## Abstract

Many lines of theoretical and experimental investigation have suggested that gamma oscillations provide a temporal framework for cortical information processing, acting to either synchronize neuronal firing, restrict neuron's relative spike times, and/or provide a global reference signal to which neurons encode input strength. Each theory has been disputed and some believe that gamma is an epiphenomenon. We investigated the biophysical plausibility of these theories by performing in vitro whole-cell recordings from 6 cortical neuron subtypes and examining how gamma-band and slow fluctuations in injected input affect precision and phase of spike timing. We find that gamma is at least partially able to restrict the spike timing in all subtypes tested, but to varying degrees. Gamma exerts more precise control of spike timing in pyramidal neurons involved in cortico-cortical versus cortico-subcortical communication and in inhibitory neurons that target somatic versus dendritic compartments. We also find that relatively few subtypes are capable of phase-based information coding. Using simple neuron models and dynamic clamp, we determine which intrinsic differences lead to these variations in responsiveness and discuss both the flexibility and confounds of gamma-based spike-timing systems.

## Introduction

Cortical network function emerges from interactions among diverse neuron types. One window into these interactions is the rhythmic or oscillatory signal they generate: Various cortical rhythms are associated with different cognitive, behavioral, or motivational states, are generated through different intrinsic and circuit mechanisms, and likely reflect different types of cell–cell or cell–network interactions. It is therefore of interest to understand precisely what types of interactions these rhythms reflect, and the mechanistic relationship (if any) between their presence or absence and the cognitive functions with which they are associated.

Oscillatory activity in the gamma (Y) band (30–80 Hz) is of particular interest, both because of its clear association with processing of salient, task-relevant, attended, or otherwise cognitively engaging stimuli [reviewed in Womelsdorf and Fries (2007); Berens et al. (2008)] and because of its frequent disruption in diseases of cognition or attention, most notably schizophrenia [reviewed in Lewis et al. (2011)]. This rhythm has been proposed to serve numerous roles in circuit function, many of which rely on its ability to provide a framework for temporally organizing activity (Singer and Gray 1995; Varela et al. 2001). Among these, it has been proposed to implement network-level amplification or routing, by synchronizing neurons' spiking to facilitate coincidence detection in their targets (Salinas and Sejnowski 2000, 2001; Womelsdorf et al. 2007), to facilitate learning, by restricting neurons' relative spike times to those optimal for inducing spike-timing-dependent plasticity (Masquelier et al. 2009), to underlie a winner-take-all selection scheme, where earlier firing neurons recruit widespread inhibition that blocks other neurons' firing for the duration of the oscillation (Buzsaki and Draguhn 2004; Börgers and Kopell 2008; Fries 2009), to provide the carrier wave for a phase code, in which information is carried in neurons' phase of firing with respect to the oscillation (Fries 2009; Tiesinga and Sejnowski 2011; Vinck et al. 2011) as well as to be an epiphenomenon (Wilson and Bower 1992; Jurgens et al. 1995). These hypotheses have vastly different implications for our understanding of cortical operation.

Resolving these possibilities is made more difficult by the complexity of the cortical architecture: Cortex contains numerous types of neuron, which differ in their laminar positioning, local and long-distance connectivity, intrinsic biophysics, sensitivity to neuromodulation, and expression of peptides and calcium-binding proteins [for reviews, see Somogyi et al. (1998); Markram et al. (2004); Haider and McCormick (2009)]. These neurons need not all participate in, or be affected by, oscillatory activity in the same ways. Indeed, in vivo and in vitro recordings have demonstrated that while many neurons' firing is to some extent synchronized with gamma-band oscillations in the local field, neuron types vary in the strength and phase of these relationships (Klausberger et al. 2003; Hasenstaub et al. 2005). These studies have also demonstrated that synchronized, rhythmic inhibition of cells' somata is an intracellular correlate of the extracellularly recorded gamma oscillations (Hasenstaub et al. 2005). This implies that the potential computational roles of these oscillations may be limited by the ability of rhythmic synchronized inhibition to modulate spike timing, in various cell types, in ways consistent with these functional hypotheses—in other words, by the ability of rhythmic inhibition to restrict action potential timing to occur in specific time windows (Fig. 1a), to encode the strength of other inputs in spike phase with respect to the oscillation (Fig. 1b), or both.

Figure 1.

Two requirements for gamma-based spike-timing systems. (a) In order for gamma-band (40 Hz) network oscillations to provide a viable framework for temporally organizing activity, gamma-band oscillatory changes in synaptic drive (red) must at least partly restrict neurons' action potential times (black) to occur within specific windows. (b) In order for gamma oscillations to provide a viable substrate for phase coding, changes in the strengths of neuron's other inputs (blue) must systematically shift its phase of action potential output with respect to the gamma oscillation (red).

Figure 1.

Two requirements for gamma-based spike-timing systems. (a) In order for gamma-band (40 Hz) network oscillations to provide a viable framework for temporally organizing activity, gamma-band oscillatory changes in synaptic drive (red) must at least partly restrict neurons' action potential times (black) to occur within specific windows. (b) In order for gamma oscillations to provide a viable substrate for phase coding, changes in the strengths of neuron's other inputs (blue) must systematically shift its phase of action potential output with respect to the gamma oscillation (red).

To investigate these possibilities, we use intracellular recordings from several types of cortical excitatory and inhibitory neurons to characterize the relationship between gamma-band and slow fluctuations in cells' somatic inputs and the phase and precision of their spike timing. We then use a simple model to predict which intrinsic biophysical differences can account for the observed differences in control of spike timing. Next, we test these predictions in multiple neuron types by using a dynamic clamp to modify these intrinsic properties. Finally, we evaluate additional factors likely to act as confounds to phase-based coding strategies.

## Materials and Methods

### Mouse Lines

All animals use was approved by the Institutional Animal Care and Use Committee at The Salk Institute for Biological Studies. The G42 transgenic mice were originally generated by Josh Huang at Cold Spring Harbor (Lopez-Bendito et al. 2004) and were obtained from Jackson Laboratories (http://www.jax.org). G30 transgenic mice were originally generated by Gabor Szabo at the Department of Functional Neuroanatomy at the Institute of Experimental Medicine in Budapest, Hungary (Chattopadhyaya et al. 2004) and obtained from Sascha Nelson at Brandeis University. GIN transgenic mice were generated in John Swann's Laboratory at the Baylor College of Medicine (Oliva et al. 2000) and obtained from Jackson Laboratories. C57/Bl6J mice were obtained from Jackson Laboratories.

