King—Altman method

The King-Altman method is most convenient for singleloop mechanisms. In practice, there is no need to write down the patterns. One can use an object say, a paper clip, to block one branch of the loop, write down the appropriate term for each enzyme species, then repeat the process until every branch in the loop has been blocked once. 

Comparison of Different Steady-State Methods. For relatively simple mechanisms, all the diagrammatic and systematic procedures illustrated in the foregoing sections are quite convenient. The King-Altman method is best suited for single-loop mechanisms, but becomes laborious for more complex cases with five or more enzyme forms because of the work involved in the calculation and drawing of valid patterns. With multiloop reaction schemes involving four to five enzyme species, the systematic approach requires the least effort, especially... 

ENZYME ENERGETICS ISQTQPIC PERTURBATION KINETIC PARAMETERS KINETIC RESOLUTION KING-ALTMAN METHOD... 

For mechanisms involving random addition of substrates, the King-Altman method gives squared terms in numerator and denominator of the rate equations, which are messy and difficult to work with. The method of Cha (10) treats each random segment as if it were in rapid equilibrium, and this simplifies the rate equation. The fact that data fit such a simplified equation does not prove that the mechanism is a rapid equilibrium one (see the rules in Section V,A,2 below) but does facilitate initial velocity analysis. 

The method described above is essentially based on the general King-Altman method, the application of which we will describe below for a case of enzymatic reactions occurring via the following sequence... 

Please note, these approximations are all dealing with the simple reaction sequence from Scheme 4.2. The application of e.g. the King-Altman method for multistep reactions will lead to the Michaelis-Menten equation in its typical form but with much more complex values for and Vkf The typical curve resulting from applying eqn (4.1) with = 4at = 1 is shown in Figure 4.1 adapted from ref. 26. 

The depicted mechanism is of course much more complex than the simple Michaelis-Menten scheme, but it can be simplified by employing the steady state approximation. This may be done in a relatively simple manner by applying either the King-Altman method or the less well-known Christiansen formalism. Applying the King-Altman method to the catalytic cycle given in Scheme 4.3 leads to a rate equation that is equal to the substi-tuted-enzyme mechanism, the detailed derivation of which was debated by Cornish-Bowden. ... 

The method of King and Altman rendered an invaluable service to enzymology because, with its help, the rate laws for many major reaction mechanisms in enzyme kinetics were developed. It is not necessary to understand the theory of the King-Altman method in order to apply it in practice, and indeed the theory is considerably more difficult than the practice. Therefore, we shall describe in the following sections the derivation of rate laws for several simple mechanisms... 

In Chapter 3 (Section 3.4), we have derived the rate law for the reversible Michaelis-Menten mechanism with two central complexes (Reaction (3.31)) with the aid of the steady-state roximation. We shall proceed now with the derivation of the same rate law with the aid of the King-Altman method. In order to apply the King-Altman method efficiently to a specific mechanism, a rigorous procedure must be strictly followed (Fromm, 1975 Wong, 1975 Punch Allison, 2000). 

The first step in the King-Altman method is to write the mechanism of enzymatic reaction in the usual form (Reaction (3.31)) ... 

A comparison of the derivation procedure for Eq. (3.36) described in Chapter 3 (Section 3.4) with the derivation procedure of the King-Altman method, clearly shows the advantage of the latter method. With increased complexity of mechanisms, the advantage of the King-Altman method increases dramatically. 

Let us proceed with the derivation of a rate law for this mechanism with the aid of the King-Altman method. First, let us draw a master pattern as a closed loop, showing all enzyme forms and the reaction between them (Fig. 1). 

The first task in the application of the King-Altman method is to write down the correct mechanism. The second task is to write aU possible patterns from the mechanism. This is the difficult part, because some patterns may be easily... 

The last example in Figure 2 clearly shows why, in complex cases, the finding of partial patterns from the master pattern is the most difficult part of the King-Altman method. Often, especially in complex mechanisms, it is not easy to write down all possible King-Altman patterns, and errors are a common occurrence. 

In this respect, very efficient modifications of the King-Altman method have been described by Wong and Hanes (1962), Volkenstein and Goldstein (1966), Gulbinsky and Cleland (1968), Fromm (1975) and others. A special attention deserves the method of Cha (1968) which is a very useful and a very widespread simplification of the King-Altman method (Topham Brockelhurst, 1992). 

The above example clearly illustrates that the systematic approach has some advantages over the King-Altman method, in a sense that it does away with pattern drawing. The systematic approach, described above, can be expanded and made more efficient by using several simple graphic mles described by Fromm (1975). 

The velocity equation in the presence of a dead-end inhibitor can be derived in the usual manner by the King-Altman method. However, if we know the velocity equation for the uninhibited reaction, then we can easily write the new velocity equation as modified by the inhibitor, without going through an entire derivation. The effect of a dead-end inhibitor is to multiply certain terms in the denominator of the uninhibited velocity equation by the factor F (F = i -t-//Xj), ths fractional concentration of an inhibitor. The terms multiplied by F, are those representing the enzyme form, or enzyme forms, combining with the inhibitor. Then, the Kj represents the dissociation constant of the specific enzyme form-inhibitor complex. 

The rate Eq. (9.8) is written in Cleland s nomenclature, with one inhibition constant defined for each reactant in the mechanism (KIa. iq This rate equation was dended in Chapter 4 with the aid of the King-Altman method (Eq. (4.39)). 

The complete rate equation, obtained with the King-Altman method, and after grouping similar terms, is quite complex ... 

Let us consider the Ordered Bi Bi mechanism in reaction (16.3) and derive the initial rate equation for the A-Q isotope exchange with the aid of the King-Altman method. The basic King-Altman figure for this case is shown in Fig. 1. 

Equations for the initial rate of isotope exchange in Ping Pong mechanisms may be derived by one of the methods described in Chapter 4 the usual procedure will be to apply the King-Altman method or the net rate constant method (Cleland, 1975) (Table 4). 

Rat equation in Enzyme kinetics (see), an equation expressing the rate of a reaction in terms of rate constants and the concentrations of enzyme spedes, substrate and product. When it is assumed that steady state conditions obtain, the Michaelis-Menten equation (see) is a suitable approximation. R.e. are represented graphically (see Enzyme graph) they may be derived by the King-Altman method (see). 

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