Determining Protein Structures from NOESY Distance Constraints by Semidefinite Programming
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Bibliographic record
Abstract
Contemporary practical methods for protein nuclear magnetic resonance (NMR) structure determination use molecular dynamics coupled with a simulated annealing schedule. The objective of these methods is to minimize the error of deviating from the nuclear overhauser effect (NOE) distance constraints. However, the corresponding objective function is highly nonconvex and, consequently, difficult to optimize. Euclidean distance matrix (EDM) methods based on semidefinite programming (SDP) provide a natural framework for these problems. However, the high complexity of SDP solvers and the often noisy distance constraints provide major challenges to this approach. The main contribution of this article is a new SDP formulation for the EDM approach that overcomes these two difficulties. We model the protein as a set of intersecting two- and three-dimensional cliques. Then, we adapt and extend a technique called semidefinite facial reduction to reduce the SDP problem size to approximately one quarter of the size of the original problem. The reduced SDP problem can be solved approximately 100 times faster, and it is also more resistant to numerical problems from erroneous and inexact distance bounds.
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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 it