experimental and modelling data contradict the idea of respiratory down-regulation in plant tissues...

Experimental and modelling data contradict the idea ofrespiratory down-regulation in plant tissues at aninternal [O2] substantially above the critical oxygenpressure for cytochrome oxidase

William Armstrong1,2 and Peter M. Beckett1

1Department of Biological Sciences, University of Hull, Kingston upon Hull, HU6 7RX, UK; 2School of Plant Biology, Faculty of Natural and Agricultural

Sciences, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia

Author for correspondence:William ArmstrongTel: +44 1964 550135

Email: [email protected]

Received: 17 August 2010

Accepted: 1 October 2010

New Phytologist (2011) 190: 431–441doi: 10.1111/j.1469-8137.2010.03537.x

Key words: critical oxygen pressure, down-regulation, modelling, pea, respiration,respirometry, roots.

Summary

• Some recent data on O2 scavenging by root segments showed a two-phase

reduction in respiration rate starting at ⁄ above 21 kPa O2 in the respirometer med-

ium. The initial decline was attributed to a down-regulation of respiration, involving

enzymes other than cytochrome oxidase, and interpreted as a means of conserving

O2. As this appeared to contradict earlier findings, we sought to clarify the position

by mathematical modelling of the respirometer system.

• The Fortran-based model accommodated the multicylindrical diffusive and respi-

ratory characteristics of roots and the kinetics of the scavenging process. Output

included moving images and data files of respiratory activity and [O2] from root

centre to respirometer medium.

• With respiration at any locus following a mitochondrial cytochrome oxidase O2

dependence curve (the Michaelis-Menten constant Km = 0.0108 kPa; critical O2

pressure, 1–2 kPa), the declining rate of O2 consumption proved to be biphasic: an

initial, long semi-linear part, reflecting the spread of severe hypoxia within the

stele, followed by a short curvilinear fall, reflecting its extension through the peri-

cycle and cortex.

• We conclude that the initial respiratory decline in root respiration recently noted

in respirometry studies is attributable to the spread of severe hypoxia from the root

centre, rather than a conservation of O2 by controlled down-regulation of respira-

tion based on O2 sensors.

Introduction

Respirometer studies of oxygen scavenging by microorgan-isms and animal cells have shown almost invariably thatoxygen uptake is unaffected by declining O2 concentrationin the stirred surrounding medium until very low levels havebeen reached (for a review, see Harrison & Stouthamer,1973). For nine species of bacteria, yeast, pig’s heart and oxheart in suspension culture, Longmuir (1954) found thatthe O2 depletion curves fitted the Michaelis equation andthat the Km values were very low, ranging from 1.1 · 10)8

to 1.57 · 10)6 M (0.00825–0.234 kPa). In addition, apartfrom yeast with its peripheral mitochondria, the largerthe microorganism, the greater the value of Km. Longmuir

concluded that the Km–size relationship was unlikely to be aresult of variation in the affinity of the respiratory enzymesfor O2, but rather of differences in internal diffusion pathlength to the respiratory systems within the cells. Oxygenscavenging by cell-free preparations supported this predic-tion, with cell-free Km values for each of three microorgan-isms being very similar to one another and not much lessthan the Km value of the smallest organism.

Much has been written on how the relationship betweenoxygen concentration and respiration rate should be treated,particularly if cell growth is involved and if enzyme contentcan change a great deal with changes in growth conditions(Harrison & Stouthamer, 1973). Chance (1957), for exam-ple, argued against treating the O2 affinity of cells as a

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simple Michaelis–Menten relationship. Nevertheless, usinga multi-enzyme model, he showed that the O2 uptakewould still be independent of dissolved O2 until a very lowcritical value is reached. For many practical purposes, how-ever, it is most convenient to apply Michaelis–Mentenkinetics using an ‘apparent Km’ to approximate the oxygendependence of the respiratory processes. As cytochrome oxi-dase is the major terminal oxidase for plant respiration, andmitochondria are the major sites of oxygen consumption inthe plant cell, we have used for our modelling in this articlea Km value of 0.14 lM (0.0108 kPa O2), averaged fromthe values cited for isolated mitochondria from several plantspecies (Barzu & Satre, 1970, 0.15 lM; Rawsthorne &LaRue, 1986, 0.1–0.12 lM; Millar et al., 1994, 0.125–0.147 lM). The corresponding oxygen affinity curve isshown in Fig. 1, from which it can be seen that such a lowKm goes hand in hand with a very low critical oxygen pres-sure (COPR) which is being approached at 1 kPa O2.Because of the asymptotic nature of the curve, it is not pos-sible to give a precise figure, but 95% of the maximumrespiratory rate is reached at c. 0.25 kPa O2. The typicalform of a scavenging curve for root segments and of the O2

dependence curve derived from it are shown in Fig. 1(b):the respiration rate at any [O2] is determined from the slopeof the scavenging curve, ¶C ⁄ ¶t, the tissue mass ⁄ volume andthe respirometer volume. These curves were computer gen-erated but, if the data are processed from recorder charts, itcan be difficult to determine accurately the respiration rateat any point on the scavenging curve, or the COPR atwhich the scavenging line changes almost imperceptiblyfrom a straight line to a curve.

