This is fixed-backbone sequence design: the 3D backbone (a four-helix bundle) never moves — only the amino-acid identity at each of the 56 residue positions is searched, exactly as Rosetta-style design or early ProteinMPNN-style pipelines optimize a sequence for a target fold. Each position is reduced to one of four chemical classes.
Every alpha helix twists ≈100° per residue, so a side chain's outward direction sweeps around the helix axis as you go up the chain. A position is core-facing when its side chain points toward the bundle's central axis (knobs-into-holes packing against the other three helices) and surface-facing otherwise:
coreFacing(i) = sideChainDir(i) · inwardDir(i) ∈ [−1, +1]
E_burial = Σ w_b · (target[type(i)] − coreFacing(i))²
E_elec = w_e · Σ_{i<j, r<cutoff} charge(i)·charge(j) / r_ij
E_total = E_burial + E_elec
Hydrophobic residues have target burial +1 (energy penalty when exposed), polar and charged residues target −0.3 to 0 (penalty when buried) — this alone drives a hydrophobic core to self-assemble. The electrostatic term additionally penalizes like-charge residues that end up close together at helix-helix interfaces and rewards opposite-charge pairs, favoring salt bridges.
- Metropolis Monte Carlo: each attempt mutates one random position to a random class; if the energy change ΔE ≤ 0 it is always accepted, otherwise accepted with probability exp(−ΔE / T).
- Temperature controls how often uphill (energy-raising) moves are accepted — high T explores broadly, low T greedily settles into a local energy minimum.
- Auto-cool runs a simulated-annealing schedule, slowly lowering T so the design "freezes" into a low-energy sequence, mirroring how real annealing-based design protocols converge.
Real-world relevance: this hydrophobic-core / polar-surface partitioning is the single most important rule in de novo protein design — David Baker's lab's first stable designed four-helix bundles and TIM-barrels were built by optimizing exactly this kind of burial and packing objective before neural methods (ProteinMPNN, RFdiffusion) took over the same core idea.