The legacies of Langmuir, Ising, and Pauling: ligand binding and the helix-coil transition

Multiple, independent sites or domains behave, on chemical change, in a manner predicted by Langmuir. Distortions of this behavior have been attributed to interactions between the domains, which vary with the progress of the changes occurring at the sites or domains. The two main models for nearest neighbor interactions perturbing the Langmuir prediction for independent domains are those of Ising and Pauling. If we designate the initial site as (-) and the changed site as (+), then the Langmuir requirement for independence of sites yields a set of nearest neighbor interactions such that the (- -), (- +), (+ -), and (+ +) interactions are all identical. This identity is usually characterized as "no interactions." Ising, in dealing with electron pairs, invoked nearest neighbor interactions such that the interactions of the (- -) paris equaled those of the (+ +) pairs, but with the (- +) and (+ -) pairs differing from the reference (- -) pair. Pauling, on the other hand, postulated that only the (- -) and (+ -) pairs interacted differently. A dichotomy has arisen in the application of these two models, with some investigators ignoring or overlooking one of the models. We explore these models, alone and combined, with exact partition functions generated in reasonable computer times for hundreds of sites employing our combinatorial algorithm.