Free Energy Simulations: Thermodynamic Reversibility and Variability
Bibliographic record
Abstract
The energetic consequences of amino acid substitutions were investigated using molecular dynamics free energy simulations (MD/FES). A focus of the present study is how one can treat some of the intrinsic problems associated with the use of dummy atoms, which are introduced in standard MD/FES procedures working with a constant number of particles. Specifically, we show how one can introduce dummy atoms, which retain all the covalent interactions, in a “hybrid residue”, in such a way that the influence of the bonded interactions with dummy atoms do not influence the final free energy change. The simulations thus can be done using a transformation protocol in which all covalent bond contributions are maintained invariant throughout the calculations; only the nonbonded interactions are varied. That is, the number of atoms is maintained constant by introducing dummy atoms, which are covalently linked to the protein in question, but which have no nonbonded interactions at one or the other of the two end point reference states. The potential energy function describing the transformation was constructed such that all internal energy terms are invariant with respect to the thermodynamic coupling parameter λ (0 ≤ λ ≤ 1). This simulation procedure therefore has similarities with both the “single topology” and “dual topology” methods, which have been used in other investigations. This transformation and MD/FES strategy was evaluated using three different systems, in which an Ala is transformed into a Val (the italicized residues were transformed): formyl-Ala-ethanolamine; formyl-(Ala)3-Ala-Ala-Ala-(Ala)3-ethanolamine (as an α-helix); and formyl-(Ala)3-Val-Ala-Val-(Ala)3-ethanolamine (as an α-helix). The calculations examined how the free energy difference associated with an Ala-to-Val transformation depends on the choice of transformation path, the equilibration time, and the number windows used in the calculation. The results show that MD/FES provides for stable energy estimates for any intermediate state, as defined by the coupling parameter λ, including the end point reference states: λ = 0 and λ = 1. With an appropriate choice of sigmoid transformation path, free energy changes with minimal variability and good reversibility were obtained for all three systems using MD/FES lasting longer than 2.4 ns.
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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) | 0.001 | 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 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".