J Neurophysiol 114: 624 – 637, 2015.
First published May 13, 2015; doi:10.1152/jn.00304.2015.
Properties of precise firing synchrony between synaptically coupled cortical
interneurons depend on their mode of coupling
Hang Hu and Ariel Agmon
Department of Neurobiology and Anatomy and the Sensory Neuroscience Research Center, West Virginia University,
Morgantown, West Virginia
Submitted 25 March 2015; accepted in final form 11 May 2015
cortical interneurons; firing synchrony; gap junctions; electrical coupling; unitary IPSP; temporal precision
PRECISE (SHARP) FIRING SYNCHRONY,
with action potentials of two
or more neurons occurring within a few milliseconds of each
other, has been observed in various brain regions and cell
types, but the mechanisms for such synchrony, and what role(s)
it may or does play in processing, transmitting and encoding
information by the brain, are still unresolved (Atencio and
Schreiner 2013; Bruno 2011; Diba et al. 2014; Doucette et al.
2011; Hatsopoulos et al. 1998; Histed and Maunsell 2014;
Riehle et al. 1997; Stanley et al. 2012). Of particular interest is
precise synchrony between inhibitory cortical interneurons,
proposed to drive various cortical rhythms such as gamma
oscillations (Bartos et al. 2007; Cardin et al. 2009; Fries et al.
Address for reprint requests and other correspondence: A. Agmon, Dept. of
Neurobiology and Anatomy and the Sensory Neuroscience Research Center,
PO Box 9303, West Virginia Univ., Morgantown, WV 26506-9303 (e-mail:
[email protected]).
624
2007; Penttonen et al. 1998; Sohal et al. 2009). Gamma
oscillations, in turn, are suggested to be the neural correlates of
conscious perception and cognition (Jensen et al. 2007; Melloni et al. 2007; Ward 2003).
Two network “motifs” can drive interneuron synchrony:
shared excitatory inputs, via pyramidal-interneuron connections, and mutual coupling, via interneuron-interneuron connections. Cortical interneurons share excitatory inputs with
specific subsets of other excitatory or inhibitory cortical neurons (Otsuka and Kawaguchi 2013; Yoshimura and Callaway
2005), and such shared excitatory postsynaptic potentials
(EPSPs) may drive sharp synchrony between neocortical interneurons in vivo (Constantinidis and Goldman-Rakic 2002;
Swadlow et al. 1998). Mutual interneuron-interneuron coupling can be chemical, through inhibitory synapses, electrical,
through gap junctions, or both, and all three modes can generate highly precise synchrony in vitro (Galarreta and Hestrin
1999; Gibson et al. 2005, 1999; Hu et al. 2011; Merriam et al.
2005; Tamas et al. 2000). Thus cortical interneurons can
potentially synchronize through several distinct mechanisms.
This begs several questions. First, do different subtypes of
cortical interneurons preferentially synchronize through some
of these mechanisms and not others? Second, is firing synchrony driven by these different mechanisms distinguishable in
any way, qualitatively or quantitatively? Last, are these mechanisms consistent with current models of gamma oscillations?
In the present study we examined precise interneuron synchrony in vitro driven by mutual coupling. To address the
above questions, we recorded intracellularly from over 150
homotypic pairs of mouse somatostatin-containing (SOM) and
parvalbumin-containing, fast-spiking (FS) interneurons, characterized their coupling mode as chemical, electrical, or dual,
and quantified their firing synchrony using a novel synchrony
index. We then tested the dependence of the synchrony on
firing rate and quantified the temporal precision of synchrony.
We report that chemical coupling between FS interneurons
gave rise to synchrony that was strongly firing rate dependent,
requiring firing rates of 80 Hz or higher. FS-FS synchrony,
driven by either chemical or dual connectivity, was also significantly more precise than SOM-SOM synchrony, driven by
electrical coupling. To determine if the differences in synchrony properties depended on differences in intrinsic properties between the two interneuron subtypes, we performed
computer simulations of pairs of neurons with identical intrinsic properties but different modes of connectivity. Our results
reveal that the properties of interneuron synchrony depend on
the mode of synaptic connectivity and pose specific constraints
on interneuron-based models of cortical oscillations.
0022-3077/15 Copyright © 2015 the American Physiological Society
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Hu H, Agmon A. Properties of precise firing synchrony between
synaptically coupled cortical interneurons depend on their mode of
coupling. J Neurophysiol 114: 624 – 637, 2015. First published May
13, 2015; doi:10.1152/jn.00304.2015.—Precise spike synchrony has
been widely reported in the central nervous system, but its functional
role in encoding, processing, and transmitting information is yet
unresolved. Of particular interest is firing synchrony between inhibitory cortical interneurons, thought to drive various cortical rhythms
such as gamma oscillations, the hallmark of cognitive states. Precise
synchrony can arise between two interneurons connected electrically,
through gap junctions, chemically, through fast inhibitory synapses, or
dually, through both types of connections, but the properties of
synchrony generated by these different modes of connectivity have
never been compared in the same data set. In the present study we
recorded in vitro from 152 homotypic pairs of two major subtypes of
mouse neocortical interneurons: parvalbumin-containing, fast-spiking
(FS) interneurons and somatostatin-containing (SOM) interneurons.
We tested firing synchrony when the two neurons were driven to fire
by long, depolarizing current steps and used a novel synchrony index
to quantify the strength of synchrony, its temporal precision, and its
dependence on firing rate. We found that SOM-SOM synchrony,
driven solely by electrical coupling, was less precise than FS-FS
synchrony, driven by inhibitory or dual coupling. Unlike SOM-SOM
synchrony, FS-FS synchrony was strongly firing rate dependent and
was not evident at the prototypical 40-Hz gamma frequency. Computer simulations reproduced these differences in synchrony without
assuming any differences in intrinsic properties, suggesting that the
mode of coupling is more important than the interneuron subtype. Our
results provide novel insights into the mechanisms and properties of
interneuron synchrony and point out important caveats in current
models of cortical oscillations.
PROPERTIES OF FIRING SYNCHRONY BETWEEN CORTICAL INTERNEURONS
MATERIALS AND METHODS
by chance; it can assume values from ⫺1 (least possible synchrony)
to 1 (maximum possible synchrony), with 0 indicating chance-level
synchrony. To calculate the JBSI, a synchrony window ⫾ S (S ⫽ 2
ms) was centered on each of the spikes of the faster spike train, and
the number SYN(S) of spikes in the slower spike train occurring within
synchrony windows was counted. A jitter window ⫾ J (J ⫽ 2S) was
then centered on each of the N spikes of the slower spike train, and the
probability that a jittered spike would fall within a synchrony window
was computed analytically, rather than by Monte Carlo simulations as
in previous implementations of jitter methods (Amarasingham et al.
2012). The number of coincidences expected after a random jitter
of ⫾ J, 具SYNJ(S)典, is given by the sum of these probabilities; the JBSI
is then defined as JBSI ⫽ 2[SYN(S) ⫺ 具SYNJ(S)典]/N. This definition
differs somewhat from the Jitter-Sensitive Synchrony Index (JSSI)
used in our previous study (Hu et al. 2011), but the two indexes are
strongly correlated (r2 ⬎ 0.97 in the current data set); the JBSI is
preferable to the JSSI because of its robustness against firing rate
differentials between the two neurons. Unlike commonly used synchrony measures, the JBSI is independent of firing rates and is not
sensitive to slow comodulations in firing rates (Agmon 2012).
