Mapping of chemical space

Mapping of Chemical Space Using Forward Chemical Genetics... 

Computational Framework for Forward Chemical Genetics Legacy of Morgan and Sturtevant 325 Mapping of Chemical Space Using Forward Chemical Genetics 326... 

Dimensionality reduction and data visualization Kernel Principal Component Analysis (KPCA) [6], Kernel Feature Analysis (KFA) [77] Drawing maps of chemical space... 

There is ako a common imsconception that novel compoimds or concepts will lead to dramatically different structural features. It k unlikely that the drugs of the future will be built from radically other structural classes than today s drugs. There may be heterocycles never seen before or a few new functional groups, for example, the sulfonimidamides [18], but the majority of the compounds will still be built from the functional features known already today, yet they may still occupy white areas on the map of chemical space. 

How is dimension reduction of chemical spaces achieved There are a number of different concepts and mathematical procedures to reduce the dimensionality of descriptor spaces with respect to a molecular dataset under investigation. These techniques include, for example, linear mapping, multidimensional scaling, factor analysis, or principal component analysis (PCA), as reviewed in ref. 8. Essentially, these techniques either try to identify those descriptors among the initially chosen ones that are most important to capture the chemical information encoded in a molecular dataset or, alternatively, attempt to construct new variables from original descriptor contributions. A representative example will be discussed below in more detail. 

Rg. 6-10 Mapping chemical space [76]. Principle component models of chemical space are shown for 480 small molecules analyzed using 24 computed molecular descriptors and 60 measured phenotypic descriptors derived from a cell-based assay of cell proliferation. By considering the elements of S as coordinates, small molecules can be modeled as vectors,... 

The specification super-operator is common in quantum chemical emd physical literature for linear mappings of Fock-space operators. It is very helpful to transfer this concept to the extended states A, B) and define the application of super-operators by the action on the operators A and B. We will see later how this definition helps for a compeict notation of iterated equations of motion and perturbation expansions. In certain cases, however, the action of a super-operator is fully equivalent to the action of an operator in the Hilbert space Y. The alternative concept of Y-space operators allows to introduce approximations by finite basis set representations of operators in a well-defined and lucid way. 

S., Hofmann, B., Wetzel, S., Schuffenhauer, A., Erd, P., Oprea, T.I., Steinhilber, D., Brunsveld, L., Rauh, D and Waldmann, H. (2009) Bioactivity-guided mapping and navigation of chemical space. Nature Chemical Biolc, 5, 585-592. 

The integration of structural similarity and activity within a single visualization approach provides a consistent framework for the elucidation of SAR trends, continuity regions, and activity cliffs in a dataset. Again dimensionality reduction approaches are essential for mapping the chemical space onto a 2D-plot. The first... 

Awale M, van Deursen R, Reymond JL (2013) MQN-Mapplet visualization of chemical space with interactive maps of DrugBank, ChEMBL, PubChem, GDB-11, and GDB-13. J Chem Inf Model 53(2) 509-518. doi 10.1021/ci300513m... 

A data set can be split into a training set and a test set randomly or according to a specific rule. The 1293 compounds were divided into a training set of 741 compounds and a test set ot 552 compounds, based on their distribution in a K.NN map. From each occupied neuron, one compound was selected and taken into the training set, and the other compounds were put into the test set. This selection ensured that both the training set and the test set contained as much information as possible, and covered the chemical space as widely as possible. 

In addition to looking for data trends in physical property space using PCA and PLS, trends in chemical structure space can be delineated by viewing nonlinear maps (NLM) of two-dimensional structure descriptors such as Unity Fingerprints or topological atom pairs using tools such as Benchware DataMiner [42]. Two-dimensional NLM plots provide an overview of chemical structure space and biological activity/molecular properties are mapped in a 3rd and/or 4th dimension to look for trends in the dataset. 

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