The cooperative binding effects of viologens and pyridines to a synthetic bivalent porphyrin receptor are used as a model system to study how the magnitudes of these effects relate to the experimentally obtained values. The full thermodynamic and kinetic circles concerning both activation and inhibition of the cage of the receptor for the binding of viologens were measured and evaluated. The results strongly emphasize the apparent character of measured binding and rate constants, in which the fractional saturation of receptors with other guests is linearly expressed in these constants. The presented method can be used as a simple tool to better analyze and comprehend the experimentally observed kinetics and thermodynamics of natural and artificial cooperative systems.kinetics ͉ slippage ͉ supramolecular chemistry ͉ thermodynamics C ooperative binding plays an important role in nature, where it is used to construct well-defined assemblies and is used as a tool to transfer information at the cellular level (1). The formation of the tobacco mosaic virus (2) and the binding of oxygen to hemoglobin (3) are 2 well-known examples of cooperative processes. Cooperative binding interactions can be homotropic or heterotropic, when the combined binding to a multivalent receptor involves the same or different types of guests. In additions, these interactions can be positive or negative, when the binding of a guest promotes or obstructs the binding of a second guest (4).One of the challenges in the field of supramolecular chemistry is to design artificial systems that display cooperative binding effects, not only to better understand the mechanisms involved in the natural processes but also to prepare functional materials and catalysts that benefit from such binding interactions. Over the years, a large number of artificial receptors displaying positive (5-8) and negative (9-11) homotropic and positive (12-20) and negative (21-23) heterotropic cooperative binding phenomena have been developed. Although in many cases the origins of the cooperative effects could be identified, few studies have dealt in detail with the kinetics and thermodynamics of such complicated multicomponent receptor-guest systems. This is surprising, because unlike the complex biological systems, the artificial receptor-guest systems can be easily studied, and the fine details of cooperative behavior can be uncovered. It is generally known that measured association constants are context dependent in the sense that apparent values that depend on, e.g., the solvent system, salt concentrations, pH, and in the worst case impurities, are obtained (4). As a consequence, the observed cooperative binding effects might often deviate from the intrinsic ones.To investigate how the measured cooperative binding effects as derived from the observed experimental binding constants are related to the intrinsic ones, we present a detailed study of the combined binding of viologens and pyridines to the bivalent zinc porphyrin receptor Zn1 (24, 25) (Scheme 1). Pyridine ligan...