Among the first workers to use respirometry to examinethe relationship between root respiration and O2 concen-tration [O2] were Berry & Norris (1949). The general formof their O2 dependence plots, typical of those from mostsubsequent studies on roots, was similar to that for micro-organisms, although the COPRs were very much higher.With declining oxygen, there was a plateau at which the res-piration was still at a maximum and independent of [O2],until a COPR was reached, after which there was an acceler-ating decline to zero. For onion root segments at 20�C, thisCOPR was very much greater than for microorganismrespiration: COPRs of 21 (Fig. 2), 15 and 10 kPa O2,respectively, were recorded for the zones 0–5, 5–10 and10–15 mm above the onion root apex. At 30�C, the criticalpressures were c. 48 (Fig. 2), 21 and 10 kPa, respectively.Oxygen consumption in the apical 5 mm of the onion rootwas twice that of the 5–10 mm zone, and this latter zonerespired at a rate greater than that at 10–15 mm from theapex (Berry & Brock, 1946). Consequently, the magnitudeof COPR was revealed to be dependent on the respiratoryrate of the tissue and the temperature of the system. Thediscrepancy between high in vitro COPR and the affinity ofcytochromes for O2 was attributed by Berry and Norris to

the diffusional impedances within the tissues, creating a coreof anaerobiosis at O2 concentrations below the COPR.Indeed, the CO2 output below the COPR values was suchthat the respiratory quotients (RQs) consistently exceededunity, indicating a significant leve1 of fermentation (Fig. 2).Ethanol production and active pyruvate decarboxylase in thestele of maize, but not in the cortex, at low cortical O2 partialpressures (Thomson & Greenway, 1991) also support Berryand Norris’s supposition of a developing core of anaerobiosisbelow COPR, as do direct measurements of O2 profilesacross roots (Armstrong et al., 1994; Gibbs et al., 1998;Darwent et al., 2003). Nonporous tissues, such as the steleand epidermal ⁄ hypodermal cell layers, would normally be

Oxygen partial pressure (kPa)

Res

pira

tion

rate

(fr

actio

n of

max

imum

)

0.0

0.5

1.0

(a)

(b)

Mitochondrial O2 dependence plot

Km = c. 0.14 µM (0.0108 kPa O2)

0.0 0.2 0.4 0.6 0.8 1.0

Respirometer O2 partial pressure (kPa)

0 4 8 12 16 20

Res

pira

tion

rate

(ng

cm

–3 s

–1)

0

50

100

150

Time (s)

4000 6000 8000 10 000

Respirom

eter O2 (kP

a)

0

5

10

15

20

COPR

Fig. 1. (a) The O2 dependence curve used as the basis forprogramming the relationship between the respiratory rate and O2

concentration at any locus in respiring root segments. Plot based onthe Michaelis–Menten formula, with Km (0.0108 kPa) being that forthe respiration of isolated plant mitochondria, and approaching anasymptote at c. 1.0 kPa approximating the critical oxygen pressure(COPR). (b) Modelling output showing O2 scavenging curve andO2 dependence curve derived from it. COPR is indicated as thepoint at which the scavenging plot departs from a straight line.

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the most significant resistances to the radial transfer of O2,and the porous cortex would be the least significant.Consequently, the larger the stelar diameter and ⁄ or thethicker the nonporous epidermal ⁄ hypodermal cell layers, thehigher will be the expected COPRs when assessed in thisway. In respirometer cuvettes, in which root segments aresuspended in a stirred bathing medium, diffusive boundarylayers (DBLs) at the surface of the root segments also playa part in determining the position of the perceivedCOPR (Asplund & Curtis, 2001; Curtis & Tuerk, 2008;Armstrong et al., 2009): the slower the rate of stirring, thethicker the DBL and the higher the COPR. COPRsmeasured on intact roots by methods which exclude theeffects of the diffusive resistances of cortex, epidermis andDBL have revealed stelar COPRs for rice, pea, maize andEriophorum angustifolium of £ 2.5 kPa O2 (Armstrong et al.,2009).

The work described here was prompted by recent reportsof high COPRs in pea and barley roots, and oxygen depen-dence curves that showed a decline in respiration apparentlyfrom above atmospheric concentrations of O2 and that had abiphasic form (Gupta et al., 2009; Zabalza et al., 2009). Arelatively long initial decline to about one-half the initial res-piration rate was followed by a steeper curvilinear decline toreach zero at zero [O2] in the respirometer fluid (control

plots, Fig. 3a,b). Oxygen dependence curves were also deter-mined for roots previously fed with pyruvate (Fig. 3a,b) andother substrate sources. These data have raised a number ofquestions: (1) how should the biphasic shape of the controlplots be interpreted; and (2) how can pyruvate feedingincrease the maximum respiration rate when roots alreadyappear to be O2 deficient? Zabalza et al. (2009) and Guptaet al. (2009) interpreted the initial, apparently linear, declinein respiratory rate of the control roots as evidence of a grad-ual O2-sensitive down-regulation of respiration, which hasevolved as a means of saving O2 as its availability is reduced.The suggestion that the respiratory decline in pea could bethe result of diffusion limitations was dismissed on the basisof claims that similar shaped plots were obtained for

1

RQ

2 RQ: 0–5 mm

O2 concentration in bathing medium (%)

0 10 20 30 40 50 60 70 80 90 100

0 10 20 30 40 50 60 70 80 90 100

µl O

2 co

nsum

ed (

per

root

seg

men

t h–1

)

0

30°C

30°C

20°C

0–5 mm segments

COPR ≥ 48 kPa

COPR c. 18 kPa

Increase in RQ indicating fermentationat point farthest from O2 source

30

20

10

Air-saturation

Fig. 2. Oxygen consumption (ll per root segment h)1) andcorresponding respiratory quotients (RQs) (CO2 evolved : O2

consumed) for 0–5 mm root tips of onion (diameter, c. 0.75 mm) inrelation to O2 concentration in the bathing medium and at twotemperatures. Measurements by Warburg respirometry using2-d-old roots. COPR, critical oxygen pressure. Drawn from data ofBerry & Norris (1949).


