Steady-state kinetics initial velocity studies

The electron transfer from cytochrome c to O2 catalyzed by cytochrome c oxidase was studied with initial steady state kinetics, following the absorbance decrease at 550 nm due to the oxidation of ferrocyto-chrome c in the presence of catalytic amounts of cytochrome c oxidase (Minnart, 1961 Errede ci a/., 1976 Ferguson-Miller ei a/., 1976). Oxidation of cytochrome c oxidase is a first-order reaction with respect to ferrocytochrome c concentration. Thus initial velocity can be determined quite accurately from the first-order rate constant multiplied by the initial concentration of ferrocytochrome c. The initial velocity depends on the substrate (ferrocytochrome c) concentration following the Michaelis-Menten equation (Minnart, 1961). Furthermore, a second catalytic site was found by careful examination of the enzyme reaction at low substrate concentration (Ferguson-Miller et al., 1976). The Km value was about two orders of magnitude smaller than that of the enzyme reaction previously found. The multiphasic enzyme kinetic behavior could be interpreted by a single catalytic site model (Speck et al., 1984). However, this model also requires two cytochrome c sites, catalytic and noncatalytic. 

Hexokinase does not yield parallel reciprocal plots, so the Ping Pong mechanism can be discarded. However, initial velocity studies alone will noi discriminate between the rapid equilibrium random and steady-state ordered mechanisms. Both yield ihe same velocity equation and families of intersecting reciprocal plots. Other diagnostic procedures must be used (e.g., product inhibition, dead-end inhibition, equilibrium substrate binding, and isotope exchange studies). These procedures are described in detail in the author s Enzyme Kinetics behavior and Analysis of Rapid Equilibrium and Steady-State Enzyme Systems, Wiley-Interscience (1975),... 

Except for very simple systems, initial rate experiments of enzyme-catalyzed reactions are typically run in which the initial velocity is measured at a number of substrate concentrations while keeping all of the other components of the reaction mixture constant. The set of experiments is run again a number of times (typically, at least five) in which the concentration of one of those other components of the reaction mixture has been changed. When the initial rate data is plotted in a linear format (for example, in a double-reciprocal plot, 1/v vx. 1/[S]), a series of lines are obtained, each associated with a different concentration of the other component (for example, another substrate in a multisubstrate reaction, one of the products, an inhibitor or other effector, etc.). The slopes of each of these lines are replotted as a function of the concentration of the other component (e.g., slope vx. [other substrate] in a multisubstrate reaction slope vx. 1/[inhibitor] in an inhibition study etc.). Similar replots may be made with the vertical intercepts of the primary plots. The new slopes, vertical intercepts, and horizontal intercepts of these replots can provide estimates of the kinetic parameters for the system under study. In addition, linearity (or lack of) is a good check on whether the experimental protocols have valid steady-state conditions. Nonlinearity in replot data can often indicate cooperative events, slow binding steps, multiple binding, etc. 

Initial rate measurements, especially with alternative substrates and with a product or substrate analog as inhibitor, and measurements of the rate of isotope exchange at equilibrium, can give a great deal of information about mechanism, and in some cases allow estimates of individual velocity constants and dissociation constants. The results of such studies, which require little enzyme, are an essential basis for the proper interpretation, in relation to the overall catalytic reaction, of pre-steady-state studies and kinetic and thermodynamic studies of enzyme-coenzyme reactions in isolation. 

The two important kinetic results obtained from studies of the steady state of enzyme-catalyzed reactions are the Michaelis constant Ku and the maximum velocity Fmax. These constants are determined from one of a number of graphical procedures relating the initial velocity To to the initial substrate concentration [(S]o over a range of [[Pg.285]

The initial acceleration of enzyme reactions can be observed by a study of the rate of appearance of the final product during the short time interval between mixing of enzyme and substrate and the attainment of the steady-state concentrations of all the intermediate compounds. Apart from the final steady-state velocity, this method can, in principle, give information about the kinetics of two reaction steps. In the first place, the second-order constant ki which characterizes the initial enzyme-substrate combination can be determined when [ S]o, the initial substrate concentration, is sufficiently small to make this step rate-determining during the pre-steady-state period. Kinetic equations for the evaluation of rate constants from pre-steady-state data have recently been derived (4). Under suitable conditions ki can be evaluated from... 

According to the relevant power and momentum balance, Eqs. (38) and (39), the electron kinetics in steady-state plasmas is characterized by tbe conditions that at any instant the power and the momentum input from the electric field are dissipated by elastic and inelastic electron collisions into the translational and internal energy of the gas particles. This instantaneous complete compensation of the respective gain from the field and the loss in collisions usually does not occur in time-dependent plasmas, and often the collisional dissipation follows with a more or less large delay—for example, the temporally varying action of a time-dependent field. Thus, the temporal response of the electrons to certain disturbances in the initial value of their velocity distribution or to rapid changes of the electric field becomes more complicated, and the study of kinetic problems related to time-dependent plasmas naturally becomes more complex and sophisticated. Despite this extended interplay between the action of the binary electron collisions and the action of the electric field, the electron kinetics in time-... 

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