Steady-State Ping Pong

Consider a Steady-State Ping Pong Bi Bi system in which an inhibitor, I, combines in a dead-end fashion with the free enzyme, E. 

A procedure used to assist in identifying sequential mechanisms when the double-reciprocal plots exhibit parallel lines ". In some cases, bireactant mechanism can have various collections of rate constants that result in so-called parallel line kinetics, even though the mechanism is not ping pong. However, if the concentrations of A and B are kept in constant ratio with respect to each other, a sequential mechanism in a 1/v v. 1/[A] plot would be nonlinear (since in the denominator the last term of the double-reciprocal form of the rate expression contains [A] for example, for the steady-state ordered Bi Bi reaction scheme in which [B] = a[A], the double-reciprocal rate expression becomes 1/v =... 

A mathematical equation indicating how the equilibrium constant of an enzyme-catalyzed reaction (or half-reaction in the case of so-called ping pong reaction mechanisms) is related to the various kinetic parameters for the reaction mechanism. In the Briggs-Haldane steady-state treatment of a Uni Uni reaction mechanism, the Haldane relation can be written as follows ... 

The steady-state derivation of the ping pong Bi Bi mechanism provides the following determinants for each of the enzyme forms ... 

The complete steady-state rate expression for the ping pong Bi Bi reaction is... 

A procedure that assists in the characterization of binding mechanisms for sequential (/.e., non-ping pong) reactions . The same general initial rate expression applies to the steady-state ordered Bi Bi reaction, the rapid-equilibrium random Bi Bi reaction, and the Theorell-... 

One less kinetic parameter can be obtained from an analysis of the data for a ping-pong mechanism than can be obtained for ordered reactions. Nevertheless, in Eq. 9-47, twelve rate constants are indicated. At least this many steps must be considered to describe the behavior of the enzyme. Not all of these constants can be determined from a study of steady-state kinetics, but they may be obtained in other ways. 

In many ways, ping-pong kinetics is the most mechanistically informative of all the types of steady state kinetics, since information is given about the occurrence of a covalent intermediate. The finding of ping-pong kinetics is often used... 

LiP catalyzes the oxidation of 3,4-dimethoxybenzyl alcohol (veratryl alcohol) to veratryl aldehyde. Since this reaction can be easily followed at 310 nm, it is the basis for the standard assay for this enzyme (26,27). The enzyme exhibits normal saturation kinetics for both veratryl alcohol and H202 (28,43). Steady-state kinetic results Indicate a ping-pong mechanism in which H202 first oxidizes the enzyme and the oxidized intermediate reacts with veratryl alcohol (43). The enzyme has an extremely low pH optimum ( 2.5) for a peroxidase (43,44) however, the rate of formation of compound I (kx, Fig. 2) exhibits no pH dependence from 3.0-7.0 (45,46). Addition of excess veratryl alcohol at pH 3.0 results in the rapid conversion of... 

Under typical experimental conditions, the enzyme system is saturated with O2 and H+. Thus this enzyme system includes four substrates and four products. However, the initial steady state kinetics of this enzyme system obeys a simple Michaelis-Menten equation (a rectangular hyperbolic relation) for each kinetic phase of the two phases at low and high ferrocytochrome c concentrations as described above. This result indicates that the four ferrocytochromes c react with the enzyme in a ping-pong fashion in each substrate concentration range. That is, each ferroferrocytochrome c reacts with the enzyme after the previous cytochrome c in the oxidized state is released from the enzyme. Cytochrome c... 

Steady-state kinetic analysis shows that biotin-dependent reactions proceed by way of a two-site ping-pong mechanism the two-part reactions are catalyzed at distinct sites in the enzyme. These sites may be on the same or different polypeptide chains in different biotin-dependent enzymes. The e-amino linkage of lysine to the side chain of biotin in biocytin allows considerable movement of the coenzyme - the distance from C-2 of lysine to C-5 of biotin is IdA, thus allowing movement of biotin between the carboxylation and carboxyltransfer sites. 

Steady-state kinetic studies showed that the kinetics of the enzyme resemble those of the vanadium bromoperoxidases. The chloroperoxidase exhibits a pH profile similar to vanadium bromoperoxidases although the optimal pH of 4.5-5.0 is at a lower value. At low pH the enzyme is inhibited by chloride in a competitive way whereas at higher pH values the activity displays normal Michaelis-Menten type of behavior (see Michaelis Constant). The log Km for chloride increases linearly with pH whereas that for hydrogen peroxide decreases with pH demonstrating that in the catalytic mechanism protons are involved. These observations have led to a simplified ping-pong type of mechanism for the chloroperoxidase similar to that shown in (Figure 1). 

A ping-pong di Theorell-Chance mechanism has been deduced for tree laccase from steady-state kinetics (123). This mechanism is characterized by the sequential entry of the two substrates and the immediate... 

The steady state rate equation for this ping pong mechanism is Equation 4. 

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),... 

Steady-state kinetics have been used to determine the kinetic mechanisms of many of these enzymes. The questions that have been primarily addressed are the sequence of steps that occur in substrate binding prior and subsequent to the catalytic reaction and the potential formation of covalent enzyme intermediates. Classical interpretation of kinetic analyses has been the determination of the relevant reactions occurring via a random or an ordered sequential reaction, or if the reaction is a double-displacement or Ping-Pong reaction. In the former case, phosphoryl transfer occurs in the ternary complex that contains enzyme, phosphoryl donor, and phosphoryl acceptor. In the latter case, enzyme reacts with... 

---