Michaelis-Menten kinetics enzyme activity measurement

Furthermore, it can be shown that, in the limiting cases of first-order kinetics [Equation (11.35) also holds for this case] and zero-order kinetics, the equal and optimal sizes are exactly the same. As shown, the optimal holding times can be calculated very simply by means of Equation (11.40) and the sum of these can thus be used as a good approximation for the total holding time of equal-sized CSTRs. This makes Equation (11.31) an even more valuable tool for design equations. The restrictions are imposed by the assumption that the biocatalytic activity is constant in the reactors. Especially in the case of soluble enzymes, for which ordinary Michaelis-Menten kinetics in particular apply, special measures have to be taken. Continuous supply of relatively stable enzyme to the first tank in the series is a possibility, though in general expensive. A more attractive alternative is the application of a series of membrane reactors. 

These problems were overcome by immobilizing the enzyme. Since the usual methods for immobilization of laccase did not work, we adopted a new method, details of which will be described elsewhere (29). Reasonable measurements were possible with this technique. Typical patterns of laccase activity could be monitored via the changes of absorbance of 2,6 DMP and syringaldazine. When the reaction took place in organic solvents, the absorption spectra of the products were similar to those obtained for the same reaction in buffer. Furthermore, the catalytic action of the T. versicolor laccase followed Michaelis-Menten-kinetics in most of the organic solvents which were tested (see Table II for specific examples). 

Any enzyme-based analysis consists of measurement of enzyme activity with or without the presence of substances other than substrate. If these substances, when present, modulate the enzyme activity, that is, if they activate or inhibit the activity, then their amounts can be quantified by using classical Michaelis-Menten kinetics. Thus, an enzyme can be used to assay the follovting broad classes of substances substrates, activators, and inhibitors. 

A rigorous kinetic description of interfacial catalysis has been hampered by the ill-defined physical chemistry of the lipid—water interface (Martinek et ai, 1989). Traditional kinetic assumptions are undermined by the anisotropy and inhomogeneity of the substrate aggregate. For example, the differential partitioning of reactants (enzyme, calcium ion, substrate) and products (lysolecithins, fatty acids) between the two bulk phases prevents direct measurement of enzyme and substrate concentrations. This complicates dissection of the multiple equilibria that contribute to the observed rate constants. Only recently has it become possible to describe clearly the activity of SPLA2S in terms of traditional Michaelis— Menten kinetics. Such a description required the development of methods to reduce experimentally the number of equilibrium states available to the enzyme (Berg etai, 1991). 

In the authors judgment, catalytic action in the strict sense of the term, implying regeneration of the catalyst, has been rigorously proven in two cases. With other reactions, however, true catalysis has not been unequivocally established. Michaelis-Menten kinetics, indicative of the formation of a substrate-polymer complex, has been shown with each type of reaction. Some of the activities have been very weak, with reaction times for incomplete conversion of substrate measured in days. Others, although not as rapid as enzyme-catalyzed rates, are relatively fast, e.g., the catalytic decarboxylation of OAA by equimolar amounts of lysine residue in polymeric form was over 90% complete in less than 1 hour. 

How can we determine whether a reversible inhibitor acts by competitive or noncompetitive inhibition Let us consider only enzymes that exhibit Michaelis- Menten kinetics. Measurements of the rates of catalysis at different concentrations of substrate and inhibitor serve to distinguish the three types of inhibition. In competitive inhibition, the inhibitor competes with the substrate for the active site. The dissociation constant for the inhibitor is given by... 

Since, as in simple Michaelis-Menten kinetics, the reaction rate depends linearly on the enzyme concentration, the accuracy of activator determinations depends on the precision with which the enzyme concentration is known. Although it is not necessary to employ pure enzymes for the purpose of activator quantification, problems may arise if several isoenzymes exist of which only one is able to degrade the glycolipid substrate in the presence of the activator but all of them hydrolyze the artificial substrates employed for measuring the enzyme. This is, for example, the case for a-galactosidase, p-hexosaminidase, and arylsulfatase. In these cases separation of the isoenzymes, say by ion-exchange chromatography, is required. 

L-Iduronic Acid 2-Sulphate Sulphatases.—2,5-Anhydro-4-0-(a-L-idopyranuronosyl 2-sulphate)-D-[l- H]mannitol 6-sulphate has been recommended as a substrate for the measurement of L-iduronic acid 2-sulphate sulphatase activity, since it furnishes a radioactive monosulphate that is readily separated by paper chromatography or electrophoresis. The enzymic reaction followed Michaelis-Menten kinetics 3 mmol 1 ) and was strongly inhibited by phosphate ions. 

