INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION CONCLUSIONS REFERENCES

The ability to identify neuronal types is of fundamental importance to developing a cellular and network level understanding of the operations of the cerebral cortex. Cortical neurons can be identified by any of a wide variety of characteristics including laminar location, dendritic and axonal morphology, neurotransmitter content and receptors, axon conduction velocity, receptive field characteristics, and intrinsic electrophysiological properties. Knowledge about intrinsic electrophysiological properties is of primary importance, not only as a tool to identify neurons, but also because they strongly influence the input-output relationships and operation of cortical neurons and circuits.

Multiple schemes have been proposed to classify cortical neurons on the basis of their discharge pattern and intrinsic membrane properties. Early extracellular recording studies in vivo differentiated cortical cells into two broad categories: those that had thin (or "fast") action potentials and exhibited high spontaneous activity were termed "fast spiking" cells, while neurons with broader action potentials and lower levels of spontaneous activity were termed "regular spiking" cells (Mountcastle et al. 1969; Simons 1978). These cells were hypothesized to correspond to nonpyramidal and pyramidal neurons, respectively (Mountcastle et al. 1969). However, other studies performed in the motor cortex reported large differences in action potential width between two subtypes of pyramidal neurons, the slow (broad spikes) and fast (thin spikes) pyramidal tract cells (Baranyi et al. 1993b; Calvin and Sypert 1976; Deschênes et al. 1979; Stafstrom et al. 1984; Takahashi 1965). Intracellular recording combined with labeling techniques revealed that RS cells were often pyramidal or spiny stellate cells, while FS neurons showed morphological features of subtypes of inhibitory neurons (Ahmed et al. 1998; Azouz et al. 1997; Chagnac-Amitai et al. 1990; Chen et al. 1996a; Foehring et al. 1991; Gupta et al. 2000; Hirsch 1995, Kaneko et al. 1995; Kawagushi 1995; Krimer and Goldman-Rakic 2001; Larkman and Mason 1990; McCormick et al. 1985, 1993; Neagele and Katz 1990; Pockberger 1991; Thomson et al. 1996; Tseng and Prince 1993; Zhou and Hablitz 1996).

Intra- and extracellular recording studies in vivo also emphasized the presence of burst firing in a subset of cortical neurons (e.g., Bair et al. 1994; Baranyi et al. 1993a; Calvin and Sypert 1976; Cattaneo et al. 1981; Dégenètais et al. 2002; Istvan and Zarzecki 1994; Nuñez et al. 1993; Pockberger 1991). Bursting, however, does not appear to be a feature homogeneous enough to characterize one single cell type, because multiple types of bursting neurons have been described in terms of action potential width or intraburst frequency in different species and cortical areas. In vitro, one type of neuron generates inactivating bursts of action potentials in response to depolarization through intrinsic membrane mechanisms (Connors et al. 1982; Franceschetti et al. 1995; Jones and Heinemann 1988; Mason and Larkman 1990; McCormick et al. 1985; Tseng and Prince 1993). These intrinsically bursting (IB) neurons were often (but not always) large layer 5 pyramidal cells (McCormick et al. 1985; Chagnac-Amitai et al. 1990; Larkman and Mason 1990; Pockberger 1991; Wang and McCormick 1993; Franceschetti et al. 1995). Additional in vivo and in vitro recordings revealed another class of burst-generating neurons, called "chattering" cells (Brumberg et al. 2000; Gray and McCormick 1996; Steriade et al. 1998, 2001). These cells generate bursts with high intraburst frequency of relatively short-duration action potentials in a rhythmic fashion in response to both depolarizing current pulses as well as sensory stimulation (Gray and McCormick 1996). In visual cortex, these cells were found to be layer II/III pyramidal cells (Gray and McCormick 1996).

More recent in vitro studies described multiple subtypes of GABAergic neurons. Although many of these, especially basket and chandelier cells, exhibited the fast-spiking pattern of action potentials, many did not. The electrophysiological properties of GABAergic interneurons vary widely, with different studies reporting the existence of between two and eight different subtypes (Cauli et al. 1997, 2000; Foering et al. 1991; Gibson et al. 1999; Gupta et al. 2000; Hestrin and Armstrong 1996; Hirsch 1995; Kawaguchi 1995; Kawaguchi and Kubota 1997; Krimer and Goldman-Rakic 2001; Llinas et al. 1991; Steriade et al. 1998; Thomson et al. 1996). These differences in electrophysiological features are correlated with differences in morphological features and peptide and calcium binding protein content.

