Krista E Perks1, Nathaniel B Sawtell2. 1. Department of Biology, Wesleyan University, Middletown, CT 06459, USA; Zuckerman Mind Brain Behavior Institute, Department of Neuroscience, Columbia University, New York, NY 10027, USA. 2. Zuckerman Mind Brain Behavior Institute, Department of Neuroscience, Columbia University, New York, NY 10027, USA. Electronic address: ns2635@columbia.edu.
Abstract
The latency of spikes relative to a stimulus conveys sensory information across modalities. However, in most cases, it remains unclear whether and how such latency codes are utilized by postsynaptic neurons. In the active electrosensory system of mormyrid fish, a latency code for stimulus amplitude in electroreceptor afferent nerve fibers (EAs) is hypothesized to be read out by a central reference provided by motor corollary discharge (CD). Here, we demonstrate that CD enhances sensory responses in postsynaptic granular cells of the electrosensory lobe but is not required for reading out EA input. Instead, diverse latency and spike count tuning across the EA population give rise to graded information about stimulus amplitude that can be read out by standard integration of converging excitatory synaptic inputs. Inhibitory control over the temporal window of integration renders two granular cell subclasses differentially sensitive to information derived from relative spike latency versus spike count.
The latency of spikes relative to a stimulus conveys sensory information across modalities. However, in most cases, it remains unclear whether and how such latency codes are utilized by postsynaptic neurons. In the active electrosensory system of mormyrid fish, a latency code for stimulus amplitude in electroreceptor afferent nerve fibers (EAs) is hypothesized to be read out by a central reference provided by motor corollary discharge (CD). Here, we demonstrate that CD enhances sensory responses in postsynaptic granular cells of the electrosensory lobe but is not required for reading out EA input. Instead, diverse latency and spike count tuning across the EA population give rise to graded information about stimulus amplitude that can be read out by standard integration of converging excitatory synaptic inputs. Inhibitory control over the temporal window of integration renders two granular cell subclasses differentially sensitive to information derived from relative spike latency versus spike count.
The latency of spikes evoked by sensory stimuli convey information about
non-temporal features (e.g., stimulus amplitude, location, or identity) at various
processing stages across sensory modalities, including in vision (Gawne et al., 1996; Gollisch and Meister, 2008; VanRullen et al., 2005), audition (Ashida
and Carr, 2011; Chase and Young,
2007; Furukawa and Middlebrooks,
2002; Grothe and Klump, 2000;
Heil, 2004; Zohar et al., 2011), olfaction (Bathellier et al., 2008; Cury and
Uchida, 2010; Shusterman et al.,
2011), somatosensation (Johansson and
Birznieks, 2004; Panzeri et al.,
2001; Saal et al., 2016), and
active electrosensation (Bell, 1990b; Hall et al., 1995; Szabo and Hagiwara, 1967). Latency codes have potential
advantages over conventional rate codes in terms of speed (Gollisch and Meister, 2008; VanRullen et al., 2005), information capacity (Rieke et al., 1996; Theunissen
and Miller, 1995), and energy efficiency (Lennie, 2003). Moreover, latency information appears to be sufficient
for aspects of olfactory (Chong et al., 2020;
Chong and Rinberg, 2018; Smear et al., 2011), tactile (Thomson and Kristan, 2006), and electrosensory
(Hall et al., 1995) mediated behavior.
However, unlike conventional spike rate codes, latency codes ostensibly require
explicit postsynaptic readout mechanisms, the nature of which remains controversial
(Stanley, 2013). Motor corollary
discharge (CD) has been hypothesized to provide a central reference signal for
reading out latency codes in cases in which sensory input is time locked to behavior
(Bell, 1989; Crapse and Sommer, 2008; Moore
et al., 2013; Shusterman et al.,
2011). Alternatively, latency codes could be read out based on
information contained in the relative timing of spikes across a population of inputs
(Haddad et al., 2013; Panzeri et al., 2014; Uchida et al., 2014; Zohar and
Shamir, 2016).The active electrosensory system of weakly electric mormyrid fish offers a
number of advantages for examining how latency information is utilized by
postsynaptic neurons. Mormyrid fish emit brief pulsed electrical fields known as
electric organ electric discharges (EODs). Nearby objects with conductivity higher
(lower) than the surrounding water increase (decrease) the amplitude of the
EOD-induced field (Figure 1A). A-type
mormyromast electroreceptors on the skin transduce increases (decreases) in the
local amplitude of the EOD pulse into highly precise, smoothly graded decreases
(increases) in spike latency (Bell, 1990b;
Sawtell et al., 2006; Szabo and Hagiwara, 1967). Although most EAs
also fire more spikes in response to EOD amplitude increases, evidence from
intra-axonal recordings (Bell, 1990a),
information theoretic analysis of EA responses (Bell,
1990b; Sawtell and Williams,
2008), and behavioral studies (Hall et al.,
1995) suggest the functional importance of latency coding in this system.
EAs project somatotopically to the hindbrain electrosensory lobe (ELL) where they
form excitatory synapses predominantly with two anatomically distinct subclasses of
interneurons known as deep and superficial granular cells (DGCs and SGCs) (Bell et al., 1989, 2005; Zhang et al.,
2007) (Figure 1B). Granular cells send
their axons to the superficial layers of the ELL where they synapse onto the output
cells of the ELL and hence serve as an obligatory relay for electrosensory
information (Bell et al., 2005). CD inputs
related to the EOD motor command are prominent in the ELL and have been hypothesized
to provide a reference signal that could serve to read out latency-coded input at
the level of the ELL granular cells (Bell,
1989, 1990a; Hall et al., 1995) (Figure
1C). However, the small size and dense packing of granular cells has,
until now, prevented in vivo recordings required to test this
hypothesis.
Figure 1.
Central readout of a latency code for electrosensory stimulus amplitude based
on corollary discharge
(A) Weakly electric mormyrid fish emit brief pulses of electricity known
as electric organ discharges (EODs; bottom plane). Nearby objects induce
“electrical images” on the body surface by changing local current
density (amplitude) of the resulting electric field. Electrical image amplitude
is encoded by the latency and number of spikes fired by afferent fibers
innervating electroreceptors on the skin (EAs). Increased electric image
amplitude yields decreased EA spike latency and increased EA spike number.
(B) Two distinct classes of granular cells in the electrosensory
lobe—superficial (SGC; green) and deep (DGC; teal)—integrate
excitatory input from EAs with a centrally originating corollary discharge (CD)
input related to the motor command to discharge the electric organ.
(C) Latency coded information is hypothesized to be read out in granular
cells (GCs) based on summation of EA input (yellow line) with a fixed temporal
reference signal provided by CD (black line). In such a scheme, a short-latency
EA spike arriving near the peak of the CD-evoked depolarization (yellow) would
yield a larger amplitude granular cell postsynaptic response. EA receptive field
location is shown on the body surface in (A).
