Progress curve for enzyme-catalyzed reaction

Programmed cell death. See Apoptosis Progress curve for enzyme-catalyzed reaction 455 Proinsulin 519 Projection formula Fisher 42 Newman 44... 

Duggleby, R. G. (1994). Analysis of progress curves for enzyme-catalyzed reactions application to unstable enzymes, coupled reactions, and transient state kinetics. Bkdhimica et Biophyska Acta (BBA) - General subjects, vol. 1205, no.2, (April 1994), pp. 268-274, ISSN 0304-4165... 

An algorithm for solving integrated rate equations, thereby facilitating the systematic analysis of progress curves of enzyme-catalyzed reactions. 

Figure 4-6 Progress curve for a catalyzed reaction where the initial reaciant (substrate) concentration, [S]o, is significantly greater than the initial enzyme concentration, [E],. As the ratio of [S]o/[E]i increases, the steady-state region accounts for an increasing fraction of the total reaction time. T represents the presteady-state interval.

Figure 4.3 Product progress curves for an enzyme-catalyzed reaction in the absence (closed circles) and presence open circles) of an inhibitor at a concentration that reduces the reaction rate by 50%. Inset The initial velocity phase of these progress curves.

A straight line whose perpendicular distance from a curve becomes progressively smaller as the distance from the origin at [0,0] becomes greater. For example, in a plot of velocity versus [Substrate Concentration] for an enzyme-catalyzed reaction, the asymptote reaches the maximal velocity when the enzyme molecules become saturated with substrate. 

Figure E5.7 displays the kinetic progress curve of a typical enzyme-catalyzed reaction and illustrates the advantage of a kinetic assay. The rate of product formation decreases with time. This may be due to any combination of factors such as decrease in substrate concentration, denaturation of the enzyme, and product inhibition of the reaction. The solid line in Figure E5.7 represents the continuously measured time course of a reaction (kinetic assay). The true rate of the reaction is determined from the slope of the dashed line drawn tangent to the experimental result. From the data given, the rate is 5 jumoles of product formed per minute. Data from a fixed-time assay are also shown on Figure E5.7. If it is assumed that no product is present at the start of the reaction, then only a single measurement after a fixed period is necessary. This is shown by a circle on the experimental rate curve. The measured rate is now 16 jumoles of product formed every 5 minutes or about 3 /rmoles/minute, considerably lower than the rate derived from the continuous, kinetic assay. Which rate measurement is correct Obviously, the kinetic assay gives the true rate because it corrects for the decline in rate with time. The fixed-time assay can be improved by changing the time of the measurement, in this example, to 2 minutes of reaction time, when the experimental rate is still linear. It is possible to obtain...

Figure Cl. 1.2 shows a typical time course resulting from a continuous assay of product formation in an enzyme-catalyzed reaction. The hyperbolic nature of the curve illustrates that the reaction rate decreases as the reaction nears completion. The reaction rate, at any given time, is the slope of the line tangent to the curve at the point corresponding to the time of interest. Reaction rates decrease as reactions progress for several reasons, including substrate depletion, reactant concentrations approaching equilibrium values (i.e., the reverse reaction becomes relevant), product inhibition, enzyme inactivation, and/or a change in reaction conditions (e.g., pH as the reaction proceeds). With respect to each of these reasons, their effects will be at a minimum in the initial phase of the reaction—i.e., under conditions corresponding to initial velocity measurements. Hence, the interpretation of initial velocity data is relatively simple and thus widely used in enzyme-related assays.

The V0 of an enzyme-catalyzed reaction depends not only on [S] but also on the enzyme concentration. When [S] is sufficient to saturate the enzyme, doubling the amount of enzyme will double VV increasing the enzyme by fourfold will correspondingly increase V0 by fourfold, and so on. Figure 5.6 shows progress curves for increasing concentration of enzyme with saturating levels of substrate. The final equilibrium position is the same for all enzyme concentrations, but the velocities at which it is attained will be different. 

Figure 3. Progress curve for the enzyme-catalyzed reaction A + E sssuming that ki = ka = k, and Ao — ioEq.

It is theoretically possible to derive Vmax and values for an enzyme from a single progress curve (Fig. 3.11). This is certainly an attractive proposition since measuring initial velocity as a function of several substrate concentrations can be a lengthy and tedious task. The velocity of an enzyme-catalyzed reaction can be determined from the disappearance... 

Figure 1.2 shows the plots of the IF-Lambert and logistic progress curves (1.5 5) for an enzyme-catalyzed reaction in vitro where k =k 10 s , j=10 M" s", [5 J=10 M, and [ J=10 M. The quantitative behavior of the reactant concentrations in both the IF-Lambert and logistic cases are strikingly similar. In addition, time-dependent product curves may be used instead of the initial velocity curves in Figure 1.1. 

FIGURE 1.14 The first two rows show the normal absorptions for substrate (continuous curves) and product (dashed curves) concentrations of the enzyme-catalyzed reaction without inhibition, based on the logistical temporal approximation, and on the IF-Lambert temporal solution, respectively the third row depicts the difieience between IF-Lambert and logistical counterpart for substrate or product normal absorption progress curves on the columns, the plots are presented for the enzyme/substrate ratio e taking the in vitro and almost the in vivo values, from 10" to 10 and equal or greater than 10, respectively the employed kinetic parameters are the maximum velocity of enzyme reaction 1 O Mxsr and the Michaelis... 

Duggleby provides a lucid account of how one can extract useful kinetic information from reaction progress curves. The nonlinear regression methods allow one to treat many cases, and they account for the fact that, after an enzyme is mixed with its substrate, the catalyzed rate... 

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