represents the Lennard-Jones potential, with ϵ = 0.8368 kJ/mol as the energy scale. The parameter σ, reflecting the effective size of interacting amino acids, is determined by the arithmetic mean of the sizes of the i-th and j-th amino acids. Similarly, the hydrophobicity parameter λ is calculated as the arithmetic average of the hydrophobicity values of the involved amino acids. In total, the HPS-Urry model has 20