Enzymes 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... 

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... 

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 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. 

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). 

The King and Altman Method. King and Altman developed a systematic approach for deriving steady-state rate equations, which has contributed to the advance of enzyme kinetics. The first step of this method is to draw an enclosed geometric figure with each enzyme form as one of the corners. Equation (5), for instance, can be rewritten as ... 

A useful procedure for deriving steady-state rate expressions for enzyme-catalyzed reactions . Although not as commonly used as the King and Altman method, it is far more convenient (and less error-prone) when attempting to obtain expressions for complicated reaction schemes. One of its values is that the approach is very systematic and straightforward. The systematic nature of the procedure can be illustrated by the derivation of the steady-state ordered Bi Bi reaction. 

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... 

King, E.I. and Altman, C., A schematic method of deriving rate laws for enzyme-catalyzed reactions,... 

As has already been shown, graph theory methods were first used in chemical kinetics by King and Altman who applied them to linear enzyme mechanisms [1] to derive steady-state kinetic equations. Vol kenshtein and Gol dshtein in their studies during the 1960s [2 1] also elaborated a new formalism for the derivation of steady-state kinetic equations based on graph theory methods ("Mason s rule , etc.). 

In principle, the steady-state rate expression for any enzyme with any number of reactants can be derived using the methods of the previous section. In practice, the procedure is very laborious, so use is made of an algorithmic method, introduced by King and Altman in 1956 it is not applicable to (1) nonenzymatic reactions (each reactant concentration must be S>[E]0), (2) mixtures of enzymes, or (3) reactions with nonenzymatic steps. However, these are not severe restrictions. It is applied as follows ... 

Many enzyme reactions have more than one intermediate for which King and Altman (1956) devised a method, based on matrix algebra, by establishing the rate equation of a given enzymic reaction simply by inspecting all complexes and the reactions between them. 

At the time that the previous chapter in Volume 11 was written, the method of King and Altman (7) was the method of choice for deriving steady-state rate equations for enzymic reactions, and this is still true for any mechanism involving branched reaction pathways. The best description of this method may be found in Mahler and Cordes (8). A useful advance was made in 1975 with the introduction of the net rate constant method (9), and because it is the simplest method to use for any nonbranched mechanism, as well as for equations for isotopic exchange, positional isotopic exchange, isotope partitioning, etc., we shall present it here. 

Mechanism I is referred to as a compulsory-pathway mechanism since the order of addition of substrates to the enzyme is fixed mechanism II is often called a shuttle or ping pong mechanism because part of a substrate is shuttled back and forth between substrates and enzyme and mechanism III involves a random addition of substrates to the enzyme. Obviously a large number of additional mechanisms could be written by permuting the substrates and by combining two of the mechanisms. If (C) = (D) = 0, the initial velocities for the first two mechanisms can be easily obtained using the method of King and Altman ... 

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