The identification of different neuronal subtypes facilitates relating data across studies, since the correlation of physiologically defined subtypes with other properties helps in predicting the likely morphology, laminar location, input-output synaptic connections, and functional properties of the recorded cell. For example, identifying a neuron as an FS cell indicates with high probability that the cell is a parvalbumin-containing GABAergic neuron, which likely synapses on the cell bodies and/or axon hillocks of nearby pyramidal cells (e.g., Somogyi 1977; Somogyi et al. 1983). However, the identification of the physiological subtype of cortical neurons, as it is traditionally done, has four marked problems:

The first is that electrophysiological properties are dependent at least in part on the environment, condition, and age of the animal. In vitro studies are particularly prone to variation, since nearly all parameters are under the control of the experimenter, including the thickness of the tissue (and therefore oxygenation and the degree to which morphological processes are maintained), the temperature, ionic environment, age, and so on (for some consequences of age and ionic environment on membrane properties and spontaneous activity see Brumberg et al. 2000; Kasper et al. 1994b; McCormick and Prince 1987; Sanchez-Vives and McCormick 2000; for in vivo extracellular ionic concentration see Hansen 1985; Massimini and Amzica 2001). The second problem relates to the skill and bias of the investigator in correctly and consistently applying the physiological criteria. The third problem stems from whether or not the subjectively defined category exists as a distinct entity, or whether it is part of a continuum of physiological properties that vary in a continuous way within a larger population. Finally, in subjective classification schemes, the choice of a value from a given variable distribution as a boundary separating two different cell types is often somewhat arbitrary.

We have attempted to solve some of these limitations by using a quantitative method (cluster analysis of intracellularly recorded data from the adult cat primary visual cortex in vivo) to identify subgroups of neurons without a priori assignment of possible cell classes. We found that cortical cells in vivo form four primary classes that correspond to RS, FS, IB, and CH cells, with each of these four classes consisting of statistically significant subclasses. Once the different cell classes and subclasses are defined, we examine and illustrate which variables are most useful in the segregation of cells into their respective classes. Finally, we examine the morphological features and receptive field properties of the cells with respect to the electrophysiological classes they belong to.

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION CONCLUSIONS REFERENCES

Cat preparation

All experiments were performed on anesthetized and paralyzed male or female adult cats (2-3 kg). The protocol for surgery has been given in previous publications (Gray and McCormick 1996; Sanchez-Vives et al. 2000) and is briefly summarized here. Anesthesia was induced with ketamine (12-15 mg/kg, im) and xylazine (1 mg/kg, im). After cannulation of a forelimb vein for perfusion and insertion of an endotracheal tube for ventilation, the cat was placed in a stereotaxic frame. For the remainder of the surgical procedure, the animal was ventilated with either a 2:1 mixture of nitrous oxide and oxygen combined with halothane (1.5%), or with oxygen and isoflurane (2.5%). To minimize cortical motion arising from the heartbeat and respiration, cisternal drainage and a bilateral pneumothorax were performed and the animal was suspended by the rib cage to the stereotaxic frame. All intracellular recordings were performed in area 17. A craniotomy (3-4 mm wide) was made above the representation of the area centralis of area 17. A small opening was made in the dura before recording.

Following surgery, the animal was paralyzed with pancuronium bromide (Pavulon, 0.3 mg/kg for induction followed by a constant intravenous perfusion at 0.3 mg/kg/h in Ringer solution containing 5% dextrose). The nictitating membranes were retracted using ophthalmic phenylephrine, and the pupils were dilated and accommodation paralyzed with ophthalmic atropine. The eyes were focused onto a computer monitor at either 57 or 114 cm using corrective, gas-permeable contact lenses. The area centralis and optic discs were localized using the tapetal reflection technique. During recording, anesthesia was maintained with 0.4-1% halothane or with 0.5-2% isoflurane. The heart rate, expiratory CO₂ concentration, rectal temperature, and blood O₂ concentration were monitored throughout the experiment and maintained at 150-180 bpm, 3-4%, 37-38°C, and >95%, respectively. The depth of anesthesia was adjusted so that noxious stimuli produced no observable changes in the EEG or heart rate. After the recording session, the animal was killed by a lethal injection of sodium pentobarbital. This protocol was approved by the Yale University and University of California Institutional Animal Care and Use Committees and conforms to the guidelines recommended in "Preparation and Maintenance of Higher Mammals During Neuroscience Experiments", National Institutes of Health publication No. 91-3207.

Recording and electrophysiological signal acquisition

Conventional sharp micropipettes were pulled on a P-80 micropipette puller (Sutter Instruments, Novato, CA) from medium-walled glass capillaries (1BF100, Sarasota, FL), filled with 2 M K⁺-acetate and 2% biocytin (Molecular Probe, Eugene, OR), and beveled to a final resistance of 50-100 M on a Sutter Instruments beveller. After a microelectrode was positioned just above the cortical surface, stability was achieved by application of agar (4% in artificial cerebrospinal fluid) to the cortical surface before penetrating the cortex. Intracellular signals were amplified with an Axoclamp-2B amplifier (Axon Instruments, Foster City, CA). The signals were digitized for storage on video tape. Signals were also digitized and acquired on-line and off-line with a 1401 interface and Spike2 software (CED, Cambridge, UK). For examining action potential features, the sampling rate was 50 kHz. In parallel, the intracellular signal was filtered to isolate action potentials (band-pass 200-20,000 Hz) and fed into a window discriminator. The timing (10 µs resolution) of the spikes was then acquired on-line. The resulting time series were used for analyzing the discharge properties of the neurons.