(D) Same as in (C), but for a longer latency EA spike (purple) arriving
on the falling phase of the depolarization evoked by CD input (black line),
which yields a smaller amplitude granular cell postsynaptic response than in
(C).
RESULTS
Two physiologically distinct granular cell subclasses integrate EA and CD
input
Granular cell responses were characterized using blind whole-cell
recordings from the medial zone of the ELL in awake paralyzed fish (STAR Methods). In this preparation,
neuromuscular paralysis blocks the EOD, but EOD motor commands continue to be
emitted spontaneously by the fish at a rate of ~3–5 Hz, leaving CD input
to the ELL intact. The EOD is mimicked by a brief electrical pulse delivered
either at a brief (4.5 ms) delay relative to the EOD motor command,
approximating normal conditions, or at a long (50 ms) delay. The former
condition (termed short delay) is used to study the normally occurring
interactions between electrosensory and CD inputs, while the latter (termed long
delay) allows sensory and CD inputs to be observed separately.Histological recovery of subset of recorded granular cells filled with
biocytin revealed laminar locations and morphological properties consistent with
previous anatomical descriptions of DGCs and SGCs (Bell et al., 2005; Zhang et
al., 2007) (Figure 2A). We
report exclusively on subthreshold responses because somatically recorded action
potentials were small and often difficult to distinguish, likely due to an
electrotonically remote site of initiation at the distal end of a thin initial
segment (Bell et al., 2005; Zhang et al., 2007). Electrosensory
stimulation evoked short-latency synaptic excitation in both DGCs and SGCs,
consistent with monosynaptic input from EAs. Excitation in DGCs was sharply
peaked and appeared to be truncated by inhibition (Figures 2B and 2D, gray
arrow), while excitation in SGCs decayed much more slowly (Figures 2C and 2D). Prior electron microscopy and in vitro studies
indicate that GABAergic interneurons, known as large multipolar intermediate
layer (LMI) cells, form inhibitory synapses onto granular cells (Han et al., 2000; Meek et al., 2001; Zhang et
al., 2007).Differences in the time course of electrosensory responses
in DGCs and SGCs may reflect differences in the strength of LMI-mediated
inhibition.
Figure 2.
Responses of granular cells to electrosensory and corollary discharge
inputs
(A) Confocal z stacks of an SGC and a DGC labeled with biocytin (yellow)
during whole-cell recording. DAPI (blue) and Neurotrace (magenta) staining show
the layers of the ELL. Scale bar, 10 μm (gang, ganglion layer; plex,
plexiform layer; gran s, superficial granular cell layer; gran d, deep granular
cell layer).
(B) Example DGC response to electrosensory input (three trials overlaid)
aligned to stimulus onset (solid arrowhead). Baseline membrane potential was
−58 mV. The rapid decay of the EPSP is likely due to synaptic inhibition
(gray arrow). Inset: three trials overlaid in response to a weaker
electrosensory stimulus at threshold for evoking an IPSP (gray arrow) that
truncates the electrosensory-evoked EPSP. The black trace shows a trial in which
the EPSP occurred in the absence of the IPSP.
(C) Example SGC response to electrosensory input (three trials overlaid)
aligned to stimulus onset (solid arrowhead). Baseline membrane potential was
−63 mV.
(D) Average response of DGCs (teal, n = 24) and SGCs (green, n = 18) to
the electrosensory stimulus. Responses aligned to the EPSP onset (time = 0) to
average across cells. Shading denotes SEM. DGC responses (n = 24) peaked earlier
(2.5 ± 1 ms versus 11 ± 8.2 ms; t(42) = −4.99, p <
0.001), decayed more rapidly (2.6 ± 1.3 ms versus 33.3 ± 32.8 ms;
t(42) = −4.61, p < 0.001), and were narrower (half-width at
half-height 3.6 ± 1.7 ms versus 24.8 ± 11.4 ms; t(42) =
−9.04, p < 0.001) than those of SGCs (n = 18).
(E) Example DGC response to electric organ corollary discharge (CD)
input (three repeated trials overlaid). Open arrowhead indicates the time of the
EOD motor command recorded by an electrode near the electric organ.
(F) Example SGC response to CD input (three repeated trials overlaid).
Inset: CD response for a different SGC illustrating an excitatory response (gray
arrow) evident at a hyperpolarized membrane potential near reversal for the
inhibitory response in this cell (gray; trial average). At a depolarized
membrane potential (black; trial average), this cell showed rapid, early onset
inhibition followed by a depolarizing deflection (gray arrow). Open arrowheads
indicate the time of the EOD motor command.
(G) Average CD responses across a subset of DGCs (teal; n = 5) and SGCs
(green; n = 5) selected for their similar resting membrane potentials
(−50 to −60 mV). Shading denotes SEM. Open arrowhead indicates the
time of the EOD motor command. Gray boxed region indicates the range of latency
shifts observed in EAs (6.5–18.5 ms), shown relative to the timing of
granular cell CD responses. CD input evoked short-latency EPSPs in DGCs (onset
5.7 ± 0.8 ms; peak 9.7 ± 2.7 ms, n = 24) and even shorter latency
IPSPs in SGCs (4.9 ± 0.5 ms, n = 12). A depolarizing PSP was observed
after inhibition onset (gray arrow; onset 7.6 ± 2.2 ms; peak 14.4
± 5.8 ms) in 12/18 SGCs. In 3/24 DGCs, we observed a prominent IPSP at
around 7.7 ms. See also Figure
S1.
The possibility that granular cells receive CD input related to the EOD
motor command has been suggested based on prior work but not directly shown
(Bell, 1990a). Our intracellular
recordings confirmed prominent CD input to granular cells. DGCs exhibited highly
stereotyped, short-latency excitation time-locked to the EOD motor command
(Figures 2E, 2G, and S1). In some DGCs, CD excitation appeared to be truncated by
inhibition (see Figure 3C, black
trace), similar to their responses to electrosensory input. In
contrast, SGCs typically exhibited a stereotyped, short-latency
hyperpolarization followed by a depolarization (Figure 2F, 2G, and S1). At more
hyperpolarized potentials, CD responses consisted mainly of a
depolarization(Figure 2F,
inset, gray arrows), suggesting that CD input to SGCs is
comprised of synaptic inhibition followed by excitation. Prior studies suggest
that CD input to the ELL originates from the medial juxtalobar nucleus (JLm)
(Bell and von der Emde, 1995; Mohr et al., 2003). Consistent with this,
electrical microstimulation in the vicinity of the JLm evoked synaptic responses
resembling naturally occurring CD responses, including short-latency
depolarizations in DGCs and hyperpolarizations in SGCs (Figure S1). However,
since JLm neurons are thought to be glutamatergic (Bell and von der Emde, 1995; Mohr et al., 2003), the origin of CD-inhibition in SGCs is
unclear.
