where q i and q j are the respective charges of the i-th and j-th beads, ϵ r = 80 represents the relative dielectric constant of water, and κ -1 is the Debye length indicative of ionic effects on electrostatic screening, with κ -1 = 0.304/ √ I nm, where I denotes the solution's ionic strength in molarity. The hydrophobicity interaction term U HPS (x) quantifies the nonbonded interactions among amino acid pairs, excluding those directly bonded. It is defined as