When classifying neurons according to their electrophysiological features, it is important that these properties be stable and representative of a healthy cell. Our criteria for a healthy and stable recording included a resting membrane potential negative to -55 mV, stable electrophysiological properties without the use of "retaining" currents, the ability to generate repetitive action potentials in response to depolarizing current pulses, and an input resistance >20 M (2 fast spiking cells displayed input resistance lower than 20 M, owing to exceptionally strong anomalous rectification; they were nevertheless maintained in the sample as they displayed perfectly healthy discharge patterns and were capable of firing at a very high rate). Periods during which either the membrane potential or the electrophysiological properties were not stable (e.g., immediately on impalement or as the recording was lost) were discarded. Intracellular recordings from putative axons (positive going only action potentials and low apparent input resistance) and dendrites (large and prolonged spikes generated in response to depolarizing current pulses) were excluded from the present analysis. Bridge balance was continuously monitored and adjusted accordingly.

Quantification of responses to current pulses and cluster analysis

Once a stable intracellular recording was obtained, square current pulses (usually 0.3 s duration) were injected through the recording micropipette to characterize the electrophysiological features of the cells. Input resistance was measured from the response to hyperpolarizing current pulses (0.2 to 0.5 nA), after averaging responses to about 10 pulses to reduce noise. The membrane time constant was evaluated from the averaged trace by fitting a single exponential to the membrane potential decay.

Depolarizing current pulses of different intensities (usually 0.1-0.9 nA, in steps of 0.1 nA) were used to evoke suprathreshold activation (Fig. 1). The first step of the analysis was to determine if a neuron was burst-generating or not. This is reflected in the interspike interval histograms (ISIH; bin width = 1 ms): burst-generating neurons were characterized by a bimodal distribution of interspike intervals, or by an ISIH with two different slopes beyond the modal value (Fig. 2, C-F), whereas a unimodal ISIH with a monotonic decay characterizes nonbursting neurons (Fig. 2, A and B). Histograms using the log values of the interspike intervals (logISIHs) helped in visualizing if an ISIH was bimodal or unimodal by concentrating long interspike intervals to a narrow range (Fig. 2, insets) and were used to decide if a neuron was burst-generating or not. Because the dividing line separating unimodal from bimodal logISIHs was difficult to identify, we supplemented our semi-quantitative approach using discriminant analysis. This analysis was based on seven variables extracted from the log values of the interspike intervals (logISIs): 1) the mean logISI; 2) the geometric mean of the logISI; 3) the logISI median; 4) the coefficient of variation (SD/mean); 5) the skewness of the logISI distribution; 6) the kurtosis of the logISI distribution; and 7) the interquartile range (the distance between the 1st and 3rd quartile of the logISI distribution).

View larger version (39K): [in this window] [in a new window]   Fig. 1. Examples of action potential responses to depolarizing current injection in the 4 subjectively classified subtypes of cortical neuron. A: regular spiking (RS) cell. B: fast spiking (FS) cell. C: chattering (CH) cell. D: intrinsic bursting (IB) neuron. Top of each panel shows responses to 3 different current intensities. Bottom plots show average action potential and dV/dt. The individual action potentials and dV/dt in each panel are the result of averaging of 10 spikes. Therefore the amplitude and time course of the 2nd spikes in Cb and Db are not accurate, owing to jitter in the timing of these events.

View larger version (39K): [in this window] [in a new window]   Fig. 2. Interspike interval histograms (ISIHs) in bursting and nonbursting neurons. ISIHs and histograms for the log values of the interspike intervals corresponding to the cells shown in Fig. 1 are presented in A-D. The logISIH better identifies bursting cells. E and F: additional examples of ISIHs in 2 other bursting neurons, illustrating the diversity of cellular behavior. Examples of action potential response to current pulses are shown above each ISIH. Note in E and F that the bimodal nature of the ISIH is more clearly seen in the logISIH.