Figure 3.
Corollary discharge enhances but is not required for electrosensory responses
in granular cells
(A) Responses of an example SGC across amplitudes (color bar, top) to
stimuli delivered either at a short (top) or long (bottom) delay relative to the
EOD motor command. Middle: average response to corollary discharge (CD) input
alone. Solid arrowhead indicates time of the electrosensory stimulus. Open
arrowhead indicates the time of the EOD command.
(B and C) Same displays as in (A), but for two example DGCs.
(D) Mean peak response versus stimulus amplitude for the same SGC shown
in (A) in long delay (filled circle) versus short delay (open square)
conditions. The predicted response at a short delay (“sum,” gray
dashed) was calculated by adding the long delay response at each stimulus
amplitude to the CD response.
(E and F) Same displays as in (D) but for the example DGCs shown in (B)
and (C).
(G) Response onset latency (relative to stimulus onset at a long delay
relative to the CD; mean ± SEM) versus stimulus amplitude for SGCs
(green; n = 5) and DGCs (teal; n = 13).
(H) Peak response amplitude versus stimulus amplitude under long delay
(filled circle) versus short delay (open square) conditions for SGCs (n = 5;
mean ± SEM). Responses within each cell were normalized by the maximum
long delay response amplitude before averaging across cells. The delay between
the electrosensory stimulus and the command had a significant effect on peak
response amplitude, F(1,88) = 55, P < 0.001 (two-factor
repeated measures ANOVA). Across the range of −10 to 10% stimulus
amplitude, the sensitivity at a long delay was 8.3 ± 5.6 mV, and the
sensitivity increased to 27.9 ± 8.8 mV at a short delay. Out of four SGCs
with at least five trials in every condition, all had a significant effect of
stimulus delay on raw peak response amplitude (p < 0.001). (I) Same as in
(H), but for DGCs (n = 13; mean ± SEM). The delay between the
electrosensory stimulus and the command had a significant effect on peak
response amplitude, F(1, 264) = 21, p < 0.001 (two-factor repeated
measures ANOVA). Across the range of −10 to 10% stimulus amplitude, the
sensitivity at a long delay was 8.1 ± 8.1 mV, and the sensitivity
increased to 26.8 ± 14.6 mV at a short delay. Out of nine DGCs with at
least five trials in every condition, seven had a significant effect of stimulus
delay on raw peak response amplitude (p <= 0.001).
(H and I) Significant effects of stimulus amplitude and delay, but not
delay-by-amplitude interaction at p < 0.001 on the mean peak response
amplitudes across cells. See also Figures S2 and S3.
CD input enhances but is not required for reading out EA input to granular
cells
Next we characterized granular cell responses to modulations of
electrosensory stimulus amplitude. Such modulations mimic increases and
decreases in EOD amplitude due to conducting and nonconducting objects,
respectively (STAR Methods). To test the
role of CD input, we compared granular cell responses evoked by electrosensory
stimuli delivered at short (naturally occurring) versus long delays relative to
the EOD command. In both conditions, increases in electrosensory stimulus
amplitude led to decreases in postsynaptic response onset in granular cells
(Figures 3A–3C, and 3G), as
expected based on well-characterized latency shifts in EAs (Bell, 1990b; Szabo and Hagiwara, 1967). Large graded changes in postsynaptic
response amplitude (>10 mV) were observed in response to stimuli
presented at both short and long delays (Figures
3A–3C, 3H, and 3I). These findings are consistent with the hypothesis that latency
coded EA input induces changes in postsynaptic response amplitude in granular
cells but suggest that CD input is not required for this transformation.To further evaluate the effect of CD input, we compared measured
granular cell responses to those calculated based on a linear sum of the
granular response to electrosensory stimuli delivered at a long delay and the
response to the CD input alone (Figures
3D–3F, dashed
line). Most SGCs exhibited supralinear summation of electrosensory
and CD input, particularly at high stimulus amplitudes (Figures 3A, 3D, 3H, and S2). The enhancement of
sensory-evoked depolarizations in SGCs is notable given that SGCs typically
exhibited CD-evoked inhibition (Figures 3A
and S2). Supralinear
summation was not observed between CD input and EPSP waveforms generated by
somatic current injections in SGCs (Figure S2), suggesting that facilitatory interactions
between CD and EA input might occur electrotonically distant from the soma in
the long, thin dendrites of SGCs (Bell et al.,
2005; Zhang et al., 2007).
More varied interactions between CD and electrosensory inputs, including both
supralinear (Figures 3B and 3E) and sublinear (Figures 3C and 3F)
summation, were observed in DGCs. Sublinear summation is expected for cells,
like the example shown in Figure 3C, in
which CD excitation is followed by inhibition. On average, DGC responses were
modestly enhanced by CD input (Figure
3I).Finally, we recorded subthreshold responses to modulations of
electrosensory stimulus amplitude in E-type output cells of the ELL, one of the
major postsynaptic targets of granular cells (Bell et al., 2005; Grant et al.,
1996). Responses of E cells resembled those of granular cells in that
long delay electrosensory stimuli evoked graded changes in subthreshold response
magnitude that were enhanced when stimuli were delivered at the natural delay
relative to the EOD motor the command (Figure S3). Overall, these results argue against the
hypothesis that CD is required for reading out electrosensory input, but are
consistent with a role for CD in enhancing or “gating-in”
responses to the fish’s own EOD (Meyer
and Bell, 1983).
Diverse spike latency and number tuning in EAs
Granular cells pool excitatory input from an estimated 4–7 EAs
innervating nearby electroreceptors on the skin (Bacelo et al., 2008; Bell,
1990a). To determine the potential implications of such convergence
for reading out electrosensory input, we obtained intracellular recordings from
EAs in the granular layers of the ELL near their central terminals. Responses to
identical electrosensory stimuli were obtained from 7–21 individual EAs
in each of four fish. Recording locations were restricted to the same
somatotopic region of the ELL to minimize potential response variability due to
electroreceptor location on the skin. All EAs exhibited smoothly graded
decreases in spike latency with increases in stimulus amplitude and most also
exhibited increases in spike number (Figures
4A–4C), consistent with
prior studies (Bell, 1990b; Sawtell et al., 2006; Szabo and Hagiwara, 1967). Although responses were highly
reliable across repeated trials within individual EAs, substantial heterogeneity
was observed in latency tuning across the population (Figures 4A–4C).
