The generation of rhythmic patterns by neuronal networks is a complex phenomenon, relying on the interaction of numerous intrinsic and synaptic currents, as well as modulatory agents. To investigate the functional contribution of an individual ionic current to rhythmic pattern generation in a network, we constructed a hybrid system composed of a silicon model neuron and a heart interneuron from the heartbeat timing network of the medicinal leech. When the model neuron and a heart interneuron are connected by inhibitory synapses, they produce rhythmic activity similar to that observed in the heartbeat network. We focused our studies on investigating the functional role of the hyperpolarization-activated inward current (I h ) on the rhythmic bursts produced by the network. By introducing changes in both the model and the heart interneuron, we showed that I h determines both the period of rhythmic bursts and the balance of activity between the two sides of the network, because the amount and the activation/deactivation time constant of I h determines the length of time that a neuron spends in the inhibited phase of its burst cycle. Moreover, we demonstrated that the model neuron is an effective replacement for a heart interneuron and that changes made in the model can accurately mimic similar changes made in the living system. Finally, we used a previously developed mathematical model (Hill et al. 2001) of two mutually inhibitory interneurons to corroborate these findings. Our results demonstrated that this hybrid system technique is advantageous for investigating neuronal properties that are inaccessible with traditional techniques.
We have designed, fabricated, and tested an analog integrated-circuit architecture to implement the conductance-based dynamics that model the electrical activity of neurons. The dynamics of this architecture are in accordance with the Hodgkin-Huxley formalism, a widely exploited, biophysically plausible model of the dynamics of living neurons. Furthermore the architecture is modular and compact in size so that we can implement networks of silicon neurons, each of desired complexity, on a single integrated circuit. We present in this paper a six-conductance silicon-neuron implementation, and characterize it in relation to the Hodgkin-Huxley formalism. This silicon neuron incorporates both fast and slow ionic conductances, which are required to model complex oscillatory behaviors (spiking, bursting, subthreshold oscillations).
Although conductance-based neural models provide a realistic depiction of neuronal activity, their complexity often limits effective implementation and analysis. Neuronal model reduction methods provide a means to reduce model complexity while retaining the original model's realism and relevance. Such methods, however, typically include ad hoc components that require that the modeler already be intimately familiar with the dynamics of the original model. We present an automated, algorithmic method for reducing conductance-based neuron models using the method of equivalent potentials (Kelper et al., Biol Cybern 66(5):381-387, 1992) Our results demonstrate that this algorithm is able to reduce the complexity of the original model with minimal performance loss, and requires minimal prior knowledge of the model's dynamics. Furthermore, by utilizing a cost function based on the contribution of each state variable to the total conductance of the model, the performance of the algorithm can be significantly improved.
Neural models are increasingly being used as design components of physical systems. In order to best use models in these novel contexts, we must develop design rules that describe how decisions in model construction relate to the functional performance of the resulting system. In the accompanying paper, we described a series of related neuron models of varying complexity. Here, we use these models to build several half-center oscillators, and investigate how model complexity influences the robustness and flexibility of these oscillators. Our results indicate that model complexity has a significant effect on the robustness and flexibility of systems that incorporate neural models.
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