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First published online January 22, 2004; 10.1104/pp.103.032318 Plant Physiology 134:801-812 (2004) © 2004 American Society of Plant Biologists Adenylate Gradients and Ar:O2 Effects on Legume Nodules: I. Mathematical Models1Department of Biology, Queen's University, Kingston, Ontario, Canada K7L 3N6 (H.W., D.B.L.); and Botany, School of Plant Biology, The University of Western Australia, Nedlands, Western Australia 6907, Australia (C.A.A.)
Mathematical models were developed to test the likelihood that large cytosolic adenylate concentration gradients exist across the bacteria-infected cells of legume nodules. Previous studies hypothesized that this may be the case to account for the unusually low adenylate energy charge (AEC; 0.65) measured in the plant fraction of metabolically active nodules (M.M. Kuzma, H. Winter, P. Storer, I. Oresnik, C.A. Atkins, D.B. Layzell [1999] Plant Physiol 119: 399–407). Simulations coupled leghemoglobin-facilitated O2 diffusion into the infected cell, through bacteroid nitrogenase activity, with the ATP demand for transport and ammonia assimilation in the plant fraction of ureide- and amide-producing nodules. Although large cytosolic adenylate gradients were predicted to exist in both nodule types, amide nodules were predicted to have steeper AEC gradients (0.82–0.52) than ureide nodules (0.82–0.61). The differences were attributed to an additional ATP demand for Asn synthesis in the amide nodule. Simulations for nodules transferred to an Ar:O2 atmosphere predicted a major reduction in the magnitude of adenylate gradients and an increase in the AEC of the plant fraction. Results were consistent with a number of experimental studies and were used to propose an experimental test of the models.
Carbon (C) metabolism and N2 fixation in legume nodules is limited by O2 supply. Using a nonaqueous technique to quantify adenylate pools in intracellular fractions, Kuzma et al. (1999  ) found that the adenylate energy charge (AEC = [ATP + 0.5 ADP]/[ATP + ADP + AMP]) was 0.65 ± 0.04 in the plant fraction of active, N2-fixing nodules, whereas bacteroids had an AEC of 0.76 ± 0.09. However, when nodule metabolism was more severely O2 limited by exposure to 10% (v/v) O2 for 3 min, AEC in the plant cell compartment was not affected but in the bacteroids decreased from 0.76 ± 0.09 to 0.56 ± 0.06. The decrease in bacteroid AEC accounted for the decrease in whole-nodule AEC (from 0.70–0.61, Kuzma et al., 1999) after low O2 treatment. Other treatments known to reduce infected cell pO2 (e.g. NO3– fertilization and stem girdling) also reduced the AEC of whole nodules (de Lima et al., 1994), presumably because of a decrease in bacteroid rather than plant AEC.
These data (de Lima et al., 1994
Nevertheless, at 0.65 ± 0.04, AEC of the plant fraction is lower than that normally associated with hypoxic tissues (approximately 0.75 or higher; Pradet and Raymond, 1983
To develop a framework for an experimental test of this hypothesis, the present study modified the model of Thumfort et al. (1994
The simulations were also used to explore the effect of Ar:O2 exposure on ATP demand and the resulting cytosolic adenylate and AEC gradients across the cell. In Ar:O2, N2 fixation ceases, but nitrogenase activity continues, and we predicted that there should be less of an ATP gradient in Ar:O2-treated nodules. If true, this would help account for the results of de Lima et al. (1994
Developing the Models The infected cell was assumed to be a three-dimensional (3D) rhombic dodecahedron, which was reduced to a one-dimensional (1D) representation and divided into 400 layers. Layers 400 to 365 were considered to be within the MZ adjacent to the gas space interface, whereas layers 364 to 1 (ureide nodules) or 364 to 181 (amide nodules) were identified as the BZ. In the amide nodules, layers 180 to 1 constituted a central vacuole zone (VZ). The O2 was assumed to diffuse from the gas space interface (i.e. layer 400) into the innermost layer of the BZ (i.e. layer 1 in ureide nodules or layer 181 in amide nodules). Mathematical models of O2 and adenylate diffusion were developed in two phases. In the first, rates of ATP demand and synthesis were calculated in the plant cytosol within both the BZ and MZ of infected cell. This was done by coupling the C, N, and energy demands of 400 cell layers to the modeled O2 concentration gradients that are thought to exist between the intercellular spaces and the center of the cell. The second phase of the models used these values for ATP demand to generate gradients of cytosolic ATP, ADP, and AMP across the infected cell. For ureide- and amide-based models, the O2 concentration gradient was anchored by setting an O2 concentration at the innermost layer to achieve a volume-weighted average fractional oxygenation of leghemoglobin (Lb; FOLAvg) of 0.4. The ATP gradient was anchored by setting the cytosolic ATP concentration at the innermost layer such that the AEC in the cytosol adjacent to the gas space (AEC400) was 0.82. The amide model differed from the ureide model in two biochemical parameters: (a) A demand of three ATPs per N (versus one per N for ureide nodules) would be required for NH3 assimilation in cytosol of BZ, and (b) a value of 78 nM for O2 concentration at which 50% of Lb is oxygenated (KsLb; versus 48 nM for ureide model).
