We studied bursting patterns underlied by bifurcation phenomena and chaotic spiking in a computational leech heartbeat model. We observed the gradient physical properties of the ISI trains and amplitude (shift of the membrane potential) when the parameter g leak was mildly changed and found different bistable areas. The resulting computation implies that (i) classification of the intensity of the input information is feasible in this regime, (ii) a neuron's working level can be marked by its range in a typical bifurcation, and (iii) there are invisible triggers underlying subtle mechanisms in the model.
Leech heartbeat interneurons (HN cells) interconnected by inhibitory synapses have been simulated using several modified models based on the Hodgkin-Huxley equations; yet, adequate characteristics of HN cells are hardly possible to be summarized due to the complexity of these models. The Winnerless Competition (WLC) model created as an inhibitory-connected nervous network is more appropriate for networks consisting of HN cells. We investigated different firing patterns produced by such model under application of various stimuli simulating changes in the leech's environment. By means of recording the firing frequency, synchronization, interspike intervals (ISIs), and maxima of action potentials (APs) and also by application of the theory of mixed-mode oscillations (MMOs), different properties of firing patterns in HN cells were examined. According to the results of computational analyses, DC and AC stimulations were found to play different roles in modulating the leech's heartbeat rhythm; external stimuli could influence the intensity and duration of the network reaction by changing both AP frequency and amplitude. Besides, changes in the recovery abilities of neurons can lead to various release modes of HN cells. Combined with physiological experiments on medical leeches, numerical analysis allows us to gain a deeper understanding of how HN cells coordinate with each other to bring the rhythm to the leech heartbeat system.
Endogenous bursters in central pattern generators (CPGs) generate rhythmic firing patterns controlling regular movements in the organism. Based on a pacemaker kernel model of the stomatogastric ganglion (SGG) of crustaceans, we constructed three reduced models, (i) dendrite-reduced model (DRM), (ii) axon-reduced model (ARM), and (iii) primary neuritereduced model (PNRM). Similar firing patterns were observed in two models except the axonreduced one. Perturbing of various parameters in the models induced bifurcation phenomena in the occurrence of interspike intervals (ISIs), which depicted variation of the firing patterns. By comparing and analyzing two-dimensional parameter planes derived from the above different models, the effects of compartments on varying firing patterns were detected. In particular, a different kind of period-doubling transition mode of firing patterns, which varied via a ring-shape mode, was found.
Spike timing-dependent plasticity (STDP) plays an important role in sculpting informationstoring circuits in the hippocampus, since motor learning and memory are thought to be closely linked with this classical plasticity. To further understand the information delivery in a hippocampus circuit, we build a computational model to study the potential role of linear changes in the synaptic weight and synaptic number. Several key results have been obtained: (i) Changes in the synaptic weight and numbers lead to different long-term modification; (ii) the first paired spiking from two neurons significantly influences the adjusted subsequent paired spiking; the pre-post spiking pair strengthens the following paired spiking; however, the post-pre spiking pair depresses the subsequent spiking; (iii) when the synaptic weight and synaptic numbers are changed, the interval of the first spiking pair may undergo reduction, and (iv) when we stimulate a stellate neuron weakly or decrease the capacitance of CA1 pyramidal neuron, LTP is more easily produced than LTD; on the contrary, LTD is more easily produced in an opposite situation; increase in the synaptic numbers can promote activation of the CA1 pyramidal neuron.
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