Case Studies On Dynamics Of Excitable Cells

Excitable cells are cells that have the ability to generate and spreadaction potentials to surrounding cells. Apart from neurons and musclescells, electrical excitability can be observed in fertilized eggs, some pantsand glandular tissue. Excitable cells play an important role in electricalsignals generation, propagation and processing. Though they differ functionallyand morphologically from each other, excitable cells share samedynamical behavior. This thesis is devoted to study several dynamical relatedto excitable cells. Basically, two topics are concerned in this thesis.One is effects of ion channel noise on the neural system dynamics. Theother is low amplitude control of spiral waves and spatiotemporal chaos incardiac tissue.We first introduced the basic physiology of excitable cells in chapterâ… , then the models that used to study the excitable cells computationally inchapterâ…¡. Due to the issues we concerned in this thesis, we emphasized onthe simulation of stochastic HH mode and the Morris-Lecar model basedcardiac tissue model we proposed.In chapterâ…¢, we discussed effects of ion channel noise on synchronizationof two coupled neurons. We found the ion channel noise affectssynchronization of neurons in different ways. When coupling is strong, ionchannel noise tends to damage synchronization. Whereas when coupling isweak, ion channels could induce and enhance synchronization.In chapterâ…£, we focus on subthreshold pulse detection in neuronswith channel noise. First, using the stochastic Hodgkin-Huxley(SHH) neuronmodel, we study the effects of channel noise on the response propertiesof a single neuron to subthreshold pulse input. We find that a SHH neuronfires spikes a higher than average level in response to a subthreshold stimulus.The average response time decreases while the variance increases as the channel noise amplitude increases. Then, we evaluate the subthresholdsignal detection ability of a SHH neuron under a pulse detection scenario.We found single neuron has limited subthreshold signal detection ability.Therefore, we propose a feasible solution for a neuronal population to overcomethis predicament. We find that subthreshold signal detection can begreatly enhanced with the neuronal networks we propose. The phenomenonof intrinsic SR induced by channel noise is also observed. We argue thisSR may be a strategy that neural systems would take to optimize theirdetection ability for subthreshold signals. We have shown that the reliabledetection of subthreshold signals with the network is predictable withprobability theory. The possible application of this subthreshold signaldetection method is discussedIn chapterâ…¤, with Morris-Lecar model based cardiac tissue model, weproposed two novel methods to eliminate spiral waves and spatiotemporalchaos in cardiac tissue, namely voltage clamp method and subthresholdperiodical perturbation method. The results show both two methods areeffective in suppression spiral waves and spatiotemporal chaos.A summary was made in the last chapter.