SOLUTION OF NONLINEAR SCHRÃDINGER EQUATION OF DAVYDOV SOLITON WITHIN THE ALPHA-HELIX PROTEIN STRUCTURE OF MYOSIN BY ANALYTICAL AND HIROTA METHOD - Marvin Tanuardi, Hans
For years, biologists have struggled to discover the details of the human muscle contraction mechanism in a microscopic scale. Many experts have adopted the sliding filament theory that will involve the movement of the myosin structure. The myosin structure is the structure that will move the muscle filaments using energy gained from ATP hydrolysis. One of the more mysterious aspect of this mechanism is the mechanism on how the chemical energy of ATP hydrolysis gets converted into mechanical energy used to move the myosin structure or more specifically, the alpha-helix protein structure. Few experts have pointed towards amide-I vibrations occuring within the peptide group to be an essential component to the conversion mechanism. This idea is then developed by a Soviet physicist named Alexander Sergeevich Davydov. Davydov develops a model in which a solitary wave or a soliton is the energy-carrying medium along the alpha-helix protein structure, enabling the myosin structure to move; such soliton is now called Davydov soliton. Davydov states that this soliton is created as a result of nonlinear interaction between amide-I vibrations and the longitudinal displacement of the peptide group chain. Davydov soliton is governed by the solution to a nonlinear partial differential equation named Nonlinear Schrödinger Equation (NLSE). This research focuses on the dynamics of the soliton based upon the hamiltonian model created by Davydov. The NLSE will be derived from Davydov hamiltonian with classical approach and usage of ansatz. The NLSE will be solved with the usage of ansatz and the Hirota bilinear method. This research will also analyze certain soliton models derived from an expanded Davydov hamiltonian. The expanded hamiltonian will include additional interactions that have not been included in the simplified model. In this research, the soliton model being analyzed will include long-range interactions between amide-I vibrations. Results of analysis will be presented in the forms of graphs visualization.