To quantify this, we fit exponential functions to first spike latency-stimulus
amplitude response curves for all recorded EAs (Figure 4D) and plotted the distribution of parameters for each fish
(Figures 4E–4G). Substantial heterogeneity was observed across EAs
within each fish in terms of the sensitivity of latency shifts to stimulus
amplitude (decay), the total range of latency shifts (amplitude), and the
minimum first spike latency (offset). To isolate effects of relative latency
shifts from recruitment, we identified the range of stimulus amplitudes over
which EAs fire at least one spike (Figure
4H, gray box).
Figure 4.
Electroreceptor afferents exhibit diverse first spike latency and spike count
tuning
(A) Left: intracellular responses of a recorded EA at stimulus
amplitudes of −10, 0, and +10% (colored according to the scatterplot at
right). Three trials overlaid at each amplitude. Right: spike latency versus
stimulus amplitude (mean ± SEM).
(B and C) Same as (A), but for two other example EAs with notable
differences in latency and spike count tuning. In (C), three trials at +40%
amplitude are also shown.
(D) Exponential fits of first spike latencies across stimulus amplitudes
for 21 electroreceptor afferents recorded from a single fish (fish 3 in
E–G).
(E–G) Heterogeneity of fit parameters among EAs recorded in four
fish (n = 7, 11, 21, 15 EAs per fish).
(H) Mean pairwise latency among first spikes (n = 58 total EAs in four
fish). Shading denotes stimulus range for which >94% of EAs have at least
one spike.
(I) Scatterplot of spike offset (mean ± SEM) for second (1.6
± 0.5 ms, n = 360 spikes), third (3.6 ± 0.8 ms, n = 145 spikes),
and fourth (6.6 ± 0.8 ms, n = 13 spikes) spikes relative to first spike
latency. For each datapoint (mean ± SEM), EAs without that spike number
were ignored.
(J) Probability of EAs having zero, one, two, three, or four spikes at
the maximum stimulus amplitude (+40%) for recorded data (red) and the prediction
(black) based on recorded first spike latency and mean spike offsets, as in (I)
(n = 58 EAs).
(K) Median number of spikes per EAs across stimulus amplitude for actual
(red) and predicted (black) spikes (n = 58 EAs).
Because first spike latencies converge onto a minimum value, presumably
set by biophysical limits, heterogeneous latency tuning results in a
stimulus-dependent decrease in the interval between first spikes across the
population (Figure 4H). This implies that a
rate code for stimulus amplitude exists at the level of the input population
even when the total number of EA spikes remains constant.EAs also exhibited diversity in their spike count tuning (Figures 4A–4C). Consistent with prior results, second and subsequent
spikes followed earlier spikes by a fixed offset (Figure 4I) (Bell, 1990b; Sawtell et al., 2006). Notably, the number
of spikes fired by an individual EA appeared unrelated to its first spike
latency tuning. To demonstrate that the maximum number of spikes in an
EA’s response is not simply predicted by its first spike’s
latency, we compared the actual distribution of the number of spikes fired by
EAs at the maximum stimulus amplitude (Figure
4J, red) to the distribution of the number of spikes
predicted by adding subsequent spikes at the experimentally determined offsets
from each EA’s first spike (Figure
4J, black) (see STAR
Methods for more detail on how this condition was simulated; same as
in Figures 5E–5H, orange). Recorded EAs exhibited a broader distribution
of total spikes than expected based on the simulation, suggesting that spike
latency and spike count tuning vary independently within EAs. Comparing the
median EA spike count as a function of stimulus amplitude for recorded versus
simulated populations suggests that this independent tuning results in spike
count grading over a wider range of stimulus amplitudes (Figure 4K).
Figure 5.
Summation of diversely tuned EAs accounts for graded readout of stimulus
amplitude in granular cells
(A) Responses of an example SGC to electrosensory stimuli of different
amplitudes (color bar, top) delivered at a long delay from CD input.
(B) Example responses of a model granular cell receiving four excitatory
EA inputs.
(C) Responses of an example DGC to electrosensory stimuli of different
amplitudes delivered at a long delay from CD input.
(D) Example responses of a model granular cell with the same excitatory
EA input as in (B), but with an inhibitory conductance driven by the first spike
in the EA input population, at a 4-ms delay.
(E) Examples of four sets of EA population inputs (n = 4 EAs per
population) designed to test the effects of diverse latency (effecting the input
inter-spike interval) and spike count tuning on granular cell responses (see
main text). Circles denote the time of EA spikes with the size indicating the
number of spikes. Black, subsampled recorded EA data. Orange, diverse latency
tuning is preserved while diverse spike count tuning is removed. Purple, diverse
latency tuning is removed while diverse spike count tuning is preserved. Blue,
diverse latency and spike count tuning are both removed from the input
population.
(F) Peak response amplitude versus stimulus amplitude across model DGCs
(mean ± SEM; n = 200 different EA input populations) under each condition
shown in
(E) with inhibition delayed by 2 ms relative to the first EA spike.
(G) Same as in (F), but for model SGCs.
(H) Same as in (F), but with inhibition delayed by 4 ms relative to the
first EA spike.
(I) Shifts in a second EA input B relative to a first
EA input A (dotted red arrow) cause a predictable change in the
amplitude of the second EPSP when an inhibitory input (blue), time locked to
input A, cuts off the response during the EPSP rise. The
predicted response amplitude change (red, solid line) depends on the slope of
the EPSP rise. See also Figure
S4.
Postsynaptic readouts in SGCs and DGCs based on EA convergence
The foregoing results suggest that the EA population contains graded
information about stimulus amplitude that could be read out based on simple
input summation in granular cells independent of a fixed reference signal. To
test this, we constructed conductance-based model neurons with parameters
adjusted to match the rise and decay of near-threshold EPSPs recorded in SGCs
and DGCs (Figure S4).
