Effect of oxygen on the growth (yield) of Chlorella vulgaris

The growth yield of Chlorella vulgaris, Y _kJ defined as g cells harvested per kJ of light energy absorbed by the cells, was assessed in a turbidostat culture by varying CO₂ and O₂ partial pressures ( and ). The value of Y _kJ ranged from 3.1×10^-3 to 5.0×10^-3 g cells/kJ under light-limited conditions [ = 1.02.4%, = 065%; total pressure of gas (composed of CO₂, O₂ and N₂)=1 atm]. In the light-limited environment, the algal specific growth rate deteriorated appreciably with the increase of . The deterioration accounts for the above range of Y _kJ observed. The growth inhibition due to oxygen that was defined by subtracting from 1.0 the ratio of at given values of to that at = 0% extended from 0.07–0.30 (7–30%). However, glycolate could not be detected in the turbidostat culture. Isotopic experiments on the specific rate of ¹⁴CO₂ uptake also revealed that the inhibition due to oxygen was from 22–38% when was varied from 0 to nearly 100%. These effects of oxygen were discussed, referring to the activity of ribulose-1,5-bisphosphate carboxylase that is inhibited competitively by oxygen.Non-Standard Abbreviations INH isonicotinic acid hydrazide - PPO 2,5-diphenyloxazole - DCMU 3-(-3,4-dichlorophenyl)-1,1-dimetylurea - CA carbonic anhydrase - RuP₂ ribulose-1,5-bisphosphate     

High groundwater nitrate concentrations inhibit eutrophication of sulphate-rich freshwater wetlands

During the last 60 years, pollution of the groundwater with has greatly increased in many parts of Europe, as a consequence of excessive use of manure and synthetic fertilisers. Monitoring of groundwater-fed wetlands indicated that sediments with high concentrations had the lowest Fe and concentrations in the pore water. A comparison of two restored open water fens, differing in supply via the groundwater, indicated that the redox potential and the sulphate ( ) reduction rate were lower when the groundwater contained not only but also high concentrations. The lower reduction rates in the -rich open water fen were associated with lower concentrations and the presence of plant species characteristic of clear water. In contrast, the higher reduction rates in the -poor open water fen were associated with very high concentrations and massive development of plant species characteristic of eutrophic environments. Investigations at -rich seepage sites in black alder carrs, showed that high concentrations in the pore water caused chlorosis in the alder carr vegetation, due to lower availability of Fe in the pore water and less Fe uptake by the plants. Experimental desiccation of sediments proved that the -rich seepage sites contained no oxidisable FeS _x , contrary to -poor locations, which became acidified and mobilised extremely high amounts of due to FeS _x oxidation. A laboratory experiment showed that addition to sediments led to reduced releases of Fe, and S^2–, very likely due to the oxidation of reduced Fe and S compounds. Overall, the results confirmed that is an energetically more favourable electron acceptor in anaerobic sediments than Fe and , and that high loads function as a redox buffer, preventing reduction of Fe and . Limited reduction prevents S^2– -mediated mobilisation of from Fe- complexes. At a higher redox potential, reduced Fe, including FeS _x , was oxidised, increasing the content of Fe(III) capable of binding . This prevented increased availability and the concomitant massive development of plant species characteristic of eutrophic environments.     

Growth yields and saturation constant of Desulfovibrio vulgaris in chemostat culture

Desulfovibrio vulgaris (strain Marburg) was grown on H₂ and sulfate as sole energy source in a chemostat limited by the sulfate supply. The biomass concentration and the sulfate concentration in the culture were determined as a function of the dilution rate. From the data a K _S (saturation constant) for sulfate of 10 M, a _max of 0.23 h^–1, and a of 13 g/mol were calculated. The organism was also grown in chemostat culture on H₂ and sulfite, H₂ and thiosulfate, and pyruvate (without sulfate). was found to be 35 g/mol, 36 g/mol, and Y _pyr ^max 10 g/mol. The growth yields are discussed with respect to ATP gains in dissimilatory sulfate reduction.     

