Briggs W E
Biophys Chem. 1986 Aug;24(3):311-8. doi: 10.1016/0301-4622(86)85036-0.
Given a binding polynomial in Adair form, A(x) = 1 + beta 1 x + ... + beta n x n, beta i greater than or equal to 0, a basic problem is to determine a method of fitting a model polynomial to A(x) and a quantitative measure of the goodness of fit. This paper presents such a method for fitting Monod-Wyman-Changeux (MWC) model polynomials when A(x) is of degree three or four. The method of fitting is based on the property that the zeros of an MWC polynomial of any degree lie on a circle in the complex plane. The parameters in the MWC model are determined so that if possible this circle coincides with the circle on which lie the zeros of A(x). The measure of goodness of fit is provided by a probabilistic model which gives the probability that a binding polynomial has its zeros on a circle on which lie the zeros of an MWC polynomial and if so, the probability that the juxtaposition of the two sets of zeros can occur by chance alone.
给定一个阿代尔形式的结合多项式(A(x)=1 + \beta_1x + \cdots + \beta_nx^n)，其中(\beta_i \geq 0)，一个基本问题是确定一种将模型多项式拟合到(A(x))的方法以及拟合优度的定量度量。本文提出了一种当(A(x))的次数为三或四时拟合莫诺 - 怀曼 - 尚热（MWC）模型多项式的方法。拟合方法基于这样一个性质，即任何次数的MWC多项式的零点位于复平面上的一个圆上。确定MWC模型中的参数，以便在可能的情况下，这个圆与(A(x))的零点所在的圆重合。拟合优度的度量由一个概率模型提供，该模型给出了一个结合多项式的零点位于MWC多项式的零点所在圆上的概率，如果是这样，两组零点并列出现仅仅是偶然的概率。
