root system for maize are shown in Fig. 2. Here, axial
conductance and radial conductivity are considered to be
constant in the whole root system. The imposed total
outflow at the collar of the root system is the same for all
simulations (2±45¬10−$ cm$ s−"). The axial conductance was
varied between simulations while the radial conductivity
was kept constant at the value given by Frensch and Steudle
(1989) for young maize roots (2±2¬10−( m s−" MPa−"). In a
recent review by Moreshet et al. (1996), the range of
experimentally determined axial conductances are 1 to
42¬10−"" m% s−" MPa−". The three values of axial conductance used in the simulations shown in Fig. 2 are :
5¬10−"", 42¬10−"" and 1¬10−) m% s−" MPa−". The first
value (case 1) is that measured by Frensch and Steudle
(1989), 8 to 12 cm from the tip. The second (case 2) is the
maximum value given by Moreschet et al. (1996). Finally,
the third (case 3) is a calculation using the Poiseuille law for
a bundle of four mature metaxylem vessels (100 µm
diameter, McCully, 1995).
It can be seen in Fig. 2 that the conducting capacity of
xylem is the limiting factor for water flow in case 1
(measured value for maize) and the water uptake occurs
only within the first 40 cm of the root from the base.
Absorption is accompanied by a large water potential
gradient in this zone. An approximate ten-fold increase in
axial conductance (case 2) extends the absorption zone
down to the tip while reducing the water potential gradient.
Finally, for mature metaxylem (case 3), water is uniformly
absorbed along the root and radial conductivity limits the
water uptake.
However, as exemplified by comparing Figs 1 and 2, a
uniform distribution of hydraulic conductances in the root
system does not reproduce the water influx profile in maize
roots reported by Varney and Canny, whatever the axial
conductance used. Indeed, the combination of a constant
axial conductance and radial conductivity along a root leads
to a monotonous decrease in water flux towards the tip,
with no maximum. This is not only true for main axes but
also for branch roots (Fig. 2) ; however, this is not confirmed
by Varney and Canny’s data.
Thus, from the above considerations, we see that it is
necessary to introduce a heterogeneous conductance distribution in the model to reproduce the experimentally
determined water absorption profiles. In this case, the
gradients of hydraulic axial conductance and radial conductivity are probably related to the ontogenic development
of roots.
DISTRIBUTION OF ROOT HYDRAULIC
CONDUCTANCES IN MAIZE : ESTIMATION
USING THE HYDRAULIC TREE MODEL OF
THE ROOT SYSTEM
The ‘ Hydraulic Tree Model ’ was adapted to obtain a maize
root system architecture similar to that described in Varney
and Canny’s experiment (the age of the simulated maize is
43 d, the density of branch roots is 9 cm−" and their mean
length 2±6 cm. Main axes and branch roots diameters are 1
and 0±35 mm, respectively.) By adjusting the conductance
distribution in the root system, we attempted to reproduce
the water absorption profile along roots measured by
Varney and Canny (Fig. 1). The fit of the model to the
experimental flux data is considered to be satisfactory if the
mean error of the fit is equivalent to the experimental error.
Since without a priori knowledge, different conductance
distributions may possibly fit the same set of experimental
data, it is necessary to formulate certain constraints and
assumptions for the solution : (a) the distribution of
conductances in the root system is represented by the
evolution of the axial conductance and radial conductivity
in each root with distance from the tip or with the age of the
tissue ; (b) this evolution of conductances in a root is the
same for all roots with the same branching order (i.e. main
axes or branch roots) ; (c) the axial conductance in a root is
a monotonous increasing function, of the distance from
the tip or the age of the tissue, and is related to xylem
maturation ; (d ) the influence of tertiary roots is assumed
negligible (i.e. their axial conductance is considered too low
to influence water uptake ; e.g. Wind, 1955) ; (e) as Varney
and Canny mainly used roots from nodes 2 and 3, the fit is
determined using the average of the water fluxes calculated
by the model for roots originating from nodes 2 and 3 ; and
Radial water inflow (cm3 cm–2 s–1 × 107)
Doussan et al.—Modelling of the Hydraulic Architecture of Root Systems
20
227
Experimental
Model
Main axes
Branch roots
15
10
5
0
20
40
60
80
Distance from main axis tip (cm)
100
F. 3. Data of Varney and Canny (1993) for water flux into maize
roots (points) fitted using the ‘ Hydraulic Tree Model ’ of the root
system (continuous lines). Vertical bars represent one s.d. in the
experimental data.
