Experimentaland Theoretical Studies on Neural Coding

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For the study of information processing mechanisms in the nervous system, it is crucial to understand how events from the outer world and their relationships are encoded. Much work has been done along these lines. A report on neural coding was published in the 60's by Perkel et al.and they introduced several physiological processes for information transmission in single cells and also the candidate codes by which the nervous system sends and retrieves information. Takahashi et al.stimulated the squid giant axon by periodic current stimuli and measured the corresponding membrane voltage. Segundo et al.observed how the firing patterns and frequency of a single cell were modulated when it received periodic inhibitory inputs. Harmon's model was an electric analog mimicking single neuron activities. The Hodgkin-Huxley(abbreviated by H-H)and Nagumo equations were mathematical models. Perkel carried out computer simulations of pacemaker neurons of Aplysia driven by excitatory or inhibitory sy … More naptic inputs. The H-H equation were used to clarify the underlying mechanisms of the membrane excitations related to the periodic and chaotic responses of single neurons. The Bonhoeffer-van der Pol(BVP)model is used to simulate the neural behaviors since it provides a simpler model.All these publications are relevant to neural coding, namely implications of an individual neuron's dynamics and nonlinearlity for its computational properties.Results obtained in the present research program on neural coding are as follows :1)The characteristics of the BVP neuron model response to periodic pulse stimulus are investigated. Temporal patterns of the output of the model are analyzed as a function of the stimulus intensity and period. The BVP model exhibits the same chaotic behavior and a Cantor function like graph of the response frequency(mean frequency)as in electrophysiological experiments. This shows that the BVP model describes the complicated response characteristics of the neuron at least qualitatively.2)A recent investigation of the influence of periodic inhibitory trains on a crayfish pacemaker neuron showed not only well-known locked periodic responses but also intermittent, messy and hopping responses. This communication studies the responses of the BVP model with self-sustained oscillation when exposed to periodic pulse trains inputs. The analysis is similar to that used in crayfish and reveals interesting features, both comparable and complementary to those seen in the living preparation.3)The BVP oscillator is a valuable dynamical system model of pacemaker neurons. Isochron, phase transition curves(PTC)and two dimensional bifurcation diagrams served to analyze the neuron's response to periodic pulse stimuli. Responses are described and explained in terms of the nonlinear dynamical system theory. An important issue in the generation of spikes by pacemaker neurons is the existence of both slow and fast dynamics in the state point's trajectory in the phase plane. It is this feature in particular that makes the BVP oscillator a faithful model of living pacemaker neurons. Comparison of the model's responses with those of a living pacemaker was based also on return maps of interspike intervals. Analyzed in detail were the complex discharges called 'stammering'which involve interspike intervals that arise unexpectably and exhibit histgrams with several modes separated by the equal intervals.4)A simple mathematical model of living pacemaker neurons is proposed. The model has a unit circle limit cycle and radial isochrons and the state point moves slowly in one region and fast in the remaining region ; regions can correspond to the subthreshold activity and to the action potentials of pacemaker neurons, respectively. The global bifurcation structure when driven by periodic pulse trains was investigated using one-dimensional maps(PTC), two-dimensional bifurcation diagrams, and skeletons involving stimulus period and intensity. The existence of both the slow and the fast dynamics has a critical influence on the global bifurcation structure of the oscillator when stimulated periodically. Less