Rational drug design and drug discovery have rapidly evolved into some of the most important and exciting research fields in mathematical medicine and biology, with the potential to have a profound impact on human health. The ultimate goal in these fields is to determine and predict whether a given molecule will bind to a biomolecule so as to activate or inhibit its function, which in turn results in a therapeutic benefit to the patient. Most successful drugs are small organic molecules in the past, while, biopolymer-based, protein-based drugs, mRNA-based and CRISPR-based drugs have become increasingly common recently. A successful drug must be non-toxic, have little side effect, be acceptable to the human metabolic system, and bind to a target sufficiently strongly. As a result, the multi-objective optimization in terms of drug safety, selectivity, stability and affinity poses grand challenges to mathematics, biology, bioengineering and biotechnology. A fundamental strategy in addressing these challenges is to explore the molecular mechanism of drug and protein interaction, dynamics and transport, which involve a large number of effects, including stereospecificity, charge, polarization, hydrogen bond, ionic effect, electrostatic effect, solvation, mobility, lipophilicity and allosteric effect. A new approach is to apply molecular mechanism towards entire proteomes, enzyme pathways/families (e.g. catecholamine biosynthesis, botulinum neurotoxins), and high value drug targets, including G-protein coupled receptors (GPCRs). Recently, nano-bio engineering and technology for drug transport and drug delivery have emerged as an important area of research.

Some of the most fruitful approaches in the field are computer-aided drug design and drug-delivery design that offer the improved understanding of molecular mechanism, dramatically reduced number of experimental drug candidates and efficient strategies for drug discovery. Recent years have witnessed rapid advances in computer-aided drug design and discovery, driven by the substantial progress in theoretical models for drug-protein interactions, geometric representations for drug binding, optimization protocols for consensus drug scoring, statistical analysis for high throughput drug screening, computational methods for structure-based analysis of molecular dynamics and quantum mechanical calculations, nano-particle based drug delivery devices and associated convection-diffusion models, machine learning algorithms for knowledge based analysis of toxicity, metabolic instability and side effect, and parallel and GPU architectures for massive simulations.

Mathematics underpins all of the aforementioned progress. Many mathematical theories, such as differential and algebraic geometry, algebraic topology, graph theory, combinatorics, algebra and differential equations play an integral and essential role in most new developments in computer-aided drug design and discovery. Additionally, mathematical approaches, such as geometric and charge analysis for protein-drug binding site analysis, persistent homology for protein-drug binding detection, manifold learning for discriminating false protein-drug interfaces, and machine learning techniques for high throughput drug screening, have been widely used for drug design and drug discovery. To design successful drugs, it takes collaborative efforts from biologists, biochemists, computer scientists and mathematicians to come up with better homology modeling, efficient structural optimization, rapid molecular docking, fast sampling, linear-scaling quantum algorithms, robust statistical analysis and advanced de novo design.

Thus the ingredients that make up much of the interdisciplinary research in this area involves not only biophysics, but differential geometric methods, geometric PDEs, multi scale modelling, numerical methods (higher order interface and boundary methods, wavelet local spectral methods etc.), statistical methods as well computational methods to tackle "big data" problems.

This workshop will bring together experts from both academia and pharmaceutical industry (mathematical and computational scientists, biophysicists, and experimentalists) to develop solutions to challenging problems in drug design and discovery. It will act as a catalyst to fully exploit the synergies between mathematicians and other scientists, and create a network of collaborations that will sustain future activities in the design of new drugs and delivery systems. We envision that the workshop will be of particular benefit to junior mathematicians who are looking for ways to make an impact in society by using their mathematical skills and tools in medically and biologically areas for the ultimate benefit of society as a whole.