Steady-State Ping Pong products

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... 

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),... 

The steady state kinetics of arsenite oxidoreductase from A. faecalis indicate a so-called double displacement (or ping-pong ) mechanism (15) in which the enzyme cycles between oxidized and reduced forms in its reaction with arsenite and azurin (or cytochrome c). This overall kinetic scheme is common in redox-active proteins. Arsenite must bind, the oxygen atom transfer chemistry take place, and arsenate dissociate before the subsequent reaction of a second molecule of substrate. Since arsenate is not an inhibitor of arsenite oxidoreductase (43), product dissociation must be effectively irreversible. The turnover number (kcai) of 27 sec and for arsenite of 8 pM are reasonable parameters for the detoxification of arsenite, especially since A. faecalis is able to survive in at least 80 mM (1%) sodium arsenite. The considerable catalytic power of the enzyme is reflected by the kinetic parameter k JK of 3.4 X 10 M sec , which is fairly close to the diffusion-controlled maximum of 10 -10 M sec for proteins in... 

TABLE 11.5 Cleland nomenclature for bisubstrate reactions exemplified. Three common kinetic mechanisms for bisubstrate enzymatic reactions are exemplified. The forward rate equations for the order bi bi and ping pong bi hi are derived according to the steady-state assumption, whereas that of the random bi bi is based on the quasi-equilibrium assumption. These rate equations are first order in both A and B, and their double reciprocal plots (1A versus 1/A or 1/B) are linear. They are convergent for the order bi bi and random bi bi but parallel for the ping pong bi bi due to the absence of the constant term (KiaKb) in the denominator. These three kinetic mechanisms can be further differentiated by their product inhibition patterns (Cleland, 1963b)... 

Three substrates can combine with an enzyme to produce two or three products of reaction, in a wide variety of ways. If aU the binding steps are much faster than the catalytic step, which is the rate-limiting, then aU forms of enzyme are in a rapid equilibrium, and aU kinetic constants are true dissociation constants of respective enzyme-substrate complexes. If the catalytic step is not the slowest step in the kinetic mechanism, aU forms of enzyme attain a steady-state concentration shortly after the mixing of enzyme with substrates. AH kinetic mechanisms of steady-state reactions fall into only two major groups. Those in which all reactants must combine with the enzyme before reaction can take place and any product can be released, are called sequential. Mechanisms in which one or more products are released before aU substrates have added are called Ping Pong (Cleland, 1963). 

There are four basic steady-state Ter Ter systems an Ordered Ter Ter mechanism, and three Ping Pong Ter Ter mechanisms. In trisubstrate reactions with three substrates and three products of reaction, it is possible to envisage three different Ping Pong Ter Ter systens ... 

For this mechanism, the enzyme must bind substrate A first, followed by the release of product P and the formation of the enzyme species E. This is followed by binding of substrate B to E and the breakdown of the E B complex to free enzyme E and the second product Q. Thus, for ping pong mechanisms, no ternary complex is formed. A general steady-state scheme for this type of reactions is... 

Equation 9.10 represents the kinetics for the reaction given in Equation 9.2d. In the same way, Equation 9.11 gives the kinetics for Equation 9.2b (equivalent versions can be written for Equations 9.1a and 9.1b by flipping the red/ox subscripts). Electrons are passed from the reduced mediator to the enzyme, and the product (P) is produced by reduction of S. The concentrations of the intermediate complexes ES and EM are assumed to be low and at steady state. Expressions for individual kinetic rates can be written for both substrate and mediator. When coupled, these result in the bi-bi ping-pong expression for total reaction rate with respect to the enzyme Vg (Equation 9.12) [10,11] ... 

---