...,
.
!_.4ae@'4.}.1*l
J.
rrH,:r1.Jil,
ANDorHERASpECrs
oFRoor AERATT.N
By
pErER
e{.BECKErr2,
sAMuEL
H.F.!r.
;Xttrfyri+#srRoNcr,
JUSrrNr,
and
"i:iT #; Tt"tr:,f:l; ;: i;:o #*' o'oartment ofApptied Matbe,n
atics, rbe
Abstracr
(l) Examples are given of
the radial and axjal variarion
in porosity and oxygen demand
within individual
to be found
differences
which arise becausJoi,t.
multicyrindrical narure of tissue
arrangementsand .roots;
becauseof developttl',llchange
orrid*1*..arion
and limitations of the mathematicarLoJerfing
and ageing.(2) The advantages
of-roor ";;";;;;
is
discussed;Ji
!liop,. murricyrin"' radiar
:r:?#:ff:r::l
oxvgen
e::j'-...n
isdescribed
Daraderived
1;;;;;;;,ource
rrom
sib,e
noc
onry
u*Jti!?::::'":T::1?#,::ffi::'l_T**;,j::j,fi:T,:":lTll,?*":?:
shown that
CopR co.uld-easiry
""., r-i,-.
gr.",.. than 100 kpa. (3) A
presentedfor extendingthe
caseis
:g:-i?;j;.,
multicylindricalapproach
in aeraiionmodelling ro accomodare also
gitudinalinternil sl'P-hase
rhe lonoxygeriit*rior, necessary
for root surviva.lin flooded soils.
on this approachcanquantifythe
Models
based
compitirion for o*yg.r, u.i*...,
rhizosphereand roor, show how
stelaranoxiamight developwithout
iniil,,r'g roo, gr"*in, ""-J predicr
sion into floodedsoits.(4)ir i, poin,.J
the limiurions on roor €xren_
oJ, ,i,r.tnyp8*i"i"l"rir"Oi.uted
increasedethanollevelsand towereaetre'rgy
by.enhanced
ADH acdvity,
chargen..a noi ,,Jcessarilybe
opmentand might'.byimproving
deieterious
ro roor develoxygensupplyelsewn.r. i., it.
root, help prolong root growth
anaerobicmedia'(5)A variery
in
orJtr'ti loncluri,r* r.g".il;;;.*ration
cylindricalradial(MR),and axial
and derivedfrom themurti"r,J rJil, (MAR),models are
listed.
l. Introduction
In the modelling of biological
systemsrhe use of mathemarically
convenient
assumptionsconcerningeiiher
the organismsor the nature
of
the
processes
work' is not uncommon, not
at
alwaysdesirable,orien.unavoidable,
irresistible'For the modelling
and usually
of ,oor and soil aeiarionthe following
four assumptions are usually.applied:(ligas
,rrrlrpo^r,is chiefly diffusive; (2)
rhere is uniformity in radial diffusive chaiafrerirri.r,
(3) rhere is Lniformity in the
and level of respiratorydemana,
distriburion
and
locus is unaffecttg uy iht pr.uriiirrg 1<yiespiiarory o"ygen consumpdon at any
oryg.n concentration unril armost
of oxygen extinction. narety .ro
the point
ri.r.'ril;;;j;;s
ue wtroly corre* bur their
applicationhas resultedin numerous
analytiiar sorurionsro aerarionproblems
which have fitted torerabrywett-wirtr
.*p.ri*.rri"i'our.rrrrtion. consequentry,
they can' in appropriateciicumsmnces,
ue regaro.o ", quanritativelyacceprable
;#:iHfiTr:Tfl::irications
whichareimi.rr;;y known,o,,oooifficurt
to
Assumptio"(t)"t::
exampreof compromisesincethere
will arways
IIT:
someconvectiveflow componenr
operatingin the aerailonsysrem(seepage be
in roots the differentialdiffusivities
2g3):
ana soir.roirii*r"r the oxygen,nitiogen
and
:t::t .tf !:!", ortgen depriuation, pp. 267_282
e1lited
by M.B. Jachson,D.D. Dauiei ")a
i. Lambers
@t99t SpB Academicpubtisbing
Ar, ii" i"eue, Tbe Netbertands
,^j.L;
268
l!-'-
:
W'. Armstrong et al.
