Fixed time methods, kinetic

Walash et al. [14] described a kinetic spectrophotometric method for determination of several sulfur containing compounds including penicillamine. The method is based on the catalytic effect on the reaction between sodium azide and iodine in aqueous solution, and entails measuring the decrease in the absorbance of iodine at 348 nm by a fixed time method. Regression analysis of the Beer s law plot showed a linear graph over the range of 0.01 0.1 pg/mL for penicillamine with a detection limit of 0.0094 pg/mL. 

Determmation of reaction rate involves the kinetic measurement of the amount of change produced in a defined time interval. Both fixed-time and continuous-monitoring methods are used to measure reaction rates. In the fixed-time method, the amount of change produced by the enzyme is measured after stopping the reaction at the end of a fixedtime interval. In the continuous-monitoring method, the progress of the reaction is monitored continuously. These two methods have different advantages and limitations. To appreciate these, it is necessary to consider the way in which the rate of an enzymatic reaction varies with time. 

Equation 18.12 is the basis for the derivative approach to rate-based analysis, which involves directly measuring the reaction rate at a specific time or times and relating this to [A]fl. Equation 18.11 is the basis for the two different integral approaches to kinetic analysis. In one case, the amount of A reacted during a fixed time is measured and is directly proportional to [A]o ( fixed-time method) in the other case, the time required for a fixed amount of A to react is measured and is also proportional to [A]o variable-time method). Details of these methods will be discussed in Section... 

Differential fixed-time method Implementation of this kinetic method involves measuring the concentration of a reactant or product at a preset time from the start of the reaction according to the following equation... 

Hgure 2 Implemenlation of the fixed-time method. (Reproduced with permission from Perez-Bendito D and Silva M (1988) Kinetic Methods in Analytical Chemistry. Chichester Ellis Honvood.)... 

The earliest examples of analytical methods based on chemical kinetics, which date from the late nineteenth century, took advantage of the catalytic activity of enzymes. Typically, the enzyme was added to a solution containing a suitable substrate, and the reaction between the two was monitored for a fixed time. The enzyme s activity was determined by measuring the amount of substrate that had reacted. Enzymes also were used in procedures for the quantitative analysis of hydrogen peroxide and carbohydrates. The application of catalytic reactions continued in the first half of the twentieth century, and developments included the use of nonenzymatic catalysts, noncatalytic reactions, and differences in reaction rates when analyzing samples with several analytes. 

Fluorimetric methods are useful for monitoring reactions involving the nucleotide coenzymes. The natural fluorescence of the reduced forms in the region of 460 nm can be used in kinetic assays. However, this fluorescence is destroyed at pH values below 2.0, whereas any oxidized forms of the coenzymes present are stable. If the pH of the solution is then raised above 10.5 and heated, the oxidized forms are themselves converted to fluorescent derivatives. This latter procedure lends itself to fixed time assays such as is illustrated in Procedure 8.6. 

TTie classification of kinetic methods proposed by Pardue [18] is adopted in the software philosophy. TTie defined objective of measurement in the system is to obtain the best regression fit to a minimum of 10 data points, taken over either a fixed time (i.e. the maximum time for slow reactions) or variable time (for reactions complete in less than 34 min, which is the maximum practical observation time). In an analytical system generating information at the rate of SO datum points per second, with reactions being monitored for up to 2040 s, effective data-reduction is of prime importance. To reduce this large quantity of analytical data to more manageable proportions, an algorithm was devised to optimize the time-base of the measurements for each individual specimen. 

Activity assays of enzymes bound to solid phases in EIA systems have previously been limited to fixed-time spectrophotometric methods following incubation of substrate and solid phase for extended periods of time. Kinetic assays of enzyme activity have not been used to date because of the difficulty in directly monitoring initial rates of enzyme reactions in a turbid solid phase suspension. With urease as the label, an ammonia gas sensing electrode can be used to directly quantitate the amount of urease-labeled antigen or hapten bound to a double-antibody solid phase by continuously measuring the initial rate of ammonia produced from urea as a substrate. 

Two different types of pulsed EPR experiments are possible a spectrum can be measured at a fixed time after the pulse by variation of the field strength B (Eq. 72), or the time profile of a particular spectral line can be measured at constant B to give kinetic information. One vziriation of this kinetic method is to detect the recombination of singlet-state radical ion pairs in liquid hydrocarbons by the fluorescence of the product excited state [142]. This technique is known as fluorescence-detected magnetic resonance (FDMR) and provides information on the spin dynamics of the radical ion pair as well as the chemical kinetics. 

One salient advantage of fixed-time kinetic methods is significantly increased selectivity. Tolerated concentrations of interfering metal ions are often reported to be one to two orders of magnitude higher than in equilibrium methods. The increased tolerance to interferences of kinetic methods may be the result of the following facts ... 