Input to the model consisted of spikes from four EAs randomly subsampled from
the recorded population. Though we chose to focus on simplified models to gain
insight into the functional significance of EA convergence, numerous additional
factors may contribute to measured subthreshold responses in granular cells,
e.g., mixed chemical and electrical synapses between EAs and granular cells and
voltage-gated conductances (Zhang et al.,
2007). Responses in model cells receiving only excitatory EA input
were broad in duration and exhibited large, graded increases in peak
depolarization as a function stimulus amplitude, similar to recorded SGCs (Figures 5A and 5B). To mimic the brief electrosensory responses exhibited by DGCs,
we added strong inhibitory input at a short delay (2–4 ms) after the
onset of the excitatory response, effectively truncating the time window for
integrating EA input. Model responses were much briefer under these conditions,
resembling recorded DGCs, but still exhibited large, graded increases in peak
depolarization as a function stimulus amplitude (Figures 5C and 5D). Aside from
changes in the absolute magnitude of responses, results were similar over a
range of values for EA input number and inhibitory input delay (Figure S4). These results
suggest that granular cell responses to electrosensory stimuli observed
in vivo can largely be explained based on convergence of a
small numbers of excitatory EA inputs and, for DGCs, sensory-evoked
inhibition.Next, we used the model to test the respective contributions of
diversity in latency versus spike count tuning in EAs to postsynaptic responses
in granular cells. Model SGC and DGC responses to subsampled EA inputs were
compared for three sets of manipulated EA inputs in which (1) diversity in both
latency and spike count tuning was eliminated; (2) diversity in latency tuning
was eliminated but diverse spike count tuning remained intact; and (3) diversity
in spike count tuning was eliminated but diverse latency tuning remained intact
(STAR Methods). These four sets of
input are illustrated in Figure 5E. In the
absence of diverse latency tuning, the EA population inter-spike-interval is
approximately the same across stimulus amplitudes. Similarly, in the absence of
diverse spike count tuning, most EAs fire a maximal number of spikes even at
relatively low stimulus amplitudes. Consistent with this, removal of diversity
in both latency tuning and spike count tuning resulted in postsynaptic responses
that were near maximal across a wide range of stimulus amplitudes for both SGCs
and DGCs (Figures 5F–5H, blue).The relative importance of diversity in latency tuning versus diversity
in spike count tuning depended on the temporal window of postsynaptic
integration as set by the timing of inhibition (Figure S4). When
inhibition onset was rapid, removing diversity in latency tuninghad the major
impact onmodel responses (Figure 5F,
purple). In the absence of inhibition, removing diversity in spike count tuning
had the major impact on model responses(Figure
5G, orange). For intermediate values of inhibition delay, graded
responses could be supported by either diversity in latency tuning or spike
count tuning (Figure 5H). These results
suggest that narrower versus wider temporal integration windows render DGCs and
SGCs differentially sensitive to information contained in the relative timing
versus the overall number of EA spikes, respectively. Sensitivity of peak
response amplitude to the relative timing of EA inputs can be explained by
powerful sensory-evoked inhibition and steep rising sensory-evoked excitation
(both notable features of DGCs). Assuming that inhibition is triggered by the
first EA input to a granular cell (see discussion), a decrease in the relative
timing of subsequent EA inputs will result in the postsynaptic response reaching
a more depolarized level before being truncated by inhibition (Figure 5I).
Comparing ELL zones provides additional evidence for the importance of
diverse EA tuning
Given that some degree of heterogeneity in response properties across a
neuronal population is inevitable, we sought further evidence that diverse EA
tuning represents a functional specialization. In addition to the EAs studied
here (termed A-type), mormyrid fish also possess additional B-type receptors
sensitive to object-induced changes in both the amplitude and shape of the EOD
waveform (von der Emde and Bleckmann,
1992, 1997). B-type EAs
project to granular cells located within an adjacent region of the ELL known as
the dorsolateral zone (DLZ) (Bell et al.,
1989). Although circuitry, cell types, and CD input appear generally
similar between the medial zone (MZ) and DLZ, prior work has shown that spike
threshold is highly uniform across B-type EAs (Bell, 1990b). If diverse tuning is essential for the postsynaptic
readout of information conveyed by A-type EAs, the absence of such diversity in
B-type EAs would be expected to manifest as differences in postsynaptic
responses in the MZ versus the DLZ.As an initial test of this hypothesis, we compared field potential
responses evoked by identical modulations of electrosensory stimulus amplitude
for series of closely spaced electrode penetrations that passed through
somatopically aligned regions of the MZ and the DLZ. The early negative
component of such field potentials reflects excitation in the granular layer
evoked by EAs innervating a small region of the skin (Bell et al., 1992; Gomez et
al., 2004; Grant et al., 1998;
Sawtell and Williams, 2008). In the
MZ, field potential onset latency decreased while the amplitude exhibited
prominent grading as a function of stimulus amplitude (Figure 6A). Such amplitude grading can be understood in the
same terms as granular cell postsynaptic responses, i.e., as due to an increase
in the summed input of a local population of EAs. In the DLZ, field potential
onset latency also decreased; however, the amplitude of the field potential
exhibited little grading as a function of stimulus amplitude (Figure 6B). To confirm that the difference in
response amplitude changes across zones was not due to differences in overall
sensitivity to sensory input, we plotted peak field potential amplitude as a
function of peak latency across stimulus amplitude (Figures 6C–6F).
The slope of this relationship was about four times greater in MZ compared with
DLZ, though the range of latency shifts was similar (Figures 6F–6H).
We hypothesize that the weaker amplitude grading in the DLZ is due to
homogeneous response properties of B-type EAs, similar to the results obtained
in the model with simulated EA populations lacking diverse tuning. These results
further support the functional importance of diverse tuning in A-type EAs and
motivate future studies of the postsynaptic readout of B-type EA input in the
granular cells of the DLZ.
Figure 6.
Differences in EA tuning variability result in different stimulus readouts in
MZ and DLZ
(A) Local field potential (LFP) in the medial zone (MZ) of ELL in
response to different stimulus amplitudes (color bar, top).
(B) Same as in (A), but for the dorsolateral done (DLZ).
(C) Scatterplot of LFP amplitude versus LFP peak latency relative to
stimulus onset for MZ.
(D) Same as in (C), but for DLZ. Shifts in stimulus amplitude cause
shifts in peak latency for both zones, but peak amplitude changes are greater in
the MZ.
(E) Sensitivity of LFP amplitude to latency shifts for a series of
closely spaced electrode penetrations at different mediolateral locations
(spaced approximately 200 μm apart) spanning the MZ-DLZ border, as
determined by shifts in receptive location on the skin. Note the abrupt jump in
sensitivity around the zonal border.
(F) Sensitivity of LFP amplitude is greater in MZ compared with DLZ
(t(25) = 4.6, p < 0.001; n = 14 MZ sites, n = 13 DLZ sites). Boxplots
denote 25%, 50%, and 75% quartiles (with error bars denoting the rest of the
distribution, excluding outliers). Sensitivity was calculated as the change in
LFP amplitude (mV) divided by the change in LFP peak latency (ms) across the
full range of stimulus amplitudes.
(G) LFP peak latency in MZ and DLZ shifts similar amounts (measured
across the full stimulus amplitude range; t(25) = 0.63, p = 0.53; n = 14 MZ
sites, n = 13 DLZ sites).
(H) LFP amplitude changes are greater in MZ versus DLZ (measured across
the full stimulus amplitude range; t(25) = 5.8, p < 0.001; n = 14 MZ
sites, n = 13 DLZ sites).
