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Switching in Cerebellar Stellate Cell Excitability in Response to a Pair of Inhibitory/Excitatory Presynaptic Inputs: A Dynamical System Perspective
- Source :
- Neural Computation. 32:626-658
- Publication Year :
- 2020
- Publisher :
- MIT Press - Journals, 2020.
-
Abstract
- Cerebellar stellate cells form inhibitory synapses with Purkinje cells, the sole output of the cerebellum. Upon stimulation by a pair of varying inhibitory and fixed excitatory presynaptic inputs, these cells do not respond to excitation (i.e., do not generate an action potential) when the magnitude of the inhibition is within a given range, but they do respond outside this range. We previously used a revised Hodgkin–Huxley type of model to study the nonmonotonic first-spike latency of these cells and their temporal increase in excitability in whole cell configuration (termed run-up). Here, we recompute these latency profiles using the same model by adapting an efficient computational technique, the two-point boundary value problem, that is combined with the continuation method. We then extend the study to investigate how switching in responsiveness, upon stimulation with presynaptic inputs, manifests itself in the context of run-up. A three-dimensional reduced model is initially derived from the original six-dimensional model and then analyzed to demonstrate that both models exhibit type 1 excitability possessing a saddle-node on an invariant cycle (SNIC) bifurcation when varying the amplitude of [Formula: see text]. Using slow-fast analysis, we show that the original model possesses three equilibria lying at the intersection of the critical manifold of the fast subsystem and the nullcline of the slow variable [Formula: see text] (the inactivation of the A-type K[Formula: see text] channel), the middle equilibrium is of saddle type with two-dimensional stable manifold (computed from the reduced model) acting as a boundary between the responsive and non-responsive regimes, and the (ghost of) SNIC is formed when the [Formula: see text]-nullcline is (nearly) tangential to the critical manifold. We also show that the slow dynamics associated with (the ghost of) the SNIC and the lower stable branch of the critical manifold are responsible for generating the nonmonotonic first-spike latency. These results thus provide important insight into the complex dynamics of stellate cells.
- Subjects :
- Cerebellum
Cognitive Neuroscience
Models, Neurological
Action Potentials
Stimulation
Inhibitory postsynaptic potential
01 natural sciences
010305 fluids & plasmas
03 medical and health sciences
0302 clinical medicine
Arts and Humanities (miscellaneous)
0103 physical sciences
Inhibitory synapses
medicine
Humans
Neurons
Quantitative Biology::Neurons and Cognition
Chemistry
Perspective (graphical)
medicine.anatomical_structure
Synapses
Hepatic stellate cell
Excitatory postsynaptic potential
Neuroscience
030217 neurology & neurosurgery
Subjects
Details
- ISSN :
- 1530888X and 08997667
- Volume :
- 32
- Database :
- OpenAIRE
- Journal :
- Neural Computation
- Accession number :
- edsair.doi.dedup.....428143b525a86feffd6cc47d54e70a8e