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•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 medium. 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 respiratory 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 pericycle 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 respiration based on O2 sensors.
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Respirometer studies of oxygen scavenging by microorganisms and animal cells have shown almost invariably that oxygen uptake is unaffected by declining O2 concentration in the stirred surrounding medium until very low levels have been reached (for a review, see Harrison & Stouthamer, 1973). For nine species of bacteria, yeast, pig’s heart and ox heart in suspension culture, Longmuir (1954) found that the O2 depletion curves fitted the Michaelis equation and that 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, apart from yeast with its peripheral mitochondria, the larger the microorganism, the greater the value of Km. Longmuir concluded that the Km–size relationship was unlikely to be a result of variation in the affinity of the respiratory enzymes for O2, but rather of differences in internal diffusion path length to the respiratory systems within the cells. Oxygen scavenging by cell-free preparations supported this prediction, with cell-free Km values for each of three microorganisms being very similar to one another and not much less than the Km value of the smallest organism.
Much has been written on how the relationship between oxygen concentration and respiration rate should be treated, particularly if cell growth is involved and if enzyme content can change a great deal with changes in growth conditions (Harrison & Stouthamer, 1973). Chance (1957), for example, argued against treating the O2 affinity of cells as a simple Michaelis–Menten relationship. Nevertheless, using a multi-enzyme model, he showed that the O2 uptake would still be independent of dissolved O2 until a very low critical value is reached. For many practical purposes, however, it is most convenient to apply Michaelis–Menten kinetics using an ‘apparent Km’ to approximate the oxygen dependence of the respiratory processes. As cytochrome oxidase is the major terminal oxidase for plant respiration, and mitochondria are the major sites of oxygen consumption in the plant cell, we have used for our modelling in this article a Km value of 0.14 μM (0.0108 kPa O2), averaged from the values cited for isolated mitochondria from several plant species (Barzu & Satre, 1970, 0.15 μM; Rawsthorne & LaRue, 1986, 0.1–0.12 μM; Millar et al., 1994, 0.125–0.147 μM). The corresponding oxygen affinity curve is shown in Fig. 1, from which it can be seen that such a low Km goes hand in hand with a very low critical oxygen pressure (COPR) which is being approached at 1 kPa O2. Because of the asymptotic nature of the curve, it is not possible to give a precise figure, but 95% of the maximum respiratory rate is reached at c. 0.25 kPa O2. The typical form 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 slope of the scavenging curve, ∂C/∂t, the tissue mass/volume and the respirometer volume. These curves were computer generated but, if the data are processed from recorder charts, it can be difficult to determine accurately the respiration rate at any point on the scavenging curve, or the COPR at which the scavenging line changes almost imperceptibly from a straight line to a curve.
Among the first workers to use respirometry to examine the relationship between root respiration and O2 concentration [O2] were Berry & Norris (1949). The general form of their O2 dependence plots, typical of those from most subsequent studies on roots, was similar to that for microorganisms, although the COPRs were very much higher. With declining oxygen, there was a plateau at which the respiration was still at a maximum and independent of [O2], until a COPR was reached, after which there was an accelerating decline to zero. For onion root segments at 20°C, this COPR was very much greater than for microorganism respiration: COPRs of 21 (Fig. 2), 15 and 10 kPa O2, respectively, were recorded for the zones 0–5, 5–10 and 10–15 mm above the onion root apex. At 30°C, the critical pressures were c. 48 (Fig. 2), 21 and 10 kPa, respectively. Oxygen consumption in the apical 5 mm of the onion root was twice that of the 5–10 mm zone, and this latter zone respired at a rate greater than that at 10–15 mm from the apex (Berry & Brock, 1946). Consequently, the magnitude of COPR was revealed to be dependent on the respiratory rate of the tissue and the temperature of the system. The discrepancy between high in vitro COPR and the affinity of cytochromes for O2 was attributed by Berry and Norris to the diffusional impedances within the tissues, creating a core of anaerobiosis at O2 concentrations below the COPR. Indeed, the CO2 output below the COPR values was such that the respiratory quotients (RQs) consistently exceeded unity, indicating a significant leve1 of fermentation (Fig. 2). Ethanol production and active pyruvate decarboxylase in the stele of maize, but not in the cortex, at low cortical O2 partial pressures (Thomson & Greenway, 1991) also support Berry and Norris’s supposition of a developing core of anaerobiosis below COPR, as do direct measurements of O2 profiles across roots (Armstrong et al., 1994; Gibbs et al., 1998; Darwent et al., 2003). Nonporous tissues, such as the stele and epidermal/hypodermal cell layers, would normally be 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 the thicker the nonporous epidermal/hypodermal cell layers, the higher will be the expected COPRs when assessed in this way. In respirometer cuvettes, in which root segments are suspended in a stirred bathing medium, diffusive boundary layers (DBLs) at the surface of the root segments also play a part in determining the position of the perceived COPR (Asplund & Curtis, 2001; Curtis & Tuerk, 2008; Armstrong et al., 2009): the slower the rate of stirring, the thicker the DBL and the higher the COPR. COPRs measured on intact roots by methods which exclude the effects of the diffusive resistances of cortex, epidermis and DBL have revealed stelar COPRs for rice, pea, maize and Eriophorum angustifolium of ≤ 2.5 kPa O2 (Armstrong et al., 2009).