DISCUSSION
Compared with the many studies characterizing the encoding of sensory
information by spike latency shifts, there have been relatively few tests of whether
and how such information is actually utilized by postsynaptic neurons. The active
electrosensory system is advantageous in this regard because latency decoding is
hypothesized to occur in granular cells located just one synapse from the sensory
periphery. In addition, central reference signals hypothesized to perform the
decoding can be easily monitored and manipulated in vivo. However,
until now, their small size and dense packing have precluded in
vivo recordings from individual granular cells. Using in
vivo whole-cell recordings we demonstrate that granular cells exhibit
large stimulus-evoked changes in postsynaptic response amplitude, consistent with
prior hypotheses that latency shifts in EAs are transformed into changes in response
amplitude (Bell, 1990a). Although granular
cells integrate EA input with motor CD signals providing a precise reference signal
related to stimulus onset, such signals appear to gate or enhance responses rather
than being strictly required to decode sensory input. Instead, we find that diverse
latency and spike count tuning across the EA population gives rise to graded
information about stimulus amplitude in the form of a rate code. Modeling indicates
that sensory-evoked postsynaptic responses in two distinct subclasses of granular
cells can be explained, without a fixed reference signal, simply by summation of
excitatory input from a small number of converging EA inputs. Finally, a brief
integration window set by powerful sensory-evoked inhibition renders DGCs highly
sensitive to information contained in the relative latency of EA spikes, while the
absence of strong inhibition renders SGCs more sensitive to total spike count.
Comparison to latency readout schemes proposed for other systems
One common proposal for reading out latency codes relies on fixed
reference signals related to stimulus onset. CD signals are hypothesized to
provide a reference signal for reading out latency codes in systems where the
timing of sensory input is determined by the behavior of the animal (Crapse and Sommer, 2008; Cury and Uchida, 2010; Hall et al., 1995; Smear et al., 2011), for example saccades in vision,
sniffing in olfaction, active touch in somatosensation, or the EOD in
electrolocation. Alternatively, fixed reference signals could be contained in
the sensory input itself, for example, by subsets of sensory neurons with short,
stereotyped response latencies (Brasselet et
al., 2012; Chase and Young,
2007; Gollisch and Meister,
2008). Other readout schemes rely on postsynaptic specializations
such as specialized learning rules for tuning synaptic strength (Gutig and Sompolinsky, 2006; Thorpe et al., 2001) or competitive
interactions mediated by recurrent inhibition (Haddad et al., 2013; Stern et al.,
2018; Zohar and Shamir, 2016).
The present findings are notable in that no fixed reference signal is required.
Furthermore, diverse tuning across sensory input populations has been reported
in numerous systems (see Bale et al.,
2013; Goldberg, 2000; Raman et al., 2010), suggesting that the
mechanism described here may be of general relevance for understanding how
latency codes are utilized by the brain. In the mammalian auditory system, for
example, there is wide variation in the sensitivity of auditory nerve fibers
that co-varies with spontaneous firing rate, axonal morphology, and
transcriptional patterns, and has been functionally linked to the wide dynamic
range of human hearing (Liberman, 1982;
Liberman and Oliver, 1984; Petitpre et al., 2018; Viemeister, 1983; Winter et al., 1990).Although the origin of the diverse tuning observed across A-type
electroreceptors is not known, a prior electrophysiological study noted that
A-type electroreceptors exhibit widely varying spike thresholds, and an electron
microscopy study observed notable variation in the area of the outer membrane of
A cells (Bell, 1990b; Bell et al., 1989). Differences in types,
distributions, or densities of voltage-gated channels across A-type
electroreceptor cells or their afferent fibers have not been investigated but
could also contribute to diverse responses. Another question for future studies
is whether convergence of A-type EAs onto granular cells is random (as in our
model) or subject to some forms of tuning or optimization. Although we did not
systematically examine non-random connectivity, certain rules might be expected
to enhance postsynaptic responses. For example, convergence of EAs with
intersecting latency tuning curves is expected to give rise to non-monotonic
postsynaptic responses (i.e., maximal responses at the intersection point).
Response grading could potentially be enhanced if granular cells avoided pooling
such EAs.
Implications for active electrosensory processing
The observation that precise central reference signals are present in
granular cells raises the question of what advantages, if any, are conferred by
the readout scheme proposed here. In contrast to the fixed temporal window
provided by CD, sensory-evoked inhibition in DGCs provides a window for reading
out relative latency information that shifts along with the sensory input. This
may provide a means for maintaining sensitivity to small latency shifts, such as
those due to prey (Gottwald et al.,
2018), superimposed on larger shifts due to the animals’ own
behavior or large environmental features (Chen
et al., 2005; Sawtell and Williams,
2008; Sawtell et al., 2006).
Anatomical studies have shown that the myelinated dendrites of LMI cells form
large GABAergic synapses onto granular cells. LMI dendrites lack conventional
synaptic inputs and are hypothesized to be activated directly by depolarization
within granular cells via ephaptic coupling (Han
et al., 2000; Meek et al.,
2001). This unusual synaptic organization appears well-suited to
mediate the rapid and powerful inhibition observed in DGCs. Whereas DGCs, LMI
cells, and latency coding in EAs appear to be specializations of the active
electrosensory system (all three are absent from an adjacent zone of the ELL
that subserves the more evolutionarily ancient passive electrosense), SGCs are
found in both systems (Bell et al.,
2005). Based on our finding that SGCs are mainly sensitive to spike count
while DGCs are sensitive to input timing, it is tempting to speculate that DGCs
and LMIs are adaptations for utilizing temporal information associated with the
evolution of the active electrosense. More broadly, our results are consistent
with key roles for inhibition in temporal processing suggested by studies of a
wide range of sensory systems, including olfaction, audition, and
electrocommunication (Grothe, 2003; Heil, 2004; Lyons-Warren et al., 2013; Uchida et
al., 2014). Finally, encoding stimulus amplitude independent of CD
could enable a dual role for the active electrosensory system in utilizing
information derived from the EODs of other fish. Consistent with such a
function, one prominent close-range electrocommunication behavior, the echo
response, has been suggested (though not yet proven) to be triggered by
activation of mormyromast electroreceptors (Russell et al., 1974).
Limitations of the study
An important limitation of the present study was our inability to
reliably measure the spiking output of granular cells. Similar difficulties were
noted in a prior in vitro study and likely reflect a spike
initiation site electrotonically remote from the soma (Bell et al., 2005; Zhang et
al., 2007). Issues related to recording quality (e.g., filtering due
to high access resistance) are unlikely, as synaptic responses in DGCs were both
large and extremely rapid. Moreover, granule cells of the eminentia granularis
(comparable in size to ELL granular cells) recorded in the same preparation with
identical methods routinely exhibit overshooting action potentials (Kennedy et al., 2014; Sawtell, 2010). Spike threshold, as well as additional
postsynaptic non-linearities, could enhance sensitivity to small changes in EOD
amplitude. Nevertheless, the observation that subthreshold responses to
electrosensory stimuli in E-type output cells were similar to those in granular
cells support our conclusions that CD enhances, but is not required for,
encoding electrosensory stimulus amplitude (Figure S3). A second
limitation relates to the use of spatially uniform electrosensory stimulation.
