Spectral reconstruction of phase response curves reveals the synchronization properties of mouse globus pallidus neurons

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.

Evidence of two modes of spiking evoked in human firing motoneurones by Ia afferent electrical stimulation

Neurone firing behaviour is a result of complex interaction between synaptic inputs and cellular intrinsic properties. Intriguing firing behaviour, delayed spiking, was shown in some neurones, in particular, in cat neocortical neurones and rat pyramidal hippocampal neurones. In contrast, the similar spiking mode was not reported for animal spinal motoneurones. In the present study, an attempt was made to look for possible evidence of delayed spiking in human motoneurones firing within the low-frequency, sub-primary range, characteristic for voluntary muscle contractions and postural tasks. Forty-seven firing motor units (MUs) were analyzed in ten experiments on three muscles (the flexor carpi ulnaris, the tibialis anterior, and the abductor pollicis brevis) in four healthy humans. Single MUs were activated by gentle voluntary muscle contractions. MU peri-stimulus time histograms, durations of inter-spike intervals, and motoneurone excitability changes within a target interspike interval were analyzed. It was found that during testing the firing motoneurone excitability by small, transient excitatory Ia afferent volley, depending firstly on volley timing within a target interspike interval and excitatory volley strength, the same motoneurone displayed either the direct short-latency response (the H-reflex) or the delayed response (with prolonged and variable latency). Thus, the findings, for the first time, provide evidence for a possibility of two modes of spiking in firing motoneurones. Methods of the estimation of delayed responses and their possible functional significance are discussed. It is emphasized that, for understanding of this issue, the integration of data from studies on experimental animals and humans is desirable.

Broadband Entrainment of Striatal Low-Threshold Spike Interneurons

Striatal interneurons and spiny projection (SP) neurons are differentially tuned to spectral components of their input. Previous studies showed that spike responses of somatostatin/NPY-expressing low threshold spike (LTS) interneurons have broad frequency tuning, setting these cells apart from other striatal GABAergic interneurons and SP neurons. We investigated the mechanism of LTS interneuron spiking resonance and its relationship to non-spiking membrane impedance resonance, finding that abolition of impedance resonance did not alter spiking resonance. Because LTS interneurons are pacemakers whose rhythmic firing is perturbed by synaptic input, we tested the hypothesis that their spiking resonance arises from their phase resetting properties. Phase resetting curves (PRCs) were measured in LTS interneurons and SP neurons and used to make phase-oscillator models of both cell types. The models reproduced the broad tuning of LTS interneurons, and the differences from SP neurons. The spectral components of the PRC predicted each cell's sensitivity to corresponding input frequencies. LTS interneuron PRCs contain larger high-frequency components than SP neuron PRCs, providing enhanced responses to input frequencies above the cells' average firing rates. Thus, LTS cells can be entrained by input oscillations to which SP neurons are less responsive. These findings suggest that feedforward inhibition by LTS interneurons may regulate SP neurons' entrainment by oscillatory afferents.

A practical method for estimating coupling functions in complex dynamical systems

A foremost challenge in modern network science is the inverse problem of reconstruction (inference) of coupling equations and network topology from the measurements of the network dynamics. Of particular interest are the methods that can operate on real (empirical) data without interfering with the system. One such earlier attempt (Tokuda et al. 2007 Phys. Rev. Lett. 99, 064101. (doi:10.1103/PhysRevLett.99.064101)) was a method suited for general limit-cycle oscillators, yielding both oscillators' natural frequencies and coupling functions between them (phase equations) from empirically measured time series. The present paper reviews the above method in a way comprehensive to domain-scientists other than physics. It also presents applications of the method to (i) detection of the network connectivity, (ii) inference of the phase sensitivity function, (iii) approximation of the interaction among phase-coherent chaotic oscillators, and (iv) experimental data from a forced Van der Pol electric circuit. This reaffirms the range of applicability of the method for reconstructing coupling functions and makes it accessible to a much wider scientific community. This article is part of the theme issue 'Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences'.

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.

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

The theory of phase oscillators is an essential tool for understanding population dynamics of pacemaking neurons. GABAergic pacemakers in the substantia nigra pars reticulata (SNr), a main basal ganglia (BG) output nucleus, receive inputs from the direct and indirect pathways at distal and proximal regions of their dendritic arbors, respectively. We combine theory, optogenetic stimulation and electrophysiological experiments in acute brain slices to ask how dendritic properties impact the propensity of the various inputs, arriving at different locations along the dendrite, to recruit or entrain SNr pacemakers. By combining cable theory with sinusoidally-modulated optogenetic activation of either proximal somatodendritic regions or the entire somatodendritic arbor of SNr neurons, we construct an analytical model that accurately fits the empirically measured somatic current response to inputs arising from illuminating the soma and various portions of the dendritic field. We show that the extent of the dendritic tree that is illuminated generates measurable and systematic differences in the pacemaker’s phase response curve (PRC), causing a shift in its peak. Finally, we show that the divergent PRCs correctly predict differences in two major features of the collective dynamics of SNr neurons: the fidelity of population responses to sudden step-like changes in inputs; and the phase latency at which SNr neurons are entrained by rhythmic stimulation, which can occur in the BG under both physiological and pathophysiological conditions. Our novel method generates measurable and physiologically meaningful spatial effects, and provides the first empirical demonstration of how the collective responses of SNr pacemakers are determined by the transmission properties of their dendrites. SNr dendrites may serve to delay distal striatal inputs so that they impinge on the spike initiation zone simultaneously with pallidal and subthalamic inputs in order to guarantee a fair competition between the influence of the monosynaptic direct- and polysynaptic indirect pathways.

