One-way catalysis in a solvable lattice model

Catalysts speed up chemical reactions with no energy input and without being transformed in the process, therefore leaving equilibrium constants unchanged. Some catalysts, however, are much more efficient at accelerating one direction of a reaction. Is it possible for catalysis to be strictly unidirectional, accelerating only one direction of a reaction? Can we observe directional catalysis by analyzing the microscopic trajectory of a single reactant undergoing conversions between a substrate and a product state? We use the framework of a simple but exactly solvable lattice model to study these questions. The model provides examples of strictly one-way catalysts and illustrates a mathematical relationship between the asymmetric transition rates that underlie directional catalysis and the symmetric transition fluxes that underlie chemical equilibrium. The degree of directionality generally depends on the catalytic mechanism and we compare different mechanisms to show how they can obey different scaling laws.