Steady state velocity data, initial

The initial steady state velocity data from flavoprotein oxidase reactions, when plotted in double reciprocal form, almost invariably generate families of parallel and usually straight lines see Figures la and lb). 

Figure 6.20 Concentration-response plot for the initial inhibitor encounter complex between COX1 open circles) and COX2 closed circles) and DuP697. For COX1, the data were taken from steady state velocity measurements. For COX2, the data were obtained from the y-intercept values of the data fits in Figure 6.19.

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... 

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. 

The booster-and-attenuator system is selected to provide about the desired shock pressure in the sample wedge. In all but a few of the experiments on which data are presented here, the booster-and-attenuator systems consisted of a plane-wave lens, a booster expl, and an inert metal or plastic shock attenuator. In some instances, the attenuator is composed of several materials, The pressure and particle velocity are assumed to be the same on both sides of the attenuator-and-sample interface. However, because initiation is not a steady state, this boundary condition is not precisely correct. The free-surface velocity of the attenuator is measured, and the particle velocity is assumed to be about half that. The shock Hugoniot of the attenuator can be evaluated using the free-surface velocity measurement. Then, the pressure (P) and particle velocity (Up) in the expl sample are found by determining graphically the intersection of the attenuator rarefaction locus and the explosives-state locus given by the conservation-of-mom-entum relation for the expl, P = p0UpUs where Us = shock velocity and p0 = initial density. The attenuator rarefaction locus is approximated... 

Experimental data on multiple steady-state profiles in tubular packed bed reactors have been reported in the literature by Wicke et al. 51 -53) and Hlavacek and Votruba (54, 55) (Table VI). The measurements have been performed in adiabatic tubular reactors. In the following text the effects of initial temperature, inlet concentration, velocity, length of the bed, and reaction rate expression on the multiple steady state profiles will be studied. 

A study of the initiation of lead azide by the impact of flyer plates (Section F) showed that stress excursions behind the shock front produce pressure waves which travel through the shock-compressed azide at a velocity at least equal to the sonic velocity. The sonic velocity in the precompressed explosive is higher than in the uncompressed explosive, so the amplitude of the initial shock increases rapidly until steady-state detonation is achieved in less than 1 mm, as indicated by the data in Table IV. For an initial stress over 4 kbar, instantaneous detonation occurred however, pressures this high are not normally present at the input to the azide in an explosive train. 

Propane aromatization reaction (at 550°C) was carried out at atmospheric pressure in a continuous flow quartz reactor (id 13 mm), using a propane-nitrogen mixture (33.3 mol-% propane) as a feed with a space velocity of 3100 cm g h". The catalytic activity and selectivity were measured as a function of time-on-stream (up to about 6.7 + 0.2 h). The reaction products were analyzed by an on-line GC with FID, using Poropak-Q (3 mm x 3 m) and Benton-34 (5%) and dinonylphthalate (5%) on Chromosorb-W (3 mm x 5 m) columns. The activity and selectivity data at different space velocities in the absence of catalyst deactivation (i.e. initial activity/selectivity) at 550°C were obtained by the square pulse technique by passing the reaction mixture at different space velocities over fresh catalyst for a short period (2-5 min) under steady state and then replacing the reactant mixture by pure Nj during the product analysis by the GC. 

Base Metal vs. Platinum Catalysts. When the emission control performances of these two types of catalyst were compared, two points were evident. First, the base metal and platinum catalysts controlled exhaust HC and CO equally (or nearly so) at very large catalyst volumes (low space velocities). This had been reported for laboratory evaluations of these catalysts (14) thus these data for vehicles confirm the findings from steady-state bench tests. Second, initial activity of the platinum catalysts was very high. There was essentially no change in the emissions control performance of the platinum catalysts even at very small catalyst volumes, and this behavior can be utilized in two ways. 

In this case, v is the velocity of the reaction, [S] is the substrate concentration, Vmax (also known as V or Vj ) is the maximum velocity of the reaction, and is the Michaelis constant. From this equation quantitative descriptions of enzyme-catalyzed reactions, in terms of rate and concentration, can be made. As can be surmised by the form of the equation, data that is described by the Michaelis-Menten equation takes the shape of a hyperbola when plotted in two-dimensional fashion with velocity as the y-axis and substrate concentration as the x-axis (Fig. 4.1). Use of the Michaelis-Menten equation is based on the assumption that the enzyme reaction is operating under both steady state and rapid equilibrium conditions (i.e., that the concentration of all of the enzyme-substrate intermediates (see Scheme 4.1) become constant soon after initiation of the reaction). The assumption is also made that the active site of the enzyme contains only one binding site at which catalysis occurs and that only one substrate molecule at a time is interacting with the binding site. As will be discussed below, this latter assumption is not always valid when considering the kinetics of drug metabolizing enzymes. 

Should one use the Hill plot in practice to examine the initial velocity behavior of enzymes Because infinite cooperativity is assumed to be the basis of the Hill treatment, only rapidly equilibrating systems are suitable for the Hill analysis. However, enzyme systems displaying steady-state kinetic behavior will not satisfy this requirement for this reason, one must avoid the use of kinetic data in any application of the Hill equation to steady-state enzyme systems. 

The front velocity is the slope of a plot of front position vs. time. This plot is prepared for each concentration, and the data are compared with the predictions of the steady-state model. Students observe that as the initiator concentration increases, the velocity of the front increases according to a power function. 

FIG. 8. Profiles of the density of dissociated atoms, p/Po ( ) of Fig-7, vs lattice plane number at different times. Data have been smoothed by averaging over 2 neighboring planes ahead of the reaction front, and 6 behind the reaction front, and over 15 time steps. Solid lines are the steady-state trajectories of the head and foot of the reaction front. Dashed lines are the corresponding trajectories of the shock front obtained from a similar plot of the stress profiles vs time and distance. Dotted line marks the trajectories of some local reaction sites initiated by shock compression. Velocities refer to the stationary mirror plane. From reference [38b]. 

The Build-up Model - An empirical model for engineering purposes that depends on experimental data for calibration. The model assumes that a real nonsteady-state detonation can be adequately approximated by a series of steady-state detonations with instantaneous reaction and constant detonation velocity whose effective C-J pressures vary with the distance of run for a particular initiation system. 

---