One-dimensional Ising model applied to protein folding

We study protein folding by introducing a simplified one-dimensional analogy of a protein consisting of N contacts. Closed contacts are assigned a binding energy while open contacts represent several configurations of equal (zero) energy. Furthermore, two neighboring contacts in different states are assigned an unfavorable energy. We show that the statistical mechanics of this problem becomes that of the one-dimensional Ising model of N spins. This model generalizes the “zipper” model that has been studied earlier by the authors and co-workers. The distinct new feature of the present model is the possibility to have folding/unfolding simultaneously at several places along the protein. This is a likely feature, in particular for long proteins, and influences especially the sharpness of the folding/unfolding transition. This sharpness is expressed in terms of a vanʹt Hoff enthalpy relation which we study here. By replacing the total length of the protein by an effective one, results can be directly related to and are similar to those of the “zipper” model. Upon introduction of water interactions both cold and warm destabilization of the protein are exhibited, which also is similar to the results of the “zipper” model.