The work described here was prompted by recent reports of high COPRs in pea and barley roots, and oxygen dependence curves that showed a decline in respiration apparently from above atmospheric concentrations of O2 and that had a biphasic form (Gupta et al., 2009; Zabalza et al., 2009). A relatively long initial decline to about one-half the initial respiration rate was followed by a steeper curvilinear decline to reach zero at zero [O2] in the respirometer fluid (control plots, Fig. 3a,b). Oxygen dependence curves were also determined for roots previously fed with pyruvate (Fig. 3a,b) and other substrate sources. These data have raised a number of questions: (1) how should the biphasic shape of the control plots be interpreted; and (2) how can pyruvate feeding increase the maximum respiration rate when roots already appear to be O2 deficient? Zabalza et al. (2009) and Gupta et al. (2009) interpreted the initial, apparently linear, decline in respiratory rate of the control roots as evidence of a gradual O2-sensitive down-regulation of respiration, which has evolved as a means of saving O2 as its availability is reduced. The suggestion that the respiratory decline in pea could be the result of diffusion limitations was dismissed on the basis of claims that similar shaped plots were obtained for Arabidopsis roots, which are only 200 μm thick, compared with 2 mm for pea, and for Chlamydomonas cultures for which the cell size is only 20 μm. The increased respiratory rate in response to pyruvate and succinate feeding was taken as an indication that the first phase of respiratory decline in the control treatment roots could not have been the result of O2 becoming a limiting substrate. Radial oxygen profiles through intact pea roots from the various treatments showed no evidence of anoxia, but, at the same time, showed no evidence of having entered the stele in any example, where, usually, a steep fall in O2 concentration is noted (cf. Fig. 1 from 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 aforementioned 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), and by the conclusions presented. Consequently, we wondered whether it might be possible to resolve the apparent contradictions by modelling the experiments. To this end, we developed a Fortran-based mathematical model of O2 scavenging in closed respirometer systems. This allowed us to reproduce the types of scavenging curve obtained and to predict the O2 dependence relationships as a function of the diffusive resistances, respiratory activities of the various tissues, boundary layer effects and respirometer reservoir dimensions. Our hypothesis was that the biphasic response curves of Zabalza et al. (2009) and Gupta et al. (2009) could be explained in terms of impaired respiration as O2 concentrations below the COPR for cytochrome oxidase were reached within the root under the combined effects of respiration and diffusive resistance.
The model was designed to simulate a cylindrical respirometer cuvette with an in-built O2 sensor (e.g. polarographic electrode or micro-optode) filled with continuously stirred aqueous medium and containing root segments. The relative proportion of respirometer cuvette radius to root radius depends on the chosen number and dimensions of the root segments and chamber size. The diffusive and respiratory characteristics of roots vary from species to species, but we chose to use input data estimated to be as close as possible to those of the pea root segments used by Zabalza et al. (2009). For modelling purposes, a root segment was treated as a series of concentric cylinders, each potentially having different radial O2 diffusivities, respiratory demands and oxygen storage capacity. The tissue regions in pea were divided as shown in Fig. 4. At time zero, the respirometer medium was uniformly O2 saturated at some predetermined level which, in experimental practice, is ensured by stirring. At this stage, the steady-state distribution of oxygen from respirometer medium to root centre was recorded. The model then simulated the sealing of the respirometer from the atmosphere and commenced the time-dependent O2 scavenging run. As the oxygen concentration throughout the respirometer and root declined under the scavenging activities of the root tissues, the changing concentrations and respiratory rates from root centre to respirometer medium could be viewed as moving images. The results were also imported to data files for subsequent processing and plotting.
