Population dynamics and entrainment of basal ganglia pacemakers are shaped by their dendritic arbors

Optogenetic Interrogation of Electrophysiological Dendritic Properties and Their Effect on Pacemaking Neurons from Acute Rodent Brain Slices

Understanding dendritic excitability is essential for a complete and precise characterization of neurons' input-output relationships. Theoretical and experimental work demonstrates that the electrotonic and nonlinear properties of dendrites can alter the amplitude (e.g., through amplification) and latency of synaptic inputs as viewed in the axosomatic region where spike timing is determined. The gold-standard technique to study dendritic excitability is using dual-patch recordings with a high-resistance electrode used to patch a piece of distal dendrite in addition to a somatic patch electrode. However, this approach is often impractical when distal dendrites are too fine to patch. Therefore, we developed a technique that utilizes the expression of Channelrhodopsin-2 (ChR2) to study dendritic excitability in acute brain slices through the combination of a somatic patch electrode and optogenetic activation. The protocol describes how to prepare acute slices from mice that express ChR2 in specific cell types, and how to use two modes of light stimulation: proximal (which activates the soma and proximal dendrites in a ~100 µm diameter surrounding the soma) with the use of a high-magnification objective and full-field stimulation through a low-magnification objective (which activates the entire somato-dendritic field of the neuron). We use this technique in conjunction with various stimulation protocols to estimate model-based spectral components of dendritic filtering and the impact of dendrites on phase response curves, peri-stimulus time histograms, and entrainment of pacemaking neurons. This technique provides a novel use of optogenetics to study intrinsic dendritic excitability through the use of standard patch-clamp slice physiology. Key features • A method for studying the effects of electrotonic and nonlinear dendritic properties on the sub- and suprathreshold responses of pacemaking neurons. • Combines somatic patch clamp or perforated patch recordings with optogenetic activation in acute brain slices to investigate dendritic linear transformation without patching the dendrite. • Oscillatory illumination at various frequencies estimates spectral properties of the dendrite using subthreshold voltage-clamp recordings and studies entrainment of pacemakers in current clamp recordings. • This protocol uses Poisson white noise illumination to estimate dendritic phase response curves and peri-stimulus time histograms.

Phase Delays between Mouse Globus Pallidus Neurons Entrained by Common Oscillatory Drive Arise from Their Intrinsic Properties, Not Their Coupling

A hallmark of Parkinson's disease is the appearance of correlated oscillatory discharge throughout the cortico-basal ganglia (BG) circuits. In the primate globus pallidus (GP), where the discharge of GP neurons is normally uncorrelated, pairs of GP neurons exhibit oscillatory spike correlations with a broad distribution of pairwise phase delays in experimental parkinsonism. The transition to oscillatory correlations is thought to indicate the collapse of the normally segregated information channels traversing the BG. The large phase delays are thought to reflect pathological changes in synaptic connectivity in the BG. Here we study the structure and phase delays of spike correlations measured from neurons in the mouse external GP (GPe) subjected to identical 1-100 Hz sinusoidal drive but recorded in separate experiments. First, we found that spectral modes of a GPe neuron's empirical instantaneous phase response curve (iPRC) elucidate at what phases of the oscillatory drive the GPe neuron locks when it is entrained and the distribution of phases at which it spikes when it is not. Then, we show that in this case the pairwise spike cross-correlation equals the cross-correlation function of these spike phase distributions. Finally, we show that the distribution of GPe phase delays arises from the diversity of iPRCs and is broadened when the neurons become entrained. Modeling GPe networks with realistic intranuclear connectivity demonstrates that the connectivity decorrelates GPe neurons without affecting phase delays. Thus, common oscillatory input gives rise to GPe correlations whose structure and pairwise phase delays reflect their intrinsic properties captured by their iPRCs.

How neuronal morphology impacts the synchronisation state of neuronal networks

The biophysical properties of neurons not only affect how information is processed within cells, they can also impact the dynamical states of the network. Specifically, the cellular dynamics of action-potential generation have shown relevance for setting the (de)synchronisation state of the network. The dynamics of tonically spiking neurons typically fall into one of three qualitatively distinct types that arise from distinct mathematical bifurcations of voltage dynamics at the onset of spiking. Accordingly, changes in ion channel composition or even external factors, like temperature, have been demonstrated to switch network behaviour via changes in the spike onset bifurcation and hence its associated dynamical type. A thus far less addressed modulator of neuronal dynamics is cellular morphology. Based on simplified and anatomically realistic mathematical neuron models, we show here that the extent of dendritic arborisation has an influence on the neuronal dynamical spiking type and therefore on the (de)synchronisation state of the network. Specifically, larger dendritic trees prime neuronal dynamics for in-phase-synchronised or splayed-out activity in weakly coupled networks, in contrast to cells with otherwise identical properties yet smaller dendrites. Our biophysical insights hold for generic multicompartmental classes of spiking neuron models (from ball-and-stick-type to anatomically reconstructed models) and establish a connection between neuronal morphology and the susceptibility of neural tissue to synchronisation in health and disease.

