Some recent advances in enzyme kinetics.

Estimation of initial rates The vast majority of enzyme kinetic analyses presented in the literature involve the measurement and analysis of initial rates; this is so because the interpretation of properly estimated initial rates is a relatively robust procedure. It is, however, not infrequent to find that it is difficult to obtain good estimates of initial rates owing to premature curvature of product-time traces. This may result, for example, from product inhibition or enzyme inactivation. It is well known that it is notoriously difficult to estimate tangent slopes accurately, and it is undoubtedly the case that many results that have been presented in the literature are subject to this source of error (see, e.g., Atkins & Nimmo. 1980; Waley, 1981). Accordingly, considerable attention has been paid in recent times to the possibility of improving estimation of initial-rate values in circumstances in which the progress curve is significantly non-linear near the start of the reaction. All of the methods described below rely on analysis of the integrated Michaelis equation, which, of course, relates substrate depletion or product accumulation to the passage of time. Several empirical methods based on the fitting of polynomials have been proposed I see, e.g., Cornish-Bowden (1975) for a critical discussionl, but these are not described here, since they involve either laborious computation or the availability of a computer program. Szawelski (1983) has recently proposed a very simple polynomial procedure based on the smoothing method of Savitzky & Golay (1964). The earliest suggestions as to how the estimates of initial rates might be improved by a simple procedure was provided by Lee & Wilson (1971). They proposed that a chord be constructed (say between 0% and 20% reaction) and that its slope be taken as the reaction rate at a substrate concentration represented by the mean of the values at the chord ends, i.e. 10% in this case. This procedure, although quite accurate if the reaction is less than 50% complete, does not provide an estimate of the initial rate at the initial substrate concentration, and so the estimate will be affected by any product inhibition that occurs. Cornish-Bowden (1975) has presented an ingenious method based on the integrated Michaelis equation, which uses a form of the direct linear plot (see below) for the estimation of initial velocities in non-ideal circumstances. This method, illustrated in Fig. 1 and described in the legend, performs well in many circumstances provided that the extent of reaction is restricted to approx. 50% when the approximated form of the integrated equation is used. The approximation obviates the need for calculations involving logarithms to be made and is very accurate at low concentrations of product. Boeker (1982a) has suggested a simple accurate method based on a plot of AlPl/t against A[PI, where A[Pl is the change in product concentration during time t (i.e. AIPl = [PI [PI , ) . This type of plot, which gives the initial rate at zero time as the ordinate intercept, is easy to construct and seems to be accurate in most circumstances. The method relies on the same approximation used by Cornish-Bowden (1975) in the directlinear-plot method. Boeker’s (1982a) method is similar to one proposed long ago by Alberty & Koerber (1957), in which AIPI/t is plotted against time. The initial rate is again given by the ordinate intercept. The relative efficacy of these two plots for