Improving scoring functions for protein-protein docking with LambdaLoss

Richard Zhu; Darren Xu; Lee-Shin Chu; Jeffrey J. Gray

q-bio.QMSep 18, 2026

Improving scoring functions for protein-protein docking with LambdaLoss

Authors: Richard Zhu, Darren Xu, Lee-Shin Chu, Jeffrey J. Gray

Organizations: Department of Statistics Harvard University · Department of Chemical and Biomolecular Engineering Johns Hopkins University

Abstract

Modeling protein-protein interactions requires accurate scoring functions that can rank potential poses (conformations) of a protein-protein complex to differentiate near-native poses from incorrect ones. Here, we propose a general framework for improving protein-protein pose ranking and other biomolecular interaction models using the LambdaLoss loss function from the Learning-to-Rank field. We test this framework by fine-tuning the energy prediction head of DFMDock with the LambdaLoss on an augmented dataset of 2.9M decoy poses derived from the DIPS dataset. On targets from the CAPRI score set benchmark, our fine-tuned ranking model LambdaDockScore is better at identifying correct poses in its top-1 and top-5 predictions compared to EuDockScore, a state-of-the-art method. LambdaDockScore also improves upon baseline DFMDock ranking performance for scoring antibody-antigen complexes and protein-protein complexes with very large or small binding interfaces.

Figures & tables

Figure 1: Benchmarking results on 69 protein-protein complexes from the CAPRI Score Set (filtered for <30% seq. identity to training data). Each complex averaged

{\sim}

1.1k decoys. The top-1 and top-5 ranked decoys from each model were analyzed. Exact success rates for all models are provided in Supplementary Table S3 .

Figure 2: Benchmarking results on 253 protein-protein complexes from Docking Benchmark 5.5. 120 decoys were generated per protein-protein complex using baseline DFMDock. The top-1 and top-5 ranked decoys from each model were analyzed. DFMDock with LambdaDockScore as its ranking model outperforms baseline DFMDock on both top-1 and top-5 ranking accuracy for acceptable and medium quality poses. Bar heights show the mean performance from 10,000 bootstrap samples, and error bars show the 95% confidence interval. Exact success rates and 95% confidence intervals are provided in Supplementary Table S4 .

Figure 3: Benchmarking results on antibody-antigen complexes from Docking Benchmark 5.5. Results are for 120 decoys generated and ranked per protein-protein complex. DFMDock with LambdaDockScore as its ranking model (red) outperforms baseline DFMDock (blue). Exact success rates and 95% confidence intervals are provided in Supplementary Table S5 .

Appendix figures & tables10 assets

Supplementary material from the paper’s appendix.

Appendix

Decoy set	Translation std. dev. (Å)	Rotation std dev. (°)	# poses
Perturbed GT — small	0.1	1.0	20
Perturbed GT — medium	1.0	7.0	100
Perturbed GT — large	2.5	20.0	100
DFMDock samples	N/A	N/A	50
Total (per GT complex)			270

Appendix

Table S1: Decoy pose sampling details. GT stands for ground truth. Standard deviations are for Normal distributions centered at 0, which were used to sample random translations and rotations for the perturbed GT poses.

Figure S1: Distribution of poses for eight randomly sampled protein-protein complexes from the DIPS-hetero fine-tuning dataset. The majority of complexes in the fine-tuning dataset have a distribution of poses across the full DockQ [0,1] interval, though some complexes lack sufficient numbers of high DockQ poses.

Figure S2: Top-

k

success rate on the CAPRI score set (69 complexes) for LambdaDockScore (red), baseline DFMDock (blue), and EuDockScore (purple), shown for high (left), medium (center), and acceptable (right) quality thresholds. Each curve is the percentage of complexes with at least one pose above the quality threshold among the

k

lowest-energy poses.

Figure S3: Top-

k

success rate on DB5.5 (253 complexes) for LambdaDockScore (red) and baseline DFMDock (blue), shown for high (left), medium (center), and acceptable (right) quality thresholds. Poses were sampled with baseline DFMDock and ranked by each model. Each curve is the percentage of complexes with at least one pose above the quality threshold among the

k

lowest-energy poses.

Figure S4: Benchmarking results on Docking Benchmark 5.5, segmented by the change in accessible surface area (

\Delta

ASA). This is a measure of how the model performs based on the size of the binding interface. Protein-protein complexes were ordered by

\Delta

ASA and split into five evenly sized bins based on their

\Delta

ASA percentile. Panels (a)-(e) show the performance of baseline DFMDock’s energy prediction head (blue) compared to LambdaDockScore (red) for each bin, in order of increasing interface size. Exact success rates and 95% confidence intervals are provided in Supplementary Table S6 .

