Predictions of Phase-Locking in Excitatory Hybrid Networks: Excitation Does Not Promote Phase-Locking in Pattern-Generating Networks as Reliably as Inhibition

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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...

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

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“…even uses the estimated synaptic current, injected somatically, to measure the PRC (Netoff et al 2005a(Netoff et al , 2005bOprisan et al 2004;Preyer and Butera 2005;Sieling et al 2009). The difference we observed between synaptic and current pulse iPRCs suggests that this will not be an effective strategy in subthalamic neurons, but it is still instructive to compare the synaptic currents inferred from current-clamp recordings with the synaptic currents recorded in voltage clamp.…”

Section: Fig 4 Effect Of Intrinsic Firing Rate On Synaptic Iprcsmentioning

confidence: 99%

“…For neurons like those in the basal ganglia, which receive thousands of diverse synaptic inputs, it may still be possible to apply this method by using the infinitesimal PRC (iPRC), the rate at which an applied current changes a cell's phase as a function of input phase, to predict the response to arbitrary synaptic currents. The iPRC can be estimated from the response of a cell to small, brief current pulses (Bennett and Wilson 1998;Galán et al 2005;Mancilla et al 2007;Phoka et al 2010;Fetz 1993a, 1993b;Stiefel et al 2008;Tateno and Robinson 2007;Tsubo et al 2007) or simulated conductance changes (Netoff et al 2005a(Netoff et al , 2005bPreyer and Butera 2005;Sieling et al 2009), and, combined with knowledge of synaptic currents, it should in principle be possible to predict the cell's response to its combined input from all other cells in the network. Phase models are especially suited for studying the conditions required for network synchrony (e.g., Ermentrout 1996; Hansel et al 1995;van Vreeswijk et al 1994), and this approach to modeling the basal ganglia may be useful in explaining why its neurons tend to fire asynchronously under normal conditions but participate in synchronized oscillations in Parkinson's disease (Rivlin-Etzion et al 2010) and how inputs arriving in the striatum and subthalamic nucleus affect basal ganglia output.…”

mentioning

confidence: 99%

Phase response curves of subthalamic neurons measured with synaptic input and current injection

Farries

Wilson

2012

Farries MA, Wilson CJ. Phase response curves of subthalamic neurons measured with synaptic input and current injection. J Neurophysiol 108: 1822-1837. First published July 11, 2012 doi:10.1152/jn.00053.2012.-Infinitesimal phase response curves (iPRCs) provide a simple description of the response of repetitively firing neurons and may be used to predict responses to any pattern of synaptic input. Their simplicity makes them useful for understanding the dynamics of neurons when certain conditions are met. For example, the sizes of evoked phase shifts should scale linearly with stimulus strength, and the form of the iPRC should remain relatively constant as firing rate varies. We measured the PRCs of rat subthalamic neurons in brain slices using corticosubthalamic excitatory postsynaptic potentials (EPSPs; mediated by both AMPA-and NMDA-type receptors) and injected current pulses and used them to calculate the iPRC. These were relatively insensitive to both the size of the stimulus and the cell's firing rate, suggesting that the iPRC can predict the response of subthalamic nucleus cells to extrinsic inputs. However, the iPRC calculated using EPSPs differed from that obtained using current pulses. EPSPs (normalized for charge) were much more effective at altering the phase of subthalamic neurons than current pulses. The difference was not attributable to the extended time course of NMDA receptor-mediated currents, being unaffected by blockade of NMDA receptors. The iPRC provides a good description of subthalamic neurons' response to input, but iPRCs are best estimated using synaptic inputs rather than somatic current injection.

“…The theoretical method for predicting the existence and stability of phase-locked modes using single-pulse PRCs for networks of two bursting neurons has been previously developed (Oprisan et al 2004;Sieling et al 2009). We describe it here to show how the new methods based on the fPRC are an improvement.…”

Section: Existence and Stability Criteria For Two-neuron Networkmentioning

confidence: 99%

Functional Phase Response Curves: A Method for Understanding Synchronization of Adapting Neurons

Cui¹,

Canavier²,

Butera³

2009

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Cui J, Canavier CC, Butera R. Functional phase response curves: a method for understanding synchronization of adapting neurons. J Neurophysiol 102: 387-398, 2009. First published May 6, 2009 doi:10.1152/jn.00037.2009. Phase response curves (PRCs) for a single neuron are often used to predict the synchrony of mutually coupled neurons. Previous theoretical work on pulse-coupled oscillators used single-pulse perturbations. We propose an alternate method in which functional PRCs (fPRCs) are generated using a train of pulses applied at a fixed delay after each spike, with the PRC measured when the phasic relationship between the stimulus and the subsequent spike in the neuron has converged. The essential information is the dependence of the recovery time from pulse onset until the next spike as a function of the delay between the previous spike and the onset of the applied pulse. Experimental fPRCs in Aplysia pacemaker neurons were different from single-pulse PRCs, principally due to adaptation. In the biological neuron, convergence to the fully adapted recovery interval was slower at some phases than that at others because the change in the effective intrinsic period due to adaptation changes the effective phase resetting in a way that opposes and slows the effects of adaptation. The fPRCs for two isolated adapting model neurons were used to predict the existence and stability of 1:1 phase-locked network activity when the two neurons were coupled. A stability criterion was derived by linearizing a coupled map based on the fPRC and the existence and stability criteria were successfully tested in two-simulated-neuron networks with reciprocal inhibition or excitation. The fPRC is the first PRC-based tool that can account for adaptation in analyzing networks of neural oscillators.