Binding of a Phosphorylated Inhibitor to Ribulose Bisphosphate Carboxylase/Oxygenase during the Night

The activity of ribulose-1,5-bisphosphate carboxylase/oxygenase was measured at various times during the purification of the enzyme from leaves of Nicotiana tabacum which were collected either 1 hour before the start of the photoperiod (predawn) or in the middle of the photoperiod (midday). The activity of the enzyme in extracts of the predawn leaves (0.8 units/mg enzyme) was consistently about 2-fold lower than that measured in extracts of midday leaves (1.7 units/mg enzyme). The activity of the predawn enzyme was increased to that of the midday enzyme following removal of CO₂ and Mg²⁺ (deactivation), (NH₄)₂SO₄ precipitation, or incubation in SO₄²⁻ (18 millimolar required for one-half maximal increase). Following purification to >95% homogeneity, the predawn enzyme was found to have ~0.5 moles of bound organic phosphate per mole of enzyme active sites, while the midday enzyme had only ~0.08 moles of bound organic phosphate per mole of enzyme active sites. Deactivation of the predawn enzyme or treatment with 0.2 molar SO₄²⁻ resulted in the removal of most of the bound organic phosphate. These findings support the hypothesis that following the night period about 50% of the enzyme is catalytically inactive because of the tight-binding of a small molecular weight, phosphorylated inhibitor at the active site.     

水稻叶片在自然衰老过程中1，5-二磷酸核酮糖羧化酶/加氧酶的降解(英文)

１,５二磷酸核酮糖羧化酶／加氧酶（Ｒｕｂｉｓｃｏ）是光合碳同化的关键酶,研究其降解机理对合理调控水稻生长后期光合衰退具有重要意义。前人用人为诱导植物衰老的方法,研究了Ｒｕｂｉｓｃｏ的降解机理,认为该酶降解之前,必需发生亚基间的交联聚合和向类囊体膜转移,这样在结构和空间上有利于水解酶的作用。我们用自然衰老叶片进行研究的结果表明：Ｒｕｂｉｓｃｏ在降解过程中其比活基本保持恒定,意味着未发生酶的失活,也就是说酶结构未发生根本性改变,由此也可初步判断酶未发生亚基间的交联聚合（已证明亚基交联可导致酶失活）。接着用ＳＤＳＰＡＧＥ和蛋白印迹技术证实了上述观点：Ｒｕｂｉｓｃｏ降解之前只有极少量的大亚基聚合体,随后同未聚合大亚基一起很快降解。此外,研究结果进一步表明酶分子在降解之前有少量与叶绿体膜结合,但降解过程中并未见膜结合蛋白增加。根据上述结果我们认为,亚基间交联聚合和向膜转移并非水稻叶片自然衰老时Ｒｕｂｉｓｃｏ降解的必要条件。     

Drought Stress and Elevated CO(2) Effects on Soybean Ribulose Bisphosphate Carboxylase Activity and Canopy Photosynthetic Rates

Soybean (Glycine max [L.] cv Bragg) was grown at 330 or 660 microliters CO₂ per liter in outdoor, controlled-environment chambers. When the plants were 50 days old, drought stress was imposed by gradually reducing irrigation each evening so that plants wilted earlier each succeeding day. On the ninth day, as the pots ran out of water CO₂ exchange rate (CER) decreased rapidly to near zero for the remainder of the day. Both CO₂-enrichment and drought stress reduced the total (HCO₃⁻/Mg²⁺-activated) extractable ribulose-1,5-bisphosphate carboxylase (RuBPCase) activity, as expressed on a chlorophyll basis. In addition, drought stress when canopy CER values and leaf water potentials were lowest, reduced the initial (nonactivated) RuBPCase activity by 50% compared to the corresponding unstressed treatments. This suggests that moderate to severe drought stress reduces the in vivo activation state of RuBPCase, as well as lowers the total activity. It is hypothesized that stromal acidification under drought stress causes the lowered initial RuBPCase activities. The K_m(CO₂) values of activated RuBPCase from stressed and unstressed plants were similar; 15.0 and 12.6 micromolar, respectively. RuBP levels were 10 to 30% lower in drought stressed as compared to unstressed treatments. However, RuBP levels increased from near zero at night to around 150 to 200 nanomoles per milligram chlorophyll during the day, even as water potentials and canopy CERs decreased. This suggests that the rapid decline in canopy CER cannot be attributed to drought stress induced limitations in the RuBP regeneration capability. Thus, in soybean leaves, a nonstomatal limitation of leaf photosynthesis under drought stress conditions appears due, in part, to a reduction of the in vivo activity of RuBPCase. Because initial RuBPCase activities were not reduced as much as canopy CER values, this enzymic effect does not explain entirely the response of soybean photosynthesis to drought stress.     