Getzin and Rosefield" have extracted from soil and partially purified an arylesterase which hydrolysed the insecticide malathion to its monoacid. Under the conditions of assay the reaction proceeded with zero order kinetics. Purification of the extracted enzymes included precipitation of co-extracted humic compounds, resulting in a 9.3 fold increase in specific activity. Following further treatment with ammonium sulphate and separation by ion-exchange chromatography, the specific activity of the partially-purified enzyme had increased to 22 times that of the crude soil extract, with an overall recovery of activity of 32%. The enzyme was optimally active at pH 7.0. Measurements of initial velocities of reaction for different substrate concentrations showed that the reaction conformed to Michaelis-Menten kinetics a Km value for the malathion esterase was calculated to be 2.12 x 10 % for the two enzyme levels tested. 

It can be shown that Km equals the concentration of the substrate at which the reaction velocity is one half of its maximum. The Michaelis-Menten constant is an important figure of merit for the enzyme. It is the measure of its activity. Although it describes a kinetic process, it has the physical meaning of dissociation constant, that is, a reciprocal binding constant. It means that the smaller the Km is, the more strongly the substrate binds to the enzyme. 

Before we can discuss the measurement of active-site concentration, we need to consider the kinetics of the substrate reaction. The majority of kinetic studies of enzymes are carried out on systems described by Scheme 11.16 where all terms have their usual meanings and where the intermediates have come to a steady-state concentration otherwise, studies of the kinetics of the pre-steady-state conditions usually require the use of specialist, fast reaction, equipment. The Michaelis-Menten equation, Equation 11.12, where all terms again have their usual meanings, can be derived from Scheme 11.16 when the system has reached a steady state at this point the values of [ES] and [P] are still very much less than that of [S] ... 

A number of questions might be addressed in the discussion of the results. How reproducible are the initial rate measurements (Note that runs D5 and E3 are duplicates also, runs El and the standard assay for enzyme activity have identical initial concentrations.) Are the enzyme-catalyzed data compatible with the Michaelis-Menten mechanism Do the data from both runs C and D follow apparent zero-order kinetics, and how does this agree with expectations based on comparing (S) with KJ Which of the two types of analysis, Lineweaver-Burk or Eadie-Hofstee, seems to give the better results and why How does 2 agree with the estimate of the turnover number based on the specific activity Are the acid-catalyzed data consistent with the rate law given in Eq. (10) ... 

Most measurements of glycosidase kinetics are carried out under steady-state conditions. Substrate is in large excess over enzyme and the reaction is monitored on a time-scale that is long compared with the reciprocals of the rate constants for individual molecular events, so that changes in the concentrations of various liganded and unliganded forms of the enzyme can be set to zero. If only one substrate is involved and the active sites are independent, eqn. (5.1), the Michaelis-Menten equation, holds ... 

The substrate concentration at which an enzyme reaches one-half of its maximal catalytic activity is often used as a measure of the sensitivity of an enzyme to substrate saturation. This particular substrate concentration usually has about the same numerical value as Km, sometimes known as the Michaelis-Menten constant for the enzyme. The maximum rate of reaction per mole of enzyme is often given the symbol cat. and the maximum rate of reaction for a given enzyme concentration is often symbolized as Vmax- Often, the kinetics of more complex enzyme-catalyzed reactions can be placed in this form under some restricted range of conditions [1]. 

In direct analogy to the Michaelis-Menten mechanism for reaction of enzyme with a substrate, the inactivator, I, binds to the enzyme to produce an E l complex with a dissociation constant K. A first-order chemical reaction then produces the chemically reactive intermediate with a rate constant k. The activated species may either dissociate from the active site with a rate constant to yield product, P, or covalently modify the enzyme ( 4). The inactivation reaction should therefore be a time-dependent, pseudo-first-order process which displays saturation kinetics. This is verified by measuring the apparent rate constant for the loss of activity at several fixed concentrations of inactivator (Fig. lA). The rate constant for inactivation at infinite [I], itj act (a function of k2, k, and k4), and the Ki can be extracted from a double reciprocal plot of 1/Jfcobs versus 1/ 1 (Fig. IB) (Kitz and Wilson, 1962 Jung and Metcalf, 1975). A positive vertical... 

Quantitation of small molecules with enzymatic methods provides insight into the ccMicentration and activity of the proteins associated with those molecules. A great variety of these enzymatic assays have been carried out in microfluidic devices. Another function of enzymatic assays is in kinetics measurements of properties of enzymes such as the Michaelis-Menten constant (the concentration of substrate when the reactimi rate is half the maximum rate) and the turnover number (the number of moles of substrate that are converted to product per catalytic site per unit time) are vital to understanding the mechanics of the proteome and are used to characterize the effects of known drugs and discover new ones. 

Biosensors require highly active enzymes/biomolecules therefore, the immobilisation methods must be chosen in such a way that they can achieve a high sensitivity and functional stability. This is important for economic reasons also. The measurable activity gives an idea about the biocatalytic efficiency of an immobilised enzyme. The rate of substrate conversion should rise linearly with enzyme concentration. The measured reaction rates depend not only on the substrate concentration and the kinetic constants (Michaelis Menten constant) and (maximum velocity of the reaction) but also on the immobilisation effects. The following effects have been observed [157] due to the immobilisation process ... 

---