Morales JC, Higgs MH, Song SC and Wilson CJ (2020) Broadband Entrainment of Striatal Low-Threshold Spike Interneurons. Front. Neural Circuits 14:36. doi: 10.3389/fncir.2020.00036

Striatal interneurons and projection neurons are differentially tuned to spectral components of synaptic input signals, and this is especially apparent in their responses to oscillations.  The broad frequency tuning of spike responses in somatostatin/NPY-expressing low threshold spike (LTS) interneurons sets them apart from other GABAergic interneurons in the striatum as well as from the spiny projection (SP) neurons.  The mechanism of LTS interneuron spiking resonance was unrelated to its membrane impedance resonance; abolition of membrane impedance resonance did not alter the spiking resonance.  A comparison of the phase resetting curves (PRCs) and spiking resonance profiles of LTS interneurons and SP neurons revealed a relationship between the frequency sensitivity of the neurons and the spectral components of their infinitesimal PRCs.  Sine wave input currents could control spike timing in SP neurons and LTS interneurons only to the extent that their PRCs contained Fourier modes of corresponding frequency. LTS interneurons’ PRCs contain larger high-frequency components, endowing the neurons with enhanced responses to input frequencies faster than the cells’ autonomous firing rates.  This enables the LTS cells to be entrained by frequency components of the input signal to which SP neurons are less responsive. In addition to its effects on firing rate, striatal feedforward inhibition by LTS interneurons may regulate the entrainment of SP neurons by oscillatory afferents.

Figure 1.  Identification of striatal neurons.  A.  Panoramic view of the striatum in sagittal section in the NPY-GFP mouse.  Most cells are LTS interneurons, but there are a few neurogliaform (NGF) cells, which are brighter (arrows).  B.  A NGF cell at higher magnification, characterized by many primary dendrites that branch frequently.  C. An LTS interneuron, with fewer and straighter dendrites. D. Responses of NGF cells to hyperpolarizing and depolarizing current pulses.  Note stable hyperpolarized membrane potential in the absence of current.  E.  An LTS interneuron, with continuous autonomous firing in the absence of current, and a prominent rebound burst at the offset of a hyperpolarizing current pulse. F. A spiny neuron, with characteristic long delay to first spike in response to depolarizing currents.  G. Repetitive firing of an LTS interneuron in the absence of injected current (blue) an a SP neuron, firing repetitively (black) when depolarized to approximately match the firing rate of an LTS interneuron. H. The interspike membrane potential trajectory of the same LTS interneuron (blue) and SP neuron (black) shown in G.  SP neurons show separate fast and slow afterhyperpolarizations, whereas LTS interneurons have a single afterhyperpolarization.

Figure 2.  Measurement of spiking resonance.  A.  An example 1 second of the injected current (top), bandpass filtered components of the same current centered on different frequencies, and the resulting voltage waveform and perturbed spiking in a striatal LTS interneuron.  The spike times are indicated with dotted lines crossing the filtered current waveforms.  B. Measurement of spike phases on the filtered waveform.  Phase was measured between positive slope zero crossings.  C.  The summation of phase measurements from many action potentials as a vector sum.  The resultant vector in red, points in the direction of the average phase, and its length is the vector strength.  D. A spectrum of vector strength measurements from an example LTS interneuron taken for a range of bandpass center frequencies.  The frequency producing the peak resonance, fpeak, and the half width of the spectrum (bandwidth) were measured as shown using the half-height taken between the maximum and minimum vector strengths.

Figure 3.  Comparison of spiking resonance in SP neurons and LTS interneurons.  A. An example spiking resonance spectrum from an SP neuron.  The cell’s firing rate is indicated by the dotted line.  B.  An example LTS interneuron shown the same way.  C. Superimposed spiking resonance spectra (gray) and the average spiking resonance (black) for 18 SP neurons. D. Superimposed individual spectra (gray) and average spectrum (blue) for 18 LTS interneurons.  Error bars are standard errors of the mean at each frequency.  The dotted lines indicate the average firing rates for the two groups of cells. E. LTS interneurons showed a higher vector strength overall than SP neurons.  F. The frequency at the peak resonance was higher in LTS interneurons. G. The difference between the firing rate and peak frequency for each cell was greater in LTS interneurons. H. The bandwidth of resonance (measured as shown in Figure 2) was greater in LTS interneurons.

Figure 4.  Lack of effect of Cav2 channel blockade on spiking resonance in LTS interneurons.  A. Current waveform, membrane potential, and firing pattern for an example LTS interneuron.  B.  The same example neuron after treatment with 1 µM ω-conotoxin GVIA. C.  Spiking resonance spectra for an example LTS interneuron before (blue) and after (red) conotoxin treatment.  D.  Superimposed spectra for all cells before (light blue) and after (light red) conotoxin treatment, and the mean spectra.  Error bars are standard errors of the mean. E. Difference spectra for each cell before and after conotoxin treatment (light blue) and the mean difference spectrum.  There was no significant frequency trend for the difference spectra F=0.68, df = 8,21, p=0.85).

