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. 2019 May 14;116(20):10097-10102.
doi: 10.1073/pnas.1812171116. Epub 2019 Apr 26.

Differentially synchronized spiking enables multiplexed neural coding

Milad Lankarany  1   2   3 , Dhekra Al-Basha  1   2 , Stéphanie Ratté  1   2   3 , Steven A Prescott  4   2   3
Affiliations

Differentially synchronized spiking enables multiplexed neural coding

Milad Lankarany et al. Proc Natl Acad Sci U S A. .

Abstract

Multiplexing refers to the simultaneous encoding of two or more signals. Neurons have been shown to multiplex, but different stimuli require different multiplexing strategies. Whereas the frequency and amplitude of periodic stimuli can be encoded by the timing and rate of the same spikes, natural scenes, which comprise areas over which intensity varies gradually and sparse edges where intensity changes abruptly, require a different multiplexing strategy. Recording in vivo from neurons in primary somatosensory cortex during tactile stimulation, we found that stimulus onset and offset (edges) evoked highly synchronized spiking, whereas other spikes in the same neurons occurred asynchronously. Stimulus intensity modulated the rate of asynchronous spiking, but did not affect the timing of synchronous spikes. From this, we hypothesized that spikes driven by high- and low-contrast stimulus features can be distinguished on the basis of their synchronization, and that differentially synchronized spiking can thus be used to form multiplexed representations. Applying a Bayesian decoding method, we verified that information about high- and low-contrast features can be recovered from an ensemble of model neurons receiving common input. Equally good decoding was achieved by distinguishing synchronous from asynchronous spikes and applying reverse correlation methods separately to each spike type. This result, which we verified with patch clamp recordings in vitro, demonstrates that neurons receiving common input can use the rate of asynchronous spiking to encode the intensity of low-contrast features while using the timing of synchronous spikes to encode the occurrence of high-contrast features. We refer to this strategy as synchrony-division multiplexing.

Keywords: multiplexing; neural coding; rate code; synchrony; temporal code.

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Conflict of interest statement

The authors declare no conflict of interest.