carbondioxide,cytoplasmicstreamingand warer
throughflowswill all contribute
to some degreeof mass transferof the respiratory
gases.However, thosewho
have observedthe gas transport kinetics in
roots, or compared experimental
observationwith predictions basedon diffusion
modelling,have nor yer found
causeto abandonthe view that diffusion can
accounrfor thi bulk of gastransference in roots' The models describedbelow
are thereforediffusion based.
concerningassumptions(2), (l) and (4) comprtmise
is againobviousbut for
many applicationsthe level proves acceprabte.
witrr ,.g"io ro roor aerarion,
however' we believeit necessaryto move away
from the notional expediencyof
total uniformity, and accommodatesomeof the
more obvious spatialdifferences
in root structureand respiratory
This
requires
taking a multicylindrical
femld,
approachto root aerationmodelling.
such t., ,ppio"ch should be of benefirnot
only in caseswhere gasexchangeis enrirely ,roLt,
e.g., inaeratedsoil, solution
culture,or respirometry,but alsowhere conditions
externalto the roor areanoxic
and rhe oxygenfor respirationis suppliedby internar
gas_phase
rrrnrpor, from rhe
aerialparts.
some of the reasonsfor developingmufticylindrical
models are given below,
a simplemulticylindricalradial(MR)model is
construcred,and some-applications
of both radialand combined axial-radial(MAR)
modelsare illustrated.Basedon
the MR-model,calculationsof tissuecylinder
oxygen deficitsand predigions of
whole-root respiratorycritical oxygen pressures
in the presence
boundary layersafe presented.By meansof MAR-podelling, and absenceof
the potenrialfor a
co-existence
of partialstelaranoxia wirh cortical aerobiosisis
explored,and possiblereasonsfor differencesbetweencriticaloxygen
pressuresfor respirationand
for extension-growth(coPR and coPE; are rev-ealed.
The term criricaloxygen
pressurerefersto the lowest partial pressure
of oxygen that failsro rerardexrension or oxygen consumption.
2. structural and metabolic considerationsrelevant
to the designand
programming of models
2.1. Root structure and diffusiuity
In transverse
section'a root approximatesin structureto a series
of threeconcentric tissueshells,the stele, the-cortex,and the
wall (hypodermaland epidermal)
layer(s)'The stele may be relatively homogeneous
in the senserhar ir may be
aporous, especiallyin dicotyledonous species.
In many monocoryledonous
plants,however, it may consiit of two sub-cylinders:
an ourer, non-porousshelr
of vascularelementsand pericycle,and an inner parenchymatous
cylinder of low
gas-filledporosity. The cortex is usuallyporous,
althoughsub-shellswhich differ
in porosity are common. rvail layers are non-porous,
or have extremeryrow
porosity, and may be sub-shelledin so far
as a thick-walled hypodermal cell
cylinder, the exodermis,may be surroundedby a rhin-walled
epidermalcylinder.
A number of thesefeaturesare illustratedin Figs I
and,2.
It is difficult to make accurateestimatesof gls transporr
coefficientsfor nonporous tissuesfor, whilst the oxygen diffusion
coefficienrfor cytoplasmis con-
-. . .r:.
-
:
50Q
+ F
.DE' >
i \ i = C )
s x E
il
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a
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-
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'
I
=-:
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t
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'
r)
(
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o N J
a
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o r D
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( D 5
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El,
a D -
( D x
0q =.
rDoa
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o
o
rJ'
-\
270
lri7.Afrnstrong et al.
Fig' 2' showing the changes in porosity,
overall diamerer and rhe relailve dirnensions
of the various
tissue cylinders along a maize root
grown in anaerobic solution curture.
sidered to be close to thar of water (Tyree
1970),cytoplasmic streaming can
enhancetransport,especiallyin a wicle
tissue.It hasieen calculatedhowever that
for tissuethicknesses
up to 2.5 x r o-?c,r(a-n"-tJrr.lar
radiusfor non-woody
ilon by diffusion
27r
roots), the enhancemenrfactor should not
exceed 1.3 (Armstrong 1979).For
thinner rissues,such as an epidermallayer
of path tengirrt0 ;-i0-4 cm, the
factor falls to 1'005' on the other hand, the
celi wall materialswill reduce rares
of transportand the net effectof theseenhancements
and constraintsis probably
a transportcoefficientcloseto the oxygen diffusivity
in water. Accordingly,in the
exampleswhich follow, a figure of z.l x 10-5
.*i rtl ;;;;;;;opted
for the
programmingof the stelarand other non-porous
Zoo€s;this correspondsro the
diffusion coefficienrof oxygen in water at 2OoC.
