Regression analysis structure-activity

Furthermore, QSPR models for the prediction of free-energy based properties that are based on multilinear regression analysis are often referred to as LFER models, especially, in the wide field of quantitative structure-activity relationships (QSAR). 

Topliss JG, Costello RJ. Chance correlations in structure-activity studies using multiple regression analysis. J Med Chem 1972 15 1066-9. 

Martin H) has written a perceptive analysis of the possible ways in which an ionized species may behave in various models and contribute to or be responsible for a given activity. QSAR studies that have dealt with ion-pair partitioning include a study of fibrinolytics ( ) and the effect of benzoic acids on the K ion flux in mollusk neurons ( ). Schaper (10) recently reanalyzed a large number of absorption studies to include terms for the absorption of ionized species. Because specific values were not available for log Pj, he let the relation between log Pi and log P be a parameter in a nonlinear regression analysis. In most cases he used the approximation that the difference between the two values is a constant in a given series. This same assumption was made in the earlier studies (, ) Our work suggests that the pKa of an acid can influence this differential (see below). The influence of structure on the log P of protonated bases or quaternary ammonium compounds is much more complex (11,12) and points out the desirability of being able to easily measure these values. 

At this point it was clear that the highest potential for increased activity was by substitution in the 2-position of the biphenyl alcohol. We prepared the sequence of compounds shown in Table 1. Substituents were again chosen to maximize the parameter space covered within the relatively stringent synthetic limitations of the biphenyl substitution pattern. The application of regression analysis to the data for these compounds provided no clear relationship between structure and activity when the parameters in our standard data base were used. The best linear fit was found for B4, the STERIMOL maximum radius. However, the correlation coefficient was only 0.625. 

Regression equations descriptive of multi-dimensional structure/ activity relationships in quantitative terms too frequently are intellectual curiosities developed retrospectively after work in optimization of the biological properties of a series by analog or homolog synthesis has been completed. Retrospective analysis serves well to document that critical factors in the relationship between structural features/physiochemical factors and biological potency are well understood and that optimum compounds have been achieved. Structure/activity understanding developed during the course of a synthesis project, however, lends direction and efficiency to the property optimization effort. 

Human perception of flavor occurs from the combined sensory responses elicited by the proteins, lipids, carbohydrates, and Maillard reaction products in the food. Proteins Chapters 6, 10, 11, 12) and their constituents and sugars Chapter 12) are the primary effects of taste, whereas the lipids Chapters 5, 9) and Maillard products Chapter 4) effect primarily the sense of smell (olfaction). Therefore, when studying a particular food or when designing a new food, it is important to understand the structure-activity relationship of all the variables in the food. To this end, several powerful multivariate statistical techniques have been developed such as factor analysis Chapter 6) and partial least squares regression analysis Chapter 7), to relate a set of independent or "causative" variables to a set of dependent or "effect" variables. Statistical results obtained via these methods are valuable, since they will permit the food... 

Partial least squares regression analysis (PLS) has been used to predict intensity of sweet odour in volatile phenols. This is a relatively new multivariate technique, which has been of particular use in the study of quantitative structure-activity relationships. In recent pharmacological and toxicological studies, PLS has been used to predict activity of molecular structures from a set of physico-chemical molecular descriptors. These techniques will aid understanding of natural flavours and the development of synthetic ones. 

A relatively recent development in QSAR research is molecular reference (MOLREF). This molecular modelling technique is a method that compares the structures of any number of test molecules with a reference molecule, in a quantitative structure-activity relationship study (27). Partial least squares regression analysis was used in molecular reference to analyse the relation between X- and Y-matrices. In this paper, forty-two disubstituted benzene compounds were tested for toxicity to Daphnia... 

Aside from this concern, a prospective user should ascertain what precision level he / she needs and what structural features can be included while retaining that precision. In some research, the estimation of the relative hydrophobicity of a set of analogs is crucial, but the absolute values need not be precise. For instance, if one wants to know if hydrophobicity contributes to the activity of a certain toxiphore, regression analysis using a calculated log P can provide an answer even if the parent is mispredicted, as long as all of the analogs deviate by this same amount. Of course, the equation intercept, which is a measure of intrinsic activity, is then in error. 

Hansch analysis Hansch analysis is a common quantitative structure-activity relationship approach in which a Hansch equation predicting biological activity is constructed. The equation arises from a multiple linear regression analysis of both observed biological activities and various molecular property parameters (Hammett, Hansch, and Taft parameters). 

HQSARhologram quantitative structure-activity relationship, MLR multiple linear regression, PCA principal component analysis, PLS-QSAR partial least-squares quantitative structure-activity relationship, TAACF Tuberculosis Antimicrobial Acquisition and Coordinating Facility STATOO Consulting (Berne, Switzerland)... 

Substituent Parameters. A significant advance was made, in the structure-activity studies with the Hill reaction, when Hansch and Deutsch (12) evaluated some of the published Hill inhibition data with a multiple regression analysis, an extra-thermodynamic approach, or the so-called sigma, pi (a, T ) regression analysis. The principle of the approach rests on the assumption that changes in biological activity can be correlated with measurable molecular or substituent parameters. This analysis involved equations of the following type ... 

QSAR Quantitative structure-activity relationship. Quantitative structure-bio-logical activity model derived using regression analysis and containing as parameters physical-chemical constants, indicator variables, or theoretically calculated values. 

Quantitative structure-activity/pharmacokinetic relationships (QSAR/ QSPKR) for a series of synthesized DHPs and pyridines as Pgp (type I (100) II (101)) inhibitors was generated by 3D molecular modelling using SYBYL and KowWin programs. A multivariate statistical technique, partial least square (PLS) regression, was applied to derive a QSAR model for Pgp inhibition and QSPKR models. Cross-validation using the leave-one-out method was performed to evaluate the predictive performance of models. For Pgp reversal, the model obtained by PLS could account for most of the variation in Pgp inhibition (R2 = 0.76) with fair predictive performance (Q2 = 0.62). Nine structurally related 1,4-DHPs drugs were used for QSPKR analysis. The models could explain the majority of the variation in clearance (R2 = 0.90), and cross-validation confirmed the prediction ability (Q2 = 0.69) [ 129]. 

Based on the earlier work of Meyer and Overton, who showed that the narcotic effect of anesthetics was related to their oil/water partition coefficients, Hansch and his co-workers have demonstrated unequivocally the importance of hydrophobic parameters such as log P (where P is, usually, the octanol/water partition coefficient) in QSAR analysis.28 The so-called classical QSAR approach, pioneered by Hansch, involves stepwise multiple regression analysis (MRA) in the generation of activity correlations with structural descriptors, such as physicochemical parameters (log P, molar refractivity, etc.) or substituent constants such as ir, a, and Es (where these represent hydrophobic, electronic, and steric effects, respectively). The Hansch approach has been very successful in accurately predicting effects in many biological systems, some of which have been subsequently rationalized by inspection of the three-dimensional structures of receptor proteins.28 The use of log P (and its associated substituent parameter, tr) is very important in toxicity,29-32 as well as in other forms of bioactivity, because of the role of hydrophobicity in molecular transport across cell membranes and other biological barriers. 

Structure—Activity Studies Using Multiple Regression Analysis. 

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