Simulations. We constructed an integrate-and-fire model of two
neurons based on a minimal number of assumptions. At any given
time point the membrane potential of each neuron was assumed to
relax with a time constant ␶ (typically set at 10 ms) toward an
asymptotic value determined by the experimenter. A spike was fired
whenever firing threshold was crossed from below and was followed
by an absolute refractory period of 2 ms. A low level of random noise
(0.5 mV peak to peak) was added to the membrane potential to
generate realistic-looking spike trains; noise was added independently
to each cell at each integration step (0.1 ms), so no spurious correlations were introduced. After a spike, the presynaptic neuron’s membrane potential decremented instantaneously by a fixed value (representing the afterhyperpolarization, AHP), and after a delay d a
synaptic conductance G was activated in the postsynaptic neuron for
a duration RT, representing the rise time of the PSP (typically set at
2 ms). This synaptic conductance caused the postsynaptic membrane
potential to relax toward a predefined synaptic reversal potential with
a time constant proportional to 1/G. Inhibitory postsynaptic potentials
(IPSPs) were modeled as PSPs with a reversal potential of ⫺60 mV
and a 1-ms delay, and electrical synapses were modeled as PSPs with
a reversal potential of 0 mV and 0 delay; minor variations in these
parameters did not affect our conclusions (see RESULTS). The subthreshold effects of electrical coupling were not included in the model.
Computations were done in Mathcad (PTC).
Statistics. Other than multiple regression, all statistical tests were
done in Mathcad, using in-house algorithms, by comparing the observed value of the statistic with the distribution of 10,000 values
computed from random permutations of the data; in cases where
10,000 permutations yielded no more extreme values, the P value is
listed as ⬍0.0001. Comparisons of means were two-tailed; comparisons of correlation coefficients and cumulative distributions were
one-tailed. Multiple linear regression was done in Statistica (StatSoft).
Data are means ⫾ SE unless indicated otherwise.
RESULTS
Electrophysiological characteristics of SOM and FS interneurons. To examine the relative contributions of electrical
coupling, inhibitory synapses, and shared inputs to synchronous firing of cortical interneurons, we conducted simultaneous whole cell current-clamp recordings from pairs of interneurons in the somatosensory (“barrel”) cortex in brain slices from
juvenile mice. Our data set consisted of 60 SOM pairs and 54
FS pairs, which were pooled with 40 additional FS pairs
recorded in a previous study (Hu et al. 2011) and which we
reanalyzed for this study. With the exception of 8 SOM pairs
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Animals. All experimental protocols were approved by the West
Virginia University Animal Care and Use Committee. Experiments
were conducted on juvenile mice of either sex (postnatal days 15–22;
see RESULTS for justification of this age range). SOM pairs were
recorded either in X94 mice (Ma et al. 2006), in which a subset of
layers 4 –5 SOM interneurons express green fluorescent protein
(GFP), or in progeny of SOM-IRES-Cre (Taniguchi et al. 2011) and
Ai9 reporter mice (Madisen et al. 2010), in which all SOM interneurons express tdTomato, a red fluorescent protein (SOM-RFP mice).
FS pairs were recorded in X94 animals, in which they were targeted
by their cell body shape and size; in G42 mice (Chattopadhyaya et al.
2007), in which a subset of FS interneurons express GFP; or in
progeny of PV-Cre (Hippenmeyer et al. 2005) and Ai9 mice, in which
all FS interneurons express tdTomato (PV-RFP mice). All mouse lines
are available from the Jackson Laboratory (Bar Harbor, ME). Mouse
lines were maintained as hemizygotes by breeding mutant males with
outbred wild-type females; as a result, the four genotypes used did not
have a homogeneous genetic background.
Electrophysiological recordings. For preparation of brain slices,
mice were anesthetized deeply with isoflurane and decapitated. The
brains were removed and submerged in ice-cold artificial cerebrospinal fluid (ACSF) bubbled with 95% O2-5% CO2; ACSF was composed of (in mM) 126 NaCl, 3 KCl, 1.25 NaH2PO4, 2 CaCl2, 1.3
MgSO4, 26 NaHCO3, and 20 D-glucose. With the use of a Vibroslicer
(World Precision Instruments), 350-␮m-thick coronal slices were cut,
transferred into a holding chamber filled with recirculated ACSF, and
incubated for 30 – 45 min at 32°C and then at room temperature until
used. For recording, slices were transferred to the recording chamber
and continuously superfused at a rate of 2–3 ml/min with ACSF at
32°C. Glass micropipettes (typically 5– 8 M⍀ in resistance) were
filled with (in mM) 134 K-gluconate, 3.5 KCl, 0.1 CaCl2, 10 HEPES,
1.1 EGTA, 4 Mg-ATP, 10 phosphocreatine-Tris, and 2 mg/ml biocytin, adjusted to pH 7.25 and ⬃290 mosM. Neurons were visualized
under differential interference contrast and fluorescence illumination
using an Olympus BX50WI microscope equipped with a ⫻40 waterimmersion objective and a Hamamatsu Orca camera. Simultaneous
current-clamp whole cell recordings were performed from pairs of
(mostly) layer 4 interneurons in somatosensory (barrel) cortex, using
an AxoClamp 2B amplifier (Molecular Devices). To block GABAA,
AMPA, and NMDA receptors, gabazine, 6-cyano-7-nitroquinoxaline2,3-dione disodium (CNQX), and D-(⫺)-2-amino-5-phosphonopentanoic acid (APV; Tocris) were added to the ACSF at a final concentration of 10, 20, and 20 ␮M, respectively.
Electrophysiological parameters. Intrinsic electrophysiological parameters were defined and measured as previously described (Ma et
al. 2006). The electrical coupling coefficient (ECC) was defined as the
ratio of the voltage deflection in the noninjected cell to the voltage
deflection in the injected cell just before offset of a 600-ms, ⫺30-mV
hyperpolarizing step and was averaged between the two directions of
connectivity. Pairs with ECC ⱖ0.5% in at least one direction were
considered electrically coupled. Synaptic connections were tested by
eliciting action potentials in the presynaptic cell every 8 s while
holding the postsynaptic cell at a depolarized potential (typically ⫺50
mV); 10 –15 responses were averaged. The one-way connection probability was calculated as (u ⫹ 2r)/2n, and the reciprocation probability
was calculated as 2r/(u ⫹2r), where u is the number of unidirectionally connected pairs, r is the number of reciprocally connected pairs,
and n is the total number of pairs. To test for bias toward reciprocal
connectivity, the unidirectionally connected FS pairs were nominally
defined as either A¡B or B¡A, and the 2 ⫻ 2 contingency table
(reciprocal, A¡B, B¡A, not connected) was tested using Fisher’s
exact test.
Synchrony analysis. Synchrony was quantified using the JitterBased Synchrony Index (JBSI) (Agmon 2012). The JBSI is a normalized measure of the rate of synchrony above (or below) that expected
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PROPERTIES OF FIRING SYNCHRONY BETWEEN CORTICAL INTERNEURONS
recorded in layers 3 and 5, all pairs were recorded in cortical
layer 4, typically from the same barrel. The largest center-tocenter separations between paired cells were 83 and 105 ␮m
for SOM and FS pairs, respectively. We used four different
mouse genotypes to target SOM or FS interneurons for recording (see MATERIALS AND METHODS); the majority of recorded
neurons were targeted by their fluorescence, but FS cells in
X94 mice were nonfluorescent and were targeted by their cell
body size and shape. The identity of each neuron as FS or SOM
was further verified by its characteristic firing pattern (Fig. 1A);
this was especially important when recording from SOM-RFP
mice, because about 15% of tdTomato-expressing neurons in
these animals were found to be FS interneurons (Hu et al.
2013) and were excluded from analysis. We measured seven
basic electrophysiological parameters for each neuron (Table 1);
with the exception of resting potential, differences in these
parameters between the two groups were both highly significant and large. When the two parameters with the most pronounced differences, spike width and adaptation ratio, were
plotted against each other, FS and SOM interneurons segregated nearly perfectly, whereas interneurons of the same subtype but different genotypes had largely overlapping distributions (Fig. 1B), suggesting that electrophysiological characteristics of an interneuron are strongly dependent on its subtype
but, at most, weakly dependent on its genotype.
Electrical and chemical connectivity in SOM and FS pairs.