oxygen diffusivity of cortical tissueswill be governed
chiefly by the amounr
of intercellulargas-spaceand the degree
of ils interconnexion. Longitudinal
spacesare strikingly obvious, relativelynon-tortuous,
and clearly continuousin
the plane of the root axis. The oxygen diffusion
coefficient in the correx in rhis
plane,even in roots of relativerylow porosity,
e.g., pea,can amount to 1 x 10_2
cm2 s-l (valueb-asedon po.ori ies given by-arrisirong,
Healy and \rebb r9gz,
with correctionfor the lack of gasspacein
the steleand wall). Radialand circumferentialspacesare usuallyrnu.rr narrower, possibly
fewer and much lessreadiiy
.' observed'Their continuity is bestseenby carefulexamination
of sequenrialrransverseroot sections'on the basisof observations
made on radial and transverse
ultra-thinsectionsof resin-embedded
materiari;;;", we esrimarethat iadial and
circumferentialdiffusivitiesare ar least6.5 x
70!4 cmzr-i ""Jirri, is the value
we have adopted throughout to programme
for cortical gas-phasediffusion.
Another structural influence on aeration is
of course diffusion parh length.
Provided that gas-spacetortuosity is insignificant
the parh for longitudinal gas
transfer will equate with root length. For radiar
transfer rhe roor and tissue
cylinder radii arethe chief determinantsand it
should be noted,rr", iiriu. cylinder
dimensionsdo not alwaysremainconsrantwith
distancealong the root (Figs2 and
3)' This can have important implicationsfor root aerarion
whether in anoxic or
aeratedmedia.
2.2. Respiration
Little information is availableconcerningthe
respirarorydemandsof the various
tissuecylindersin roots and, if .*pr.rs.d as
o, .bnru*p,ion per unit of protein,
very greatdifferencesmight not be anticipateol
nor aerarionmodelling purposes,
however, it is the respirationper unit uolumewhich
is the more critical.on this
basis,it is probablethat considerableradialdifferences
in demandmay occur.The
mitochondrialfrequenciesin the rice roor TEM
photomicrograph(Fig. 1)suggest
that stelarand exodermaloxygen demands
on i
unit uotumeuairsare likely
to be very much greaterthan corticaldemand. i;;
Indeed,vacuolarionand expansion
of the cortical cellsis such that extremelylow rates
of corrical oxygen consumption might be expected.
A similarpicture emergesin maizealthoughhere
rheremay be a relativelynonporous ourer cortex (Fig. 2) which.,_formodelling
purposes,may be combined
with the epidermaland hypodermal layers.ne
spira'tory d,atafor maizewhichgive
somesupport to the notion of radialdifferenceJ
in respiratorydemandareshown
in Fig' 4' It should be noted that where the i"".t jorou,
and ourer
cortex and wall layersare treatedasone tissue(the 'cortex') 'cortical,non-porous
respiration
272
W. Armstrong et al.
rodius (Rsl
Stetor rodius (R5l
200
300
400
Distoncc from opex (mml
500
Fig 3. Denils of tissue cylinder and root diameters along maize 100ts grown in anaerobic NO; -free
solution culture. flustin and Armstrong, unpublished data). Inset: sectional plan of root depicting the
multicylindrical basisof MR modelling. The symbols assignedsignify the radii rs,c,wl,sr, oxygen consumpdon rates Qr,a,*;,st and oxygen diffusivities Ds.c,*r.,sL of stele, correx, wall and boundary
layers respecdvely.
\'
I
Aefenchymo
I
o
I
N
I
I
6
E
t n o
c
o
o
E
N
o
,Estimoted woll respirqtion
s
)n
o
x
o
o
a
o
200
Oistoncefrom opex (mml
Fig. 4. Aerenchyma development and detailed changes in respiratory oxygen consumpdon found
along maize roots grown in anaerobic NOr-free media, Qustin and Armsrrong, unpublished data).
is lessthan half that of the stele.If it is assumedthat respirationin the inner highly
vacuolated (and later aerenchymatous)cortex is small to negligible then the
demandattributedto the outer non-porous (non-aerenchymatous)
outer cortex
and wall layersapproachesor exceedsthat in the stele.