In the ureide model, innermost O2 concentration (O21) was fixed at 13 nM to generate a FOLAvg of 0.4. The resultant O2 concentration adjacent to the space (O2400) was 400 nM, and the volume-weighted O2 concentration (O2avg) was predicted to be 38 nM (Fig. 1A, solid line). As a consequence, the O2avg values were slightly higher than the average O2 concentration calculated from the average fractional oxygenation of Lb [FOL; i.e. O2avg(FOL) = 32 nM; O2avg(FOL) = FOL x KsLb/(1 – FOL), KsLb = 48 nM], an observation consistent with previous reports (Thumfort et al., 1994
A steep O2 gradient was predicted to exist from the gas space interface to the center of the BZ (Fig. 1A). The decline in O2 concentration across the MZ, from 400 to 70 nM over a diffusion path of 2.8 µm, was much steeper than that in the BZ, where O2n declined from 70 to 13 nM over a path of 28.4 µm (Fig. 1A). A steep gradient in FOL was also predicted, declining from 0.90 to 0.22 across the infected cell (Fig. 1B). The volume-specific respiration rates in the MZ (0.35–0.23 mol O2 m–3 s–1) were predicted to be considerably higher than those in the BZ (0.07–0.04 mol O2 m–3 s–1; Fig. 1C) as a result of the different kinetic constants for O2 uptake [i.e. Vmax and Km(O2)] were chosen for the two regions. The sharp discontinuity in respiration rate between the two zones (Fig. 1C) would be dampened if a thin, mixed zone of mitochondria and bacteroids was inserted between MZ and BZ, without altering the respiration rate in most of the layers in MZ and BZ. Total O2 consumption was 2.5 x 10–15 mol O2 s–1 cell–1 5.7 x 10–15 mol O2 s–1 cell–1 in the MZ and in the BZ. The amide model predicted profiles for infected cell O2 concentration, FOL, and tissue respiration that were similar to those generated by the ureide model (Fig. 1, A–C, dotted lines). The innermost O2 concentration (O2181) was fixed at 32 nM to generate an FOLAvg of 0.4. The resultant O2 concentration adjacent to the space (O2400) was 600 nM. The volume-weighted O2 concentration (O2avg) was predicted to be 63 nM (Fig. 1A, dotted lines), and this value was slightly higher than the calculated O2avg(FOL) (52 nM) based on a KsLb value of 78 nM. In any layer between layer 400 and 181, the modeled O2 concentration was slightly higher in amide than in ureide nodules. By running a series of simulations, these differences were attributed to the higher value chosen for KsLb. Total O2 consumption was 2.7 x 10–15 mol O2 s–1 cell–1 in the MZ and 5.8 x 10–15 mol O2 s–1 cell–1 in the BZ.
The models predicted a rate of NH3 production within the BZ (NH3n) that ranged from 0.030 to 0.014 mol NH3 m–3 s–1 in ureide nodules and from 0.033 to 0.024 mol NH3 m–3 s–1 in amide nodules (Fig. 2). Integrated over the entire infected cell, NH3 production was calculated to be 2.3 x 10–15 and 2.4 x 10–15 mol NH3 s–1 cell–1 in ureide and amide nodules, respectively.
Large differences were observed in predicted ATP metabolic demand (PATPn) in the plant cytosol, with values for amide nodules being approximately twice that for ureide nodules (Fig. 3A), despite the fact that the models predicted similar rates of NH3 assimilation in the two nodule types (Fig. 2). These differences were attributed to a 3-fold higher ATP cost per NH3 assimilated for amide than ureide nodules.