In each interneuron pair, we used subthreshold current steps to
measure the steady-state ECC (see MATERIALS AND METHODS)
and recorded the synaptic response of one cell to an action
potential elicited in the other. As previously observed (Gibson
et al. 1999; Hu et al. 2011; Pfeffer et al. 2013), SOM pairs were
never connected by chemical synapses; however, 93% of SOM
pairs were coupled electrically (Fig. 2A; Table 2), with ECCs
ranging from our detection limit of ⬃0.5% to 24% (median
ECC: 6.0%). Within our data set, there was a weak negative
correlation between ECC and cell-cell distance (r2 ⫽ 0.09, P ⫽
0.03). In strongly coupled pairs, an action potential fired by one
neuron elicited a depolarizing junctional PSP (JPSP) in the
paired neuron [Fig. 2B; JPSPs are also referred to in the
literature as “electrical PSPs” (Gibson et al. 2005), “gap
junction potentials” (Tamas et al. 2000), or “spikelets”
Table 1. Intrinsic membrane parameters of FS and SOM
interneurons
SOM
FS
Parameter
Mean
SD
Mean
SD
P Value
Age, postnatal days
Vrest, mV
Vthreshold, mV
AHP, mV
Rin, M⍀
Spike height, mV
Spike width, ms
Adaptation ratio
18.5
⫺64.7
⫺38.4
11.0
104.8
72.4
0.35
0.38
2.2
1.7
4.1
2.1
28.8
8.6
0.06
0.09
18.7
⫺64.3
⫺35.6
17.9
69.5
67.5
0.21
0.77
1.9
1.8
5.2
3.5
13.9
9.4
0.03
0.18
0.48
0.07
⬍10⫺4
⬍10⫺4
⬍10⫺4
⬍10⫺4
⬍10⫺4
⬍10⫺4
Values are parameters in fast-spiking (FS; N ⫽ 185) and somatostatincontaining (SOM; N ⫽ 119) interneurons. Vrest, resting potential; Vthreshold,
threshold potential; AHP, afterhyperpolarization; Rin, input resistance.
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Fig. 1. Electrophysiological characteristics of somatostatincontaining (SOM) and parvalbumin-containing, fast-spiking
(FS) interneurons. A: voltage responses (top) to negative
and positive intracellular current steps (bottom). Compare
the adaptation in both firing frequency and spike height in
the SOM cell to the nearly constant firing rate and spike
height in the FS cell. Inset shows spike waveforms at a
faster time base (scale bar: 20 mV, 0.5 ms); note the wider
and taller waveform of the SOM spike and the deeper
afterhyperpolarization (AHP) of the FS spike. B, left: scatter
plot of adaptation ratio vs. spike width for 119 SOM and
185 FS interneurons included in our data set, color coded by
mouse line and layer. The diagonal line separates the 2
subtypes nearly perfectly, with only 1 cell per subtype
misclassified. Right, the same data plotted as boxes spanning the 10 –90 percentile ranges for each subgroup; the
2-dimensional median of each subgroup is indicated by a
marker. Note that the ranges for data points from different
mouse lines but belonging to the same subtype (SOM or FS)
nearly totally overlap, with the exception of layer 3 (L3) and
L5 SOM interneurons, which had somewhat wider spikes
and weaker adaptation compared with L4 SOM neurons
(Ma et al. 2006). See MATERIALS AND METHODS for details of
mouse lines.
PROPERTIES OF FIRING SYNCHRONY BETWEEN CORTICAL INTERNEURONS
627
(MacVicar and Dudek 1981)]. JPSP amplitudes (median: 0.6
mV, range: 0.2–3.0 mV, N ⫽ 38) were strongly correlated with
the ECC (r2 ⫽ 0.66, P ⬍ 0.0001). Note that we recorded JPSPs
at a depolarized holding potential (typically ⫺50 mV), so their
time course and amplitude were likely enhanced by intrinsic
subthreshold conductances (Curti and Pereda 2004; Gibson et
al. 2005; Mann-Metzer and Yarom 1999).
In contrast to SOM pairs, 85% of FS pairs were connected
chemically by one-way or reciprocal inhibitory synapses (Fig.
2D; Table 2); the distribution between one-way, reciprocal, and
no connectivity (39%, 46%, and 15%, respectively) was similar to that previously reported in adult mice (Galarreta and
Hestrin 2002). The one-way connection probability was 0.64,
but the reciprocation probability (the probability that a synapse
from A¡B will be reciprocated by a synapse from B¡A; see
MATERIALS AND METHODS) was 0.70, suggesting that a synaptic
connection in one direction slightly increases the probability of
a connection in the reciprocal direction; however, this bias did
not reach statistical significance (P ⫽ 0.12, Fisher’s exact test,
2-tailed). Unitary IPSP (uIPSP) amplitudes, measured at a
holding potential of ⫺50 mV, ranged from our noise limit of
about 0.2 mV to 4.7 mV, with one outlier of 8.1 mV (median:
1.2 mV, N ⫽ 121). The uIPSP reversal potential in our
recordings (not corrected for the liquid junction potential
introduced by the micropipette) was ⫺76.2 ⫾ 0.8 mV (N ⫽ 6).
Table 2. Summary of chemical and electrical coupling of FS and
SOM pairs
FS pairs
Not electrically
coupled
Electrically coupled
Total
SOM pairs
Not electrically
coupled
Electrically coupled
Total
No Chemical
Connection
One-Way
IPSP
Reciprocal
IPSP
Total
11 (12%)
3 (3%)
14 (15%)
18 (20%)
18 (20%)
36 (39%)
24 (26%)
18 (20%)
42 (46%)
53 (58%)
39 (42%)
92 (100%)
4 (7%)
56 (93%)
60 (100%)
4 (7%)
56 (93%)
60 (100%)
Values are numbers of interneuron pairs, with percentages given in parentheses. IPSP, inhibitory postsynaptic potential.
As measured for all uIPSPs ⱖ1.4 mV (N ⫽ 46), the synaptic
latency (from peak presynaptic spike to uIPSP onset) was 0.61 ⫾
0.02 ms, and the effective IPSP duration (from peak presynaptic spike to 10% of the IPSP peak) was 20.4 ⫾ 0.7 ms.
Also in contrast to SOM pairs, only 42% of FS pairs in our
data set were coupled electrically, and the great majority of
these were also coupled chemically (Fig. 2, E and F; Table 2).
ECCs of electrically coupled FS pairs were markedly small,
ranging from the noise limit of ⬃0.5% to 5.0% (median of
detectable ECCs: 1.5%). Thus FS pairs were 0.4 times as likely
as SOM pairs to be electrically coupled, and if coupled, they
were 4 times less strongly so, implying that electrical coupling
between FS interneurons was only ⬃10% as effective as
between SOM cells. An identical probability of FS-FS electrical coupling (42%) was reported in juvenile mice (PangratzFuehrer and Hestrin 2011), and identical average coupling
strength was reported in adult mice (Galarreta and Hestrin
2002). Within our data set, neither chemical nor electrical
connectivity of FS pairs was correlated with cell-to-cell distance. Chemically connected FS pairs, whether connected oneway or reciprocally, were more than twice as likely to be
electrically coupled as nonconnected pairs (0.43, 0.50, and
0.21 coupling probability in reciprocally, one-way, and nonconnected pairs, respectively; P ⫽ 0.054, Fisher’s exact test,
2-tailed). In contrast, electrically coupled FS pairs were only
slightly more likely to also be connected chemically, compared
with noncoupled pairs (0.92 vs. 0.79). Similar enrichment of
electrical coupling in chemically connected compared with
nonconnected pairs has been noted before in adult mice (Galarreta and Hestrin 2002) and juvenile rats (Gibson et al. 2005);
this suggests that chemical connectivity between two interneurons is linked in some manner (causal or otherwise) to formation or stabilization of gap junctions.
In this article, we refer to paired interneurons communicating only through chemical synapses, whether one-way or
reciprocal, as chemically coupled, or C-coupled; to pairs communicating only through electrical synapses as electrically
coupled, or E-coupled; and to pairs communicating through
both types of synapses as dually coupled, or D-coupled. Pairs
with neither chemical nor electrical connections are referred to
as noncoupled. By these definitions, 45% of FS pairs were
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Fig. 2. Electrical and chemical connectivity of SOM and FS
pairs. Response of 1 cell (top trace) to a hyperpolarizing current
step (A, C, E) or to an action potential (B, D, F) in the paired
cell (bottom trace). Schematics at right illustrate the respective
mode of coupling: electrical (E-coupled; top), chemical (Ccoupled; middle) or dual (D-coupled; bottom). In E- or D-coupled pairs (A and E), a hyperpolarizing step induced by current
injection in 1 cell was reflected by a passively conducted,
smaller hyperpolarization in the paired cell. In strongly E-coupled pairs (B), an action potential in 1 cell was followed by a
passive slower depolarizing potential (JPSP) in the paired cell.
