Statistical Convergence of Equilibrium Properties in Simulations of Molecular Solutes Embedded in Lipid Bilayers
Bibliographic record
Abstract
In recent years, atomistic molecular simulations have become a method of choice for studying the interaction of small molecules, peptides, and proteins with biological membranes. Here, we critically examine the statistical convergence of equilibrium properties in molecular simulations of two amino acid side-chain analogs, leucine and arginine, in the presence of a hydrated phospholipid bilayer. To this end, the convergence of the standard binding free energy for the reversible insertion of the solutes in the bilayer is systematically assessed by evaluating dozens of separate sets of umbrella sampling calculations for a total simulation time exceeding 400 μs. We identify rare and abrupt transitions in bilayer structure as a function of solute insertion depth. These transitions correspond to the slow reorganization of ionic interactions involving zwitterionic phospholipid headgroups when the solutes penetrate the lipid-water interface and when arginine is forced through the bilayer center. These rare events are shown to constitute hidden sampling barriers that limit the rate of convergence of equilibrium properties and result in systematic sampling errors. Our analysis demonstrates that the difficulty of attaining convergence for lipid bilayer-embedded solutes has, in general, been drastically underestimated. This information will assist future studies in improving accuracy by selecting a more appropriate reaction coordinate or by focusing computational resources on those regions of the reaction coordinate that exhibit slow convergence of equilibrium properties.
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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 | 0.010 |
| 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 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".