Density Glue LDG Bonding in Proteins

The formal bodies of molecules do not have boundaries and the actual shape of molecules is determined by the fuzzy electron distribution. Realistic models describing molecular shapes and chemical bonding must reflect this natural fuzziness [27]. 

One approach involves the following question to what extent do various points r of the three-dimensional space belong to a single, isolated molecule X Such problems are typically addressed using fuzzy sets [22-27], 

Consider a spatial domain D containing the nuclei of molecule X, and let Pmax denote the maximum value of the electron density within D  

In terms of pmax, a fuzzy membership function px(r) is defined for points r of the space, expressing the degree of their belonging to molecule X  

In a similar spirit, if molecule X is not isolated, then a point r may belong to several different molecules to different degrees, that can also be expressed using fuzzy membership functions. In particular, the total electron density p(r) at some point r can be regarded as a sum of electron densities px(r) and py(r) attributed to individual molecules X and Y, respectively. In this case, the fuzzy membership functions of various points r with respect to the two molecules X and Y are determined by the relative magnitudes of the individual electron densities px(r) and py(r)  

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