( f ) available data from the literature are included in the
model especially the maximum axial conductance and radial
conductivity which limit the range of allowed conductances.
For the main axes, axial conductance and radial conductivity up to 12 cm from the tip were set to those
experimentally determined by Frensch and Steudle (1989).
The axial conductance near the base of the main axes
(mature metaxylem—maximum value) was set to
5¬10−* m% s−" MPa−", in accordance with the conductance
measurements published by Luxova' and Kozinka (1970,
1973) and the Poiseuille law based calculations of Jordan et
al. (1993).
Much less is known about the hydraulic properties of
branch roots. Huang and Nobel (1994) measured the axial
conductance to be approx. 10 % of that in the root axes of
desert succulents. Varney et al. (1991) showed that for
0±35 mm diameter branch roots of maize, the axial conductance is 0±1–0±01 % of that of the axile root with mature
metaxylem. Based on the Poiseuille law, an axial conductance of 1±7¬10−"" m% s−" MPa−" can be calculated for a
0±35 mm diameter root with Wind’s data (1955) for grass
roots. However, it is well known that the theoretical axial
conductance may deviate considerably from the measured
values. In accordance with these figures, an upper limit of
2¬10−"# m% s−" MPa−" for the axial conductance of branch
roots was chosen and used in the model. The maximum
value of the radial conductivity of branch roots was set to
the same value as for the main axes measured by Frensch
and Steudle (1989) i.e. 2±2¬10−( m s−" MPa−".
Results of the fitting process are presented in Fig. 3. Apart
from the experimental points 12±5 cm from the tip, the
model agrees well with experimental data (mean relative
error 3 % for axes and 7 % for branch roots). Experimental
points corresponding to the distal part of the root in Fig. 3
present a higher variability due to the irregular deposition
of the mist containing the dye in the aeroponic chamber
(Varney and Canny, 1993).
Main axes
Axial conductance
Radial conductivity
4
2.0
1.5
3
1.0
2
1
0.5
0
0.0
20
0
2.0
40
60
80
Distance from tip (cm)
A
100
Branch roots
Axial conductance
Radial conductivity
2.0
1.5
1.5
1.0
1.0
0.5
0.5
0.0
B
0
5
10
15
20
Time after emergence (d)
0.0
F. 4. Estimated evolution of axial conductance and radial conductivity
in main axes (A) and branch roots (B) for a maize root system.
Conductances are derived from fitting Varney and Canny’s (1993) data
to the water flux into roots with the ‘ Hydraulic Tree Model ’ of the root
system (Doussan et al., 1998).
The calculated distribution of axial conductance and
radial conductivity is shown in Fig. 4A and B for main axes
and branch roots, respectively. A remarkable feature is the
high variation in conductances for main axes and branch
roots.
Considering the root axes, radial conductivity shows a
ten-fold decrease from the distal to the proximal ends, but
on the contrary, the axial conductance increases by about
three orders of magnitude (in the case of the axial
conductance, the range in variation is imposed by data in
the literature). The high absorption zone in the distal part of
the main axes is characterized by a high radial conductivity
and increasing axial conductance. The subsequent decrease
in water flow along the main axes is related to the decrease
in radial conductivity towards the proximal part. This
evolution in radial conductivity agrees with observations
and double pressure probe measurements by Frensch,
Hsiao and Steudle (1996) who attribute this decrease to the
progressive thickening of the endodermal cell walls. An
interesting feature of Fig. 4A is that the evolution of radial
conductivity is characterized by a two step decrease
occurring approx. 20 and 50 cm from the tip. At 50 cm from
the tip, the endodermis should already be mature and this
decrease may be related to the differentiation of other
Branch root water flux (cm3 cm–2 s–1 × 107)
5
Radial conductivity (m s–1 MPa–1 × 107)
Doussan et al.—Modelling of the Hydraulic Architecture of Root Systems
Radial conductivity (m s–1 MPa–1 × 107)
Axial conductance (m4 s–1 MPa–1 × 1012)
Axial conductance (m4 s–1 MPa–1 × 109)
228
8
6
4
2
0
20
40
60
80
Distance from main axis tip (cm)
100
F. 5. Evolution of the branch root water flux with distance from the
main axis tip calculated by the model in the case of constant axial
conductance (5¬10−"" m% s−" MPa−") and radial conductivity
(2±2¬10−( m s−" MPa−") in the branch roots. Conductances of main
axes are as in Fig. 4A.
tissues (epidermis, hypodermis). On the contrary, axial
conductance increases towards the root base, with more or
less sudden increments, corresponding to the progressive
maturation of early metaxylem and late metaxylem, in
accordance with the anatomical observations of Saint Aubin
et al. (1986) and McCully (1995).
