Soliton in alpha helical proteins with interspine coupling at higher order

Nonlinear Dynamics of FPU Lattice Type Protein Molecular Chain

“…Davydov [1] considered a mathematical model to study the energy transfer in alpha-helical proteins, and he showed that the transport of the hydrolysis energy of ATP along alpha-helical proteins is through the formation of solitons moving without loss of energy [2][3][4][5]. In all the works [6][7][8][9][10][11][12] that followed Davydov, the dynamics is studied by proposing suitable Hamiltonian including interactions of different types such as molecular excitations, dipole-dipole interactions, vibrational excitations, coupling between exciton and phonon, quadrupole-quadrupole type interactions, interspine coupling etc. The dynamics associated with the above models is found to be governed by nonlinear Schrӧdinger type equations.…”

Energy transport in the three coupled α-polypeptide chains of collagen molecule with long-range interactions effect

“…Primatarowa and Kamburova 20 showed that the dynamics of three coupled molecular chains depends on the interchain coupling and the initial number of excitations. Daniel and Latha, 21,22 following the study of Scott 23 showed interdependency between the spines and discussed energy sharing between them in terms of solitons. It has been also pointed by Hennig 24 that the dynamics of a-helical proteins should include not only the excitonic part, but also a vibronic part which includes radial and longitudinal displacements of the peptide units, connected to the deformation of the covalent and hydrogen bonds, respectively.…”

Lax pair, conservation laws and solitons for a (2+1)-dimensional fourth-order nonlinear Schrödinger equation governing an α-helical protein

“…It has been proposed that the energy from the ATP can be trapped in the amide-I (C=O) vibration and transported in an α-helical protein [1,8,[10][11][12]. α helix, a periodic helical structure, is one of the secondary structures of proteins [13][14][15].…”

“…Solitons, one type of the nonlinear excitations in the α-helical proteins and other physical systems, can appear as the stable carriers capable of transferring the energy, released in the ATP hydrolysis, along the α-helical proteins at the large distances without losses [1][2][3][4]9,[17][18][19][20][21]. The idea has aroused the interest of the scientists in studying the solitonic excitations in the α-helical proteins, at the classical and quantum levels [7,8,10,[13][14][15]22].…”

“…For example, some studies on the dynamics of (1 + 1)-dimensional continuous and discrete α-helical protein systems have been conducted analytically and numerically [7,10,15,27]. In an α-helical protein structure, as the interaction between the neighbouring chains can give rise to a (2 + 1)-dimensional structure, the NLS equations in (2 + 1) dimensions have been proposed [13,23].…”