Introduction and the basic steady-state model The physical problem focused on finding the oxygen distribution in a respiring root and its surrounding reservoir into which there was a constant influx of O2 to maintain a steady-state O2 distribution. The time-dependent distribution was then calculated as the O2 supply into the reservoir was reduced.
The root and the reservoir were modelled as a set of coaxial cylinders, the number of which was chosen to accommodate regions with different characteristics. Cylinder 1 modelled the stele (or the inner stele if the stele itself was to be subdivided) and the O2 concentration was denoted as C1(r), where r is the distance from the root axis; C2(r) is the concentration in the second cylinder, etc.; the radius of the first cylinder was denoted as r1, the second cylinder by r2, etc.
The respiration within the root sections was modelled as a sink, the strength of which reflected the local structure and the local O2 concentration. Here, we used the Michaelis–Menten form of the respiration as a function of concentration, namely:
This models a respiration rate Ri approaching a constant value Qi as the concentration increases, but decreasing to zero as the concentration approaches zero; vmei is a constant (potentially different in each cylinder i) that defines the form of Ri(C), so for a chosen value of C.
The initial steady-state distribution of O2 was found by solving a set of steady-state simultaneous differential equations for the distribution within each cylindrical section using standard techniques of diffusion dynamics. Denoting the respiration in section i as Ri(Ci(r)) and the diffusion coefficient within that section by Di, the steady-state O2 concentration Ci(r) within a typical cylinder is governed by:
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 root does not scavenge the gas space. The zero on the left-hand side reflects the steady state in which there is no rate of change of concentration with respect to time (cf. with Eqn 7).
The mathematical model was completed by imposing a set of boundary conditions expressing the continuity of the concentration at the interfaces between the cylinders: where ri is the outer radius of the ith cylinder
where r = 0 and there is zero diffusion at the axis
and for equal O2 diffusion rate at each side of an interface
and an imposed concentration C∞ at the extremity, where rN is the outer radius of the reservoir by
With the respiration modelled by the Michaelis–Menten formula (Eqn 1), it is not possible to construct an analytical solution, unlike cases in which the respiration is constant and it is possible to find solutions in terms of Bessel functions; therefore, it is necessary to find numerical solutions using finite difference approximations of the derivatives to generate a set of nonlinear algebraic equations that are solved by iterative matrix inversion.
It is relevant to note that the gradient , when r = rN, is not specified among the boundary conditions. Indeed, as , when r = rN, is the expression for the total amount of O2 that diffuses into the system to meet the total respiration of the root, it is possible to calculate this gradient without finding the O2 distribution.
Time-dependent model Given that the steady-state distribution is sustained by having a constant influx, where , when r = rN, the rate at which the concentration distribution changes is controlled by the rate at which the O2 influx changes. Any experimental technique can be simulated by defining a function of time, which is introduced as flux(t), that defines the amount of oxygen diffusing into the reservoir. Here, we can choose instantaneous denial of O2 influx by defining flux(t) = 0 for t > 0, but this can lead to instabilities in the mathematical solution, similar to the phenomenon of ‘water hammer’, if there are sudden changes to the water flow in a pipe. However, in practice, any switch from the steady-state situation is made over a finite time span (possibly small), and by defining the function as
This is both realistic and avoids instabilities: by defining small values of t1 (a few seconds) to simulate a rapid cut-off of O2 diffusion into the reservoir and was used to generate most of the results shown in this paper by choosing a temporal step length dt in the following analysis, thus ensuring a smooth transition at the beginning of the time-dependent phase.
The flux function can easily be modified to simulate experiments in which the restriction of O2 inflow is relaxed and to explain numerous experimental observations as another steady-state solution is established.
When the model is time dependent, we need to modify the notation so that the O2 concentration, which is now a function of space and time, is denoted by Ci(r,t), and Eqn (2) is modified to become the partial differential equation:
This is discretized by introducing a time step dt and replacing the temporal derivates by backward differences to yield a set of equations similar to those used to solve the steady-state problem, but with the addition of terms that model the incremental change from one value of time to the next.