Enzymatic assay methods are classified as fixed-time assays, fixed-change assays, or kinetic (initial rate) assays. Kinetic assays continuously monitor concentration as a function of time pseudo-first-order conditions generally apply up to 10% completion of the reaction to allow the initial reaction rate to be determined. If the initial substrate concentration is > 10Km, then the initial rate is directly proportional to enzyme concentration. At low initial substrate concentrations (< 0.1 Km), the initial rate will be directly proportional to initial substrate concentration (cf. Chapter 2). For enzyme quantitation, a plot of initial rate against [E] provides a linear... 

Methods in which some property related to substrate concentration (such as absorbance, fluorescence, chemiluminescence, etc.) is measured at two fixed times during the course of the reaction are known as two-point kinetic methods. They are theoreticahy the most accurate for the enzymatic determination of substrates. However, these methods are technically more demanding than equifibrium methods and all the factors that affect reaction rate, such as pH, temperature, and amount of enzyme, must be kept constant from one assay to the next, as must the timing of the two measurements. These conditions can readily be achieved in automatic analyzers. A reference solution of the analyte (substrate) must be used for calibration. To ensure first-order reaction conditions, the substrate concentration must be low compared to the K, (i.e., in the order of less than 0.2 X K, . Enzymes with high K , values are therefore preferred for kinetic analysis to give a wider usable range of substrate concentration. 

Fluorescence Kinetic-Based Measurements. Our studies of the reaction rate determination of thiamine (vitamin Bl) will be used to demonstrate the unique capabilities of rapid acquisition of spectra in kinetic measurements. The kinetic method is based on the oxidation of thiamine by Hg + in basic solutions to highly fluorescent thiochrome (16) The initial rate, taken as the change in fluorescence signal at 444 nm that occurs in a fixed time after mixing the sample and reagents, is directly proportional to the thiamine concentration. 

Kinetic methods. FIA, on account of Its Intrinsic features (measurements under non-equilibrium conditions), can be considered to be a fixed-time methodology. However, according to FIA jargon, a kinetic method is based on the monitoring of the evolution of the analytical signal (stopped-flow methods) or on the measurement of two or more signals at the number of times required (differential or individual kinetic determinations). 

One of the most valuable applications of electronic data-processing is in enzyme assays. Kinetic measurements of enzyme activity in which the rate of reaction is monitored (usually using UV measurement) are more specific than endpoint colorimetric methods, in which the development of color in a coupled reaction is measured after a fixed time. Modern systems continuously or intermittently monitor the growth in concentration of the reaction product or the decrease in concentration of one of the reactants (the substrate). From the rate of change in concentration or the average change in concentration over several fixed time-intervals, the circuitry calculates the activity in reportable units. Other ramifications of these systems will be discussed below. 

There are two basic methods that have been used to simulated kinetics via Monte Carlo approaches[ l. The first is termed the fixed-time approach, in which every site on the surface has a set of probabilities associated with the different kinetic events that can occur at these sites. This could include diffusion, reaction, adsorption, and desorption processes. The state of the system then moves in fixed incremented steps of time and subsequently surveys all of the physicochemical steps to determine which of them can take place within the given (short) time step. This is accomphshed by sampling every site and determining whether it changes due to the occurrence of a kinetic process. This is determined by drawing a random munber for each potential step and comparing it with the transition probability P s for that particular kinetic step (r) at site (s) ... 

Loss of [ f PJGTP bound to Arfl. This assay is less labor intensive than the assay using [a PJGTP and, therefore, suitable for performing multiple time courses required for determining initial rates for saturation kinetic analyses (Che et al, 2005). This method will also work for fixed time point analysis. In this assay, 1-200 //M myrArfl or [L8K]Arfl is loaded with [7 P]GTP, with a total GTP concentration in 4-fold excess of Arfl, in buffer B. When using myrArfl, 500 fiM of total phospholipids in the form of an LUV is used. Arfl GTP is added to a reaction mixture containing GAP and 500 fiM of the appropriate phosphoUpids in GAP cocktail. The amount of GAP should be sufficient to hydrolyze about 50% of the GTP on Arfl in 2-5 min. Samples are taken from 0 to 10 min and diluted into ice-cold stop buffer. The samples are filtered on nitrocellulose as described... 

Various experimental methods to evaluate the kinetics of flow processes existed even in the last centuty. They developed gradually with the expansion of the petrochemical industry. In the 1940s, conversion versus residence time measurement in tubular reactors was the basic tool for rate evaluations. In the 1950s, differential reactor experiments became popular. Only in the 1960s did the use of Continuous-flow Stirred Tank Reactors (CSTRs) start to spread for kinetic studies. A large variety of CSTRs was used to study heterogeneous (contact) catalytic reactions. These included spinning basket CSTRs as well as many kinds of fixed bed reactors with external or internal recycle pumps (Jankowski 1978, Berty 1984.)... 

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