In C-coupled pairs (D), an action potential in the presynaptic
cell was followed by an inhibitory postsynaptic potential (IPSP)
in the paired cell. In some D-coupled pairs (F), an action
potential in the presynaptic cell was followed by a biphasic,
electrical-chemical postsynaptic response in the paired cell.
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PROPERTIES OF FIRING SYNCHRONY BETWEEN CORTICAL INTERNEURONS
the postnatal day 15–22 age range and suggests that the major
phase in postnatal interneuron development is over (or nearly
so) by the third postnatal week, although we cannot rule out a
second, late phase of maturation beyond the ages we examined.
SOM and FS pairs displayed long-lasting, stable firing
synchrony. To examine firing synchrony and compare it between E-, C-, and D-coupled pairs, we evoked firing in interneuron pairs by injecting periodic currents steps (600-ms
steps at 5-s intervals) into one cell (the “driver”; Figs. 3, A and
B, and 4, A–C, red traces) and constant current into the other
(the “follower”; blue traces); in C- or D-coupled FS pairs, the
cell eliciting the stronger IPSP was selected as driver. The
firing rates of both driver and follower cells varied over a wide
range (see below); however, the driver cell always fired ⬃1.5
to 4 times faster than the follower. We quantified firing synchrony using a novel index, the JBSI, which is a normalized
measure of the fraction of follower spikes synchronous with
any driver spikes (see MATERIALS AND METHODS and Agmon
2012 for computational details). The JBSI is derived by subtracting out any synchrony that survives a virtual jitter of spike
times; it therefore depends on both the chosen synchrony
window (the maximum lag between 2 spikes considered synchronous) and the jitter window. Unless stated otherwise, these
two parameters were ⫾2 ms and ⫾4 ms, respectively. A
by-product of the JBSI computation is an estimate of the
statistical significance of the observed synchrony, in the form
of a Z score; we considered Z scores ⬎2.6 (i.e., ⬎2.6 SD from
the mean, equivalent to P ⬍ 0.01) to indicate nonrandom
synchrony. In general, pairs with JBSI ⱖ 0.08 displayed
statistically significant synchrony. The two pairs illustrated in
Fig. 3, A and B, had JBSI values of 0.40 and 0.67 and Z scores
Fig. 3. SOM and FS pairs displayed long-lasting, stable firing
synchrony. A and B: the basic protocol used to identify and
estimate synchrony. One cell in the pair (driver cell; red traces)
was strongly activated by 600-ms current steps repeated every
5 s, whereas the other (follower cell; blue traces) was depolarized above threshold by constant current; the red and blue traces
are displaced vertically for clarity. Asterisks at top indicate
synchronous spikes (peaks within 2 ms of each other); the
circled asterisk indicates the spike pair shown at a faster time
base at bottom. C and D: a traditional cross-correlogram representation of the same pairs, computed from 400 spikes in the
follower cell; bins are 4 ms wide. The height of the central bin
indicates the fraction of follower spikes that are within ⫾2 ms
of a driver spike. E and F: a synchrony index (JBSI) was
calculated for 10 representative SOM and 12 FS pairs from
increasingly longer segments of the full spike train and normalized to its value at 1,000 spikes (JBSI1000); note the shortterm fluctuations, especially in FS pairs, but the long-term
stability of the JBSI.
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C-coupled and 38% were D-coupled, but only 3% were E-coupled. A similar scarcity of E-coupled FS pairs was previously
reported in adult mice (4%; Galarreta and Hestrin 2002) and
juvenile rats (7%; Gibson et al. 2005).
Age-dependent changes in intrinsic and synaptic properties
were minor. Rodent cortical interneurons are still developing
during the third and early fourth postnatal weeks, the age range
represented by our data set (Angulo et al. 1999b; Doischer et
al. 2008; Goldberg et al. 2011; Okaty et al. 2009; reviewed by
Le Magueresse and Monyer 2013); we therefore examined our
data for age-dependent changes in intrinsic and synaptic properties of SOM and FS interneurons. Most membrane and spike
parameters showed no significant correlations with age, and
those that did changed only slightly over the age range of our
sample. In SOM cells, the only parameter that showed a
statistically significant age-dependent changes was spike
width, with the trend line decreasing over the sampled age
range by about 0.08 ms (r2 ⫽ 0.18, P ⬍ 0.0001). In FS cells,
the spike height trendline increased by ⬃5 mV (r2 ⫽ 0.03, P ⫽
0.03) and spike threshold became more negative by ⬃3 mV
(r2 ⫽ 0.04, P ⫽ 0.009). Importantly, neither subtype exhibited
any statistically significant age-dependent changes in uIPSP or
ECC amplitudes. These findings are consistent with previous
studies showing that by the beginning of the third postnatal
week, the developmental trend in most intrinsic and synaptic
properties of FS interneurons has leveled out, or nearly so
(Doischer et al. 2008), FS-FS connection probability has stabilized (Pangratz-Fuehrer and Hestrin 2011), SOM interneurons have acquired their ability to synchronize (Long et al.
2005), and the process of programmed interneuron death is
over (Southwell et al. 2012). This justifies pooling data over
PROPERTIES OF FIRING SYNCHRONY BETWEEN CORTICAL INTERNEURONS
synchrony. As an estimate of the contribution of chemical vs.
electrical synapses to firing synchrony, we used the regression
equation derived from C-coupled FS pairs (Fig. 4E) to predict
the JBSI expected in D-coupled pairs based on their chemical
connectivity alone. The actual JBSI was, on average, 1.66
times higher than that predicted from the IPSP alone, suggesting that electrical coupling contributed, on average, 40% of the
synchrony in D-coupled FS pairs.
In pairs of cortical neurons, correlations in the number of
spikes (counted over tens or hundreds of milliseconds) fired in
response to repeated stimuli have been shown to increase with
firing rate (de la Rocha et al. 2007; Greenberg et al. 2008); we
therefore asked whether millisecond-scale synchrony between
coupled interneurons was also firing rate dependent. Unlike
some commonly used measures of synchrony (Turker and
Powers 2002), the JBSI is intrinsically independent of firingrate (Agmon 2012) and can therefore report correctly any firing
rate dependency of synchrony. To test for correlation between
synchrony and firing rate, we computed for each pair the
average firing rate of the driver (phasically driven) and follower (tonically driven) cell from the same spike trains used for
computing the JBSI. Synchrony in all three groups was correlated with the driver firing rate (Fig. 4, G–I; r2 ⫽ 0.29, 0.20,
and 0.58, P ⫽ 0.0001, 0.003, and ⬍0.0001 for SOM, C-coupled FS, and D-coupled FS pairs, respectively, after exclusion
of the 3 outliers circled in Fig. 4, G–I), but only SOM pair
synchrony was correlated with the follower firing rate, and
weakly at that (r2 ⫽ 0.16, 0.001, and 0.09, P ⫽ 0.003, 0.19,
and 0.08, respectively), thus justifying the terms “driver” and
“follower.”
To estimate the relative contributions of electrical coupling,
inhibitory synaptic connections, and driver firing rate to pairwise interneuron synchrony, we performed multiple linear
regression of the JBSI on these three variables (Table 3). More
than half the variance in JBSI (R2 ⫽ 0.54 and 0.60 for SOM
and FS pairs, respectively) was explained by these variables.
The relative contribution of each variable to pairwise synchrony was estimated from its standardized multiple regression
coefficient (␤). In SOM pairs, the contribution of the ECC was
more than twice as strong as that of the firing rate, and in FS
pairs the contribution of the uIPSP was ⬎1.5 times stronger
than either firing rate or the ECC (Table 3). Interestingly,
replacing the ECC in FS cells with a categorical variable
(“coupled/not-coupled”) increased the R2 value to 0.64 while
approximately equalizing the contributions of electrical and
chemical coupling (Table 3), suggesting that even weak coupling between chemically connected FS cells can have a
significant effect on synchrony and that electrical and chemical
synapses interact in a nonlinear manner to promote firing
synchrony, as predicted theoretically (Traub et al. 2001).
