Michaelis equation

In our previous work [63], we studied the hydrolysis kinetics of lipase from Mucor javanicus in a modified Lewis cell (Fig. 4). Initial hydrolysis reaction rates (uri) were measured in the presence of lipase in the aqueous phase (borate buffer). Initial substrate (trilinolein) concentration (TLj) in the organic phase (octane) was between 0.05 and 8 mM. The presence of the interface with octane enhances hydrolysis [37]. Lineweaver-Burk plots of the kinetics curve (1/Uj.] = f( /TL)) gave straight lines, demonstrating that the hydrolysis reaction shows the expected kinetic behavior (Michaelis-Menten). Excess substrate results in reaction inhibition. Apparent parameters of the Michaelis equation were determined from the curve l/urj = f /TL) and substrate inhibition was determined from the curve 1/Uj.] =f(TL) ... 

The Michaelis equation describes the relationship between substrate concentration and the rate of an enzymt-catalysed reaction. 

Substituting in equation [6] results in the common form of the Michaelis equation ... 

Along with theisoelectricpoint determined from electrokinetics, one can also distinguish the isoionic point, which is defined as the pH corresponding to equal number of ionized acidic and basic groups. The position of isoionic point, pH , is primarily influenced by the strongest acidic and basic groups with the dissociation constants of Ka and Kb, respectively. For a 1 1 electrolyte the Michaelis equation,... 

The rate of cell growth practically follows the same expression of the rate, according to Michaelis equation. However, we must also take into acconnt the concentration of cells, as follows ... 

In the treatments discussed so far, it has been assumed that the back reaction could be neglected. The reactions catalysed by many enzymes are essentially irreversible or the products are immediately subject to further reaction, so that the assumption of irreversibility is valid. However, if the reaction is reversible, the Michaelis equation must be modified. Haldane suggested a notation in which V, and V, are the maximal velocities in the forward and reverse directions, and and K ,p are the Michaelis constants for the substrate and product. The Haldane relationship for a system with a single substrate and single product is then = V,K pA, K s. 

The mechanism described in Figs. 2 and 3 accounts for most of the characteristics of enzyme-catalyzed reactions and will be used in the present chapter for this purpose. As previously described, the Michaelis equation and its modifications usually account for the influence of glycoside concentration on the rate of reaction. The action of various substances such as... 

Several methods for transformation of the Michaelis equation were proposed for finding K and v,. They are shown in Fig. 14.1. 

Fig. 14.1. Types of anamorphoses used for the determination of the parameters in the Michaelis equation (K is the Michaelis constant v ax is the maximum rate 1—3 correspond to the systems with different parameters (a), Km (b), or substrate concentration (e)).

The values of the constants in the Michaelis equation can be found by the analysis of the data on the pre-stationary kinetics, for example, from the kinetic curve of changing the concentration of the ES complex... 

If the reaction is carried out at the saturating concoitration of one of the substrates, the equation presorted can be reduced to the Michaelis equation. 

The experimental plot of the reaction rate vs. initial eutyme concoitration is a criterion for the dissociative mechanism. The shift of the equilibrium due to different bindings of the substrate by the dimmer and monomer results in die deviation from the simple Michaelis equation because the effective binding constant K becomes a function of the local Michaelis constants for the dimmer KmE and monomer K e and initial substrate concentration [S]o... 

From Equation (16) and the Michaelis equation the modification of the apparent K )app due to the potential gradient is ... 

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