### In Vitro Slice Experiments

To prepare brain slices, mice aged P16–P26 were deeply anesthetized with Nembutal (100 mg/kg i.p.) and rapidly decapitated. A vibratome (Series 1000, Vibratome) was used to cut 300 μm thick coronal brain slices from the somatosensory cortex (S1). Slices were cut in ice-cold artificial cerebral spinal fluid (ACSF; 24 mM NaCl, 5 mM KCl, 26 mM NaHCO3, 1 mM KH2PO4, 1 mM MgSO4, 10 mM glucose, 1.2 mM CaCl2, and 1 mM kynurenic acid) and incubated at 35° C for at least 30 min in ACSF bubbled with 95% O2/5% CO2 before transferring to a room temperature-submerged chamber for recording.

### Whole-Cell Recordings

Neurons were visualized at ×40 magnification using a DIC/fluorescent Olympus microscope and a video camera (VE 1000; MTI-Dage). Multiple cell types were recorded (Fig. 1, Otte et al. 2010). Pyramidal neurons from layer III and V were identified by their laminar location, pyramidal-shaped cell bodies, and long apical dendrite. GFP+ cells from G42, G30, and GIN mice were identified by their fluorescence. Whole-cell recordings were performed using glass pipettes pulled on a P-97 micropipette puller (Sutter Instruments, Novato, CA, USA) from borosilicate glass (Sutter Instruments) to 3–5 MΩ, filled with 130 mM K-gluconate, 0.2 mM EGTA, 2 mM MgCl2, 6 mM KCl, 10 mM HEPES, 2.5 mM Na-ATP, 0.5 mM Na-GTP, and 10 mM K-phosphocreatine (pH 7.2). Signals were amplified with a MultiClamp 700B amplifier (Molecular Devices). Data were acquired and digitized using the Spike2 Power 1401 collection system (Cambridge Electronic Designs, Cambridge, UK). All recordings were performed in a current-clamp mode. Intracellular recordings were accepted if they showed a stable resting membrane potential of below −50 mV throughout the experiment with a standard deviation of <0.9 mV, and had stable-size action potentials with heights at least 60 mV (for pyramidal neurons) or 40 mV (for interneurons).

### Cell Characterization

The membrane time constant and input resistance were evaluated using current pulses sufficient to cause 2–5 mV hyperpolarizations. Afterhyperpolarization (AHP) duration and amplitude were measured from the average of >5 action potentials separated by at least 200 ms. AHP amplitude was measured as the maximum negative voltage deflection relative to spike threshold. AHP duration was measured as the time when mean voltage was 2/3 recovered toward rest. Pyramidal cells were classified by injecting current at threshold to elicit action potentials. Cells were classified as intrinsically bursting (IB) if current injection elicited a complex of decreasing amplitude action potentials that rode upon a slow depolarization envelope and regular spiking (RS) if current injection elicited single action potentials (McCormick 1985).

### Stimulus Protocol

Cells were stimulated with a constant depolarizing current Ibase sufficient to maintain firing at 3–5 Hz. Stimuli (500 ms) consisting of 1 of 10 levels of tonic inhibition (equal intervals, ranging from 0 to Ibase), superimposed on 1 of 10 levels of 40 Hz zero-mean gamma-wave amplitude (equal intervals, ranging from 0 to Ibase), were tested in each block of trials. At least 5 repeats of each trial condition were tested. Step size was adjusted separately for each neuron so that the neuron responded to 30–50% of AC/DC combinations. Only stimulus conditions with moderate to large oscillation amplitudes (defined as amplitudes between 40% and 100% of the largest stimuli tested), which evoked action potentials on at least 50% of the 500-ms blocks, and which evoked at least 5 action potentials across all the blocks, were used for later analysis and shown in display figures.

### Dynamic Clamp

A fast real-time dynamic clamp was implemented using RTLDC (Boston University; [dorval/white 22]) combined with the Real-Time Application Interface (www.rtai.org), device drivers from the COMEDI project (www.comedi.org), and a NI DAQ PCI-MIO-16XE-50 board (National Instruments). Artificial changes in leak conductances were implemented as constant-amplitude conductances with reversal potentials equal to the cell's natural resting potential. Artificial AHPs were implemented as exponential-decay conductances with reversal potentials of −75 mV.

### Model

A single-compartment neuron adaptive exponential integrate-and-fire model was implemented in Matlab (Izhikevich 2003). The model consists of 2 sets of differential equations

$CdVdt=−gL(V−EL)+gLΔTexp⁡(V−VT)ΔT+I−w,τwdwdt=a(V−EL)−w$
and a reset condition
$ifV>20mVthenV→Vrandw→w+b.$
Default values for the model were set as follows: C = 550 pF, EL = −70 mV, VT = −48 mV, ΔT = 2.1 mV, a = 1 nS, b = 550 pA, Vr = −65 mV. The model neurons were stimulated with an Ornstein–Uhlenbeck noise current (Rudolph and Destexhe 2003) with time constant 10 ms, scaled to replicate the small amount of spontaneous membrane potential variability observed in silent slices (voltage standard deviation 0.5 mV). Model neurons were subjected to the same protocol used in real cells: Repeated blocks of 500 ms stimuli consisting of summed random amplitude 40 Hz (AC) and random amplitude DC current, varied in 10 equal steps, step size scaled so that each model cell responded to 30–50% of the AC/DC combinations. After each 500 ms AC/DC combination, the model was reset by setting the voltage (V) and adaptation current (w) to random values between [−65 55] and [15 25], respectively. Each stimulus was presented 8 times. The leak conductance (gL) and the adaptation time constant (τw) were systematically changed as indicated in the results (Fig. 6, middle).

