Lotka-Volterra Rate ExpressionsWe can write the steps in the Lotka-Volterra mechanism as A + X -> 2 X (Rate constant k1) X + Y -> 2 Y (Rate constant k2) Y -> B (Rate constant k3) so that the rate laws for the intermediates are d[X]/dt = k1[A][X] – k2[X][Y] d[Y]/dt = k2[X][Y] – k3[Y] If [A] is a constant ([A]0) and if we assume steady state for X and Y, we can write d[X]/dt = k1[A]0[X] – k2[X][Y] = 0 d[Y]/dt = k2[X][Y] – k3[Y] = 0 or [Y] = k1[A]0/k2 = constant [X] = k3/k2 = constant which is what a steady-state assumption should give, but we know this assumption misses the key feature of this reaction mechanism: the oscillation in time of the intermediates' concentrations.  |