$\Delta$ ASA bin	Targets	Targets with zero acceptable poses	Percent with zero acceptable poses
0–20th	51	32	62.7%
20–40th	50	30	60%
40–60th	51	36	70.6%
60–80th	50	34	68%
80–100th	51	30	58.8%

Appendix

Table S2: The number of target complexes in each

\Delta

ASA percentile bin, the number containing no acceptable pose among the sampled decoys, and the percent of target complexes with no acceptable pose.

Evaluation Metric	Model	Acceptable (%)	Medium (%)	High (%)
Top-1	Baseline DFMDock	30.4	17.4	7.2
Top-1	LambdaDockScore	31.9	26.1	1.4
Top-1	EuDockScore	20.3	13.0	0.0
Top-5	Baseline DFMDock	44.9	31.9	7.2
Top-5	LambdaDockScore	49.3	34.8	7.2
Top-5	EuDockScore	40.6	26.1	4.3

Appendix

Table S3: Success rates for the CAPRI Score Set (n=69), corresponding to Figure 1 .

Evaluation Metric	Model	Acceptable (%) [95% CI]	Medium (%) [95% CI]	High (%) [95% CI]
Top-1	Baseline DFMDock	3.4 [2.4, 4.3]	0.8 [0.4, 1.6]	0.0 [0.0, 0.0]
Top-1	LambdaDockScore	5.0 [3.6, 6.3]	1.3 [0.8, 2.0]	0.3 [0.0, 0.4]
Top-5	Baseline DFMDock	7.2 [5.5, 8.7]	2.0 [1.2, 2.8]	0.2 [0.0, 0.4]
Top-5	LambdaDockScore	9.4 [7.9, 11.1]	2.3 [1.6, 3.2]	0.3 [0.0, 0.4]
Oracle	Baseline DFMDock	31.1 [28.9, 33.2]	6.1 [4.7, 7.1]	0.3 [0.0, 0.4]
Oracle	LambdaDockScore	31.1 [28.9, 33.2]	6.1 [4.7, 7.1]	0.3 [0.0, 0.4]

Appendix

Table S4: Success rates and 95% confidence intervals for DB5.5 (n=253), corresponding to Figure 2 . Success rate values represent the mean performance from 10,000 pose-bootstrap samples.

Evaluation Metric	Model	Acceptable (%) [95% CI]	Medium (%) [95% CI]	High (%) [95% CI]
Top-1	Baseline DFMDock	1.2 [0.0, 1.8]	0.0 [0.0, 0.0]	0.0 [0.0, 0.0]
Top-1	LambdaDockScore	1.9 [0.0, 3.6]	0.0 [0.0, 0.0]	0.0 [0.0, 0.0]
Top-5	Baseline DFMDock	2.5 [0.0, 5.5]	0.0 [0.0, 0.0]	0.0 [0.0, 0.0]
Top-5	LambdaDockScore	5.1 [1.8, 7.3]	0.0 [0.0, 0.0]	0.0 [0.0, 0.0]
Oracle	Baseline DFMDock	17.6 [14.5, 20.0]	0.0 [0.0, 0.0]	0.0 [0.0, 0.0]
Oracle	LambdaDockScore	17.6 [14.5, 20.0]	0.0 [0.0, 0.0]	0.0 [0.0, 0.0]

Appendix

Table S5: Success rates and 95% confidence intervals for DB5.5 Antibody-Antigen Complexes (n=55), corresponding to Figure 3 . Success rate values represent the mean performance from 10,000 pose-bootstrap samples.

$\Delta$ ASA Bin	Metric	Model	Acceptable (%) [95% CI]	Medium (%) [95% CI]	High (%) [95% CI]
0–20th pct (799-1316 Å 2 n=51)	Top-1	Baseline DFMDock	0.2 [0.0, 2.0]	0.2 [0.0, 2.0]	0.0 [0.0, 0.0]
	Top-1	LambdaDockScore	2.1 [0.0, 5.9]	0.2 [0.0, 2.0]	0.0 [0.0, 0.0]
	Top-5	Baseline DFMDock	1.9 [0.0, 3.9]	1.2 [0.0, 2.0]	0.0 [0.0, 0.0]
	Top-5	LambdaDockScore	7.6 [3.9, 11.8]	1.7 [0.0, 3.9]	0.0 [0.0, 0.0]
	Oracle	Baseline DFMDock	31.5 [25.5, 37.3]	5.0 [2.0, 7.8]	0.0 [0.0, 0.0]
	Oracle	LambdaDockScore	31.5 [25.5, 37.3]	5.0 [2.0, 7.8]	0.0 [0.0, 0.0]

Appendix

Table S6: Success rates and 95% confidence intervals for DB5.5 split into 5

\Delta

ASA bins, corresponding to Supplementary Figure S4 . Success rate values represent the mean performance from 10,000 pose-bootstrap samples across 5 interface area bins.

