Exciton and phonon dynamics in the presence of an impurity in a two-dimensional alpha-helix chain: Formation, stability and interactions of breathers

This paper examines the impact of mass impurity on exciton–phonon dynamics in a two-dimensional alpha-helix protein chain. Using the semi-discrete approximation and the multiple time scale method, we derive discrete and continuous two-dimensional nonlinear Schrödinger equations, respectively. Besides the mass impurity defect, two other parameters of the system under study attracted our attention, namely, the dipole–dipole interaction coefficient and the off-diagonal coupling parameter. Through intensive numerical simulations, firstly, the effect of these parameters was verified on the energy localization in the alpha-helix by means of the two-dimensional breather propagation. A transition between stability and instability is clearly manifested in the spatial evolution of the mode. Then, an analysis of the time evolution and stability of the impure mode in this model is made. Finally, we examine the complex dynamics that emerge when local modes, called breathers, interact with an impurity in our model. Some physical phenomena appear in this work, the total barrier phenomenon, the excitation phenomenon, the dissipation phenomenon and the partial barrier phenomenon, to name a few. One biological implication of this work is that laser pulses could be used to generate controlled breathers, activating therapeutic proteins such as light-sensitive ion channels.