Effects of Light and Elevated Atmospheric CO(2) on the Ribulose Bisphosphate Carboxylase Activity and Ribulose Bisphosphate Level of Soybean Leaves

Soybean (Glycine max L. Merr. cv Bragg) was grown throughout its life cycle at 330, 450, and 800 microliters CO₂ per liter in outdoor controlled-environment chambers under solar irradiance. Leaf ribulose-1,5-bisphosphate carboxylase (RuBPCase) activities and ribulose-1,5-bisphosphate (RuBP) levels were measured at selected times after planting. Growth under the high CO₂ levels reduced the extractable RuBPCase activity by up to 22%, but increased the daytime RuBP levels by up to 20%.

Diurnal measurements of RuBPCase (expressed in micromoles CO₂ per milligram chlorophyll per hour) showed that the enzyme values were low (230) when sampled before sunrise, even when activated in vitro with saturating HCO₃⁻ and Mg²⁺, but increased to 590 during the day as the solar quantum irradiance (photosynthetically active radiation or PAR, in micromoles per square meter per second) rose to 600. The nonactivated RuBPCase values, which averaged 20% lower than the corresponding HCO₃⁻ and Mg²⁺-activated values, increased in a similar manner with increasing solar PAR. The per cent RuBPCase activation (the ratio of nonactivated to maximum-activated values) increased from 40% before dawn to 80% during the day. Leaf RuBP levels (expressed in nanomoles per milligram chlorophyll) were close to zero before sunrise but increased to a maximum of 220 as the solar PAR rose beyond 1200. In a chamber kept dark throughout the morning, leaf RuBPCase activities and RuBP levels remained at the predawn values. Upon removal of the cover at noon, the HCO₃⁻ and Mg²⁺-activated RuBPCase values and the RuBP levels rose to 465 and 122, respectively, after only 5 minutes of leaf exposure to solar PAR at 1500.

These results indicate that, in soybean leaves, light may exert a regulatory effect on extractable RuBPCase in addition to the well-established activation by CO₂ and Mg²⁺.

     

A Non-radioisotopic Anion-exchange Chromatographic Method to Measure the CO2/O2 Specificity Factor for Ribulose Bisphosphate Carboxylase/Oxygenase

A non-radioisotopic anion-exchange ion chromatographic method for measuring the carboxylation/ oxygenation specificity (τ) of ribulose 1, 5-bisphosphate carboxylase/oxygenase (RubisCO) is presented. The assay measures the amounts of fixation products at varying [CO₂]/[O₂] ratios to measure the relative rates of CO₂ and O₂ fixation reactions. The amount of 3-phosphoglycerate (3-PGA) and phosphoglycolate (PG) in the reaction mixture were measured with a conductivity detector and the specific factor was calculated using the following equations: ν_c = ([3-PGA] – [PG])/2 and ν_o = [PG]. By this method, specificity factors for RubisCOs were measured without using radioactive reagents.     

Electron Transport through photosystem I Stimulates Light Activation of Ribulose Bisphosphate Carboxylase/Oxygenase (Rubisco) by Rubisco Activase

The activation state of ribulose bisphosphate carboxylase/oxygenase (rubisco) in a lysed chloroplast system is increased by light in the presence of a saturating concentration of ATP and a physiological concentration of CO₂ (10 micromolar). Electron transport inhibitors and artificial electron donors and acceptors were used to determine in which region of the photosynthetic electron transport chain this light-dependent reaction occurred. In the presence of DCMU and methyl viologen, the artificial donors durohydroquinone and 2,6-dichlorophenolindophenol (DCPIP) plus ascorbate both supported light activation of rubisco at saturating ATP concentrations. No light activation occurred when DCPIP was used as an acceptor with water as electron donor in the presence of ATP and dibromothymoquinone, even though photosynthetic electron transport was observed. Nigericin completely inhibited the light-dependent activation of rubisco. Based on these results, we conclude that stimulation of light activation of rubisco by rubisco activase requires electron transport through PSI but not PSII, and that this light requirement is not to supply the ATP needed by the rubisco activase reaction. Furthermore, a pH gradient across the thylakoid membrane appears necessary for maximum light activation of rubisco even when ATP is provided exogenously.     

