Tag Archives: Michaelis-Menten equation
On true and apparent michaelis constants in enzymology. I. Differences
S. O. Karakhim
Palladin Institute of Biochemistry, National Academy of Sciences of Ukraine, Kyiv;
e-mail: laserlab@biochem.kiev.ua
Differences between both true and apparent rate constants and Michaelis constants have been examined. Rate constants of elementary stages of real mechanisms are true ones. True Michaelis constant Km is expressed by equation Km = (k-1 + k2)/k1. True constants may be determined for reliable mechanism only for which the equation of initial rate was obtained which displays physical sense of these constants and permits to find the method of their calculation. The true constant values are independent of concentration of reactants, activators, inhibitors, extraneous agents and pH.
The apparent rate constants are such constants of the composite reaction which are observed when this reaction is described by the equation of simple reaction. Michaelis constant calculated by a half of the ultimate constant is an apparent constant. The apparent constants may be functions of several true rate constants and/or concentrations of reacting substances. The evident physical sense of apparent constants being absent, only formal relation between the reaction rate and reactant concentration independent of the investigated mechanism is provided.
On true and apparent Michaelis constants in enzymology. III. Is it linear dependence between apparent Michaelis constant and limiting rate and is it possible to determine the substrate constant value using this dependence?
S. O. Karakhim
Palladin Institute of Biochemistry, National Academy of Sciences of Ukraine, Kyiv;
e-mail: laserlab@biochem.kiev.ua
The Slater-Bonner method which is used for graphic determination of substrate constant (Ks) by linear dependence of apparent Michaelis constant (Kmapp) on the limiting rate (Vapp) of enzyme-catalysed reactions with activator participation has been critically analysed. It has been shown that although it is possible to record the mechanisms of such reactions as a scheme similar to Michaelis-Menten model which allow to find correlation Kmapp and Vapp as equation Kmapp = Ks + Vapp/k1[E]0 ([E]0 is a total enzyme concentration, k1 is a rate constant of enzyme-substrate complex formation from free enzyme and substrate) in order to calculate Ks and individual rate constants (k1, k-1), but this approach for investigation of all reactions with activator participation ought not to be used. The above equation is not obeyed in general, it may be true for some mechanisms only or under certain ratios of kinetic parameters of enzyme-catalysed reactions.
On true and apparent Michaelis constants in enzymology. II. Is the equation K(m)(app) = K(s) + k(cat)/k(1) true for enzyme-catalysed reactions with activator participation?
S. O. Karakhim
Palladin Institute of Biochemistry, National Academy of Sciences of Ukraine, Kyiv;
e-mail: laserlab@biochem.kiev.ua
The article is dedicated to analysis of equation which expresses apparent Michaelis constant Kmapp of enzyme-catalysed reactions with activator participation by means of the substrate constant Ks and rate constant of enzyme-substrate complex decomposition kcat. It has been shown that although it is possible to record the mechanisms of such reactions as a scheme similar to Michaelis-Menten model and to derive equation of apparent Michaelis constant as Kmapp = Ks + kcat/k1, but this approach cannot be used for investigation of all reactions with activator participation. The equation mentioned above is not obeyed in the general case, it may be true for some mechanisms only or under certain ratio of kinetic parameters of enzyme-catalysed reactions.
Influence of Са(2+) on kinetic parameters of pancreatic acinar mitochondria in situ respiration
B. O. Manko, V. V. Manko
Ivan Franko National University of Lviv, Ukraine;
e-mail: mankobo@gmail.com
The dependence of respiration rate of rat permeabilized acinar pancreacytes on oxidative substrates concentration was studied at various [Ca2+] – 10-8–10-6 M. Pancreacytes were permeabilized with 50 µg of digitonin per 1 million cells. Respiration rate was measured polarographically using the Clark electrode at oxidation of succinate or pyruvate either glutamate in the presence of malate. Parameters of Michaelis-Menten equation were calculated by the method of Cornish-Bowden or using Idi-Hofsti coordinates and parameters of Hill equation – using coordinates {v; v/[S]h}. In the studied range of [Ca2+] the kinetic dependence of respiration at pyruvate oxidation is described by the Michaelis-Menten equation, and at oxidation of succinate or glutamate – by Hill equation with h = 1.11–1.43 and 0.50–0.85, respectively. The apparent constant of respiration half-activation (K0.5) did not significantly change in the studied range of [Ca2+] while at 10-7 M Ca2+ it was 0.90 ± 0.06 mM for succinate, 0.096 ± 0.007 mM for pyruvate and 0.34 ± 0.03 mM for glutamate. Maximum respiration rate Vmax at pyruvate oxidation increased from 0.077 ± 0.002 to 0.119 ± 0.002 and 0.140 ± 0.002 nmol O2/(s·million cells) due to the increase of [Ca2+] from 10-7 to 5×10-7 or 10-6 M, respectively. At oxidation of succinate or glutamate Ca2+ did not significantly affect Vmax. Thus, the increase of [Ca2+] stimulates respiration of mitochondria in situ of acinar pancreacytes at oxidation of exogenous pyruvate (obviously due to pyruvate dehydrogenase activation), but not at succinate or glutamate oxidation.