% r

espi

rato

ry r

ates

rel

ativ

e to

con

trol

at 2

1 kP

a O

2

0

50

100

150

200

Control

Air-saturation

1.5 h 10 mM Pyruvate

0 4 8 12 16 20

0 20 40 60 80 100

0

5

10

15

20

25

30

35

40

Pyruvate-fed

Res

pira

tory

rat

e(%

O2

min

–1 1

00 m

g–1

FW

)

Respirometer O2 concentration(% of air saturation)

Control

(a)

(b)

Fig. 3. (a) Two O2 dependence plots for pea root segments,redrawn from Zabalza et al. (2009). Bottom: ‘control roots’ grownfor 21 d in air-saturated culture medium; measurements onsegments (d = 2 mm) taken at 5 cm from the apex; top: similarroots, but pyruvate (8 mM) added to the culture solution for 24 hbefore assaying. (b) Two O2 dependence plots for barley rootsegments, redrawn from Gupta et al. (2009). Bottom: ‘controlroots’ grown for 2 wk in air-saturated culture medium before assay;position and diameters not given; top: root segments pre-incubatedin 10 mM pyruvate before assay.

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Arabidopsis roots, which are only 200 lm thick, comparedwith 2 mm for pea, and for Chlamydomonas cultures forwhich the cell size is only 20 lm. The increased respiratoryrate in response to pyruvate and succinate feeding was takenas an indication that the first phase of respiratory decline inthe control treatment roots could not have been the result ofO2 becoming a limiting substrate. Radial oxygen profilesthrough intact pea roots from the various treatments showedno evidence of anoxia, but, at the same time, showed noevidence of having entered the stele in any example, where,usually, a steep fall in O2 concentration is noted (cf. Fig. 1from Zabalza et al. (2009) with Fig. 9 from Armstrong et al.(2009); see also Armstrong et al., 1994; Gibbs et al., 1998;Darwent et al., 2003).

We were puzzled by the differences between the afore-mentioned data of Zabalza et al. (2009) and Gupta et al. (2009),and previous data on the O2 dependence of roots (Berry &Norris, 1949; Atwell et al., 1985; Asplund & Curtis, 2001)and of plant cell protoplasts (Lammertyn et al., 2001), andby the conclusions presented. Consequently, we wonderedwhether it might be possible to resolve the apparent con-tradictions by modelling the experiments. To this end, wedeveloped a Fortran-based mathematical model of O2

scavenging in closed respirometer systems. This allowed usto reproduce the types of scavenging curve obtained and topredict the O2 dependence relationships as a function of thediffusive resistances, respiratory activities of the varioustissues, boundary layer effects and respirometer reservoir

dimensions. Our hypothesis was that the biphasic responsecurves of Zabalza et al. (2009) and Gupta et al. (2009) couldbe explained in terms of impaired respiration as O2 concen-trations below the COPR for cytochrome oxidase werereached within the root under the combined effects of respi-ration and diffusive resistance.

Description

Features simulated

The model was designed to simulate a cylindrical respirom-eter cuvette with an in-built O2 sensor (e.g. polarographicelectrode or micro-optode) filled with continuously stirredaqueous medium and containing root segments. The rela-tive proportion of respirometer cuvette radius to root radiusdepends on the chosen number and dimensions of the rootsegments and chamber size. The diffusive and respiratorycharacteristics of roots vary from species to species, but wechose to use input data estimated to be as close as possibleto those of the pea root segments used by Zabalza et al.(2009). For modelling purposes, a root segment was treatedas a series of concentric cylinders, each potentially havingdifferent radial O2 diffusivities, respiratory demands andoxygen storage capacity. The tissue regions in pea weredivided as shown in Fig. 4. At time zero, the respirometermedium was uniformly O2 saturated at some predeter-mined level which, in experimental practice, is ensured by

r = 0 r1 r 2 r 3 r4 r 5 r6 r7 r 8

21 3 4 5 6 7 8

Pea root with modelled zones

Fig. 4. Transverse section of pea root showing zones 1–8 chosen for modelling purposes. These were: zone 1 (0.012 cm) between radii 0 and1, early metaxylem; zone 2 (0.015 cm) between radii 1 and 2, primary phloem, cambium plus any derivatives, late metaxylem andprotoxylem; zone 3 (0.008 cm) between radii 2 and 3, pericycle and endodermis; zone 4 (0.038 cm) between radii 3 and 4, inner cortex; zone5 (0.025 cm) between radii 4 and 5, outer cortex; zone 6 (0.002 cm) between radii 5 and 6, hypodermis and epidermis; zone 7 (0.002 cm)between radii 6 and 7, the diffusive boundary layer beyond the root surface; zone 8 (0.398 cm) between radii 7 and 8, the stirred fluid in therespirometer. Only the cortex has any gas-filled pores. Oxygen diffusivities (D) and maximum respiratory demands (Qmax) were ascribed toeach zone as D1–8 and Q1–8.

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stirring. At this stage, the steady-state distribution of oxygenfrom respirometer medium to root centre was recorded.The model then simulated the sealing of the respirometerfrom the atmosphere and commenced the time-dependentO2 scavenging run. As the oxygen concentration throughoutthe respirometer and root declined under the scavengingactivities of the root tissues, the changing concentrationsand respiratory rates from root centre to respirometermedium could be viewed as moving images. The resultswere also imported to data files for subsequent processingand plotting.

Mathematical formulation

Introduction and the basic steady-state model The physi-cal problem focused on finding the oxygen distribution in arespiring root and its surrounding reservoir into which therewas a constant influx of O2 to maintain a steady-state O2

distribution. The time-dependent distribution was thencalculated as the O2 supply into the reservoir was reduced.