13C shieldings, 18O isotope effects on 13C shieldings, and 57Fe-13C spin couplings of the Fe-C-O unit in superstructured hemoprotein models: Comparison with hemoproteins, C-O vibrational frequencies, and X-ray structural data

¹³C NMR spectra of several carbon monoxide (99.7% ¹³C and 11.8% ¹⁸O enriched) hemoprotein models with varying polar and steric effects of the distal organic superstructure and constraints of the proximal side are reported. This enables the ⁵⁷Fe-¹³C(O) coupling constants ( ), ¹³C shieldings ((¹³C)), and ¹⁸O isotope effects on¹³ C shieldings (¹¹³C(¹⁸O/¹⁶O)) to be measured and hence comparisons with hemoproteins, C-O vibrational frequencies and X-ray structural data to be made. Negative polar interactions in the binding pocket and inhibition of Fe//CO back-donation or positive distal polar interactions with amide NH groups appear to have little direct effect on couplings. Similarly, the axial hindered base 1,2-dimethylimidazole has a minor effect on the values despite higher rates of CO desorption being observed for such complexes. On the contrary,¹³ C shieldings vary widely and an excellent correlation was found between the infrared C-O vibrational frequencies ((C-O)) and¹³ C shieldings and a reasonable correlation with¹⁸ O isotope effects on ¹³C shieldings. This suggests that (¹³C), (C-O) and^{1 13} C(¹⁸O/¹⁶O) are accurate monitors of the multiple mechanisms by which steric and electronic interactions are released in superstructured heme model compounds. The ¹³C shieldings of heme models cover a 4.0 ppm range which is extended to 7.0 ppm when several HbCO and MbCO species at different pH values are included. The latter were found to obey a similar linear (¹³ (¹³C) versus (C-O) relationship, which proves that both heme models and heme proteins are homogeneous from the structural and electronic viewpoint. Our results suggest that (C-O), (¹³C) and ¹¹³C(¹⁸O/¹⁶O) measurements reflect similar interaction which is primarily the modulation of back-bonding from the Fe d to the CO * orbital by the distal pocket polar interactions. The lack of correlation between^{1 13} C(¹⁸O/¹⁶O) and crystallographic CO bond lengths (r(C-O)) reflects significant uncertainties in the X-ray determination of the carbon and oxygen positions.     

Energetics of the growth of Methanobacterium thermoautotrophicum and Methanococcus thermolithotrophicus on ammonium chloride and dinitrogen

Methanobacterium thermoautotrophicum was grown in continuous culture in a fermenter gassed with H₂ and CO₂ as sole carbon and energy sources, and in a medium which contained either NH₄Cl or gaseous N₂ as nitrogen source. Growth was possible with N₂. Steady states were obtained at various gas flow rates with NH₄Cl and with and the maintenance coefficient varied with the gas input and with the nitrogen source. Growth of Methanococcus thermolithotrophicus in continuous culture in a fermenter gassed with H₂, CO₂ as nitrogen, carbon and energy sources was also examined.Abbreviations molecular growth yield (g dry weight of cells per mol of CH₄ evolved) - growth rate (h^-1) - D dilution rate (h^-1) - rate (h_-1); relation of Neijssel and Tempest and of Stouthamer and Bettenhaussen - energy     

Larmor frequency selective model free analysis of protein NMR relaxation

Summary The Lipari-Szabo dynamical formalism is extended by setting the time constants of the Lorentzian terms to and . This analysis is compared to the earlier proposed three-parameter extended model free formalism with regard to the range of equivalence and the advantages of the simplified two-parameter (S _inff ^sup2 ,S _infH ^sup2 ) and (S _inff ^sup2 ,S _infN ^sup2 ) representations. Spectral density components are calculated and compared to those obtained from the spectral density analysis formalism. Protein relaxation data, commonly analyzed in terms of the two-parameter representation, may correspond to a dynamically heterogeneous behaviour that is more appropriately represented in terms of a fast limit order parameter and a second, lower frequency order parameter.     

