Reaction progress curves

Figure 4.5 Example of a reaction progress curve obtained by discontinuous measurement of 33P incorportation into a peptide substrate of a kinase. Each data point represents a measurement made at a discrete time point after initiation of the reaction with y-33P-ATP.

In this chapter we have reviewed some of the basic biochemical considerations that must be taken into account in the design of assays for HTS purposes. We saw that activity measurements must be made during the initial velocity phase of the reaction progress curve to ensure the best chances of observing inhibition by library... 

The hallmark of slow binding inhibition is that the degree of inhibition at a fixed concentration of compound will vary over time, as equilibrium is slowly established between the free and enzyme-bound forms of the compound. Often the establishment of enzyme-inhibitor equilibrium is manifested over the time course of the enzyme activity assay, and this leads to a curvature of the reaction progress curve over a time scale where the uninhibited reaction progress curve is linear. We saw... 

Thus, if the reaction progress curve can be followed for a long enough time, under conditions where the unihibited enzyme remains stable, one may be able to measure a small, but nonzero, value for vs. Combining this value with y and obs would allow one to determine k6 from Equation (6.12). 

Figure 8.1 Typical enzyme reaction progress curve in the presence of an irreversible enzyme inactivator, highlighting the initial velocity region (v ) and the fact that the terminal velocity (vs) is zero for such compounds.

An important point to realize here is that attempts to quantify the relative potency of irreversible enzyme inactivators by more traditional parameters, such as IC50 values, are entirely inappropriate because these values will vary with time, in different ways for different compounds. Hence the SAR derived from IC50 values, determined at a fixed time point in the reaction progress curve, is meaningless and can be misleading in terms of compound optimization. Unfortunately, the literature is rife with examples of this type of inappropriate quantitation of irreversible inactivator potency, making meaningful comparisons with literature data difficult, at best. 

Figure 8.9 Reaction progress curve in the presence of a mechanism-based inactivator when a second aliquot of enzyme is added to the reaction solution. The reaction is allowed to reach a plateau before a second, equal concentration aliquot of enzyme is added at the indicated time point. Note that the rate of inactivation for this second aliquot of enzyme is the same as that seen in the initial progress curve.

Figure A 1.2 Determination of instantaneous velocity at various points in a reaction progress curve, from the slope of a tangent line drawn to a specific time point.

The presence of a lag period in many coupled assays and difficulties in determining the linear portion of a curve present the main problems in the calculation of enzyme activity using reaction rate analysers. In the simplest instruments the slope of the curve in the first few seconds of the reaction is extrapolated into a straight line or, if the reaction is known to show a lag period, the rate of reaction after a defined period of time can be measured. The more sophisticated instruments use microcomputers to determine the linear portion of the curve and calculate the enzyme activity directly from the slope. The second derivative of the reaction progress curve (rate of change of the slope) can be monitored by the computer and when a value of zero is held for a period of time (10—15 seconds) this indicates a linear section of the graph. From the value for the slope, the enzyme activity can be calculated. 

Initial Rate Assumption. The entire reaction progress curve, or at least a substantial portion of it, is typically required to accurately determine the rate constant for a first-order or second-order reaction. Nonetheless, one can frequently estimate the rate constant by measuring the velocity over a brief period (known as the initial rate phase) where only a small amount of reactant is consumed. This leads to a straight-line reaction progress curve see Fig. 6) which is drawn as a tangent to the initial reaction velocity. 

Although enzyme-catalyzed reactions are described in many other entries in this Handbook, some mention of the time-evolution of an enzymatic process should be considered here. Shown in Fig. 10 is an representation of a typical reaction progress curve. A rapid rise in the concentration of reactant-bound species ES + +... 

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... 

Figure C1.2.3 Reaction progress curves for the production of new reducing ends (measured as galacturonic acid equivalents) at different enzyme loads.

Create a reaction progress curve by plotting the quantity of fatty acid liberated over the time of reaction (Fig. C3.1.1). Determine the activity (initial velocity, v0) of the lipase from the slope of the linear portion (see Critical Parameters) using the following equation ... 

Construct a reaction progress curve by plotting the concentration of oleic acid versus reaction time. Draw a tangent to the initial portion of the progress curve to obtain initial reaction rates (v0 in mM/min) as follows ... 

Analysis of three lipase reactions using the titrimetric method illustrates typical reaction progress curves and how, as well as the need, to estimate initial rates by tangential analysis (Fig. C3.1.1). The corresponding initial reaction velocities were 27.5 U/mg forBurkholderia cepacia (formerly, Pseudomonas cepacia) li-... 

