An integrated rate equation for determining initial velocities

Abstract

The initial velocities of enzyme catalyzed reactions are usually determined by measuring the slope near the origin of a product concentration vs. time plot. However, experimentally, it may be difficult to measure the product concentration accurately in the region of linearity. An integrated rate equation has been derived which can be used to calculate initial velocities from product concentration data taken in the time range from zero until the reaction has nearly reached completion. Using the partial enzymatic mechanism E P ⇌ k − 1 k 1 E + P and the steady-state approximation, an equation, In ( 1 − [ P ] / [ P ] e q ) = − v t / [ P ] e q has been derived in which [P]is the product concentration at time t, [P]eq is the product concentration at equilibrium, and v is the initial velocity. If ln (1 −[P]/[P]eq) is plotted vs. t, v can be calculated from the slope. The advantage of this method is that measurements of [P]are not restricted to less than 10% of [P]eq to maintain linearity. In most cases ln (1−[P]/[P]eq) vs. t plots are linear up to [P]/[P]eq equal to 0·9.