Stiff-spring approximation revisited: inertial effects in\n non-equilibrium trajectories
Bibliographic record
Abstract
Use of harmonic guiding potentials is the most common method for implementing\nsteered molecular dynamics (SMD) simulations, performed to obtain potentials of\nmean force (PMFs) of molecular systems using non-equilibrium work (NEW)\ntheorems. Harmonic guiding potentials are also the natural choice in single\nmolecule force spectroscopy experiments. The stiff spring approximation (SSA)\nof Schulten and coworkers enables to use the work performed along SMD\ntrajectories to obtain the PMF.\n We discuss and demonstrate how a high spring constant, k, required for the\nvalidity of the SSA can violate another requirement of this theory, i.e., the\nvalidity of Brownian dynamics of the system. Violation of the Brownian\ncondition results in the introduction of kinetic energy contributions to the\nexternal work, performed during SMD simulations. These inertial effects result\nin skewed work distributions, rather than the Gaussian distributions predicted\nby SSA. The inertial effects also result in broader work distributions, which\nworsen the effect of the skewness when calculating work averages. Remarkably,\nour results strongly suggest that the skew and width of work distributions are\nindependent of the average drift velocity and physical asymmetries.\n The skew and broadening of work distributions result in biased estimation of\nthe PMF. The bias manifests itself in the form of a systematic error that\nincreases with simulation time. We discuss the proper upper limit for k, such\nthat the inertial effects are avoided. This limit, used together with the\nrelation for the lower limit of k, enables to conduct accurate steering while\nsatisfying the Brownian dynamics. Furthermore, we argue and demonstrate that\nusing the peak-value (rather than the statistical mean) of the work\ndistributions vastly reduces the bias in the calculated PMFs and improves the\naccuracy.\n
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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 | 0.002 | 0.007 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".