Michaelis constant calculation

If, as it is usually done, the interaction of enzyme with glycal is studied in the presence of substrate S having Michaelis constant K , the observed rate constant k pp, for the approach to the steady-state inhibition has to be corrected for the competition of substrate for the free enzyme, in order to calculate the rate constants kp , kp, and k yj, from the experimental data. 

Michaelis constant K for D-glyca] hydration. Approximate value calculated from specific activity with M, 50,000. 

Using these equations, Lowe and Walmsley [48] have calculated the dissociation constants for sugar binding at the extracellular surface of the membrane (K s = b a in Fig. 2) and at the cytoplasmic surface (K. = elf = bid) x [dgich]) from the estimated rate constants for carrier re-orientation and the measured Michaelis constants. The dissociation constant for binding at the extracellular surface of the membrane, calculated in this way, is approximately lOmM and is largely unaffec-... 

Calculate the maximum rate parameter, Vmax, and the Michaelis constant, Km, from these... 

The values lor the Michaelis constant i A. i anJ the iiiasimiim velocits. are calculated from the intercepts on each of the axis which give the reciprocals of the Am and the Vmax. 

From the intercepts and slopes Vg, k2 and Kg could, be calculated. For the analog DMBA the values of Vs and k2 were directly taken from the constant maximum rate as shown in Figure 5. Most of our results are gathered in Table I ( 1 5,2J, 2 2 ), which demonstrates that the observed increase in rate with a is governed by an increase of the electron transfer rate constant, k2, whereas the Michaelis constant, Kg, changed in the wrong way considering eq. (4). ... 

Figure 1. Plot of v/V ax versus the millimolar concentration of total substrate for a model enzyme displaying Michaelis-Menten kinetics with respect to its substrate MA (i.e., metal ion M complexed to otherwise inactive ligand A). The concentrations of free A and MA were calculated assuming a stability constant of 10,000 M k The Michaelis constant for MA and the inhibition constant for free A acting as a competitive inhibitor were both assumed to be 0.5 mM. The ratio v/Vmax was calculated from the Michaelis-Menten equation, taking into account the action of a competitive inhibitor (when present). The upper curve represents the case where the substrate is both A and MA. The middle curve deals with the case where MA is the substrate and where A is not inhibitory. The bottom curve describes the case where MA is the substrate and where A is inhibitory. In this example, [Mfotai = [Afotai at each concentration of A plotted on the abscissa. Note that the bottom two curves are reminiscent of allosteric enzymes, but this false cooperativity arises from changes in the fraction of total "substrate A" that has metal ion bound. For a real example of how brain hexokinase cooperatively was debunked, consult D. L. Purich H. J. Fromm (1972) Biochem. J. 130, 63.

B 2. Design an experiment using the immobilized peroxidase to calculate the Michaelis constant, Ku, and the maximum velocity, Vmix. 

The parameters of the Michaelis-Menten type kinetics were calculated for the reactions and are summarized in Table II. The apparent Michaelis constant values (Km) are rather large, indicating that the concentration of the complex at the equilibrium state is not high, unlike ordinary enzymatic reactions. The ratio of kJKm against the second-order rate constant with sulfuric acid (k2) can be considered to be an indication of the rate enhancement. The ratio increased with increasing mole fraction of the vinyl alcohol repeating unit in the copolymer and with... 

From the slope, which is 0.02 s, we can calculate the Michaelis constant, K ... 

Temperature dependence of Km and Vmax- Since both Km and Vmax are encountered in the calculation of the inhibition constant (Kj) at various temperatures, the temperature dependence of Km and Vmax should be a priori determined. Figure 1 shows the temperature dependence of Michaelis constant (Km)... 

Once the rate constant for reaction is known, it then becomes possible to calculate the enthalpy for the reaction for all time points of the reaction and obtain an average for the lifetime of the first-order reaction. Once the enthalpy is found, it is possible to calculate the value of from a consideration of the zero-order output and hence the Michaelis constant is now accessible from the slope of the first-order In dq/dt vs. t plot (the slope of this plot is equal to... 

