Efficient Algorithms To Enumerate Isomers and Diamutamers with More Than One Type of Substituent

Abstract

In this paper we describe numeric as well as symbolic algorithms for the enumeration of substitutional isomers with an unlimited number of different achiral substituents. We consider three different scenarios: first, the enumeration of diamutamers with a given set of ligand types and ligand multiplicity, second, the enumeration of diamutamer libraries with a given ligand assortment pattern, and, third, the enumerations of libraries with diamutamers exhibiting a limited number of ligands.

Design of Small-Sized Libraries by Combinatorial Assembly of Linkers and Functional Groups to a Given Scaffold: Application to the Structure-Based Optimization of a Phosphodiesterase 4 Inhibitor

“…The complete number N of enumerated molecules can be expressed as: where L is the number of linker fragments, F is the number of functional groups, and S is the number of substitution points marked on the scaffold. The complete enumeration with a core structure showing a local symmetry in substitution points gives a lower number of unique structures according to the Pólya counting theory . The complete enumeration method is implemented in SLF_LibMaker, a C++ program based on OpenEye's OEChem 1.3 library .…”

“…The complete enumeration with a core structure showing a local symmetry in substitution points gives a lower number of unique structures according to the Po ´lya counting theory. 28 The complete enumeration method is implemented in SLF_LibMaker, a C++ program based on OpenEye's OEChem 1.3 library. 29 The molecular fragments (scaffolds, linkers, functional groups) are encoded as SMILES 30 or SDF 31,32 file formats with connecting pseudo-atoms represented by "*" in both formats.…”

Symbolic calculation in chemistry: Selected examples

“…van Almsick et al developed an algorithm to enumerate isomers and diamutamers (same central skeleton but different arrangements of ligands) and wrote an implementation. They used the Cauchy–Frobenius lemma and Pólya polynomials 298, 299.…”

Symmetry specified enumeration of substituted derivatives: an easy solution to the complex problem

“…Firstly, the use of the over all numbers (or coefficients of the generating functions) corresponding to one supergroup often makes it possible to simplify the calculations. The alternative procedures for counting the total number of completely asymmetric (C 1 ) prismane derivatives may serve as examples, see Eqs (20), (21), and (22). representation in Fig.…”