Modelling, and otber aspects of root aeration by diffusion
273
For the purposesof the modelling described here we have continued wirh
assumption(4) but, in the.,,future,
some modification would be desirableherealso
and someanaerobicmetabolismin the presenceof tracelevelsof oxygen mustbe
a possibility.
3. Radialmodels
! i
Analyticalsolutionsareavailablefor predictingthe oxygen regimein roorsaerated
by radial diffusion from soil or solution culture. These solutions help clarify a
number of aspectsof root aerationand the ropicsdealtwirh below include:(a)rhe
influenceof gas-space
continuity acrossthe cortex, and (b) the influenceof tissue
cylinder radiusand respiratorydemand,and boundary layer rhicknesseson oxygen deficits and respirarorycritical oxygen pressures(COPR).
J.1. Oxygen deficit equations
As with electricalsystemswhere the potential difference(volts) is rhe product of
current(amperesi.e., coulombs-l) and resistance
(ohms):
V= l R
( 1)
so it is with diffusionsystemsthat concentrationdifferences(deficirs:A: g cm-3),
are the product of flow rate (J:g s-l) and diffusive resistance(s.--3; and:
4 =J x R
(2)
Although sometimesobscuredin more detailedmathemaricalexpressions,this is
the relationshipsunderlyingthe radialoxygen deficit equarionspresentedbelow
in which the root is consideredto consistof a centralsolid stelarcylinder (S)surroundedby successive
hollow cylinders:rhe correx (C),rhe wall layers('WL),and,
externalto the root, a stationaryboundary of warer (BL), (Fig. 3 - inseg).At rhe
outer surfaceof the boundary layer is the oxygen source of concentration Co.
The total oxygen deficit radially across the roor, Ar, can be shown to be the
sum of a seriesof component deficits developed inwardly acrossthe various
cylinders and this is expressedin the following equation:
AT=As+Ac+A*r+Au,
(3)
More accuratelyhowever the equation may be written as
Ar = A, + (Ai + A[) + (Awr, + A{ir1) + AsL
(4)
since,in both cortical and wall cylinders there are deficits causedby oxygen consurnption witbin the cylinder itself (in situ: Ac.*r) and by oxygen tbroughflux to
the inner cylinder(s) (A'6.wr,).
The detailsof the component deficitsin equatioo(2)are as follows where
Qr,c,*,.
= respiratoryoxygen demand (g cm-r t-t; of stele,cortex or wall
layers
274
V. Arrnstrong et al.
= oxygen diffusivities(cm2r- t; of the respectivetissueandboundDs,c,,orrL,BL
ary cylinders
:
rs,c,wr,sL the respecriveradii of the cylinders
=ft's
As
A. =
Qt
Arir,=
,*
1'
,3 f'3 - zlog.5 - tJ Vnsitul
rc
(5)
4 D c ' st (
46=
Awr=
(5)
l,or. (rhroughfiow)
fr'l
:
F
#,4
[o,r,
(7)
+ ZLog.* r] unsitu>
(8)
+ e.(r3- '3t r.or. Qbrougn4owl (e)
T
(
rBt
2.?
,.) - tt)t
ABL= ^- |orr! + ec(r3- t3l
+ e,usr.(rtvt
rog.:
-wL' w"
-'
"')
2DBL (
r*,
(10)
If conditionsare suchas to causean anoxic core to developin the stele,the stelar
componentsin equations(7),(9) and (10) (Qrr3) must be modified to Qr(r!-rl)
whilst 6quation (5) becomes:
a, =
Qs , (tt
ao,
t:
6;
r^
+ zLog.; - -)
tJ
(1r)
where r" is the radius of the anoxic core. The derivation of individual equarions
may be found in Armstrong (1979).
It should be noted that when it is necessaryto accommodategas-phase
concentration and both liquid- and gas-phase
diffusion pethswithin a model then account
must be taken of the 30-fold drop in oxygen concentration at the gas-liquidinterfaces.This can be effected by appropriately reducing the liquid-phaseoxygen
diffusioncoefficiente.9.,Dw x 0.033 at20"C.