Figure 5. Comparison of SP neuron and LTS interneuron entrainment by injected sinusoidal currents of frequencies between 1 and 25 Hz. A. Low-frequency (1 Hz) sine wave stimulation produced firing rate modulation in both cell types, with neurons firing throughout the positive phase of the stimulus but with little spike time reliability.  Example traces for one cycle of the stimulus are shown on the left, and a histogram of spike phases on the stimulus is shown on the right.  The peak of the sine wave is phase 0.25, and the trough is phase 0.75.  The degree of entrainment is measured as the entropy of the histogram, with low entropies meaning better entrainment.  B.  Sinusoidal current waveforms at a frequency near the cells’ unperturbed firing rates (about 10 Hz in both cells) evoke 1:1 entrainment of firing at a reliable phase of the stimulus in both cell types. C. At frequencies higher than the cell’s firing rate, 1:1 entrainment failed, but LTS interneurons continued to be more entrained than SP neurons, whose spike times were almost completely unrelated to the stimulus sine wave.  D. Entrainment spectra for the example neurons used in A-C.  Entrainment was better in the LTS interneuron at all frequencies except for those close to the cells’ unperturbed firing rates.  The difference is especially clear at frequencies near 1.5 times the cells’ rates, at which the SP neuron showed almost no entrainment.  The expected entropy for zero entrainment is indicated by the dotted line. E. The sine wave frequency producing peak entrainment (Fsine) was close to the cells’ unperturbed firing rate (Fcell) in both cell types. One exception is an LTS interneuron that had slightly stronger entrainment at twice the unperturbed firing rate.  F.  Mean entrainment profile for a sample of 6 LTS interneurons and 7 SP neurons.  Fsine is plotted as a proportion of Fcell. Note the absence of any second entrainment peak corresponding to the membrane impedance resonance.  Compared to SP neurons, LTS neurons are much less frequency-selective, showing substantial entrainment over the entire frequency range.

Figure 6.  Comparison of PRCs of SP neurons and LTS interneurons. A.  Two example LTS interneuron PRCs. B. The mean PRC for the sample of 18 LTS interneurons.  Error bars are standard errors of the means. C.  Examples PRCs from two SP neurons.  D.  Mean PRC for the group of SP neurons. The consistent differences in shape include the more pronounced skew in the LTS interneuron PRC and its broader late peak.  SP neurons’ PRCs were more symmetrical, except for a very narrow late peak, only one or two bins wide, at the end of the ISI. E.  Amplitudes of the Fourier modes of the PRCs of LTS interneurons and SP neurons.  25 modes are shown, calculated from the 50 points in the PRC.  Mode 0 is the DC component, which is the average amplitude of the PRC. The differences between cell types are confined to the first 10 modes.  F. Modes 0-9 of the average LTS interneuron PRC. G. Modes 0-9 of the average SP neuron PRC.  H.  Mean LTS interneuron PRC, assembled from the modes shown In F.  Points shown are the original mean PRC.  I.  SP neuron average PRC (points) and PRC reassembled from modes shown in G (red line).

Figure 7.  The responses of phase neurons. A. Response to a brief current pulse.  Charge delivered by a current pulse (top) causes a phase shift in a noise-free neuron, whose phase otherwise advances at a constant rate Fcell. The cell fires when its phase reaches a value of 1. The depolarizing pulse produces a change in spike time. The size of the phase shift and the change in the spike time are determined by the value of the phase resetting curve at the time of the stimulus.  The expected evolution of phase over time in the absence of any perturbation is indicated by the dotted line. B.  Pulsed noise, like that used to measure spiking resonance, produces a sequence of phase shifts.  Each pulse arrives at a phase determined by the entire sequence of preceding pulses. Pulses arriving at phases near the peak of the PRC are more influential than others, but the time of firing is determined by the entire waveform of input current.   C. Sinusoidal current produces a smoothly accumulating change in the evolution of phase.  A sine wave stimulus can advance or delay the next action potential, depending on the phase of the stimulus relative to each spike.

