Pharmaceutical product design using combinatorial optimization

A two-step computational method for designing new molecules in medicinal chemistry is described. In the first step, topological indices are used to develop structure-based correlations for properties of interest. Zeroth and first order connectivity indices are employed to develop linear correlations for three physical properties of interest in pharmaceutical chemistry: octanol–water partition coefficient (OWPC), melting point and water solubility. These correlations are then used within an optimization framework to design molecules having the desired properties. This step involves formulating a mixed integer linear program (MILP) which includes the property correlations, structural constraints which ensure that a stable, connected molecule is formed, and an objective function which minimizes the deviation from a set of property targets. A new data structure, known as a partitioned adjacency matrix, is employed to allow the connectivity index definitions to be written linearly, such that they can be included in an MILP and solved using a standard branch-and-bound method. The connectivity of the molecule is ensured by the inclusion of network flow constraints within the formulation. Three examples show the efficacy of this approach. © 2003 Elsevier Ltd. All rights reserved.