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 xi 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 xi. Correction to the helicity degree expression is reported. For the exact partition function we have additionally found, that: at N/xi approximate to 10 the transition temperature Tm reaches its asymptotic behavior of infinite N; the transition interval Delta T 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.