It is important to note that it was impossible to fit the
model to measured water fluxes in branch roots by simply
considering a spatial evolution of conductances along the
branch root (i.e. with distance from the branch root tip).
Temporal evolution (i.e. tissue age) proved to be the
pertinent parameter describing the evolution of conductance
in branch roots. This is mainly due to the determinate
growth exhibited by branch roots, contrary to main axes,
and in this case the relation between position (distance from
tip) and time (age of the tissue) is not unique. The maturation
of xylem in branch roots is rather slow (more than 10 d, cf.
Fig. 4B) and the axial conductance limits flow during this
period. Due to the determinate growth pattern, when the
branch root shows little growth the maturation of xylem
progresses towards the apex, increasing the water conducting
capacity of the root, but at the same time radial conductivity
decreases. Moreover, this implies that even if branch roots
are the same length, they do not necessarily possess the same
efficiency when taking up water, but on the contrary they
show a marked dependence with their position on the main
axes. It is interesting to note (Fig. 4B) that radial
conductivity is already at its lowest level when xylem has
fully matured, in accordance with the anatomical observations of Wang, McCully and Canny (1994).
The position of the maximum uptake by branch roots,
40 cm from the tip (Fig. 3), is related to the increase in axial
conductance along the main axes (Fig. 4A) and thus an
improved evacuation of water from branch roots in the
main axes downstream, as emphasized by Varney and
Canny (1993). Nevertheless, this modelling experiment
shows that it is not a sufficient condition. For example, Fig.
5 presents water flux simulation results for branch roots in
Doussan et al.—Modelling of the Hydraulic Architecture of Root Systems
the case of a constant conductance in these roots (axial
conductance ¯ 5¬10−"" m% s−" MPa−", radial conductivity
¯ 2±2¬10−( m s−" MPa−" ; the main axis conductances are
those given in Fig. 4A). Clearly, in this case, the water flux
in branch roots increases monotonously with distance from
the tip and there is no maximum of water uptake as found
in experimental data. Consequently, together with the
increasing flow capacity of the main axes, it is necessary to
consider the evolution of conductances in branch roots with
age and growth.
CONSEQUENCES FOR WATER UPTAKE AT
THE ROOT SYSTEM LEVEL
Figure 6 presents calculated water fluxes and potentials with
distance from the tip in the main axes originating from
different nodes on the maize plant (seminal and roots issued
from nodes 2 and 4 of the 43-d-old maize plant). The fluxes
0.0
A
Main axis water flux
Branch roots water flux
Axis xylem water potential
2.0
–0.02
–0.04
1.5
–0.06
–0.08
1.0
–0.10
0.0
–0.12
0.0
B
–0.02
2.0
–0.04
7b
1.5
–0.06
–0.08
1.0
–0.10
0.5
0.0
7a
7c
–0.12
Xylem water potential (MPa)
Radial water inflow (cm3 cm–2 s–1 × 106)
0.5
0.0
C
–0.02
2.0
–0.04
1.5
–0.06
–0.08
1.0
–0.10
0.5
–0.12
–0.14
0
20
40
60
80
100
Distance from main axis tip (cm)
F. 6. Calculated water fluxes into branch roots and main axes, as well
as xylem water potential of axes, with distance from the main axis root
tip for roots originating from the seminal (A), node 2 (B) and node 4
(C) of a 43-d-old maize plant. Axial conductance and radial conductivity
of roots are as in Fig. 4. References 7a, 7b and 7c on Fig. 6B show the
position on the main axis of the branch roots shown in Fig. 7.
229
towards the main axes show a similar profile for different
nodal roots, but the maximum value increases from the
seminal to the nodal roots at the base of the root.
