Descriptor decoding

Let us summarize the three important prerequisites for a 3D structure descriptor It should be (1) independent of the number of atoms, that is, the size of a molecule (2) unambiguous regarding the three-dimensional arrangement of the atoms and (3) invariant against translation and rotation of the entire molecule. Further prerequisites depend on the chemical problem to be solved. Some chemical effects may have an undesired influence on the structure descriptor if the experimental data to be processed do not account for them. A typical example is the conformational flexibility of a molecule, which has a profound influence on a 3D descriptor based on Cartesian coordinates. The application in the field of structure-spectrum correlation problems in vibrational spectroscopy requires that a descriptor contains physicochemical information related to vibration states. In addition, it would be helpful to gain the complete 3D structure from the descriptor or at least structural information (descriptor decoding). 

Spectrum-like descriptors give information about molecular size and are dependent on molecule alignment, i.e. on the two perpendicular circles onto which the atom projections fall. From - variable selection, partial -> reversible decoding can also be performed. 

Reversible decoding is of great importance, since once a SRC model is established optimal values of the response can be chosen and values of the model molecular descriptors calculated by using the estimated SRC model. Then the possible molecular structures corresponding to the optimized descriptor values can be designed (and synthesized). This last operation is a troublesome task as the model molecular descriptors are not simple and easily interpretable. 

A great advantage of the substituent descriptors is that they are calculated just once and then can be used in a congeneric series whenever the substituent is present in a site of the parent molecule, independently of the different molecules to which they are attached, without further calculations. Approaches based on the substituent descriptors usually allow us to perform a reversible decoding however, they need the congenericity of the training set compoimds and in most cases do not account for substituent-substituent and substituent-molecule skeleton interactions. 

The ideal descriptor can be decoded to obtain the original chemical structure or the properties that have been used to calculate the descriptor. Although this is definitely desired, the real world shows that the information used to calculate the descriptor is usually too complex to use it at its full size. A descriptor shall have a reasonable size for effective computation, and this is mostly achieved by reducing information to the facts that are of major importance for the task. The need for a fixed descriptor dimension also contradicts this requirement. 

Reversible Decoding is a desired property of a molecular descriptor to mathematically decode it to obtain the underlying chemical structure or the properties that have been used to calculate the descriptor. 

As in the database approach, the structure descriptor is calculated without hydrogen atoms, which can be added implicitly after the decoding process. However, the positions of the hydrogen atoms are stored and used later as potential vectors pointing to new atoms. Besides the previously used similarity criteria (RMS and R) for RDF descriptors, the difference in number and position of peaks between two descriptors can be applied as improvement criterion. 

Moreover, the RDF vectorial descriptor is interpretable by using simple rules and, thus, it provides a possibility of —> reversible decoding. Besides information about distribution of interatomic distances in the entire molecule, the RDF vector provides further valuable information for example, about bond distances, ring types, planar and nonplanar systems, and atom types. This fact is a most valuable consideration for a computer-assisted code elucidation. 

Another relevant aspect in structure/response correlations is the ability to obtain information about molecular structure from QSAR/QSPR models. In particular, the term reversible decoding (or inverse QSAR) denotes any procedure capable to reconstruct the molecular structure or fragment starting from molecular descriptor values, that is, once molecular... 

---