The root and the reservoir were modelled as a set of coaxialcylinders, the number of which was chosen to accommodateregions with different characteristics. Cylinder 1 modelledthe stele (or the inner stele if the stele itself was to be subdi-vided) and the O2 concentration was denoted as C1(r), wherer is the distance from the root axis; C2(r) is the concentrationin the second cylinder, etc.; the radius of the first cylinderwas denoted as r1, the second cylinder by r2, etc.

The respiration within the root sections was modelled asa sink, the strength of which reflected the local structureand the local O2 concentration. Here, we used theMichaelis–Menten form of the respiration as a function ofconcentration, namely:

Ri Cð Þ ¼ QiC

vmei þ C: Eqn 1

This models a respiration rate Ri approaching a constantvalue Qi as the concentration increases, but decreasing tozero as the concentration approaches zero; vmei is a con-stant (potentially different in each cylinder i) that definesthe form of Ri (C ), so RiðC Þ = 1

2 Qi for a chosen value of C.The initial steady-state distribution of O2 was found by

solving a set of steady-state simultaneous differential equa-tions for the distribution within each cylindrical sectionusing standard techniques of diffusion dynamics. Denotingthe respiration in section i as Ri(Ci(r)) and the diffusioncoefficient within that section by Di, the steady-state O2

concentration Ci(r) within a typical cylinder is governed by:

0 ¼ Di1

r

d

d r

rd Ci

d r

� �� Ri Ci rð Þð Þ: Eqn 2

The values of Di are relevant to diffusion in water;although the cortex may have significant gas space, it is

irrelevant in the steady state when respiration within the rootdoes not scavenge the gas space. The zero on the left-handside reflects the steady state in which there is no rate of changeof concentration with respect to time (cf. with Eqn 7).

The mathematical model was completed by imposing aset of boundary conditions expressing the continuity of theconcentration at the interfaces between the cylinders: whereri is the outer radius of the ith cylinder

Ci rið Þ ¼ Ciþ1 rið Þ; Eqn 3

where r = 0 and there is zero diffusion at the axis

d C1 rð Þd r

� �r¼0

¼ 0; Eqn 4

and for equal O2 diffusion rate at each side of an interface

Did CiðrÞ

d r

� �r¼ri

¼Diþ1d Ciþ1ðrÞ

d r

� �r¼ri

for 1� i �N �1:

Eqn 5

and an imposed concentration C¥ at the extremity, whererN is the outer radius of the reservoir by

CN ðrN Þ ¼ C1: Eqn 6

With the respiration modelled by the Michaelis–Mentenformula (Eqn 1), it is not possible to construct an analyticalsolution, unlike cases in which the respiration is constantand it is possible to find solutions in terms of Bessel func-tions; therefore, it is necessary to find numerical solutionsusing finite difference approximations of the derivatives togenerate a set of nonlinear algebraic equations that aresolved by iterative matrix inversion.

It is relevant to note that the gradientd CN ðrÞ

d r

� �, when

r = rN, is not specified among the boundary conditions.Indeed, as 2 p rN DN

d CN ðrÞd r

� �, when r = rN, is the expres-

sion for the total amount of O2 that diffuses into the systemto meet the total respiration of the root, it is possible tocalculate this gradient without finding the O2 distribution.

Time-dependent model Given that the steady-state distri-bution is sustained by having a constant influx, whereFLUX = dCN ðrÞ

dr

� �, when r = rN, the rate at which the con-

centration distribution changes is controlled by the rate atwhich the O2 influx changes. Any experimental techniquecan be simulated by defining a function of time, which isintroduced as flux(t), that defines the amount of oxygendiffusing into the reservoir. Here, we can choose instantaneousdenial of O2 influx by defining flux(t) = 0 for t > 0, but thiscan lead to instabilities in the mathematical solution, similarto the phenomenon of ‘water hammer’, if there are suddenchanges to the water flow in a pipe. However, in practice,






any switch from the steady-state situation is made over afinite time span (possibly small), and by defining the func-tion as

fluxðt Þ = 0:5� FLUX � cosp t

t1

� �þ 1

� �

if t � t1 and = 0 if t > t 1

This is both realistic and avoids instabilities: by definingsmall values of t1 (a few seconds) to simulate a rapid cut-offof O2 diffusion into the reservoir and was used to generatemost of the results shown in this paper by choosing a temp-oral step length dt in the following analysis, thus ensuring asmooth transition at the beginning of the time-dependentphase.

The flux function can easily be modified to simulateexperiments in which the restriction of O2 inflow is relaxedand to explain numerous experimental observations asanother steady-state solution is established.

When the model is time dependent, we need to modifythe notation so that the O2 concentration, which is now afunction of space and time, is denoted by Ci(r,t), andEqn (2) is modified to become the partial differential equa-tion:

@Ci

@t¼ Di

1

r

@

@rr@Ci

@r

� �� Ri Eqn 7

This is discretized by introducing a time step dt andreplacing the temporal derivates by backward differences toyield a set of equations similar to those used to solve thesteady-state problem, but with the addition of terms thatmodel the incremental change from one value of time tothe next.

The results presented in this article ignore the capacitanceof the gas space in the cortex. Although the model is pro-grammable to account for the O2 in the cortical gas spaceby multiplying the term ¶Ci ⁄ ¶t for the cortex by a ‘capac-ity’ factor, this has been seen to be insignificant in thecurrent quantitative results and irrelevant when analysingthe qualitative changes in the concentration.

