Design of novel pharmaceutical products via combinatorial optimization

Abstract This paper describes a new methodology for the application of computer-aided molecular design to the design of pharmaceutical products with prespecified physical properties. For a pharmaceutical product to be effective, it must not only cause a desirable therapeutic effect, but it must also have proper values of physical properties such as solubility and density. In order to apply computer-aided molecular design to the discovery of new pharmaceuticals, it is therefore necessary to be able to first predict the physical and biological properties of a given molecule, and then optimize over an entire set of molecules to find one which matches target values on those properties. This work employs topological descriptors to predict the physical properties of pharmaceutical molecules. The descriptors used here, called connectivity indices, are easy to compute, yet contain valuable information about the internal molecular structure of a molecule. Property prediction, via connectivity indices, can be viewed as an improvement over group contribution methods, since these indices take into account molecular connectivity and internal electronic structure in addition to the identity of each group in the molecule. Thus these indices correlate well with physical properties which are important in pharmaceutical design. Furthermore, these indices are fairly simple to compute, and a proper choice of variables to describe the molecule allows the equations for these indices to be written in a linear form. The optimization problem used here combines a set of basic groups, which are defined as a non-hydrogen atom at a given valency state bonded to a given number of hydrogens, to form a candidate molecule. Each candidate molecule can then be tested by computing estimated property values and comparing those to prespecified target values. Structural constraints are also added to the problem to ensure a connected, stable molecule is generated. The set of constraints and the correlation equations for property prediction are then combined and reformulated, resulting in a mixed integer linear program (MILP). If a certain functional group is known to be required in the molecule, this requirement can also be added to the constraint set. For problems consisting of a smaller number of basic groups or property targets, commercial solvers can be employed to solve the resulting MILP. The effectiveness of this method is presented through the solution of a small example problem.