## Problem 084 — rank:67

**Title:** Membrane insertion energetics

**Added binding assumptions (LaTeX):**

```latex
A PMF is a density relative to specified depth and orientation measures, including angular Jacobians. Pointwise PMF differences are not generally basin binding free energies: for basins $A,B$, use $-k_BT\log(P(B)/P(A))$ with the prescribed standard-state correction. Predicting final insertion additionally requires an initial law and kinetic model or an explicitly equilibrated two-basin assumption.
```

**Direct edits:** 0. **Fresh external checks:** None; supplied sources retained as provenance.