3.2. Radial deficits and respiratory critical oxygen pressure
It follows from assumption (4) and equations (3) and (4) that where A1 = Cs,
then Co will representthe critical oxygen pressurefor'whole root' respiration,
COPR,as 'viewed' from the outer surfaceof the boundary layer and it should be
noted this is the locus for oxygen determination in respirometerand other solution culture methods for studying oxygen consumption by roots.
Table I has been derived by solving the component deficits in equation(4)
Modelling, and otber aspectsof root aeration by diffusion
275
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Fi$. 5. Showing the 'smooth' curved radial oxygen concentration profile predicted for non-porous
roo6, and the 'stepped' profile expected in roots having a porous cortex. The dimensionlessradius
r = 1.00, rePresen$ the outer limit of a narrow stationary boundary layer of warer on rhe root
surface at which the dissolved oxygen concentration source, Co varies as shown (air-saturadonto
2 x l0-6 I cm-3;. It should be noted that as Ce declines the shape of rhe oxygen profiie remains rhe
same, although ar a lower level, until some anoxia arisesin the stele. Vhere this occurs two lines are
shown on each graph: the shallower of the two takes accounr of the reduced oxygen demand in the
stele (after Armstrong and Becketr 1985).
(seeequations(5)-(i0)). They show the likely effectsof tissuecylinder size,of
oxygen demand and of boundary layer thicknesson the oxygen deficirsin roots.
3.3. Radial profiles
From the deficits shown in Table 1, it is clear that mulricylindrical models will
predict ^stepped oxygen concentration profile for roors having radially interconnecting cortical pore space.For aporousroots, Da will be similar to D, and D*,
eod smoofb profiles can be expected. The examples in Fig. 5 (for equationssee
Armstrong and Beckett 1985) illustrate these differences and rhe greaterdeficirs
to be expectedin aporousroots. To date the only example of a steppedoxygen
profile to have been recorded experimentally in a plant organ was in applefruits
(Brandle1968).
Conclusionswhich may be drawn include the following:
(i) Oxygen deficits and hence critical oxygen pressuresare likely ro vary enormously between speciesand even individual roots becauseof the considerable
range of tissuedimensions and respiratory demand which can occur.
(ii) The multicylindrical approach highlights the effect of the oxygen consumption of inner tissueson the oxygen deficits developedacrossouter tissues,e.g.,
the throughflux deficitsof both cortex and wall layersare grearerrhan the deficits
causedby respirationwithin the respectivetissuesthemselves.Again,while stelar
Modelling, and otber aspects of root aeration by diffusion
277
and wall deficits apparentlycontribute mosr to the magnirudeof the COpR ir
should be realisedthat the deficit in the wall layersis largelythe resultof throughflux to stele and cortex.
(iii) Radial$as-pbasediffusion in the cortex will keep cortical oxygen deficits
to a minimum.
(iv) Boundary layerresistancemay have a significanteffect on observedCOpR
in roots but the magnitudeof the effect remains to be discovered.rvith only
moderatebubbling rares(25 ml min-l in solution volume of 350 ml) we have
the thicknesses
to be ca.40 pm; the implicationsare evident in the Aur,
::f1na1eO
I aDle l.
(v) For a root havingthe characteristics
singledout in the rables(bracketed,[ ]),
the deficitstotal 11.2kPa.Thesecharacteristics
were basedon some of our own
maizeroot data(Justinand Armstrong,unpublished)and rhis COPRis similar ro
that found by Saglioet al. L984.It should be noted, however, thac a flooding
of cortical spaceswhich would considerablyaiter Ai and A[, or a doubling of
respiratorydemandshould have a much grearerinfluence on COpR than likely
boundary-layer resistances.
(vi) If the oxygen supply for the root is by inrernal longitudinaltransporr,the
highest oxygen levelswill be found in the correx and the analogousCOPRwill
equalAs. By monitoring the oxygen levelsin such roors usingsleevingcylindrical
Pt-electrodes(Armstrong and Gayard 1976), a figure close to A, is obtained:
throughflux acrossthe wall occurs only outwards to the electroOe-witna consequently reduced deficit and the effects of boundary layer resistancealso disappear.The narrow stelarradiusof rice roots is consistenrwith the relativelylow
COPRswhich havebeen found (2 kPa). Maizeroot COPRmeasuredby the same
techniquelies ca. 5 -6 kPa(vebb and Armstrong, unpublished).Again,however,
from considerationsof root and tissuecylinder dimensionsshown in FigsZ and
3 it will be evident that the COPR might even changeconsiderablyduring the
growth of an individualroot and it is at leasttheorericailypossiblefor the COpRs
to be considerablyhigher than 100 kPa.Also, ir should be borne in mind that rhe
COPRfor whole root respiration,measuredby monitoring O, levelsexternalro
the root, could be a function of an oxygen stressdevelopingsub-apically,where
stelardimensionsor, stelarand endodermaldiffusive resistances,
may be greater,
ratherthan in the apex or extensionzone. Factorssuch as rhis might accountfor
the reported differencesin the cortical oxygen pressuresfor root respirationand
extension,(Armstrongand \febb 1985).