Input data

Zabalza et al. (2009) recorded their data from pea roots at5 cm from the root apex, where the diameter was 2 mm,and, from control roots at 21 kPa O2 in the respirometermedium, the respiratory rate was c. 300 nmol O2 g)1 FW(not mg)1 as published) min)1 at 25�C. On the assumptionthat 1 g FW was approximately equal to 1 cm3, we tookthis respiration rate to be 160 ng cm)3 s)1. A diameter of2 mm, 5 cm from the root apex, is, in our experience,unusually large for pea and, in the absence of any specificinternal structural data for these pea roots, we assumed that

the radii, r1–8 (cm), would have been approximately thoseshown in Fig. 4: r1, 0.012; r2, 0.027; r3, 0.035; r4, 0.073;r5, 0.098; r6, 0.10; r7, 0.102; r8, 0.50. However, it shouldbe noted that the anatomy of a pea root can vary enor-mously along its length and be very much influenced by theconditions in the medium in which it is grown. Conditionswhich cause O2 deficiency (among other things) commonlylead to a failure of early metaxylem development in pea,which leaves just a few large thin-walled elements at the rootcentre, or even just a cavity (Gladish & Niki, 2000). Theboundary layer thickness adopted here (20 lm) was basedon values determined by Asplund & Curtis (2001); the res-pirometer cuvette radius was based on the ratio of the rootsegment to respirometer volumes used by Zabalza et al.(2009). The corresponding O2 diffusion coefficients D1,D2, etc. (10)5 cm2 s)1) for the tissues, that is between 0and r1, r1 and r2, and so on, were: 2.2, 2.2, 2.4, 25, 20, 2.4,2.4 and 2000. The value of 2.4 · 10)5 cm2 s)1 is the diffu-sion coefficient for O2 in water at 25�C; the slightly lowervalues from 0 to r2 reflected the greater resistance offered bythe lignified xylem elements. We split the cortex into twozones with different diffusivities in each (quite low valuesfor porous cortical tissue). Our reason for doing this was totry to mimic the shape of the radial O2 profiles found byZabalza et al. (2009) in the intact root. Cortical tissuesoften have relatively high gas-filled porosity when viewed intransverse section but, radially, the gas-filled connectionsare much smaller in section and fewer in number. Never-theless, the radial diffusivity can be sufficiently high to give analmost flat O2 profile across the cortex (Gibbs et al., 1998)and, even in pea, a relatively flat profile has been recordedpreviously across the inner cortex (Armstrong et al., 2009).However, even in transverse section, the fractional porosity ofpea roots can be as low as 0.018 and the corresponding radialfractional porosity will be very much lower than this. The val-ues used to try to bring some correspondence with the profilesof Zabalza et al. (2009) were 9.8 · 10)4 and 1.23 · 10)3

(outer and inner cortex). In addition, values as low as this werenecessary to obtain a pronounced curvilinear decline in thelower half of the O2 dependence curve. A diffusion coefficientof 2 · 10)2 cm2 s)1 for the respirometer fluid was necessaryto mimic the stirring.

The respiratory rates assigned to the various tissues werebased on a distribution of activities which would add up tothe global figure obtained by Zabalza et al. (2009) at21 kPa O2 in the respirometer. It is well established that themost active tissues in roots are the apical meristems, theepidermal ⁄ hypodermal layers and the pericycle, phloemand lateral meristems. Asplund & Curtis (2001) found that,for root tips of three contrasting plant species in hairyroot culture, the respiration rate in the O2 dependencecurves reached an asymptotic value of approximately0.08 lmol cm3 s)1 (2560 ng cm3 s)1). For maize roots,Armstrong et al. (1991) reported that the stelar respiration

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rate in maize was approximately 10 times that of the cortex.However, a high proportion of the stelar respiration lay inthe outer annulus of the late metaxylem, phloem and peri-cycle. By volume, a large proportion of the stelar tissuewould have had a relatively low metabolic rate, namely thelate metaxylem and pith; in pea, secondary growth activityshould greatly increase stelar O2 demand. We programmedthe cambium, phloem and late metaxylem tissues in peawith a respiratory rate > 20 times that of the cortex; in pea,the cortical cells at 5 cm from the apex consist largely ofvacuole. For the pericycle, we adopted a rate that was fourtimes that of the cortex. To achieve the same respiratory rate(160 ng cm)3 s)1) as found by Zabalza et al. (2009) fortheir control roots at 258 lM (21 kPa) dissolved O2 in therespirometer medium, default values of the respiration rates(ng cm)3 s)1) for Q1–Q8 (Fig. 4) were: Q1, 13.5; Q2, 2308;Q3, 362; Q4–Q6, 90. For Q7–Q8, a nominal and insignifi-cant value of 0.002 was used to prevent ‘divide by zero’errors in the model. To ensure that respiration rates wouldasymptote, the scavenging runs were begun with the respi-rometer medium at an O2 partial pressure of 80 kPa, andthe values of Q1–Q6 are the values at this asymptote, that isQmax. On a whole-root basis, this equated to 232 ng cm)3 s)1,with the stele accounting for two-thirds of this and theextra-stelar tissues one-third. It should be emphasized thatthese values of Q were derived by a process of trial and errorto arrive at a result that tolerably resembled the publishedO2 dependence curves of Zabalza et al. (2009).

Results and Discussion

Case 1 – control roots

Using the default data described in the Materials andMethods section, which were derived as representative ofthe control roots examined by Zabalza et al. (2009), themodel predicted the O2 dependence curve between 0 and21 kPa shown as the major plot in Fig. 5(a). The similarityto the experimental O2 dependence curve of Zabalza et al.(2009) (Fig. 3a) is striking: the two phases can be clearlyrecognized, although the initial long decline in activity isvery slightly convex rather than strictly linear. However,it should be noted that the root segments first experienced anoxygen deficiency when the O2 in the respirometer was stillas high as 52 kPa (the perceived COPR: Fig. 5a – inset).

