Master Thesis Defense by Søren Nissen – Niels Bohr Institute - University of Copenhagen

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Master Thesis Defense by Søren Nissen

With the emergence of the soliton model, a different way to see nerve signal has been introduced. Instead of an electric signal that runs along the nerve, as described by the Hodgkin-Huxley model, the soliton model describes the nerve signal as a sound wave. These sound waves have the characteristics of and behave like solitons. Solitons in a biological membrane are a local density change of the membrane moving at constant speed.

The master thesis defence will include an introduction to the soliton model, the theory about the biological membranes where sound waves and solitons can propagate and the methods used to calculate the solitons.

The aim of Søren Nissen’s master thesis was to get a better understanding of solitons in biological membranes. It was investigated what is required of a membrane to sustain both negative and positive solitons. It was shown, that such a medium must have two local maximum in the compressibility. In addition, the membrane should be in the state where the compressibility has a minimum between the two maximum. In such a membrane, collision of two solitons, of any kind, is shown to happen without annihilation. The two solitons will pass right through each other with a small amplitude loss, accelerated speed, and a delay in their future process. This delay is shown to depend on the velocity, and that the delay will be negative for solitons with a velocity near the lower limit velocity.

A small distortion of a soliton will result in a rapid decay from the unstable to a stable one. If the distortion exceeds a certain threshold, the soliton will split into two solitons, which will propagate in opposite direction. The solitons will not be of the same size and not have the same velocity.

It was shown that a local distortion in the membrane would result in solitons of same type propagating in opposite direction. The appearance of pairs of solitons (a negative and a positive soliton) depend on the energy given to the membrane, and over which range it is distributed. It was shown that it is more likely to have pairs of solitons or no solitons, than only have one type in a membrane where both types of solitons can propagate.

Supervisor: Thomas Heimburg