Although the analysis above indicates that synchrony was
correlated with the strength of the electrical and/or chemical
coupling and with the driver firing rate, correlations do not
necessarily imply causation. To test for causality between
inhibitory synapses and synchrony, we compared JBSI values
in 33 pairs before and after pharmacologically blocking fast
GABAergic neurotransmission (GABAA receptors were blocked
in isolation or together with ionotropic glutamate receptors). As
expected, blocking GABAA receptors in E-coupled SOM pairs
left JBSI values unchanged (increased by 0.9 ⫾ 2.4%, N ⫽ 5;
Fig. 4J), whereas JBSI values in C-coupled FS pairs were
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of 8.6 and 14.4, respectively, calculated from the first 400
follower spikes in the train. For comparison, the conventional
cross-correlogram representations of the same spike trains are
shown in Fig. 3, C and D. Note that the cross-correlogram
peaks were symmetric around 0 lag, indicating that within each
synchronous spike pair there was no systematic firing order to
the two neurons.
Because synchrony computation required long spike trains,
we were concerned that the JBSI might not be a stable
parameter but would decay with time or with the number of
spikes due to rundown of electrical or synaptic connections. To
test for such rundown, we compared the JBSI calculated from
the first 1,000 follower spikes (JBSI1000) with that calculated
from the first 200 spikes (JBSI200) for all pairs with JBSI ⬎ 0.4
(N ⫽ 12 SOM pairs and 26 FS pairs). With the exception of 5
SOM pairs (below), the ratio JBSI200/JBSI1000 varied between
0.86 –1.22 (geometric mean: 1.06) and 0.48 –1.65 (geometric
mean: 1.03) for SOM and FS pairs, respectively, and was not
significantly different from 1 (P ⫽ 0.06 and P ⫽ 0.29). (In 5
SOM pairs recorded sequentially using the same batch of
intracellular solution, there was a clear rundown of synchrony,
with a JBSI200/JBSI1000 ratio of 2–3; these pairs were excluded
from further analysis.) For 10 representative SOM and 12 FS
pairs, we also calculated the JBSI for an increasing number of
follower spikes, from 100 to 1,000, at 200-spike increments.
JBSI values of SOM pairs remained within ⬃20% of their
JBSI1000 (Fig. 3E). JBSI values of FS pairs fluctuated relative
to JBSI1000, but these fluctuations were in general symmetric
between different pairs, and with increasing number of spikes
the JBSI approached a steady value (Fig. 3F). Beyond simply
a manifestation of the law of large numbers, this analysis
suggested that synchrony was a stable parameter and that
deviations from the long-term value at lower spike counts were
statistical fluctuations rather than a systematic shift. On the
basis of this analysis, we selected 200 follower spikes as a
minimum requirement for computing synchrony; in actuality,
synchrony in most pairs was calculated from many more spikes
(on average ⬃800, typically collected over a 5-min period).
Interneuron synchrony depended on electrical coupling,
chemical connectivity, and driver firing rate. As expected from
their strong electrical coupling, 96% of all SOM pairs tested
with current steps (N ⫽ 49) exhibited nonrandom synchrony.
JBSI values of SOM pairs (0.43 ⫾ 0.04) were well correlated
with the ECC (r2 ⫽ 0.45, P ⬍ 0.0001; Fig. 4D) and even better
correlated with the JPSP (r2 ⫽ 0.65, N ⫽ 38). The majority
(89%) of all FS pairs similarly tested (N ⫽ 79) also fired
synchronously. As previously demonstrated (Gibson et al.
2005; Hu et al. 2011), synchrony between interneurons can be
driven by one-way or reciprocal inhibitory synapses, and
indeed JBSI values of C-coupled FS pairs (0.22 ⫾ 0.03, N ⫽
42) were well correlated with the amplitude of the uIPSP (r2 ⫽
0.58, P ⬍ 0.0001; Fig. 4E; for reciprocal connections, the JBSI
is plotted against the larger of the two uIPSPs). Even though
the average uIPSP was not significantly different between
C-coupled and D-coupled FS pairs (P ⫽ 0.30), the average
JBSI in D-coupled pairs (0.48 ⫾ 0.04, N ⫽ 36) was more than
twice as high as in C-coupled pairs (P ⬍ 0.0001). Moreover,
the JBSI in D-coupled pairs was not as well correlated with the
uIPSP (r2 ⫽ 0.27, P ⫽ 0.0002; Fig. 4F), suggesting that
synchrony was only partially attributable to chemical synapses
and that electrical coupling also contributed to the observed
629
630
PROPERTIES OF FIRING SYNCHRONY BETWEEN CORTICAL INTERNEURONS
reduced by 90 ⫾ 5.3% (N ⫽ 10; Fig. 4K), confirming that
GABAergic synapses were necessary for synchrony between
C-coupled FS interneurons (see also Hu et al. 2011). In
D-coupled FS pairs, blocking GABAA receptors reduced JBSI
values by 69 ⫾ 5.8% (N ⫽ 18; Fig. 4L), implying that
electrical coupling contributed about 30% of firing synchrony
in this subset.
Next, we tested for causality between firing rate and
synchrony in a subset of SOM pairs and FS pairs by firing
the driver cell at predetermined frequencies of 40, 80, and
120 Hz with brief current steps while depolarizing the
follower cells tonically with constant current (Fig. 5, A and
B). The follower firing rates in these experiments were
allowed to co-vary with the driver rates but were two to four
times slower. This protocol, in which the precise spike times
of the driver cell were predetermined by the experimenter,
resulted in considerably lower JBSI values compared with
the protocol illustrated in Fig. 4, especially in SOM pairs.
To avoid floor and ceiling effects, we excluded from this
analysis pairs in which JBSI values at all frequencies remained ⱕ0.1 (3 FS and 4 SOM pairs) or ⱖ0.9 (1 SOM pair).
Within the remaining pairs, synchrony between E-coupled
SOM interneurons (N ⫽ 11) increased modestly with the
firing rate of the driver cell, with the average JBSI increasing by 0.08 ⫾ 0.03 between 40 and 120 Hz (Fig. 5C). In
contrast, synchrony in C-coupled FS pairs (N ⫽ 8) was
strongly firing rate dependent, with JBSI values increasing
by 0.41 ⫾ 0.07 over the same range of firing rates, 5 times
more than in SOM cells (P ⫽ 0.0006; Fig. 5D). Comparing
the degree of increase (fold increase) in JBSI values between 40 and 120 Hz yielded a similar result: a 1.32 ⫾
0.28-fold increase in SOM pairs (geometric mean) compared with a 7.13 ⫾ 1.27-fold increase in FS pairs (Fig. 5,
E and F; P ⬍ 0.0001). The fold increase in JBSI was not
correlated with the JBSI (r2 ⬍ 0.01). Importantly, half of the
FS pairs showed no statistically significant synchrony at 40
Hz (Fig. 5D), which is notable in light of the proposed role
for FS interneurons in generating 40-Hz oscillations (see
DISCUSSION). Interestingly, the one E-coupled FS pair tested
(blue triangles in Fig. 5C) exhibited a 1.9-fold increase in
JBSI, from ⬃0.2 at 40 Hz to ⬃0.4 at 120 Hz, and thus
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Fig. 4. Interneuron synchrony depends on electrical synapses, chemical synapses, and firing rate. A–C: to test for
firing synchrony, paired spike trains were elicited by suprathreshold current steps in the driver cell (red traces) and
by tonic suprathreshold depolarization in the follower cell
(blue traces). D–F: strength of synchrony (as quantified by
the JBSI) was well correlated with the electrical coupling
coefficient (ECC) in E-coupled SOM pairs (r2 ⫽ 0.45) and
with the unitary IPSP (uIPSP) in C-coupled FS pairs (r2 ⫽
0.58) and not as well correlated with the uIPSP in D-coupled FS pairs (r2 ⫽ 0.27). Data points corresponding to the
example pairs are circled in red. G–I: the JBSI correlated
with the firing rate of the driver cell (r2 ⫽ 0.29, 0.20, and
0.58, respectively), but not the follower cell (not shown).
