Abstract
The concept of chemical space is playing an increasingly important role in many areas of chemical research, especially medicinal chemistry and chemical biology. It is generally conceived as consisting of numerous compound clusters of varying sizes scattered throughout the space in much the same way as galaxies of stars inhabit our universe. A number of issues associated with this coordinate-based representation are discussed. Not the least of which is the continuous nature of the space, a feature not entirely compatible with the inherently discrete nature of chemical space. Cell-based representations, which are derived from coordinate-based spaces, have also been developed that facilitate a number of chemical informatic activities (e.g., diverse subset selection, filling ‘diversity voids’, and comparing compound collections).These representations generally suffer the ‘curse of dimensionality’. In this work, networks are proposed as an attractive paradigm for representing chemical space since they circumvent many of the issues associated with coordinate- and cell-based representations, including the curse of dimensionality. In addition, their relational structure is entirely compatible with the intrinsic nature of chemical space. A description of the features of these chemical space networks is presented that emphasizes their statistical characteristics and indicates how they are related to various types of network topologies that exhibit random, scale-free, and/or ‘small world’ properties.
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Notes
When all vertices are connected to each other the network is called complete. Complete undirected networks with n vertices have n (n − 1)/2 edges.
Similarity values that are strictly greater than a given threshold are called proper threshold values.
Note that in rare cases the similarity between two dissimilar molecules may, nonetheless, be unity. This is due to limitations of the molecular representation that do not properly account for all the features that distinguish the two molecules from one another.
\({\text{SALI}}(i,j) = {{\left| {\varDelta {\text{Act}}(i,j)} \right|} \mathord{\left/ {\vphantom {{\left| {\varDelta {\text{Act}}(i,j)} \right|} {\left[ {1 - {\text{Sim}}(i,j)} \right]}}} \right. \kern-0pt} {\left[ {1 - {\text{Sim}}(i,j)} \right]}}\), where ∆Act(i, j) is the difference in the activities of a given compound pair (i, j), and Sim(i, j) is their corresponding the similarity value.
In the case of directed graphs, the degree of incoming connections (‘in-degree’) is considered separately for that of the outgoing connections (‘out-degree’).
Hence, shortest paths are integer valued. Note that it is possible that more than one shortest path exists between a given pair of vertices.
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Acknowledgments
The authors wish to thank Dr. Vijay Gokhale for reading the manuscript and for his helpful comments and Dr. Dagmar Stumpfe for the design of exemplary network representations and review of the manuscript.
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Maggiora, G.M., Bajorath, J. Chemical space networks: a powerful new paradigm for the description of chemical space. J Comput Aided Mol Des 28, 795–802 (2014). https://doi.org/10.1007/s10822-014-9760-0
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DOI: https://doi.org/10.1007/s10822-014-9760-0