Source
Koneru, Reid & Robustelli (2025), LIT-076 (arXiv 2505.01860, written as a book chapter), read in full in NOTE-076, with a spot-check of the accompanying repository.
What was actually shown
Why few replicas suffice (Eq. 8). In REST2 only the solute’s own energy and the solute–solvent energy enter the swap criterion. The water–water energy drops out, so a few replicas span a wide range of effective solute temperature. This is the standard result of Wang, Friesner & Berne (2011), and NOTE-076 rates it strong.
The price. The upper rungs are scaled Hamiltonians, not physical temperatures. Disordered proteins over-collapse there: higher effective solute temperature gives more compact states, more contacts and less secondary structure in the chapter’s own example (Fig. 3). The over-collapse is cited to refs. 23–24; the chapter shows only the qualitative trend.
The diagnostic split (pp. 17–18, Figs. 2–4). The chapter separates two kinds of check. Per demultiplexed replica it reports the fraction of time at the base rung, the mean effective temperature and the round-trip time. Those measure movement along the ladder. Across demultiplexed replicas it compares structural distributions with Flyvbjerg–Petersen blocking errors. Its verdict: “Obtaining high acceptance rates on swap attempts is not, in isolation, sufficient evidence of robust conformational sampling or convergence. It is therefore essential to compare the distributions of conformations sampled in each demultiplexed replica” (p. 18).
Where it bites. Ensembles from 1–10 µs per replica “will usually retain some starting-structure dependence” (p. 10). For chains over about 40 residues some demultiplexed replicas “will occasionally become stuck”.
The example. The α-synuclein C-terminal 20-mer (residues 121–140), with a99SB-disp, 10 replicas from 300 to 450 K, swaps every 1.6 ps and a target of at least about 20% acceptance. The chapter states no numerical outcome for it.
What could have come out otherwise. Nothing in the chapter could. It shows a run that passes both checks and no run that passes one and fails the other.
What this does not say
- That acceptance is useless. It is necessary for mixing. The claim is that it is not sufficient for sampling.
- How much agreement is enough. The criterion, agreement “within statistical sampling errors”, is a visual comparison with no threshold. NOTE-076 lists a quantitative test as an open question.
- That REST3 or REHT fix the collapse. The chapter names them as remedies and compares nothing.
- That the point transfers to tempered MCMC in general. NOTE-076 notes that the logic would carry over to parallel tempering anywhere, but that is its own informal argument. The chapter does not make the link.
- That the chapter’s other claims hold. Its statement that tREMD’s replica count “scales exponentially with the degrees of freedom” is misstated (NOTE-076, C2), and its printed sequence is not the simulated construct. The repository is authoritative for the example.
Connections
- The chapter’s force field is the authors’ own (Robustelli et al. 2018). It is the kind of protocol from which reference ensembles for machine- learned ensemble generators are made, which is the only bearing NOTE-076 finds on ML. That bearing carries no instruction, so nothing here is for the anthology.
- No other THEORY in the record treats sampling convergence.