The linear extrapolation method to determine protein stability from denaturant-induced unfolding experiments is based on the observation that the free energy of unfolding is often a linear function of the denaturant concentration. The value in the absence of denaturant is then estimated by extrapolation from this linear relationship. Parameters and their confidence intervals are typically estimated by nonlinear least-squares regression. We have compared different methods for calculating confidence intervals and found that a simple method based on linear theory gives accurate results. We have also compared three different parameterizations of the linear extrapolation method and show that the most commonly used form is problematic since the stability and m-value are correlated in the nonlinear least-squares analysis. Parameter correlation can in some cases causes problems in the estimation of confidence intervals and regions and should be avoided when possible. Two alternative parameterizations show much less correlation between parameters.

中文翻译：

---

剖析确定蛋白质稳定性的线性外推法的统计性质。

从变性剂诱导的展开实验确定蛋白质稳定性的线性外推方法是基于以下观察：展开的自由能通常是变性剂浓度的线性函数。然后根据该线性关系通过外推法估算不存在变性剂的值。通常通过非线性最小二乘回归估计参数及其置信区间。我们比较了计算置信区间的不同方法，发现基于线性理论的简单方法可以得出准确的结果。我们还比较了线性外推方法的三种不同参数设置，并表明最常用的形式存在问题，因为非线性最小二乘法分析中的稳定性和m值相关。在某些情况下，参数相关会导致置信区间和区域估计方面的问题，应尽可能避免使用。两个替代参数化显示参数之间的相关性要小得多。