Response Properties And Dynamical Behaviours Of Single Neuron

The nervous system of all animals is inherently both highly complex and highly nonlin-ear in the natural world. The complexity is most obvious from the consideration of the enormous number of neurons and the complex neural network. Moreover, the activi-ties of the neurons and their connections exhibit the feature of nonlinear dynamics. The main function of such complex nonlinear system is to integrate and encode the external environment stimuli into neural code information, then process those information and make response. Success in these steps is the essence of survival. Under certain forms of external stimulus, neurons can fire action potentials (spikes), which are known to be re-sponsible for transmitting information in the nervous system. In this thesis, the response properties of the neuron with different intrinsic dynamical mechanism and the effect of autapse have both been investigated theoretically.Firstly, considering the diversity of neuron, a kind of modified Morris-Lecar neu-ron model has been introduced to simulate the intrinsic dynamical feature of Hodgkin’s three kinds of neurons. Based on the rate coding and temporal coding scheme, we have investigated the frequency and the first spike latency (FLS) of the three kind of neu-rons. For different input stimulus (DC, sine wave and random synaptic), the complete phase plots have been given in color map. With low frequency sinusoidal input over the threshold, the class Ⅰ and class Ⅱ neuron show the complicated mode locking firing behaviors, but a class Ⅲ neuron does not fire action potentials in this area even if the amplitude is much higher. Whereas, the response frequency of all neurons will decrease even fall to zero in the high-frequency input area.For the amplitude, frequency and initial phase of the input stimuli, all of the three classes of neurons can encode those information into first spike latency. The FSLs of all of the neurons decrease with the input amplitude and frequency. Considering the initial phase of the sine wave input, the onset stimuli at the rising phase have the short rising time and trigger the first spike quickly (a short FSL), and vice versa.When the random ISI synaptic pulse-like stimulus are injected into the neurons, all the three classes of neurons exhibit low-pass filter behavior. As mean ISI of random input increases, the output ISI histograms are more and more similar to that of the in-put. Clearly, in both the cases of Poisson and Gamma distribution ISI input, all three classes of neurons fail to respond to full information in the case of low mean ISI inputs. However, assembling class3to class1or2neurons in a network, it would be possible to respond to the full input information. It was suggested that the intrinsic dynamical cellular properties are very important to neuronal information processing. Moreover, our results also show that the FSL and firing rate responses are mutually independent processes and that neurons can encode the external stimulus into different FSLs and fir-ing rates simultaneously. This finding is consistent with the current theory of dual or multiple complementary coding mechanisms.Secondly, we consider a special structure, autapse, in the nervous system. With the effect of autapse, the responses of the Hodgkin-Huxley (regular-spiking) neuron and the Hindmarsh-Rose (bursting spiking) neuron have been investigated in detail, respec-tively. As we found the autapse serves as a control option for adjusting the neuron firing behaviors.For the regular spiking neuron, the interspike interval and mean frequency of the output spike train in response to DC or time variable stimuli are both exhibiting periodic behavior as the delay time increasing. When the neuron was subjected to a DC stimulus, this period is approximate to the intrinsic period of the neuron. When autaptic delay time is near the odd multiples of the half intrinsic period, the ISIs of the firing spike train are far away from the intrinsic ISI. When the input is a synaptic-like pulse train with random interspike intervals, we observed the low-pass and band-pass filtering behaviors induced by the autapse. And the cut-off frequencies change with the autaptic parameters. When the proper autaptic parameters were chosen, most of input ISIs can be filtered and the response spike trains can also be nearly regular, even with a high random input.For the bursting neuron, the firing patterns are completely changed. With the ef-fect of autapse, the firing pattern can transform among the silent, periodic bursting and chaotic firing. The electrical and inhibitory chemical autapse both exhibit suppressions on the chaotic firing. While, the excitatory chemical autapse plays a positive role in generating and enhancing the chaotic state. We also observe there are two main ways of the transition to chaos from periodic firing:one is discontinuous and another is con-tinuous.The results of current study indicate the occurrence of a state-to-state transition by adjusting a self-delay feedback in a dynamic system. These dynamic transitions also offer some mechanisms for the switch between different neuronal activities as well as the corresponding relevant neuronal behaviors.In the last chapter, we have made a summary of this thesis and prospected future research based on the current work.