Long-range interactions of polaron states in dynamic of β-sheet proteins

We investigate long-range polaron transfer, modeled as electron–vibration coupling in the nonlinear dynamics of β-sheet proteins represented by a two-dimensional oscillator network of peptide units. In the stationary regime, the dynamics are governed by a (2+1)D discrete nonlinear Schrodinger equation. Linear stability analysis shows that increasing long-range interaction parameters narrows instability zones, enhancing electron transfer localizations. Numerical simulations, validating the modulational instability analysis, reveal the emergence of localized polaron structures, confirming electron transfer dynamics induced by the interplay of the vibrations of the protein scaffolding and improve long-lived localized excitations traveling through the interactions of peptide units lattice under appropriate cubic nonlinearity within the molecular system.