Effect of Ear Removal on CO(2) Exchange and Activities of Ribulose Bisphosphate Carboxylase/Oxygenase and Phosphoenolpyruvate Carboxylase of Maize Hybrids and Inbred Lines

The effects of ear removal on gas exchange traits, chlorophyll, and leaf N profiles, and activities of ribulose 1,5-bisphosphate carboxylase/oxygenase and phosphoenolpyruvate carboxylase were examined using four maize hybrids (B73 × Mo17, B73 × LH38, FS854, and CB59G × LH38) and four inbred lines (B73, Mo17, LH38, and CB59G) as experimental material. A diverse genotypic response to ear removal was observed which was generally typified by (a) greatly accelerated loss of chlorophyll, leaf N, enzyme activities, and CO₂ exchange relative to controls for B73, B73 × Mo17, and B73 × LH38, (b) intermediate rate of decline for leaf constituents for FS854, LH38, and Mo17, or (c) loss of leaf constituents at similar or slower rates than for control plants for CB59G and CB59G × LH38. For all genotypes which had accelerated senescence relative to controls, loss of CO₂ exchange activity was correlated with increased internal CO₂ concentrations. Thus, it was concluded that metabolic factors and not stomatal effects were responsible for loss of CO₂ exchange activity. Loss of chlorophyll, leaf N, and enzyme activities correlated well with loss of CO₂ exchange activity only for some of the genotypes. Accelerated leaf senescence in response to ear removal for the inbred line B73 and the hybrids B73 × Mo17 and B73 × LH38, as well as the apparent delayed leaf senescence for the inbred line CB59G and the hybrid CB59G × LH38 show that the contrasting responses to ear removal, rapid versus delayed senescence, can be transmitted as dominant traits to F₁ hybrids. The intermediate response by some genotypes, and the dominance of contrasting senescence traits, suggested a relatively complex inheritance for expression of the ear removal response.     

Photosynthetic and Photorespiratory Enzymes in Widely Divergent Plant Species with Special Reference to the Moss Ceratodon purpureus: Properties of Ribulose Bisphosphate Carboxylase/ Oxygenase, Phosphoenolpyruvate Carboxylase and Glycolate Oxidase

Rintamäki, E. and Aro, E.-M. 1985. Photosynthetic and photorespiratoryenzymes in widely divergent plant species with special referenceto the moss Ceratodon purpureus: Properties of ribulose bisphosphatecarboxylase/oxygenase, phosphoenolpyruvate carboxylase and glycolateoxidase.—J. exp. Bot. 36: 1677–1684. Km(CO₂) values and maximal velocities of ribulose bisphosphatecarboxylase/oxygenase (E.C. 4.1.1.39 [EC] ) were determined for sixplant species growing in the wild, consisting of a moss, a fernand four angiosperms. The maximum velocities of the RuBP carboxylasesvaried from 0.13 to 0.;62 µmol CO₂ fixed min^–1 mg^–1soluble protein and the Km(CO₂) values from 15 to 22 mmol m^–3CO₂. The highest Km(CO₂) values found were for the moss, Ceratodonpurpureus, and the grass, Deschampsia flexuosa. These plantsalso had the highest ratios of the activities of RuBP carboxylaseto RuBP oxygenase. Glycolate oxidase (E.C. 1.1.3.1 [EC] ) activitieswere slightly lower in D.flexuosa, but not in C. purpureus,than for typical C₃ species. Phosphoenolpyruvate carboxylase(E.C. 4.1.1.31 [EC] ) was not involved in the photosynthetic carboxylationby these two plants. However, another grass, Phragmites australis,was intermediate in PEP carboxylase activity between C₃ andC₄ plants The properties of RuBP carboxylase/oxygenase are discussedin relation to the activities of PEP carboxylase and glycolateoxidase and to the internal CO₂ concentration. Key words: RuBP carboxylase, oxygenase, Km(CO₂), moss     

