Some comments on ‘Urease activity and its Michaelis constant for soil systems’, by Viraj Beriet al.

Summary Recently Beri, Goswami and Brar made a very valuable contribution to our knowledge of soil urease activity. Unfortunately some errors crept into their experimental approach and the mathematical treatment of the experimental data. Rectification leads in some points to conclusions different from those of the authors.Viraj Beri, K. P. Goswami and S. S. Brar, Plant and Soil49, 105–115 (1978).     

Natural selection and the Michaelis constant

Natural selection operating on a biological process with Michaelis-Menten kinetics adjusts the Michaelis (half-saturation) constant relative to ambient substrate concentration. From the perspective developed here, the relative fitnesses of alternative evolutionary “strategies” determine the trajectory of the Michaelis constant (K_m) over evolutionary time. If substrate concentration is held relatively constant or fluctuates randomly about mean concentration over evolutionary time, while processing rate increases, K_m tends toward a value greater than or equal to substrate concentration; if processing rate is held relatively constant over evolutionary time, K_m tends to become large relative to substrate concentration. The diversity of the supportive evidence cited suggests a broad applicability of this argument across taxonomic groups and levels of biological organization.     

A new method for determining the Michaelis constant

A new method is described for evaluating the parameters K(m) and V in the Michaelis-Menten equation, and is illustrated with experimental data from the literature.     

pH-Stat titration method for dihydrofolate reductase activity measurements: application to determination of substrate Michaelis constant and antifolate inhibition constant

A pH-Stat titration method was developed for measuring dihydrofolate reductase (DHFR) activity; this method permits detection of very low DHFR activities corresponding to 100 pmol of substrate reduced per minute. This value is about ten times lower than those observed using the classical spectrophotometric method. This sensitivity makes it possible to measure the DHFR in crude tissue extracts. With beef liver DHFR, Michaelis constants for the cofactor NADPH and the natural substrate determined by this method were 1.9 +/- 0.3 X 10(-5) and 8.5 +/- 0.5 X 10(-7) M, respectively. The inhibition constant of methotrexate, a competitive inhibitor of dihydrofolate, was 3.4 +/- 1.3 X 10(-11) M.     

Measurement of Michaelis constant for human erythrocyte transketolase and thiamin diphosphate

Human erythrocyte transketolase could be resolved from thiamin diphosphate (TDP) by acidification of the ammonium sulfate precipitate to pH 3.5, but not by other tested procedures. Resolution was 98% by chemical measurement of residual thiamin and 95% by residual enzyme activity. Reconstitution of the resolved preparation by incubation with TDP was dependent upon TDP concentration, duration, temperature, and the presence of dithiothreitol. At low TDP concentrations, 1 h was required for maximum activation; kinetic analysis then yielded an apparent Km value for TDP of 65 nM (SD 14 nM) from 100 erythrocyte lysates and similar values for reconstituted resolved preparations previously purified 400-fold and 10,000-fold. Velocity data obtained by transketolase assays in which the TDP was added to resolved preparations simultaneously with substrates yielded an apparent Km value for TDP of 2.3 microM (SD 1.6 microM) from 114 erythrocyte lysates and similar values for purified preparations. The recovery of activity following resolution and reconstitution ranged from 21 to 60% from lysates and 38 to 70% from purified preparations. Residual ammonium sulfate up to 4.9 mM decreased the apparent Km value for TDP, while a concentration of 11.3 mM increased the value in a manner competitive with TDP and with an apparent Ki value of 2.3 mM. The spectrophotometric assay of transketolase activity was greatly affected by storage of frozen solutions of the substrate ribose 5-phosphate.     

Pooling and comparing estimates from several experiments of a Michaelis constant for an enzyme

Often the Michaelis constant of an enzyme will be determined several times. This may be done for various reasons such as ensuring reproducibility, comparing different enzyme preparations, or examining the effects of variations in experimental conditions. In these circumstances, two questions arise. First, how can the various estimates of the Michaelis constant be compared to determine whether they are the same within the limits of experimental variation? Secondly, if they are all the same, how can the values be combined to give an overall estimate? These questions are addressed here and a solution proposed in which the sets of data are pooled and analyzed with a separate maximum velocity for each set but a common Michaelis constant. The pooled data are partitioned in suitable ways and reanalyzed to examine, by means of a variance ratio test, whether a single Michaelis constant gives a satisfactory fit to the data.     

Estimation of Michaelis constant and maximum velocity from the direct linear plot

When estimates of Michaelis-Menten parameters are obtained from kinetic observations taken in pairs, as in the direct linear plot, bias can arise in the final estimates if any pairs lead to negative values of the maximum velocity V. This bias can be removed by treating such negative values as if they were large and positive, and by treating the corresponding values of Km in the same way.     

Influences of nonuniform activity distributions on the apparent maximum reaction rate and apparent Michaelis constant of immobilized enzyme reactions

The influences of nonuniform activity distribution within a porous solid support on the apparent kinetic parameters, V_m^app and K_m^app, of immobilized enzyme reactions following the Michaelis-Menten kinetics were theoretically investigated. As the enzyme is distributed to the neighborhood of the external surface of the support, V_m^app and K_m^app approach their respective intrinsic values over a wide range of substrate concentration. There is a close relationship between the nonuniform distribution and internal diffusional resistance. Changes in these two factors provide similar effects on V_m^app and K_m^app. As long as the immobilized enzyme reaction follows Michaelis-Menten kinetics, the nonuniform activity distribution never makes K_m^app less than its intrinsic value.     

