Generalized Model of Cooperative Covalent Polymerization: Connecting the Supramolecular Binding Interactions with the Catalytic Behavior

The dynamic assembly of actin and tubulin microfilaments from their subunits is imperative in enabling cell motility, cell division, and organismal muscle function. The nucleation-controlled growth kinetics that characterizes these protein polymerizations is facilitated by the cooperative and reversible noncovalent interactions of protein subunits. Although this growth kinetics has been realized in the supramolecular polymerization of numerous synthetic molecules, it is rare in covalent polymerizations since a cooperative binding event between a monomer and a polymer must also lead to catalysis of the polymerization. The ring-opening polymerization of N-carboxyanhydride monomers is one such system that has been shown to result in large degrees of cooperativity and self-acceleration depending on the polymer architecture. Herein, we apply recent experimental data to introduce a simple and generalized kinetic model of cooperative covalent polymerizations, incorporating a Michaelis–Menten-like equation into the rate laws to describe the binding of a monomer to the growing polymer chain explicitly. The treatment of the growing polymer chain as both a cooperative system and as a primitive “enzyme” with a distinct binding event not only increases the applicability of the model but also reduces the number of variables used to describe the system. The theoretical predictions are compared to experimental data with various levels of cooperativity. The application of this simple kinetic model across a broad range of macromolecular architectures with varying levels of cooperativity will help polymer chemists to discover similar mechanisms in nonpolypeptide systems and utilize them to create covalent analogues of natural cooperative systems. The model can be extended to cover a variety of cases in which additional intermediates or competitive reactants occur in the reaction pathway of cooperative covalent polymerization.