  DNA-encoded library (DEL) screening and quantitative structure-activity
relationship (QSAR) modeling are two techniques used in drug discovery to find
small molecules that bind a protein target. Applying QSAR modeling to DEL data
can facilitate the selection of compounds for off-DNA synthesis and evaluation.
Such a combined approach has been shown recently by training binary classifiers
to learn DEL enrichments of aggregated "disynthons" to accommodate the sparse
and noisy nature of DEL data. However, a binary classifier cannot distinguish
between different levels of enrichment, and information is potentially lost
during disynthon aggregation. Here, we demonstrate a regression approach to
learning DEL enrichments of individual molecules using a custom negative
log-likelihood loss function that effectively denoises DEL data and introduces
opportunities for visualization of learned structure-activity relationships
(SAR). Our approach explicitly models the Poisson statistics of the sequencing
process used in the DEL experimental workflow under a frequentist view. We
illustrate this approach on a dataset of 108k compounds screened against CAIX,
and a dataset of 5.7M compounds screened against sEH and SIRT2. Due to the
treatment of uncertainty in the data through the negative log-likelihood loss
function, the models can ignore low-confidence outliers. While our approach
does not demonstrate a benefit for extrapolation to novel structures, we expect
our denoising and visualization pipeline to be useful in identifying SAR trends
and enriched pharmacophores in DEL data. Further, this approach to
uncertainty-aware regression is applicable to other sparse or noisy datasets
where the nature of stochasticity is known or can be modeled; in particular,
the Poisson enrichment ratio metric we use can apply to other settings that
compare sequencing count data between two experimental conditions.