These simple stimuli greatly facilitated quantitative comparisons, which would
have been difficult with local stimuli given the difficulty of maintaining
stable recordings from small granular cells while mapping receptive fields.
However, they obviously restricted us from studying potentially important
effects of the spatial structure of electrosensory input. Due to the inherent
blur in electrical images, EAs converging onto a given granular cell probably
convey similar signals. However, LMIs likely receive electrosensory input from
large regions of the body surface and may perform spatial computations such as
lateral inhibition (Han et al., 2000;
Meek et al., 2001). Given the
apparent differences in sensory-evoked inhibition between DGCs and SGCs, these
two sub-classes may differ not only in the temporal profiles of their sensory
responses but also in their spatial tuning. Additional key questions relate to
synaptic and functional connectivity patterns linking granular cells to the rest
of the ELL. While both DGCs and SGCs send axons to the superficial layers of the
ELL where they contact several anatomically and functionally distinct neuronal
subclasses, the details of their connectivity patterns are not known (Hollmann et al., 2016; Meek et al., 1999).
STAR★METHODS
RESOURCE AVAILABILITY
Lead contact
Further information and requests for resources and reagents should
be directed to and will be fulfilled by the lead contact, Nathaniel Sawtell
(ns2635@columbia.edu).
Materials availability
This study did not generate new unique reagents.Raw and processed data have been deposited on G-Node:
https://doi.org/10.12751/g-node.suibcf and are
publicly available as of the date of publication.All original code has been deposited on G-Node: https://doi.org/10.12751/g-node.suibcf and is
publicly available as of the date of publication.Any additional information required to reanalyze the data
reported in this paper is available from the lead contact upon
request.
EXPERIMENTAL MODEL AND SUBJECT DETAILS
Animals
Male and female wild-caught Mormyrid fish of the species
Gnathonemus petersii were used in these experiments
(fish were 7–12 cm in length, of unknown age, and sex was not
specifically selected for). Fish were housed in 60 gallon tanks in groups of
5–20. Water conductivity was maintained between 70 and 150
microsiemens both in the fish’s home tanks and during experiments.
All experiments performed in this study adhere to the American Physiological
Society’s Guiding Principles in the Care and Use of Animals and were
approved by the Institutional Animal Care and Use Committee of Columbia
University.
METHOD DETAILS
Surgical procedures
For surgery to expose the brain for recording, fish were
anesthetized (MS:222, 1:25,000) and held against a foam pad. Skin on the
dorsal surface of the head was removed and a long-lasting local anesthetic
(0.75% Bupivacaine) was applied to the wound margins. A plastic rod was
cemented to the anterior portion of the skull to secure the head. The
posterior portion of the skull overlying the ELL was removed. The valvula
cerebelli was reflected laterally to expose the eminentia granularis
posterior and the molecular layer of the ELL, facilitating whole-cell
recordings. Gallamine triethiodide (Flaxedil) was given at the end of the
surgery (~20 μg/cm of body length) and the anesthetic was removed.
Aerated water was passed over the fish’s gills for respiration.
Paralysis blocks the effect of electromotoneurons on the electric organ,
preventing the EOD, but the motor command signal that would normally elicit
an EOD continues to be emitted at an average rate of 2–5 Hz.
Electrophysiology
The EOD motor command signal was recorded with a Ag-AgCl electrode
placed over the electric organ. The command signal is the synchronized
volley of electromotoneurons that would normally elicit an EOD in the
absence of neuromuscular blockade. The command signal lasts about 3 msec and
consists of a small negative wave followed by three larger biphasic waves.
Onset of EOD command was defined as the negative peak of the first large
biphasic wave in the command signal.For in vivo whole-cell recordings, electrodes
(8–15 MΩ) were filled with an internal solution containing, in
mM: K-gluconate (122); KCl (7); HEPES (10); Na2GTP (0.4); MgATP (4); EGTA
(0.5), and 0.5%–1% biocytin (pH 7.2–7.4, 280–315 mOsm).
No correction was made for liquid junction potentials. Only cells with
stable membrane potentials more hyperpolarized than −45 mV were
analyzed. Membrane potentials were recorded and filtered at 3–10 kHz
(Axoclamp 2B amplifier, Axon Instruments) and digitized at 20–40 kHz
(CED micro1401 hardware and Spike2 software; Cambridge Electronics Design,
Cambridge, UK). In vivo local field potentials in Figure 6 were made with low resistance
(<5MOhm) glass microelectrodes filled with 2 M NaCl.
Electrosensory stimulation
The EOD mimic was a 0.2 msec duration monophasic square pulse
delivered between an electrode in the stomach and another positioned near
the electric organ in the tail. In between recordings, the EOD mimic was
presented at a baseline amplitude of 350 mA (stomach electrode negative) at
the output of the stimulus isolation unit. To characterize neural tuning
curves, stimulus amplitude was varied from +40% to − 40% from the
baseline amplitude. Specifically, the following shifts from baseline
amplitude (as percent of baseline) were presented in pseudo-random order:
−40, −30, −20, −10, −5, 0, +5, +10, +20,
+30, and +40 (note that for the data presented in Figure 6, this range was reduced to −30% to +30%
with 5% increments). To characterize interactions between electrosensory and
corollary discharge inputs, responses were compared across conditions in
which the EOD mimic was presented at a delay of either 50 msec (long delay)
or 4.5 msec (short delay) following the EOD command.
Medial juxtalobar nucleus stimulation
The precise location of the medial juxtalobar nucleus (JLm) was
determined by monitoring corollary discharge-evoked field potentials with
extracellular recording electrodes. Low resistance, broken-tip glass
capillary microelectrodes filled with 3 M NaCl were used for recording field
potentials and for electrical stimulation of the JLm (stimulus duration was
a single square wave pulse with a duration of 200 microseconds). The
electrodes were directed at angles of about 45° with respect to the
mid-sagittal plane and with a slight posterior to anterior direction. With
the valvula reflected, entry points for the electrode tracks were just
dorsal to the anterior tip of the exposed electrosensory lobe molecular
layer. The corollary discharge-driven field potential characteristic of the
JLm was recorded in such tracks at depths of 800–1500 microns below
the surface (depending on fish size and exact tilt). Prior to searching for
and recording granular cells, JLm electrode placement was confirmed by the
ability of a near-threshold stimulus to evoke characteristic field potential
responses in the granular layers of ELL (Mohr et al., 2003). Minimum stimulus thresholds for evoking
responses in ELL were 2–4 uA. For evoking responses in granular
cells, a near threshold stimulus of 5uA was used.
