King-Altman patterns

The presence of an enzyme intermediate(s) that is not part of a loop will not affect the number of King-Altman patterns. For instance, the addition of a competitive inhibitor, I, to the above system will result in the same number of patterns. 

The additional E El branch is present in all the diagrams. Thus, in calculating the number of valid King-Altman patterns, only the closed loops need be considered. The determinants of E, EA, EAB, and El can be obtained by the method just described ... 

For more complex mechanisms having alternate pathways that form several closed loops, the precise number of valid King-Altman patterns must be calculated to avoid omission of terms. To illustrate the various situations that may occur, let us consider Scheme 1. 

Lam CF, Priest DG (1972) Enzyme kinetics. Systematic generation of valid King-Altman patterns. 

Table l. Assignment of King-Altman patterns shown in Fig. a for m or steady-state mechanisms... 

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. 

However, two King-Altman patterns contain closed loops ... 

Cha (1968) has described a method for analyzing mechanisms that contain steps in equilibrium that is much simpler than the complete King-Altman andysis because each group of enzyme forms at equilibrium can be treated as a single species. Thus, the method of Cha provides for a condensation of King-Altman patterns and shortens considerably the procedure of derivatioa... 

In the King-Altman figure, all enzyme forms are labeled and, therefore, there are four three-lined King-Altman patterns necessary to obtain the denominator term of the velocity equation. 

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... 

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 shaded area represents the rapid equilibrium segments. The binding and dissociation of the first substrate and the last product are both significantly faster than the other steps in the above reaction. The King-Altman master pattern can now be condensed into only two lines connecting X and the central complexes (EAB + EPQ), where [X] = [E] + [EA] + [EQ] (Reaction 4.51). 

Thus, the King-Altman master pattern has now only two comers instead of four and consequently only two partial patterns. However, only a proportion of X will react now in one direction and an another proportion of X in the other direction. The symbols a and p now represent the fractional concentrations and stand for the relative proportion of the rapid equihbrium segment, X, that actually is involved in the given reaction. That is, of aU the species comprising X, only EA will react with B to yield EAB and, in the opposite direction, only EQ wiU react with P to produce EPQ. 

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). 

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