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This Concept Map, created with IHMC CmapTools, has information related to: Quantum model for nerve pulse, QUANTUM MODEL FOR NERVE PULSE 2. e) Physical solutions represent rotation - a soliton sequence propagating along the axon. The angular velocity of rotation is essentially Ω=ZeV/h_eff, where V is the restring potential and h_eff=nh the Planck constant. The propagation velocity v of solution sequence is a new para- meter. f) There are two types of propa- gating solutions. Type I depends on x-vt and reduces to a solution depending on coordinate z for v→0. Type II depends on t-vx/c and depends only on t at this limit. The velocity parameter could correspond to the velocity of nerve pulse conduction for type I and velocity of propagation of EEG waves for type II., QUANTUM MODEL FOR NERVE PULSE 3. A model for nerve pulse generation. a) Nerve pulse is generated when the membrane voltage goes below the critical value defined by action potential. b) Potential is reduced below the action potential if the rotation rate of the pendulum reduces below its critical value. A possible interpretation for the critical value would be in terms of the critical value of oscillation frequency for small oscillations above which os- cillation is transformed to rotation. c) The anatomy of nerve pulse shows that the rotation rate must go through zero to opposite value for time of about 1 ms and then return to the original value with magnitude slightly higher than before the pulse (hyperpolariza- tion). As if one of the penduli in the sequence were kicked so that it starts to rotate in opposite di- rection and returns back. In order to conserve angular momentum it kicks the next pendulum in the sa- manner. Nerve pulse results as a kind of domino effect., QUANTUM MODEL FOR NERVE PULSE 1. Basic assumptions of the model. a) Cell is super conductor. The minimum assumption is that only electronic super-conducti- vity is involved but also protonic and ionic super-conductivities can be considered. b) The lipid layers of axonal membrane form cylindrical Josephson junction of thickness about 10 nm. c) The angular frequency asso- ciated with phase difference is Josephson frequency f_J= ZeV/h_eff. Large values of h_eff allow arbitrarily small fre- quencies. The energy ZeV for Z=2 is just above thermal thres- hold meaning minimization of metabolic energy lost as Josephson radiation. c) In improved resolution membrane proteins defining receptors, channels and pumps define the Josephson junctions (not all the time). They carry Josephson current and generate Josephson radiation. d) The idealization as cylind- rical Josephson junction is made for modeling purposes., QUANTUM MODEL FOR NERVE PULSE 2. Mathematical treatment. a) The equations for the cylin- drical Josephson junction redu- ce to Sine-Gordon wave equ- ation for the phase difference over the junction. This can be interpreted as a limit of dynamics for a sequence of mathematical penduli coup- led to each other. b) For propagating waves the equations reduces to that of mathematical pendulum but with time coordinate replaced with z-vt so that one can use the intuition provided by it. c) The solutions correspond to either small oscilations ana- logous to oscillations of pendu- lum around the minimum of gravitational potential or to a full rotation possible when the kinetic energy is high enough. d) For small oscillations the resting potential would oscil- late sinusodally around zero so that the solution is not physical.