The changes in the radial distribution of [O2] and respi-ratory activity across the root segments during the scaveng-ing run from 21 kPa O2 are shown in Fig. 5(b) as profilesat 200 s time intervals. These show that, even when the res-pirometer was at air saturation (c. 21 kPa O2), the centre ofthe stele to radius 0.02 cm was already severely hypoxic(< 1.5 · 10)20 kPa), and the first semi-linear phase ofrespiratory decline comparable with that of Zabalza et al.(2009) (Fig. 3a – control) is attributable to severe hypoxia

radiating further outwards through much of the remainingstele. After 1200 s, 4000 s after starting the scavenging run,(profile 7 in Fig. 5b), this has extended to the inner edge ofthe pericycle, and, at 1400 s (profile 8 in Fig. 5b), respirationin the innermost cortex is just beginning to decline. Corres-ponding to this, the O2 partial pressure in the respirometermedium can be seen to be c. 4 kPa. This is recognizable as thepoint around which the second phase of respiratory declinebegins. It can be seen from Fig. 5 that this is attributable tothe spread of hypoxia through the pericycle, into the cortexand across the remainder of the root segment.

The respiration rates in our ‘control’ plot and that ofZabalza et al. (2009) still appear to be rising at values> 21 kPa O2 in the respirometer medium. No indication isgiven of where COPR would have been for the pea rootsused in the original experiments, but the model predicts aCOPR value of c. 52 kPa O2 (Fig. 5a insert): a high value,but not dissimilar to that obtained by Berry and Norris fortheir narrower onion root tips at 30�C, and well within therange of other predictions for COPRs when O2 sensing isexternal to the root (Armstrong & Drew, 2002).

The boundary layer thickness used (20 lm) assumes thatthere is a vigorous stirring rate in the respirometer cuvette.This may not always be the case. In addition, as the rootsegments are carried on currents, rather than remainingfixed, the shearing forces on the segments could be insuffi-cient to achieve such a narrow boundary layer. However,even with a boundary layer thickness of 120 lm, the bipha-sic decline is still prominent (Supporting InformationFig. S1), although the perceived COPR is higher (66 kParather than 52 kPa noted above), and the start of the secondphase of respiratory decline is at a higher oxygen pressure(c. 9 kPa), rather than 5 kPa shown in Fig. 5(a). The over-all effect is to stretch the plot along the x-axis.

Case 2 – pyruvate feeding

For pea root segments, Zabalza et al. (2009) found that, ifthe roots had been supplied previously for 1 d with 8 mMpyruvate in the growing medium, the respiratory demand at21 kPa O2 in the respirometer medium (based on standarderrors) was 1.7–2.4-fold greater than that of control roots;pyruvate was also added to the medium in the respirometer.The O2 dependence curve obtained is shown in Fig. 3(a).As a result of some scatter in the data, the initial decline inactivity is not as clearly defined as for the control roots, andmight be perceived to be nearer its asymptote; in addition,the second phase commences at a higher respirometer O2

concentration than in control roots.To model the pyruvate-fed condition, we first doubled

the respiratory input data for the control roots. The O2

dependence plot from 0 to 21 kPa is shown in Fig. 6(a),together with the plot for the ‘control’ roots. Again, thebiphasic response is evident and, although the second phase






starts at a higher respirometer O2 concentration, the twoplots have a very similar form; however, in contrast withthat of Zabalza et al. (2009) (Fig. 3a), our pyruvate plotappears to be further from an asymptote than the controlroots, rather than nearer. This probably reflects our failureto arrive at an exact correspondence between our input dataand the anatomical characteristics and distribution of respi-ratory demand of the pea roots examined by Zabalza et al.(2009). Clearly, however, the higher potential respiratorydemand introduced to simulate pyruvate feeding results inan increased respiratory rate, namely c. 1.53 times that ofthe ‘control’ roots at 21 kPa O2 in the respirometer med-ium. Although not quite so large as the increases noted byZabalza et al. (2009) and Gupta et al. (2009) (1.54–1.9), itis sufficient to contradict their supposition that, if controlroots are already O2 stressed at 21 kPa, pyruvate feedingshould not increase the measured respiratory rate.

Although it might be counter-intuitive to expectincreased O2 consumption in a root already experiencingsome O2 deficiency, the model reveals that there can still besufficient aerobic tissue to benefit from the increased sub-strate, and hence raise the overall rate of O2 consumption.

A similar explanation can account for the degree to which a10�C rise in temperature raises the respiration rate in analready partially O2-deficient root (Fig. 2). Although theO2 diffusion coefficient rises by 27%, this is insufficient toaccount for the increased O2 consumption and, further-more, the O2 solubility (and hence the concentration of theO2 source) falls by 17%; this would counter the effect ofthe increased diffusivity. The rise in respiration must there-fore be caused by increased consumption in those roottissues outside the severely hypoxic core.

Case 3 – effects of temperature and root diameter

The predictions made so far relate to measurements madeat 25�C on roots 2 mm in diameter. These are both likelyto lead to high perceived COPRs when sensed by monitor-ing [O2] in the bathing medium. ‘Fat’ roots are often unli-kely to be fully satisfied if O2 is only available radially fromthe surroundings at atmospheric concentrations.

The effects of halving the root diameter to 1 mm (tissueradii all reduced proportionately) for the previous controland pyruvate-fed examples, and of a reduction in temperature

Respirometer O2 partial pressure (kPa)0 4 8 12 16 20

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Fig. 5. (a) Predicted O2 dependencerelationship for ‘control’ pea root segmentsplotted over the range zero to 21 kPa O2 inthe respirometer medium. Qmax occurred at acritical oxygen pressure (COPR) of 52 kPa(see inset). Arrowheads, air saturation inrespirometer medium. (b) Predicted radialprofiles of O2 distribution and respiratoryactivity in the root segments during part ofthe scavenging run. The profiles presentedare at 200 s intervals, starting from the stageat which the respirometer medium hadreached approximately air saturation (plot 1),2800 s after the start of the scavenging run.Arrow, air saturation in respirometermedium. Stelar zone is shaded grey.