Histology and morphological reconstructions
After recording, fish were deeply anesthetized with a concentrated
solution of MS:222 (1:10,000) and perfused through the heart with a teleost
Ringer solution followed by a fixative, consisting of 4% paraformaldehyde in
0.1 M phosphate buffer. The brains were postfixed for 12–24 h,
cryoprotected with 30% sucrose, and sectioned at 60 mm on a cryostat.
Sections were subsequently processed with an Alexa Fluor 488 Streptavidin
complex (Jackson Immuno Research Laboratories; Antibody ID - AB_2337249; at
1:500) to label the biocytin filled cells, and DAPI (Sigma Aldrich # D9542;
at 1:1000) and NeuroTrace 640 (ThermoFisher Scientific #N21483; at 1:500) to
visualize the layers of ELL. Sections were then mounted on slides, dried of
excess PBS, and coverslipped with either VectaShield Antifade (Vector
Laboratories # H-1000-10) or Molecular Probes™ ProLong™
Diamond Antifade Mountant (Fisher Scientific; Molecular Probes™
P36965). Morphologically recovered neurons were inspected and subsequently
photographed using a confocal microscope (Inverted Nikon A1R point-scanning
laser confocal microscope with high-sensitivity GaAsP detectors) with either
a 20× air objective or a 40× oil immersion objective. Images
were collapsed along the Z-dimension implementing the maximum brightness per
pixel. Each fluorescence channel was pseudo-colored as specified in Figure 2.
Modeling
Circuit architecture
The circuit consisted of one model granular cell receiving input
from a small number (4 used in the main results, 4–7 tested in
supplemental) of simulated afferents and one simulated inhibitory
input.
Model granular cell
Each model granular cell is described by a single compartment
with a membrane potential that evolves according to:Membrane capacitance (CM) values were chosen such
that the model EPSP evoked by a single presynaptic input matched near
threshold electrosensory responses of DGCs and SGCs (Figure S4). These
values were 6 pF for DGCs and 12 pF for SGCs. The leak current
(IL) is described by: where v is the membrane potential of the
model granular cell, the leak conductance gL = 1 nS and the
reversal potential EL = −70 mV. These values were
consistent with a prior in vitro study of ELL granular
cells (Zhang et al., 2007).
Model synapse
Each synaptic current (IE and II) is
described by the standard equation: where the reversal potential of the
excitatory conductance is 0 mV and the reversal potential of the
inhibitory conductance is −90 mV. The timecourse of the
excitatory conductance (gE) follows a double exponential with
a rise time constant τE1 = 4 msec and a decay time
constant τE2 = 1 ms. The conductance parameter
‘s’ is increased by we upon a spike event in a
presynaptic electrosensory afferent and decays exponentially with time
constant τE2. The excitatory conductance then evolves
according to: whereThe inhibitory conductance (gI) is increased by
wI upon a spike event in the stimulated presynaptic LMI
and decays exponentially with time constant τI = 5
ms.
Electrosensory afferent (EA) input
For each model granular cell, a set of 4 EA inputs were either
subsampled from recorded afferent data or simulated. The main results
were not affected by the exact number of EA inputs to each model
granular cell (Figure
S4), for values within a plausible range based on past
studies of the ELL (Bell, 1990a;
Bell et al., 2005; Zhang et al., 2007). We simulated
afferents by first calculating an exponential tuning curve of first
spike latency versus stimulus amplitude. We randomly selected each set
of exponential fit parameters from a multivariate Gaussian distribution
that was fit to the recorded afferent data (Figures 4E–4G). We then added multiple spikes according to the mean
spike offsets calculated in recorded EAs (Figure 4I). We constructed three different EA input
conditions to separately test the effects of diverse latency tuning and
diverse spike tuning and the combined effect of both (Figure 5E). To test the effect of
diverse latency tuning on model granular cell responses (purple in Figures 5E–5H), we constructed a model EA tuning
curve using the afferent population mean value for each latency tuning
parameter, which was held constant, and added subsequent spikes with an
offset determined by the recorded EA data (Figure 4I). We then randomly selected spike count tuning
from recorded EAs to mask spikes in the latency tuning curve. To test
the effect of diverse spike count tuning on granular cell responses
(orange in Figures 5E–5H), we constructed model EA tuning
curves by randomly selecting each set of exponential fit parameters from
a multivariate Gaussian distribution that was fit to the recorded
afferent data. We then added subsequent spikes with an offset determined
by the recorded EA data (Figure
4I). Spikes were cutoff after a maximum spike latency calculated
from the recorded EA data (11 ms). To test both diverse latency and
spike count tuning (blue in Figures
5E–5H), we
constructed a model EA tuning curve using the afferent population mean
value for each latency tuning parameter, which was held constant, and
added subsequent spikes with an offset determined by the recorded EA
data (Figure 4I). Spikes were
cutoff after a maximum spike latency calculated from the recorded EA
data (11 ms).
LMI inhibitory input
We simulated electrosensory-evoked inhibitory input to the model
by specifying an input spike time with a constant onset latency relative
to the earliest simulated EA input spike (we tested a range of onset
latency from 2–5 msec; Figure S4). The weight of the inhibitory synapse
(wI) was varied as a sigmoid function of the membrane
potential of the post-synaptic granular cell (v) at the time of the LMI
spike, which provided a nice fit to the data (Figures 5C and 5D). This is meant to approximate the proposed ephaptic
mechanism of LMI recruitment suggested by prior work (Han et al., 2000; Meek et al., 2001). However,
equivalent results were obtained if the strength of inhibitory input was
held constant as long as it was strong enough to truncate the response
and suppress its normal peak.
Model simulation
All simulations were done in Python 3 with the BRIAN 2 simulator
package (Stimberg et al., 2019).
The model had a time step of 0.1 msec and was simulated for 50 msec in
response to each electrosensory stimulus. Model GC responses were then
quantified by measuring the peak membrane potential as was done for the
real GCs recorded in this study. Each model cell was a simulation with a
different EA input population.
QUANTIFICATION AND STATISTICAL ANALYSIS
Data were processed and analyzed offline using Python 3. Biophysical
models were simulated and analyzed using the BRIAN 2 simulator package in Python
3 (Stimberg et al., 2019) (as noted
above). No statistical methods were used to predetermine sample size. The
experimenters were not blinded to the condition during data collection or
analysis. Statistical test identity is indicated along with each result.
Differences were considered significant at p < 0.05.
KEY RESOURCES TABLE
REAGENT or RESOURCE
SOURCE
IDENTIFIER
Antibodies
Alexa Fluor 488 Streptavidin complex
Jackson Immuno Research Laboratories
RRID: AB_2337249
Chemicals, peptides, and recombinant
proteins
DAPI
Sigma Aldrich
D9542
NeuroTrace 640
ThermoFisher Scientific
N21483
Deposited data
Full dataset (including raw and processed
data and custom scripts)