Polyelectrostatic interactions of disordered ligands suggest a physical basis for ultrasensitivity
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Bibliographic record
Abstract
Regulation of biological processes often involves phosphorylation of intrinsically disordered protein regions, thereby modulating protein interactions. Initiation of DNA replication in yeast requires elimination of the cyclin-dependent kinase inhibitor Sic1 via the SCF(Cdc4) ubiquitin ligase. Intriguingly, the substrate adapter subunit Cdc4 binds to Sic1 only after phosphorylation of a minimum of any six of the nine cyclin-dependent kinase sites on Sic1. To investigate the physical basis of this ultrasensitive interaction, we consider a mean-field statistical mechanical model for the electrostatic interactions between a single receptor site and a conformationally disordered polyvalent ligand. The formulation treats phosphorylation sites as negative contributions to the total charge of the ligand and addresses its interplay with the strength of the favorable ligand-receptor contact. Our model predicts a threshold number of phosphorylation sites for receptor-ligand binding, suggesting that ultrasensitivity in the Sic1-Cdc4 system may be driven at least in part by cumulative electrostatic interactions. This hypothesis is supported by experimental affinities of Cdc4 for Sic1 fragments with different total charges. Thus, polyelectrostatic interactions may provide a simple yet powerful framework for understanding the modulation of protein interactions by multiple phosphorylation sites in disordered protein regions.
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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 | 0.001 |
| 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