The results presented in this article ignore the capacitance of the gas space in the cortex. Although the model is programmable to account for the O2 in the cortical gas space by multiplying the term ∂Ci/∂t for the cortex by a ‘capacity’ factor, this has been seen to be insignificant in the current quantitative results and irrelevant when analysing the qualitative changes in the concentration.
Zabalza et al. (2009) recorded their data from pea roots at 5 cm from the root apex, where the diameter was 2 mm, and, from control roots at 21 kPa O2 in the respirometer medium, the respiratory rate was c. 300 nmol O2 g−1 FW (not mg−1 as published) min−1 at 25°C. On the assumption that 1 g FW was approximately equal to 1 cm3, we took this respiration rate to be 160 ng cm−3 s−1. A diameter of 2 mm, 5 cm from the root apex, is, in our experience, unusually large for pea and, in the absence of any specific internal structural data for these pea roots, we assumed that the radii, r1–8 (cm), would have been approximately those shown 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 should be noted that the anatomy of a pea root can vary enormously along its length and be very much influenced by the conditions in the medium in which it is grown. Conditions which cause O2 deficiency (among other things) commonly lead to a failure of early metaxylem development in pea, which leaves just a few large thin-walled elements at the root centre, or even just a cavity (Gladish & Niki, 2000). The boundary layer thickness adopted here (20 μm) was based on values determined by Asplund & Curtis (2001); the respirometer cuvette radius was based on the ratio of the root segment 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 0 and 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 diffusion coefficient for O2 in water at 25°C; the slightly lower values from 0 to r2 reflected the greater resistance offered by the lignified xylem elements. We split the cortex into two zones with different diffusivities in each (quite low values for porous cortical tissue). Our reason for doing this was to try to mimic the shape of the radial O2 profiles found by Zabalza et al. (2009) in the intact root. Cortical tissues often have relatively high gas-filled porosity when viewed in transverse section but, radially, the gas-filled connections are much smaller in section and fewer in number. Nevertheless, the radial diffusivity can be sufficiently high to give an almost flat O2 profile across the cortex (Gibbs et al., 1998) and, even in pea, a relatively flat profile has been recorded previously across the inner cortex (Armstrong et al., 2009). However, even in transverse section, the fractional porosity of pea roots can be as low as 0.018 and the corresponding radial fractional porosity will be very much lower than this. The values used to try to bring some correspondence with the profiles of 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 were necessary to obtain a pronounced curvilinear decline in the lower half of the O2 dependence curve. A diffusion coefficient of 2 × 10−2 cm2 s−1 for the respirometer fluid was necessary to mimic the stirring.
The respiratory rates assigned to the various tissues were based on a distribution of activities which would add up to the global figure obtained by Zabalza et al. (2009) at 21 kPa O2 in the respirometer. It is well established that the most active tissues in roots are the apical meristems, the epidermal/hypodermal layers and the pericycle, phloem and lateral meristems. Asplund & Curtis (2001) found that, for root tips of three contrasting plant species in hairy root culture, the respiration rate in the O2 dependence curves reached an asymptotic value of approximately 0.08 μmol cm3 s−1 (2560 ng cm3 s−1). For maize roots, Armstrong et al. (1991) reported that the stelar respiration rate in maize was approximately 10 times that of the cortex. However, a high proportion of the stelar respiration lay in the outer annulus of the late metaxylem, phloem and pericycle. By volume, a large proportion of the stelar tissue would have had a relatively low metabolic rate, namely the late metaxylem and pith; in pea, secondary growth activity should greatly increase stelar O2 demand. We programmed the cambium, phloem and late metaxylem tissues in pea with a respiratory rate > 20 times that of the cortex; in pea, the cortical cells at 5 cm from the apex consist largely of vacuole. For the pericycle, we adopted a rate that was four times that of the cortex. To achieve the same respiratory rate (160 ng cm−3 s−1) as found by Zabalza et al. (2009) for their control roots at 258 μM (21 kPa) dissolved O2 in the respirometer 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 insignificant value of 0.002 was used to prevent ‘divide by zero’ errors in the model. To ensure that respiration rates would asymptote, the scavenging runs were begun with the respirometer medium at an O2 partial pressure of 80 kPa, and the values of Q1–Q6 are the values at this asymptote, that is Qmax. On a whole-root basis, this equated to 232 ng cm−3 s−1, with the stele accounting for two-thirds of this and the extra-stelar tissues one-third. It should be emphasized that these values of Q were derived by a process of trial and error to arrive at a result that tolerably resembled the published O2 dependence curves of Zabalza et al. (2009).
