Accurate and Scalable Continuum Electrostatics for Large Biomolecular Systems: The <i>pyDelPhi</i> Poisson–Boltzmann Framework
Bibliographic record
Abstract
Electrostatic interactions are central to biomolecular structure, recognition, and assembly, making their efficient and accurate evaluation essential for biophysics, drug discovery, and materials modeling. The Poisson–Boltzmann equation (PBE) provides a rigorous implicit-solvent description, yet large macromolecular systems remain challenging for conventional CPU-based solvers. Here, we introduce pyDelPhi, a modern finite-difference PBE framework designed for numerical accuracy, scalability, and reproducibility across heterogeneous architectures. Implemented in Python with just-in-time compilation via Numba, pyDelPhi preserves the established DelPhi numerical framework while supporting traditional, Gaussian-density, and regularized dielectric models and enabling multiprecision execution on CPUs and NVIDIA GPUs via a CUDA backend. Benchmarking across three curated data sets shows that pyDelPhi reproduces DelPhi reaction-field energies within fractions of a percent and achieves 7–20× GPU acceleration for the linearized PBE. A cuboidal grid-box option reduces memory by up to 80% and accelerates runtimes several-fold for anisotropic systems. A complete viral-capsid calculation (∼5 × 10 5 atoms, 10 9 grid points) yields an order-of-magnitude reduction in wall time relative to the single-core DelPhi baseline while maintaining close numerical agreement. These results establish pyDelPhi as a unified and extensible platform that advances continuum electrostatics toward reproducible, high-performance modeling of biomolecular systems at both routine and large scales.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.005 | 0.002 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".