### Data Analysis and Statistics

The first 100 ms of each trial was discarded to avoid carryover from preceding stimulus conditions. Spike times and phases were measured with respect to the peaks (i.e., periods of maximal inhibition) in the ongoing gamma oscillation. For each stimulus type (each AC/DC combination), mean phase and phase jitter were calculated using circular statistics (circular mean and circular standard deviation). Each cell's overall jitter was defined as the median of the jitters across stimulus conditions. To compare the effects of changes in stimulus strength on spike timing, across neurons with different input resistances, all sizes of current stimuli were converted to the voltage change, in millivolts, induced by that amount of DC current. This conversion was calculated from the IV curve for 0–AC stimuli using the 4 smallest stimulus sizes, using only stimuli that did not evoke action potentials. Each cell's tendency to precess in response to changes in DC stimulus strength or AC stimulus size was measured, in ms/mV, from the slope of a two-dimensional polynomial fit of mean spike time versus AC and DC stimulus size. Coding quality was measured by dividing the overall spike time jitter (in ms) by the overall strength of precession (in ms/mV).

Significant differences among timing-related response properties for the 3 pyramidal or the 3 interneuron cell types were determined using a multiple comparison-corrected Kruskal–Wallis nonparametric ANOVA with P = 0.05 (adjusted). Statistical significance of the effect of changing cell-intrinsic properties using a dynamic clamp on response properties was evaluated using Page's trend statistic L, an extension of Spearman's R to multiple subjects. Significance was calculated by comparing the L statistic calculated for the real data with the set of L statistics calculated for 1000 Monte Carlo reassignments. A relationship was considered to be significant at P = 0.05 if the true L was outside the [2.5, 97.5] percentiles of the Ls calculated by random reassignment.

## Results

To evaluate the biophysical plausibility of different potential roles of gamma-band oscillatory inhibition in cortical computation, we measured how 40 Hz oscillatory currents of different amplitudes (AC) affected the precision and timing of action potentials generated from slow depolarizing (DC) potentials of different strengths. Neurons were recorded in a whole-cell current-clamp mode and stimulated with 500 ms current stimuli consisting of varying levels of 40 Hz oscillatory (AC) current superimposed on varying levels of DC current (Fig. 2a). These AC and DC stimuli were varied in equal step sizes, which were scaled for each cell so that the cell responded to 30–50% of the AC/DC combinations. Each stimulus type was presented 6–10 times, and stimuli were randomly interleaved.

Figure 2.

Measuring control of action potential timing by oscillatory inhibition. (a) Neuronal responses (black) to combinations of random amplitude 40-Hz sinusoidal currents (red) and random levels of DC current (blue). (b) Timing (phase and jitter) of spike responses (left, black) with respect to the AC oscillation (left, red) are represented on a best-fit von Mises (circular Gaussian) circular histogram (right) in which both angle and color represent spike phase, histogram height represents spike rate, and color saturation is proportional to the circular standard deviation of action potential times. (c) Systematic decreases in spike time jitter appear as progressively narrower histograms with brighter overlays. (d) Systematic changes in spike phase appear as orderly changes in the orientation and color of the histograms and overlays.

Figure 2.

Measuring control of action potential timing by oscillatory inhibition. (a) Neuronal responses (black) to combinations of random amplitude 40-Hz sinusoidal currents (red) and random levels of DC current (blue). (b) Timing (phase and jitter) of spike responses (left, black) with respect to the AC oscillation (left, red) are represented on a best-fit von Mises (circular Gaussian) circular histogram (right) in which both angle and color represent spike phase, histogram height represents spike rate, and color saturation is proportional to the circular standard deviation of action potential times. (c) Systematic decreases in spike time jitter appear as progressively narrower histograms with brighter overlays. (d) Systematic changes in spike phase appear as orderly changes in the orientation and color of the histograms and overlays.

For each AC/DC combination, the phase at which spikes were generated with respect to the Y oscillation (Fig. 2b, left) is represented on a circular histogram (Fig. 2b, right). Superimposed on each histogram is a best-fit von Mises (circular Gaussian) distribution whose color and saturation indicate the mean and standard deviation (jitter) of the action potential phases. In these plots, decreases in spike time jitter appear as progressively narrower histograms with brighter overlays (Fig. 2c), whereas systematic changes in spike phase (such as precession) appear as orderly changes in the orientation and color of the histograms and overlays (Fig. 2d).

The interacting effects of systematically varying oscillation amplitude and DC stimulus strength can thus be represented by arrays of these circular histograms. An example array, produced from a cortical fast-spiking interneuron, is shown in Figure 3. This neuron's spike response exhibits 2 key features necessary for oscillation-based spike-timing schemes to be viable. First, oscillations in the input markedly restrict the phase at which the neuron fires action potentials: The neuron is more likely to fire as inhibition is withdrawn (phases near π), than to fire when inhibition is maximal (phases near 0). This ability of gamma-band inputs to restrict action potential timing is a broad prerequisite for functions that depend either on synchronizing neurons with respect to one another (e.g., input-specific amplification or routing), on ensuring that neurons fire with specific delays relative to one another (e.g., controlling spike-timing-dependent plasticity or allowing winner-take-all lateral suppression), or that require precise spike timing with respect to a global gamma oscillation (e.g., phase-based coding schemes). Secondly, in this neuron, the phase at which the neuron fires advances systematically as the strength of the slow depolarizing input is increased (left to right), and—equally importantly—the amount of this phase change is substantial compared with the width of the time window in which spikes occur. Substantial phase precession, as observed here, is a prerequisite for schemes that require postsynaptic neurons to “readout” differences in input strengths from differences in action potential time.

Figure 3.

Interactions between tonic excitation, oscillatory inhibition, and action potential phase in a representative fast-spiking interneuron. A circular histogram array depicting the response of an individual fast-spiking interneuron to varying combinations of oscillation amplitude (y-axis) and DC stimulus strength (x-axis). Stimulus combinations that did not evoke action potentials are depicted by gray circles. This neuron's spike response exhibits both key features necessary for gamma-based spike-timing systems to be viable: Input oscillations markedly restrict the phase of the neuron's firing, and the neuron's firing phase systematically advances as the strength of its DC input increases.

Figure 3.