Results and Discussion
Case 1 – control roots
Using the default data described in the Materials and Methods section, which were derived as representative of the control roots examined by Zabalza et al. (2009), the model predicted the O2 dependence curve between 0 and 21 kPa shown as the major plot in Fig. 5(a). The similarity to the experimental O2 dependence curve of Zabalza et al. (2009) (Fig. 3a) is striking: the two phases can be clearly recognized, although the initial long decline in activity is very slightly convex rather than strictly linear. However, it should be noted that the root segments first experienced an oxygen deficiency when the O2 in the respirometer was still as high as 52 kPa (the perceived COPR: Fig. 5a– inset).
The changes in the radial distribution of [O2] and respiratory activity across the root segments during the scavenging run from 21 kPa O2 are shown in Fig. 5(b) as profiles at 200 s time intervals. These show that, even when the respirometer was at air saturation (c. 21 kPa O2), the centre of the stele to radius 0.02 cm was already severely hypoxic (< 1.5 × 10−20 kPa), and the first semi-linear phase of respiratory decline comparable with that of Zabalza et al. (2009) (Fig. 3a– control) is attributable to severe hypoxia radiating further outwards through much of the remaining stele. After 1200 s, 4000 s after starting the scavenging run, (profile 7 in Fig. 5b), this has extended to the inner edge of the pericycle, and, at 1400 s (profile 8 in Fig. 5b), respiration in the innermost cortex is just beginning to decline. Corresponding to this, the O2 partial pressure in the respirometer medium can be seen to be c. 4 kPa. This is recognizable as the point around which the second phase of respiratory decline begins. It can be seen from Fig. 5 that this is attributable to the spread of hypoxia through the pericycle, into the cortex and across the remainder of the root segment.
The respiration rates in our ‘control’ plot and that of Zabalza et al. (2009) still appear to be rising at values > 21 kPa O2 in the respirometer medium. No indication is given of where COPR would have been for the pea roots used in the original experiments, but the model predicts a COPR value of c. 52 kPa O2 (Fig. 5a insert): a high value, but not dissimilar to that obtained by Berry and Norris for their narrower onion root tips at 30°C, and well within the range of other predictions for COPRs when O2 sensing is external to the root (Armstrong & Drew, 2002).
The boundary layer thickness used (20 μm) assumes that there is a vigorous stirring rate in the respirometer cuvette. This may not always be the case. In addition, as the root segments are carried on currents, rather than remaining fixed, the shearing forces on the segments could be insufficient to achieve such a narrow boundary layer. However, even with a boundary layer thickness of 120 μm, the biphasic decline is still prominent (Supporting Information Fig. S1), although the perceived COPR is higher (66 kPa rather than 52 kPa noted above), and the start of the second phase of respiratory decline is at a higher oxygen pressure (c. 9 kPa), rather than 5 kPa shown in Fig. 5(a). The overall effect is to stretch the plot along the x-axis.
Case 2 – pyruvate feeding
For pea root segments, Zabalza et al. (2009) found that, if the roots had been supplied previously for 1 d with 8 mM pyruvate in the growing medium, the respiratory demand at 21 kPa O2 in the respirometer medium (based on standard errors) 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 in activity is not as clearly defined as for the control roots, and might 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, the biphasic response is evident and, although the second phase starts at a higher respirometer O2 concentration, the two plots have a very similar form; however, in contrast with that of Zabalza et al. (2009) (Fig. 3a), our pyruvate plot appears to be further from an asymptote than the control roots, rather than nearer. This probably reflects our failure to arrive at an exact correspondence between our input data and the anatomical characteristics and distribution of respiratory demand of the pea roots examined by Zabalza et al. (2009). Clearly, however, the higher potential respiratory demand introduced to simulate pyruvate feeding results in an increased respiratory rate, namely c. 1.53 times that of the ‘control’ roots at 21 kPa O2 in the respirometer medium. Although not quite so large as the increases noted by Zabalza et al. (2009) and Gupta et al. (2009) (1.54–1.9), it is sufficient to contradict their supposition that, if control roots are already O2 stressed at 21 kPa, pyruvate feeding should not increase the measured respiratory rate.
