Briggs W E
Department of Mathematics, Campus Box 426, University of Colorado, Boulder, CO 80309, USA.
Biophys Chem. 1983 Jul;18(1):67-71. doi: 10.1016/0301-4622(83)80028-3.
An allosteric binding system consisting of a single ligand and a nondissociating macromolecule having multiple binding sites can be represented by a binding polynomial. Various properties of the binding process can be obtained by analyzing the coefficients of the binding polynomial and such functions as the binding curve and the Hill plot. The Hill plot has an asymptote of unit slope at each end and the departure of the slope from unity at any point can be used to measure the effective interaction free energy at that point. Of particular interest in detecting and measuring cooperativity are extrema of the Hill slope and its value at the half-saturation point. If the binding polynomial is symmetric, then there is an extremum of the Hill slope at the half-saturation point. This value, the Hill coefficient, is a convenient measure of cooperativity. The purpose of this paper is to express the Hill coefficient for symmetric binding polynomials in terms of the roots of the polynomial and to give an interpretation of cooperativity in terms of the geometric pattern of the roots in the complex plane. This interpretation is then applied to the binding polynomials for the MWC (Monod-Wyman-Changeux) and KNF (Koshland-Nemethy-Filmer) models.
由单个配体和具有多个结合位点的非解离大分子组成的别构结合系统可用结合多项式来表示。通过分析结合多项式的系数以及诸如结合曲线和希尔图等函数，可以获得结合过程的各种性质。希尔图在两端各有一条单位斜率的渐近线，斜率在任何一点偏离单位值都可用于测量该点的有效相互作用自由能。在检测和测量协同性方面，特别令人感兴趣的是希尔斜率的极值及其在半饱和点处的值。如果结合多项式是对称的，那么在半饱和点处希尔斜率存在一个极值。这个值，即希尔系数，是衡量协同性的一个便利指标。本文的目的是根据多项式的根来表示对称结合多项式的希尔系数，并根据复平面中根的几何模式对协同性作出解释。然后将这种解释应用于MWC（莫诺 - 怀曼 - 尚热）模型和KNF（科什兰德 - 内梅西 - 菲尔默）模型的结合多项式。