Nitrate reductase in needles,roots and trunk wood of spruce trees [Picea abies (L.) Karst.]

Summary Nitrate reductase (EC 1.6.6.2) activity (NRA), as measured by an in vivo assay, is present in needle leaves and mycorrhizal fine root tips of adult Norway spruce [Picea abies (L.) Karst.] in at least equal amounts on a fresh weight basis, in both adult and 5-year-old trees. NRA could also be demonstrated in trunk wood of deroted trees after fertilization with 5 mM , exhibiting a longitudinal profile in the trunk. Inducibility in needles can more efficiently be achieved by NO₂ (100 g·m^-3) than by 5 mM nitrate, which is effective only in root-amputated trees. A remarkably high level of needle-NRA in unfertilized trees, which are characterized by a very low level of nitrate in the xylem sap, suggests that NRA in spruce needles may in part be constitutive. Organic-N is a major nitrogen source for the needles even in root-amputated trees, indicating pronounced exchange processes between ray parenchyma and trunk xylem, which in turn are modified by the nitrogen source fed to the trunk stump. Intact trees exhibit a very similar amino acid composition of the xylem sap, regardless of whether or has been fed. The amino acid pattern of the needles is not thrown out of balance by flooding with and , which occurs in fertilized derooted trees. This indicates a distinct potential for homoeostasis of nitrogen entrance-metabolism (i.e. NRA and glutamine synthetase activity) in the needles. In the ectomycorrhiza/fine root-system (EMC), marked differences in NRA were observed depending on root-tip diameter and along the longitudinal profile of the fine roots. EMC-nitrate reductase is strongly enhanced by . Needle-NRA exhibits a circannual rhythm. An early summer maximum is followed by a December minimum. This activity pattern matches well the transitory increase of soluble nitrogen in spring and the total protein maximum in winter. In an indirect way assimilatory NRA may well contribute to nitrogen overfertilization (by consumption of NO_X) as one possible cause of the contemporary decline of spruce populations.     

Minimal Functional Unit of Lactate Dehydrogenase

The tetrameric heart isozyme of lactate dehydrogenase (H₄) is modified by p-chloromercuribenzoate (PCMB) to produce the inactive tetramer and then hybridized with native tetrameric muscle isozyme (M₄). The hybrid mixture was isolated by polyacrylamide gel electrophoresis (PAGE) and then stained for enzyme activity and with Coomassie brilliant blue. Only three bands were found on the gels in either case. The hybrid enzymes as isolated by PAGE have half the specific activity of the native muscle enzyme. The electrophoresis properties of HM₃ are very similar to those of HM₃, while the electrophoresis properties of are very similar to those of H₂M₂. The above results strongly suggest that the tetramer having enzymatic activity contains at least two native subunits, and the di-subunit in the tetrameric enzyme is the minimal functional unit.     

Times to exhaustion at 100% of velocity at [(V)\dot]\textO\text2 \dot V{\text{O}}_{\text{2}} max and modelling of the time-limit / velocity relationship in elite long-distance runners

The aim of this study was to measure running times to exhaustion (Tlim) on a treadmill at 100% of the minimum velocity which elicits _{max max} in 38 elite male long - distance runners _max = 71.4 ± 5.5 ml.kg^–1.min^–1 and _max = 21.8 ± 1.2 km.h^–1). The lactate threshold (LT) was defined as a starting point of accelerated lactate accumulation around 4 mM and was expressed in _max. Tlim value was negatively correlated with _max (r = -0.362, p< 0.05) and _max (r = –0.347, p< 0.05) but positively with LT (%v _max) (r = 0.378, p < 0.05). These data demonstrate that running time to exhaustion at _max in a homogeneous group of elite male long-distance runners was inversely related to _max and experimentally illustrates the model of Monod and Scherrer regarding the time limit-velocity relationship adapted from local exercise for running by Hughson et al. (1984) .     