Interactions between tonic excitation, oscillatory inhibition, and action potential phase in a representative fast-spiking interneuron. A circular histogram array depicting the response of an individual fast-spiking interneuron to varying combinations of oscillation amplitude (y-axis) and DC stimulus strength (x-axis). Stimulus combinations that did not evoke action potentials are depicted by gray circles. This neuron's spike response exhibits both key features necessary for gamma-based spike-timing systems to be viable: Input oscillations markedly restrict the phase of the neuron's firing, and the neuron's firing phase systematically advances as the strength of its DC input increases.

Are these response properties universal features of cortical neurons? Cortical circuits contain diverse cell types whose circuit roles are constrained by multiple factors including differences in their long-range and local targets, transmitter content, and electrical properties [reviewed in DeFelipe and Farinas (1992); Kawaguchi (1993); Somogyi et al. (1998); Markram et al. (2004)]. The ability of gamma oscillations to support the different potential functions attributed to them depends on whether and how they affect spike timing in cells of particular types. We therefore evaluated gamma control of spike timing in 3 types of projection neuron (Fig. 4ad: layer 5 bursting, layer 5 RS, and layer 2/3 RS), identified by their laminar location and intrinsic electrical properties, and in 3 types of local circuit interneuron [Fig. 4eh: parvalbumin-positive, cholecystokinin (CCK)-positive, and somatostatin (SST)-positive], identified by GFP expression in transgenic mouse lines (Otte et al. 2010). The physiological properties of GFP-identified cells in the transgenic mouse lines were consistent with those of these neuronal types identified by post-histological examination in WT mice (Xu et al. 2006).

Figure 4.

Example responses of 6 different cortical neuron types. (a) Schematic of laminar location and projection patterns of 3 types of pyramidal neuron. (bd) Response properties of representative layer 5 bursting (b), layer 5 RS (c), and layer 2/3 RS (d) neurons. Top left: voltage responses (black) to DC current step (blue). Top right: Spike time rasters (black) and histograms (dark gray) generated in response to repeated oscillatory inhibition (red). Bottom: circular histogram arrays depicting the response to multiple combinations of oscillation strength and DC stimulus strength. (e) Schematic of morphology and subcellular targets of cortical interneurons from the GIN, G30, and G42 mouse lines that label interneurons that are SST-positive, CCK-positive, and parvalbumin (PV)-positive, respectively. (fh) Response properties of representative GIN/SST (f), G30/CCK (g), and G42/PV (h) neurons. Top left: voltage responses (black) to DC current step (blue). Top right: Spike time rasters (black) and histograms (gray) generated in response to repeated oscillatory inhibition (red). Bottom: circular histogram arrays depicting the response to multiple combinations of oscillation strength and DC stimulus strength.

Figure 4.

Example responses of 6 different cortical neuron types. (a) Schematic of laminar location and projection patterns of 3 types of pyramidal neuron. (bd) Response properties of representative layer 5 bursting (b), layer 5 RS (c), and layer 2/3 RS (d) neurons. Top left: voltage responses (black) to DC current step (blue). Top right: Spike time rasters (black) and histograms (dark gray) generated in response to repeated oscillatory inhibition (red). Bottom: circular histogram arrays depicting the response to multiple combinations of oscillation strength and DC stimulus strength. (e) Schematic of morphology and subcellular targets of cortical interneurons from the GIN, G30, and G42 mouse lines that label interneurons that are SST-positive, CCK-positive, and parvalbumin (PV)-positive, respectively. (fh) Response properties of representative GIN/SST (f), G30/CCK (g), and G42/PV (h) neurons. Top left: voltage responses (black) to DC current step (blue). Top right: Spike time rasters (black) and histograms (gray) generated in response to repeated oscillatory inhibition (red). Bottom: circular histogram arrays depicting the response to multiple combinations of oscillation strength and DC stimulus strength.

Projection neurons were targeted for recording based on the presence of a pyramid-shaped soma and apical dendrite when visualized under DIC microscopy. Based on their laminar location and spiking phenotype, these neurons were separated into 3 classes (layer 2/3, layer 5 bursting, and layer 5 RS) known to correlate with their dendritic anatomy and axonal projection patterns. Sensory cortices typically receive feedforward thalamic inputs on nonpyramidal neurons in layer 4, which project to regular- or adapting-firing pyramidal neurons in layers 2 and 3. These superficial pyramids (L2/3) project to neurons in the deeper layers of cortex (Callaway 1998). Within layer 5, previous work has shown that layer 5 bursting neurons (L5B) possess a large cell body, extensive dendritic arbor, and a thick-tufted apical dendrite, whereas layer 5 regular- or adapting-spiking neurons have smaller, more elongated somata, less-expansive dendritic arbors, and simpler or no tufts; while thick-tufted neurons' long-range projections are primarily to subcortical structures, thin-tufted and nontufted neurons' long-range projections are primarily to other regions of cortex (Mason and Larkman 1990; Larsen et al. 2007). An example recording from a L5B neuron is shown in Figure 4b. In response to DC somatic current injections (top left), this neuron generated repeated bursts of action potentials, while when stimulated with strong oscillatory currents, it exhibited a clear, although moderate, tendency to spike following relief of inhibition (top right). Constructing phase histograms for multiple AC/DC combinations (bottom) reveals that while this phase restriction is preserved (albeit somewhat reduced) for weaker strengths of gamma oscillation, the cell's phase of spiking depends little, if at all, on the strength of excitatory/DC input. In comparison, neurons with regular firing properties, found in layers 2/3 and 5, exhibited much clearer tendencies to spike immediately following relief of inhibition, and often displayed systematic phase precession with increased strength of excitatory input, although the degree of phase precession was small compared with the trial-to-trial variability in spike timing (Fig. 4c,d). These tendencies were preserved across multiple neurons of these 3 types (Fig. 5a). Median spike time jitter was significantly greater in L5B cells (2.5 ± 0.9 ms, n = 9 cells) than in L5R or L2/3 cells (1.6 ± 0.5 ms, n = 10 cells; 1.5 ± 0.3 ms, n = 9 cells; Fig. 5a, top), although all 3 pyramidal cell types showed a strong tendency to decrease response jitter as Y amplitude increased (L5B: −0.5 ± 0.13 ms/mV; L5R: −0.45 ± 0.19 ms/mV; L23: −0.4 ± 0.18 ms/mV). To compare phase precession across neurons with different input resistances, each neuron's average phase advance (in ms/pA) was normalized by its subthreshold input resistance, to calculate the average phase advance caused by the addition of current sufficient to depolarize the neuron by 1 mV. Although more RS cells than IB cells exhibited significant phase precession, the amount of precession exhibited, even in response to substantial changes in mean drive, was small (L5B: 0.04 ± 0.25 ms/mV depolarization, 3 of 9 significant; L5R: 0.16 ± 0.07 ms/mV, n = 7 of 9 significant; L23: 0.11 ± 0.11 ms/mV, n = 5 of 9 significant, Fig. 5a, middle). These phase changes were particularly modest when compared with the degree to which oscillatory inhibition was capable of restricting each cell's spike timing: in these neurons, even 10 mV of depolarization advanced a response phase by much less than a single standard deviation, implying that these neurons would be ill suited to encoding input strength in an action potential phase with respect to a 40-Hz oscillation (“coding quality” L5B: 0.22 ± 0.79 sigma/10 mV depolarization; L5R: 0.79 ± 0.39 sigma/10 mV; L23: 0.66 ± 0.70 sigma/10 mV; Fig. 5a, bottom).

