Enzymes substrate concentration

The rate of reaction 9t0 depends upon the catalytic rate constant and upon the enzyme-substrate concentration. 

Enzyme-substrate concentration Enzyme-substrate-inhibitor concentration Volumetric flowrate Volumetric flowrate of feed Volumetric flowrate of recycle stream Dimensionless substrate concentration... 

Analytical Determinations Involving Rate Assays. Rate assays must be used to determine the concentration of enzyme, of an activator, or of an inhibitor, and they may be used to determine the concentration of a compound which serves as a substrate for an enzyme. Substrate concentration may also be determined by a total change method. The advantages of a rate assay over a total change method are its speed and the requirement for less enzyme. 

The overall advantage of enzymatic dismutation of superoxide is illustrated in Fig. 2, where the rate constants for dismutation for three of the enzyme classes are plotted as a function of pH on a graph that also has the self-dismutation rate constants for superoxide/perhy-droxyl radical plotted as a function of pH. It should be noted, though, that the enzymatic rate constants are catalytic and therefore only depend upon the enzyme concentiation whereas the self-dismu-tation is bimolecular in superoxide. This leads to very important ramifications with regards to the enzyme-substrate concentrations. Figure 3 illustrates three different scenarios and shows the relative rate constants at different extremes of [S0D] [02 ]. The in vivo implications of this are profound. 

Brooks, S. P. J. Storey, K. B. (1993). Control of glycolytic enzyme binding effect of changing enzyme substrate concentrations on in vivo enzyme distributions. Mol. Cell. Biochem. 122, 1-7. 

Using this techniquegOn immobilized enzymes substrate concentrations down to 10"° - 10 M can could be determined. As the assay principle is applicable in all cases where volatile products are formed, one might imagine a wide range of applications of the technique (40). 

Another method would be to consider the constants in the model to be random variables, each with their own associated distribution. To do this, we would need measurements on several enzyme-substrate concentrations for i = 1,..., n, where i indexes the experiment performed. 

The pyroelectric effect can also be employed as a sensor of an enzymic reaction. Dessy et al (57) placed two poly(vinylldene fluoride) films into contact, with one exposed surface coated with enzyme and contacting a flow injection sample stream. The potential resulting from the thermal bias across the films could be related to the enzyme substrate concentration. 

In Scheme (6.121), the numbering of steps correspond to numbers in Fig. 6.61. The number of independent routes can be calculated following the Horiuti-Temkin rule (Eq. 4.4). There are six steps in this mechanism (the far right vertical line in Fig. 6.61 is the same as step 3), four intermediates (Ei, EiS, E2, E2S) and one balance equation (the sum of all free enzyme and enzyme-substrate concentrations is equal to the total enzyme concentration). This gives three independent routes. The dependent zero routes relate the constants of steps. These routes can be obtained from the independent ones in the following way — isf As the overall... 

Michaelis constant An experimentally determined parameter inversely indicative of the affinity of an enzyme for its substrate. For a constant enzyme concentration, the Michaelis constant is that substrate concentration at which the rate of reaction is half its maximum rate. In general, the Michaelis constant is equivalent to the dissociation constant of the enzyme-substrate complex. 

To be analytically useful equation 13.16 needs to be written in terms of the concentrations of enzyme and substrate. This is accomplished by applying the steady-state approximation, in which we assume that the concentration of ES is essentially constant. After an initial period in which the enzyme-substrate complex first forms, the rate of formation of ES... 

A plot of equation 13.18, shown in figure 13.10, is instructive for defining conditions under which the rate of an enzymatic reaction can be used for the quantitative analysis of enzymes and substrates. Eor high substrate concentrations, where [S] Kjq, equation 13.18 simplifies to... 

Plasteins ate formed from soy protein hydrolysates with a variety of microbial proteases (149). Preferred conditions for hydrolysis and synthesis ate obtained with an enzyme-to-substrate ratio of 1 100, and a temperature of 37°C for 24—72 h. A substrate concentration of 30 wt %, 80% hydrolyzed, gives an 80% net yield of plastein from the synthesis reaction. However, these results ate based on a 1% protein solution used in the hydrolysis step this would be too low for an economical process (see Microbial transformations). 

Eor measurement of a substrate by a kinetic method, the substrate concentration should be rate-limiting and should not be much higher than the enzyme s K. On the other hand, when measuring enzyme activity, the enzyme concentration should be rate-limiting, and consequentiy high substrate concentrations are used (see Catalysis). 

