On the generalization of the logistic law of growth

This communication presents a discussion of some extensions of the formalism of Verhulst's simple logistics, which may constitute an autonomous growth model of a more general scope.For that purpose, the basis concept of growth diagram or trajectory is called upon, as it affords the graphic representation of the change in the growth variable y, using two relevant kinetic parameters: the instantaneous rate and the instantaneous acceleration. The two possible kinds of trajectories are in relation to the use of absolute (V = dyldt; = dV/dt) or relative (or specific) values (R = (1/y)(dy/dt); _R = dR/dt).In the case of simple logistics, the trajectory (V, ) allows 4 growth phases or states to be distinguished. The diagram (R, _R ) shows that the deceleration of the specific rate is not monotonous.In the case of Richards - Nelder's generalized logistics, the qualitative variation of the growth trajectory depends on the value of the dissymmetry parameter (occurrence of a critical value which determines the number of growth states).Blumberg's model is characterized by an analogous property and, moreover, can account for a non monotonous variation of the specific growth rate.     

Papain kinetics in the presence of a water-miscible organic solvent

The effects of various concentrations of a water-miscible organic solvent [a 7:3 (v/v) mixture of N, N dimethylformamide and dimethylsulfoxide] on the kinetics of papain have been investigated. The parameters k(cat) and K(m) for the amidase and esterase activity of papain using N-alpha-benzoyl-DL-arginine-p-nitroanilide (BAPNA) and N-alpha-benzoyl-L-arginine ethyl ester (BAEE) as substrates were determined. For both types of activity, k(cat) initially increased (up to about 15% solvent), and then decreased with increasing concentrations of organic solvent. In contrast, K(m) increased sharply with the organic solvent concentration. Active site titration at 0 and 50% solvent indicated no change in the amount of active enzyme. Fluorometric measurements of the emission spectrum of papain did not indicate any major conformational changes with increasing concentrations of organic solvent.     

Kinetics of aerobic biodegradation of benzene and toluene in sandy aquifer material

Monod's equation adequately described aerobic biodegradation rates of benzene and toluene by the microbial population of a sandy aquifer when these compounds were initially present at concentrations lower than 100 mg/l each. Concentrations higher than 100 mg/l were inhibitory, and no benzene or toluene degradation was observed when these compounds were initially present at 250 mg/l each. The Monod coefficients were calculated as k = 8.3 g-benzene/g-cells/day and Ks = 12.2 mg/l for benzene, and k = 9.9 g-toluene/g-cells/day and Ks = 17.4 mg/l for toluene. Specific first-order coefficients would be 0.68 l/mg.day for benzene and 0.57 l.mg.day for toluene.     

Influence of inoculum age on hybridoma culture kinetics

To determine the influence of the inoculum age on the kinetics of hybridoma growth and metabolism, spinner flasks have been inoculated with cells previously propagated in T flasks for 43, 52, 62 and 71 hr respectively. Increasing the age of the inoculum is found to result in a longer lag phase, in a lower maximum specific growth rate and in a reduced maximal cell density. During the growth phase specific rates of glucose and glutamine uptake and of ammonia and lactate production are similar. However, with the older inoculum, much higher metabolic activities are observed during the lag phase. The production of antibodies is delayed with increasing inoculum age, but the final antibody concentrations are similar, which indicates a higher specific antibody production rate when inoculating with older cells.     

Mineralization of 2,4-dichlorophenoxyacetic acid (2,4-D) in soil inoculated with Pseudomonas cepacia DBO1(pRO101), Alcaligenes eutrophus AEO106(pRO101) and Alcaligenes eutrophus JMP134(pJP4): effects of inoculation level and substrate concentration

Mineralization of 2,4-dichlorophenoxyacetic acid (2,4-D) by two Alcaligenes eutrophus strains and one Pseudomonas cepacia strain containing the 2,4-D degrading plasmids pJP4 or pRO101 (=pJP4::Tn1721) was tested in 50 g (wet wt) samples of non-sterile soil. Mineralization was measured as ¹⁴C-CO₂evolved during degradation of uniformly-ring-labelled ¹⁴C-2,4-D. When the strains were inoculated to a level of approximately 10⁸ CFU/g soil, between 20 and 45% of the added 2,4-D (0.05 ppm, 10 ppm or 500 ppm) was mineralized within 72 h. Mineralization of 0.05 ppm and 10 ppm, 2,4-D by the two A. eutrophus strains was identical and rapid whereas mineralization by P. cepacia DBO1(pRO101) occurred more slowly. In contrast, mineralization of 500 ppm 2,4-D by the two A. eutrophus strains was very slow whereas mineralization by P. cepacia DBO1 was more rapid. Comparison of 2,4-D mineralization at different levels of inoculation with P. cepacia DBO1(pRO101) (6×10⁴, 6×10⁶ and 1×10⁸ CFU/g soil) revealed that the maximum mineralization rate was reached earlier with the high inoculation levels than with the low level. The kinetics of mineralization were evaluated by nonlinear regression analysis using five different models. The linear or the logarithmic form of a three-half-order model were found to be the most appropriate models for describing 2,4-D mineralization in soil. In the cases in which the logarithmic form of the three-half-order model was the most appropriate model we found, in accordance with the assumptions of the model, a significant growth of the inoculated strains.Abbreviations 2,4-D 2,4-dichlorophenoxyacetic acid - CFU colony forming units - PTYG peptone, tryptone, yeast & glucose - DPM disintegrations per minute     

Continuous culture of suspended plant cells

Summary Continuous culture is an attractive research tool in physiologic and growth and production kinetics research. However, fulfillment of the basic assumptions of continuous culture in the experimental set-up may cause problems. The homogeneity of plant cell cultures and effluent, particularly, may cause problems. This paper presents an experimental set-up which solves these problems and describes the use of this equipment in a study of the growth kinetics of plant cells. Industrial application of the continuous culture of plant cells in the production of secondary metabolites seems to be profitable when compared with batch or fed-batch cultures. However, various problems such as uncoupled product formation and strain instability make fed-batch culture a better choice. Presented in the Session-in-Depth Batch Production and Fermentation at the 1991 World Congress on Cell and Tissue Culture, Anaheim, California, June 16–20, 1991.     

