Relating ion channel expression, bifurcation structure, and diverse firing patterns in a model of an identified motor neuron

Herrera-Valdez, Marco Arieli; McKiernan, Erin C.; Berger, Sandra D; Ryglewski, Stefanie; Duch, Carsten; Crook, Sharon

doi:10.1007/s10827-012-0416-6

Cited by 36 publications

(60 citation statements)

References 87 publications

(145 reference statements)

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“…If h were to remain slow compared with v, the fixed point would lose stability via a Hopf bifurcation when it lands on the right branch. The fast-slow analysis explained above is an approximation; it is possible for fixed points on the middle branch to gain stability near the turns (Herrera-Valdez et al 2013). In this particular example, the analysis based on a separation of timescales breaks down because the voltage-dependent time constant for h becomes quite fast at depolarized potentials, so the Hopf bifurcation occurs slightly before the right branch is reached.…”

Section: Resultsmentioning

confidence: 96%

“…Although Bianchi et al (2012) do not explicitly state this, their bifurcation diagram captures the essence of Hodgkin's (1948) type 3 excitability in which step current changes induce a train of spikes but can never induce sustained pacemaking. Therefore the I-V curve determined under voltage clamp may be a helpful diagnostic tool for characterizing the bifurcation structure of neural oscillators, although other techniques are required to complement the I-V curves (Herrera-Valdez et al 2013).…”

Section: Discussionmentioning

confidence: 99%

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Mathematical analysis of depolarization block mediated by slow inactivation of fast sodium channels in midbrain dopamine neurons

Qian

Tucker

et al. 2014

Journal of Neurophysiology

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ES, Canavier CC. Mathematical analysis of depolarization block mediated by slow inactivation of fast sodium channels in midbrain dopamine neurons. J Neurophysiol 112: 2779 -2790, 2014. First published September 3, 2014 doi:10.1152/jn.00578.2014.-Dopamine neurons in freely moving rats often fire behaviorally relevant high-frequency bursts, but depolarization block limits the maximum steady firing rate of dopamine neurons in vitro to ϳ10 Hz. Using a reduced model that faithfully reproduces the sodium current measured in these neurons, we show that adding an additional slow component of sodium channel inactivation, recently observed in these neurons, qualitatively changes in two different ways how the model enters into depolarization block. First, the slow time course of inactivation allows multiple spikes to be elicited during a strong depolarization prior to entry into depolarization block. Second, depolarization block occurs near or below the spike threshold, which ranges from Ϫ45 to Ϫ30 mV in vitro, because the additional slow component of inactivation negates the sodium window current. In the absence of the additional slow component of inactivation, this window current produces an N-shaped steady-state current-voltage (I-V) curve that prevents depolarization block in the experimentally observed voltage range near Ϫ40 mV. The time constant of recovery from slow inactivation during the interspike interval limits the maximum steady firing rate observed prior to entry into depolarization block. These qualitative features of the entry into depolarization block can be reversed experimentally by replacing the native sodium conductance with a virtual conductance lacking the slow component of inactivation. We show that the activation of NMDA and AMPA receptors can affect bursting and depolarization block in different ways, depending upon their relative contributions to depolarization versus to the total linear/nonlinear conductance. substantia nigra; depolarization block; bursting THE MECHANISMS by which dopamine neurons enter into depolarization block are potentially of interest for three reasons. First, antipsychotics used to treat schizophrenia have been hypothesized to exert their therapeutic effects by inducing depolarization block in mesolimbic dopamine neurons (Grace and Bunney 1986). Second, drugs that induce depolarization block in nigrostriatal neurons cause extrapyramidal side effects. Finally, the tendency of these neurons to go into depolarization block affects their ability to generate the high firing rates that are achieved during behaviorally relevant bursts in vivo (Hyland et al. 2002).Depolarization block limits the maximum firing rate of dopamine neurons in vitro (Richards et al. 1997). Depolarizing current steps elicit steady firing rates up to 10 Hz, and additional depolarization causes a cessation of spiking, although transients as fast as 30 Hz have been evoked by current steps (Blythe et al. 2009). Our previous modeling work ( Kuznetsova et al. 2010) and experimental studies (Deister et al. 200...

