The Law of Mixtures method for multivariate calibration

Delaunay triangulation with partial least squares projection to latent structures: a model for G-protein coupled receptors classification and fast structure recognition

As an important transmembrane protein family in eukaryon, G-protein coupled receptors (GPCRs) play a significant role in cellular signal transduction and are important targets for drug design. However, it is very difficult to resolve their tertiary structure by X-ray crystallography. In this study, we have developed a Delaunay model, which constructs a series of simplexes with latent variables to classify the families of GPCRs and projects unknown sequences to principle component space (PC-space) to predict their topology. Computational results show that, for the classification of GPCRs, the method achieves the accuracy of 91.0 and 87.6% for Class A, more than 80% for the other three classes in differentiating GPCRs from non-GPCRs and 70% for discriminating between four major classes of GPCR, respectively. When recognizing the structure of GPCRs, all the N-terminals of sequences can be determined correctly. The maximum accuracy of predicting transmembrane segments is achieved in the 7th transmembrane segment of Rhodopsin, which is 99.4%, and the average error is 2.1 amino acids, which is the lowest in all of the segments prediction. This method could provide structural information of a novel GPCR as a tool for experiments and other algorithms of structure prediction of GPCRs. Academic users should send their request for the MATLAB program for classifying GPCRs and predicting the topology of them at liml@scu.edu.cn .

Updating multivariate calibrations with the delaunay triangulation method

Multivariate calibrations must be updated when new samples show different spectral characteristics. In this paper, we discuss how to do this when the calibration is performed with a topological multivariate calibration method based on Delaunay triangulation (DT). The updating leads either to the expansion of the original calibration set or to the creation of a new local model. Outliers in the new samples with respect to the original calibration set are first detected and divided in two groups, namely, marginal outliers, which are considered to be extensions of the calibration set and are used for updating the calibration set, and true outliers. If a sufficient number of true outliers are found to be situated close enough to each other, they can form the basis for a new local model. Several updating simulations performed on a real data set show that the updating procedure performs well. The results for prediction with the DT method after updating are comparable to or better than those after updating with partial least squares (PLS) and it is concluded that, in many cases, the DT method is a valuable alternative for multivariate calibration.