Hydrogen exchange kinetics of nucleic acids: Double and triple helices with Hoogsteen-type basepairs

The kinetics of hydrogen-tritium exchange reaction have been followed by a Sephadex technique of a double-helical poly(ribo-2-methylthio-adenylic acid)·poly(ribouridylic acid) complex with the Hoogsteen-type basepair. Only one hydrogen in every 2-methylthio-adenine·uracil basepair has been found to exchange at a measurably slow rate, 0.023 s^?1 (at 0°C), which is, however, much greater than that for a double-helix with the Watson-Crick type A·U pair. The kinetics of hydrogen-tritium exchange were also examined by triple-helical poly(rU)·poly(rA)·poly(rU) which involves both the Watson-Crick and Hoogsteen basepairings. Here, three hydrogens in every U·A·U base triplet have been found to exchange at a relatively slow rate, 0.0116 s^?1 (at 0°C). The kinetics of hydrogen-deuterium exchange reactions of these polynucleotide helices have also been followed by a stopped-flow ultraviolet absorption spectrophotometry at various temperatures. On the basis of these experimental results, the mechanism of the hydrogen exchange reactions in these helical polynucleotides was discussed. In the triple helix, the rate-determining process of the slow exchange of the three (one uracil-imide and two adenine-amino) hydrogens is considered to be the opening of the Watson-Crick part of the U·A·U triplet. This opening is considered to take place only after the opening of the Hoogsteen part of the triplet.     

Sulphate uptake in the unicellular marine red algaRhodella maculata

Sulphate uptake by the unicellular marine red algaRhodella maculata conforms to Michaelis-Menten kinetics. Two uptake systems have been found: a low affinity system with an apparentK _m of 22 mM, and a high affinity system with an apparentK _m of 63.4 M. Transition from the low to the high affinity system can occur within 2.5 min, in response to a decrease in the ambient sulphate concentration to below 10 mM. Assimilation rates in the dark are about 20% those in the light, although enhancement by light is independent of the quanlity of light supplied above 27 mol m^-2 s^-1. Use of metabolic inhibitors indicates that photophosphorylation provides the main source of energy for sulphate assimilation, through both cyclic and non-cyclic electron flow.Abbreviations used APS-kinase ATP:adenylyl-sulphate 3-phosphotransferase (E.C. 2.7.1.25) - ATP-sulphurylase ATP:sulphate adenylyltransferase (E.C.2.7.74) - DCMU [3-(3,4-dichlorophenyl)]-1,1 dimethylurea - 2,4 DNP 2,4-dinitrophenol - DBMIB Dibromothymoquinone (2,5-dibromo-3-methyl-6-isopropyl-p-benzoquinone)     

Kinetics of sugar transport byThiobacillus A2

ApparentK _s andV _max values, for the transport byThiobacillus A2 of¹⁴C-labelled sucrose, hexoses and pentoses, were estimated using flow dialysis and membrane filtration techniques. Transport systems of varying degrees of specificity could be inferred from the data. For most sugars tested including glucose, fructose and arabinose, there was a close correlation between maximum rate of sugar transport and observed growth rate. Differences in transport rate were sufficient to explain slow and fast growth on glucose by wild type and GF strains ofThiobacillus A2.Abbreviations Butyl PBD 2-(4-tert-butylphenyl)-5-(4-biphenylyl)-1,3,4-oxadiazole - Tris tris(hydroxymethyl)-amino-methane - PEP phosphoenolpyruvate     

Electron transfer between horse heart and Candida krusei cytochromes c in the free and bound states

Electron transfer between horse heart and Candida krusei cytochromes c in the free and phosvitin-bound states was examined by difference spectrum and stopped-flow methods. The difference spectra in the wavelength range of 540–560 nm demonstrated that electrons are exchangeable between the cytochromes c of the two species. The equilibrium constants of the electron transfer reaction for the free and phosvitin-bound forms, estimated from these difference spectra, were close to unity at 20°C in 20 mM Tris-HCl buffer (pH 7.4). The electron transfer rate for free cytochrome c was (2–3) · 10⁴ M^?1 · s^?1 under the same conditions. The transfer rate for the bound form increased with increase in the binding ratio at ratios below half the maximum, and was almost constant at higher ratios up to the maximum. The maximum electron exchange rate was about 2 · 10⁶ M^?1 · s^?1, which is 60–70 times that for the free form at a given concentration of cytochrome c. The activation energy of the reaction for the bound cytochrome c was equal to that for the free form, being about 10 kcal/mol. The dependence of the exchange rate on temperature, cytochrome c concentration and solvent viscosity suggests that enhancement of the electron transfer rate between cytochromes c on binding to phosvitin is due to increase in the collision frequency between cytochromes c concentrated on the phosvitin molecule.