ACGA a Novel Biomimetic Hybrid Optimisation Algorithm Based on a HP Protein Visualizer: An Interpretable Web-Based Tool for 3D Protein Folding Based on the Hydrophobic-Polar Model

. 2025 Nov 12;10(11):763. doi: 10.3390/biomimetics10110763

Algorithm 1 Metropolis Monte Carlo Algorithm for HP lattice Model

1:
Input: S, iterations, lattice_type ▹ HP sequence: $S = (s_{1}, s_{2}, \dots, s_{n})$ with $s_{i} \in {H, P}$
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Output: $C *$ ▹ RULDFB string (Best conformation found)
3:
Initialize a valid conformation $C_{0}$
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Compute energy of $C_{0} : E (C_{0})$ , $C * \leftarrow C_{0}$
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$E_{0} \leftarrow E (C_{0})$
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for $i = 1$ to $i t e r a t i o n s$ do
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$C^{'} \leftarrow M u t a t i o n (C_{i - 1})$ ▹ Generate a new conformation, $C^{'}$
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if $C^{'}$ is valid then ▹ Check for overlaps
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Compute energy $E^{'} \leftarrow E (C^{'})$
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$Δ E \leftarrow E^{'} - E_{i - 1}$
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if $Δ E \leq 0$ then
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Accept $C^{'}$ : $C_{i} \leftarrow C^{'}$ , $E_{i} \leftarrow E^{'}$ , $C * \leftarrow C^{'}$
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else
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$p \leftarrow exp (- \frac{Δ E}{T})$ ▹ Compute acceptance probability
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Generate random number $r \in [0, 1]$
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if $r < p$ then
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Accept $C^{'}$ : $C_{i} \leftarrow C^{'}$ , $E_{i} \leftarrow E^{'}$
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else
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Reject $C^{'}$ : $C_{i} \leftarrow C_{i - 1}$ , $E_{i} \leftarrow E_{i - 1}$
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end if
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end if
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else
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Reject $C^{'}$ : $C_{i} \leftarrow C_{i - 1}$ , $E_{i} \leftarrow E_{i - 1}$
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end if
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end for
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return $C *$ ;