In the ureide nodule, total metabolic ATP demand
Model estimates of metabolic ATP demand in each cell layer within the BZ were incorporated into a group of simultaneous equations describing the diffusion of cytosolic ATP, ADP, and AMP and the equilibrium between these pools as catalyzed by cytosolic AK. These simultaneous equations provided an estimate of the ATP "demand" [PATP(AK)n] associated with AK activity for each layer (n). Across most of the BZ, PATP(AK)n values for amide nodules were predicted to be more negative than in ureide nodules (Fig. 3B), denoting enhanced ATP regeneration and AMP production in the AK reaction (i.e. 2ADP
It was noteworthy that the values of ATP "demand" by AK [PATP(AK)n] at layers 358 to 364 for amide nodules were predicted to be positive, implying that in these seven layers bordering the MZ, AK catalyzes the reaction in the direction of ATP + AMP
The total ATP "demand" by AK [
The total metabolic ATP demand in the plant fraction of BZ for the entire cell was assumed to be met by oxidative phosphorylation within the MZ. The volume-specific metabolic ATP "demand" in layer "n" of the MZ [PATP(metab)n, moles ATP per meter cubed per second] was set as proportional to the contribution of that layer to the total O2 uptake and, therefore, was calculated to be –750 to –480 mmol ATP m–3 s–1 for ureide nodules and –1300 to –970 mmol ATP m–3 s–1 for amide nodules (Fig. 3A).
Estimates of metabolic ATP "demand" in each cell layer within the MZ were incorporated into a group of simultaneous equations describing the diffusion of cytosolic ATP, ADP, and AMP and the equilibrium between these pools as catalyzed by AK. These simultaneous equations provided an estimate of ATP "demand" by cytosolic AK [PATP(AK)n] for each layer "n" of MZ, which was predicted to be 220 to 180 mmol ATP m–3 s–1 for ureide nodules and 400 to 410 mmol ATP m–3 s–1 for amide nodules at layers 400 to 365 (Fig. 3B). The positive value of PATP(AK)n at layers 400 to 365 indicated that AK catalyzes the reaction in the direction of ATP + AMP
Based on metabolic ATP demand and AK activity in maintaining adenylate equilibrium, the transfer of adenylates into layer n from layer n + 1 (moles per second) was solved at each layer (n). The predicted rates of adenylate transfer were converted into fluxes (nanomoles per meter squared per second) by dividing by the surface area of each layer. The resultant values, shown in Figure 4, A to C, provide a comparison of adenylate diffusion at various distances from the gas space interface (layer 400) to the innermost layer. The flux was positive for ATP but negative for ADP and AMP because ATP diffused from layer 400 to the innermost layer, whereas ADP and AMP diffused in the opposite direction.
ATP flux between layers 399 and 364 of the MZ was predicted to increase from 39 to 716 nmol m–2 s–1 in the ureide nodule and from 69 to 1,330 nmol m–2 s–1 in the amide nodule (ATP flux was 0 at layer 400 according to the definition). In contrast, ATP flux between layers 364 and the innermost layer of BZ was predicted to decrease from 730 to 2 nmol m–2 s–1 in the ureide nodule and 1,350 to 4 nmol m–2 s–1 in the amide nodule. The highest ATP flux was predicted in layer 364, i.e. at the MZ:BZ interface for both ureide and amide nodules (Fig. 4A). The fluxes of ADP and AMP showed a similar trend but in the opposite diffusion direction and are, therefore, negative in Figure 4, B and C. Similarly, the largest absolute value for ADP and AMP flux was observed at the MZ:BZ interface at layer 364 but with a lower magnitude than that predicted for ATP. At any layer within the infected cell, the sum of cytosolic ATP, ADP, and AMP fluxes equaled zero, reflecting the assumption of models that the total cytosolic adenylate concentration was constant throughout the infected cell.
The simultaneous equations also solved for concentrations of cytosolic ATP, ADP, and AMP in each layer of the infected cell. To ensure that the models predicted an AEC of 0.82 for AEC400, the innermost ATP (ATP1) had to be set to 1.04 mM in the ureide model and 0.79 mM in the amide model. The cytosolic ATP, ADP, and AMP gradients across the infected cells were predicted to be greater in amide than in ureide nodules (Fig. 5, A–C).