Figure C3.1.3 Comparison of lipase activities using the copper soap colorimetric assay as affected by the degree of homogenization of olive oil substrate. The lipase used in the reaction mixture was from C. rugosa (at 0.40 mg/ml) in the presence mechanically homogenized (triangles) or poorly homogenized (shaken by hand diamonds) substrate emulsion. For comparison of linearity of reaction progress curves, the time course of C. rugosa lipase (at 0.20 mg/ml circles) is provided.

In the event that lipase preparations are too active to allow for facile estimation of initial rates, the enzyme can be diluted and assayed again. This is illustrated using the copper soap method where the reduced level of C. rugosa lipase addition afforded a longer period of linearity to the reaction progress curve than did the more active B. cepacia lipase (Fig. C3.1.3). 

For the other reactive system for which T is lower than its Tgoo (= 177°C), the behavior is initially dominated by ionic conductivity and, as the reaction progresses, curves exhibit peaks due to vitrification (Fig. 6.9b). The higher the frequency, the lower the time at which this relaxation peak appears. 

The dynamics were run for several concentrations of substrate and variations in the Pc values. Initial velocities of the reaction were recorded. The Michaelis-Menten model was observed and characteristic Lineweaver-Burk plots were found from the model. Systematic variation of the lipophilicity of substrates and products showed that a lower affinity between a substrate and water leads to more of the S —> P reaction at a common point along the reaction progress curve. This influence is greater than that of the affinity between the substrate and the enzyme. The study created a model in which the more lipophilic substrates are more reactive. The water-substrate affinity appears... 

Figure 8.10 illustrates the results of increasing the solvent polarity on the energy versus reaction progress curve for the SN1 reaction. Because the transition state, which resembles the carbocation, is more polar than the reactant, the rate of an SN1 reaction is much faster in a more polar solvent. 

Transition state (Section 8.3) The structure of the complex at the maximum on the energy versus reaction progress curve and in which all the requirements for a reaction have been met. 

The most useful concentrations are those around Km. In fact, a useful rule of thumb is 1/5 to 5 Km this way, u0 will range from 0.17 to 0.83 times V a - In other words, w0 will be —5 times greater at the highest concentration than at the lowest. If initial concentrations are too low, then velocity estimates become less accurate because of the nonlinearity of the reaction-progress curves near time t = 0. 

Figure 17.13. Reaction progress curves in the presence of increasing concentrations of a slow-binding inhibitor.

The inhibitor could be displaced from Factor Xa by substrates and, based on steady-state assumptions, the dissociation constant for (19) was found to be 14 pM (87). However, the reaction progress curves indicated a slow-binding process, probably by mechanism B. Stopped-flow fluorescence studies, combined with kinetic analysis, showed that the isomerization step (E. I -I- E. I ) is unusually fast and that the formation of E I is, at least, partially rate limiting. 

Product inhibition is a cause of nonlinearity of reaction progress curves during fixed-time methods of enzyme assay. For example, oxaloacetate produced by the action of aspartate aminotransferase inhibits the enzyme, particularly the mitochondrial isoenzyme. The inhibitory product may be removed as it is formed by a coupled enzymatic reaction malate dehydrogenase converts the oxaloacetate to malate and at the same time oxidizes NADH to NADL... 

The process of bond cleavage or bond formation is called a transition state and appears as a maximum in the potential energy diagram curve. An intermediate is a short lived species formed in a multi-step reaction mechanism and is the result of a transition it appears as a minimum on the reaction progress curve. The rate of a reaction depends on the difference in energy between that of the starting materials and an intermediate (or the products in a one step reaction) this is the energy of activation. 

Another measure of the asymmetric kinetic properties of the two bases in the alanine racemase mechanism is the qualitative behavior of the equilibrium overshoots observed. Overshoots are often observed in reaction progress curves run in deuterium oxide that are initiated with a single stereoisomer that is protiated at the Ca position (Fig. 7.3). The optical activity is monitored by polarimetry or circular dichroism (CD). At equilibrium, the signal is zero, since the product is a racemic mixture of d- and L-isomers. However, when there is a significant substrate-derived KIE on the reverse direction (product being fully deuterated in a two-base mecha-... 

The limit to the chain reaction is determined by the relative values of the rate constants for the propagation step and the branching or transfer reactions involving solvent or inhibitor molecules. As the concentration of the oxidizable molecule falls in the solution, the reaction rate also falls. The reaction is characterized by a steady-state or maximum rate represented by the linear portion of the sigmoidal reaction progress curve. This is achieved when the rate of generation of new initiating radicals is equal to their termination rate. Here, the kinetics is simplified by the steady-state approximation, and the maximum rate is first order with respect to the benzaldehyde concentration. 

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