Origin‐Dependence of Dipole Moments of Charged Proteins: Theoretical Foundations and Implications, Revisited
Bibliographic record
Abstract
ABSTRACT Electric dipole moments are widely employed in structural biology and computational chemistry as global descriptors of macromolecular charge distribution, contributing to the understanding of protein interactions, solvation, and orientation in external fields. However, for systems bearing a nonzero net charge, the dipole moment becomes explicitly dependent on the choice of coordinates origin, a consequence grounded in classical electrostatics and sometimes overlooked in structural analyses. This origin‐dependence is particularly relevant in biological systems, as proteins are typically charged at physiological pH which differs from their isoelectric points (pI's). Moreover, coordinate manipulations such as centering and alignment are routinely performed during molecular dynamics simulations, docking, and structural comparisons, potentially altering the calculated dipole moment of charged systems. This study reviews the theory of the changes in the dipole moment of charged macromolecules accompanying displacements of the origin of the coordinates system. The theory is illustrated by numerical examples on representative proteins. Using the classical expression , we demonstrate that displacements of the order of a protein's radius of gyration or larger can induce dipoles several hundreds to thousands of debyes. We examine this effect across a range of proteins with varying sizes and identify trends correlating the extent of origin‐induced changes with molecular size. These examples highlight the need for standardization in defining coordinate systems in dipole‐related analyses. The quantum mechanical status of the dipole moment operator is discussed clarifying that only neutral systems satisfy Dirac's criteria for a true “observable”. Altogether, theory, numerical benchmarks, practical guidelines, and pedagogical insights are presented for reliably calculating and interpreting dipole moments of charged biological macromolecules.
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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 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
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".