Department of Biochemistry, University of Toronto, Toronto, Ontario, Canada M5G 1L7.
Anal Biochem. 2012 Feb 1;421(1):181-90. doi: 10.1016/j.ab.2011.10.050. Epub 2011 Nov 4.
Kinetic experiments provide much information about protein folding mechanisms. Time-resolved signals are often best described by expressions with many exponential terms, but this hinders the extraction of rate constants by nonlinear least squares (NLS) fitting. Numerical inverse Laplace transformation, which converts a time-resolved dataset into a spectrum of amplitudes as a function of rate constant, allows easy estimation of the rate constants, amplitudes, and number of processes underlying the data. Here, we present a Tikhonov regularization-based method that converts a dataset into a rate spectrum, subject to regularization constraints, without requiring an iterative search of parameter space. This allows more rapid generation of rate spectra as well as analysis of datasets too noisy to process by existing iterative search algorithms. This method's simplicity also permits highly objective, largely automatic analysis with minimal human guidance. We show that this regularization method reproduces results previously obtained by NLS fitting and that it is effective for analyzing datasets too complex for traditional fitting methods. This method's reliability and speed, as well as its potential for objective, model-free analysis, make it extremely useful as a first step in analysis of complicated noisy datasets and an excellent guide for subsequent NLS analysis.
动力学实验提供了大量关于蛋白质折叠机制的信息。时间分辨信号通常最好用具有许多指数项的表达式来描述，但这会阻碍通过非线性最小二乘（NLS）拟合来提取速率常数。数值逆拉普拉斯变换将时间分辨数据集转换为幅度谱作为速率常数的函数，允许轻松估计数据背后的速率常数、幅度和过程数。在这里，我们提出了一种基于 Tikhonov 正则化的方法，该方法将数据集转换为速率谱，同时受正则化约束，而无需在参数空间中进行迭代搜索。这允许更快速地生成速率谱，以及分析噪声太大而无法通过现有迭代搜索算法处理的数据集。该方法的简单性还允许进行高度客观、基本自动的分析，而无需人工指导。我们表明，这种正则化方法再现了以前通过 NLS 拟合获得的结果，并且对于分析传统拟合方法过于复杂的数据集非常有效。该方法的可靠性和速度，以及其用于无模型分析的潜力，使其成为分析复杂噪声数据集的第一步非常有用，并且是后续 NLS 分析的极好指南。
