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Protein-protein interaction prediction from structure alone, embedding each protein once so a proteome-wide dot product replaces pairwise queries.
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Whether two proteins physically interact is a one-to-one question, and accurate methods answer it one pair at a time. That works for a shortlist and fails for a proteome: roughly 10^5 human proteins give 10^10 possible pairs, and applying a structure predictor to all of them would cost between 90 million and 900 million GPU hours by the estimate the authors cite. Deep Kernel Inversion (DKI) attacks that arithmetic rather than the per-pair model. It projects each protein into a 1,024-dimensional complex-valued vector once, and the conjugate-transpose dot product between two vectors is the interaction prediction — so a whole network follows from n embeddings instead of n² model queries.
The name describes the mechanism. Kernel methods substitute a nonlinear similarity function for a dot product; DKI inverts that substitution, starting from the expensive nonlinear kernel — will these two proteins bind? — and learning the higher-dimensional space in which a plain dot product approximates it. Complex-valued vectors fix a failure mode specific to interactions: a real vector always has a large positive dot product with itself, making every protein a predicted self-binding dimer. The imaginary component instead carries complementary "anti-self" surface properties — convex against concave, hydrogen-bond donor against acceptor — that cancel when a vector meets itself.
DKI was developed at Nosis Bio, an RNA-therapeutics company in Berkeley. It reads structure only — amino-acid types, Cα backbone distances and residue surface depth — and uses no multiple sequence alignment, because the company's design work targets de novo protein ligands with no natural homologs to align against.
The encoder is a residue-pair transformer: 12 blocks of paired self-attention holding one residue constant while the other varies, at head dimension 128 across 8 heads. An attention "reducer" collapses the residue-pair encodings into one vector, which three two-layer feed-forward networks turn into the real component, imaginary component and bias scalar. Interaction probability is sigmoid(b_i + b_j + v_i^H v_j / √D) with D = 1,024. Public training data came from the PDB — 13,252 protein pairs whose chains contact across at least three residues and map to distinct UniProt IDs, split 80/10/10 with Uniref90 cluster-aware partitioning. That data alone reached PR-AUC 0.17; pretraining instead on a proprietary 2.92-million-example structural PPI corpus and then fine-tuning on the 13K public pairs raised it to PR-AUC 0.57 at a 1:79 positive-to-negative ratio.
Applied unchanged to five yeast interactome datasets, DKI scored PR-AUC 0.908–0.960 against PEPPI's 0.761–0.931, finishing in minutes on a small GPU where the MSA-dependent baseline took days of CPU time. On human mitochondrial PPIs at a 1:100 ratio it reached PR-AUC 0.304 versus 0.132 for an AlphaFold 2-based method, 0.113 for RoseTTAFold and 0.014 for direct-coupling analysis. Fine-tuned on 1,601 PDBBind interactions with measured Kd, it achieved Pearson R = 0.677. The full human run embedded 20,425 AlphaFold Protein Structure Database models and predicted 147,291 interactions from 57,120 seed-residue vectors in 4.5 hours on four A100s.
DKI was built for specificity screening during protein design. Nosis embeds roughly 120,000 human extracellular epitopes once and reuses those vectors, so each iteration of a designed binder is scored against every one for off-target interaction — unaffordable when each pair costs a model query. The same embeddings serve target discovery and pathway mapping: Leiden clustering of the human seed-residue vectors produces groups whose most differentiated Gene Ontology terms are binding annotations such as antigen binding and ubiquitin ligase activity.
DKI reframes interaction prediction as a representation problem rather than a scoring problem, and that trade — a learned embedding space in place of pairwise inference — is what makes proteome-scale interactomics and design-time specificity optimization tractable. The caveats are substantial. No weights, code or hosted API have been released, and the pretraining corpus and a companion all-atom encoder's design are held as trade secrets, so the results cannot be independently reproduced. The authors did not run head-to-head comparisons against several related methods, citing unavailable datasets or code and overlapping examples they could not remove. The affinity evaluation rests on a small test set, and the work remains a preprint that has not been peer-reviewed.
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