Acclimation to High CO(2) in Bean : Carbonic Anhydrase and Ribulose Bisphosphate Carboxylase

Young bean plants (Phaseolus vulgaris L. cv Seafarer) grew faster in air enriched with CO₂ (1200 microliters per liter) than in ambient CO₂ (330 microliters per liter). However, by 7 days when increases in overall growth (dry weight, leaf area) were visible, there was a significant decline (about 25%) in the leaf mineral content (N, P, K, Ca, Mg) and a drop in the activity of two enzymes of carbon fixation, carbonic anhydrase and ribulose 1,5-bisphosphate (RuBP) carboxylase under high CO₂. Although the activity of neither enzyme was altered in young, expanding leaves during the acclimation period, in mature leaves the activity of carbonic anhydrase was reduced 95% compared with a decline of 50% in ambient CO₂. The drop in RuBP carboxylase was less extreme with 40% of the initial activity retained in the high CO₂ compared with 50% in the ambient atmosphere. While CO₂ enrichment might alter the flow of carbon into the glycolate pathway by modifying the activities of carbonic anhydrase or RuBP carboxylase, there is no early change in the ability of photosynthetic tissue to oxidize glycolate to CO₂.     

Photosynthesis and Activity of Ribulose Bisphosphate Carboxylase of Wheat and Maize Seedlings during and following Exposure to O(2)-Low, CO(2)-Free N(2)

Seven day old wheat and maize seedlings were exposed to 1300 or 2000 microeinsteins per square meter per second photosynthetically active radiation in CO₂-free air for 3 hours with either 1% O₂ in N₂ or N₂-only and then returned to normal air of 340 microliters per liter CO₂, 21% O₂ in N₂. Activity of the ribulose bisphosphate carboxylase and amount of the substrate, ribulose 1,5-bisphosphate, were measured during and following the CO₂-free treatments as was photosynthetic CO₂ fixation. Photoinhibition of photosynthesis was observed only with wheat seedlings following the N₂ only treatment. During the CO₂-free treatments, the levels of RuBP rose during all experiments except when wheat was photoinhibited. The activity of the ribulose bisphophate carboxylase, measured directly upon grinding the leaves, declined during the CO₂-free conditions. The carboxylase total activity increased in minutes in the leaf during and following the CO₂-free treatments. The specific activities of the wheat carboxylase went from 0.16 to 1.06 micromoles CO₂ fixed per milligram protein per minute while the maize carboxylase varied from 0.05 to 0.36 micromole CO₂ fixed per millogram protein per minute. This suggests that in these seedlings considerable inactive carboxylase must be stored in a form not activatable in extracts by CO₂ and Mg²⁺. Possible mechanisms of regulation of photosynthesis by the ribulose bisphosphate carboxylase must consider not only the amount of active enzyme, but the amount of enzyme which the plant can make activatable upon demand.     

Regulation of Ribulose Bisphosphate Carboxylase Activity in Intact Wheat Leaves by Light, CO2, and Temperature

The activity of the enzyme ribulose bisphosphate carboxylase(RuBPCase) was estimated after rapidly extracting it from intactwheat leaves pretreated under different light and CO₂ levels.No HCO₃^– was added to the extraction buffer since it isshown to inhibit RuBPCase. The activity increased as light intensityor CO₂ concentration during pretreatment was increased. Enzymeactivity increased as temperature during pretreatment was decreased.Light activation did not affect the affinity of RuBPCase forCO₂. A K_m of 30 µM CO₂ under air level O₂ was determined.CO₂, light and temperature are three main limiting factors ofphotosynthesis. It seems that the activity of RuBPCase is regulatedby these factors according to the requirements for CO₂ fixation.     

Changes in Photosynthetic Characteristics Induced by Transferring Air-Grown Cells of Chlorococcum littorale to High-CO2 Conditions

When air-grown cells of Chlorococcum littorale was enrichedwith CO₂, growth was enhanced after a lag period of one to twodays at 20% CO₂, and 3 to 6 days at 40% CO₂. Changes in therate of photosynthesis measured as oxygen evolution and CO₂fixation, were similar to those observed for growth. Duringthe initial inhibition of photosynthesis in 40% CO₂, the activityof PSII was suppressed. In contrast, PSI activity was greatlyenhanced. Air-grown cells of C. littorale possessed comparatively highcarbonic anhydrase (CA) activity which was localized insidethe cells and on the cell surface. Under high CO₂ concentrationsextracellular CA activity was greatly suppressed and intracellularactivity almost completely abolished. Phosphoenol pyruvate carboxylaseactivity was also suppressed in high CO₂-grown cells. Ribulose-l,5-bisphosphatecarboxylase activity was higher in high-CO₂ grown cells thanin air-grown cells. The above results indicated that the lagphase induced by 40% CO₂ was due to suppression of PSII activity. ¹Part of this work was reported in the International PhotosynthesisCongress, Nagoya, 1992.     