Following this segregation into two broad categories corresponding to bursting and nonbursting neurons, we performed additional analyses on each group to further characterize the data. For bursting neurons, the gap in the bimodal logISIH parted the spikes between those that belong to the same burst and those that belong to different bursts or those that correspond to isolated, single spikes. We used this property to identify the first spike of each burst, the spikes that occurred during a burst, and the spikes that occurred outside the bursts. This allowed us to calculate the intraburst frequency, the interburst frequency, the number of spikes per burst, the percentage of spikes that occurred in bursts, and a burst inactivation index corresponding to the percentage of bursts that occurred in the first half of the pulse versus the total number of bursts. This index provides an estimate of a burst inactivation mechanism. A value of 50% corresponds to a neuron that fires bursts of action potentials throughout the current pulse, while a value of 100% corresponds to a neuron that fired bursts only in the first half of the current pulse, i.e., of a neuron for which the burst generation mechanism inactivates as a function of time (see Figs. 1, C and D, and 2, E and F).

For all the cells, the action potential features were measured after averaging several (>10) action potentials together (Fig. 1). For burst-generating neurons, only the first spike of each burst was used for averaging. We also calculated the time differential of the voltage (dV/dt). The spike threshold time was defined as the point in the dV/dt that was 3 SD above the mean noise level calculated for the dV/dt trace before the action potential. The amplitude (height) of action potentials was measured from threshold. The spike width was measured as the width at half height. The positive and negative peaks in the dV/dt yield the maximum rate of depolarization and repolarization, respectively. A dV/dt ratio was calculated as maximum rate of fall divided by maximum rate of rise.

For all the cells, whether bursting or not, we calculated the relationship between injected current intensity and the total number of spikes per pulse (normalized by the pulse duration). Cells that did not display a significant correlation between these two variables were excluded from further analysis. The slope (in Hz/nA) of the linear regression characterizes the current-frequency relationship of the neuron (Fig. 3).

View larger version (25K): [in this window] [in a new window]   Fig. 3. Slope of firing rate vs. current intensity (f-I curves). Examples of f-I curves for the cells shown in Fig. 1. The slope of the relationship between injected current and mean firing rate during the current pulse is considerably steeper in the FS cell (519 Hz/nA) compared with that for the RS (85 Hz/nA), IB (56 Hz/nA), and CH (87 Hz/nA) cells. Each point is the average of the mean firing rate for 2-10 repeats of a given current intensity (only 1 repeat at 0.9 nA for the FS cell). Bars represent SE.

For all the cells, we also applied a measure of adaptation by taking the ratio of the number of spikes in the first 50 ms versus the number of spikes in the first 100 ms of the current pulse, expressed as a percentage ("Ada50" index). The less a cell adapts, the closer to 50% this value.

The adaptation properties of nonbursting neurons were characterized with more precision by calculating the instantaneous firing rate as a function of the time elapsed since the beginning of the pulse (Fig. 5). Due to the presence of high instantaneous intraburst firing rates, this type of analysis was not applied to burst-generating neurons. For each current intensity, the change in firing rate was derived from a single exponential fit to the data. The plateau of the exponential curve corresponds to the adapted firing rate (F_ad). The strength of adaptation (adaptation index) was quantified as 100 × (1 - F_ad/F₁), where F₁ corresponds to the firing rate of the first interspike interval. The time constant of adaptation corresponds to the time constant derived from the exponential fit. For some cells (especially FS neurons), adequate fitting was not obtained and therefore no adaptation time constant was extracted. For these cells, F_ad was calculated as the mean firing rate for the last 100 ms of the current pulse and used to calculate the adaptation index. Data have been taken into account only when F₁ was above 60 Hz. Below this limit, the firing pattern appeared to be affected by spontaneous activity, as reflected by an increased variability in the distribution of adaptation-related values. For any given cell, values of adaptation strength and time constant obtained for each current intensity were thereafter averaged. (For specific cells, adaptation index and time constant varied with current intensity, but at the population level no consistent trend was observed.)

Cluster analysis was used to classify the cells by combining some of the variables described above. This method allowed us to classify the cells without a priori knowledge of the number of groups. Before performing the cluster analysis all variables were normalized to their z-scores. Some variables have not been used for the clustering and this requires some justification: the action potential height was not used as it could be influenced by the quality of the capacitance compensation, which itself depends on the depth of the electrode below the agar surface among other factors. The input resistance and time constant are reported here, but were not used in the cluster analysis, since in the in vivo preparation ongoing activity is likely to affect these measures (e.g., Bernander et al. 1991; Destexhe and Pare 1999). Finally, when two variables were strongly correlated (for example, spike width and dV/dt ratio), only one was used for cluster analysis to avoid redundancy. Joining trees were constructed using Ward's method of amalgamation. The results of this classification method are plotted as a hierarchical tree (Fig. 6), in which the horizontal axis denotes the linkage distance calculated as Euclidean distance.