Figure 5.

Oscillatory control of spike timing in 6 cortical neuron types. (a) Spike time jitter (top), DC phase precession (middle), and coding quality (bottom) of n = 9 layer 5 bursting (L5B), n = 10 layer V RS (L5R), and n = 9 layer 2/3 RS (L23) neurons. Significant between-type differences (P = 0.05, multiple comparisons-corrected test) are indicated with asterisks, Jitter: median spike time standard deviation across stimulus conditions, error bars represent 2.5th–97.5th percentiles of observations. Precession: slope of best-fit plane (see Materials and Methods), error bars represent 2.5th–97.5th percentiles of fits. Coding: number of spike time standard deviations of phase advance per mV depolarization (see Materials and Methods), error bars represent 2.5th–97.5th percentiles of fits. (b) Spike time jitter (top), DC phase precession (middle), and coding quality (bottom) of n = 12 GIN/SST neurons, n = 9 G30/CCK neurons, and n = 12 G42/PV neurons. Calculations are as in (a).

Figure 5.

Oscillatory control of spike timing in 6 cortical neuron types. (a) Spike time jitter (top), DC phase precession (middle), and coding quality (bottom) of n = 9 layer 5 bursting (L5B), n = 10 layer V RS (L5R), and n = 9 layer 2/3 RS (L23) neurons. Significant between-type differences (P = 0.05, multiple comparisons-corrected test) are indicated with asterisks, Jitter: median spike time standard deviation across stimulus conditions, error bars represent 2.5th–97.5th percentiles of observations. Precession: slope of best-fit plane (see Materials and Methods), error bars represent 2.5th–97.5th percentiles of fits. Coding: number of spike time standard deviations of phase advance per mV depolarization (see Materials and Methods), error bars represent 2.5th–97.5th percentiles of fits. (b) Spike time jitter (top), DC phase precession (middle), and coding quality (bottom) of n = 12 GIN/SST neurons, n = 9 G30/CCK neurons, and n = 12 G42/PV neurons. Calculations are as in (a).

Specific interneuron subtypes were targeted based on fluorescence in the GIN, G30, and G32 mouse lines. Previous work has shown that GFP+ neurons in the GIN line express SST and are predominantly dendrite-targeting Martinotti cells (Oliva et al. 2000; Xu et al. 2006). In our recordings, consistent with previous work, these neurons generated slower, accommodating trains of action potentials (Fig. 4f, top left) and often exhibited low-threshold spiking behavior. GIN–GFP neurons are heterogeneous in their action potential waveforms, AHPs, and expression of other chemical markers (Halabisky et al. 2006; Xu et al. 2006; Xu and Callaway 2009), but were not further subdivided in this study. Like L5B cells, these neurons generally exhibited relatively weak phase restriction even in response to strong oscillatory input (mean 2.5 ± 0.8 ms, n = 12 cells; Figs 4f and 5b, top) and modest if any phase precession (0.09 ± 0.11 ms/mV, 3 of 12 significant; 0.031 ± 0.033 sigma/10 mV; Fig. 5b, middle).

The G30 line (Fig. 4g) labels several neuron types with various morphologies and firing patterns (Chattopadhyaya et al. 2004). In this study, we restricted our recordings to irregular-firing GFP+ neurons; previous work has demonstrated that these neurons belong to a discrete subnetwork of multipolar, soma-targeting neurons which secrete CCK and express type 1 cannabinoid receptors (Galarreta et al. 2004; Xu and Callaway 2009). Like RS pyramidal neurons, these CCK neurons generally exhibited clear phase restriction (1.3 ± 0.2 ms, n = 9 cells, Fig. 5b, top). These neurons reliably exhibited moderate phase precession (9 of 9 significant, 0.25 ± 0.07 ms/mV, Fig. 5b, middle) that was modest but nonnegligible compared with each cell's typical spike time variability (mean 1.50 ± 0.38 sigma/10 mV, Fig. 5b, bottom).

Finally, the G42 line labels parvalbumin-positive, soma-targeting “basket” interneurons that generate fast, nonadapting trains of action potentials (Lopez-Bendito et al. 2004) and which have been hypothesized to be the key cell type responsible for generating or transmitting gamma-band oscillatory inhibition. Unlike any of the other cell types examined, these neurons' timing was extremely sensitive to gamma-band fluctuations in their input (Fig. 4h): Their response phases were tightly restricted (0.7 ± 0.2 ms, n = 12 neurons, Fig. 5b, top) even when oscillatory inputs were relatively weak, their action potential timing with respect to the input oscillation changed substantially with changes in their DC inputs (12 of 12 significant, 0.6 ± 0.2 ms/mV; Fig. 5b, middle), and the combination of tight action potential timing with substantial phase precession made these neurons uniquely able to convert changes in the level of slow/DC input into clear changes in the response phase (7.10 ± 2.68 sigma/10 mV; Fig. 5b, bottom).