Water economy in bird nests

Summary Nest humidity ( ) under an incubating bantam hen was measured at ambient ranging from 1.3 to 25.0 mmHg. Weight loss of eggs was recorded in clutches of varying size. Nest and ambient were also measured in wild incubating willow ptarmigan nests in dry and wet habitats.Nest increased linearly with ambient in a way predictable on the assumption that the water vapour conductance ( ) of brood patch skin, plumage and eggs were constant and independent of ambient . Nest was also dependent of clutch size. Egg dehydration was quantitatively predicted from measured values and the laws of diffusion.Our findings confirm earlier conclusions that the adult bird does not actively regulate nest at varying ambient . Birds can presumably achieve appropriate egg dehydration by a strategy combining nest site, nest construction, egg shell conductance and incubation behaviour which meets the requirements of their breeding climate.Abbreviations water vapur pressure - water vapur conductance - water flux     

Mobility of NH bonds in DNA-binding protein HU of shape Bacillus stearothermophilus from reduced spectral density mapping analysis at multiple NMR fields

The dynamics of the backbone NH bonds of protein HU from Bacillus stearothermophilus (HUBst) have been characterized using measurements of cross-relaxation, longitudinal and transverse relaxation rates at 11.7, 14.1 and 17.6 T. Linear regression of the values with the squared Larmor frequency _N ² has revealed global exchange processes, which contributed on the order of 0.5–5.0 s^-1to the transverse relaxation rate. Subsequently, the experimental values were corrected for these exchange contributions. A reduced spectral density mapping procedure has been employed with the experimental relaxation rates and seven values of the spectral density function J() have been extracted. These spectral densities have been fitted within the framework of the model-free approach. The densities agree well with an axially symmetric rotational diffusion tensor with a diffusion anisotropy D_/D_ of 1.15, indicating that the flexible arms of HUBst do not significantly contribute to the rotational diffusion. The overall correlation time is 8.9 ± 0.6 ns/rad. The fast internal motions of most of the NH bonds in the core display order parameters ranging between 0.74 and 0.83 and internal correlation times between 1 and 20 ps. For the residues in the DNA-binding -arms, an extended version of the model function has been used. The slow internal motions show correlation times of 1–2 ns. The concomitant order parameters (0.3–0.6) are lower than those observed on the fast time scale, indicating that the flexibility of the -arms is mainly determined by the slower internal motions. A substantial decrease of the generalized order parameters in the -arms starting at residues Arg⁵⁵ and Ser⁷⁴, opposite on both strands of the -ribbon arms, has been explained as a hinge motion. A comparison of the order parameters for free and DNA-bound protein has demonstrated that the slow hinge motions largely disappear when HU binds DNA.     

Foam behavior of biological media

Summary The influence of the alcohol concentration on the foaminess, , of-BSA-solutions is considered. This effect is calculated by means of the function (C_BSA . f), where f=1 for pure protein solutions and f>1 for alcohol solutions. f is calculated by f = 2^TT_eff. Here, where T_T is the turbidity temperature change due to solvent structure effects and T_D, the temperature correction due to alcohol-protein interaction. The constants necessary to calculate T_T and T_D are tabulated. The agreement between the calculated and measured foaminess , as a function of the n-propanol concentration is satisfactory and for methanol or ethanol excellent.     

