Kinetic investigations of enzymatic reactions

The hydrolysis of sucrose has been the model reaction for the analysis of enzymatic reactions in the aborning of enzyme kinetics investigations. The discrepancy between the kinetic at low and high substrate concentrations led to a number of models describing the mechanism of the enzymatic reaction. The model of ADRIAN BROWN[8], who introduced an enzyme-substrate complex, is now commonly accepted (see equation 1.6).

$$E + S \overset{k_1}{\underset{k_{-1}}{\leftrightarrows}} ES \overset{k_2}{\rightarrow} E + P$$ (1.6)

His work has been used by VICTOR HENRI to model the enzymatic reaction mathematically[32]. This work was verified later by LEONOR MICHAELIS and MAUD MENTEN[57] and lead to the commonly known MICHAELIS-MENTENequation (see equation 1.7), $v$: rate, $k_0$: $k_2$; $e_0$: initial enzyme concentration; $a$: substrate concentration, $K_m$: MICHAELIS-constant $\left(\frac{k_{-1}+k_2}{k_1}\right)$; $V_{max}$: maximal velocity $\left(k_2 \times e_0\right)$).

$$v = \frac{k_0e_0a}{K_m+a}$$ (1.7)

To obtain the kinetic constants, $V_{max}$ and $K_m$, several graphical methods have been developed, in particular by B. WOOLF (unpublished, but cited by HALDANE et al. [29]) in which the MICHAELIS-MENTEN-equation is linearised. WOOLF's different plots were later published by several authors, e.g. the double-reciprocal plot by HANS LINEWEAVER and DEAN BURK[53] or the plot of $a/v$ against $a$ by C. HANES [30]. The direct linear plot by ATHEL CORNISH-BOWDEN and ROBERT EISENTHAL, introduced 1974, plots $-a$ as intercept on the abscissa and $v$ as intercept on the ordinate. This plot has the advantage, that no calculation is needed at all and that the procedure leads to more reliable results[14]. With the introduction of modern computers, it is also possible to estimate the kinetic parameters directly by a non-linear least square fit.