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to 20�C for the control roots, are shown in Fig. 6(b). Althoughat 20�C the respiratory rate per unit volume of the controlroot remains constant, the halving of the root diameter resultsin Qmax = 232 ng cm)3 s)1 being achieved at c. 13 kPa O2

with the perceived COPR falling from 52 kPa to 14.5 kPa.Previously, a respiratory rate of only c. 160 ng cm)3 s)1 wasrealized when the respirometer medium was air saturated.For the ‘pyruvate-fed’ condition, the halving of the root

diameter resulted in the potential Qmax of 464 ng cm)3 s)1

being realized at c. 28 kPa, and the COPR was reducedfrom c. 106 kPa to 28 kPa. Previously, at 21 kPa, a respi-ratory rate of only 240 ng cm)3 s)1 was realized; withthe halving of root diameter this has been raised to c.410 ng cm)3 s)1. Lowering the temperature to 20�Creduces the perceived COPR for ‘control’ roots by a further4.5 kPa to 11 kPa. However, even these temperatures wouldbe regarded as high for soils in northern temperate latitudes:narrower roots and lower temperatures would together resultin even lower perceived COPRs. At any locus within the rootitself, however, respiratory activity will probably be underthe control of the major oxidase, cytochrome oxidase, withKm = 0.0108 kPa and COPR < 1.0 kPa. Even the alter-native oxidase, although having a Km value an order ofmagnitude greater than that of cytochrome oxidase (Millaret al., 1994), would not greatly influence the picture thathas emerged from these modelling results. Using controlroot characteristics, but with respiration controlled solelyby the alternative oxidase (Km = 1.7 lM or 0.134 kPa), theplots obtained (Fig. S2) are very similar to those in Fig. 5(a)obtained using the Km value for cytochrome oxidase.

Perspective and conclusions

Whether roots are, or are not, able to down-regulate theirrespiration rates at concentrations much higher than COPRfor cytochrome oxidase, our modelling data strongly suggestthat results such as those in Fig. 3 cannot be used in supportof a down-regulation hypothesis. The results emphasizewhat has been generally accepted for some time, namely thatthe degree and distribution of respiratory demand and diffu-sive resistance, both within and without the root, play amajor role in determining the sufficiency of O2 supply, andthat a dependence only on the oxygen-affinity characteristicsof cytochrome oxidase is sufficient to explain findings suchas those in Fig. 3. Diffusive resistances within the root arevery substantial and, in respirometry, where the O2 sensor isin the medium external to the root segments, this wouldnormally be expected to result in a perceived COPR verymuch greater than that for mitochondria, microorganismsor isolated protoplasts. At temperatures from 25 to 30�C,COPRs sometimes much greater than 21 kPa have beenfound for a variety of roots ranging in diameter from 0.23 to0.75 mm (Berry & Norris, 1949; Asplund & Curtis, 2001).However, what is not always clear from O2 dependenceplots is the complete form of the relationship. Plots are usu-ally derived from the fitting of curves to respiratory ratesmeasured at several discrete respirometer O2 concentrations.These may be recorded from slopes measured at severalpoints along a complete O2 scavenging curve, or the respiratoryrates may have been measured with the respirometer med-ium equilibrated at a range of different O2 concentrations.Plots derived in this way can give a ‘global’ picture, but fail


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Fig. 6. (a) Predicted O2 dependence relationship for ‘control’ and‘pyruvate-fed’ pea root segments (diameter, 2 mm) plotted over therange zero to 21 kPa O2 in the respirometer medium. The criticaloxygen pressure (COPR) for both plots (not shown) is above 21 kPa(52 kPa for control roots and 106 kPa for pyruvate-fed roots). Thepotential Qmax attained at the COPR was 232 ng cm)3 s)1 for‘control’ roots and 464 ng cm)3 s)1 for ‘pyruvate-fed’ roots. (b)Predicted O2 dependence relationship for ‘control’ and ‘pyruvate-fed’ pea root segments of 1 mm in diameter plotted over the rangezero to 30 kPa O2. The effect of decreasing the temperature from25 to 20�C is also shown for the ‘control’ roots. Each plot revealsCOPR (black arrows) and potential Qmax: at 25�C, 232 ng cm)3 s)1

(‘control’ roots) and 464 ng cm)3 s)1 (‘pyruvate-fed’ roots); at20�C, 160 ng cm)3 s)1 (‘control’ roots) [correction added afteronline publication 6 January 2011: in part (b) of Fig. 6, the lowestplot value was corrected from 25�C to 20�C].






to expose some subtle features that might be evident in amore complete curve. For pea root segments, Zabalza et al.(2009) revealed a biphasic decline in respiration ratebetween 21 and 0 kPa O2 in the respirometer medium.Unfortunately, they did not examine the relationship above21 kPa, but, nevertheless, a biphasic decline along part ofthe O2 dependence curve has not been identified previously.If extra points had been available in the Berry and Norrisdata (Fig. 2), it is conceivable that they could have shownan almost linear decline between 45 and 21 kPa. Zabalzaet al. (2009) interpreted the long almost linear declinebetween 21 kPa and c. 4 kPa as evidence of a conservationof O2 by a controlled down-regulation of respiration in theroot. The same explanation was given by Gupta et al.(2009) to explain the form of the O2 dependence curve forbarley root segments shown in Fig. 3(b). Our data show, atleast for pea roots, that the form of the O2 dependencecurves (Fig. 3a,b) can be explained in terms of the spread ofsevere hypoxia radially through the steles of root segmentsthat are already very O2 stressed with 21 kPa O2 in therespirometer medium. Our data also reveal that increasedrespiration rates found after pyuvate feeding cannot there-fore be used as an indication of a lack of O2 stress beforepyuvate feeding, as claimed by Gupta et al. (2009).

