Biophysical Instrumentation and Methodology

在分析性超离心数据分析领域，在应用鲁棒回归（也称为L-1回归）拟合超离心光吸光度数据方面进行了进一步的改进。它的误差分布不像通常假设的那样是正态分布，但很容易证明它具有对数偏斜的柯西型分布。这些特征被称为“肥尾”分布，之所以这样称呼，是因为与总分布的中心部分相比，尾部的偏差分布相对较大。结果表明，采用L-1回归可以较好地拟合具有这类误差分布的数据。该方法利用残差绝对值之和的最小值与每个点的标准误差的倒数作为其权重。与最小二乘（L-2）回归相比，L-1回归具有对数据“异常值”异常不敏感的进一步优点。将L-1回归应用于分析性超离心机的吸光度数据，其中标准误差是径向位置的函数，非常快速和简单，并且产生了非常出色的结果，现在是本实验室选择的拟合技术。L-1回归通常（不适当地）不提供与非线性最小二乘回归一起使用的参数误差估计方法。针对L-1回归拟合参数的标准误差估计，提出了一种参数无关的平衡自举算法。该方法也为非线性最小二乘回归提供了优越的误差估计。对系统误差对超离心分析得到的平衡常数自然对数值的影响的研究表明，转子温度误差大到1摄氏度对得到的热力学参数的影响很小，并且在温度变化后不能达到超离心平衡是热力学研究中主要的和最显著的误差来源。使非平衡误差最小化的步骤正在改进中。进一步改进这些分析的工作仍在继续。

In the areas of the analysis of data from analytical ultracentrifugation, further refinements have been made in the application of robust regression (also known as L-1 regression) for the fitting of ultracentrifugal light absorbance data. Such has an error distribution that is not normally distributed, as is commonly assumed, but can be readily demonstrated to possess a logarithmically-skewed Cauchy-type distribution. These are characterized as "fat-tailed" distributions, so called because of the relatively large distribution of deviations in the tails when compared to those in the central portion of the total distribution. It has been demonstrated that data with these types of error distribution are better fit by the L-1 regression. This method utilizes minimization of the sum of the absolute values of the residuals with the reciprocal of the standard error of each point as its weight. L-1 regression has the further virtue of being singularly insensitive to data "outliers," when compared to least-squares (L-2) regression. The application of L-1 regression to absorbance data from the analytical ultracentrifuge, where the standard error is a function of radial position, is singularly rapid and easy and has yielded such outstandingly superior results that it is now the fitting technique of choice in this laboratory. L-1 regression does not provide the means of parameter error estimation normally (and inappropriately) used with non-linear least-squares regression. An algorithm for performing a balanced bootstrap procedure which is parameter independent for the estimation of the standard errors of the fitting parameters obtained by L-1 regression has been developed. This method also yields superior error estimates for non-linear least-squares regression. Investigation of the effects of systematic errors on the values of the natural logarithm of the equilibrium constant obtained by ultracentrifugal analysis has demonstrated that rotor temperature errors as large as one degree Celsius have very little effect on the obtained thermodynamic parameters and that failure to attain ultracentrifugal equilibrium following a temperature change was the dominant and the most marked source of error in thermodynamic studies. Steps to minimize non-equilibrium error are in the process of being refined. Work on further refinements in these analyses is continuing. The objective of these methodological studies has been to obtain the best possible data for the temperature dependence of the values of the natural logarithms of the equilibrium constants for the molecular interactions being studied. These values permit calculation of the values of the standard Gibbs free energy changes (delta G) as a function of temperature. Using standard thermodynamic functions, the value of delta G as a function of temperature can be described in terms of the standard values of the changes of enthalpy (delta H), entropy (delta S), heat capacity (delta C-sub-P), and the first derivative of the heat capacity with respect to temperature, all at an appropriately selected reference temperature. If the reference temperature is taken as fixed (usually the mid-point of the temperature range), then the function is linear with respect to the other thermodynamic parameters and linear least-squares fitting gives optimized values for the parameters and their standard errors, but only if the function is orthogonal. This is not the case for this function and, as a result, the parameter cross-correlation coefficients and the resulting dependency values are very large, and the model is mathematically very ill-conditioned, since changes in any of the parameter values can be very well compensated by changes in the other parameter values. A method for making this function almost orthogonal has been developed, giving parameter cross-correlation coefficients and dependency values that are small enough that the function may be considered to be well-behaved, and good and meaningful values for the thermodynamic parameters and their standard errors can be obtained. Work is continuing in an effort to increase the efficiency of this procedure. Further optimization of thermodynamic analysis giving meaningful parameter values should permit these obtained values to be correlated to the nature of the mechanism(s) of the molecular interaction(s) and to the structure and function of the reactants and their complexes. Studies have been initiated on the application of global techniques of analysis, combining data from ultracentrifugal analysis to be coanalyzed with data from other techniques, such as light scattering or isothermal titration calorimetry, so that the globally obtained thermodynamic parameters are more rigorously defined, further validating the analyses and their applicability.