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In recent years, machine learning and deep learning applications have permeated all fields of science thanks to rapid algorithmic advances and computer hardware developments. A very active area of research is the use of deep learning in structure-based drug design, where the goal is to design effective drugs against a pharmacological target of interest. In this work, we explored the use of deep learning in the early stages of drug discovery. In particular, we focussed on structure-based virtual screening, binding affinity prediction, and de novo drug design. First, we enabled docking with flexible residues within Gnina, a state-of-the- art docking software based on convolutional neural networks, and we performed a large-scale cross-docking study of such methodology, outlining its strengths and weaknesses. Second, we extracted the convolutional neural network scoring function from the docking software into a standalone package for fast prototyping. With the new software at hand, we explored different annotations for supervised learning to improve the convolutional neural network scoring function for docking with flexible residues. Third, we developed a novel scoring function for binding affinity prediction based on a successful deep learning architecture used to develop machine learning force fields. Finally, we carefully evaluate a generative model for de novo design for the application in industrial drug discovery pipelines. We outline the weaknesses of the method and the problems with current evaluations of generative models.

The biochemical community has been using graphical (topological, chemical) indices in the study of Quantitative Structure-Activity Relationships (QSAR) and Quantitative Structure-Property Relationships (QSPR), as they have been shown to have strong correlations with the chemical properties of certain chemical compounds (i.e. boiling point, surface area, etc.). We examine some of these chemical indices and closely related pure graph theoretical indices: the Randić index, the Wiener index, the degree distance, and the number of subtrees. We find which structure will maximize the Randić index of a class of graphs known as cacti, and we find a functional relationship between the Wiener index and the degree distance for several types of graphs. We also develop an algorithm to find the structure that maximizes the number of subtrees of trees, a characterization of the second maximal tree may also follow as an immediate result of this algorithm.