Circuits that contain the Model Concept : Axonal Action Potentials

(The model is used to investigate action potential propagation in axons.)
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    Models   Description
1. CA1 pyramidal cell: reconstructed axonal arbor and failures at weak gap junctions (Vladimirov 2011)
Model of pyramidal CA1 cells connected by gap junctions in their axons. Cell geometry is based on anatomical reconstruction of rat CA1 cell (NeuroMorpho.Org ID: NMO_00927) with long axonal arbor. Model init_2cells.hoc shows failures of second spike propagation in a spike doublet, depending on conductance of an axonal gap junction. Model init_ring.hoc shows that spike failure result in reentrant oscillations of a spike in a loop of axons connected by gap junctions, where one gap junction is weak. The paper shows that in random networks of axons connected by gap junctions, oscillations are driven by single pacemaker loop of axons. The shortest loop, around which a spike can travel, is the most likely pacemaker. This principle allows us to predict the frequency of oscillations from network connectivity and visa versa. We propose that this type of oscillations corresponds to so-called fast ripples in epileptic hippocampus.
2. Dentate gyrus network model (Santhakumar et al 2005)
Mossy cell loss and mossy fiber sprouting are two characteristic consequences of repeated seizures and head trauma. However, their precise contributions to the hyperexcitable state are not well understood. Because it is difficult, and frequently impossible, to independently examine using experimental techniques whether it is the loss of mossy cells or the sprouting of mossy fibers that leads to dentate hyperexcitability, we built a biophysically realistic and anatomically representative computational model of the dentate gyrus to examine this question. The 527-cell model, containing granule, mossy, basket, and hilar cells with axonal projections to the perforant-path termination zone, showed that even weak mossy fiber sprouting (10-15% of the strong sprouting observed in the pilocarpine model of epilepsy) resulted in the spread of seizure-like activity to the adjacent model hippocampal laminae after focal stimulation of the perforant path. See reference for more and details.
3. Mechanisms of very fast oscillations in axon networks coupled by gap junctions (Munro, Borgers 2010)
Axons connected by gap junctions can produce very fast oscillations (VFOs, > 80 Hz) when stimulated randomly at a low rate. The models here explore the mechanisms of VFOs that can be seen in an axonal plexus, (Munro & Borgers, 2009): a large network model of an axonal plexus, small network models of axons connected by gap junctions, and an implementation of the model underlying figure 12 in Traub et al. (1999) . The large network model consists of 3,072 5-compartment axons connected in a random network. The 5-compartment axons are the 5 axonal compartments from the CA3 pyramidal cell model in Traub et al. (1994) with a fixed somatic voltage. The random network has the same parameters as the random network in Traub et al. (1999), and axons are stimulated randomly via a Poisson process with a rate of 2/s/axon. The small network models simulate waves propagating through small networks of axons connected by gap junctions to study how local connectivity affects the refractory period.
4. Neocort. pyramidal cells subthreshold somatic voltage controls spike propagation (Munro Kopell 2012)
There is suggestive evidence that pyramidal cell axons in neocortex may be coupled by gap junctions into an ``axonal plexus" capable of generating Very Fast Oscillations (VFOs) with frequencies exceeding 80 Hz. It is not obvious, however, how a pyramidal cell in such a network could control its output when action potentials are free to propagate from the axons of other pyramidal cells into its own axon. We address this problem by means of simulations based on 3D reconstructions of pyramidal cells from rat somatosensory cortex. We show that somatic depolarization enables propagation via gap junctions into the initial segment and main axon, while somatic hyperpolarization disables it. We show further that somatic voltage cannot effectively control action potential propagation through gap junctions on minor collaterals; action potentials may therefore propagate freely from such collaterals regardless of somatic voltage. In previous work, VFOs are all but abolished during the hyperpolarization phase of slow-oscillations induced by anesthesia in vivo. This finding constrains the density of gap junctions on collaterals in our model and suggests that axonal sprouting due to cortical lesions may result in abnormally high gap junction density on collaterals, leading in turn to excessive VFO activity and hence to epilepsy via kindling.
5. Synaptic gating at axonal branches, and sharp-wave ripples with replay (Vladimirov et al. 2013)
The computational model of in vivo sharp-wave ripples with place cell replay. Excitatory post-synaptic potentials at dendrites gate antidromic spikes arriving from the axonal collateral, and thus determine when the soma and the main axon fire. The model allows synchronous replay of pyramidal cells during sharp-wave ripple event, and the replay is possible in both forward and reverse directions.
6. Thalamic network model of deep brain stimulation in essential tremor (Birdno et al. 2012)
"... Thus the decreased effectiveness of temporally irregular DBS trains is due to long pauses in the stimulus trains, not the degree of temporal irregularity alone. We also conducted computer simulations of neuronal responses to the experimental stimulus trains using a biophysical model of the thalamic network. Trains that suppressed tremor in volunteers also suppressed fluctuations in thalamic transmembrane potential at the frequency associated with cerebellar burst-driver inputs. Clinical and computational findings indicate that DBS suppresses tremor by masking burst-driver inputs to the thalamus and that pauses in stimulation prevent such masking. Although stimulation of other anatomic targets may provide tremor suppression, we propose that the most relevant neuronal targets for effective tremor suppression are the afferent cerebellar fibers that terminate in the thalamus."

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