Although it might be counter-intuitive to expect increased O2 consumption in a root already experiencing some O2 deficiency, the model reveals that there can still be sufficient aerobic tissue to benefit from the increased substrate, and hence raise the overall rate of O2 consumption. A similar explanation can account for the degree to which a 10°C rise in temperature raises the respiration rate in an already partially O2-deficient root (Fig. 2). Although the O2 diffusion coefficient rises by 27%, this is insufficient to account for the increased O2 consumption and, furthermore, the O2 solubility (and hence the concentration of the O2 source) falls by 17%; this would counter the effect of the increased diffusivity. The rise in respiration must therefore be caused by increased consumption in those root tissues outside the severely hypoxic core.
Case 3 – effects of temperature and root diameter
The predictions made so far relate to measurements made at 25°C on roots 2 mm in diameter. These are both likely to lead to high perceived COPRs when sensed by monitoring [O2] in the bathing medium. ‘Fat’ roots are often unlikely to be fully satisfied if O2 is only available radially from the surroundings at atmospheric concentrations.
The effects of halving the root diameter to 1 mm (tissue radii all reduced proportionately) for the previous control and pyruvate-fed examples, and of a reduction in temperature to 20°C for the control roots, are shown in Fig. 6(b). Although at 20°C the respiratory rate per unit volume of the control root remains constant, the halving of the root diameter results in 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 was realized 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 reduced from c. 106 kPa to 28 kPa. Previously, at 21 kPa, a respiratory rate of only 240 ng cm−3 s−1 was realized; with the halving of root diameter this has been raised to c. 410 ng cm−3 s−1. Lowering the temperature to 20°C reduces the perceived COPR for ‘control’ roots by a further 4.5 kPa to 11 kPa. However, even these temperatures would be regarded as high for soils in northern temperate latitudes: narrower roots and lower temperatures would together result in even lower perceived COPRs. At any locus within the root itself, however, respiratory activity will probably be under the control of the major oxidase, cytochrome oxidase, with Km = 0.0108 kPa and COPR < 1.0 kPa. Even the alternative oxidase, although having a Km value an order of magnitude greater than that of cytochrome oxidase (Millar et al., 1994), would not greatly influence the picture that has emerged from these modelling results. Using control root characteristics, but with respiration controlled solely by the alternative oxidase (Km = 1.7 μM or 0.134 kPa), the plots 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 their respiration rates at concentrations much higher than COPR for cytochrome oxidase, our modelling data strongly suggest that results such as those in Fig. 3 cannot be used in support of a down-regulation hypothesis. The results emphasize what has been generally accepted for some time, namely that the degree and distribution of respiratory demand and diffusive resistance, both within and without the root, play a major role in determining the sufficiency of O2 supply, and that a dependence only on the oxygen-affinity characteristics of cytochrome oxidase is sufficient to explain findings such as those in Fig. 3. Diffusive resistances within the root are very substantial and, in respirometry, where the O2 sensor is in the medium external to the root segments, this would normally be expected to result in a perceived COPR very much greater than that for mitochondria, microorganisms or isolated protoplasts. At temperatures from 25 to 30°C, COPRs sometimes much greater than 21 kPa have been found for a variety of roots ranging in diameter from 0.23 to 0.75 mm (Berry & Norris, 1949; Asplund & Curtis, 2001). However, what is not always clear from O2 dependence plots is the complete form of the relationship. Plots are usually derived from the fitting of curves to respiratory rates measured at several discrete respirometer O2 concentrations. These may be recorded from slopes measured at several points along a complete O2 scavenging curve, or the respiratory rates may have been measured with the respirometer medium equilibrated at a range of different O2 concentrations. Plots derived in this way can give a ‘global’ picture, but fail to expose some subtle features that might be evident in a more complete curve. For pea root segments, Zabalza et al. (2009) revealed a biphasic decline in respiration rate between 21 and 0 kPa O2 in the respirometer medium. Unfortunately, they did not examine the relationship above 21 kPa, but, nevertheless, a biphasic decline along part of the O2 dependence curve has not been identified previously. If extra points had been available in the Berry and Norris data (Fig. 2), it is conceivable that they could have shown an almost linear decline between 45 and 21 kPa. Zabalza et al. (2009) interpreted the long almost linear decline between 21 kPa and c. 4 kPa as evidence of a conservation of O2 by a controlled down-regulation of respiration in the root. The same explanation was given by Gupta et al. (2009) to explain the form of the O2 dependence curve for barley root segments shown in Fig. 3(b). Our data show, at least for pea roots, that the form of the O2 dependence curves (Fig. 3a,b) can be explained in terms of the spread of severe hypoxia radially through the steles of root segments that are already very O2 stressed with 21 kPa O2 in the respirometer medium. Our data also reveal that increased respiration rates found after pyuvate feeding cannot therefore be used as an indication of a lack of O2 stress before pyuvate feeding, as claimed by Gupta et al. (2009).