These cytosolic adenylate gradients resulted in predictions of large gradients in AEC (Fig. 6A) or ATP to ADP ratio (Fig. 6B) for both nodule types but much steeper gradients in amide than in ureide nodules. Although model parameters were chosen to give an AEC of 0.82 (ATP:ADP = 3.1) at the gas space interface (n = 400), the AEC predicted to exist in the cytosol at the innermost layer was 0.62 (ATP:ADP = 1.4) in the ureide nodule and 0.52 (ATP:ADP = 1.0) in the amide nodule. The average AEC (AECAvg) of the entire plant fraction of the cell (BZ and MZ) was predicted to be 0.61 in the amide nodules and 0.70 in the ureide nodules. The latter values were similar to the experimentally determined value for soybean (Glycine max) nodules (0.65 ± 0.04; Kuzma et al., 1999
The models were also used to simulate the effect of exposing ureide- or amide-forming nodules to an Ar:O2 atmosphere, a treatment that prevents N2 fixation and NH3 assimilation without immediate effects on nitrogenase activity or nodule carbohydrate metabolism. Extended exposure to Ar:O2 is known to decrease the nodule's permeability to O2 diffusion (Hunt and Layzell, 1993 Cessation of NH3 production in bacteroids would reduce ATP demand for NH3 assimilation in the plant fraction. Therefore, the models predicted much lower ATP demand [PATP(metab)n] in Ar:O2-treated (Fig. 3D) than in N2:O2-treated nodules (Fig. 3A). As a consequence, the AK activity indicated by its ATP demand [PATP(AK)n] was also predicted to be lower in Ar:O2-treated nodules (Fig. 3E). As a result of lower adenylate demand, diffusive fluxes of adenylate were predicted to be much lower in Ar:O2 (Fig. 4, D–F) than in N2:O2 (Fig. 4, A–C). Although parameters of models were chosen to give an AEC of 0.82 (ATP:ADP = 3.1) in layer 400, the simulation showed that the cytosolic adenylate gradients predicted during steady-rate N2 fixation in N2:O2 were significantly reduced after the switch to Ar:O2 (compare Fig. 5, D to F with A to C). The average AEC in the plant fraction of an infected cell was 0.77 in both ureide and amide nodules treated with Ar:O2 (Fig. 6C). Thus, the ureide model predicted a rise of average plant AEC from 0.70 in N2:O2 to 0.77, whereas the amide model predicted a rise from 0.61 in N2:O2 to 0.77.
Cytosolic Adenylate Gradients in Legume Nodules The models predicted that substantial gradients in adenylate concentration could occur in the plant cytosol of the infected cell, even in the absence of membrane barriers. Both adenylate and AEC gradients would be reduced dramatically after short-term exposure of nodules to an Ar:O2 atmosphere, a treatment that stops N2 fixation and NH3 assimilation but not nitrogenase activity.
The predictions from these models are the first of their kind, to our knowledge, and may account for a number of physiological observations that to date have defied easy explanation. For example, Oresnik and Layzell (1994
Results of this study may also account for the observation of de Lima et al. (1994
To test the validity of models, the predicted rates of respiration and NH3 assimilation in the infected cell were converted and then compared with measured values.