The enzyme urease, which catalyzes the hydrolysis of urea, is widely used to determine urea in blood. Details of this application are given in Feature 29-3 on page 901. The Michaelis constant for urease at room temperature is 2.0 mM, and k2 = 2.5 X 10 s at pH 7.5. (a) Calculate the initial rate of the reaction when the urea concentration is 0.030 niM and the urease concentration is 5.0 p,M, and (b) find v, ax-... 

Numerically calculated values of q are available when only substrate diffusion in Michaelis-Menten type kinetics is considered. They can be presented in graphical form, expressing q as a function of the Thiele modulus and of a dimensionless substrate concentration or occasionally in its reciprocal form as a dimensionless Michaelis constant f) according to Lee and Tsao [84] (reviewed in [82,83] see Table 3 for explanation of symbols), hence ... 

Penicillin G amidase was immobilized on pre-fabricated carriers or insolubUized as crosslinked crystals. Eupergit-related value for R (mean particle radius of swelled carrier) was 80 pm [87]. V , (assuming maximum intrinsic activity per accessible catalyst volume, based on active enzyme molecules 1 unit=l pmol min at 28°C) was 90 and 170 U cm for Eupergit C and 250L, respectively [87]. D ff (effective diffusion coefficient) was taken from literature [87] or calculated as shown in the text. Km (intrinsic Michaelis constant) was uniformly taken as 13 mM [87] and S = 268 mM corresponds to the substrate concentration at catalyst surface of a 10 % solution of penicillin G salt, q was calculated according to Atkinson et al. for spherical particles [85]. For simplification, surface and pore related indices have been omitted. 

Enzyme catalysis—Michaelis constant (key equation 22.14) using spreadsheets to calculate, pp. 646, 649... 

There is evidence that the specificity of the histidine decarboxylase of rat foetal liver may be even greater than was originally suspected. Thus, not only is its activity confined to L-histidine, but it appears to be further restricted to one particular ionic form of histidine. Over the pH range regarded as optimal for this enzyme, the substrate, histidine, exists as a mixture of ionic forms (V, VI, VII, VIII), and the concentration of each species present in a given solution can be calculated from the Henderson-Hasselbach equation. When the Michaelis constant for the decarboxylation was measured in terms of the... 

Plot V against [S], l/v against 1/[S], and u/[S] against a, and from each plot calculate the Michaelis constant and the limiting rate V. 

The Thiele modulus, calculated from reaction rate data, diffusion length, and diffusion coefficient, can be used to evaluate internal mass transfer effects. Expressed with the Michaelis constant and maximum reaction velocity, the Thiele modulus is given by... 

Michaelis constant was calculated to be 0.12 and 0.045, respectively, for cupric sulfate and nickel sulfate. 

Using Eq. (6.61), it is possible to construct a curve showing how the value of the Michaelis constant varies with pH. To do this, we need to assume values for Kj, Ki, and K2, which will be taken as 5 x 10 , 10 , and 10 , respectively. By varying [H ], values can be computed for Km. To simplify the drawing, we will calculate the negative logarithm of Km... 

The Michaelis constant (Ka), dimension [concentration]. One can easily appreciate from Rg. 4 that the value of the Michaelis constant is obtained when Vo = Vmai/2. Ka is equal to dissociation constant of the enzyme-substrate complex only in the simple Michaelis-Menten mechanism, and in all other cases, it is a complex function of several rate constants (Table 1). However, Ka maybe treated for some purposes as an apparcnr dissociation constant for example, the concentration of free enzyme in solution may be calculated from the relationship ... 

The Michaelis constants and inhibition constants are now rather complex relationships ofMichaehs pH functions. However, the relationships expressed by Eqs. (14.42)-(14.45) are each a function of a single Michaelis pH function (Laidler, 1955 Schulz, 1994). Thus, in this particular mechanism, by a pmdent choice of parameters, one can calculate the pXa values of all forms of the enzyme in reaction (14.34). For example, Eq. (14.42) can be expanded to obtain... 

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