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Ivan Leonov «  Yunyun Li »  Norbert Lingg
Yunyun Li
Noise assisted transport in artificial channels and neuronal membranes
Supervisor: Prof. Dr. Peter Hänggi [Theoretical physics I]
Date of oral examination: 07/01/2011
99 pages, english
We analytically and numerically study the noise effects on transport: 1) noisy transport in confined geometries and 2) noise-assisted generation and propagation of electrical signals in neurons. In the study of nano-scaled transport, the geometrical confinement must be taken into account and we need to deal with the novel entropic transport. The so-called entropic transport has been studied analytically by means of the Fick-Jacobs equation based on the assumption of fast equilibrium in certain directions. Therefore, the high dimensional system can be described by an effective one-dimensional system where the geometric confinement leads to an entropic potential contribution. Within two important characteristics, namely the mean particle current and the effective diffusion coefficient, the entropic transport is quantitatively characterized. In presence of entropic potential barriers, some peculiar features are found. The average current is suppressed by the increase of effective temperature, which is totally in contrast to the energetic transport where the thermal activation actually induces the particle current. Furthermore, we have considered the system subjected to an periodic energetic potential with the same periodicity as the channels and investigated the intrinsic interplay between the energetic and entropic contributions to the transport. In presence of this periodic energetic potential, a resonance-like behavior was found for the mobility. In the study of noise-assisted generation and propagation of electrical signals in neurons, one focus is on the role of the autapse phenomena, in which the dendrites form synapses transmitting information to its own. This phenomena can be modeled by a stochastic Hodgkin-Huxley model with a Pyragas-like delayed feedback mechanism. The fluctuations stem from the intrinsic channel noise. The influence of the delayed stimulus has been systematically analyzed by investigating the Interspike Interval Histograms (ISIH) and the averaged interspike interval. The delayed stimulus induced a new time scale in the system and a specific frequency-locking mechanism is detected. Another focus is on noisy saltatory spike propagation along myelinated axons within a multi-compartmental, stochastic Hodgin-Huxley model. Accordingly, each node of the Ranvier is modeled by a stochastic Hodgin-Huxley model and couples linearly to its nearest neighbors. Constant external current stimulus is applied only on the first node. As a measurement for the signal propagation reliability, we focus on the ratio between the number of the initiated spikes and the transmitted spikes (the transmission coefficient). As noise increases, the transmission reliability coefficient decreases until the causal relationship is completely lost.