Model Hodgkin-Huxley type

Fig. 1.7. Comparison of the map based neurons (defined by equation (1.15)) (A) to an equivalent Hodgkin-Huxley type model (details in (Nowotny et al. 2005)) (B). The response time to an EPSP (which is the most important parameter within this context) is almost identical for both (C). The inset shows the corresponding response curve of the honeybee KC model of (Wustenberg et al. 2004) which is also virtually identical. (Modified from (Nowotny et al. 2005)).

To test this idea of symmetry breaking with lateral excitation, we have built a full size model of the locust olfactory system using Hodgkin-Huxley type model neurons for PNs, leaky integrate-and-fire neurons for KCs and a single Hodgkin-Huxley neuron to represent the global inhibition from lateral horn interneurons onto the KCs. The KCs... 

As was recalled by Keynes (1994a), it was first observed by Chandler Meves (1970) that in squid axons perfused with NaF a small flow of Na ions persisted in the inactivated steady state. Their tentative conclusion based on the Hodgkin-Huxley model was to suppose that the inactivation parameter h was the sum of two components h, and Zij, where A, predominated at negative potentials, and Zij predominated at positive ones. This proposition predicted the existence of one type of Na+ conductance that increased transiently with depolarization as in the Hodgkin—Huxley system, and a second type that persisted with depolarization to give a steady low level of conductance. Combined with m kinetics the idea fitted well with the experimental data. 

Oscillations of the bursting type have been modelled mainly in neurobiology, whieh is the field where they are most frequently observed. These models consist in modifications of the Hodgkin Huxley equations, which generally take into account the effect of Ca "" and the slow, cyclical variation of some ionic conductances (Plant Kim, 1976 Plant, 1978 Carpenter, 1979 Hindmarsh Rose, 1984 Chay Rinzel, 1985 Ermentrout Koppell, 1986 Rinzel Lee, 1986 Canavier etal, 1991 Smolen Keizer, 1992 Destexhe, Babloyantz Sejnowski, 1993 Bertram, 1994). 

Figure 13.10 Voltage clamp data (current vs. time) for (a) Hodgkin-Huxley ( delayed rectifier )-type potassium current and (b) calcium-activated potassium current i . Noisy traces are experimental data, smooth curves are model simulations. Note that has no inactivation, so current remains at higher level, while / contains inactivation, so that current reaches a peak and declines. (Adapted from Buchholtz et ah, 1992.)...

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