Biological Model of Flagella Motor

Abstract

We proposed a sample of stochastic motor, which moved by using principle of stochastic resonance. First we introduced Lagrangian, having dissipative terms caused by water molecules. Using Eular-Lagrange method, we got the motion of equations for motA-membranes complex of flagella motor. Proton-pumps attached between cell-membranes make proton electro static potential gradients according written as Nernst Equation. It is said that their potential gradients accelerate and flow in protons through a base of flagella motor. Under the process of the diffusion into cell body caused by protons gradient, many protons collide with motA complex imbedded into cell-membranes. We can consider eight numbers of the mota complex as a kind of a closed ring chain model connected by springs, because of the motA complex combined with a elastic cell-membranes. Each motA complex connected with elastic membranes give rise to stochastic resonance, what is call, lattice vibration. That vibration corresponds to a correction motion in classical physics, and its phenomena called coherent state in quantum mechanics. This quantum coherent state generated by external force (collision of protons) lowers potential energies curves of spring. From that coherent motion, the ground sate is not in the lowest energy state, but in the upper sated from the point of the reduced potential energy curves. We see same phenomena in elementary particle physics as the phase transition of vacuum energy, and the energy of old ground sate is higher than that of new one. The old ground state naturally releases its excess energy in itself. The electrostatic potential generated by proton pump and the stochastic resonance (coherent state) caused by the collision of protons are always used for maintaining those shift of ground state, and the reduction of potential curves.