The result of the cluster analysis indicates the degree of similarity among neurons but does not assign statistical significance to the grouping. To determine whether the clusters contained cells with statistically distinct properties, we used the multiple ANOVA (MANOVA) test applied to the variables used to produce the clusters. For any pair of clusters, the Fisher's posthoc protected least significant difference (PLSD) test was thereafter applied to compare the means. For variables not used to compute the cluster structure, either the posthoc PLSD Fisher's test or the classical t-test was used. All paired comparisons have also been made using the nonparametric, Mann-Whitney U test. In all cases, both parametric and nonparametric tests gave the same results (in terms of significance of differences) and the results obtained with the parametric tests are given. Unless mentioned, data are reported as mean ± SD.

Receptive field properties

Three different methods have been used to determine if a receptive field was of the simple or complex category. First, the response to small bars flashed within the receptive field was used to localize ON and OFF subregions (Hubel and Wiesel 1962). Cells exhibiting spatially nonoverlapping ON and OFF subfields, or a single ON or OFF subfield, were classified as simple, while cells showing clear overlap of the ON and OFF responses were classified as complex. Second, we used the peri-stimulus time histograms (PSTH)s obtained in response to broad drifting light and dark bars. Responses to the light-to-dark and dark-to-light edges did not overlap in simple cells, while they did overlap in the complex cells (Schiller et al. 1976). Third, we used the spike response to drifting sinewave gratings of various spatial frequencies to classify cells as simple or complex. For this purpose, PSTHs were computed by taking the average response to one cycle of the grating. The amplitude of the DC component (F₀) and the first harmonic (F₁) at the temporal frequency of the stimulus were computed from the PSTH using Fourier analysis (after subtraction of the mean spontaneous activity level). For the spatial frequency that yielded the strongest response of either the F₀ or F₁ component, we calculated the ratio of F₁/F₀ to yield a "relative modulation index" (Skottun et al. 1991). The distribution of the relative modulation indices was bimodal, with a gap at 1. Based on this distribution, we considered cells as simple when the index was larger than 1 and complex when it was lower.

Histology

Following the experiment, the animal was given an overdose of sodium pentobarbital by intravenous injection and perfused with phosphate-buffered saline (PBS), followed by PBS containing 2-4% paraformaldehyde and 1.25% glutaraldehyde. After perfusion, the region of primary visual cortex containing the labeled cells was blocked and left in 30% sucrose until the tissue sunk. Coronal sections, 60-80 µm thick, were cut on a freezing microtome. Biocytin staining was revealed using standard techniques (Horikawa and Armstrong 1988) with the Vectastain ABC kit from Vector (Burlingame, CA). Cortical layers were identified either through counter-staining or staining adjacent sections with cresyl violet, or by using Normarski optics and using standard measures and landmarks. Measurements have not been corrected for shrinkage.

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION CONCLUSIONS REFERENCES

During the performance of intracellular recordings in cat area 17 in vivo, a large number of neurons could be subjectively characterized as RS, FS, IB, or CH (e.g., Gray and McCormick 1996), while others appeared intermediate to these categories. Subjectively, RS neurons were identified based on their relatively broad action potentials (Fig. 1Ab) that exhibited spike frequency adaptation during injection of a constant depolarizing current pulse (Fig. 1Aa). FS cells exhibited thinner action potentials (Fig. 1Bb), apparently higher firing rates in response to depolarizing current pulses (Fig. 1Ba), and relatively little spike frequency adaptation (Fig. 1Ba).

CH cells were able to generate repetitive, high-frequency bursts of two or more relatively short-duration action potentials (Fig. 1C, a and b). Within each burst, each spike was followed by a fast afterhyperpolarization and an afterdepolarization (ADP; Fig. 1C). This ADP activated the next action potential in the burst. The bursts were terminated by the failure of the ADP to generate an action potential and were followed by a 15- to 100-ms afterhyperpolarization.

The final category of readily distinguishable neurons were the IB cells. These cells were distinguished from CH cells by their tendency to fire bursts of spikes only at the beginning of depolarizing current pulses (Fig. 1Da), and they rarely displayed repetitive bursting. Their action potentials were broader than those of CH cells (Fig. 1Db), and the frequency of firing during a burst appeared to be lower. Finally, the action potential amplitudes of IB neurons often decreased during the generation of a burst.

Figure 1 illustrates so called "typical" examples of each cell class for one possible classification scheme. However, in the overall population there was a large amount of variability in discharge pattern across cells, and some neurons exhibited properties intermediate to those illustrated. One intermediate behavior was the generation of repetitive burst discharges throughout the duration of the current pulse, like a CH neuron, but with bursts that were typical for that of an IB cell (Fig. 2F). Another intermediate behavior corresponded to cells that generated short-duration action potentials, like an FS cell, but displayed spike frequency adaptation like an RS cell. We also observed neurons that appeared similar to CH cells, but that only occasionally generated bursts of action potentials. Finally, RS cells differed in their adaptation properties, in that some cells adapted rapidly and/or strongly while other cells adapted slowly and/or weakly.

