Applications Of Stochastic Theory In Motor Proteins And FHN Neural Model

Various important effects brought by noise in nonlinear systems, such as noise inducing phase transition, stochastic resonance, nonequilibrium fluctuation-induced transport, open up a wide range of applicability of the stochastic theory. These years, biologic research with this theory has permeated into several fields in Biophysics. For example, the application in protein folding in molecular biophysics, protein transport in cell biophysics, electrical neuron systems and ionic channel in neuron biophysics has become one of the important forward subjects hi international theory physics and biophysics.Thus, we have deeply studied the applications of stochastic theory in protein motor and FHN neuron model, and obtained some important results, especially the opposing role of the amplitude and correlation strength in protein transport, the locked phenomenon in FHN neuron model, the dependence of the effect on initial condition, the phase transition and resonance in globally coupled neuron system. In this thesis, the investigations of the application of stochastic theory in protein motor and FHN neuron model are systematically reported, which include four aspects: effects of random potential on motor protein transport; noise-induced transition in a FHN neural model; stochastic resonance in a bistable system subject to multiplicative and additive noise; coherence and stochastic resonance in a globally coupled FHN neural model.The transport of motor protein is studied. A fundamental nonlinear motion equation about motor protein subject to random force and random potential is derived. The expression of the probability flux of this system was obtained. It is found that the effects of the random potential on the transport process as the amplitude of random potential increased are much more remarkable than those as the correlation length of random potential increased. The amplitude and the correlation length of random potential play opposing roles in the transport of the motor protein.We firstly draw the viewpoint of the noise-induced phase transition into a FHN neural model. We introduce a two-dimensional motion model of neural system, FHN neural model. Then by using of adiabatic elimination method and the presenceof noise, the system becomes a special double singular stochastic system. The effects of parameter , which marks the singular degree of stochastic at singular point, on the phase transition of the FHN model is discussed when is non-integer. It is shown that the parameter plays an important role in phase transition of thesystem, and there is a locking phenomenon in the FHN model.The stochastic resonance phenomenon in a bistable system under the simultaneous action of multiplicative and additive noise and periodic signal is studied by using the theory of signal-to-noise (SNR) ratio in the adiabatic limit. Two cases have been considered: the case of no correlations between multiplicative and additive noise and the case of correlations between two noises. The expressions of the SNR for both cases are obtained. The effects of intensity of multiplicative and additive noise and the intensity of the correlations between noises on the SNR are discussed for both cases. It is found that the existence of a maximum in the SNR is the identifying characteristic of the SR phenomenon. "The main-unexpected--novelty is the dependence of the effect on initial condition." (Report of The Phys.Rev.E Referee)The coherence resonance (CR) and the stochastic resonance (SR) phenomenon in a globally coupled FitzHugh-Nagumo neurons model are studied. In the absence of signals, there is a transition phenomenon hi the firing rate which is only occurred under condition of the coupling between each neuron units, and there are two regions in the transition diagram of noise intensity and coupling strength plane: one is the non-sensitive to both noise intensity and coupling strength region, the other is the sensitive one. The existence of a peak of firing rate is the identifying characteristic of the CR phenomenon. In the p...