Distribution of greenhouse gases, nitrite, and δ13C of dissolved inorganic carbon in Lake Biwa: Implications for hypolimnetic metabolism

The vertical distribution of dissolved greenhouse gases (CH₄,CO₂ and N₂O), NO ,and ¹³C of CO₂ in Lake Biwa during a stagnantperiod was precisely determined. CO₂ as well as NO was accumulated in the hypolimnion, whereas NO and CH₄concen\-trations were generally higher in theepilimnion than in the hypolimnion. In August, NO andCH₄ were ephemerally accumulated at the thermocline. Theconcentration of CH₄ always exceeded equilibrium with respectto air/water exchange. N₂O was rather uniformly distributed inboth time and space, and remained near equilibrium with respect toair/water exchange. All of these observations are similar to otherstratified, oligotrophic lakes, in which the hypolimnia were welloxygenated. The ¹³C of CO₂ became morenegative with increasing depth, and showed a strong negativecorrelation with apparent oxygen utilization. From the data, the ¹³Cvalue of organic matter decomposed into CO₂ inthe hypolimnion was calculated by isotope mass-balance, and found tobe in a similar range to ¹³C of phytoplankton and benthic algaeand distinctively higher than ¹³C of both terrestrial andsedimentary organic matters. This suggests that autochthonous organicmatter was the major source of CO₂.     

A comparative study of the mechanism of Na+ and Cl? excretion by the gill ofMugil capito andFundulus heteroclitus: Effects of Stress

Summary In seawater (SW)-adaptedMugil andFundulus, gill effluxes of Na⁺ and of Cl^– and the simultaneously recorded transgill potential (P.D.) differ according to whether they are measured in stressed or rested animals.In rested animals of the two species, transfer to Ringer's solution considerably reduces the P.D. but not . InFundulus, is also decreased. Transfer of the two species from SW to fresh water (FW) reduces and by 75 to 85% and leads to a large inversion of P.D. When K⁺ is added to FW, a gill depolarization occurs, as well as a large increase of and .These results suggest that: 1) the P.D. originates primarily from the diffusion of cations, the gill permeability to Na⁺ ( ) being greater than that to Cl^– ( ), 2) a Cl^–/Cl^– exchange independent of P.D. is associated with the Cl^– pump; 3) Cl^– pump activity is linked to Na⁺/K⁺ exchange which in turn is associated to a Na⁺/Na⁺ exchange diffusion mechanism.In stressed individuals of the two species, the P.D. in SW, as well as the P.D. changes observed during transfer experiments, are considerably reduced. The decrease of and observed after transfer from SW to FW are also minimised. Changes are smaller inFundulus. The decrease of P.D. characterizing stressed animals may be at least in part due to a 3 to 4 fold increase of which becomes equal to in both species.As a result of stress, the K⁺-activated Na⁺ and Cl^– excretion mechanisms are totally inhibited inFundulus and partially so inMugil.Stress response seems more intense inFundulus and recovery from stress faster inMugil.     

A method for determining the maximal steady state of blood lactate concentration from two levels of submaximal exercise

The aim of this study was to estimate the characteristic exercise intensity _CL which produces the maximal steady state of blood lactate concentration (MLSS) from submaximal intensities of 20 min carried out on the same day and separated by 40 min. Ten fit male adults [maximal oxygen uptake _max 62 (SD 7) ml · min^–1 · kg^–1] exercisOed for two 30-min periods on a cycle ergometer at 67% (test 1.1) and 82% of _max (test 1.2) separated by 40 min. They exercised 4 days later for 30 min at 82% of _max without prior exercise (test 2). Blood lactate was collected for determination of lactic acid concentration every 5 min and heart rate and O₂ uptake were measured every 30 s. There were no significant differences at the 5th, 10th, 15th, 20th, 25th, or 30th min between , lactacidaemia, and heart rate during tests 1.2 and 2. Moreover, we compared the exercise intensities _CL which produced the MLSS obtained during tests 1.1 and 1.2 or during tests 1.1 and 2 calculated from differential values of lactic acid blood concentration ([1a^–]_b) between the 30th and the 5th min or between the 20th and the 5th min. There was no significant difference between the different values of _CL [68 (SD 9), 71 (SD 7), 73 (SD 6),71 (SD 11) % of _max (ANOVA test,P<0.05). Four subjects ran for 60 min at their _CL determined from periods performed on the same day (test 1.1 and 1.2) and the difference between the [la^–]_b at 5 min and at 20 min ( ([la^–]_b)) was computed. The [la^–]_b remained constant during exercise and ranged from 2.2 to 6.7 mmol · l^–1 [mean value equal to 3.9 (SD 1) mmol · l^–1]. These data suggest that the _CL protocol did not overestimate the exercise intensity corresponding to the maximal fractional utilization of _max at MLSS. For half of the subjects the _CL was very close to the higher stage (82% of _max where an accumulation of lactate in the blood with time was observed. It can be hypothesized that _CL was very close to the real MLSS considering the level of accuracy of [la^–]_b measurement. This study showed that exercise at only two intensities, performed at 65% and 80% of _max and separated by 40 min of complete rest, can be used to determine the intensity yielding a steady state of [la^–1]_b near the real MLSS workload value.     