Do cells displaying these (and other) patterns of activity represent their own unique categories, or are they just members of those subjectively defined, but on one end of a continuum? In a related question, how many subgroups of neurons are there in our recordings from cat visual cortex?

To answer these questions, a more detailed quantitative analysis of the spike discharge patterns had to be conducted. To achieve this goal, we performed cluster analysis of the discharge parameters from a total of 220 cells recorded intracellularly in vivo in area 17. Among these cells, 48 were successfully labeled with biocytin and their morphology examined.

Quantitative analysis of electrophysiological properties

PARTITIONING BETWEEN BURSTING AND NONBURSTING NEURONS. The first step in our analysis was to decide whether a neuron was burst-generating or not. One essential aspect of bursting behavior is that an action potential occurring within a burst is not independent from the one that preceded it: in general (Fig. 1, C and D), the second action potential of a burst is triggered by an ADP resulting from the first action potential, and so on for each subsequent spike of the burst. One way to illustrate this type of dependence on a short (milliseconds) time scale is through the use of interspike interval histograms (ISIHs). These histograms show how often a spike is followed by another spike at a given interval.

VARIABLES USEFUL IN THE CLASSIFICATION OF NEURONS. The ISIHs and the statistics that can be extracted from the logISIs, although quite useful to distinguish bursting from nonbursting neurons, do not reflect all the intrinsic properties of cortical neurons. To obtain a more precise classification of cortical neurons, we analyzed other discharge properties that varied between different neurons.

View larger version (21K): [in this window] [in a new window]   Fig. 4. Distributions obtained for some of the variables used for quantitative and subjective classification of cells. A: slope of the f-I relationship. B: distribution of adaptation indices (ada50). A value of 50% indicates the same number of spikes is present in the 1st and 2nd 50-ms epochs of the response (i.e., no adaptation). Values larger than 50% indicate adaptation in firing rate. C: distribution of action potential widths (measured at half height). D: ratio of the maximum rate of fall to the maximum rate of rise of the action potential. E: percentage of spikes in bursts. F: intraburst frequency (for burst generating neurons only). Arrows point to possible modes in the distributions.

CLUSTER ANALYSIS OF NONBURSTING NEURONS. For nonbursting neurons, we included the magnitude and time constant of firing rate adaptation as additional variables (Fig. 5). This adaptation was quantified by fitting the data relating instantaneous firing rate as a function of time with a single exponential function. The strength of adaptation (adaptation index) was calculated as 100  (100 × F_ad/F₁), where F_ad is the adapted firing rate (horizontal asymptote of exponential fit) and F₁ the firing rate for the first interspike interval. The adaptation index expresses the reduction in firing rate over time, with respect to the firing rate at the beginning of the current pulse. The adaptation time constant is derived from the time constant of the exponential fit. Values of the adaptation index and time constant were averaged across the different current intensities (for details see METHODS).

View larger version (44K): [in this window] [in a new window]   Fig. 5. Adaptation of action potential discharge in nonbursting neurons. A. instantaneous firing rate plotted as a function of time for the RS cell of Fig. 1A. Mean adaptation time constant is 14.9 ms. B: similar plot for the FS neuron of Fig. 1B. Note the lack of adaptation and overall higher discharge rate than in the cells of parts A, C, and D. C and D: adaptation in 2 additional RS cells, with intermediate (C, mean = 26.3 ms) and long (D, mean = 64.5 ms) adaptation time constants. For any given interspike interval and current intensity, several points appear superimposed due to the fact that several pulses with the same current intensity were used.

View larger version (30K): [in this window] [in a new window]   Fig. 6. Hierarchical tree plots illustrating the results of cluster analysis. A. dendrogram for nonbursting neurons. There are 2 main branches corresponding to RS and FS categories. Within the RS class, there are 2 subclasses, which we have termed RSTS and RSC. RSTS cells exhibited thinner spikes and less spike frequency adaptation than RSC cells. The main difference between the 2 subtypes of FS cells was the slope of their f-I plot, with FSLFI cells having a less steep f-I relation than FSC cells. B: dendrogram for bursting neurons. The 2 main branches correspond to IB and CH cells. Three statistically significant subclasses of IB cells and 2 subclasses of CH cells are also considered.

CLUSTER ANALYSIS OF BURSTING NEURONS. Three variables, measured in bursting neurons, proved to be particularly useful in segregating neuronal subtypes. These included the intraburst firing rate, spike width, and the burst inactivation index (i.e., the ratio of the number of bursts occurring during the first half of the pulse to the number of bursts over the whole pulse duration; see METHODS). The dendrogram of the cluster analysis based on these three indices (Fig. 6B) revealed two main branches corresponding to the subjectively identified CH cells and IB neurons. The vast majority (94%) of the subjectively classified IB cells were found in the quantitatively established cluster of IB cells. They were characterized (on average) by relatively broad action potentials, lower intraburst firing rates, and pronounced burst inactivation during maintained depolarization. In the second class of bursting neurons, 73% of the subjectively classified CH cells were found in the quantitatively established cluster. These cells generated high-frequency bursts of relatively thin spikes, and displayed much less burst inactivation.