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Section: Resultsmentioning

confidence: 96%

Section: Discussionmentioning

confidence: 99%

Mathematical analysis of depolarization block mediated by slow inactivation of fast sodium channels in midbrain dopamine neurons

Qian

Tucker

et al. 2014

Journal of Neurophysiology

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“…Most neurons express many voltage-dependent conductances, some of which may have overlapping or degenerate physiological functions (1)(2)(3)(4)(5)(6). Furthermore, neurons in the brains of long-lived animals must maintain reliable function over the animal's lifetime while all of their ion channels and receptors are replaced in the membrane over hours, days, or weeks.…”

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confidence: 99%

Correlations in ion channel expression emerge from homeostatic tuning rules

O’Leary

Williams

Caplan

et al. 2013

Proc. Natl. Acad. Sci. U.S.A.

187

228

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Experimental observations reveal that the expression levels of different ion channels vary across neurons of a defined type, even when these neurons exhibit stereotyped electrical properties. However, there are robust correlations between different ion channel expression levels, although the mechanisms that determine these correlations are unknown. Using generic model neurons, we show that correlated conductance expression can emerge from simple homeostatic control mechanisms that couple expression rates of individual conductances to cellular readouts of activity. The correlations depend on the relative rates of expression of different conductances. Thus, variability is consistent with homeostatic regulation and the structure of this variability reveals quantitative relations between regulation dynamics of different conductances. Furthermore, we show that homeostatic regulation is remarkably insensitive to the details that couple the regulation of a given conductance to overall neuronal activity because of degeneracy in the function of multiple conductances and can be robust to "antihomeostatic" regulation of a subset of conductances expressed in a cell.neuronal excitability | robustness | computational models | control theory T he electrophysiological signature of every neuron is determined by the number and kind of voltage-dependent conductances in its membrane. Most neurons express many voltage-dependent conductances, some of which may have overlapping or degenerate physiological functions (1-6). Furthermore, neurons in the brains of long-lived animals must maintain reliable function over the animal's lifetime while all of their ion channels and receptors are replaced in the membrane over hours, days, or weeks. Consequently, ongoing turnover of ion channels of various types must occur without compromising the essential excitability properties of the neuron (5, 7-10).Both theoretical and experimental studies suggest that maintaining stable intrinsic excitability is accomplished via homeostatic, negative feedback processes that use intracellular Ca 2+ concentrations as a sensor of activity and then alter the synthesis, insertion, and degradation of membrane conductances to achieve a target activity level (11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27). Among the modeling studies are several different homeostatic tuning rules that differ in how sensor readout is coupled to the changes in conductance necessary to achieve a target activity (11,13,14,28). Regardless, these models can self-assemble from randomized initial conditions, and they will change their conductance densities in response to perturbation or synaptic drive. In one of these homeostatic self-tuning models (14), similar activity patterns can be associated with different sets of conductance densities.Thus, it is perhaps not surprising that experimental studies also find a considerable range in the conductance densities of voltagedependent channels and in the mRNA expression of their ion channel genes (29-36). The experimental st...

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“…Recordings were stored using PClamp 8.2 (Molecular Devices) and 107 were imported into Spike2 (Cambridge Electronic Design) for processing. All recordings 108 are publicly available via a GitHub repository (github.com/emckiernan/eki-study), 109 which is archived via figshare (DOI: 10.6084/m9.figshare.1437747).…”

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Relating ion channel expression, bifurcation structure, and diverse firing patterns in a model of an identified motor neuron

Cited by 36 publications

References 87 publications

Mathematical analysis of depolarization block mediated by slow inactivation of fast sodium channels in midbrain dopamine neurons

Mathematical analysis of depolarization block mediated by slow inactivation of fast sodium channels in midbrain dopamine neurons

Correlations in ion channel expression emerge from homeostatic tuning rules

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