The Michaelis-Menten formalism assumes that the elementary steps of an enzymatic mechanism follow traditional mass-action kinetics. Recent evidence has shown that elementary bimolecular reactions under dimensionally-restricted conditions, such as those that might occur in vivo when reactions are confined to two-dimensional membranes and one-dimensional channels, do not follow traditional mass-action kinetics, but fractal kinetics. A Michaelis-Menten-like reaction operating under conditions of dimensional restriction is shown to exhibit new types of synergism and noninteger kinetic orders. These properties are likely to have an important influence on the behavior of intact biochemical systems, which is largely dependent upon the kinetic orders of the constituent biochemical reactions.