INITIAL RATE CONDITION

Most measurements of the rates of enzyme-catalyzed reactions employ relatively short time periods, conditions that approximate initial rate conditions. Under these conditions, only traces of product accumulate, hence the rate of the reverse reaction is negligible. The initial velocity (vj) of the reaction thus is essentially that of... 

A measurement of the rate of an enzyme-catalyzed reaction generally employs initial rate conditions, for which the essential absence of product precludes the reverse reaction. 

Whenever using alternative substrate inhibition procedures, the investigator must demonstrate that initial rate conditions remain valid throughout the course of the experiment. This is particularly true of the other sub-strate(s) in multisubstrate enzymes. Because both the substrate under study and its analog are present in the reaction mixtures, the other cosubstrates will be depleted faster. This should always be a consideration in the design of the experiment. 

The velocity of an enzyme-catalyzed reaction can be measured either by a continuous assay or by a stopped-time protocol. Whenever possible, the continuous measurement of a velocity (e.g., the increase or decrease in absorbance vx. time) should be utilized. In stopped-time assays, the investigator must demonstrate that the reaction is completely terminated at the specified point in time and that products are readily and quantitatively separated from substrates. In addition, one must show that the system is under initial rate conditions. Thus, at least three or four different time points should be chosen. Stopped-time assays also require an assay blank (for t = 0). In this blank, typically the quenching conditions are applied prior to the initiation step. Whenever practicable, replicate kinetic analyses should be done, even with continuous assay protocols. See Enzyme Assay Methods Basal Rate... 

A dimensionless quantity, symbolized by ea, used to assess the extent of activation by a particular compound on the initial rate of an enzyme-catalyzed reaction. The degree of activation is equal to (Va - Vo)/Vo where Va is the reaction rate in the presence of the activator and Vo is the initial rate in the absence of the activator. Whenever 6a values are reported, the activator concentration and initial rate conditions have to be reported as well. The degree of activation, a useful parameter in the initial stages of an investigation, does not address issues related to the mechanism of activation. See Activation Basal Rate... 

Downward curvature can also be seen if steady-state and initial rate conditions are not observed (e.g., the product concentration approaches inhibitory levels or substrate depletion occurs). 

The assay protocol should measure true initial rates (See Initial Rate Condition). For most systems, this represents a time period in which less than ten percent of the substrate concentration has undergone conversion. However, if a reaction is not significantly favored thermodynamically or if product inhibition is particularly potent, then a much smaller percentage of substrate conversion may be needed such that true initial rate conditions are obtained. Addition of an auxiliary enzyme system may prove necessary to avoid product accumulation. See Coupled Enzyme Assays... 

Under initial rate conditions, where the product concentrations are effectively zero [P] 0, [Q] 0, and [R] 0), the steady-state expression for this reaction mechanism is... 

An oft-suggested check on the initial rate condition is that, over the duration of the assay, the initial substrate concentration (ie., [S]) should not decrease by more than 5% (and ideally, significantly less). However, the validity of this suggestion depends on a number of other factors. If the reaction equilibrium constant Keq favors substrate(s), rather than product(s), then 10% conversion may amount to a significant fraction of that attainable... 

Provide a reference or direct experimental proof that the conditions chosen do provide initial rate measurements. At a minimum, the percentage of substrate consumed during the course of an initial rate determination should be specified. One should also show that under initial rate conditions a doubling of enzyme concentration should exactly produce a doubling in the observed initial rate. Likewise, if an auxiliary enzyme assay is used to monitor the primary enzyme s activity the observed rate at low or high substrate concentration should not depend on the concentration of additional enzyme(s), substrate(s), or factors used for the coupled assay. 2. Describe all assay conditions (eg., concentrations of substrates, products, inhibitors, and/or activators enzyme concentration temperature pH and buffer composition ... 

Occasionally, one can maintain initial rate conditions by using a coupled reaction system to regenerate one of the limiting substrates. For example, to regenerate ATP in a phosphotransferase reaction, one can use creatine phosphate and creatine kinase acetylphosphate and acetate kinase or phosphoenolpyruvate and pyruvate kinase. 

Under initial rate conditions [P] and [Q] = 0) and no abortive complexes being formed, the initial-rate expression is... 

In this rapid equilibrium mechanism, with all binding steps expressed with dissociation constants, then under initial rate conditions (i.e., [P] = 0) the initial rate expres-... 

Rapid Equilibrium Case. In the absence of significant amounts of product (i.e., initial rate conditions thus, [P] 0), the rate expression for the rapid equilibrium random Bi Uni mechanism is v = Uniax[A][B]/(i iai b + i b[A] + i a[B] + [A][B]) where is the dissociation constant for the EA complex, and T b are the dissociation constants for the EAB complex with regard to ligands A and B, respectively, and Umax = 9[Etotai] where kg is the forward unimolecular rate constant for the conversion of EAB to EP. Double-reciprocal plots (1/v v. 1/[A] at different constant concentrations of B and 1/v v. 1/[B] at different constant concentrations of A) will be intersecting lines. Slope and intercept replots will provide values for the kinetic parameters. 

