Optimization in product design with properties correlated with topological indices

Inverse-QSPR for de novo Design: A Review

The use of computer tools to solve chemistry-related problems has given rise to a large and increasing number of publications these last decades. This new field of science is now well recognized and labelled Chemoinformatics. Among all chemoinformatics techniques, the use of statistical based approaches for property predictions has been the subject of numerous research reflecting both new developments and many cases of applications. The so obtained predictive models relating a property to molecular features - descriptors - are gathered under the acronym QSPR, for Quantitative Structure Property Relationships. Apart from the obvious use of such models to predict property values for new compounds, their use to virtually synthesize new molecules - de novo design - is currently a high-interest subject. Inverse-QSPR (i-QSPR) methods have hence been developed to accelerate the discovery of new materials that meet a set of specifications. In the proposed manuscript, we review existing i-QSPR methodologies published in the open literature in a way to highlight developments, applications, improvements and limitations of each.

New Vistas in Chemical Product and Process Design

Design of chemicals-based products is broadly classified into those that are process centered and those that are product centered. In this article, the designs of both classes of products are reviewed from a process systems point of view; developments related to the design of the chemical product, its corresponding process, and its integration are highlighted. Although significant advances have been made in the development of systematic model-based techniques for process design (also for optimization, operation, and control), much work is needed to reach the same level for product design. Timeline diagrams illustrating key contributions in product design, process design, and integrated product-process design are presented. The search for novel, innovative, and sustainable solutions must be matched by consideration of issues related to the multidisciplinary nature of problems, the lack of data needed for model development, solution strategies that incorporate multiscale options, and reliability versus predictive power. The need for an integrated model-experiment-based design approach is discussed together with benefits of employing a systematic computer-aided framework with built-in design templates.

Lattice enumeration for inverse molecular design using the signature descriptor

We describe an inverse quantitative structure-activity relationship (QSAR) framework developed for the design of molecular structures with desired properties. This framework uses chemical fragments encoded with a molecular descriptor known as a signature. It solves a system of linear constrained Diophantine equations to reorganize the fragments into novel molecular structures. The method has been previously applied to problems in drug and materials design but has inherent computational limitations due to the necessity of solving the Diophantine constraints. We propose a new approach to overcome these limitations using the Fincke-Pohst algorithm for lattice enumeration. We benchmark the new approach against previous results on LFA-1/ICAM-1 inhibitory peptides, linear homopolymers, and hydrofluoroether foam blowing agents. Software implementing the new approach is available at www.cs.otago.ac.nz/homepages/smartin.

Designing Novel Polymers with Targeted Properties Using the Signature Molecular Descriptor

A method for solving the inverse quantitative structure-property relationship (QSPR) problem is presented which facilitates the design of novel polymers with targeted properties. Here, we demonstrate the efficacy of the approach using the targeted design of polymers exhibiting a desired glass transition temperature, heat capacity, and density. We present novel QSPRs based on the signature molecular descriptor capable of predicting glass transition temperature, heat capacity, density, molar volume, and cohesive energies of linear homopolymers with cross-validation squared correlation coefficients ranging between 0.81 and 0.95. Using these QSPRs, we show how the inverse problem can be solved to design poly(N-methyl hexamethylene sebacamide) despite the fact that the polymer was used not used in the training of this model.

Can topological indices transmit information on properties but not on structures?

A survey of several topological indices (TIs) is provided according to the nature (integers or real numbers) of the local vertex invariants (LOVIs) and of the resulting molecular descriptor (TI). The 1st generation TIs such as the Wiener index when both the LOVIs and the TI are integers have a very high degeneracy. This fact can become an asset for the problem under discussion: when confronted with the "inverse problem" (reverse engineering) such indices lead to a combinatorial explosion of possible solutions. On the other extreme, TIs with very low degeneracy may also offer the possibility to transmit information on properties but not on structures, because they may be too difficult to lend themselves to reverse engineering in a reasonable amount of time. Several such indices are discussed: the novel second-generation index G (derived from the average distance-based connectivity index J in order to include a dependence on graph size and cyclicity), and third-generation indices such as the triplet TI denoted by DN2S(4) or the Kier-Hall index TOTOP. The intercorrelation of these indices is discussed: G is almost linearly-correlated with DN2S(4), and shows a different type of correlation with TOTOP.

On the solution of mixed-integer nonlinear programming models for computer aided molecular design

This paper addresses the efficient solution of computer aided molecular design (CAMD) problems, which have been posed as mixed-integer nonlinear programming models. The models of interest are those in which the number of linear constraints far exceeds the number of nonlinear constraints, and with most variables participating in the nonconvex terms. As a result global optimization methods are needed. A branch-and-bound algorithm (BB) is proposed that is specifically tailored to solving such problems. In a conventional BB algorithm, branching is performed on all the search variables that appear in the nonlinear terms. This translates to a large number of node traversals. To overcome this problem, we have proposed a new strategy for branching on a set of linear branchingfunctions, which depend linearly on the search variables. This leads to a significant reduction in the dimensionality of the search space. The construction of linear underestimators for a class of functions is also presented. The CAMD problem that is considered is the design of optimal solvents to be used as cleaning agents in lithographic printing.