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Solute binding curves for (two polymer + solute)–complex systems I. “one‐solute‐stack” systems
Author(s) -
Schmitz Kenneth S.
Publication year - 1971
Publication title -
biopolymers
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.556
H-Index - 125
eISSN - 1097-0282
pISSN - 0006-3525
DOI - 10.1002/bip.360100413
Subject(s) - chemistry , polymer , thermodynamics , matrix (chemical analysis) , cooperativity , partition function (quantum field theory) , scalar (mathematics) , statistical physics , physics , quantum mechanics , geometry , mathematics , biochemistry , organic chemistry , chromatography
The matrix method is used for calculating the grand partition function for the reaction: 2 polymer + solute = complex. The homogeneous polymers are assumed to have two types of sites within each nucleotide unit: sites for the polymer–polymer association, i.e., (p‐p) sites; sites for polymer–solute association i.e., (p‐s) sites. The respective binding parameters, P and F , and nearest‐neighbor interaction parameters, W and S , are assumed independent. Complications due to ring entropy are avoided by rest riding the model to one‐solute‐stack systems, which are physically realizable when the reciprocal of the solute cooperativity parameter is much larger than the number of nucleotides in the polymer. The 4 × 4 generating matrix is shown to be a tensor product of two 2 × 2 matrices, each the generating matrix of a particular type of site. The scalar product of the 4 × 4 matrix is shown to be equivalent to the scalar product of a 2 × 2 matrix in the weak interaction limit, W ≈ 0. Calculations are presented for the general case which restricts the (p‐s) association to occur only with (p‐p) associated nucleotide units. The nature of the binding curve in relation to partitioning the total interaction energy ( F + P + S + W ) among the parameters is discussed. Also presented is a criterion for neglecting possible states in the calculation of the grand partition function.