PROGRESS CURVE INITIAL RATE CONDITION SUBSTRATE PURITY ENZYME PURITY WATER PURITY SUBSTRATE STABILITY ENZYME STABILITY MIXING TIME INITIAL RATE CONDITION QUENCHING EXPONENTIAL EXPONENTIAL BREAKDOWN Extended Debye-Huckel equation, DEBYE-HUCKEL TREATMENT EXTENSIVE PROPERTY EXTENT OF REACTION RATE OF CONVERSION... 

Under these initial rate conditions, the reaction described is being catalyzed only in the forward direction. 

Enzyme kinetics are normally determined under steady-state, initial-rate conditions, which place several constraints on the incubation conditions. First, the amount of substrate should greatly exceed the enzyme concentration, and the consumption of substrate should be held to a minimum. Generally, the amount of substrate consumed should be held to less than 10%. This constraint ensures that accurate substrate concentration data are available for the kinetic analyses and minimizes the probability that product inhibition of the reaction will occur. This constraint can be problematic when the Km of the reaction is low, since the amount of product (10% of a low substrate concentration) may be below that needed for accurate product quantitation. One method to increase the substrate amount available is to use larger incubation volumes. For example, a 10-mL incubation has 10 times more substrate available than a 1-mL incubation. Another method is to increase the sensitivity of the assay, e.g., using mass spectral or radioisotope assays. When more than 10% of the substrate is consumed, the substrate concentration can be corrected via the integrated form of the rate equation (Dr. James Gillette, personal communication) ... 

It is important to incorporate within each assay certain controls that prove that the test system is performing as expected. To verify that each assay is performed under initial rate conditions, incubations should be performed in the absence of the dmg candidate at approximately half and twice the normal protein concentration and for approximately half and twice the normal incubation period. 

Drug concentrations should be based on kinetic experiments whenever possible so that the concentration is < Km for a given reaction, and the incubations should be carried out under initial rate conditions. 

The experimental conditions for examining the in vitro metabolism of the drug candidate by a bank of human liver microsomes are based on the results of experiments described in Steps 2 and 3 (i.e., experiments designed to establish initial rate conditions and Km and Vmax). In order to obtain clinically relevant results, the metabolism of the drug candidate by human liver microsomes must be examined at pharmacologically relevant concentrations of the drug candidate, as illustrated for lansoprazole 5-hydroxylation in Figure 20. 

Metabolite formation by high activity samples may violate initial rate conditions (<10% substrate loss). Even with multivariate analysis, correlation analysis may not positively identify multiple enzymes responsible for metabolite formation (unless correlation analysis is conducted in the presence and absence of a CYP-selective inhibitor). 

Conducted with pooled human liver microsomes, which contains all the relevant CYP enzymes and which are generally used to establish initial rate conditions as well as Km and Vmax. 

The metabolism of the drug candidate is not measured under initial rate conditions. Prior to initiating reaction phenotyping studies, a pool of human liver microsomes should always be used to establish initial rate conditions (i.e., conditions under which metabolite formation is proportional to protein concentration and incubation time), and total amount of substrate consumed should be less than 10%. 

The concept that plasma membrane transport plays a key role in the regulation of intracellular thyroid hormone levels is supported by studies with a monoclonal antibody against an antigen exposed on rat liver cells [107], This antibody inhibited the uptake of different iodothyronines by rat hepatocytes under initial rate conditions as well as the metabolism of these compounds during prolonged incubations [107]. Uptake and metabolism of T4, T3 and rT3 were affected to the same extent, suggesting that a single system operates in the transport of different iodothyronines, which is opposite to the view advanced above. However, it is not excluded that the antibody interacts with a component of the plasma membrane and thereby affects multiple transport systems. 

A minimal enzymatic reaction, in which the substrate, S, is converted into the product, P, is shown in Eq. (10.1). Under initial-rate conditions ([P]q = 0), product release is a kinetically irreversible step (k 3[P]Q = 0) as shown. 

The velocity of this reaction v = d[P]/dt) is a function of the bimolecular rate of substrate binding (ki) and the unimolecular rates of chemistry (k2,fe-2) and substrate and product release (k i,k3). The steady-state velocity expression under initial rate conditions (Eq. (10.2)) demonstrates how each microscopic rate constant contributes to the macroscopic reaction rate and the dependence of the velocity upon substrate concentration. 

As expected, increasing concentration of Tyr-O-Et influences the activity of CPD-Y but not the selectivity of the competing reactions 1 and 2. On the other hand, increasing the concentration of Arg-NH2 results in increased activity and selectivity favoring the aminolysis reaction compared to the competing hydrolysis reaction. The data in Fig. 7-9 were measured under initial rate conditions (see Sect. 7.4.1). Additionally, selectivity and yield were calculated as a function of conversion (Fig. 7-10). 

Initial rates are not significant in large-scale processes where high conversion of the substrate is desired. With rising conversion, the simultaneous effects of both substrate S and product P on the reaction rate have to be described. In the case of equilibrium reactions, the forward reaction and the back reaction have to be described by one rate equation they can only be treated separately under initial rate conditions. The overall rate equation has to describe the reaction rate as a function of all relevant components at all relevant concentration levels. A correct fit of all initial reaction rate data gives no guarantee that the kinetic model will fit the overall reaction data ... 

Eq. (47) was used for a simultaneous fit of all kinetic data measured under initial rate conditions (Figs. 7-19 and 7-20). Separate fitting of each curve gives a better coincidence in every single case, but the optimized kinetic parameter will vary from fit to fit. 

---