Extended Curtin-Hammett principle: Origin of pathway selection in reversible reaction networks under kinetic control

Curtin-Hammett principle works in a reaction sequence where slow irreversible reactions are connected to a fast reversible reaction and determines the product distribution depending only on the relative energy barriers of the two irreversible reactions, resulting in kinetic pathway selection. A basic question is whether Curtin-Hammett principle is applicable to reaction networks composed of reversible elementary reactions, though reversible reactions are generally governed by the laws of thermodynamics. Numerical simulations of model systems where reversible elementary reactions are connected linearly to an initial reversible reaction demonstrate that a metastable state far from equilibrium is transiently produced and that its lifetime is prolonged with increasing the number of connected reversible reactions. Pathway selection based on this extended concept of Curtin-Hammett principle was observed in molecular self-assembly of a Pd6L4 truncated tetrahedron, which supports the idea that the extended Curtin-Hammett principle is a key general concept underlining kinetic control in reversible reaction networks.