Fractional unstable patterns of energy in α−helix proteins with long-range interactions

Energy transport and storage in α−helix proteins, in the presence of long-range intermolecular interactions, is addressed. The modified discrete Davydov model is first reduced to a space-fractional nonlinear Schrödinger (NLS) equation, followed by the stability analysis of its plane wave solution. The phenomenon is also known as modulational instability and relies on the appropriate balance between nonlinearity and dispersion. The fractional-order parameter (σ), related to the long-range coupling strength, is found to reduce the instability domain, especially in the case 1 ≤ σ < 2. Beyond that interval, i.e., σ > 2, the fractional NLS reduces to the classical cubic NLS equation, whose dispersion coefficient depends on σ. Rogue waves solution for the later are proposed and the biological implications of the account of fractional effects are discussed in the context of energy transport and storage in α−helix proteins.