(vii) As Co declinesthe presenceof a radially porous coruex may maintain
aerobiosisin phloem and pericyclealmostuntil rhe point of oxygen exrinction in
the cortex. This has important implications for root aeration by longitudinal
oxygen transportand survival in oxygen-stressedenvironmenrs,(seebelow).
4. Combined axial and radial models
In flooded soils, root growth and survival is largely dependenrupon adequate
oxygen transportfrom the shoot via the intercellulargasspaceof shoot and root
(Vartapetiao1978;Armstrong L979;$frebband Armsrrong 1983;Armstrong and
Ifebb 1985;Jackson
and Drew 1985;Drew et a|.1985).The resultsin Fig.6 show,
278
lV. Arntstrong et al.
for a rangeof 9l wetland,non-wetlandand intermediatespecies,how root-length
achievedin flooded soil varieswith the ventilatingprovision(gas-filledporosity).
The scatterof points in the figurealmost certainly reflectsthe infinite varietyin
the magnitudesand distributionof the various factorswhich govern the oxygen
regime in the root: factorswhich, as has alreadybeen noted, can vary not only
from plant to plant and from root to root, but from baseto apex even within a
singleroot. Despitethis, the databroadly agreenumericallywith diffusion-model
predictionsbased on structuraland metabolic homogeneityin root and soil
(Fig.6; linesa-c), and give furthercredanceto the view that the mechanismof
roor aerationis chiefly diffusive.However, it seemslikely that even greatercorrespondencebetween observed and predicted data should be possibleusing
modelsin which the multicylindricalradialapproachoutlined earlieris combined
with equationsdescribinglongitudinal(axial)transportfrom the shoot system.
Such composite (MAR) models (Armstrong and Beckett 1987)give numerical,
rather than analyticalsolutions,and predict somewhatgreaterroot extensionin
flooded soils than do the models basedon homogeneity in root structureand
oxygen demand.This is not inconsistentwith the datain Fig.6 and might account
for the large number of points which lie above the line b.
The MAR model allows for axial gas-phasediffusion in the root cortex and
ndial, liquid-phase diffusion elsewhere. It accomodatesdiffusion into the
rhizosphereand axialand radialdifferencesin root propertieson a tissue-cylinder
basis.Preliminaryresultshavehighlightedthe potentialfor stelaranoxiaandsome
root 'wall-layer'anoxia in submergedroots, (Armstrongand Beckett 1987).
Conclusionsderived from programmingwith real and assumedcharacteristics
of aerenchymatousgraminaceanroots are: (i) In submergedand growing roots,
anoxiais likely to occur first in centralpartsof the steleand/ormeristem;(ii) \fith
a high and uniform diffusivity in the stele,stelaranoxiashould first occur close
ro the apex and spreadlaterallyand basallywith further root extension,(Fig.7A,B
and C); (iii) Anoxia mighr also first arisesub-apicallyand apicalregionsremain
wholly aerobicfor a time if stelaror endodermaloxygen diffusivitiesdeclinesubsranriallyin sub-apicalregionsdue to varioussecondarywall-deposits,(Fig.7D):
ethanol production, raised ADH activity, and reduced energy-chargein roots
mighr somerimesbe a function of sub-apicalstelaranoxia only; (iv) Declining
stelar oxygen diffusivity in sub-apicalregions will raise COPR but not COPE;
(v) The consequencesof stelaranoxiawill be to raiseoxygen levelselsewherein
maximum root length achievedi., noolFig. 6.The relationship berween root porosity (%) and.mean
ed soil, for the specieslisted. Symbols: o , non-wetland species; v , intermediatetypes; a , wetland
types;(s) maximum root length high but ageotropicgrowth resultedin shallow soil penetration;if any
number not shown rhen roots either dead or growrh insufficient for porosity determinations;No. 54'
maximum root length only 10 mm, but roots aros€ at a depth of ll0 mm from an aerenchymatous
rhizome Curves(a),(b), (c) and (d) areelectricalanaloguepredictionsbasedon the root and soil respiratory data shown below and assumehomogeneity in respiratory and diffusive characteristicswithin the
roor: (a) Root respiration,Qp = 30 mg m-3 s-t. No radial oxygen leakagefrom root to soil (applicable
ro all root radii); (b) Q* = 30 mg m-, s-1. Root radius (r) = 0.5 mm. Soil oxygen consumption rate
( Q s )= 5 3 m g m - l s - r ; ( c ) Q n = 1 2 0m g m - l s - r , r = 0 . 5 m m , Q s = 5 3 m g m - l s - r ; ( d ) Q n =
1 2 0 m g m - J s - 1 , r = 0 . 1 m m , Q s = 5 3 m g m - l s - 1 . ( A f t e r J u s t i na n d A r m s t r o n g 1 9 8 7 ) .