The substantia nigra pars reticulata (SNr) is a main output nucleus of the basal ganglia (BG), where inputs from the competing direct and indirect pathways converge onto the same neurons. Interestingly, these inputs are differentially distributed with direct and indirect pathway projections arriving at distal and proximal regions of the dendritic arbor, respectively. We employ a novel method combining theory with electrophysiological experiments and optogenetics to study the distinct effects of inputs arriving at different locations along the dendrite. Our approach represents a useful compromise between complexity and reduction in modelling. Our work addresses the question of high fidelity encoding of inputs by networks of neurons in the new context of pacemaking neurons, which are driven to fire by their intrinsic dynamics rather than by a network state. We provide the first empirical demonstration that dendritic delays can introduce latencies in the responses of a population of neurons that are commensurate with synaptic delays, suggesting a new role for SNr dendrites with implications for BG function.

Thinking Outside the Box (and Arrow): Current Themes in Striatal Dysfunction in Movement Disorders

The basal ganglia are an intricately connected assembly of subcortical nuclei, forming the core of an adaptive network connecting cortical and thalamic circuits. For nearly three decades, researchers and medical practitioners have conceptualized how the basal ganglia circuit works, and how its pathology underlies motor disorders such as Parkinson's and Huntington's diseases, using what is often referred to as the "box-and-arrow model": a circuit diagram showing the broad strokes of basal ganglia connectivity and the pathological increases and decreases in the weights of specific connections that occur in disease. While this model still has great utility and has led to groundbreaking strategies to treat motor disorders, our evolving knowledge of basal ganglia function has made it clear that this classic model has several shortcomings that severely limit its predictive and descriptive abilities. In this review, we will focus on the striatum, the main input nucleus of the basal ganglia. We describe recent advances in our understanding of the rich microcircuitry and plastic capabilities of the striatum, factors not captured by the original box-and-arrow model, and provide examples of how such advances inform our current understanding of the circuit pathologies underlying motor disorders.

Measurement of phase resetting curves using optogenetic barrage stimuli

BACKGROUND

The phase resetting curve (PRC) is a primary measure of a rhythmically firing neuron's responses to synaptic input, quantifying the change in phase of the firing oscillation as a function of the input phase. PRCs provide information about whether neurons will synchronize due to synaptic coupling or shared input. However, PRC estimation has been limited to in vitro preparations where stable intracellular recordings can be obtained and background activity is minimal, and new methods are required for in vivo applications.

NEW METHOD

We estimated PRCs using dense optogenetic stimuli and extracellular spike recording. Autonomously firing neurons in substantia nigra pars reticulata (SNr) of Thy1-channelrhodopsin 2 (ChR2) transgenic mice were stimulated with random barrages of light pulses, and PRCs were determined using multiple linear regression.

RESULTS

The PRCs obtained were type-I, showing only phase advances in response to depolarizing input, and generally sloped upward from early to late phases. Secondary PRCs, indicating the effect on the subsequent ISI, showed phase delays primarily for stimuli arriving at late phases. Phase models constructed from the optogenetic PRCs accounted for a large fraction of the variance in ISI length and provided a good approximation of the spike-triggered average stimulus.

COMPARISON WITH EXISTING METHODS

Compared to methods based on intracellular current injection, the new method sacrifices some temporal resolution. However, it should be much more widely applicable in vivo, because only extracellular recording and optogenetic stimulation are required.

CONCLUSIONS

These results demonstrate PRC estimation using methods suitable for in vivo applications.

Sparse pallidal connections shape synchrony in a network model of the basal ganglia

Neural synchrony in the basal ganglia, especially in the beta frequency band (13-30 Hz), is a hallmark of Parkinson's disease and considered as antikinetic. In contrast, the healthy basal ganglia show low levels of synchrony. It is currently unknown where synchrony and oscillations arise in the parkinsonian brain and how they are transmitted through the basal ganglia, as well as what makes them dependent on dopamine. The external part of the globus pallidus has recently been identified as a hub nucleus in the basal ganglia, possessing intrinsic inhibitory connections and possibly also gap junctions. In this study, we show that in a conductance-based network model of the basal ganglia, the combination of sparse, high-conductance inhibitory synapses and sparse, low-conductance gap junctions in the external part of the globus pallidus could effectively desynchronize the whole network. However, when gap junction coupling became strong enough, the effect was impeded and activity synchronized. In particular, sustained periods of beta coherence occurred between some neuron pairs. As gap junctions can change their conductance with the dopamine level, we suggest pallidal gap junction coupling as a mechanism contributing to the development of beta synchrony in the parkinsonian basal ganglia.