Gill function in an elasmobranch

Summary Highly efficient oxygen uptake in elasmobranchs, as indicated by frequent excess of over has previously been ascribed to the operation of multicapillary rather than counter-current gas exchange by the gills. Analysis of models shows that, at maximum efficiency, a multicapillary system cannot account for values of greater than . In Port Jackson sharks Heterodontus portusjacksoni) commonly exceeds , which indicates the operation of a functional counter-current at the respiratory surface. The anatomical basis of this counter-current is provided by the demonstration that a continuous flow of water passes between the secondary lamellae into septal canals and thence via the parabranchial cavities to the exterior.Queen Elizabeth II Fellow.     

Prediction of individual oxygen uptake on-step transients from frequency responses

Power-oxygen uptake ( ) frequency responses can be used to predict responses to arbitrary exercise intensity patterns. It is still an open question for which range of exercise intensities such computed response patterns yield valid predictions. In the present study, we determined the power- frequency response of nine sports students by means of pseudo-randomised switching between 20 W and 80 W during upright and supine cycle exercise. Starting from a baseline of 20 W each subject also performed sustained step increases to 40 W, 80 W, 120 W, and 160 W in both positions. The individual step responses were then compared with the expected time-courses predicted on the basis of the individual frequency responses. The comparison showed a close agreement for the 20 W–40 W and 20 W–80 W steps in both positions. With larger step amplitudes the kinetics became increasingly slower than the predicted time course in both positions. During additional ramp tests (10 W · 30 s^–1) whole blood lactic acid concentration [1a^–]_b tended to be higher in the supine position at exercise intensities higher than 160 W. The mean power at 4 mmol · 1^–1 [la^–]_b amounted to 234 (SD 32) W and 253 (SD 44) W (P<5%) in the supine and the upright position, respectively. The maximal oxygen uptake relative to body mass was not found to be significantly different [upright, mean 57 (SD 10) ml · (min · kg)^–1;supine, mean 54 (SD 10) ml · (min · kg)]. These findings would suggest that for a range of mild exercise intensities kinetics are not appreciably influenced by the step amplitude or by cardiovascular changes associated with the upright and the supine position.     

Respiration of the emersed shore crab at variable ambient oxygenation

Summary In the intertidal shore crab,Carcinus maenas, pH and values of the prebranchial venous hemolymph, and , the PO₂ values of the arterialized cardiac hemolymph, , were measured, and the ventilatory activity was assessed by measuring the hydrostatic pressures at the exits of the epibranchial cavities, under four environmental conditions: normoxic water, normoxic air, hypoxic gas, hyperoxic gas.In the crab breathing normoxic air, was lower and higher than in animals breathing normoxic water. With the switch to hypoxic gas, ventilation increased and and decreased. With the switch to hyperoxic gas, ventilation decreased, and increased and decreased.Thus these crabs breathing air were not as well oxygenated as when breathing air-equilibrated water, and because of their low , they were relatively hypervetilating and hypocapnic compared to air-breathing vertebrates. Hyperoxic breathing, increasing and reducing ventilatory drive, led to increased . Conversely, was reduced by hypoxic breathing. These observations suggest that the gas exchanger of intertidal crabs is not as successfully designed for air breathing as that of land-colonizing insects and air-breathing vertebrates.     