If the respirometer data of Zabalza et al. (2009) and Gupta et al. (2009) are not in themselves evidence for respiratory down-regulation, but rather respiratory decline caused by O2 levels falling below the COPR for cytochrome oxidase, the question remains as to whether there is a form of respiratory down-regulation in roots as a result of low O2. Roots growing in flooded soils or in stagnant hypoxic agar, and dependent only on oxygen diffusing internally from the shoot, will eventually stop growing because of O2 limitation, but will not die unless there is some additional stress, for example, from external phytotoxins. Is this evidence of some respiratory down-regulation, or is viability maintained 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 supplied through the phloem? Hand in hand with this is the possibility of down-regulation of anaerobic energy-consuming processes to a level at which they are sufficient for maintenance needs only.
There is some evidence that sugars can still reach an anaerobic root tip through the phloem, albeit at a much reduced rate (T. Webb & W. Armstrong, unpublished data): in maize roots of 12 cm in length, with the tips in de-oxygenated agar, the subapical parts girdled top and bottom, split longitudinally and exposed to an atmosphere of N2, labelled nonmetabolized deoxyglucose fed to the caryopsis accumulated in the tip to about one-third of that in control ‘aerated’ growing roots over a 24-h period. Similarly, Atwell et al. (1985) found that, although maize seedling roots ceased elongating at c. 0.04 mM O2 in the rooting medium, sugars and amino acids were higher in the tips than in aerated roots. They concluded that, although the roots are being sustained by seed reserves, the adverse effects of low O2 concentrations are unlikely to be a consequence of substrate shortage for either respiration or synthesis of macromolecules, but rather low rates of ATP regeneration in growing root tissues.
If there is still an internal O2 source in the cortex close to the tip, the tip cannot become totally anoxic (Armstrong et al., 2009), but we still do not know at what O2 concentration the root cells will cease to utilize it. However, anaerobic metabolites from the stele can be lost to a still aerobic cortex and be metabolized, lost by diffusion to the external medium 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 close to or below the Km value for cytochrome oxidase, insufficient for what might normally be conceived as O2 conservation, and not down-regulation in the sense conceived by Zabalza et al. (2009) or Gupta et al. (2009). Down-regulation of anaerobic metabolism might be more relevant for sustained viability. As Gibbs and Greenway have pointed out ‘to survive an energy crisis, plant cells need to reduce their energy requirements for maintenance, and also direct the limited amounts of energy produced during anaerobic catabolism to the energy-consuming processes that are critical to survival’. They postulate that, ‘during anoxia, reductions in ion fluxes and protein turnover achieve economies in energy consumption. Processes receiving energy from the limited supply available include the synthesis of anaerobic proteins and energy-dependent substrate transport’ (Gibbs & Greenway, 2003; Greenway & Gibbs, 2003).
Although the respirometry examples dealt with here challenge previous analyses of O2 dependence plots, they do not illustrate the full potential of the model for predicting and analysing respirometer output. The strength of the modelling approach is that it provides a means of identifying and predicting, in some detail, the changes taking place spatially in the root during the scavenging process. These can then be used to better interpret the features in the O2 dependence plot. Some appreciation of the dynamic output is available as a supplementary file (Video S1). The model also has the potential to input Km values other than that of cytochrome oxidase and, in the future, we would hope to report on the effects on scavenging and O2 dependence plots of thick nonporous hypodermal tissues, high cortical porosities and higher tissue volume to respirometer volume ratios.
We thank Jean Armstrong, Brian Atwell, Tim Colmer, Hank Greenway, Joost van Dongen, Robert Hill, Brian Sorrell, David Threlfall, David Turner and two anonymous referees for helpful discussions and/or comments on the manuscript.