Practical Aspects of Kinetic Studies Enzyme assays: discontinuous: samples are removed at intervals and analysed to determine the extent of the reaction (quenching) continuous: the progress of the reaction is monitored continuously (optical spectroscopy, fluorescence, pH-stat radioisotopic measurements)

In some cases the substrate and product of an enzymatic reaction do not provide a distinct signal for convenient measurement of their concentrations. Indirect assay: product generation can be coupled to another nonenzymatic reaction that does produce a convenient signal Coupled assays: The enzymatic reaction of interest is paired with a second enzymatic reaction, which can be conveniently measured.

glucose + ATP glucose-6-phosphate + ADP In a typical coupled assay, the product of the enzyme reaction of interest is the substrate for the enzyme reaction to which it is coupled. Hexokinase catalyzes the formation of glucose 6-phosphate and ADP from glucose and ATP. glucose + ATP glucose-6-phosphate + ADP hexokinase None of these products or substrates provide a particularly convenient means of measuring enzymatic activity.

glucose-6-phosphate + NADox 6-phosphogluconate +NADred However, the product glucose 6-phosphate is the substrate for glucose 6-phosphate dehydrogenase, which, in the presence of NADred, converts this molecule to 6-phosphogluconate. glucose-6-phosphate + NADox 6-phosphogluconate +NADred In the course of the second enzymatic reaction, NADP is reduced to NADPH, and this reduction can be monitored easily by light absorption at 340 nm Glucose-6-phosphatedehydrogenase

This example can be generalized to the following scheme: We are measuring C in this scheme, but it is the steady state velocity v1 that we wish to study. To accomplish this we must achieve a situation in which v1 is rate limiting (i.e., v1<<v2) and B has reached a steady state concentration. Under these conditions, B is converted to C almost istantaneously, and the rate of C production is v1.

If v1 is a constant (initial rate, zero order) The equation may be integrated (Storer and Cornish Bowden, 1974) Where  is a dimensionless number that depends on v2/v1 and v1/V2

The values of k2 and Km2 for the coupling enzyme are constants that cannot be experimentally adjusted without changes in reaction conditions. The maximal velocity V2 however, can be controlled by the researcher by adjusting the concentration of the coupling enzyme.

In order to calculate the time within which v2 reaches a given fraction of v1 it is necessary to know Km,2 which is measured in a preliminary experiment V2 which depends on the concentration of coupling enzyme We adjust the concentration of our enzyme of interest so that its steady state velocity is

from Table So the time required for v2/v1 = 0.99 is 2.62 min

Fast reactions ( >0.5 ms) Continuous flow Stopped flow

Quenched flow

Quenched flow

Relaxation methods T-jump p-jump

At final equilibrium