Michaelis-Menten equation kinetic parameters

The peroxidase activity of immobilized catalase on the oxidation of phenol has been studied. The immt ilization was carried out from catalase solutions with pH < 3,5 on two kinds of soot differing in the average size of the particles building them up. The effect of the initial concentration of ph iol on the rate of its peroxidase oxidation by catalase immobilized on the soot of finer-graWd structure has been studied. The relationships obtained are described by the equation of Michaelis-Menten. The kinetic parameters (the constant of Michaelis - Km. the maximum reaction rate - V, the rate constant - k and the activation energy - of the process were calculated. It was found that catalase adsorbed on the soot of larger globular particles does not take part in the peroxidase oxidation of phenol. 

The Michaelis-Menten Equation 11-15 is not well suited for estimation of the kinetic parameters and Reananging Equation 11-15 gives various options for plotting and estimating the parameters. 

In evaluation of kinetic parameters, the double reciprocal method is used for linearisation of the Michaelis-Menten equation (5.7.3). 

The nonlinear form of the Michaelis-Menten equation, 10.2-9, does not permit simple estimation of the kinetic parameters (Km and V ). Three approaches may be adopted ... 

The phosphorylation of each substrate was monitored via a one- or two-substrate reaction in real time and the kinetic parameters (Vmca, Km, kcat, and kcJKm) were determined. Figure 6.54 shows the results of the evaluations of velocity with respect to substrate (Kemptide and CREBtide) concentrations. The data were fitted using the Michaelis-Menten equation to determine the kinetic parameters shown in Table 6.8. The V , of phosphor-Kemptide (105.57 pM/min) was approximately 4.3-fold larger than the V , for CREBtide (24.33 pM/min) although both peptide substrates had similar... 

Most problems associated with approximate kinetics are avoided when Michaelis Menten-type rate equations are utilized. Though this choice sacrifices the possibility of analytical treatment, reversible Michaelis Menten-type equations are straightforwardly consistent with fundamental thermodynamic constraints, have intuitively interpretable parameters, are computationally no more demanding than logarithmic functions, and are well known to give an excellent account of biochemical kinetics. Consequently, Michaelis Menten-type kinetics are an obvious choice to translate large-scale metabolic networks into (approximate) dynamic models. It should also be emphasized that simplified Michaelis Menten kinetics are common in biochemical practice almost all rate equations discussed in Section III.C are simplified instances of more complicated rate functions. 

The parameterization of the remaining reactions is less complicated. For simplicity, the rate v2(TP,ADP) is assumed to follow mass-action kinetics, giving rise to saturation parameters equal to one. Finally, the ATPase represents the overall ATP consumption within the cell and is modeled with a simple Michaelis Menten equation, corresponding to a saturation parameter 6 e [0,1], The saturation matrix is thus specified by four nonzero entries ... 

A kinetic parameter, introduced by Koshland, to indicate the ratio of substrate concentrations needed to achieve reaction velocities equal to Q.f max and 0.9Fniax-For an enzyme obeying the Michaelis-Menten equation, o.9/ o.i equals 81, indicating that such enzymes exhibit modest sensitivity of reaction rate relative to changes in the substrate concentration. Many positively cooperative enzymes have So.g/So.i values between five and ten, indicating that they can be turned on or off over a relatively narrow substrate concentration range. 

Figure 3.6 Evaluation of kinetic parameters in Michaelis-Menten equation (a) Lineweaver-Burk plot, (b) C /r versus plot, and (c) Eadie-Hofstee plot.

The constant Km defined in equation (23) is called the Michaelis constant and is one of the key parameters in enzyme kinetics. It is a simple matter to proceed from this point to an expression comparable to the Henri-Michaelis-Menten equation (18), but with Km in place of Ks. First, rearranging equation (23) gives... 

Another approach for the determination of the kinetic parameters is to use the SAS NLIN (NonLINear regression) procedure (SAS, 1985) which produces weighted least-squares estimates of the parameters of nonlinear models. The advantages of this technique are that (1) it does not require linearization of the Michaelis-Menten equation, (2) it can be used for complicated multiparameter models, and (3) the estimated parameter values are reliable because it produces weighted least-squares estimates. 

A substrate is decomposed in the presence of an enzyme according to the Michaelis-Menten equation with the following kinetic parameters ... 

The Monod kinetic parameters, and Ks, cannot be estimated with a series of batch runs as easily as the Michaelis-Menten parameters for an enzyme reaction. In the case of an enzyme reaction, the initial rate of reaction can be measured as a function of substrate concentration in batch runs. However, in the case of cell cultivation, the initial rate of reaction in a batch run is always zero due to the presence of a lag phase, during which Monod kinetics does not apply. It should be noted that even though the Monod equation has the same form as the Michaelis-Menten equation, the rate equation is different. In the Michaelis-Menten equation,... 