These data suggest that there are strong cell type differences in the ability of oscillatory inhibition to modulate action potential timing. What variations in cellular properties account for these differences? Intuitively, in order for a cell's spike timing to be precisely controlled by fluctuating inhibition, at least the following 2 conditions must be met. First, the high-frequency fluctuations in drive must be transmitted to the site of action potential generation, a process likely to be facilitated in neurons with faster time constants (which display reduced low-pass filtering tendencies compared with neurons with longer time constants). Secondly, this fluctuating inhibition must “out-compete” other sources of temporal structure—for instance AHP or adaptation currents remaining from responses to previous stimuli. This suggests that both brief time constant and rapid AHP kinetics may be prerequisites for a cell's action potential timing to be precisely controlled by gamma-band inhibition. We examined these interactions in a reduced adaptive exponential integrate-and-fire model (Izhikevich 2003), a computationally inexpensive model that is capable of replicating a wide variety of neural firing patterns. In this model, adjusting the leak conductance increases or reduces the neuron's time constant, while adjusting the time constant with which post-depolarization adaptation decays alters the temporal window over which responses to previous stimuli can affect processing during later gamma cycles, allowing us to systematically simulate neurons having a variety of temporal response properties (Fig. 6, left). Consistent with this hypothesis, while speeding time constant or reducing AHP duration produced modest increases in temporal response properties, neither speeding time constant nor reducing AHP alone was sufficient to enable oscillatory inhibition to tightly restrict action potential timing or to subserve phase precession; both together were necessary to enable strong spike-timing control (Fig. 6, middle). To assess these relationships in our experimental data, we compared time constants and AHP durations to jitter, precession, and coding quality for n = 61 neurons (Fig. 6, right). Consistent with the model results, we found that neurons with longer time constants or longer AHPs (typical in L5B and some SST neurons) were quite poorly entrained by the oscillatory inhibition and did not phase precess, whereas neuron types with intermediate time constants (10–15 ms) and intermediate AHP durations (50–100 ms) were capable of somewhat better entrainment and precession, but the combination of narrow AHPs and rapid time constants, which was only observed in fast-spiking interneurons, was necessary to permit substantial timing control.

Figure 6.

Cell-intrinsic properties' contribution to oscillatory control of spike timing. (Left) Response properties of representative model neurons with fast (τ = 3.5 ms, AHP = 17 ms, left) and intermediate (τ = 8.1 ms, AHP = 81 ms, right) membrane properties. Top left: representative voltage responses to DC current step. Bottom left: representative spike time rasters of responses to repeated oscillatory inhibitory stimuli. Right: arrays of spike response histograms to combinations of inhibitory oscillation and depolarizing DC stimulus. (Middle) Plotting median spike-timing jitter (left panel, colored dots), DC phase precession (middle panel, colored dots), or coding quality (right panel, colored dots) versus model neurons' AHP duration (x-axis) and membrane time constant (y-axis) suggests that intrinsic membrane properties interact to determine neurons' timing responses to oscillatory inhibition. (Right) Plotting median spike-timing jitter (left panel, colored dots), DC phase precession (middle panel, colored dots), or coding quality (right panel, colored dots) for n = 61 recorded neurons reveals similar relationships. Each letter/number represents a different recorded neuron as follows: B: layer 5 bursting; 5: layer 5 RS; 2: layer 2/3 RS; a: GIN/SST adapting- or burst-firing interneurons; i: G30/CCK irregular-spiking interneurons; f: G42/PV fast-spiking interneurons.

Figure 6.

Cell-intrinsic properties' contribution to oscillatory control of spike timing. (Left) Response properties of representative model neurons with fast (τ = 3.5 ms, AHP = 17 ms, left) and intermediate (τ = 8.1 ms, AHP = 81 ms, right) membrane properties. Top left: representative voltage responses to DC current step. Bottom left: representative spike time rasters of responses to repeated oscillatory inhibitory stimuli. Right: arrays of spike response histograms to combinations of inhibitory oscillation and depolarizing DC stimulus. (Middle) Plotting median spike-timing jitter (left panel, colored dots), DC phase precession (middle panel, colored dots), or coding quality (right panel, colored dots) versus model neurons' AHP duration (x-axis) and membrane time constant (y-axis) suggests that intrinsic membrane properties interact to determine neurons' timing responses to oscillatory inhibition. (Right) Plotting median spike-timing jitter (left panel, colored dots), DC phase precession (middle panel, colored dots), or coding quality (right panel, colored dots) for n = 61 recorded neurons reveals similar relationships. Each letter/number represents a different recorded neuron as follows: B: layer 5 bursting; 5: layer 5 RS; 2: layer 2/3 RS; a: GIN/SST adapting- or burst-firing interneurons; i: G30/CCK irregular-spiking interneurons; f: G42/PV fast-spiking interneurons.

To confirm these results, we used a dynamic clamp to alter the intrinsic properties of recorded neurons and determined the effects of these manipulations on our 3 measurements of timing control. As predicted, using a dynamic clamp to add even a modest artificial AHP to individual fast-spiking interneurons substantially diminished their ability to represent input strength in output phase (Fig. 7a): even a 70-ms AHP, which is briefer than the AHP observed in any pyramidal neuron tested, substantially decreased average coding quality, from 3.9 ± 1.3 to 1.1 ± 0.5 sigma/5 mV (Fig. 7b). In other words, in neurons with moderate or prolonged AHPs, even the very rapid passive membrane properties of fast-spiking interneurons do not suffice to enable phase precession. Conversely, while using a dynamic clamp to reduce the input resistance, and thus the time constant, of large (gamma-insensitive) pyramidal neurons (Fig. 7c) was sufficient to substantially improve their action potential timing precision (from 2.0 ± 0.8 to 1.1 ± 0.2 ms, Fig. 7d), and to improve their ability to phase precess (from 0.12 ± 0.05 to 0.32 ± 0.04 ms/mV), these improvements in response timing remained sufficient to support at best modest phase coding (maximum phase advance of 1.0 ± 0.2 sigma/5 mV).

Figure 7.