The regression lines and correlation coefficients were calculated after exclusion of the 3 outlier data points circled in
blue in G and I. J–L: blocking GABAA receptors, with or
without blocking ionotropic glutamate receptors, had no
effect on synchrony between E-coupled SOM pairs (J),
abolished synchrony between C-coupled FS pairs (K),
and suppressed but did not abolish synchrony between
D-coupled FS pairs (L). CNQX, 6-cyano-7-nitroquinoxaline-2,3-dione disodium; APV, D-(⫺)-2-amino-5-phosphonopentanoic acid.
PROPERTIES OF FIRING SYNCHRONY BETWEEN CORTICAL INTERNEURONS
Table 3. Multiple linear regression of the JBSI on uIPSP, ECC,
and driver firing rate
SE
P Value
0.54
⫺0.10
0.65
0.30
0.18
0.11
0.10
0.10
⬍10⫺6
0.36
⬍10⫺6
0.005
0.60
⫺0.07
0.53
0.31
0.27
0.15
0.06
0.08
0.08
0.08
⬍10⫺6
0.24
⬍10⫺6
0.0001
0.002
0.64
⫺0.10
0.45
0.38
0.30
0.14
0.05
0.07
0.07
0.08
⬍10⫺6
0.07
⬍10⫺6
1⫻10⫺6
0.0002
chronous with a given spike in the paired train will fall after the
jitter into the synchrony window of another spike. This JBSI
decline to the right was always much slower than the drop-off
to the left.) We plotted the JBSI for jitter windows decreasing
from 16 to 0.5 ms in multiples of 公2/2, keeping the synchrony
window at half the jitter window, and defined the temporal
resolution (Rt) of a pair as the (interpolated) point at which the
JBSI dropped to half its maximal value (Fig. 6A). Thus, lower
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SOM pairs
R2
Intercept
ECC ␤
Driver rate ␤
FS pairs
R2
Intercept
uIPSP ␤
ECC ␤
Driver rate ␤
FS pairs
R2
Intercept
uIPSP ␤
Coupled Y/N? ␤
Driver rate ␤
Value
631
Multiple linear regression of the Jitter-Based Synchrony Index (JBSI) shows
relative contributions of electrical coupling (ECC, electrical coupling coefficient), inhibitory synaptic connections (unitary IPSP, uIPSP), and driver firing
rate to pairwise synchrony in SOM (N ⫽ 49 pairs) and FS (N ⫽ 80 pairs)
interneurons. Replacing the ECC in FS cells with a categorical variable
(coupled/not coupled; 2nd set of data for FS pairs) increased the R2 value and
approximately equalized the contributions of electrical and chemical coupling
(see text).
resembled E-coupled SOM pairs rather than C-coupled FS
pairs in its frequency dependence.
Chemically driven synchrony is more precise than electrically driven synchrony. Firing synchrony has two distinct
attributes: strength and precision. Strength (for example, as
measured by the JBSI) reflects the rate of synchronous firing
above chance level, whereas precision is a measure of how
“sharp” the synchrony is, or how small are the time lags
between synchronous or near-synchronous spikes. For illustration, when the well-known cross-correlogram method is used,
synchrony strength is estimated from the height of the central
peak of the cross-correlogram, whereas precision is estimated
from the width of this peak. Precision of synchrony can be
regarded as a measure of the relevant time scale used by the
neural system under study, i.e., its temporal resolution (Amarasingham et al. 2012; Hatsopoulos et al. 2003). It was therefore of interest to determine and compare precision of synchrony between pairs of interneurons of different subtypes and
different modes of connectivity. Because the JBSI is a measure
of the difference between the observed synchrony count and
the expected count after a random jitter, and because jitter by
less than the temporal resolution of the system should not
affect the synchrony count, the JBSI should rapidly fall to zero
once the jitter window falls below the system’s temporal
resolution. One can therefore estimate the system’s temporal
resolution by plotting the JBSI for decreasing jitter windows
and determining the point where the plot drops off sharply to
the left (Agmon 2012); intuitively, this point represents the
maximal spike time jitter that would not be noticed by a
downstream observer counting the rate of synchronous spikes.
(Note that the JBSI will also fall off to the right, i.e., for longer
jitter windows, because at jitter windows larger than the
interspike interval (ISI) of the paired neuron, there is an
increased probability that a spike which was originally syn-
Fig. 5. Chemically driven, but not electrically driven, synchrony is strongly
firing rate dependent. A and B: firing at predefined rates (40, 80, 120 Hz) was
elicited in the driver cell (red traces) by trains of 20 brief current pulses
repeated every 3 s, and tonic firing was elicited in the follower cell (blue traces)
by constant current injection. C and D: summary plots of JBSI at each firing
rate for all pairs tested; red symbols are group averages. Data points corresponding to the 2 example pairs are circled in red. E and F: the same data
normalized to the JBSI value at 40 Hz. Synchrony was strongly dependent on
driver firing rate in C-coupled FS pairs (D and F) and only weakly so in
E-coupled SOM pairs (C and E). One E-coupled FS pair (filled triangles) is
included with the SOM pairs in C; it resembled E-coupled SOM pairs rather
than C-coupled FS pairs.
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632
PROPERTIES OF FIRING SYNCHRONY BETWEEN CORTICAL INTERNEURONS
Rt values correspond to higher precision of synchrony. Because this calculation became noisy at low JBSI values, we
included in the analysis only pairs with JBSI ⱖ 0.15 (N ⫽ 44,
25, and 34 for SOM, C-coupled FS, and D-coupled FS pairs,
respectively). Superimposed normalized plots of JBSI vs. jitter
window for five representative pairs from each group are
shown in Fig. 6A, and cumulative histograms of Rt for each
group are plotted in Fig. 6B. As evident from these histograms,
there was no significant difference between the cumulative Rt
distributions of C-coupled and D-coupled FS pairs (red and
green data points in Fig. 6B; medians ⫽ 1.84 and 1.92 ms,
respectively; P ⫽ 0.36). There was, however, a highly significant difference between Rt of FS pairs and that of SOM pairs
(blue data points in Fig. 6B; median ⫽ 2.54; P ⬍ 0.0001). Rt
of FS pairs was independent of the JBSI (r2 ⬍ 0.03, P ⫽ 0.22),
but Rt of SOM pairs was inversely correlated with the JBSI
(r2 ⫽ 0.42, P ⬍ 0.0001), likely because higher JBSI resulted
from larger and faster-rising JPSPs, and the latter evoked
spikes in the coupled interneuron with less jitter. We conclude
that firing synchrony in E-coupled SOM pairs was about 25%
less precise than synchrony in C- or D-coupled FS pairs.
Simulations reproduced the observed differences between
electrically and chemically driven synchrony. The two major
differences we observed between FS-FS and SOM-SOM synchrony, the stronger firing rate dependence and the higher
precision of FS-FS synchrony, could be explained in two
different ways. They could result from the mode of connectivity (electrical vs. chemical synapses) or they could reflect the
well-documented differences in intrinsic properties between
these two interneuron subtypes, including shorter membrane
time constants, faster EPSP and IPSP kinetics, and presence of
autapses, characteristic of FS interneurons (Angulo et al.
1999a; Bacci and Huguenard 2006; Bartos et al. 2002; Beierlein et al. 2003; Fricker and Miles 2000; Galarreta and Hestrin
2001; Tan et al. 2008). Our observations were based on
comparison of E-coupled SOM pairs to C- or D-coupled FS
pairs; because we found no C-coupled SOM pairs and very few
E-coupled FS pairs, we could not differentiate between connectivity-based and intrinsic properties-based factors experimentally. We therefore addressed this question with computer
simulations. We implemented a reduced integrate-and-fire
model of pairs of neurons with identical intrinsic parameters,
divided into two groups differing only in their mode of con-
nectivity being electrical or chemical, so an action potential in
one cell was followed by a JPSP or an IPSP, respectively, in
the paired cell (Fig. 7, A and B; see MATERIALS AND METHODS for
details). JPSPs were depolarizing and occurred with 0 latency,
whereas IPSPs were hyperpolarizing and occurred after a 1-ms
latency. Both types of responses had a 1- to 2-ms rise time and
decayed with the time constant of the membrane, set to 10 ms;
with these settings the duration of simulated uIPSPs was about
20 ms, similar to experimental ones. Notably, the results were
robust to realistic variations in most parameters (see below).
