Figure 1.
Gap stimuli and network rate response.
(A) Schematics of the gap stimuli used in the experiments. Each pulse is 128 ms long and contains white noise between 0.5 and 12 kHz. For the 2, 4, 8, 16 and 32 ms gap sizes, 3 gaps are presented per stimulus. For the 64 ms gap stimulus, 2 gaps are presented, whereas only a single 128 ms gap was placed in the pulse train. (B) Mean firing rate of the gerbil inferior colliculus network (91 neurons) in response to the 2 ms-gap stimulus. Bin size = 10 ms. The dashed lines mark the locations of the gap-to-pulse interfaces. (C)–(H) Mean network firing rate in response to the 4, 8, 16, 32, 64, 128 ms-gap stimuli.
Figure 2.
Population rate response to gap sizes.
(A)–(C) Exemplary gerbil inferior colliculus neurons and their responses to repeated trials of the same stimulus. The stimulus is comprised of three 128 ms broadband pulses that are separated by two 64 ms silent intervals (gaps). The resultant trial-averaged post-stimulus time histograms (PSTHs) are generated with a 10 ms bin size. The first two neurons show fast onset responses, while (C) shows delayed onset behavior. (D) The mean network PSTH during the first (solid line), second (long dashed) and third (point dashed) post-gap pulse of the 2 ms gap stimulus. One sees no clear pattern as a function of pulse-repetition. Inset: the same mean PSTHs for the 32 ms gap stimulus. (E) Grey level plot of cell-wise normalized post-gap PSTHs for all 91 cells and all gap sizes obtained from averaging over all pulses in the train following a gap. The cells are ordered according to their PSTH peaks for the 128 ms gap stimulus. (F) Mean network spike count over the 13 bins for each gap size. Dark to bright means short to long gap sizes. The dashed line is the mean network response during the first pulse, i.e. the control response. Inset: the mean network spike count variance over all gap sizes during the post-gap time series. The dips in the last bin reflect the fact that it only contains 8 ms of stimulation for a 10 ms bin size.
Figure 3.
Gap-encoding network patterns.
(A) Independent component analysis (ICA) of the population response matrices in Figure 2E, taking only the first 70 ms of each neuronal response. ICA reveals 3 significant independent components (ICs) that can be interpreted as onset, delayed onset and sustained (dark to bright means short to long gap sizes). All three vertical axes possess the same scale and, for illustration purposes, the baseline values for the different gaps are shifted equidistantly relative to each other. (B) Projections onto the subspace spanned by the onset and the delayed onset components for different points in time as indicated. Based on these two components it is possible to distinguish the responses to different gap sizes (gray levels as in A) for a few tens of milliseconds after the onset of the subsequent noise pulse. (C) ICs from analyzing our neuronal spike data with 5 ms bin size.
Figure 4.
(A) Schematic of the input stream to the network. Sensory-evoked spikes (black ticks) from Poisson processes (3 shown) and spontaneous background spikes (gray) are fed into a network. Each box marks a 130 ms snippet, and the gap size is defined as the silent interval (with noise) between the two snippets. Two input patterns, with identical snippets () and differing only in the gap sizes (gap A and gap B), are shown in a single input stream, with a 900 ms spacing between them. (B) Schematic of the network's output is read out at the onset of the second snippet with a bin size of 30 ms (the first black box, latency-corrected). The output patterns are translated into population vectors of spike counts and then used to train a linear classifier (filled circle) to distinguish the gap A vectors from the gap B vectors. Later on, when we perform ICA on simulated networks, the bin size is switched to 10 ms to collect 13 bins from the second snippet.
Figure 5.
Two different input stimuli are shown at the top, with the gray pattern delivering a 64(clipped at mV) in response to each stimulus is displayed in the middle panel, for a non-adapting neuron. The difference in membrane potential between 64 ms (gray) and 128 ms (black) after the first snippet is not significant enough to result in different spike counts during the second snippet. On the other hand, for an adapting neuron with
ms, the hyperpolarization and recovery result in a large difference in membrane potential at the two time points such that the neuron produces a different spike count during the second snippet.
Figure 6.
Two-gap classification with a single neuron.
