Ter Bi mechanisms

Assuming that the ordered Ter Bi mechanism applies, plots of actual 1/v versus 1/[Sa] data obtained in the presence of various hxed concentrations of the Sb and Sc substrates, [Sb] and [Sc], should be htted by Equation (8.75) resulting in the off-axis graphical output shown in Figure 8.40. The scheme corresponding to the ordered Ter Ter kinetic scheme is also shown (Scheme 8.13). Fortunately, the initial net forward rate for the conversion of substrates into products in the presence of negligible concentrations of products obeys the same steady state rate equations as the Ter Bi kinetic scheme. 

Much more realistic are the steady-stale trisubstrale mechanisms, that occur very frequently. In the Ter Bi Mechanisms Section, we shall develop the rate equations, in the absence of all products of reaction, for major Ter Bi mechanisms ... 

Table 3 Denominator terms in Ter Bi mechanisms (Cleland, 1963 Plowman, 1972 Segel, ...

The rate equation of the Ordered Ter Bi mechanism can be written by expanding the denominator with appropriate kinetic constant terms multiplied by substrate concentration terms given in Table 3. 

Definition of Kinetic Constants in Terms of Rate Constants Ordered Ter Bi mechanism... 

Similarly, the general rate equation for all Ter Bi mechanisms has always the same form... 

Restricting ourselves to the rapid equilibrium approximation (as opposed to the steady-state approximation) and adopting the notation of Cleland [158 160], the most common enzyme-kinetic mechanisms are shown in Fig. 8. In multisubstrate reactions, the number of participating reactants in either direction is designated by the prefixes Uni, Bi, or Ter. As an example, consider the Random Bi Bi Mechanism, depicted in Fig. 8a. Following the derivation in Ref. [161], we assume that the overall reaction is described by vrbb = k+ [EAB — k EPQ. Using the conservation of total enzyme... 

GA-3-P DH shows an Ordered Sequential Ter Bi kinetic mechanism NAD" GA-3-P Pi 1,3-AiSPGA NADH... 

There are two Haldanes for Ordered Uni Bi mechanism, with n = 1, and two for Ordered Bi Bi, but the second one depends on the definition of the inhibition constants. Ping Pong mechanisms with two stable enzyme forms have four Haldanes, one each with n = 0 and n = 2, and two with n = 1. The Theorell-Chance mechanism with only six rate constants has 16 Haldanes with n equal to minus one (1), zero (4), one (6), two (4), and three (1), corresponding to 4,3,2,1, and 0 inhibition constants, respectively. Ordered mechanisms that are of Ter reactancy in either direction have two Haldanes, with n = 0 and n = (Cleland, 1982). 

The Ter Bi Ping Pong system, in the forward direction, is called Bi Uni Uni Uni Ping Pong Ter Bi system (Cleland, 1967). The reaction sequence for this mechanism can be presented as... 

The general rate equation for the Ter Bi Ping Pong system in reaction (12.42) has the same form as Eq. (12.43) and can be expanded in the same way by writing the denominator terms for this mechanism from Table 3. 

The rate equation for the Ter Bi Ping Pong mechanism can be expanded in the same way by taking denominator terms from Table 3. 

Although each trisubstrate mechanism has a unique general rate equation, the rate equations in the absence of the products of reaction sometimes have identical forms for several Ter Bi and Ter Ter mechanisms. Therefore, in order to identify unequivocally the mechanism, we must revert to the product inhibition analysis and the use of dead-end inhibitors. 

Therefore, in order to simplify the product analysis of trisubstrate reactions, and for a proper interpretation of product inhibition patterns, we shall need a suitable comparative overview of trisubstrate mechanisms. Table 5 lists the product inhibition patterns for the major Ter Bi and Ter Ter mechanisms. Table 5 shows that, ultimately, each mechanism can be identified unequivocally on the basis of its unique product inhibition patterns. Product inhibition analysis is also able to identify unequivocally each substrate in a given mechanism (Plowman, 1972 Fromm, 1975, 1995). 

A system for describing kinetic mechanisms for enzyme-catalyzed reactions . Reactants (ie., substrates) are symbolized by the letters A, B, C, D, eto., whereas products are designated by P, Q, R, S, etc. Reaction schemes are also identified by the number of substrates and products utilized (i.e.. Uni (for one), Bi (two), Ter (three occasionally Tri), Quad (four), Quin (five), etc. Thus, a two-substrate, three-product enzyme-catalyzed reaction would be a Bi Ter system. In addition, reaction schemes are identified by the pattern of substrate addition to the enzyme s active site as well as the release of products. For a two-substrate, one-product scheme in which either substrate can bind to the free enzyme, the enzyme scheme is designated a random Bi Uni mechanism. If the substrates bind in a distinct order (note that, in such cases, A binds before B for ordered multiproduct release, P is released prior to Q, etc.), the scheme would be ordered Bi Uni. If the binding scheme is different than the release of product, then that information should also be provided for example, a two-substrate, two-product reaction in which the substrates bind to the enzyme in an ordered fashion whereas the products are released randomly would be designated ordered on, random off Bi Bi scheme. If one or more Theorell-Chance steps are present, that information is also given (e.g., ordered Bi Bi-(Theorell-Chance)), with the prefixes included if there is more than one Theorell-Chance step. 

The number of kinetically important substrates or products is designated by the syllables Uni, Bi, Ter, Quad, Pent, and so on, as they appear in the mechanism. 

The sequential mechanisms can be subdivided in those which have a compulsory order and those which have a random order of S binding. These mechanisms are often described with the popular shorthand notation given by Cleland (1963), in which uni, bi, ter, etc, denote the number of S and P species. The /Cm values of the various reactants are concentration values at which half of the maxi-... 

As with polypyrrole, A- is a counterion incorporated into the polymer during growth to balance the charge on the polymer backbone, and m is a parameter proportional to the molecular weight. As with polypyrroles, the mechanism of polymerization involves formation of radical cations that react with one another or the starting monomer to develop the polymeric structure (Figure 6.1). The reaction of the radical cation with the thiophene monomer has been elegantly demonstrated in studies in which small amounts of bi- or ter-thiophene were added to reduce the polymerization potential.1 Even after the additive was consumed, polymerization continued at lower potentials. 

BiBi Uni UniPingPongTerTerMechanism. In the forward direction, therate equation is identical with that for the Bi Uni Uni Bi Ping Pong Ter Ter mechanism. 

The above analysis can also be applied to the Bi Bi segment of a trisubstrate Ping Pong mechanism, the Bi Bi Uni Uni Ping Pong Ter Ter mechanism ... 

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