Quadratic shape descriptors

Quadratic Shape Descriptors. 2. Molecular Docking Using Quadratic Shape Descriptors (QSDock). 

Goldman, B.B. and Wipke, W.T. (2000) Quadratic shape descriptors. 1. Rapid superposition of dissimilar molecules using geometrically invariant surface descriptors. J. Chem. Inf. Comput. Sci, 40, 644-658. 

Goldman BB, Wipke WT. QSD quadratic shape descriptors. 2. Molecular docking using quadratic shape descriptors (QSDock). Proteins Struct Funct Genet 2000 38 79-94. 

Goldman, B.B. Wipke, W.T. QSD Quadratic Shape Descriptors. 2. Molecular Docking Using Quadratic Shape Descriptors (QSDock). Proteins 2000, 3S (1), 79-94. 

By contrast, relative shape analysis and relative shape descriptors can change for each molecule, depending on the other molecule used for comparison. For n molecules there are n(n-l)/2 molecule pairs, hence n(n-l)/2 families of relative shape descriptors of the given type. Consequently, in the study of shape similarities in large molecular families, the quadratic dependence of the number of relative shape descriptors on the number of molecules is a disadvantage and the use of relative shape descriptors is often impractical. Shape similarity measures based on relative shape descriptors are called similarity measures of the second kind. 

The chemometric model connecting the marker yield to lethality is based on the assumption that the shape of the temperature pulse is quadratic in the dimensionless temperature descriptor, x. The temperature pulse, which is quadratic in x, where the temperature increases from room temperature to a peak temperature of 116°C over a 10 min interval, is shown in Fig. 2 as well as the actual meatball center temperature measured with a thermocouple. The actual temperature approaches the target temperature almost exponentially and is always higher than the temperature of the quadratic model. Therefore, the model prediction underestimates the actual lethality and can be used as a conservative estimate. 

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