  Protein-ligand binding is a fundamental biological process that is paramount
to many other biological processes, such as signal transduction, metabolic
pathways, enzyme construction, cell secretion, gene expression, etc. Accurate
prediction of protein-ligand binding affinities is vital to rational drug
design and the understanding of protein-ligand binding and binding induced
function. Existing binding affinity prediction methods are inundated with
geometric detail and involve excessively high dimensions, which undermines
their predictive power for massive binding data. Topology provides an ultimate
level of abstraction and thus incurs too much reduction in geometric
information. Persistent homology embeds geometric information into topological
invariants and bridges the gap between complex geometry and abstract topology.
However, it over simplifies biological information. This work introduces
element specific persistent homology (ESPH) to retain crucial biological
information during topological simplification. The combination of ESPH and
machine learning gives rise to one of the most efficient and powerful tools for
revealing protein-ligand binding mechanism and for predicting binding
affinities.
