Boosted regression trees, multivariate adaptive regression splines and their two-step combinations with multiple linear regression or partial least squares to predict blood-brain barrier passage: a case study

The use of some unconventional non-linear modeling techniques, i.e. classification and regression trees and multivariate adaptive regression splines-based methods, was explored to model the blood-brain barrier (BBB) passage of drugs and drug-like molecules. The data set contains BBB passage values for 299 structural and pharmacological diverse drugs, originating from a structured knowledge-based database. Models were built using boosted regression trees (BRT) and multivariate adaptive regression splines (MARS), as well as their respective combinations with stepwise multiple linear regression (MLR) and partial least squares (PLS) regression in two-step approaches. The best models were obtained using combinations of MARS with either stepwise MLR or PLS. It could be concluded that the use of combinations of a linear with a non-linear modeling technique results in some improved properties compared to the individual linear and non-linear models and that, when the use of such a combination is appropriate, combinations using MARS as non-linear technique should be preferred over those with BRT, due to some serious drawbacks of the BRT approaches.     

蛋白质在反相高效液相色谱梯度洗脱条件下保留时间的预测

应用微分方程模拟色谱过程,通过数值计算获得方程的解,从而建立了一种在反相高效液相色谱中梯度洗脱条件下,预测蛋白质等一些具有非线性色谱保留行为的生物大分子保留时间的新方法。利用蛋白质样品牛血清白蛋白和溶菌酶对该法进行实验验证,获得了比较满意的结果。     

烷基苯酚类化合物的气相色谱保留值与其结构参数的定量关系

计算了44个烷基苯酚类化合物的组成、拓扑、几何、静电和量子化学等结构参数,运用启发式方法对这些结构参数进行筛选,得到了含3个变量的化合物的定量结构与色谱保留值的线性关系模型,同时以这3个变量作为支持向量机模型的输入变量建立非线性回归模型。两种方法的相关系数(R2 )分别为0.98和0.92,相应的均方根误差分别是0.99和2.77。通过对两种模型的稳定性和预测能力的比较,发现线性模型能够更好地反映烷基苯酚的气相色谱保留值与其结构参数之间的定量关系。在已知烷基苯酚类化合物结构参数的情况下,线性回归模型更有助于它们的色谱分析。     

Selection of orthogonal reversed-phase HPLC systems by univariate and auto-associative multivariate regression trees

In order to select chromatographic starting conditions to be optimized during further method development of the separation of a given mixture, so-called generic orthogonal chromatographic systems could be explored in parallel. In this paper the use of univariate and multivariate regression trees (MRT) was studied to define the most orthogonal subset from a given set of chromatographic systems. Two data sets were considered, which contain the retention data of 68 structurally diversive drugs on sets of 32 and 38 chromatographic systems, respectively. For both the univariate and multivariate approaches no other data but the measured retention factors are needed to build the decision trees. Since multivariate regression trees are used in an unsupervised way, they are called auto-associative multivariate regression trees (AAMRT). For all decision trees used, a variable importance list of the predictor variables can be derived. It was concluded that based on these ranked lists, both for univariate and multivariate regression trees, a selection of the most orthogonal systems from a given set of systems can be obtained in a user-friendly and fast way.     

Comparison of interpolation polynomials with divided differences,interpolation polynomials with finite differences,and quadratic functions obtained by the least squares method in modeling of chromatographic responses

A novel approach to mathematical modeling of chromatographic responses based on interpolation polynomials with divided differences and with finite differences is discussed. These interpolational techniques as well as traditionally applied second‐order polynomial models obtained by least squares are compared. Interpolation techniques can be useful in situations where commonly used linear or quadratic models are not applicable: when the nature of dependence is complex or the investigated factor intervals are broad. The three analyzed modeling techniques are incorporated in a design of experiments methodology for systematic development and optimization of liquid chromatographic methods. The direct modeling of retention factors is carried out first, while the objective function for final quality measurement is calculated last. An interpolation polynomial with divided differences resulted in a high quality fit compared with the results obtained by the other two modeling approaches and succeeded in locating the desired optimum. It is shown that this modeling technique can be a useful alternative for modeling of chromatographic responses. Copyright © 2013 John Wiley & Sons, Ltd.