Multidimensional scoring

Terp GE, Johansen BN, Christensen IT, Jorgensen FS. A new concept for multidimensional selection of ligand conformations (multiselect) and multidimensional scoring (multiscore) of protein-ligand binding affinities. J Med Chem 2001 44 2333 13. 

A New Concept for Multidimensional Selection of Ligand Conformations (Multiselect) and Multidimensional Scoring (Multiscore) of Protein-Ligand Binding Affinities. 

In fact, the space described by two or three PCs can be used to represent the objects (score plot), the original variables (loading plot), or both objects and variables (biplot). For instance, if the first two PCs (low-order) are drawn as axes of a Cartesian plane, we may observe in this plane a fraction of the information enclosed in the original multidimensional space which corresponds to the sum of the variance values explained by the two PCs. Since PCs are not intercorrelated variables, no duplicate information is shown in PC plots. 

One of the major uses of multivariate techniques has been the discrimination of samples based on sensory scores, which also has been found to provide information concerning the relative importance of sensory attributes. Techniques used for sensory discrimination include factor analysis, discriminant analysis, regression analysis, and multidimensional scaling (8, 10-15). 

In order to set up an analytical method based on factor scores or analytical deviation in a Q.A. environment, several precautions would need to be followed. For instance, changes in raw materials would need to be monitored and either new reference materials used or factor analyses repeated. Changes in chromatographic conditions would require a system which allowed constant updating to avoid shift in factor scores. While the peak ratio technique is the simpler of the two, factor scores provide a more sophisticated method which can be used where overlap of components does not lend itself to the simpler methods. These two techniques for deriving the concentrations of the multicomponents in a mixture were shown to predict sensory response when one multicomponent was altered. However it also could be used in a multidimensional formula to predict response when more than one multicomponent has been altered. 

Figure 9 Multidimensional scaling score plots of tobacco smoke. 8l designates I98I crop year all others are 19T9 crop year.

The resulting semi-quantitative model was used in conjunction with structure-based docking and scoring, 3D-QS AR based affinity and selectivity predictions and in silico ADME models to estimate membrane permeability, solubility, and other key properties for the optimization process in this series. Hence, in this as well as in other series, multiple models can be collectively applied for ranking and prioritizing synthesis candidates and focused virtual libraries during advanced stages of multidimensional compound optimization. 

Preference mapping can be accomplished with projection techniques such as multidimensional scaling and cluster analysis, but the following discussion focuses on principal components analysis (PCA) [69] because of the interpretability of the results. A PCA represents a multivariate data table, e.g., N rows ( molecules ) and K columns ( properties ), as a projection onto a low-dimensional table so that the original information is condensed into usually 2-5 dimensions. The principal components scores are calculated by forming linear combinations of the original variables (i.e., properties ). These are the coordinates of the objects ( molecules ) in the new low-dimensional model plane (or hyperplane) and reveal groups of similar... 

Vedani A, Zumstein M, Lill MA, Ernst B. Simulating a/p specificity at the thyroid receptor Consensus scoring in multidimensional QSAR. ChemMedChem, 2007 2 78-87. 

As principal components modelling is based on projections it can take any number of descriptors into account. Projections to principal components models offer a means of simultaneously considering the joint variation of all property descriptors. By means of the score values it is therefore possible to quantify the "axes" of the reaction space to describe the variation of substrates, reagent(s) and solvents. When there are more than one principal component to consider for each type of variation, the "axes" will be multidimensional. Quantification of the axes of the reaction space offers an opportunity to pay attention to all available back-ground information prior to selecting test compounds. 

Principal component analysis (PGA) is a quahtative method where the X-data can be studied without any knowledge of the Y-data. A score plot of the X-data gives an overview of possible patterns in the data and is therefore a useful tool for classification. The X-data are explained using uncorrelated vectors in pairs called principal components (PC). The first principal component (PCI) is in the direction of the largest variation in the multidimensional X space. Fig. 3. PC2 is in the direction of the second largest variation perpendicular to PCI etc, all orthogonal to each other. The two-dimensional plane containing two principal components, e.g. PCI and PC2, is called a score plot. The munber of components to be included in the model is chosen on the basis of the amount of variation in the data that each of... 

It is useful to go back to two-way visualization in principal component analysis to find what really is seen in a plot. A score plot for a two-way PCA model has an orthonormal basis, because the loadings are orthonormal. This can be compared to projecting all points in multidimensional space on a movie screen using a strong light source at a large distance. What is seen in this projection is true Euclidean distance in the reduced space, if both... 

Fig. 6-15 Principal component analysis of multidimensional, chemical-genetic data, (a) Eigenvalues and associated variance, and eigenvectors and associated factor scores computed from the data in Fig. 6-14(a). The matrix of eigenvectors...

All methods require compound characterization by multiple molecular descriptors and appropriate dissimilarity scoring functions must be used. The purpose of the diversity selection can be formulated as follows select a subset of n representative compounds from a database S containing n compounds, which is the most diverse in terms of chemical structure. The key to each of the different methods is the mathematical fimction that measures diversity. Since each molecule is represented by a vector of molecular descriptors, it is geometrically mapped to a point in a multidimensional space. The distance between two points, such as Euclidian distance, measures the dissimilarity between two molecules. Thus, the diversity function should be based on aU pairwise distances between molecules in the subset... 

This chapter provides a tutorial on the fundamental concept of Parallel factor (PARAFAC) analysis and a practical example of its application. PARAFAC, which attains clarity and simplicity in sorting out convoluted information of highly complex chemical systems, is a powerful and versatile tool for the detailed analysis of multi-way data, which is a dataset represented as a multidimensional array. Its intriguing idea to condense the essence of the information present in the multi-way data into a very compact matrix representation referred to as scores and loadings has gained considerable popularity among scientists in many different areas of research activities. 

As mentioned in Section 3.3.2, PARAFAC is a chemometric tool for multidimensional data treatment. The scores and loadings obtained with PARAFAC can be used in two-way models for data exploration and quantitative analysis (Vosough et al., 2010). When small deviations in trilinearity exist within the data, usually due to relatively small shifts in retention time in the case of separations data, a modified version of PARAFAC called PARAFAC2 is recommended for use (Bro et al., 1999). 

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