Finite one-dimensional spin systems as models of biopolymers

New models are proposed for describing various properties of biopolymers, especially those of proteins and nucleic acids. Each model is constituted of a set of spins arranged on a chain, and each pair of spins produces an interaction. We examine the transitions of these spin systems between the ground state and the disordered state. It is found that the transitions of the present spin systems demonstrate various properties in response to values of the so-called interaction energy. If we define interaction energy parameters with no so-called frustration, the system exhibits two-state transitions, similar to the folding-unfolding transition of small proteins. The addition of frustrations to the model produces effects similar to those of mutations in proteins. On the other hand, if the interactions between two spins attenuate as a function of their separation along the chain, the transition of the system has characteristics similar to those of nucleic acids. Thus, the present spin systems can offer a unified view of the folding-unfolding transition of biopolymers in terms of differences in the pairwise interactions between spins. Based on our models, we propose a condition for two-state transition behavior for proteins.