Ribulose 1, 5-Bisphosphate Carboxylase/Oxygenase Activity and Photorespiration during the Ageing of Flag Leaves of Wheat

Photosynthesis, photorespiration, and ribulose bisphosphatecarboxylase/oxygenase activities were measured in intact flagleaves of wheat during ageing. Photorespiration declined verylittle as the leaves aged, and much less than photosynthesis.These changes could not be explained by changes in the ribulosebisphosphate carboxylase to oxygenase ratio of fraction 1 protein.As the leaves grew older the enzyme activities in extracts ofleaves declined in parallel so the ratio remained constant.     

Changes in Contents of Adenine Nucleotides and Development of Ribulose Bisphosphate Carboxylase Activity During Shooting of Mulberry Saplings

At the onset of budding in mulberry saplings (Morus alba L.,cv. Shin-ichinose), the ATP, ADP and carbohydrate contents beganto decline rapidly. This decline continued until RuBPCase activitybegan during the development of the leaves. The concentrationsof these constituents and the value for the adenylate energycharge, though partially restored, were lower than the initialvalues even eight weeks after planting. (Received March 7, 1983; Accepted May 25, 1983)     

Measurement of the Enzyme-CO(2)-Mg Form of Spinach Ribulose 1,5-Bisphosphate Carboxylase/Oxygenase

When the amount of activation of ribulose 1,5-bisphosphate carboxylase has been measured, two forms of the enzyme, not one, are actually determined experimentally. Only the enzyme-activator CO₂-Mg²⁺ form can bind ribulose bisphosphate for reaction with substrate CO₂ or O₂. A method is presented which measures only this catalytically active form by stabilizing it with ribulose bisphosphate just before dilution and assay in Mg²⁺-free reaction medium.     

Varying Photoperiod, Ribulose 1,5-Bisphosphate Carboxylase/Oxygenase and CO(2) Uptake in Thalassiosira fluviatilis (Bacillariophyceae)

The purpose of this research was to test the hypothesis that acclimation of the unicellular marine alga, Thalassiosira fluviatilis Hustedt, to short photoperiods results in decreased cellular concentrations of ribulose 1,5-bisphosphate carboxylase/oxygenase and decreased rates of light-saturated CO₂ uptake. Cells were acclimated to photoperiods of 6:18, 12:12, and 18:6 h:h light:dark, and concentrations of the large subunit of the enzyme and responses of CO₂ uptake to varying irradiance were measured. Concentrations of the large subunit, which weighed approximately 50 kilodaltons, were conserved while rates of CO₂ uptake under light saturation and limitation, and cellular contents of chlorophyll a increased as photoperiod decreased. Apparently, these cells acclimate to short photoperiods by increasing rates of CO₂ uptake under saturating irradiances by increasing in vivo activation of ribulose 1,5-bisphosphate carboxylase/oxygenase. Also, chlorophyll-specific concentrations and specific activities of the enzyme appear to be lower and higher, respectively, in diatomaceous algae than in higher plants.     

Photosynthesis by Flag Leaves of Wheat in Relation to Protein, Ribulose Bisphosphate Carboxylase Activity and Nitrogen Supply