Figure 8. Sinusoidal entrainment in phase models of the LTS interneuron (in blue) and the SP neuron (in black and gray).  A. Entrainment spectra from 1 to 50 Hz for the phase model LTS interneuron (blue) and the SP neuron (black) using a phase model with all modes present.  To test for the influence of the DC component mode 0, the SP neuron PRC was shifted to have the same mode 0 as the LTS interneuron, and the spectrum for that version of the SP neuron model is shown in gray.  This mode 0 equalization brought the entrainment spectra mostly into alignment for frequencies at and below the cells’ unperturbed rate (15 spikes/s).  The entrainment at higher frequencies continued to be different, with the SP neuron showing consistently higher entropy (less entrainment).  The amplitudes of the first 10 modes in both PRCs are shown at right, including the shift in mode zero between the measured value for SP neurons (black) , LTS neurons (blue) and the mode 0-equalized SP neuron (gray).  The PRCs used in these simulations are shown at lower right in A.  B. The effect of equalizing mode 0 as above, and removing all modes higher than mode 1, which corresponds to the cell’s firing rate.  At right are shown the amplitudes of modes and the synthetic PRCs (lines) superimposed on the original PRCs (points). The only difference between PRCs is the difference in amplitude and phase of mode 1. The cell type difference in entrainment at high frequencies is absent, except for a small range of frequencies near the cells’ firing rate.  C. The same comparison except including differences in modes 1 and 2. The secondary (1:2) entrainment at twice the cells’ frequencies is returned and the difference in entrainment in that frequency range is restored. D.  Restoring modes 1 through 3 reproduces most of the original differences in high-frequency entrainment between the cell types.

Figure 9.  Spiking resonance for broadband input in the phase model. For each of the 18 LTS interneurons and 18 SP neurons, the experimental PRC and unperturbed firing rate were used to generate spike trains in response to pulsed noise stimuli like those used to measure spiking resonance in the real cells.  A. An example spiking resonance spectrum from a phase model based on a SP neuron.  The cell’s firing rate is indicated by the dotted line.  B.  An example phase model LTS interneuron shown the same way.  C. Superimposed spiking resonance spectra (gray) and the average spiking resonance (black) for 18 SP phase model neurons. D. Superimposed individual spectra (gray) and average spectrum (blue) for phase models based on all 18 LTS interneurons.  Error bars are standard errors of the mean at each frequency.  The dotted lines indicate the average firing rates for the two groups of cells. E. Model LTS interneurons showed a higher vector strength overall than model SP neurons.  F. The frequency at the peak resonance was higher in model LTS interneurons. G. The difference between the firing rate and peak frequency for each cell was greater in model LTS interneurons. H. The bandwidth of resonance (measured as shown in Figure 2) was greater in model LTS interneurons.  

Discussion
    The input to striatal neurons from the cortex and other areas contains oscillatory components, and cells in the striatum often fire in a consistent phase relationship with that input (Courtemanche et al. 2003; Leventhal et al. 2012; Howe et al. 2011; Kalenscher et al. 2010). Phase-locking depends on cell type, with fast-spiking interneurons usually locking to high or low parts of the gamma frequency range, and SP neurons usually related to lower frequencies (Berke et al. 2004; Matthijs and Redish 2009; Sharott et al. 2009).  The frequency selectivity of each interneuron type may be a key to its circuit function, at least in the feed-forward configuration in which interneurons and principal cells receive the same input.  In that case, inhibition may reduce the response of principal cells to specific frequency components in the shared input, but not others.
    The usefulness of frequency-based measurements is not restricted to understanding responses to periodic inputs. All realizable input waveforms, even noise, can be decomposed into sine wave components.  If cells have a greater sensitivity to some frequencies than others, their responses to complex input waveforms are colored by that sensitivity.  The frequency sensitivity of neurons is also a measure of how fast they respond to changes in the stimulus.  Cells that can entrain to very high frequencies respond strongly and quickly to brief stimuli or abrupt changes in input.  