The models predicted a rate of mitochondrial respiration of 2.5 x 10–15 to 2.7 x 10–15 mol O2 s–1 cell–1 in ureide and amide nodules. Assuming 12,472 mitochondria per cell and 0.25 pg of protein per mitochondrion (Table IV of Millar et al., 1995
The method used in this study was largely based on 1D models (Thumfort et al., 1994
For simplicity, the 1D models developed in this study did not consider O2 diffusion into and out of the adjacent uninfected cell. Based on a two-cell model prediction, the amount of O2 entering the infected cell from an adjoining uninfected cell accounted for only 15% of the total amount of O2 entering when average FOL was from 0.4 to 0.5 (Thumfort et al., 1999
The O2 concentration gradient in the models was anchored by setting an O2 concentration at the innermost layer to achieve an average FOL of 0.4, a value measured by nodule oximetry and thought to exist in active, undisturbed ureide and amide nodules (Table I, item 1). Increasing the average FOL from 0.4 to 0.6 would significantly increase O2400 from 400 to 7,600 nM (Table II, item 1, a and b); this range of O2 concentrations was still in agreement with that in a two-cell model of Thumfort et al. (1999
The cytosolic ATP gradient in the models was anchored by choosing the cytosolic ATP concentration at the innermost layer such that the AEC400 was 0.82, a value similar to that measured in fully aerobic nodule cortex tissue (Oresnik and Layzell, 1994
The diffusive path for O2 was defined in both the cytosol and symbiosome of the infected cell, whereas the diffusive paths for LbO2 and plant ATP, ADP, and AMP were restricted to the cytosol. Diffusion coefficients (D) of LbO2, O2, and ATP in cell (Table I, items 2–4) used in the simulation were expected to have an impact on the predicted features of the models. The reported D values for LbO2, O2, and ATP in water were 12.5 x 10–11, 17 x 10–10, and 2.70 x 10–10 m2 s–1 (Kushmerick and Podolsky, 1969
The models used a P:O ratio of 2 (Table I, item 6) to couple bacteroid O2 consumption rate to the production of ATP in bacteroids of BZ, which was then used to generate the rate of nitrogenase activity. Wittenberg et al. (1974 It is noteworthy that the P to O ratio was not used to calculate the ATP production in mitochondria in MZ (layers 400–365). Instead, the metabolic ATP "demand" (i.e. production) in each layer of MZ was assumed to be proportional to the contribution of that layer to the total O2 uptake within the MZ.
The amide model assumed a large central vacuole in the infected cells, accounting for 12% of whole cell volume (i.e. layers 180–181 of the cell). Increasing VZ volume to 20% shortened the diffusion pathway in the BZ but did not significantly reduce the adenylate gradients (data not shown). Pugh et al. (1995
A KsLb value (the O2 concentration at which 50% of Lb is oxygenated) of 78 nM (Table I, item 7) was used for the amide model. This value was originally determined for lupin Lb II and was between the reported KsLb for soybean Lb (48 nM) and pea (Pisum sativum) Lb IV (127 nM, Kawashima et al., 2001
The apparent equilibrium constant of cytosolic AK (KAK = 0.90; Table I, item 8) was based on measurements from ureide-producing nodules. The reported values of KAK in plant tissues were in the range of 0.3 to 1.5 (Igamberdiev and Kleczkowski, 2001 The value for total cytosolic adenylate concentration (Aden, 2.29 mM; Table I, item 9) was based on measurements from ureide-producing nodules. For amide model, increasing the value for Aden would reduce the magnitude of adenylate gradients (Table II, item 2, a and e). In contrast, decreasing the value for Aden would cause the adenylate gradients to become steeper (Table II, item 2, a and f), consistent with the infected cell requiring steeper adenylate gradients to meet the ATP demand in the inner part of cell.
The central assumptions about assimilation of fixed N in the present models was that NH4+ was the sole N solute transferred from bacteroids to the plant cytosol and that it was incorporated exclusively into the amide group of Gln through cytosolic GS. Further, the ultimate products of N2 fixation were solely ureides in one and Asn in the other type of nodule. There have been a number of proposals that amino compounds may be exported from bacteroids (for review, see Day et al., 2001
If the amidotransferases of either purine (phosphoribosyl pyro-phosphate or 5'-phosphoribosyl-N-formylglycinamide amidotransferases) or AS could utilize NH4+ directly in nodules, and then ATP demand by GS would be reduced. Although Vance (2000 ATP is used in the MZ for purine synthesis, but this is unlikely to significantly affect the simulated adenylate gradients generated by the ureide model. Plastids are distributed together with mitochondria adjacent to the intercellular space. These organelles are assumed to be distributed evenly across the MZ and that in each layer, the ATP demand in plastids would be met by ATP produced by the mitochondria located in the same layer. Therefore, the extra ATP use in plastids would not affect the adenylate gradients generated by diffusion from mitochondria toward the inner cytosol.
It is known that cytosolic ATP level can regulate the activity of specific glycolytic enzymes, including phosphofructokinase, pyruvate kinase, hexokinase, enolase, and phosphoenolpyruvate carboxylase in plants (Plaxton, 1996
ATP "demand" by AK [PATP(AK)n] was negative in most layers of BZ (Fig. 3B), indicating the AK reaction was in the direction 2ADP The pyrophosphate (PPi) cleavage of ATP by AS raises one further possibility that might alter the ATP dynamics assumed in the models. If PPi is substrate for an H+-pyrophosphatase (PPase) in the PBM, then its activity could generate sufficient proton motive force for malate transport, eliminating the need for ATP to drive an alternate H+ pump. However, in PBM preparations from soybean, there is no evidence for a PBM-localized PPase (D. Day, personal communication). Thus, the models assume that PPi generated by AS is cleaved by a PPase such that there are no consequences for the adenylate dynamics of the BZ.