In the oxidation of alkanethiols to disulfides with chloramine-T (CAT), in alkaline solution, the proposed reactive species are hypochlorous acid and TsNCl- anion. A correlation of reaction rate with Taft s dual substituent parameter equation yielded p = -5.28 and 5 = -2.0, indicating the rate-enhancing effect of electron-donating substituents.133 Michaelis-Menten-type kinetics have been observed in the oxidation of atenolol with CAT in alkaline solutions. TsNHCl is assumed to be reactive species. A mechanism has been suggested and the activation parameters for the rate-determining step were calculated.134 The Ru(III)-catalysed oxidation of diphenyl... 

This is known as the Michaelis-Menten equation, where there are two kinetic parameters, the maximum velocity V = k3[E] and the Michaelis constant KS(K J = fca/ki-... 

The steady-state treatment of enzyme kinetics assumes that concentrations of the enzyme-containing intermediates remain constant during the period over which an initial velocity of the reaction is measured. Thus, the rates of changes in the concentrations of the enzyme-containing species equal zero. Under the same experimental conditions (i.e., [S]0 [E]0 and the velocity is measured during the very early stage of the reaction), the rate equation for one substrate reaction (uni uni reaction), if expressed in kinetic parameters (V and Ks), has the form identical to the Michaelis-Menten equation. However, it is important to note the differences in the Michaelis constant that is, Ks = k2/k1 for the quasi-equilibrium treatment whereas Ks = (k2 + k3)/k i for the steady-state treatment. 

Kinetic Analysis. The kinetic parameters were obtained by iterative non-linear curve fitting of raw data (current generated versus the substrate concentration).The data fitted a modified Michaelis-Menten equation ... 

Based on the result from the IC50 determination, determination of additional kinetic parameters such as Ki and the inhibition mode are useful (variation of the substrate concentration e.g. Km/4 1 Km with time). Transformation of the Michaelis-Menten equation are used both for calculation the Ki value as well as for graphical depiction of the type of inhibition (e.g. direct plot ([rate]/[substrate], Dixon plot [l/rate]/[inhibitor], Linewaver-Burk plot [l/rate]/[l/substrate] or Eadie-Hofstee plot [rate]/[rate/substrate]). 

Fig. 9 2 Lineweaver-Burk graphical procedure for determining the two steady-state kinetic parameters in the Michaelis-Menten equation.

Interestingly, a fully appropriate model was developed at the same time as the Langmuir model using a similar basic approach. This is the Michaelis-Menten equation which has proved to be so useful in the interpretation of enzyme kinetics and, thereby, understanding the mechanisms of enzyme reactions. Another advantage in using this model is the fact that a graphical presentation of the data is commonly used to obtain the reaction kinetic parameters. Some basic concepts and applications will be presented here but a more complete discussion can be found in a number of texts. ... 

Under certain conditions the steady state has the form of the Michaelis-Menten equation (Section 9.1.2). Nevertheless, the equation for APase contains more factors than that of the simple reaction given in Section 9.1.2. For detailed kinetic considerations, Fernley (1971) and Reid and Wilson (1971) should be consulted. The simplified representation of Fig. 10.3 is also often complicated by other parameters e.g. only one active site per dimer seems to be active for the bacterial enzyme at low substrate coneentrations (<10" M), whereas at higher concentrations both sites are active. Substrate activation, at high substrate concentrations (>10" M), was noted by Heppel et al. (1962) but not at high ionic strength (Simpson and Vallee, 1970). 

Michaelis-Menten equations often do not apply for enzymatic reactions at surfaces, such as bacterial walls (McLaren and Packer, 1970). Precise kinetic parameters, which can only be obtained with well-characterized low molecular weight substrates, are complicated by non-productive binding of small substrates, i.e. binding outside of the catalytic site. 

The experimental and mathematical models were divided into two hierarchical steps, as seen in Fig. 5. First, hydrolysis experiments were conducted, and the hydrolysis time profile was matched to hydrolysis rate equations. A separate hydrolysis-only model was used to match the hydrolysis data to Michaelis-Menten based kinetics and to solve for unknown parameters. Second, SSF experiments were conducted using identical enzyme loading, and these datasets were matched to a complete SSF model. The SSF model incorporated the hydrolysis parameters from the first step and was used to solve for the unknown fermentation parameters using Monod-based kinetics. 

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