(A) Binary classification performance of an adapting neuron for varying adaptation time constant and gap pairs of 4–8 ms (solid black), 16–32 ms (solid gray) and 64–128 ms (broken black). The input patterns are made of 130-and-30 ms snippets, as in Figure 3, containing identical 500 Hz periodic signal spikes. Each input pattern is repeated 10 times against 5 Hz background noise along a single input fiber. (B)–(C) The same experiment as in the top panel, this time with a particular instantiation of 500 Hz Poisson spike train for the input snippets, showing how changing spike timing can alter the peaks. (D) Same experiment as in the top panel, this time varying the membrane time constant of a non-adapting neuron, as further evidence of the advantage of adaptation in gap detection tasks.
Figure 7.
(A) Network performance is compared between a heterogeneous, non-connected network (broken lines, uniformly distributed from 0 to 20 ms) and a non-connected network that is homogeneous in
(solid lines), in tasks of classifying 4–8 ms (black), 6–12 ms (dark gray) and 8–16 ms (light gray) gap pairs.
=
= 1000,
=
= 0.05, with 10 Hz signal rate and 0.1 Hz noise rate. (B) The same experiment as (A), this time with excitatory recurrence (1.0
,
= 0.8), showing classification improvement from a non-connected network. (C) Same experiment as in (B), this time with a mixture of excitatory and inhibitory recurrence (2.0
and 0.5
), essentially reproducing the improvement seen in (B). (D) Test accuracy as a function of firing rate for heterogeneous adaptation. Network firing rate is tuned by either changing input firing rate (broken lines), starting from 10 Hz signal and 1 Hz noise and keeping signal-to-noise ratio the same, or by changing network recurrent weights, either through pure excitation (solid line) or through exc./inh. mixture (symbols), with 10 Hz signal and 1 Hz noise. The tasks are to classify 8–16 ms (black), 12–24 ms (dark gray) and 16–32 ms (light gray) gap pairs. The effect of network recurrence exhibits a maximum and can be roughly traced either through pure excitation or through exc./inh recurrence, along the network firing rate axis. (E) The 8–16 ms classification task for increasing excitatory recurrence, with input rates of 10 Hz (solid), 20 Hz (long dashed) and 30 Hz (point dashed) and a fixed ratio of background noise of
of the input rate. (F) Same as D for networks of neurons with distributed basic properties: Gaussian distribution of membrane time constants
with mean of 30 ms and standard deviation of 15 ms; Gaussian distribution of capacitance
with mean
pF and standard deviation
pF.
Figure 8.
The same paradigm from Figure 5 is employed, with the input snippets connected to three different neurons with and
ms. In addition, the top neuron (
ms) has an excitatory synapse (weight
) on the middle neuron, resulting in its discriminating firing behavior. The bottom panel shows a stand-alone
ms neuron that exhibits no discrimination to the two gap stimuli.
Figure 9.
Independent components of network simulations.
(A) Independent components from experiment. Replotted from Figure 1E for comparison. (B) Independent components of a heterogeneous recurrent network. The gap sizes (gray levels: dark to bright means 2 ms to 128 ms) are the same as those presented to the gerbils in [15], and the network contains values uniformly distributed from 0 to 1000 ms. Recurrent weights (4
and 4
) are tuned such that the network's onset firing rate matches that of the gerbil inferior colliculus neurons (
30 Hz). (C) Independent components from a recurrent, homogeneous network of
= 50 ms (4
and 12
). (D) Independent components from a non-connected, heterogeneous network (
between 0 and 1000 ms). An input rate of 9 Hz with 0.9 Hz noise rate were needed to achieve
30 Hz of network firing rate. (E) Independent components from a non-adapting recurrent network (4
and 28
).
Figure 10.
(A) Projections on the first two independent components of the gerbil recordings (128 ms pulse length): projections of activity from reduced pulse lengths (32 and 64 ms as indicated) vs. original (128 ms pulse length). Dark dots indicate short gap lengths, bright dots indicate long gaps. Dashed lines indicate identity. (B) Same as A for simulations of the network from Figure 9B. (C) Test accuracy of a linear classifier for gap discrimination trained on the simulated network from B for multiple pulse lengths (32, 64, and 128 ms). Gap pairs were 128 ms vs. 64 ms (solid line), 64 ms vs. 32 ms (dashed line), and 8 ms vs. 4 ms (dotted lines). (D) Test accuracy of a linear classifier for gap discrimination trained on the simulated network from B for multiple input rates (10, 15, 20 Hz). Gap pairs as in C.