Effects of common soil anions and pH on the uptake and accumulation of perchlorate in lettuce

A mechanistic understanding of perchlorate () entry into plants is important for establishing the human health risk associated with consumption of contaminated produce and for assessing the effectiveness of phytoremediation. To determine whether common soil anions affect uptake and accumulation in higher plants, a series of competition experiments using lettuce (Lactuca sativa L.) were conducted between (50 nM) and (4–12 mM), (1–10 mM), or Cl⁻ (5–15 mM) in hydroponic solution. The effects of (0–5 mM) and pH (5.5–7.5) on uptake were also examined. Increasing in solution significantly reduced the amount of taken up by green leaf, butter head, and crisphead lettuces. Sulfate and Cl⁻ had no significant effects on uptake in lettuce over the concentrations tested. Increasing pH significantly reduced the amount of taken up by crisphead and green leaf lettuces, whereas increasing significantly reduced uptake in butter head lettuce. The inhibition by across all lettuce genotypes suggests that may share an ion carrier with , and the decrease in uptake with increasing pH or provides macroscopic evidence for cotransport across the plasma membrane.     

Estimation of oxygen penetration depth in immobilized cells

Summary A simple method is proposed for calculating oxygen pentration depth in immobilized cells by assuming zero order kinetics in the presence of several external oxygen transport resistances. Calculations indicate that typical penetration depths of oxygen for immobilized microbial cells are in the range of 50–200 and those for immobilized or encapsulated animal and plant tissue culture are about 500–1000 . Based on calculations, oxygen transport in microencapsulation and microcarriers for tissue cultures are not transport-limited, but a slight limitation is expected for those in a hollow fiber reactor.Nomenclature a_s specific area of a support (cm) - Bi Biot number - dimensionless - C_b oxygen concentration in the bulk liquid (mM) - C _b C _b ^* -C_cr (mM) - C _b ^* bulk oxygen concentration in equilibrium with air (mM) - C_cr critical oxygen concentration (mM) - C_s oxygen concentration in the solid phase (mM) - d_p diameter or thickness of a support (cm) - D_eff effective diffusivity of oxygen in the solid phase (cm²/s) - k_m membrane permeability of oxygen (cm/s) - k _m ^* D_eff/_m - k_La_L liquid phase mass transfer rate coefficient (1/s) - k_sa_s solid phase mass transfer rate coefficient (1/s) - (OUR)_v volumetric oxygen uptake rate (mmol O₂/l) - p geometry parameter, p=0 for slab, p=1 for cylinder, p=2 for sphere - P_d oxygen penetration depth (cm) - P _d oxygen penetration depth in the absence of external diffusion limitation (cm) - Q volumetric oxygen uptake rate, (mmol O₂/l·h) - specific oxygen uptake rate (mmol O₂gm biomass (dry)·h) - r length coordinate (cm) - r_c oxygen penetration depth for sphere (cm) - r _c r_c in the absence of external diffusion limitation (cm) - r _c ^* oxygen penetration depth for cylinder (cm) - r _c ^* r _c ^* in the absence of external diffusion limitation (cm) - r_com combined mass transfer rate resistance (s) - r_d location where C_s becomes zero or C_cr (cm) - r_i radius of cylinder or sphere, half thickness of slab (cm) - U_sg superficial gas velocity (cm/s) - X cell concentration (g/l) Greek letters Thiele modulus, dimensionless - _L, _s liquid and solid phase volume fraction, respectively, dimensionless - effectiveness factor On sabbatical leave from KAIST, Seoul, Korea