Considering branch roots, the maturation of conductances with time implies variations in the absorption profiles
depending on the node of the mother primary root. Figure
6 shows that, for branch roots, the smaller the number of
the node from which the mother root has originated (older
roots), the more the absorption peak of the branch roots
shifts towards the tip of the main axis while becoming
narrower and decreasing in intensity at the same time. This
behaviour is related to : (1) the decrease in growth rate of the
main axis with age which occurs simultaneously with the
time dependent decrease in branch roots conductance ; and
(2) the appearance, closer to the tip, of branch roots in older
main axes (Doussan et al., 1998). It should be noticed that
even if the total conductance of branch roots decreases with
time in the upper layers of soil, the continuous appearance
of nodal roots from the shoot with highly conductive young
branch roots should maintain the efficiency of water uptake
in this zone.
The root water potential of main axes is also shown in
Fig. 6 and several facts are worth noting : firstly, the water
potential is not homogeneous in the root, even in mature
metaxylem where axial conductance is high. If the shape of
the water potential profiles along the main axes are similar
between main axes issued from different nodes, water
potential values show a decreasing tendency for main axes
issued from higher nodes. Water potential gradients vary
from about 0±02 MPa m−" in the proximal zone to between
0±2 and 0±25 MPa m−" in the distal younger zone. Alm,
Cavelier and Nobel (1992, and references cited therein) also
found such gradients : 0±3 MPa m−" for 20 cm long roots of
AgaŠe deserti and Opuntia ficus-indica, 0±17 MPa m−" for
Picea sitchensis and 0±2 MPa m−" for Pinus taeda. Secondly,
Fig. 6 clearly shows that root water potentials and fluxes do
not show a similar evolution. Water potential decreases
more or less monotonously, while fluxes show local maxima.
This would not be the case if conductances were distributed
homogeneously in the root system (Fig. 2). In the case of a
heterogeneous distribution of conductances, the water flux
distribution in roots cannot be deduced from knowledge of
xylem water potential alone (and reciprocally). Finally, the
main feature of the simulated water potential, i.e. a basal
zone in the main axes where the gradient of water potential
is regular and small, and an apical zone where the gradient
is less regular and greater, can be found in the data of
Frensch et al. (1996, see their Fig. 5). These authors, using
a root pressure probe and a cell pressure probe simultaneously, measured the dissipation of a pressure wave
simulating the effect of transpiration along maize roots. It is
interesting to note that the simulated and measured ratios of
the gradients between the apical and basal zone are
equivalent (about 8 in the experiment by Frensch et al. and
between 5 and 8±5 in the simulation).
Calculated water uptake and water potentials for branch
roots as a function of the distance from their apex are shown
in Fig. 7. These branch roots are from different positions on
the same mother primary root. On the one hand, the young
branch roots, on a distal position on the main axis, show
230
Doussan et al.—Modelling of the Hydraulic Architecture of Root Systems
2.0
0.0
A
Branch root water flux
Branch root xylem water potential
1.5
0
–0.02
–0.04
–20
–0.06
1.0
–0.08
Depth (cm)
–0.10
0.5
0.0
0.0
B
–0.02
1.5
–0.04
–0.06
1.0
–0.08
–0.10
0.5
–0.12
0.0
Xylem water potential (MPa)
Radial water inflow (cm3 cm–2 s–1 × 106)
–0.12
–60
–80
Water flux
3
–2 –1
(cm cm s )
0
2.9 10
–6
A
–100
–100
–50
0
Horizontal distance (cm)
50
0.0
C
0
–0.02
1.5
–0.04
–20
–0.06
1.0
–0.10
–0.12
–0.14
0.5
1.0
1.5
2.0
2.5
Distance from branch root tip (cm)
F. 7. Calculated water flux and xylem water potential along branch
roots located at 12 (A), 33 (B) and 90 (C) cm from the mother root tip
(root originating from node 2 of a 43-d-old maize plant—cf. Fig. 6).
little uptake because of a low axial conductance (Fig. 7A).
On the other hand, when metaxylem has fully matured, old
branch roots in a proximal position on the main axis also
show little uptake because of a limiting radial conductivity
(Fig. 7C). The most absorbing branch roots (Fig. 7B) show
an almost homogeneous absorption throughout their length
due to a combination of sufficiently high axial conductance
and radial conductivity. Water potential in the branch roots
may show considerable gradients, particularly in the highly
absorbing roots. For example, in Fig. 7B, the gradients vary
from 0±7 to 7±7 MPa m−".