Electrophysiological properties

The cluster analysis revealed that of the 220 cells we analyzed, 91 (41.4%) were RS (54 RS_TS and 37 RS_C), 33 (15%) were FS (15 FS_C and 18 FS_LFI), 31 (14.1%) were CH (22 CH1 and 9 CH2), and 65 (29.5%) were IB (20 IB1, 30 IB2, and 15 IB3). Following this classification, we further analyzed the distributions of the electrophysiological properties of these cells. These distributions are illustrated in Figs. 7-12 and statistical summaries, together with an indication of significance of differences, can be found in Tables 1-8. Among these different properties, those that proved to be the most relevant for classification are spike width and adaptation index for FS and RS neurons, and intraburst firing rate, used together with either spike width or burst inactivation index, for CH and IB neurons.

View larger version (25K): [in this window] [in a new window]   Fig. 7. Distribution of values for 3 variables measured in both bursting and nonbursting neurons. A: histograms of action potential width measured at half height for IB neurons (A1), CH cells (A2), FS cells (A3), and RS cells (A4). B: ratio of maximum rate of fall to maximum rate of rise of the action potential presented separately for the same 4 cell classes. Both FS and CH cells have thinner spikes than those of RS and IB neurons due to a faster rate of repolarization. C: histograms of the f-I slopes for the RS, FS, IB, and CH cell classes. FS cells display the highest slope values, indicating a much higher gain between injected current and firing rate compared with the other 3 cell classes.

View larger version (42K): [in this window] [in a new window]   Fig. 8. Comparison of the properties of spike generation between fast spiking and regular spiking neurons. A: f-I slope plotted against action potential width for RS and FS cells. The distribution shows overlap of FS and RS cells when their action potential widths are <0.5 ms and their f-I slope values are <300 Hz/nA, indicating that these 2 variables alone do not cleanly separate FS and RS cells. The vertical dotted line delimits the f-I slope value (300 Hz/nA) beyond which only FS cells are encountered, and the horizontal doted line delimits the action potential width (0.5 ms) beyond which only RS neurons are found. Subclasses of FS and RS are distinguished by different symbols to illustrate the thinner spikes in RSTS cells and the highest f-I slope values in FSC cells. B: histogram of adaptation indices illustrating a clear difference in firing rate adaptation between FS and RS neurons. Zero percent corresponds to no adaptation. Note overlap limited to adaptation index values between 20% and 35%. C: action potential widths plotted against adaptation indices. The quadrant defined by action potential width <0.5 ms and adaptation index <35% (dashed lines) contains all the FS cells and only 3 RS cells. D: histogram of adaptation time constants in RS and FS cells. E: adaptation time constants plotted against adaptation ratios shows that adaptation, when present, is faster and weaker in FS cells compared with RS cells. Two FS cells exhibited average negative adaptation ratios but showed spike frequency adaptation on some trials, and the time constant of adaptation was calculated from these trials. Adaptation time constant does not allow a separation between subclasses of RS and FS cells.

View larger version (29K): [in this window] [in a new window]   Fig. 9. Characteristics of action potential bursts in IB and CH cells. A: examples of single bursts from 8 different bursting neurons (3 IB and 5 CH cells) are shown. Note decreased spike width and more prominent fast AHP with increased intraburst frequency. B: histogram of intraburst firing rates. CH cells can be defined by intraburst frequency >425 Hz and IB neurons by intraburst frequency <350 Hz. Overlap between 350 and 425 Hz is limited to a small number of cells. C: correlation between intraburst frequency and action potential width at half height. The 2 parameters are significantly correlated, indicating that neurons with thinner action potentials generate bursts with higher intraburst firing rates. The slope of the correlation was steeper for CH cells (slope = 439 Hz/ms, r2 = 0.257, P = 0.003) compared with IB neurons (slope = 176 Hz/ms, r2 = 0.231, P < 0.0001). Note the scatter of data points for the CH cells where intraburst frequencies around 500 Hz are associated with action potential widths between 0.2 and 0.4 ms. CH neurons can be characterized as cells with intraburst frequencies >350 Hz and spike widths <0.5 ms. Subclasses of CH and IB neurons are identified by different symbols to illustrate differences in spike width and intraburst frequency.

