Continuous Chirality Measure CCM

One example of a quantitative measure of molecular chirality is the continuous chirality measure (CCM) [39, 40]. It was developed in the broader context of continuous symmetry measures. A chital object can be defined as an object that lacks improper elements of symmetry (mirror plane, center of inversion, or improper rotation axes). The farther it is from a situation in which it would have an improper element of symmetry, the higher its continuous chirality measure. 

Continuous chirality measure is then defined as follows given a configuration of points P = I, its chirality content is determined by finding the nearest configuration of points Pi - 2 which has an improper element of symmetry, and by calculating the distance between the two sets using Eq. (26). 

G is a given symmetry group, Pj are the points of the original configuration, Pi are the corresponding points in the nearest G-symmetric configuration, and n is the total number of the configuration points. For convenience, the expanded scale is S = lOOS . 

In order to calculate S, one has to find the nearest configuration of Pi points that is G-symmetric. In the majority of cases, S is the distance of a chiral object from a reflection mirror. The fblding/unfolding procedure was developed for finding that configuration. 

The S(Gj ) thus obtained is the minimal chirality measure of the given configuration, on a continuous scale of 0 S 100. 

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Two general classes of chirality measures have been recognized in the first, the degree of chirality expresses the extent to which a chiral object differs from an achiral reference object, while in the second it expresses the extent to which two enantio-morphs differ from each other [Buda et al., 1992]. The continuous chirality measure (CCM) recently proposed [Zabrodsky and Avnir, 1995] is an example of chirality measure belonging to the first class and is based on the general definition of continuous symmetry measure defined as ... 

Keinan et al. found that the quantitative degree of chirality of substrates correlates with their efficiency of reaction with active sites [7]. The degree of chirality, a global shape descriptor, was determined by the use of the continuous chirality measure (CCM) methodology developed previously, which treats chirahty as a continuous structural property and not as a binary quality (chiral/not chiral) [8]. 

The Measurement of Achirality The Continuous Chirality Measure (CCM) Approach... 

CCM = continuous chirality measure CSM = continuous symmetry measure. 

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