System Size Dependence in the Zimm–Bragg Model: Partition Function Limits, Transition Temperature and Interval

Within the recently developed Hamiltonian formulation of the Zimm and Bragg model we re-evaluate several size dependent approximations of model partition function. Our size analysis is based on the comparison of chain length N with the maximal correlation (persistence) length [Formula: see text] of helical conformation. For the first time we re-derive the partition function of zipper model by taking the limits of the Zimm–Bragg eigenvalues. The critical consideration of applicability boundaries for the single-sequence (zipper) and the long chain approximations has shown a gap in description for the range of experimentally relevant chain lengths of 5–10 persistence lengths [Formula: see text]. Correction to the helicity degree expression is reported. For the exact partition function we have additionally found, that: at [Formula: see text] the transition temperature [Formula: see text] reaches its asymptotic behavior of infinite N; the transition interval [Formula: see text] needs about a thousand persistence lengths to saturate at its asymptotic, infinite length value. Obtained results not only contribute to the development of the Zimm–Bragg model, but are also relevant for a wide range of Biotechnologies, including the Biosensing applications.