Enzyme Assays. An enzyme assay determines the amount of enzyme present in sample. However, enzymes are usually not measured on a stoichiometric basis. Enzyme activity is usually determined from a rate assay and expressed in activity units. As mentioned above, a change in temperature, pH, and/or substrate concentration affects the reaction velocity. These parameters must therefore be carefully controlled in order to achieve reproducible results. 

The Michaelis-Menten scheme nicely explains why a maximum rate, V"max, is always observed when the substrate concentration is much higher than the enzyme concentration (Figure 11.1). Vmax is obtained when the enzyme is saturated with substrate. There are then no free enzyme molecules available to turn over additional substrate. Hence, the rate is constant, Vmax, and is independent of further increase in the substrate concentration. 

The substrate concentration when the half maximal rate, (Vmax/2), is achieved is called the Km. For many simple reactions it can easily be shown that the Km is equal to the dissociation constant, Kd, of the ES complex. The Km, therefore, describes the affinity of the enzyme for the substrate. For more complex reactions, Km may be regarded as the overall dissociation constant of all enzyme-bound species. 

Figure 11.1 A plot of the reaction rate as a function of the substrate concentration for an enzyme catalyzed reaction. Vmax is the maximal velocity. The Michaelis constant. Km, is the substrate concentration at half Vmax- The rate v is related to the substrate concentration, [S], by the Michaelis-Menten equation ...

Equation 1-106 predicts that the initial rate will be proportional to the initial enzyme concentration, if the initial substrate concentration is held constant. If the initial enzyme concentration is held constant, then the initial rate will be proportional to the substrate concentration at low substrate concentrations and independent of the substrate concentration at high substrate levels. The maximum reaction rate for a given total enzyme concentration is... 

Kinetic studies involving enzymes can principally be classified into steady and transient state kinetics. In tlie former, tlie enzyme concentration is much lower tlian that of tlie substrate in tlie latter much higher enzyme concentration is used to allow detection of reaction intennediates. In steady state kinetics, the high efficiency of enzymes as a catalyst implies that very low concentrations are adequate to enable reactions to proceed at measurable rates (i.e., reaction times of a few seconds or more). Typical enzyme concentrations are in the range of 10 M to 10 ], while substrate concentrations usually exceed lO M. Consequently, tlie concentrations of enzyme-substrate intermediates are low witli respect to tlie total substrate (reactant) concentrations, even when tlie enzyme is fully saturated. The reaction is considered to be in a steady state after a very short induction period, which greatly simplifies the rate laws. 

The concentration of the enzyme-substrate complex from Equation 11-3 is... 

Lineweaver-Burk plot Method of analyzing kinetic data (growth rates of enzyme catalyzed reactions) in linear form using a double reciprocal plot of rate versus substrate concentration. 

Saturation kinetics are also called zero-order kinetics or Michaelis-Menten kinetics. The Michaelis-Menten equation is mainly used to characterize the interactions of enzymes and substrates, but it is also widely applied to characterize the elimination of chemical compounds from the body. The substrate concentration that produces half-maximal velocity of an enzymatic reaction, termed value or Michaelis constant, can be determined experimentally by graphing r/, as a function of substrate concentration, [S]. 

FIGURE 14.7 Substrate saturation curve for au euzyme-catalyzed reaction. The amount of enzyme is constant, and the velocity of the reaction is determined at various substrate concentrations. The reaction rate, v, as a function of [S] is described by a rectangular hyperbola. At very high [S], v= Fnax- That is, the velocity is limited only by conditions (temperature, pH, ionic strength) and by the amount of enzyme present becomes independent of [S]. Such a condition is termed zero-order kinetics. Under zero-order conditions, velocity is directly dependent on [enzyme]. The H9O molecule provides a rough guide to scale. The substrate is bound at the active site of the enzyme. 

The interpretations of Michaelis and Menten were refined and extended in 1925 by Briggs and Haldane, by assuming the concentration of the enzyme-substrate complex ES quickly reaches a constant value in such a dynamic system. That is, ES is formed as rapidly from E + S as it disappears by its two possible fates dissociation to regenerate E + S, and reaction to form E + P. This assumption is termed the steady-state assumption and is expressed as... 

That is, k t/K,n is an apparent second-order rate constant ior the reaction of E and S to form product. Because A , is inversely proportional to the affinity of the enzyme for its substrate and is directly proportional to the kinetic efficiency of the enzyme, A , provides an index of the catalytic efficiency of an enzyme operating at substrate concentrations substantially below saturation amounts. 

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