Modelling, and otber aspects of root aeration by diJfusion
E
279
t
E
E
3
;EgsEgisg;ifigg;s
eeEi*aaae:fuEE
tii 0iFn dHlias€j s sd is ds d Ri s pi iF ie ss i dc,idEss s ei
id;ruii-dddiie=ieisdii;:sidiiKixinlii
E s
R;si*nsssseiEeieEs?e
<6
<8
<3
o
F
<3
<B
< 3 : s
<6
<s
<8
o
RO
s
<3
=
!>
<R
<F
b{t
tu
o
( u.rrrJ) H 1 9 N 3 1 I O O U H N h l I X V N
z
x r
<3
sD(B
cg
<3
o
(\l
q
<*{*
W. Armstrong et al.
280
a ^ ,o
ill [ffi[lilL
ililL
[ltil]il]
ffiWW
Fig. 7. MAR-modelling predictions. Longitudinal half-sectional diagramsof roots in waterlogged soil
root apex tocally
ar various stagesof growth (L cm) and predicting maximum rooting depths (L1,rs:
anoxic) for aerenchymarous roors in which respiratory demand declines and fractional porosity
increaseswith disunce from the apex, but in which the oxygen permeability of the outer stele and
wall layerg (non-porous outer cortex, hypodermis and epidermis) varies as follows.
A. Root surface impermeable to oxygen over whole length of root.
B. Root surface fully permeable to oxygen over the whole length of root'
C. Oxygen permeability of roor surface decreasing basipetally to become very low at 50 mm from
apex, rhizosphere oxygenation concentrated near apex.
D. As for C, bur with steLr oxygen diffusivity declining by an order of magnitude over the apical
40 mm. Note: the changing plrmeability characteristics of stele and wall layers can increasethe
predictable rooting depth by approx. 30%".
tn iach diagram rhe vertiial lines from left to right indicate: (a) axial centre line of root, (b) radius of
inner stele or medulla, (c) overall stelarradius, (d) radius of porous cortical tissues,and (e) outer radius
of root. The curves drawn within the bounds of the porous cortex indicate the cortical oxygen concenrration profiles: basal concenrrarions = air; apical concentrations at L(inf) = zero. The shadedareas
within the roors indicare zones of anoxia. The inner edge of the shaded lines (straight or curved) at
the extreme right of each diagram marks the boundary between the root-oxygenated rhizosphereand
the surrounding anoxic sediment. (Redrawn from Armstrong and Beckett 1987).
