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Steady-State Approximation

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  1. PRE-STEADY-STATE KINETICS

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 v 0. 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 K sA 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 K mA (see section 4.1, below), to which it bears no necessary relationship in general. In the example given above K sA is equal to the ratio k -1/ k 1.


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