A critical but often overlooked question in the study of ligands binding to proteins is whether the parameters obtained from analyzing binding data are practically identifiable (PI), i.e., whether the estimates obtained from fitting models to noisy data are accurate and unique. Here we report a general approach to assess and understand binding parameter identifiability, which provides a toolkit to assist experimentalists in the design of binding studies and in the analysis of binding data. The partial fraction (PF) expansion technique is used to decompose binding curves for proteins with n ligand-binding sites exactly and uniquely into n components, each of which has the form of a one-site binding curve. The association constants of the PF component curves, being the roots of an n-th order polynomial, may be real or complex. We demonstrate a fundamental connection between binding parameter identifiability and the nature of these one-site association constants: all binding parameters are identifiable if the constants are all real and distinct; otherwise, at least some of the parameters are not identifiable. The theory is used to construct identifiability maps from which the practical identifiability of binding parameters for any two-, three-, or four-site binding curve can be assessed. Instructions for extending the method to generate identifiability maps for proteins with more than four binding sites are also given. Further analysis of the identifiability maps leads to the simple rule that the maximum number of structurally identifiable binding parameters (shown in the previous paper to be equal to n) will also be PI only if the binding curve line shape contains n resolved components.

译文

:在配体与蛋白质结合的研究中,一个关键但经常被忽略的问题是,从分析结合数据中获得的参数是否可实际识别(PI),即从拟合模型与噪声数据中获得的估计值是否准确且唯一。在这里,我们报告了一种评估和理解结合参数可识别性的通用方法,该方法提供了一个工具包,可协助实验人员设计结合研究和分析结合数据。部分分数(PF)扩展技术用于将具有n个配体结合位点的蛋白质的结合曲线准确唯一地分解为n个成分,每个成分都具有一个单点结合曲线的形式。作为n阶多项式的根的PF分量曲线的关联常数可以是实数,也可以是复数。我们展示了绑定参数可识别性与这些一站式关联常数的性质之间的基本联系:如果常数都是实数和唯一的,则所有绑定参数都是可识别的;否则,至少某些参数无法识别。该理论用于构建可识别性图谱,从中可以评估任何两个,三个或四个位点结合曲线的结合参数的实际可识别性。还给出了扩展方法以生成具有四个以上结合位点的蛋白质的可识别性图谱的说明。对可识别性图的进一步分析得出一个简单的规则,即只有在结合曲线线形包含n个分解分量的情况下,结构上可识别的结合参数的最大数量(在前一篇论文中显示为等于n)也将为PI。

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