the root and thus prolong root extension,(c/. Fig. 7C and D); (vi) The oxygen
demandsof root and rhizosphereare competitive;(vii) Root extensionmay be
reducedby radial oxygen lossesto the rhizosphete (cf. Fig. 7A and B), but the subapical decline in root wall oxygen permeability safeguardsagainstthis effect,(c/'
Fig. 7C and B); (viii) Root survivalin wet soils might be helpedby the mannerin
which anoxia spreads.If aerobicconditions persistin the phloem and pericycle
until only tracesof Oxygenremainin the cortex, the continuanceOf sugartransport should be ensuredand substrateprovided not only for remainingaerobic
Modetting, and otber aspectsof root aeration by diffusion
281
partsbut probably anoxic zonesalso;(ix) Sectionalprofilesof the rootsshow how
b*yg.n gradienrs in the srele and wall layers will increasewith increasingsub,pi.it impedancein these zonesand, in the caseof the wall-layers,by oxygen
throughflux to the rhizosphere,(seeArmstrongand Beckett 1987)'
5. Final comments
'Weigamd,Kristensenand others formulated
Ir is now thirty yearssince Lemon,
the first mathematicalmodels of root aeration,and twenty sincethe first computer-basedmodelswere developed(Luxmooreet al. l97O)'Hopefully' it will be
role
evident from the examplesgiven above, that models can still fulfil a useful
despirethe conrinuingnecesiityfor assumptionsand compromisesin their formulation. Furtherrefinementis both desirableand possiblebut existingmodels,both
much
the simple and the more complex, have yet to be fully exploited and have
srill to offer. They canbe usedto good effectin interpretative,predictive,exploratory, and teachingroles.rvith the adventof the more powerful micro-computers
and with moves towards computer compatability,the time may now Deoppor'the
tune for the creation of standardisedaerationsoftware packagesand for
mathematicalmodel' to be regardedas necessarya tool in the well-foundlaboratory as statisticalpackagesand modern labOratoryhardware'
Acknowledgments
.we
in preparing
wish to thank Mr. K. Andersonand Mrs.J. Mundy for assistance
the
the compositeof photomicrographs(Fig' 1) and MissE.M' Sharpefor typing
manuscript.
References
. !?oolhouse (ed'), Advances in Bonnical
Armstrong, W. lgTg.Aeration in higher plans. In: H.\)f-'\trf
London'
Press,
Research,Vol. 7, pp.225-332, Academic
a multishelledmathematical
Armstrong, !7. and Beckett,P.M. 1985. Root aerationin unsaturatedsoil:
blocking of the diffuwet-soil
sectoral
without
with
and
model of oxygen diffusion and disrribution
s i o n p a t h . N e w P h Y t o l .l O 0 : 2 9 3 - 3 1 1 .
of stelaranoxia in subArmsrrong, lW. and Beckett,P.M. 1985. Internal aerationand the development
of oxygen in the cortex
merged roor.s:a multishelled mathematical model combining axial diffusion
lO5:221 -245'
Phytol'
with radial lossesto the stele, the wall layers and the rhizosphere'New
for respirationin intact plants'
Armsrrong,.if. and Gaynard, TJ.l976.The critical oxygen pressure
P h Y s i o l -P l a n t ' 3 7 : 2 0 0 - 2 0 6 '
in pea' I' Pore-spaceresistancein
Armstrong, \7., Healy, M.T. and rVebb, T. 1982.Oxygen diffusion
the primary root. New Phytol. 911547-559'
root extension in rice' J' Exp' Bot'
Armsrrong, w. and \febb, T. 1985. A critical oxygen pressurefor
36: 1573-1582.
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Brindle, R. 1968. Die Verteilung der Sauerstoffkonzentrationen
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N.y.
Justin,s.H.F.w. and ArmstronS,\r. 1987.The anatomicalcharacteristics
of rootsand planrresponse
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of
oxygen diffusion in the liquid phaseof the soil. Agron.J. 56:295-3or.
Lemon,E.R.1962.Soil aerationand plant root relations.I. TheoryAgron.J.54: 16l-tlO.
Lemon,E.R.1962.Soil aeradonand plantroot reladons.lI. Rootrespirarion.
AgronJ. 54: 17l-175Luxmoore,RJ., Stolzy,L.H. and Letey,J.1970.Oxygen-diffusion
in the soil-plantsystem.Agron.J.
6 2 : 3 1 7- 3 2 2 .
Saglio,P'H., Rancillac,H., Bruzan,F. and Pradet,A. 1984.Criticaloxygen pressurefor growth and
respirationof excisedand intact roors. plant physiol.7G: l5l-154.
Tyree, M.T. 1970.The symplastconcept: a generalrheory of symplasttransporraccordingto the
thermodynamicsof irreversibleprocesses.
J. Exp. Bot. 26: lgl-214.
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AnaerobicEnvironmenc, pp. I - I l, Ann Arbor Science,Michigan.
'Webb,
T. and Armstrong,\f. 1983.The effectsof anoxiaand carbohydratcs
on the growth and viability of rice, pea and pumpkin roors.J. Exp. Bor.34: j7g-603.