3.1 Numbering of Reactions
The elementary reactions in a composite mechanism should be numbered as systematically as possible and in such a way that reverse processes are easily recognized. The reaction numbers should be used as subscripts to k, for rate constants, or v, for the individual rates (chemical fluxes). The preferred scheme for ordinary use is:
1) k1, k-1, k2, k-2 . . . . ; v1, v-1, v2, v-2, . . .
In this scheme positive subscripts may be prefixed by a + sign, i.e. k1 may be written as k+1, if it helps avoid ambiguity resulting from confusion with scheme 3 (below), or to emphasize that it refers to a step in the forward direction of the reaction. For some kinds of computer application and for theoretical discussions of enzyme mechanisms it is sometimes convenient to number the different forms of the enzyme rather than the elementary steps and then to denote the step from (e.g.) E3 to E4 as 34, etc. With this scheme the numbering of enzyme forms must be given explicity and the rate constants and rates listed above might become
2) k12, k21, k23, k32, . . .; v12, v21, v23, v32, . . .
If there are more than nine enzyme forms in the mechanism the subscripts should be separated by a comma, e.g. k10,11 but this can be omitted when it is not required for clarity.
The following scheme, in which odd subscripts refer to forward steps and even subscripts to reverse steps:
3) k1, k2, k3, k4 . . . . ; v1, v2, v3, v4, . . .
is less satisfactory, both because it conflicts with IUPAC Recommendations [3] and because it makes it more difficult to recognize the forward and reverse rate constants for particular steps.
It is unrealistic to expect any universal system of numbering rate constants to be equally satisfactory in all circumstances. For example, in a mechanism where enzyme forms in different states of protonation can undergo analogous reactions it may be clearer to assign the same numbers to the analogous steps and distinguish between them by the use of primes, etc., rather than try to apply any of the above schemes in a rigid way. Regardless of what system is used, rate constants should never be referred to except in explicit relation to a mechanism or to a kinetic equation.
3.2. Steady-State Approximation
If an intermediate is always present in amounts much less than those of the reactants (other than the enzyme) the rate of change of its concentration is much smaller than that of the reactants. This condition is ensured whenever, as is usually the case in enzyme-catalysed reactions, the concentration of substrate is much higher than that of the enzyme; it is not necessary for the amount of intermediate to be small compared with the amount of enzyme. For example, in the scheme
E + A
EA
E
+ Z
if [EA] is always much less than [A] the following equation is obeyed to a good approximation:
.
. . . . . . . (7)
The intermediate EA is said to be in a steady state. The use of this approximation to obtain an overall rate expression is known as the steady-state treatment or the steady-state approximation.
At the very beginning of the reaction the concentration of EA in the above scheme is rising from zero to its steady-state value. The steady-state approximation is not valid during these early times and the kinetics are known as pre-steady-state kinetics or transient-phase kinetics. The transient phase of an enzyme-catalysed reaction usually occupies a very brief period of time (usually a small fraction of a second), and special techniques must be used for investigating this phase of the reaction (Section 9).
The rate of reaction of an enzyme-catalysed reaction is not defined during the transient phase, because there is not a one-to-one stoichiometry between the reactants (see section 2.2). In the steady state a one-to-one stoichiometry is established and the rate of reaction can be defined. This rate, extrapolated back to zero time, is called the initial rate and given the symbol v0. The subscript 0 is normally omitted when no other kinds of rate are at issue, i.e. when extended time courses are not being analysed.
The ratio [E] [A]/[EA] at equilibrium is called the substrate dissociation constant and given the symbol KsA When only one substrate is in question the qualifier A may be omitted, and when it is included its location is a matter of typographical convenience. The substrate dissociation constant should not be confused with the Michaelis constant KmA (see section 4.1, below), to which it bears no necessary relationship in general. In the example given above KsA is equal to the ratio k-1/k1.
References for this section
1. International Union of Pure and Applied Chemistry and International Union of Biochemistry (1973) Enzyme Nomenclature, Recommendations 1972, Elsevier, Amsterdam.
2. Nomenclature Committee of the International Union of Biochemistry (1979) Enzyme Nomenclature, Recommendations 1978, Academic Press, New York.
3. International Union of Pure and Applied Chemistry (1981) Symbolism and terminology in chemical kinetics, 1980, Pure Appl. Chem. 53, 753 - 771.
4. International Union of Pure and Applied Chemistry (1979) Manual of Symbols and Terminology for Physicochemical Quantities and Units, Pergamon Press, Oxford; also in Pure Appl. Chem. 51, 1-41 (1979).
5. International Union of Pure and Applied Chemistry (1979) Glossary of terms used in physical organic chemistry (Gold, V., ed.) Pure Appl. Chem. 51, 1725-1801. [revised edition Pure Appl. Chem. 1994, 66, 1077-1184]
Symbolism and Terminology in Enzyme Kinetics (Recommendation 1981)
http://www.chem.qmul.ac.uk/iubmb/kinetics/ek4t6.html