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Kinetic study on unzippering of polynucleotides and order–order transition in polypeptides
Author(s) -
Chay Teresa Ree,
Stevens Charles L.
Publication year - 1973
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.1973.360121110
Subject(s) - chemistry , reaction rate constant , relaxation (psychology) , molecule , reversible reaction , constant (computer programming) , nucleation , thermodynamics , exponential function , order (exchange) , kinetic energy , order of reaction , kinetics , computational chemistry , physics , organic chemistry , mathematical analysis , quantum mechanics , mathematics , psychology , social psychology , finance , computer science , economics , programming language , catalysis
Solutions are presented for N + 1 sequential and reversible first‐order reactions for which the magnitude of the reverse rate constant, k b , for all steps except the last is identical. Also the magnitude of the forward rate constant, k f , for all steps except the first and last is identical. The initial and final steps are nucleation reactions; therefore, the initial and final k f are modified by the factors σ′ and γ respectively. The final k b is modified by the factor γ σ. The ratio k b / k f is defined as s , which has the same meaning as s in the Zimm‐Bragg theory. The mathematical model is intended to apply to polymeric molecules of N segments and allows the calculation of the mole fraction of molecules in state i at any time t , C i ( t ). A molecule in state i has i unreacted segments and N – i reacted ones. Because the reactions are sequential, all reacted segments are contiguous. Our numerical results show that when σ′ is much less than unity and the forward reaction is favored, the relaxation curve is sigmoidal. If, however, the forward and reverse reactions are equally favored (i.e., s ≃ 1) the relaxation curve is a straight line. When s and σ′ are near unity, the curve is exponential for a considerably large fraction of the reaction. Further, in the exponential for a considerably large fraction of the reaction. Further, in the exponential phase of the reaction, the relaxation time is proportional to N 2 for highly cooperative systems (i.e., N σ ≪ 1). As found by Pipkin and Gibbs, if N is sufficiently large and s is less than unity (e.g., N ≳ 50 and s ≃0.9) the relaxation curve is largely linear with a slope inversely proportional to N . Applications are given for the unwinding of double‐helical poly(A·U) and the order–order transition in poly‐ L ‐proline.