Protein-Protein Interaction Prediction

Protein-protein interaction prediction uses sequence, structure, and biological networks to identify interacting proteins and their binding sites or poses.

See all 17 papers

Q-Score: A Quantum-Native Scoring Function for Molecular Docking
Jul 2, 2026Kangyu Zheng, Yidong Zhou, Ruihao Li +3Protein-Ligand Binding Affinity Prediction Structure-Based Drug Design
Department of Computer Science and Engineering The Chinese University of Hong Kong Shatin, N.T., Hong Kong SAR · Department of Electrical and Computer Engineering Rutgers University Piscataway, NJ · Computational Life Sciences Cleveland Clinic Cleveland, OH +1
Benchmarking Single-Pose Docking, Consensus Rescoring, and Supervised ML on the LIT-PCBA Library: A Critical Evaluation of DiffDock, AutoDock-GPU, GNINA, and DiffDock-NMDN
May 3, 2026Youssef Abo-Dahab, Xiaoiang Xiang, Joanne Chun +1Learning to Rank Virtual Screening
Department of Bioengineering and Therapeutic Sciences, Schools of Pharmacy and Medicine, University of California, San Francisco, San Francisco, CA, USA · UCSF–Stanford Center of Excellence in Regulatory Science and Innovation (CERSI), San Francisco, CA, USA
A Large-Scale Dataset and Benchmark: Do Protein-Ligand Models Learn Binding Sites or Just Binding Likelihood?
May 21, 2026Zhaohan Meng, Zhen Bai, Ke Yuan +4Drug Discovery
School of Computing Science, University of Glasgow · School of Life Science and Technology, Institute of Science Tokyo · School of Cancer Sciences, University of Glasgow +4

Jul 2, 2026J/K move · Enter open · S save

Q-Score: A Quantum-Native Scoring Function for Molecular Docking

Kangyu Zheng, Yidong Zhou, Ruihao Li, Zixin Ding+2

Department of Computer Science and Engineering The Chinese University of Hong Kong Shatin, N.T., Hong Kong SAR · Department of Electrical and Computer Engineering Rutgers University Piscataway, NJ · Computational Life Sciences Cleveland Clinic Cleveland, OH+1

Protein-Ligand Binding Affinity Prediction Structure-Based Drug Design Drug Discovery

Open paper AskPDF arXiv

Molecular docking predicts how a small molecule binds to a protein and is a key bottleneck in drug discovery. Classical scoring functions sum empirical pairwise contacts, blind to quantum-mechanical effects like orbital charge transfer that govern binding specificity. We introduce Q-Score, encoding GNN-predicted orbital donor-acceptor energies into a weighted graph and scoring binding by solving a maximum-weight vertex clique problem via Digitized-Counterdiabatic QAOA. Each interaction anchor maps to one qubit and compatibility constraints become edges. Across 11 protein targets, DC-QAOA recovers the exact optimum on 8 at 10 qubits. On 1000 AI-generated molecules, Q-Score is orthogonal to classical scoring with Spearman rho of 0.05, driven by orbital quality with rho of 0.90, and free of molecular-weight bias, enriching for strong orbital interactions at twice the random rate. DC-QAOA achieves a mean approximation ratio of 0.94 with 52 percent exact. Execution of 1000 circuits on IBM Eagle confirms 6-qubit solvability on NISQ hardware.

Abstract

Protein-Protein Interaction Prediction

Explore similar work

Q-Score: A Quantum-Native Scoring Function for Molecular Docking

Benchmarking Single-Pose Docking, Consensus Rescoring, and Supervised ML on the LIT-PCBA Library: A Critical Evaluation of DiffDock, AutoDock-GPU, GNINA, and DiffDock-NMDN

A Large-Scale Dataset and Benchmark: Do Protein-Ligand Models Learn Binding Sites or Just Binding Likelihood?