Non-uniform distribution of dendritic nonlinearities differentially engages thalamostriatal and corticostriatal inputs onto cholinergic interneurons

The tonic activity of striatal cholinergic interneurons (CINs) is modified differentially by their afferent inputs. Although their unitary synaptic currents are identical, in most CINs cortical inputs onto distal dendrites only weakly entrain them, whereas proximal thalamic inputs trigger abrupt pauses in discharge in response to salient external stimuli. To test whether the dendritic expression of the active conductances that drive autonomous discharge contribute to the CINs’ capacity to dissociate cortical from thalamic inputs, we used an optogenetics-based method to quantify dendritic excitability in mouse CINs. We found that the persistent sodium (NaP) current gave rise to dendritic boosting, and that the hyperpolarization-activated cyclic nucleotide-gated (HCN) current gave rise to a subhertz membrane resonance. This resonance may underlie our novel finding of an association between CIN pauses and internally-generated slow wave events in sleeping non-human primates. Moreover, our method indicated that dendritic NaP and HCN currents were preferentially expressed in proximal dendrites. We validated the non-uniform distribution of NaP currents: pharmacologically; with two-photon imaging of dendritic back-propagating action potentials; and by demonstrating boosting of thalamic, but not cortical, inputs by NaP currents. Thus, the localization of active dendritic conductances in CIN dendrites mirrors the spatial distribution of afferent terminals and may promote their differential responses to thalamic vs. cortical inputs.

A tonic nicotinic brake controls spike timing in striatal spiny projection neurons

Striatal spiny projection neurons (SPNs) transform convergent excitatory corticostriatal inputs into an inhibitory signal that shapes basal ganglia output. This process is fine-tuned by striatal GABAergic interneurons (GINs), which receive overlapping cortical inputs and mediate rapid corticostriatal feedforward inhibition of SPNs. Adding another level of control, cholinergic interneurons (CINs), which are also vigorously activated by corticostriatal excitation, can disynaptically inhibit SPNs by activating α4β2 nicotinic acetylcholine receptors (nAChRs) on various GINs. Measurements of this disynaptic inhibitory pathway, however, indicate that it is too slow to compete with direct GIN-mediated feedforward inhibition. Moreover, functional nAChRs are also present on populations of GINs that respond only weakly to phasic activation of CINs, such as parvalbumin-positive fast-spiking interneurons (PV-FSIs), making the overall role of nAChRs in shaping striatal synaptic integration unclear. Using acute striatal slices from mice we show that upon synchronous optogenetic activation of corticostriatal projections blockade of α4β2 nAChRs shortened SPN spike latencies and increased postsynaptic depolarizations. The nAChR-dependent inhibition was mediated by downstream GABA release, and data suggest that the GABA source was not limited to GINs that respond strongly to phasic CIN activation. In particular, the observed decrease in spike latency caused by nAChR blockade was associated with a diminished frequency of spontaneous inhibitory postsynaptic currents in SPNs, a parallel hyperpolarization of PV-FSIs, and was occluded by pharmacologically preventing cortical activation of PV-FSIs. Taken together, we describe a role for tonic (as opposed to phasic) activation of nAChRs in striatal function. We conclude that tonic activation of nAChRs by CINs maintains a GABAergic brake on cortically-driven striatal output by ‘priming’ feedforward inhibition, a process that may shape SPN spike timing, striatal processing, and synaptic plasticity.

