Biomolecular phase boundaries are described by a solubility product that accounts for variable stoichiometry and soluble oligomers
Bibliographic record
Abstract
The solubility product is a rigorous description of the phase boundary for salt precipitation and has previously been shown to qualitatively describe the condensation of biomolecules. Here we present a derivation of the solubility product showing that the solubility product is also a robust description of biomolecule phase boundaries if care is taken to account for soluble oligomers and variable composition within the dense phase. Our calculation describes equilibrium between unbound monomers, the dense phase, and an ensemble of oligomer complexes with significant finite-size contributions to their free energy. The biomolecule phase boundary very nearly resembles the power law predicted by the solubility product when plotted as a function of the monomer concentrations. However, this simple form is concealed by the presence of oligomers in the dilute phase. Accounting for the oligomer ensemble introduces complexities to the power law phase boundary including re-entrant behavior and large shifts for stoichiometrically matched molecules. We show that allowing variable stoichiometry in the dense phase expands the two phase region, which appears as curvature of the phase boundary on a double-logarithmic plot. Furthermore, this curvature can be used to predict variations in the dense phase composition at different points along the phase boundary. Finally, we show how the solubility product power law can be identified in experiments by using dilute phase dissociation constants to account for the oligomer ensemble.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| 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".