  Explainable Graph Neural Networks (GNNs) have been developed and applied to
drug-protein binding prediction to identify the key chemical structures in a
drug that have active interactions with the target proteins. However, the key
structures identified by the current explainable GNN models are typically
chemically invalid. Furthermore, a threshold needs to be manually selected to
pinpoint the key structures from the rest. To overcome the limitations of the
current explainable GNN models, we propose our SLGNN, which stands for using
Sparse Learning to Graph Neural Networks. Our SLGNN relies on using a
chemical-substructure-based graph (where nodes are chemical substructures) to
represent a drug molecule. Furthermore, SLGNN incorporates generalized fussed
lasso with message-passing algorithms to identify connected subgraphs that are
critical for the drug-protein binding prediction. Due to the use of the
chemical-substructure-based graph, it is guaranteed that any subgraphs in a
drug identified by our SLGNN are chemically valid structures. These structures
can be further interpreted as the key chemical structures for the drug to bind
to the target protein. We demonstrate the explanatory power of our SLGNN by
first showing all the key structures identified by our SLGNN are chemically
valid. In addition, we illustrate that the key structures identified by our
SLGNN have more predictive power than the key structures identified by the
competing methods. At last, we use known drug-protein binding data to show the
key structures identified by our SLGNN contain most of the binding sites.