View larger version (24K): [in this window] [in a new window]   Fig. 10. Comparison of burst properties in CH and IB neurons. A: intraburst frequency plotted against percentage of spikes in bursts. Gray shading corresponds to the region of overlapping intraburst frequency for IB and CH neurons. B: histogram of burst inactivation indices in CH and IB cells. C: intraburst frequency and burst inactivation index plotted together. IB and CH cells could be accurately classified by these 2 criteria since all but 2 cells with an intraburst frequency >350 Hz and <70% of their bursts in the 1st half of the pulse appear to be CH neurons. Subclasses of neurons are also identified by different symbols to emphasize differences in burst inactivation between the 3 subtypes of IB cells and differences in intraburst frequency between the 2 subtypes of CH cells. D: adaptation of action potential firing in bursting neurons. Although there is substantial overlap, CH cells on average exhibit less adaptation than IB neurons.

View larger version (27K): [in this window] [in a new window]   Fig. 11. Burst firing rate and adaptation of burst firing in chattering cells. A: example of the relationship between burst discharge rate and current intensity (same cell as Fig. 1C). Burst rate was averaged from multiple pulses of the same intensity. The slope for this cell was 35.1 Hz/nA. Bars represent SE. B: histogram of the slope of the relationship between current intensity and mean interburst frequency for 20 CH cells. C: relationship between current intensity and interburst frequency for the 1st 3 consecutive interburst intervals (IBI) for the same cell as in A. Bars represent SE. Slope values for IBI1, IBI2, and IBI3 were 25.8, 37.9, and 35.4 Hz/nA, respectively. D: population data for the slope of the relationship between current intensity and interburst frequency. Mean ± SE values are presented for a sample of 7 CH cells.

View larger version (32K): [in this window] [in a new window]   Fig. 12. Adaptation of the number of spikes per burst in chattering cells. A: traces represent burst discharge of a CH cell for 3 different current intensities. Two features of the burst discharge are illustrated in this example: 1st, for a given current intensity, the number of spikes in the first burst of the discharge is usually larger than in the subsequent bursts; 2nd, the number of spikes/burst increases when the current intensity is increased. B: plot of the mean (±SE) number of spikes per burst as a function of the burst ordinal number. All cells (n = 25) and current intensities have been averaged. The number of spikes per burst decreases with the ordinal number of the burst. C: in some CH cells, the number of spikes per burst increases in proportion to the current intensity. The graph corresponds to the cell illustrated in A. The number of spikes per burst, for the 1st, 2nd, and 3rd burst of the discharge, is represented as a function of current intensity. Responses to several current pulses of the same intensity have been averaged and the bars represent SE. D: population data: the mean (±SE) value of the slope of the relationship between number of spikes per burst and current intensity is represented for the 1st (n = 18 cells with significant relationship), 2nd (n = 11), 3rd (n = 12), and 4th (n = 11) burst of the discharge. The slope is significantly steeper for the 1st burst of the discharge compared with the 2nd, 3rd, and 4th.

INPUT RESISTANCE AND MEMBRANE TIME CONSTANT. The apparent input resistance was measured for a random subset of each physiological class of cells (Table 1) and was found to be significantly lower in CH cells compared with RS cells (P = 0.02, t-test). As far as subclasses are concerned, we found significantly different input resistance between the two subclasses of RS cells (Table 2), which was lower in RS_TS neurons compared with RS_C neurons (P = 0.014).

ACTION POTENTIAL WIDTH AND MAXIMAL DEPOLARIZATION AND REPOLARIZATION RATES. Comparison of the action potential widths for the four classes of neurons revealed two distinct groups: both FS and CH cells exhibited short-duration action potentials, while IB and RS cells showed a broader distribution having, on average, more prolonged action potentials (Fig. 7A, Table 3). The average action potential width was not significantly different between IB and RS cells (P = 0.75, Fisher's PLSD). However, the distribution for RS cells was broader and included cells with short-duration action potentials, including the subclass RS_TS (Fig. 7A); approximately 15% of the RS cells (all members of the RS_TS subclass) displayed action potentials as thin as those of FS cells. The populations of bursting neurons also overlapped in their spike duration; the 50-100 percentile range for CH cells overlaps with the 0-25 percentile range for IB neurons (Fig. 7A). These results indicate that spike width alone cannot unambiguously discriminate one cell class from another in either the bursting or nonbursting categories.

FIRING RATE VERSUS INJECTED CURRENT. The distribution of the slopes of the f-I relationship revealed that FS cells are substantially different from the other three cell classes in this regard (Fig. 7C; Table 5); the median slope values for FS cells were 1.7 times larger than for CH cells, 2.3 times larger than for RS cells, and 2.7 times larger than for IB cells (P < 0.0001 in the 3 comparisons, Fisher's PLSD). In addition, CH cells exhibited a slightly steeper slope than RS and IB cells (Fig. 7C; Table 5; P = 0.01 and P = 0.02 for CH cells vs. IB and RS neurons, respectively).