Modifying cell-intrinsic properties with a dynamic clamp alters oscillatory control of spike timing. (a) Using a dynamic clamp to add an artificial AHP (green trace) to a fast-spiking interneuron (black traces) increases its timing jitter and reduces its tendency to phase precess (circular histograms). (b) Across n = 5 fast-spiking interneurons, adding an artificial AHP significantly (P < 0.05, Page's trend test) increased the jitter of action potential timing (left), reduced phase precession (center), and reduced effective temporal coding quality (right). (c) Using a dynamic clamp to add an artificial leak conductance (green trace) to a layer 5 bursting pyramidal neuron effectively decreases the neuron's time constant (black trace) while reducing its timing jitter and increasing its tendency to phase precess (circular histograms). (d) Across n = 5 layer V pyramids, adding an artificial leak conductance significantly (P < 0.05, Page's trend test) decreases the jitter of action potential timing (left), increases phase precession (center), and increases the effective temporal coding quality (right).

Figure 7.

Modifying cell-intrinsic properties with a dynamic clamp alters oscillatory control of spike timing. (a) Using a dynamic clamp to add an artificial AHP (green trace) to a fast-spiking interneuron (black traces) increases its timing jitter and reduces its tendency to phase precess (circular histograms). (b) Across n = 5 fast-spiking interneurons, adding an artificial AHP significantly (P < 0.05, Page's trend test) increased the jitter of action potential timing (left), reduced phase precession (center), and reduced effective temporal coding quality (right). (c) Using a dynamic clamp to add an artificial leak conductance (green trace) to a layer 5 bursting pyramidal neuron effectively decreases the neuron's time constant (black trace) while reducing its timing jitter and increasing its tendency to phase precess (circular histograms). (d) Across n = 5 layer V pyramids, adding an artificial leak conductance significantly (P < 0.05, Page's trend test) decreases the jitter of action potential timing (left), increases phase precession (center), and increases the effective temporal coding quality (right).

A final difficulty may be observed through visual inspection of the phase response grids for typical fast-spiking interneurons (e.g., Fig. 3): There is a strong tendency for response phase to shift systematically with changes in the amplitude of the AC gamma oscillation (top to bottom) that may confound any attempts to readout strength of the DC input (left to right). In other words, spikes may be generated at a particular phase owing to strong DC inputs interacting with a weak AC oscillation, weak DC inputs interacting with a strong AC oscillation, or anything in between (Fig. 8a). While this tendency is most pronounced for fast-spiking interneurons (Fig. 8b), it is significant in many CCK+ interneurons and RS pyramidal neurons as well. Comparing the degree of phase precession with respect to changes in AC and DC strength (Fig. 8c) reveals that, in fact, the neurons whose rapid membrane kinetics allow them to faithfully transform changes in overall input strength into changes in action potential phase are the same neurons whose spike timing is most strongly confounded by small changes in the strength of these ongoing gamma oscillations.

Figure 8.

AC oscillation strength confounds DC phase coding. (a) In an example neuron in which response phase systematically advances as DC input strength is increased (left to right), and response phase also advances as AC oscillation amplitude increases (bottom to top). A given median response phase may result from any one of several AC/DC input combinations (outlined). (b) Phase precession with respect to oscillation amplitude of n = 9 layer 5 bursting (L5B), n = 10 layer V RS (L5R), and n = 9 layer 2/3 RS (L23) neurons (left) and n = 12 GIN/SST neurons, n = 9 G30/CCK neurons, and n = 12 G42/PV neurons (right). Significant between-type differences (P = 0.05, multiple comparisons-corrected Kruskal–Wallis test) are indicated with asterisks. Precession: slope of best-fit plane (see Materials and Methods), error bars represent 2.5th–97.5th percentiles of fits. (c) Cells' ability to exhibit DC phase precession is correlated with their tendency to exhibit AC phase precession.

Figure 8.

AC oscillation strength confounds DC phase coding. (a) In an example neuron in which response phase systematically advances as DC input strength is increased (left to right), and response phase also advances as AC oscillation amplitude increases (bottom to top). A given median response phase may result from any one of several AC/DC input combinations (outlined). (b) Phase precession with respect to oscillation amplitude of n = 9 layer 5 bursting (L5B), n = 10 layer V RS (L5R), and n = 9 layer 2/3 RS (L23) neurons (left) and n = 12 GIN/SST neurons, n = 9 G30/CCK neurons, and n = 12 G42/PV neurons (right). Significant between-type differences (P = 0.05, multiple comparisons-corrected Kruskal–Wallis test) are indicated with asterisks. Precession: slope of best-fit plane (see Materials and Methods), error bars represent 2.5th–97.5th percentiles of fits. (c) Cells' ability to exhibit DC phase precession is correlated with their tendency to exhibit AC phase precession.

## Discussion

Many lines of theoretical and experimental investigation have suggested that gamma oscillations provide a temporal framework for cortical information processing. Here, we investigated the biophysical plausibility of several potential roles of gamma oscillations in cortical function by performing whole-cell recordings from a variety of cortical neuron subtypes and examining how gamma-band and slow fluctuations in cells' somatic inputs interact with control precision and phase of action potential timing in different elements of the cortical microcircuit.

Proposals regarding the potential roles of gamma oscillations in timing cortical activity fall into 2 broad categories. Those in the first category depend only on the ability of oscillatory inhibition to restrict spiking to windows of disinhibition [reviewed in Salinas and Sejnowski (2001)], but do not require specific phase differences between spike firing in neurons with different preferred stimulus properties, or between neurons' firing and the global oscillation. This category includes proposals that gamma oscillations influence network function by synchronizing groups of neurons, and thus either boost the effectiveness of particular neuronal subgroups (Womelsdorf et al. 2007) dynamically route information between multiple pathways (Akam and Kullmann 2010), or support activity-dependent plasticity by restricting spiking to occur within a time window where spike-timing-dependent plasticity is strongest (Minlebaev et al. 2011). We found that gamma oscillations were able to at least partly restrict the phase of action potential generation in all the neuronal types examined, meeting the basic biophysical requisite for all these proposals (Fig. 5). We additionally found that this ability of gamma oscillations to enforce action potential timing differed between cell types, suggesting that oscillatory inhibition may differentially regulate communication between different parts of the cortical circuit. Subcortically projecting pyramidal neurons and dendrite-targeting interneurons' spike timing were relatively weakly related to the phase of the ongoing inhibitory oscillation, whereas cortically projecting pyramidal neurons and soma-targeting interneurons' response timing were relatively well controlled by ongoing inhibition, and parvalbumin-positive fast-spiking interneurons, the neurons most strongly implicated in directly transmitting oscillatory inhibition to other neurons in the local circuit [reviewed in Otte et al. (2010)], were themselves exquisitely sensitive to changes in the timing of their synaptic inputs. However, in all the cell types tested, action potential timing was more tightly restricted during periods when the ongoing gamma oscillation was stronger, suggesting that, during periods of sufficiently intense oscillatory activity, any of these neuron types may participate in gamma-based synchronization.