Water fluxes and potentials in the whole root system,
resulting from model calculations with the conductance
distribution shown in Fig. 4, are presented in Fig. 8. Xylem
tension at the root system collar caused by transpiration
propagates through the whole root system, except in the tips
of main axes and in the young branch roots located in the
distal part of axes. Likewise, almost the whole root system
is active in taking up water (except the young parts), but flux
distribution in the root system appears to be rather
Depth (cm)
–0.08
0.5
0.0
–40
–40
–60
–80
Water potential
(MPa)
0
–0.145
B
–100
–100
–50
0
Horizontal distance (cm)
50
F. 8. Calculated water uptake (A) and xylem water potential (B) in
a 43-d-old root system of aeroponically grown maize (three-dimensional
simulated maize root system projected on a vertical plane). The
transpiration of the plant is 2±45¬10−$ cm$ s−". Water potential of the
external medium is 0 MPa.
heterogeneous, in contrast to xylem water potential. Here,
branch roots are responsible for the major part of total
water inflow (90 %). So, in the case of maize, these results
show that branch roots collect water while main axes
assume long distance axial transfer towards the stem.
CONCLUSIONS
Plant roots undergo drastic changes with time regarding the
structure of the conducting vessels and tissue resistance to
water flow. This evolution of hydraulic characteristics and
their distribution within the root system can be investigated
Doussan et al.—Modelling of the Hydraulic Architecture of Root Systems
and quantified with the help of the ‘ Hydraulic Tree Model ’
of the root system if data on water fluxes or the distribution
of conductances along the roots are available. In the case of
aeroponically grown maize, examination of the flux data of
Varney and Canny (1993) using the model highlights certain
points : (1) a constant axial conductance and radial
conductivity in the whole root system cannot describe flux
data along a root ; (2) the model predicts that, during the
maturation of root tissues, radial conductivity decreases by
one order of magnitude (while axial conductance increases
by about three orders of magnitude according to data in the
literature) ; (3) appreciable water potential gradients may
develop in the roots, particularly in branch roots but also in
main axes ; (4) because of determinate growth, time is the
pertinent parameter describing the evolution of conductance
in branch roots ; and (5) water uptake by branch roots not
only depends on the opening of main axis metaxylem
vessels, but also on the time dependent distribution of
conductances in the branch roots.
These findings have some implications for water uptake in
soil. Indeed, as the distribution of conductances is heterogeneous in the root system because of the maturation
processes, the spatial distribution of water absorption from
the soil will also be heterogeneous. At some place in the soil
colonized by an axis with branch roots, absorption will
show a non-monotonous pattern with time : first absorption
will be very low because the xylem in branch roots is not
mature, it will then reach a maximum and finally decrease to
a lower level with the decrease in radial conductivity. It
means that at a given depth, the water absorption capacity
at the root level may decrease, but owing to the continuous
emission of nodal roots from the shoot, repeatedly exploring
the soil layer with new young roots, the water absorption
capacity at the root system level can be maintained.
This time evolution of root conductances supports the
idea of a time dependent differentiated role of seminal and
nodal roots in the root system of maize. In the young plant,
seminal roots are mature with large, open conducting
vessels while the nodal roots remain weakly conductive. In
this case, water uptake relies essentially on the seminal root
system. Later, with the opening of metaxylem (and their
increasing number) the nodal roots should supply the
majority of water to the shoot. Evidence for this is provided
by different responses in leaf elongation rates according to
the water stress imposed on the seminal or nodal root
system (Kozinka, 1989 for maize ; Volkmar, 1997 for wheat),
by staining of functional vessels with dyes (Mistrı! kova and
Kozinka, 1989 ; Mistrı! k and Mistrı! kova, 1995), or by water
uptake measurements (Navara, 1987). All of these considerations show that examination of root hydraulic conductances should be done by taking into account the growth
and the age of the root system.
Finally, this modelling experiment on water uptake
highlights some gaps in the knowledge of hydraulic
characteristics in root systems : is the evolution of hydraulic
conductance the same for all roots of the same branching
order ; is the axial resistance of tertiary roots so high that
their influence on water flux is negligible ? Measured values
of hydraulic conductances, especially radial, in older
segments of main axes or in branch roots are lacking. These
231
points deserve further investigation. As different methods
are available for the estimation of root conductances (direct
measurements, calculations), the model may be used to
verify the consistency of these estimations or to interpolate
the conductances between known values.
A C K N O W L E D G E M E N TS
We thank Dr Canny and Dr Varney for providing us with
details of their experiment.
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