Ramakrishnan Anand, Sadana Ajit
Chemical Engineering Department, University of Mississippi, University, MS 38677-1848, USA.
Anal Biochem. 2002 Apr 1;303(1):78-92. doi: 10.1006/abio.2002.5581.
A mathematical approach using fractal concepts is presented for modeling the binding and dissociation interactions between analytes and nuclear estrogen receptors (ER) occurring on surface plasmon resonance biosensor chip surfaces. A kinetic knowledge of the binding interactions mediated by ER would help in better understanding the carcinogenicity of these steroidogenic compounds and assist in modulating these reactions. The fractal approach is applied to analyte-ER interaction data obtained from literature. Numerical values obtained for the binding and dissociation rate coefficients are linked to the degree of roughness or heterogeneity (fractal dimension, D(f)) present on the biosensor surface. For example, a single-fractal analysis is used to describe the binding and dissociation phases for the binding of estradiol and ERalpha in solution to clone 31 protein immobilized on a biosensor chip (C-S. Suen et al., 1998, J. Biol. Chem. 273(42), 27645-27653). The binding and the dissociation rate coefficients are 27.57 and 8.813, respectively, and the corresponding fractal dimensions are 1.986 and 2.268, respectively. In some examples dual-fractal models were employed to obtain a better fit of either the association or the dissociation phases or for both. Predictive relationships are developed for (a) the binding and the dissociation rate coefficients as a function of their respective fractal dimensions and (b) the ratio K(A) (= k/k(d)) as a function of the ratio of the fractal dimensions (D(f)/D(fd)). The analysis should provide further physical insights into the ER-mediated interactions occurring on biosensor and other surfaces.
本文提出了一种使用分形概念的数学方法，用于模拟在表面等离子体共振生物传感器芯片表面上发生的分析物与核雌激素受体（ER）之间的结合和解离相互作用。了解由ER介导的结合相互作用的动力学知识，将有助于更好地理解这些类固醇生成化合物的致癌性，并有助于调节这些反应。分形方法应用于从文献中获得的分析物-ER相互作用数据。获得的结合和解离速率系数的数值与生物传感器表面存在的粗糙度或异质性程度（分形维数，D(f)）相关。例如，单分形分析用于描述溶液中雌二醇和ERα与固定在生物传感器芯片上的克隆31蛋白结合的结合和解离阶段（C-S. Suen等人，1998年，《生物化学杂志》273(42)，27645-27653）。结合和解离速率系数分别为27.57和8.813，相应的分形维数分别为1.986和2.268。在一些示例中，采用双分形模型以更好地拟合缔合或解离阶段，或两者都拟合。建立了预测关系：（a）结合和解离速率系数作为其各自分形维数的函数；（b）比率K(A)（=k/k(d)）作为分形维数比率（D(f)/D(fd)）的函数。该分析应为在生物传感器和其他表面上发生的ER介导的相互作用提供进一步的物理见解。