The effects of nitrate supply on the composition (cell numbers,protein and chlorophyll contents) of flag leaves of winter wheatgrown with two amounts of N fertilizer and of spring wheat grownin the glasshouse under controlled nitrate supply are describedand related to photosynthesis. Nitrogen deficiency decreasedthe size of leaves, mainly by reducing cell number and, to asmaller extent, by decreasing cell volume. Protein content perunit leaf area, per cell and per unit cell volume was largerwith abundant N. Total soluble protein, ribulose bisphosphatecarboxylase-oxygenase (RuBPc-o) protein and chlorophyll changedin proportion irrespective of nitrogen supply and leaf age.Photosynthesis per unit area of flag leaf and carboxylationefficiency in both winter and spring wheat were proportionalto the amount of total soluble protein up to 7.0 g m^–2and to the amount of RuBPc-o protein up to 4.0 g m^–2.However, photosynthesis did not increase in proportion to theamount of total soluble or RuBPc-o protein above these amounts.In young leaves with a high protein content the measured ratesof photosynthesis were lower than expected from the amount andactivity of RuBPc-o. Carboxylation per unit of RuBPc-o protein,measured in vitro, was slightly greater in N-deficient leavesof winter wheat but not of spring wheat. RuBPc-o activity perunit of RuBPc-o protein was similar in winter and spring wheatleaves and remained approximately constant with age, but increasedin leaves showing advanced senescence. RuBPc-o protein fromN-deficient leaves migrated faster on polyacrylamide gels thanprotein from leaves with high N content. Regulation of the rateof photosynthesis in leaves and chloroplasts with a high proteincontent is discussed. The conductance of the cell to the fluxof CO₂ from intercellular spaces to RuBPc-o active sites iscalculated, from cell surface areas and CO₂ fluxes, to decreasethe CO₂ partial pressure at the active site by less than 0.8Pa at an internal CO₂ partial pressure of 34 Pa. Thus the decreasein partial pressure of CO₂ is insufficient to account for theinefficiency of RuBPc-o in vivo at high protein contents. Otherlimitations to the rate of photosynthesis are considered. Key words: Wheat, photosynthesis, nitrogen, ribulose, bisphosphate carboxylase     

Comparison of Patterns of Accumulation of Ribulose Bisphosphate Carboxylase Antigen and Catalytic Activity and Measurement of Antigen Half-Life during the Cell Cycle of Chlorella sorokiniana

By use of specific immunochemical procedures, ribulose-1,5-bisphosphate carboxylase (RuBPCase), antigen and catalytic activity were shown to have coincident step-patterns of accumulation during the cell cycle of Chlorella sorokiniana. Pulse-chase studies, employing radioactive sulfate, were performed during the period of rapid accumulation of enzyme activity and during the period of constant enzyme activity in the cell cycle. No degradation of RuBPCase antigen could be detected during either of these cell cycle periods. Thus, the step-pattern of accumulation of RuBPCase activity resulted from periodic synthesis of an enzyme that was stable under steady-state cell cycle conditions. Although inhibition of protein synthesis by cycloheximide, at different times in the cell cycle in the light, resulted in rapid decay of RuBPCase activity, this loss in activity occurred without detectable loss in enzyme antigen. When synchronous cells were placed into the dark, to slow the rate of protein synthesis in the absence of cycloheximide, the levels of enzyme antigen and activity decreased by 30 and 50%, respectively, during the 10-hour dark period. Thus, in C. sorokiniana changes in RuBPCase activity do not necessarily reflect parallel changes in enzyme antigen, particularly when cell growth is perturbed by changes from steady-state cultural conditions.     

Changes in the Levels of Ribulose-l,5-bisphosphate Carboxylase/Oxygenase (Rubisco) in Tetraedron minimum (Chlorophyta) during Light and Shade Adaptation

Exponentially growing cultures of the chlorophyta Tetraedronminimum were allowed to photoadapt to low (50µmole quantam^–2s^–1) and high (500µmole quanta m^–2–1)irradiance levels. In these cultures, various aspects of theorganization of the photosynthetic apparatus and related differencesin its performance were studied. In this organism, the observed five-fold increase in pigmentationof low-light adapted cells was due to increases in the numbersof PSU's, while their sizes remained constant. Using radioimmunoassay technique, we found that high-light adaptedalgae had over five times more Rubisco per PSU than their low-lightadapted counterparts. The high-light adapted algae also exhibited far higher (x2.3)light saturated photosynthetic rates per chl a. This increasewas the result of a reduction of tau, , the turnover time ofPS II reaction centers. We propose that the increase in Rubisco per PSU in high-lightadapted algae explains the reduction in , which results in thehigher P_max rates per chl a in these algae. The relationship is non linear, since the increase in Rubiscoper PSU was x5.3 whereas that in P_mM per chl a was only x2.3. (Received July 30, 1988; Accepted December 2, 1988)