Figures

Fig. 1.
Fig. 1.
Neurons in primary somatosensory (S1) cortex use spike timing and rate to encode different tactile stimulus features. (A) Rasters from 17 neurons, four trials each, during tactile simulation (Top). FRH was calculated using a narrow (σ = 5 ms; black) or broad (σ = 100 ms; green) Gaussian kernel. Black FRH was thresholded to distinguish synchronous (red) from asynchronous (blue) spikes. Arrow highlights 10 g stimulus. (B) Receiver operating characteristic curve shows sensitivity and specificity with which synchronized spiking can predict stimulus onset or offset, depending on threshold value. Numbers on graph show threshold as percentage of maximum possible firing rate. Synchrony threshold = 65% for A and D, which means the onset and offset of the weakest stimulus (2.5 g) was not detected. If only stimuli ≤10 g are considered, 100% sensitivity and 86% specificity can be achieved by lowering the threshold. (C) Local field potential (LFP) averaged across five responses to 10 g stimulation (Top) and the corresponding spectrogram (Bottom). (D) Horizontally expanded rasters at onset of 10 g stimulus. Spikes during interval when FRH exceeds synchrony threshold (red shading) are considered synchronous. Some cells produce a quick burst of two to four spikes, but most contribute a single spike per volley. All true positive synchronized volleys (i.e., those that correctly identify stimulus onset or offset) are complete within 20 ms. (E) Cumulative probability distribution of synchronous spike latency from stimulus onset (pink) or offset (orange). Each curve represents a different stimulus intensity. (Inset) Median latency (lines) and 10–90 percentile range (shading) do not vary systematically with stimulus intensity. (F) Modulation of sustained firing rate. Excluding the first 20 ms, during which synchronous spikes occur; firing rate was calculated over the first half (20–500 ms, blue) or full duration (20–1,000 ms, cyan) of each stimulus step to gauge the effects of adaptation. Regression line slopes differed significantly from horizontal (P < 0.0001, one-sample t tests). (Inset) Average rate of 17 neurons averaged across trials to give mean ± SEM. Firing rate was significantly affected by stimulus intensity (F6,42 = 21.42; P < 0.001, two-way ANOVA) and adaptation (F1,42 = 7.22; P = 0.01); firing rate evoked by 2.5 or 5 g was consistently less than that evoked by ≥7.5 g (P < 0.05, Student-Neuman-Keuls post hoc tests).
Fig. 2.
Fig. 2.
Slow and fast signals can be demultiplexed from responses to mixed signal. (A) Basis for mixed signal. (A, Top) Decomposition of image by sensory neurons behaving as low-pass (LP) or high-pass (HP) filters. (A, Bottom) Gray-scale intensity along cut through LP image corresponds to slow signal representing luminance, a first-order stimulus feature. Same cut through HP image yields a series of discrete events representing edges and other areas of high contrast, a second-order stimulus feature. Convergence of those signals creates a “mixed” signal. See also SI Appendix, Fig. S2. (B) Sample rasters from 10 model neurons (Bottom) receiving a common mixed signal (Top) and independent noise (not illustrated). Spiking evoked by the fast component is not obviously different from spiking evoked by the slow component. (C) Decoding of the mixed signal using standard reverse correlation (orange) or a Bayesian decoding method (green) applied to the response of a single neuron (open bars) or a 30-neuron ensemble (filled bars). (Inset) Original mixed signal (black) overlaid with signal reconstructed from the ensemble response (color; Methods and SI Appendix, Fig. S3). Signal reconstruction was quantified as coding fraction, CF=1−∥original−reconstructed∥2∥original∥2, where CF = 1 represents perfect reconstruction and CF ≤ 0 represents failure to explain any variance.
Fig. 3.
Fig. 3.
Differentially synchronized spiking enables multiplexed coding of slow and fast signals. (A) Same rasters as in Fig. 2B with FRHs constructed with a narrow (σ = 5 ms; black) or broad (σ = 100 ms; green) Gaussian kernel. Slow fluctuations in the green FRH track the slow signal, whereas blips in the black FRH coincide with events in the fast signal. Black FRH was thresholded to distinguish synchronous (red) from asynchronous (blue) spikes. Arrows highlight values whose distributions are shown in SI Appendix, Fig. S4. (B) Pairwise cross-correlograms (CCGs) constructed from asynchronous spikes are broad (Top) whereas those constructed from synchronous spikes are narrow (Middle), consistent with rate comodulation and precise spike time synchronization driven by the common slow and fast signals, respectively (SI Appendix, Fig. S5). (C, Left) Spike-triggered averages (STAyx) were calculated from the fast, slow, or mixed signal (identified as x) using asynchronous, synchronous, or all spikes (identified as y). STAsyncslow and STAasyncfast (gray) were both unstructured, consistent with the slow signal not driving synchronous spikes and the fast signal not driving asynchronous spikes. Conversely, STAasyncslow (dark blue) and STAsyncfast (dark red) are consistent with the slow signal driving asynchronous spikes and the fast signal driving synchronous spikes. Similar STAs were recovered from the mixed signal, depending on the spike type (pale colors). (C, Right) Reverse correlation based on convolving each spike type with each STA type. Conditions yielding good reconstructions (high CF values) are highlighted in color. (D) Decoding of the mixed signal from the ensemble response. Synchrony-based demultiplexing (pink) matched the performance of the Bayesian method (dark green). Preventing the encoding model used for the Bayesian method from learning to fit rapid rate fluctuations degraded performance (light green). (E) Demultiplexing. Spikes from conductance based models in A were convolved with a synaptic waveform (τrise = 0.5 ms; τdecay = 3 ms) and summed to provide synaptic input (in arbitrary units, A.U.) to postsynaptic firing rate models that comprise a low- or high-pass filter. Model output (color) is overlaid on the original fast or slow signals (black). Integrator-type model (blue) extracted the slow signal whereas the coincidence detector-type model (red) extracted the fast signal from the multiplexed representations encoded by conductance based models.
Fig. 4.
Fig. 4.
Pyramidal neurons can multiplex in vitro. (A) Sample rasters from short length of 100-s-long responses. All neurons received the same mixed signal but different conductance noise on each trial. Four neurons were tested with 7 trials each; brackets on left group responses by neuron. Black FRH was thresholded to identify synchronous (red) or asynchronous (blue) spikes. (B) Decoding of the mixed signal from ensemble response (28 trials) illustrated in A, based on neurons tested in the noisy, high-conductance state. Same analysis conducted on neurons tested in a noisy, low-conductance state (31 trials from six neurons) (C) or in neurons without any added noise (29 trials from five neurons) (D). For all different conditions, the four decoding strategies yielded a pattern of CF values very similar to that seen in simulations (Fig. 3D).
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