One of the great ambitions of structural biology is to describe structure-function relationships quantitatively.  Statistical thermodynamics is a powerful, general tool for computing the behavior of biological macromolecules at equilibrium, because it establishes a direct link between structure and function.  Complex behavior emerges as equilibria of multiple reactions are coupled.  Analytical treatment of linked equilibria scales poorly with increasing numbers of reactions and states as the algebraic constructs rapidly become unwieldy.  We therefore developed a generalizable, but straightforward computational method to handle arbitrarily complex systems.  To demonstrate this approach, we collected a multi-dimensional fluorescence landscape of an engineered fluorescent glucose biosensor and showed that its features could be modeled with ten intricately linked ligand-binding and conformational-exchange reactions.  This protein represents a minimalist model of sufficient complexity to encompass fundamental biomolecular structure-function relationships: two- and multi-state conformational ensembles, conformational hierarchies, osmolytes, coupling between different binding sites and coupling between ligand binding and conformational change.   The successful fit of this complex, multifaceted system demonstrates generality of the method.