Calculating diffusion and permeability coefficients with the oscillating forward-reverse method
Bibliographic record
Abstract
The forward-reverse or FR method is an efficient bidirectional work method for determining the potential of mean force $w(z)$ and also supposedly gives in principle the position-dependent diffusion coefficient $D(z)$. Results from a variation called the OFR (oscillating FR) method suggest inconsistencies in the $D(z)$ values when calculated as prescribed by the FR method. A new steering protocol has thus been developed and applied to the OFR method for the accurate determination of $D(z)$ and also provides greater convergence for $w(z)$ in molecular dynamics simulations. The bulk diffusion coefficient for water was found to be $(6.03\ifmmode\pm\else\textpm\fi{}0.16)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ cm${}^{2}$/s at 350 K with system size dependence within the statistical error bars. Using this steering protocol, $D(z)$ and $w(z)$ for water permeating a dipalmitoylphosphatidylcholine (DPPC) bilayer were determined. The potential of mean force is shown to have a barrier of peak height, ${w}_{\text{max}}/({k}_{B}T)=8.4$, with a width of about 10 \AA{} on either side from the membrane center. The diffusion constant is shown to be highest in the core region of the membrane [peak value $\ensuremath{\sim}\phantom{\rule{0.16em}{0ex}}(8.0\ifmmode\pm\else\textpm\fi{}0.8)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ cm${}^{2}$/s], lowest in the head-group region [minimum value $\ensuremath{\sim}\phantom{\rule{0.16em}{0ex}}(2.0\ifmmode\pm\else\textpm\fi{}0.3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ cm${}^{2}$/s], and to tend toward the bulk value as the water molecule leaves the membrane. The permeability coefficient $P$ for H${}_{2}$O in DPPC was determined using the simulated $D(z)$ and $w(z)$ to give values of $(0.129\ifmmode\pm\else\textpm\fi{}0.075)$ cm/s at 323 K and $(0.141\ifmmode\pm\else\textpm\fi{}0.043)$ cm/s at 350 K. The results show more spatial detail than results presented in previous work while reducing the computational and user effort.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".