Subthreshold electrical coupling was not incorporated into the
model, and neither was dual connectivity. We tested the modeled pairs for firing rate dependence of synchrony as we did in
our experiments, stimulating the driver neuron (in FS pairs, the
presynaptic) with trains of brief current steps at three different
frequencies, and depolarizing the follower neuron with constant current (Fig. 7, C and D). The firing rate of the follower
cell and the amplitudes of JPSPs and IPSPs were allowed to
vary within experimentally observed values. The results of a
set of 90 runs of the simulation (15 runs per firing rate per
group) are plotted in Fig. 7, E and F. Clearly, the simulation
reproduced the strong firing rate dependence of C-coupled
pairs and the much weaker dependency of E-coupled pairs
observed experimentally without assuming any intrinsic differences between the neurons (compare Fig. 7, E and F, to Fig. 5,
C and D, respectively). To test for differences in precision of
synchrony, we ran simulations in which both neurons were
depolarized tonically and the firing rates of both neurons, as
well as the JPSP and IPSP amplitudes, were varied within
experimentally observed ranges. We then calculated the JBSI
of each run for a range of jitter windows, as shown in Fig. 6 for
the experimental pairs. Normalized JBSI vs. Jitter Window
curves for 5 representative runs from each group are superimposed in Fig. 7G, and cumulative Rt histograms from 50
representative runs from each group are plotted in Fig. 7H.
Again, the simulation reproduced the experimentally observed
difference in temporal precision between E-coupled and Ccoupled pairs without assuming any intrinsic differences between the two groups (compare Fig. 7, G and H, to Fig. 6, A
and B, respectively).
To further explore the origin of the difference in precision
between the two modes of connectivity, and also to test the
robustness of our conclusions to variations in the assumed
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Fig. 6. Chemically driven synchrony was more precise than electrically driven synchrony. A: normalized JBSI values computed for decreasing jitter windows,
from pairs tested by current steps, are plotted against the jitter window for 5 representative pairs from each group (blue lines for E-coupled SOM pairs, red and
green lines for C- and D-coupled FS pairs, respectively). The jitter window for which the JBSI drops to half its maximum (crossing the horizontal dotted line)
is defined as the temporal resolution (Rt) of that pair and is inversely related to firing precision. B: cumulative histograms of Rt for pairs tested by current steps;
only pairs with peak JBSI ⱖ 0.15 are included. Precision of C- and D-coupled FS pairs was similar to each other but significantly better (by about 1⁄3) than
precision of E-coupled SOM pairs (note the differences in medians, the points intersecting the horizontal dotted line).
PROPERTIES OF FIRING SYNCHRONY BETWEEN CORTICAL INTERNEURONS
633
the assumed 1 ms toward the experimentally observed values
of ⬃0.6 ms) shifted the Rt histogram to the left, i.e., increased
the precision of C-coupled pairs. We conclude that our simulations, if anything, underestimated the difference in precision
between E-coupled and C-coupled pairs, and that the precision
of synchrony in E-coupled pairs was constrained mainly by the
rise time of the JPSP, whereas the precision of synchrony in
C-coupled pairs was constrained mainly by the synaptic delay.
DISCUSSION
parameters of the model, we conducted additional simulations
in which we varied the synaptic delay and rise time of the JPSP
and the IPSP. Increasing either the rise time of the JPSP (from
the assumed 1 ms) or its synaptic delay (from the assumed 0)
shifted the cumulative histogram of E-coupled pairs to the
right, i.e., reduced the precision of E-coupled pairs even
further. In contrast, increasing the rise time of the IPSP (from
the assumed 1 ms) had negligible effect on precision of
synchrony in C-coupled pairs, but reducing IPSP latency (from
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Fig. 7. Simulations reproduced the observed differences between electrically
and chemically driven synchrony. A reduced integrate-and-fire model was used
to simulate paired spike trains from interconnected neurons with identical
intrinsic properties. A and B: electrical coupling was simulated by a JPSP
following a spike in the paired neuron with 0 latency, and chemical coupling
was simulated by an IPSP following a spike in the presynaptic neuron with
1-ms latency. Both postsynaptic potentials decayed at the membrane time
constant, assumed to be 10 ms. C: simulated paired spike trains in which 1
neuron (red traces) was induced to fire at predefined frequencies while the
other (blue traces) was tonically depolarized, as in our experiments; the level
of tonic depolarization was varied within experimental values, as were the
JPSP and IPSP amplitudes. E and F: JBSI plotted against firing rate for 15
simulated pairs from each group. Filled symbols indicate medians. Synchrony
by E-coupling was weakly firing rate dependent, but synchrony by C-coupling
was strongly firing rate dependent, similarly to our experiments (compare with
Fig. 5, C and D). G: JBSI plotted at decreasing jitter windows for 5 representative simulated pairs from each group (compare with Fig. 6A). H: cumulative
firing precision for 50 simulated pairs from each group (compare with Fig. 6B).
The goals of this study were to characterize firing synchrony
between pairs of mouse neocortical interneurons and to relate
its properties to the subtype identity (SOM or FS) and synaptic
connectivity (electrical, chemical, or dual) of the paired interneurons. Our data set included over 150 homotypic pairs of
interneurons induced to fire in isolation, on the background of
quiescent brain slices, so network effects beyond mutual synaptic interactions (e.g., common excitatory or inhibitory inputs
originating in the surrounding network) were presumably absent. Our main findings were that 1) when driven to fire at
relatively high rates, pairs of interneurons exhibited strong and
stable synchrony that depended on electrical coupling in SOM
pairs and on chemical or dual coupling in FS pairs; 2) whereas
electrically driven SOM-SOM synchrony was only weakly
dependent on firing rate, chemically driven FS-FS synchrony
required high firing rates (ⱖ80 Hz) in the presynaptic (driver)
cell and was not evident at the prototypical 40-Hz gamma
frequency (see also Gibson et al. 2005); 3) precision of synchrony was about one-third higher in C- and D-coupled FS
pairs compared with E-coupled SOM pairs; and 4) a minimal
integrate-and-fire model, in which intrinsic properties were
identical in all neurons, captured the differences in firing rate
dependence and precision of synchrony observed experimentally between electrically and chemically coupled interneurons,
implying that the mode of coupling was sufficient to account
for these difference.
Limitations of our methods. Our conclusions are obviously
constrained by our use of a reduced in vitro preparation.
Extracellular recordings in vivo would have the dual advantage
of studying an intact brain while recording from a large number
of neurons simultaneously, but could not resolve subthreshold
responses, crucial for quantifying chemical and electrical coupling, and could not classify the recorded neurons by morphological and electrophysiological criteria beyond the limited
distinction possible from extracellular spike waveforms. Although these disadvantages can in principle be overcome by
paired intracellular recordings in vivo, such experiments are
extremely difficult and rarely reported (Lampl et al. 1999;
Poulet and Petersen 2008; Steriade et al. 1998). Our slices did
not maintain long-range connections from thalamus or from
other cortical areas and may have lost a considerable fraction
of local connectivity, as well (Levy and Reyes 2012; Stepanyants et al. 2009). Specifically, incidence and strength of
inhibitory FS-FS connections in the slice are likely to be an
underestimate of their values in vivo. This implies that the
reported JBSI values of FS pairs could have been underestimated; however, such an underestimate should not have affected conclusions 2) and 3) above, about frequency dependence or precision of synchrony, because these properties were
not correlated with the JBSI. Finally, our recordings were
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PROPERTIES OF FIRING SYNCHRONY BETWEEN CORTICAL INTERNEURONS
Deans et al. 2001; Galarreta et al. 2004; Galarreta and Hestrin
1999; Gibson et al. 1999). Stronger coupling generates larger
JPSPs, which are more likely to fire the follower interneuron,
explaining the dependence of the JBSI on the ECC. We found
that synchrony by electrical coupling, although strong, was
considerably less precise than synchrony by chemical or dual
connectivity (Fig. 6B). Our simulations suggest that precision
of electrically driven synchrony is constrained by the rise time
of the JPSP: the faster the rise time, the faster it will bring the
follower cell to firing threshold and the shorter the time lag
between the presynaptic and postsynaptic spikes. In many
pairs, the JPSP was relatively weak and slow rising, allowing
a broader and less precise window of opportunity and thus
generating lower precision synchrony, compared with chemically connected pairs. Note however that this conclusion is
based only on E-coupled SOM pairs and may not necessarily
be generalizable to E-coupled FS pairs, because we found very
few of the latter. As previously observed, JPSPs between
E-coupled FS pairs have biphasic waveforms, with a second,
negative phase reflecting the presynaptic AHP (Galarreta and
Hestrin 2001; Gibson et al. 2005); this may result in more
precise synchrony compared with the monophasic JPSPs observed in SOM interneurons.