The simulations with Ar:O2 indicate a rationale to test the models experimentally. Both amide and ureide models predict that the cytosolic adenylate gradients will decrease in Ar:O2, resulting in large increases in the average AEC of the plant fraction as soon as the N pools are depleted. This could be tested experimentally using a nonaqueous fractionation technique (Kuzma et al., 1999
Cell and Tissue Geometry
The central, bacteria-infected zone of nodules is assumed to consist only of tightly packed infected cells (the actual ratio of infected cell:uninfected cell volume = 10:1; Dakora and Atkins, 1990
To model the adenylate diffusion within the infected cell, the method of Thumfort et al. (1994
The 31.2-µm distance from the gas space interface to the innermost point in the cell was divided into 400 layers, each with an identical depth (0.078 µm) and with the relative surface area shown in Figure 7B. Layers 400 to 365, occupying a depth of 2.8 µm, were considered to be within the MZ adjacent to the gas space interface, whereas layers 364 to 1 (ureide nodule) or 364 to 181 (amide nodule) were identified as the BZ. In the amide nodules, layers 180 to 1 constituted a central VZ. This partitioning resulted in the volume ratio of MZ:BZ = 8.5%:91.5% in the infected cell of ureide nodules (Bergersen, 1994 A five-step process (Fig. 8) was used to model cytosolic adenylate gradients in the infected cells of ureide and amide nodules. A detailed description of the methods is described in the supplemental material or from the authors.
The modeling of O2 diffusion (Fig. 8, item 1) into the cells was similar to that described by Thumfort et al. (1994
Equations were derived that described Lb equilibrium with free O2, the diffusion of O2 and LbO2 between layers in the infected cell, and the respiratory consumption of O2 by the bacteroids or mitochondria within each layer (Eq. 1–4 in Thumfort et al., 1994 The model was built in Excel 98 (Microsoft, Redmond, WA) by first selecting an O2 concentration for the innermost layer (O2n, n = 1 for ureide nodules, n = 181 for amide nodules, moles per meter cubed; layers 180 to 1 in amide nodules were occupied by vacuole) and then calculating the corresponding oxygenated Lb concentration and O2 consumption rate for that layer. The quadratic equation was used to calculate the O2 concentration in the layer adjacent to the innermost layer (i.e. O2n+1) that the O2 demands of the innermost layer were provided through layer (n + 1). Values were then derived for the oxygenated Lb concentration, the O2 consumption rate, and the required transfer of O2 from layer n + 2. This process was repeated for all layers from n + 2 to 400. In each layer, the FOL was calculated as the LbO2 concentration divided by the total cytosolic Lb concentration (Table I, item 12). Model simulations were carried out for a range of innermost O2 concentrations (O2n = 5–30 nM O2), and for each, values were calculated for the volume-weighted average FOL (FOLAvg).
Given that the bacteroid metabolism is limited by O2 (Kuzma et al., 1999
The NH3 produced by the bacteroids was assumed to diffuse into the plant cytosol, where it was assimilated into amino acids by GS and Glu synthase, in ureide nodules or by GS, Glu synthase, and AS in amide nodules. The ATP requirements for GS (one ATP/NH3) and AS (two ATP/NH3) were assumed to be synthesized by the mitochondria in the MZ, and diffuse through the cytoplasm to the layers in which NH3 was produced. The ATP demand along the diffusion pathway included that for the transport of malate into the symbiosomes (Fig. 8, item 6) and the plant growth and maintenance (Fig. 8, item 7), in addition to the cost of NH3 assimilation.