Urease activity in soils

Summary The availability of Ca from different levels of gypsum and calcium carbonate in a non-saline sodic soil has been investigated. Different levels of tagged gypsum (Ca⁴⁵SO₄.2H₂O) and calcium carbonate (Ca⁴⁵CO₃) (i.e. 0, 25, 50, 75, and 100 per cent of gypsum requirement) were mixed thoroughly in 3.5 Kg of a non-saline alkali soil (ESP, 48.4; ECe, 2.68 millimhos/cm). Dhaincha (Sesbania aculeata) — a legume and barley (Hordeum vulgare L.) — a cereal were taken as test crops. Increasing levels of gypsum caused a gradual increase in the yield of dry matter, content of Ca and K in the plant tops and Ca:Na and (Ca+Mg):(Na+K) ratios in both the crops. Application of calcium carbonate caused a slight increase in the dry matter yield, content of Ca and Mg and Ca:Na and (Ca+Mg):(Na+K) ratios in barley, however, in case of dhaincha there was no such effect. Gypsum application caused a gradual decrease in the content of Na and P in both the crops. Total uptake of Ca, Mg, K, N and P per pot increased in response to gypsum application. The effect of calcium carbonate application on the total uptake of these elements was much smaller on dhaincha, but in barley there was some increasing trend.Increasing application of tagged gypsum and calcium carbonate caused a gradual increase in the concentration and per cent contribution of source Ca in both the crops, although, the rate of increase was considerably more in dhaincha. The availability of Ca from applied gypsum was considerably more than that from applied calcium carbonate. Efficiency of dhaincha to utilize Ca from applied sources was considerably more (i.e. about five times) than that of barley     

Urease activity inTrichophyton mentagrophytes

Urease activity was detected in the dermatophyteTrichophyton mentagrophytes cells at early exponential phase of growth. Specific activity of urease decreased with culture age. At exogenous urea concentrations above 2 mm formation of urease was inhibited. The pH optimum lay at 7–7.5, the K_m being 14 mm. No urease activity could be detected in cell-free culture fluid ofT. mentagrophytes. No endoor exocellular urease activity could be detected in aT. rubrum strain grown with or without urea.     

The original Michaelis constant: translation of the 1913 Michaelis-Menten paper

Nearly 100 years ago Michaelis and Menten published their now classic paper [Michaelis, L., and Menten, M. L. (1913) Die Kinetik der Invertinwirkung. Biochem. Z. 49, 333-369] in which they showed that the rate of an enzyme-catalyzed reaction is proportional to the concentration of the enzyme-substrate complex predicted by the Michaelis-Menten equation. Because the original text was written in German yet is often quoted by English-speaking authors, we undertook a complete translation of the 1913 publication, which we provide as Supporting Information . Here we introduce the translation, describe the historical context of the work, and show a new analysis of the original data. In doing so, we uncovered several surprises that reveal an interesting glimpse into the early history of enzymology. In particular, our reanalysis of Michaelis and Menten's data using modern computational methods revealed an unanticipated rigor and precision in the original publication and uncovered a sophisticated, comprehensive analysis that has been overlooked in the century since their work was published. Michaelis and Menten not only analyzed initial velocity measurements but also fit their full time course data to the integrated form of the rate equations, including product inhibition, and derived a single global constant to represent all of their data. That constant was not the Michaelis constant, but rather V(max)/K(m), the specificity constant times the enzyme concentration (k(cat)/K(m) × E(0)).     

Nonfixed relationship of the Michaelis constant and maximum velocity with their corresponding rate constants

The Michaelis constant (K(m)) and V(mas) (E0k(cat)) values for two mutant sets of enzymes were studied from the viewpoint of their definition in a rapid equilibrium reaction model and in a steady state reaction model. The "AMP set enzyme" had a mutation at the AMP-binding site (Y95F, V67I, and V67I/L76V), and the "ATP set enzyme" had a mutation at a possible ATP-binding region (Y32F, Y34F, and Y32A/Y34A). Reaction rate constants obtained using steady state model analysis explained discrepancies found by the rapid equilibrium model analysis. (i) The unchanged number of bound AMPs for Y95F and the wild type despite the markedly increased K(m) values for AMP of the AMP set of enzymes was explained by alteration of the rate constants of the AMP step (k(+2), k(-2)) to retain the ratio k(+2)/k(-2). (ii) A 100 times weakened selectivity of ATP for Y34F in contrast to no marked changes in K(m) values for both ATP and AMP for the ATP set of enzymes was explained by the alteration of the rate constants of the ATP steps. A similar alteration of the K(m) and k(cat) values of these enzymes resulted from distinctive alterations of their rate constants. The pattern of alteration was highly suggestive. The most interesting finding was that the rate constants that decided the K(m) and k(cat) values were replaced by the mutation, and the simple relationships between K(m), k(cat), and the rate constants of K(m)1 = k(+1)/k(-1) and k(cat) = k(f) were not valid. The nature of the K(m) and k(cat) alterations was discussed.