Low-rate firing limit for neurons with axon, soma and dendrites driven by spatially distributed stochastic synapses

Analytical forms for neuronal firing rates are important theoretical tools for the analysis of network states. Since the 1960s, the majority of approaches have treated neurons as being electrically compact and therefore isopotential. These approaches have yielded considerable insight into how single-cell properties affect network activity; however, many neuronal classes, such as cortical pyramidal cells, are electrically extended objects. Calculation of the complex flow of electrical activity driven by stochastic spatio-temporal synaptic input streams in these structures has presented a significant analytical challenge. Here we demonstrate that an extension of the level-crossing method of Rice, previously used for compact cells, provides a general framework for approximating the firing rate of neurons with spatial structure. Even for simple models, the analytical approximations derived demonstrate a surprising richness including: independence of the firing rate to the electrotonic length for certain models, but with a form distinct to the point-like leaky integrate-and-fire model; a non-monotonic dependence of the firing rate on the number of dendrites receiving synaptic drive; a significant effect of the axonal and somatic load on the firing rate; and the role that the trigger position on the axon for spike initiation has on firing properties. The approach necessitates only calculating the mean and variances of the non-thresholded voltage and its rate of change in neuronal structures subject to spatio-temporal synaptic fluctuations. The combination of simplicity and generality promises a framework that can be built upon to incorporate increasing levels of biophysical detail and extend beyond the low-rate firing limit treated in this paper.

Indirect pathway control of firing rate and pattern in the substantia nigra pars reticulata

Unitary pallido-nigral synaptic currents were measured using optogenetic stimulation, which activated up to three unitary synaptic inputs to each substantia nigra pars reticulata (SNr) cell. Episodic barrages of synaptic conductances were generated based on in vivo firing patterns of globus pallidus pars externa (GPe) cells and applied to SNr cells using conductance clamp. Barrage inputs were compared to continuous step conductances with the same mean. Barrage inputs and steps both slowed SNr neuron firing and produced disinhibition responses seen in peristimulus histograms. Barrages were less effective than steps at producing inhibition and disinhibition responses. Barrages, but not steps, produced irregular firing during the inhibitory response. Phase models of SNr neurons were constructed from their phase-resetting curves. The phase models reproduced the inhibition and disinhibition responses to the same inputs applied to the neurons. The disinhibition response did not require rebound currents but arose from reset of the cells' oscillation. The differences in firing rate and irregularity in response to barrage and step inhibition resulted from the high sensitivity of SNr neurons to inhibition at late phases in their intrinsic oscillation. During step inhibition, cells continued rhythmic firing at a reduced rate. During barrages, brief bouts of intense inhibition stalled the cells' phase evolution late in their cycle, close to firing, and even very brief respites from inhibition rapidly released single action potentials. The SNr cell firing pattern reflected the fine structure of the synaptic barrage from GPe, as well as its onset and offset.NEW & NOTEWORTHY The pallido-nigral pathway connects the striatum to spontaneously active basal ganglia output neurons in the substantia nigra. Each substantia nigra neuron receives powerful inhibitory synaptic connections from a small group of globus pallidus cells and may fire during pauses in pallidal activity. Despite lacking any hyperpolarization-activated rebound currents, they fire quickly to even brief pauses in the pallido-nigral inhibition. The mechanism of their rapid disinhibitory response is explained by features of their phase-resetting curves.

Frequency-dependent entrainment of striatal fast-spiking interneurons

Striatal fast-spiking interneurons (FSIs) fire in variable-length runs of action potentials at 20-200 spikes/s separated by pauses. In vivo, or with fluctuating applied current, both runs and pauses become briefer and more variable. During runs, spikes are entrained specifically to gamma-frequency components of the input fluctuations. We stimulated parvalbumin-expressing striatal FSIs in mouse brain slices with broadband noise currents added to direct current steps and measured spike entrainment across all frequencies. As the constant current level was increased, FSIs produced longer runs and showed sharper frequency tuning, with best entrainment at the stimulus frequency matching their intrarun firing rate. We separated the contributions of previous spikes from that of the fluctuating stimulus, revealing a strong contribution of previous action potentials to gamma-frequency entrainment. In contrast, after subtraction of the effect inherited from the previous spike, the remaining stimulus contribution to spike generation was less sharply tuned, showing a larger contribution of lower frequencies. The frequency specificity of entrainment within a run was reproduced with a phase resetting model based on experimentally measured phase resetting curves of the same FSIs. In the model, broadly tuned phase entrainment for the first spike in a run evolved into sharply tuned gamma entrainment over the next few spikes. The data and modeling results indicate that for FSIs firing in brief runs and pauses firing within runs is entrained by gamma-frequency components of the input, whereas the onset timing of runs may be sensitive to a wider range of stimulus frequency components.NEW & NOTEWORTHY Specific types of neurons entrain their spikes to particular oscillation frequencies in their synaptic input. This entrainment is commonly understood in terms of the subthreshold voltage response, but how this translates to spiking is not clear. We show that in striatal fast-spiking interneurons, entrainment to gamma-frequency input depends on rhythmic spike runs and is explained by the phase resetting curve, whereas run initiation can be triggered by a broad range of input frequencies.