The origin of frequency selectivity
    The frequency selectivity of spike generation that can be predicted from the PRC is of course not the only cellular process imposing frequency selectivity on neuron interactions in the striatal circuit.  The frequency content of the input spike train, synaptic onset and decay dynamics, dendritic filtering of synaptic input and frequency dependent short term synaptic plasticity determine the frequency content of the current delivered to the spike generation mechanism.  In our experiments, a broad range of frequencies were present and equally represented.  In the real circuits, some frequencies will be represented more than others.
    What determines the frequency selectivity of a neuron’s spiking response?  Striatal SP cells have no subthreshold membrane resonance that could contribute to spiking resonance. Their spiking resonance and entrainment are the consequence of spike-triggered currents.   Striatal LTS interneurons do have a membrane impedance resonance, but our results here show no influence of it on spiking resonance or entrainment when the cells are firing repetitively.  Why does it not influence spiking?  One possibility is that the membrane resonance of LTS neurons is engaged only at more depolarized membrane potentials.  The calcium mechanism discovered by Song et al. (2106) to underly membrane impedance resonance is engaged by ion channels that are not normally activated at subthreshold membrane potentials, but rather by action potentials.  It is possible that membrane resonance could be influential in resumption of firing after the cells' autonomous  firing pattern has been blocked, for example in the persistent depolarized state (Song et al. 2016). This function would be more consistent with known instances of spike patterning by membrane impedance resonance, in which firing is triggered on peaks of a noisy input applied to a cell near, but below the threshold for repetitive firing (e.g. Kispersky et al. 2012). In contrast, during repetitive firing, the responses of the non-resonant SP neuron and the resonant LTS interneuron could both be predicted using a phase-resetting model that includes no subthreshold dynamics.  The differences between the two cell types were the results of differences in the sizes and shapes of their PRCs.
    Of course, not all neurons in vivo are firing repetitively at any one time. In the basal ganglia there are several cell types that fire repetitively most or all of the time, because their firing is driven autonomously.  Neurons in the output nuclei, the GPi and SNr, are all autonomously active, as are the neurons in the middle layer of cells, the subthalamic nucleus and GPe (Surmeier et al. 2005; Wilson 2015).  In the striatum, the somatostatin positive LTS interneurons are autonomously active (Beatty et al. 2012), as are the cholinergic interneurons (Bennett and Wilson 1999) and a class of burst-firing GABAergic interneurons (Assous et al. 2018).  Other cells, including the SP neurons and fast-spiking interneurons, are not autonomously active but fire repetitively in brief episodes in response to stimuli or during movements.  During those responses, firing rates transiently go well into the frequencies at which the cells must be firing repetitively (e.g. Kimura 1990). When firing repetitively, even for brief periods, it is possible to characterize the change in spiking driven by any input using the phase resetting method (Wilson 2017; Higgs and Wilson 2019). The phase model of the neuron is not completely general and it is possible to force a repetitively firing neuron out of the range of its applicability (Kogh-Madsen et al. 2012).  A host of experimental and environmental conditions might alter repetitive firing and the phase resetting process. The most obvious example would be an input that abolishes repetitive firing altogether.  Neurons must be depolarized above rheobase to satisfy the assumptions of the phase model.  However, it is not required that neurons fire rhythmically.  A neuron that would fire rhythmically in the absence of perturbing stimuli but is densely perturbed by inputs and so fires irregularly may still be predicable by phase methods (Wilson et al. 2014).
    In the phase resetting formulation, the unique properties of each neuron are encapsulated in its PRC. The results presented here show that differences in PRC shape can contribute to the characteristic frequency sensitivity differences between neurons.  PRCs come in a variety of shapes, and there are a variety of ways to parameterize their shapes.  Fourier components are not fundamentally better than any other method, but they are best suited for describing the responses to sinusoidal inputs or sinusoidal components of complex inputs (Goldberg et al. 2013). The results reported here show that the first few modes of the PRC are directly responsible for frequency sensitivity differences between LTS interneurons and SP neurons.  For a neuron to respond to input frequencies higher than its own firing rate, its PRC must contain correspondingly high frequency components.

Frequency-selective feed-forward inhibition
    Striatal LTS interneurons provide feed-forward inhibition to the SP neurons, which are the striatal output cells.  There is no recurrent excitation of interneurons by SP neurons, which are themselves GABAergic and inhibitory.  SP neurons’ narrow frequency sensitivities are centered on their individual firing rates, and thus are easily tuned by rate (Wilson 2017).  At any one moment, there are SP neurons firing at a wide variety of rates, and so there are cells poised to respond differentially to a variety of frequency components in the synaptic input.  SP neurons are also very numerous, so fragmenting the frequency sensitivities among the population of SP neurons by firing rate does not cause a great loss of representational capacity.  LTS interneurons, on the other hand, are outnumbered by SP neurons by a factor of 100 or more (Tepper et al. 2010), and single LTS interneurons provide feed-forward inhibition to many SP neurons. The ability of LTS neurons to phase-lock to a wide range of frequencies may allow them to provide phase-locked inhibition to the much more numerous SP neurons across the entire frequency range.
    Compared to SP neurons, LTS interneurons are more sensitive to synaptic input, as indicated by the overall larger amplitude of their PRCs, and their firing is more phase-locked to periodic inputs at frequencies higher than their own firing rate as indicated by the higher magnitudes of their PRC modes above mode 1.  The only exception to the LTS interneurons superiority is the SP neuron’s phase-locking to input frequencies near its own firing rate.  The LTS interneuron is positioned to disrupt phase-locked firing in the SP neuron, by providing an inhibitory signal in phase with periodic excitatory inputs shared by both cell types.  Because of its broadband response, the LTS neuron’s firing is most entrained by the largest-amplitude periodic signal in the input, and its inhibition of entrainment of SP neurons will be most effective for that frequency.  This inhibition could further suppress the entrainment of SP neurons whose firing rates differ from the frequency of the dominant periodic input. Thus, the LTS interneuron could provide a broad surround inhibition to SP neurons, not in space, but in the frequency domain.