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Benefit Ledger · provisional · Mathematics

Ten numbers from the Laplace-Beltrami spectrum facilitate training-free classification of protein structures based on surface shape

The comparison of protein structures is necessary to determine molecular functions and evolutionary relationships and can also facilitate drug design and the prediction of separation options. The number of available protein structures is rapidly increasing, driven by experimental determination but also prediction methods such as AlphaFold. In this context, traditional structure comparison based on atomic superposition becomes computationally inefficient. To enable scalable analysis and surface shape comparison, alternative approaches represent protein structures using compact, fixed-length vec

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Ingest update: independent source raised evidence; added a follow-up source. Score remains provisional until review. Follow-up ingest: independent source raised evidence; added a follow-up source. Follow-up ingest: independent source raised evidence; added a follow-up source.

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The comparison of protein structures is necessary to determine molecular functions and evolutionary relationships and can also facilitate drug design and the prediction of separation options. The number of available protein structures is rapidly increasing, driven by experimental determination but also prediction methods such as AlphaFold. In this context, traditional structure comparison based on atomic superposition becomes computationally inefficient. To enable scalable analysis and surface shape comparison, alternative approaches represent protein structures using compact, fixed-length vectors known as descriptors. Current vectors often contain hundreds of entries, such as three-dimensional Zernike descriptors composed of 121 entries, or combinations of molecular and geometric properties. Here, we propose to use the Laplace-Beltrami spectrum, a mathematical representation of object surfaces derived from the eigenvalues of the Laplace-Beltrami operator, as an efficient option to capture protein structural properties and facilitate structural classification. Specifically, protein surfaces are encoded using only the first 10 non-zero eigenvalues of this spectrum. We used the SHREC 2025 dataset as a benchmark and achieved 85.8% accuracy on the original 97 protein structure classes and 97.7% accuracy on the homology-grouped 45 classes. Our method is fast, requiring ~75 min computation time for the 11,555 protein surface meshes of the SHREC 2025 dataset on a conventional AMD Ryzen 7 5700X 8-Core processor with 32 GB RAM. The approach can easily be applied to large protein structure databases because it is readily parallelizable and allows the incorporation of other descriptors, including surface features such as charge. This rapid screening tool can therefore be used to identify proteins with related surface shapes independent of sequence homology. Update (2026-09-16): Evaluation of methods for AlphaFold-based integrative modeling . Motivation Recent methods enable incorporation of experimental data into AlphaFold for predicting structures consistent with the data. However, the applicability of these methods for integrative modeling remains to be determined. It is unclear how these methods balance the input experimental data with the learned structural priors. Results We assess the performance of state-of-the-art AlphaFold-based integrative modeling methods, including AlphaLink2, Boltz2, and GRASP, on a dataset of 37 complexes based on crosslinking data. We evaluate these methods based on their ability to predict structures that satisfy the input crosslinks. We further assess the robustness of these methods to noise in the crosslinking data. Finally, we probe their ability to predict distinct states using crosslinks from multiple states. Overall, our study highlights the limitations of the AF-based IM methods and points to directions for future improvements. Availability and implementation All scripts used to obtain the predictions and perform the analysis in this study are available at https://github.com/isblab/af_im. Update (2026-09-18): TRACEDD: A Tool-grounded Reasoning and Agentic Coordination for Explainable Drug Design . Drug discovery depends on coordinated decisions across target validation, structure analysis, molecular design, developability assessment and synthetic feasibility, but current computational methods often operate as disconnected tools. Here, we introduce TRACEDD (Tool-grounded Reasoning and Agentic Coordination for Explainable Drug Design), a framework that makes three primary contributions: (1) It establishes a 'tool-first' multi agentic architecture where LLMs orchestrate validated computational tools rather than replace them, ensuring scientific rigor. (2) It implements a multi-agent system that mirrors expert discovery teams, enabling transparent and traceable decision-making through a Reason-Act-Observe loop. (3) It demonstrates an end-to-end workflow, from target validation to synthesis planning, that adaptively handles real-world data variability, such as the absence of experimental structures. The framework decomposes discovery into specialized agents for target validation, druggability assessment, molecular generation, lead optimization, ADMET evaluation, li Update (2026-09-18): BFVD v3-UniProt-complete, improved viral protein structure predictions . The Big Fantastic Virus Database (BFVD) v3 is the most comprehensive resource for ColabFold-AlphaFold2-predicted viral protein structures. It holds 5,776,417 structures of nearly all viral sequences in UniProt 2025_03, a 16.4-fold increase compared to the representative-only catalogs of BFVD v1 and v2. Structure prediction quality has also improved, with high-confidence predictions accounting for 75.3% of BFVD v3 entries. This is due to Logan's enormous sequence assembly, now mined for the entire BFVD v3 instead of only for shallow alignments, alongside continued prediction quality improvements. BFVD v3 covers 72.7% of ICTV's virus species, 1.54-fold more than BFVD v2. With this version, the fraction of fully covered viral reference proteomes increases from 1.5% to 72.6%. BFVD v3 thus brings us closer to a structural catalog of the known virosphere and is freely available at bfvd.steineggerlab.workers.dev and bfvd.foldseek.com.

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  • Ten numbers from the Laplace-Beltrami spectrum facilitate training-free classification of protein structures based on surface shape

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Revision history

  • 16 Sep 2026 · 0.00 → 0.00

    Auto-published from news ingest.

  • 17 Sep 2026 · 0.00 → 0.00

    Ingest update: independent source raised evidence; added a follow-up source.

  • 18 Sep 2026 · 0.00 → 0.00

    Ingest update: independent source raised evidence; added a follow-up source.

  • 19 Sep 2026 · 0.00 → 0.00

    Ingest update: independent source raised evidence; added a follow-up source.