Dual connectivity, electrical and chemical, has also been
described in a variety of cortical interneuron subtypes (Blatow
et al. 2003; Chu et al. 2003; Galarreta et al. 2004; Galarreta and
Hestrin 1999; Gibson et al. 1999; Olah et al. 2007; Szabadics
et al. 2001; Tamas et al. 2000), and its role in synchronizing
firing has received considerable theoretical attention, sometimes with conflicting conclusions. We found that the relatively
weak electrical coupling of D-coupled FS pairs resulted in a
twofold increase in synchrony compared with C-coupled pairs
with comparable chemical connectivity strength (Fig. 4, E and
F). This is consistent with models suggesting that addition of
weak electrical coupling to strong inhibitory coupling promotes a large, supralinear increase in synchrony, possibly
because electrical coupling keeps the subthreshold membrane
trajectories of the two neurons from diverging (Kopell and
Ermentrout 2004; Pfeuty et al. 2005, 2007; Traub et al. 2001).
Role of interneuron synchrony in gamma oscillations. The
activated state of the cortical network is often manifested as
“40 Hz,” or more generally 30 –90 Hz, field potential spectral
components known as gamma oscillations (reviewed in Buzsaki and Wang 2012; Fries et al. 2007), thought to be indicative
of conscious cognitive processes such as memory, attention,
and perception (Jensen et al. 2007; Melloni et al. 2007; Ward
2003). Synchronous firing of FS interneurons is proposed as
the major driver of gamma oscillations (reviewed in Bartos et
al. 2007), and two classes of models, so-called ING and PING,
invoke either purely interneuron-interneuron connections or
pyramidal-interneuron connections, respectively, in generating
this synchrony (Tiesinga and Sejnowski 2009; Whittington et
al. 2011). Our results imply that FS interneurons are not likely
to synchronize at ⬃40 Hz through mutual inhibition alone,
putting in question ING-like mechanisms as generators of
slower gamma rhythms. Consistent with this conclusion, genetic removal of FS-FS inhibitory synapses does not affect
gamma oscillations (Wulff et al. 2009), and hippocampal FS
cells are only weakly modulated at ⬃40-Hz gamma frequencies (Tukker et al. 2007). Note that our results do not rule out
PING-like mechanisms (Atallah and Scanziani 2009; Mann et
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limited to pairs of interneurons and thus may have missed
higher-order interactions in the network (Ohiorhenuan et al.
2010); however, much of the collective behavior of multineuron networks may be satisfactorily captured by sampling these
interactions pairwise (Schneidman et al. 2006).
How chemical inhibitory synapses drive synchrony. That
mutual inhibitory connections alone can generate precise spike
synchrony has been demonstrated experimentally in cerebellar
Purkinje cells (de Solages et al. 2008) and cortical interneurons
(Gibson et al. 2005; Hu et al. 2011; Merriam et al. 2005). How
can inhibition drive precise synchrony? When a presynaptic
inhibitory neuron fires repetitively with ISIs shorter than the
IPSP time course (which was ⬃20 ms in our data set), firing
probability in the postsynaptic neuron will follow the time
course of the IPSP; it will be highest just before the onset of the
next IPSP, when inhibition is at a local minimum. Onset of the
next IPSP will occur one synaptic delay after the next presynaptic spike; this represents the closing of the “window of
opportunity” for the postsynaptic cell to fire in that cycle,
which explains why in our simulations precision was increased
when synaptic delay was decreased. The onset of the window
of opportunity will depend on the driver firing rate; because the
decay of the IPSP follows an exponential time course, the
shorter the presynaptic ISI, the steeper will be the postsynaptic
membrane trajectory and the narrower the window of opportunity for firing. This explains the increase in synchrony with
the presynaptic (driver) firing rate. Note that the postsynaptic
cell needs to be driven strongly enough to occasionally overcome the IPSP but not strongly enough to fire more than once
per presynaptic cycle; in other words, synchrony by chemical
inhibition cannot be maintained if the follower cell fires at a
higher rate than the driver cell, a situation that was avoided in
our experiments. The follower cell can, however, fire at arbitrarily slow rates, because the JBSI depends on the relative
fraction of synchronous follower spikes, not on their absolute
number. This explains why the JBSI of C-coupled FS pairs in
our data set was not dependent on the follower firing rate. Last
and perhaps most importantly, if the driver firing rate falls
below ⬃50 Hz, the IPSP will decay to baseline before the next
presynaptic spike has arrived and the window of opportunity
will be broadened considerably, resulting in loss of synchrony.
Repetitively activated inhibitory synapses made by FS cells
on excitatory neurons or on interneurons undergo rate-dependent short-term depression (Beierlein et al. 2003; Galarreta and
Hestrin 1998; Gonzalez-Burgos et al. 2005; Ma et al. 2012;
Varela et al. 1999). Short-term depression was evident in our
recordings (e.g., Fig. 3B), but was not likely to have affected
our conclusions for three reasons. First, as shown in Fig. 3F,
we did not observe a systematic time- or spike-dependent
rundown in synchrony in our recordings. More importantly,
any depression of IPSPs would have decreased synchrony
more at higher presynaptic firing rates, opposite to the observed effect. Last, synaptic depression was not incorporated
into our computer model, and yet the simulations reproduced
the main experimental observations.
How electrical and dual synapses drive synchrony. Electrical synapses are widely observed in the central nervous system
and promote both subthreshold and spike synchrony (reviewed
in Bennett and Zukin 2004; Connors and Long 2004). In the
neocortex, electrical coupling synchronizes interneurons of
various subtypes (Beierlein et al. 2003; Caputi et al. 2009;
PROPERTIES OF FIRING SYNCHRONY BETWEEN CORTICAL INTERNEURONS
al. 2005; Oren et al. 2006); nor do they rule out contribution of
coupled FS interneurons to oscillation frequencies ⱖ80 Hz
such as fast gamma or sharp-wave-associated ripples (Colgin et
al. 2009; Sohal and Huguenard 2005; Tukker et al. 2013; Vida
et al. 2006).
ACKNOWLEDGMENTS
Qingyan Wang and Cary Johnson provided excellent technical support. The
SOM-Cre mice were generously provided by Dr. Z. Josh Huang, and the
PV-Cre mice were generously provided by Dr. Edward Callaway. We thank
Drs. Eric Tucker and Gary Marsat for critical reading of the manuscript.
GRANTS
This work was supported by National Institute of Neurological Disorders
and Stroke Grant NS050437.
The authors of this manuscript are fully and solely responsible for its
content.
DISCLOSURES
No conflicts of interest, financial or otherwise, are declared by the authors.
AUTHOR CONTRIBUTIONS
H.H. performed experiments; H.H. and A.A. analyzed data; H.H. and A.A.
interpreted results of experiments; H.H. and A.A. approved final version of
manuscript; A.A. conception and design of research; A.A. prepared figures;
A.A. drafted manuscript; A.A. edited and revised manuscript.
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