If the respirometer data of Zabalza et al. (2009) andGupta et al. (2009) are not in themselves evidence for respi-ratory down-regulation, but rather respiratory declinecaused by O2 levels falling below the COPR for cytochromeoxidase, the question remains as to whether there is a formof respiratory down-regulation in roots as a result of lowO2. Roots growing in flooded soils or in stagnant hypoxicagar, and dependent only on oxygen diffusing internallyfrom the shoot, will eventually stop growing because of O2

limitation, but will not die unless there is some additionalstress, for example, from external phytotoxins. Is this evi-dence of some respiratory down-regulation, or is viabilitymaintained because ethanol or other products of ‘anaerobic’metabolism can be continually removed from the root tip,stele and meristem, and because substrate can still be sup-plied through the phloem? Hand in hand with this is thepossibility of down-regulation of anaerobic energy-consum-ing processes to a level at which they are sufficient for main-tenance needs only.

There is some evidence that sugars can still reach ananaerobic root tip through the phloem, albeit at a muchreduced rate (T. Webb & W. Armstrong, unpublisheddata): in maize roots of 12 cm in length, with the tips inde-oxygenated agar, the subapical parts girdled top andbottom, split longitudinally and exposed to an atmosphereof N2, labelled nonmetabolized deoxyglucose fed to thecaryopsis accumulated in the tip to about one-third of thatin control ‘aerated’ growing roots over a 24-h period.Similarly, Atwell et al. (1985) found that, although maizeseedling roots ceased elongating at c. 0.04 mM O2 in the

rooting medium, sugars and amino acids were higher in thetips than in aerated roots. They concluded that, althoughthe roots are being sustained by seed reserves, the adverseeffects of low O2 concentrations are unlikely to be a conse-quence of substrate shortage for either respiration or synthesisof macromolecules, but rather low rates of ATP regenerationin growing root tissues.

If there is still an internal O2 source in the cortex close tothe tip, the tip cannot become totally anoxic (Armstronget al., 2009), but we still do not know at what O2 concen-tration the root cells will cease to utilize it. However, anaer-obic metabolites from the stele can be lost to a still aerobiccortex and be metabolized, lost by diffusion to the externalmedium or be transported to the shoot through the xylem(Thomson & Greenway, 1991). If there is down-regulation,we believe that this will possibly be at concentrations closeto or below the Km value for cytochrome oxidase, insuffi-cient for what might normally be conceived as O2 conserva-tion, and not down-regulation in the sense conceived byZabalza et al. (2009) or Gupta et al. (2009). Down-regula-tion of anaerobic metabolism might be more relevant forsustained viability. As Gibbs and Greenway have pointedout ‘to survive an energy crisis, plant cells need to reducetheir energy requirements for maintenance, and also directthe limited amounts of energy produced during anaerobiccatabolism to the energy-consuming processes that are criti-cal to survival’. They postulate that, ‘during anoxia, reduc-tions in ion fluxes and protein turnover achieve economiesin energy consumption. Processes receiving energy from thelimited supply available include the synthesis of anaerobicproteins and energy-dependent substrate transport’ (Gibbs& Greenway, 2003; Greenway & Gibbs, 2003).

Although the respirometry examples dealt with here chal-lenge previous analyses of O2 dependence plots, they do notillustrate the full potential of the model for predicting andanalysing respirometer output. The strength of the model-ling approach is that it provides a means of identifying andpredicting, in some detail, the changes taking place spatiallyin the root during the scavenging process. These can thenbe used to better interpret the features in the O2 depen-dence plot. Some appreciation of the dynamic output isavailable as a supplementary file (Video S1). The model alsohas the potential to input Km values other than that of cyto-chrome oxidase and, in the future, we would hope to reporton the effects on scavenging and O2 dependence plots ofthick nonporous hypodermal tissues, high cortical porositiesand higher tissue volume to respirometer volume ratios.

Acknowledgements

We thank Jean Armstrong, Brian Atwell, Tim Colmer, HankGreenway, Joost van Dongen, Robert Hill, Brian Sorrell,David Threlfall, David Turner and two anonymous refereesfor helpful discussions and ⁄or comments on the manuscript.

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Supporting Information

Additional supporting information may be found in theonline version of this article.

Fig. S1 Predicted O2 dependence relationship for ‘control’pea root segments plotted over the range zero to 21 kPa O2

in the respirometer medium, but with a boundary layerthickness of 120 lm.

Fig. S2 (a) Predicted O2 dependence relationships for ‘con-trol’ pea root segments plotted over the range zero to21 kPa O2 in the respirometer medium with either cyto-chrome oxidase or the alternative oxidase accounting for allthe oxygen consumption. (b) Predicted O2 dependencerelationships for ‘control’ pea root segments plotted overthe range zero to 79 kPa O2 in the respirometer mediumwith either cytochrome oxidase or the alternative oxidaseaccounting for all the oxygen consumption.

Video S1 The dynamics of the scavenging process in therespirometer.

Please note: Wiley-Blackwell are not responsible for thecontent or functionality of any supporting informationsupplied by the authors. Any queries (other than missingmaterial) should be directed to the New Phytologist CentralOffice.






experimental and modelling data contradict the idea of respiratory down-regulation in plant tissues...

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