Volume 124, number 4,5 PHYSICS LETTERS A 28 September 1987 COMPETING MECHANISMS FOR THE TRANSPORT OF ENERGY IN THE a-HELIX Patricio PEREZ Departamento de FIsica, Universidadde Santiago de Chile, Casilla 5659, Santiago 2, Chile and Nikos THEODORAKOPOULOS Max-Planck Institutflir Festkorperforschung, Heisenbergstrasse 1, 7000 Stuttgart 80, FRG and Fakultat für Physik der Universität Konstanz, Postfach 5560, 7750 Constance 1, FRG Received 4 March 1987; revised manuscript received 11 July 1987; accepted forpublication 24 July 1987 Communicated by A.R. Bishop The Davydov model for a molecular chain of hydrogen-bonded peptide groups admits lattice acoustic as well as intramolecular solitons when the anharmonicity of the H-bond is explicitly taken into account. On the basis of a numerical simulation we suggest that such (supersonic) lattice solitons may present a more efficient alternative than the original (subsonic) selftrapped Davydov soliton for transporting energies under realistic conditions. Several years ago Davydov modeled one of the Davydov and Zolotariuk [3,4] have considered spines of hydrogen-bonded peptide groups that sta- the effect of such an intrinsic lattice anharmonicity bilize the a-helix structure of a protein as a one on the propagation of coherent self-trapped states. dimensional molecular chain [1]. He assumes the They included a cubic anharmonicity in the inter- harmonic approximation for the intermolecular molecular potential, keeping fixed the rest of the potential, and allows for an internal vibrational mode ingredients of the model. One remarkable conse- (the amide-I), which once excited can be propagated quence of this modification is the widening of the along the chain due to an additional electromagnetic interval of admissible soliton velocities, including dipole—dipole interaction between peptide groups. velocities above the velocity of sound. In the har- The frequency of the intramolecular vibration can monic case only subsonic velocities are possible. In be modulated by acoustic deformations of the chain, practice, however, to obtain an analytical supersonic In principle this nonlinear coupling, characterized intramolecular soliton (in the context of Davydov’s by an effective GrUneisen parameter, provides for model), an unrealistically high anharmonicity is the energetic stabilization of coherent polaronic needed [4]. motion (self-trapping). The resulting nonlinear Recently, Yomosa [5] presented a model for the Schrodinger equation typifies the property of dis- propagation of solitons in the a-helix which does not persionless energy transport. It has been suggested consider the intramolecular amide-I vibration as a that the strength of the nonlinear coupling is a mea- possible recipient of the activation energy, but sure of hydrogenbond anharmonicity [21. This is not restricts it to deformations of the chain of hydrogen precise, since — in the framework of the model — we bonded peptide groups. The nonlinearity of the could in principle deform the chain locally by an hydrogen bond is taken into account with a cubic arbitrary amount without feeling any anharmonicity term for the relative displacements in the intermo- or exciting a vibrational state. In the following we lecular potential. In this case, the equations of propose to handle lattice anharmonicity as an inde- motion, in the continuum limit, reduce to the KdV pendent effect. 0375-960 1/87/$ 03.50 © Elsevier Science Publishers B.V. 267 (North-Holland Physics Publishing Division)