Why stability must be calibrated

The single most important adjustable quantity in a TOPO model is \(n_\mathrm{scale}\) — the nscale field in domain.yaml. To see what it controls, recall that each native contact between residues \(i\) and \(j\) is a 12-10-6 well whose depth \(\varepsilon_{ij}\) is the sum of three physical contributions (Structure-based contacts):

\[\varepsilon_{ij} = \underbrace{E_\mathrm{HB}}_{\text{hydrogen bonds}} + \underbrace{E_\mathrm{BS}}_{\text{backbone–sidechain}} + \underbrace{n_\mathrm{scale}\; E_\mathrm{SS}}_{\text{scaled sidechain–sidechain}}\, .\]

\(E_\mathrm{HB}\), \(E_\mathrm{BS}\), and \(E_\mathrm{SS}\) are fixed per-contact energies read from the input structure; \(n_\mathrm{scale}\) is the one free multiplier, and it acts on the sidechain–sidechain (SS) term only. Setting \(n_\mathrm{scale}\) therefore tunes how deep the native contacts are — i.e. how strongly the fold is held together — while leaving the backbone hydrogen-bond and backbone–sidechain energies (which encode secondary structure) untouched.

This page explains why a raw, unscaled model is rarely usable as-is and why the right value is chosen per domain and per interface rather than globally. For the file format see Domain definition file (domain.yaml); for the options that drive the automatic search see Optimization control options; for a worked run see the tutorial Tutorial A.5 — Optimizing the contact nscale (nscale).

The raw model is under-stabilized

Coarse-graining a protein to one Cα bead per residue discards the atomic detail that, in an all-atom force field, sets the exact free-energy balance between the folded and unfolded states. The SS contact energies that replace it are drawn from a transferable, knowledge-based parameterization — one generic set of well depths applied to every residue pair in every protein. That set cannot simultaneously reproduce the folding stability of proteins that differ in size, topology, and contact density.

In practice the transferable set is too weak: at \(n_\mathrm{scale} = 1\) (\(E_\mathrm{SS}\) unscaled) most proteins sit only marginally folded, and at a realistic simulation temperature (ref_t ≈ 310 K) they partially or fully unfold within a trajectory. Raising \(n_\mathrm{scale}\) deepens the SS contribution and restores the correct stability without re-parameterizing the whole force field — it is the one knob calibrated per system.

Why per-domain and per-interface, not one global value

A multidomain protein is not uniformly stable. Its domains differ in

  • secondary-structure content — an all-\(\alpha\) domain, an all-\(\beta\) domain, and a mixed \(\alpha/\beta\) domain reach the same marginal stability at different contact strengths (this is why the calibrated ladder is indexed by structural class; see Table 1);

  • size and contact density — a small, sparsely packed domain needs a deeper well to stay folded than a large, densely packed one;

  • interface character — the contacts between two domains form their own structural unit, often much weaker than either domain interior, and must be scaled separately (inter_domains in Domain definition file (domain.yaml)).

A single global scale therefore cannot win: the value that finally folds the weakest domain over-stabilizes the strongest, rigidifying it and suppressing exactly the native fluctuations you want to observe. Assigning each domain and each interface its own \(n_\mathrm{scale}\) is what makes a multidomain model faithful everywhere at once.

What the wrong value costs you

\(n_\mathrm{scale}\) sets where each unit sits on the folding landscape, so a mis-set value biases every downstream observable:

  • Too low — the domain or interface unfolds spuriously during the run. The fraction of native contacts Q (Native-contact analysis (the Q score)) drifts down, the ensemble is contaminated by non-native states, and any thermodynamic or kinetic quantity measured from it is meaningless. Under-stabilized chains are also more prone to mirror-image and other kinetic-trap artifacts (Mirror-image detection (chirality K + mirror RMSD)).

  • Too high — the fold is over-stabilized. Native fluctuations, hinge motions, and conformational sampling are damped, the effective melting temperature is pushed unrealistically high, and the model reports a stiffness the real protein does not have.

The objective is therefore the smallest \(n_\mathrm{scale}\) at which each unit stays folded — just stable enough. This keeps native dynamics intact while preventing spurious unfolding, and it is exactly the target the optimizer searches for.

How TOPO chooses it

Rather than tuning by hand, TOPO restricts \(n_\mathrm{scale}\) to a small, pre-calibrated discrete ladder — five levels per structural class plus a median fallback, calibrated on a training set of 19 small single-domain proteins (Leininger et al., PNAS 116, 5523–5532, 2019). A domain climbs the ladder for its structural class (\(\alpha\), \(\beta\), or \(\alpha/\beta\)); every domain–domain interface uses the Interface ladder.

Table 1. \(n_\mathrm{scale}\) levels per structural class.

Structural class

Level 1

Level 2

Level 3

Level 4

Level 5

Fallback (median)

\(\alpha\)

1.1954

1.4704

1.7453

2.0322

2.5044

1.7453

\(\beta\)

1.4732

1.8120

2.1508

2.5044

2.5044

2.1508

\(\alpha/\beta\)

1.1556

1.4213

1.6871

1.9644

2.5044

1.6871

Interface

1.2747

1.5679

1.8611

2.1670

2.5044

1.8611

The optimizer starts every domain and interface at level 1 and repeats one round until every unit is stable:

  1. Build a model with the current per-unit \(n_\mathrm{scale}\) values.

  2. Simulate ntraj independent trajectories at the reference temperature ref_t (produced as a single multi-copy run).

  3. Score the fraction of native contacts Q (Native-contact analysis (the Q score)) for every domain and interface in every trajectory.

  4. Decide. A unit is stable when all ntraj trajectories keep its Q above q_threshold (default 0.6688) for at least frame_fraction (default 98 %) of the frames. If every unit is stable the search is done; otherwise each unstable unit climbs one level of its ladder while the already-stable units stay frozen, and the next round runs.

A unit still unstable at level 5 is pinned at its class median fallback (the level-3 value in Table 1) for the final model. Because domains and their shared interfaces are coupled through the contact map, raising one unit’s \(n_\mathrm{scale}\) can destabilize a unit that had already held, so strongly coupled multidomain systems may need more rounds than the ladder is tall — raise max_rounds for them (see Optimization control options). The result is the smallest per-unit \(n_\mathrm{scale}\) that keeps the whole structure folded across many independent trajectories.

Where to go next