Proposals in the second category depend not only on the ability of gamma oscillations to restrict neurons' firing to limited time windows, but also require specific phase relationships between different neurons depending on stimulus properties or circuit location. This category includes proposals that more strongly driven neurons fire earlier in the gamma cycle, enabling winner-take-all lateral suppression (Tiesinga et al. 2008; Fries 2009); proposals in which either stimulus representation or learning depend on the order in which neurons fire during a gamma cycle (Delorme 2003; Masquelier et al. 2009); as well as proposals that the phase of action potential firing, with respect to the ongoing gamma oscillation, is the coding scheme by which information is communicated through the cortex (Tiesinga and Sejnowski 2011; Vinck et al. 2011). These proposals have in common 2 requirements: First, that neurons be capable of transforming differences in their inputs into differences in response phase with respect to the global gamma oscillation (phase precession), and secondly, that these differences be visible above the noise. In other words, they require that the oscillatory gamma inhibition be able to restrict action potential phase sufficiently that the amount of difference in response phase, between neurons with different inputs, be large compared with the remaining uncontrolled variability in action potential timing.

We found that many cortical neurons, including nearly all bursting pyramidal neurons and most SST-positive dendrite-targeting interneurons, were unable to perform this transformation at all. However, we found that many RS pyramids, as well as irregular- and fast-spiking inhibitory neurons, were indeed able to transform differences in the strength of their other inputs into differences in firing phase. Surprisingly, we observed this moderate phase precession in RS neurons, despite the fact that these neurons never fired in a one-to-one fashion on each gamma cycle (Coombes and Bressloff 1999; Tiesinga and Sejnowski 2011). However, because even extremely strong gamma oscillations only partially restricted these neurons' response phase, even the phase changes associated with extremely large changes in drive (sufficient to produce 10–20 mV of depolarization) were small compared with the neurons' response jitter. Because stimulus-related membrane potential changes in vivo are often relatively small, these results challenge proposals that suggest that gamma oscillations provide the substrate for phase-based information coding or storage (Buzsaki and Draguhn 2004) in projection neurons. For instance, in the visual system, membrane potential differences between optimal and worst stimuli have been reported to be in the range of 3–5 mV (Lampl et al. 1999; Tan et al. 2011). However, we find that, in a typical layer 5 RS pyramidal neuron, 5 mV of depolarization produces a spike phase advancement of 0.8 ms on average while the average spike time jitter is 1.5 ms (Fig. 5). Indeed, these results are consistent with experimental and theoretical (McLelland and Paulsen 2009) findings that slower (e.g., theta), but not gamma, oscillations provide a viable substrate for phase coding.

Unlike any other neuron type tested, we found that fast-spiking interneurons were capable of responding to changes in inputs with changes in phase that were large compared with their response jitter. However, these are the neurons most strongly implicated as being the direct source of the oscillatory synaptic drive associated with gamma oscillations in the local field. This implies that although pyramidal neurons may not themselves be capable of transforming changes in their input strength into changes in response phase, they may inherit these phase differences from their fast-spiking inhibitory partners. In other words, if inhibitory neurons and pyramidal neurons with similar stimulus preferences are organized into reciprocally connected microcircuits, then on the presentation of an optimal stimulus, pyramidal neurons may be able to take advantage of phase precession in the fast-spiking interneurons, escaping from inhibition and firing earlier than neurons receiving inhibition from less-active, fast-spiking inhibitory populations. However, the significance of any inherited phase precession is complicated by the observation that fast-spiking cells exhibit a strong tendency to shift their response phase with changes in the amplitude of gamma oscillations, as well as with changes in the overall level of synaptic drive. This confounds the ability of any downstream circuit to “readout” stimulus strength by looking at action potential phase.

We found that intrinisc properties, including both the membrane time constant and the kinetics of the AHP conductance, regulate gamma's ability to precisely control spike timing. Model and experimental manipulations suggest that both brief time constant and rapid AHP kinetics are necessary for one-to-one phase-locking and systematic phase shifts (Fig. 7). Changes in leak conductance, as may happen in vivo during barrages of intense synaptic activity, are likely to improve the ability of pyramidal neurons to be synchronized by ongoing gamma oscillations, but may not suffice to permit them to represent input strength through spike timing with respect to the gamma oscillations.

## Conclusion

These studies examine the biophysical plausibility of theories regarding the ability of gamma-band inhibition to regulate the precision and phase of spike output. We found that gamma-band inhibition is able to at least partially restrict the spike output times in all cell types tested; however, gamma exerts more precise control of spike time in pyramidal neurons involved in cortico-cortical versus cortico-subcortical communication and in inhibitory neurons that target somatic versus dendritic compartments. We also found that only the fast-spiking inhibitory cells are capable of an analog representation of stimulus strength as output phase; however, a reliable phase-based coding scheme is complicated by the fact that the output phase represents both the amplitude of the oscillatory input and the amount of drive. These differences in responsiveness between cell types are regulated by intrinsic properties that are actively modulated in vivo by ongoing synaptic activity and neuromodulation, suggesting that the influence of gamma-band inhibition on spike output timing depends not only on the identity of the recipient cells, but also the state of the network.

## Notes

Conflict of Interest: None declared.

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## Author notes

Andrea Hasenstaub and Stephani Otte equally contributed to this work.