Dissecting the\nRoles of Electrostatic Interactions\nin Modulating the Folding Stability and Cooperativity of Engrailed\nHomeodomain

Engrailed homeodomain (EngHD), a highly charged transcription\nfactor\nregulating over 200 genes, is a fast-folding protein. Recent studies\nhave shown that the abundant charged residues in EngHD not only facilitate\nprotein–DNA interactions but also influence the conformational\ndisorder of its native structure. However, the mechanisms by which\nelectrostatic interactions modulate the folding of EngHD remain unclear.\nHere, we employ a coarse-grained structure-based model that incorporates\nthe salt-dependent Debye–Hückel model to investigate\nthe (un)folding behavior of EngHD under various salt concentrations.\nOur findings demonstrate that increasing salt concentrations enhance\nboth folding stability and cooperativity, while the folding barrier\nheight remains relatively constant due to the distinct electrostatic\neffects on individual residues. By modulating the energetic balance\nbetween local and nonlocal interactions, we shift the folding of EngHD\nfrom a downhill process to a two-state process. Notably, we observe\na nonmonotonic relationship between the strength of local interactions\nand residue-level coupling degree during (un)folding, likely attributed\nto the repulsive electrostatic interactions present in the native\nstructure of EngHD. Additionally, we identify a critical turning point\nin the dependence of folding cooperativity on salt concentration,\nclassified by the energetic balance of local and nonlocal interactions.\nOur results provide valuable insights into how electrostatic interactions\ninfluence the folding of EngHD, contributing to the theoretical framework\nfor engineering highly charged proteins.