Fluctuation in Quarternary Structure of Proteins and Cooperative Ligand Binding. I : Generalizations of Monod-Wyman-Changeux Model of Allosteric Enzymes

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Thermal fluctuation in conformations of protein molecules consisting of identical sub-units is considered, and its effect on the ligand binding equilibrium is discussed. Variability of the quarternary structure, which gives common influence on all subunits, is considered as basic mechanism for cooperative ligand binding. Quarternary structure is represented by conformational coordinate(s) s. Two models are proposed. In model A the ligand affinities of all sub-units have always the same value, which, however, depends on s. Formulae for successive dissociation constants K_m(m=1, 2, ・・・) are derived and a general relation K_m≦K_<m+1> is proved. In model B independent fluctuations of internal states of sub-units are allowed under the common constraint given by the quarternary structure. It is shown that model B reduces to model A on averaging over fluctuations of internal states of sub-units.
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