The ATP demand for malate transport across the symbiosome membrane (Fig. 8, item 6) was calculated assuming one ATP per malate transported. To calculate malate transported into the symbiosomes, values were generated to account for: (a) the C requirement for bacterial growth (relative growth rate = 6.49 x 10–7 g dry weight new g–1 dry weight s–1; Bouma et al., 1997
Estimates of the ATP demand within the plant fraction of each layer [PATP(metab)n] of the BZ were used to generate the diffusion gradients of adenylates across the cells. The total cytosolic adenylate pool (Aden; Table I, item 9) was assumed to be constant for each layer, and within each layer (n), an AK was assumed to maintain a balance among the adenylate pools according to the equation of ATPn x AMPn = KAK x (ADPn)2, where KAK is the apparent equilibrium constant of AK (Table I, item 8). The ATP demand for AK activity [PATP(AK)n] was generally negative because the AK was needed primarily to build the AMP pool, which involves the production of ATP from 2ADP. The calculations of the cytosolic adenylate gradient were begun by first choosing a value for the cytosolic ATP concentration for the innermost layer (range of 0.01–2.29 mol m–3, determined according to the value of Aden; Table I, item 9). Then, a series of equations were used to calculate the diffusion of cytosolic ATP, ADP, and AMP (Fig. 8, item 11, a–c) between adjacent layers while ensuring that the adenylate pools were in equilibrium via the AK and assuming each layer met its respective demand for ATP.
Calculation of the cytosolic ATP gradients across the MZ assumed that this zone was responsible for providing the ATP needs of the plant fraction in the entire BZ. In the MZ, as in the BZ, cytosolic AK was assumed to maintain a balance among the adenylate pools. The contribution of each MZ layer to the total ATP demand of plant fraction of BZ was assumed to be proportional to the contribution of that layer to the total O2 uptake within the MZ. This permitted the calculation of the volume-specific metabolic ATP "demand" in each layer of the MZ [PATP(metab)n; Fig. 8, item 15].
Although formation of ureides relies on purine synthesis, which itself requires ATP (Smith and Atkins, 2002 Given these values, a series of equations were used to calculate the diffusion of cytosolic ATP, ADP, and AMP between adjacent layers while ensuring that the adenylate pools were in equilibrium. Finally, the AEC [AEC = ([ATP] + 0.5 x [ADP])/([ATP] + [ADP] + [AMP])] was calculated for each layer, and these values were used to calculate the volume-weighted average AEC for the plant cytosol of entire cell.
For both ureide and amide models, the cytosolic ATP concentration for the innermost layer (initialized in Step 4) was set at a value that resulted in an AEC at the gas space (AEC400) of 0.82, a value representing fully aerobic tissue (Oresnik and Layzell, 1994
The conceptual basis for this modeling exercise was developed in collaboration with Dr. Peter Thumfort (Department of Biology, Massachusetts Institute of Technology, Cambridge). Received September 1, 2003; returned for revision September 26, 2003; accepted November 10, 2003.
Article, publication date, and citation information can be found at http://www.plantphysiol.org/cgi/doi/10.1104/pp.103.032318.
1 This work was supported by the National Science and Engineering Research Council of Canada (grants to D.B.L.). * Corresponding author; e-mail layzelld{at}biology.queensu.ca; fax 613–533–6617.
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ABSTRACT
RESULTS
in the plant fraction of BZ (ie, the sum of 
from the innermost layer of n = 3) for the entire cell was 5.4 x 10–15 mol ATP s–1 cell–1 where 42%, 54%, and 4% were used for NH3 assimilation (via GS), malate transport across the PBM to the bacteroids, and growth and maintenance respiration, respectively. In contrast, the amide model predicted a total metabolic ATP demand of 10.4 x 10–15 mol ATP s–1 cell–1, where 69%, 29%, and 2% were used for NH3 assimilation (via GS and Asn synthetase [AS]), malate transport across the PBM, and growth and maintenance respiration in the plant fraction of BZ, respectively. 
ATP + AMP). In the innermost part of the infected cell, the models predicted that ATP regenerated through AK activity was equivalent to 44% (ureide) or 49% (amide) of the metabolic ATP demand by those sites (
innermost (ie, the sum of PATP(AK)n from the innermost layer to n = 364)] in the plant fraction of the BZ for the entire cell was predicted to be 1.8 x 10–15 mol ATP s–1 cell–1 in the ureide nodule and 3.7 x 10–15 mol ATP s–1 cell–1 in the amide nodule. Dividing these values by the total metabolic ATP demand in the plant fraction of BZ (described previously), it was calculated that 33% (ureide) or 36% (amide) of the total ATP metabolic requirement was regenerated through AK activity. 
