Error correction and improved precision of spike timing in converging cortical networks — TEI-tagged view

LevipersName, SpivakpersName, SloinpersName, SomeckpersName, StarkpersName (2022date). “Error correction and improved precision of spike timing in converging cortical networks.” Cell Reportstitle·j.

Object of study — whether a pool of cortical neurons can transmit an undistorted message to a target, given that every transmissionterm step adds noiseterm

Research question — how precise and reliable propagation is possible when most cortical connections are weak and probabilistic

Contribution — the postsynaptic cell is MORE precise than the cells driving it, and its spiketerm train reconstructs the signal better - error correctionterm across a synapse

Full text — tagged

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Error correctionterm and improved precisionterm·def of spiketerm timing in converging cortical networks Amir LevipersName Amir LevipersName 1 Sagol School of Neuroscience and Department of Physiology and Pharmacology, Sackler Faculty of Medicine, Tel Aviv University, Tel Aviv 6997801, Israel 1 , Lidor SpivakpersName Lidor SpivakpersName 1 Sagol School of Neuroscience and Department of Physiology and Pharmacology, Sackler Faculty of Medicine, Tel Aviv University, Tel Aviv 6997801, Israel 1 , Hadas E SloinpersName Hadas E SloinpersName 1 Sagol School of Neuroscience and Department of Physiology and Pharmacology, Sackler Faculty of Medicine, Tel Aviv University, Tel Aviv 6997801, Israel 1 , Shirly SomeckpersName Shirly SomeckpersName 1 Sagol School of Neuroscience and Department of Physiology and Pharmacology, Sackler Faculty of Medicine, Tel Aviv University, Tel Aviv 6997801, Israel 1 , Eran StarkpersName Eran StarkpersName 1 Sagol School of Neuroscience and Department of Physiology and Pharmacology, Sackler Faculty of Medicine, Tel Aviv University, Tel Aviv 6997801, Israel 1, 2, ∗ 1 Sagol School of Neuroscience and Department of Physiology and Pharmacology, Sackler Faculty of Medicine, Tel Aviv University, Tel Aviv 6997801, Israel ∗ Corresponding author eranstark@tauex.tau.ac.il 2 Lead contact Received 2022 Mar 8; Revised 2022 May 26; Accepted 2022 Aug 28; Collection date 2022 Sep 20.

© 2022 The Author(s) This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

PMCID: PMC9513803 PMID: 36130516 Summary The brain propagates neuronal signals accurately and rapidly. Nevertheless, whether and how a pool of cortical neurons transmits an undistorted message to a target remains unclear. We apply optogeneticterm·mth white noiseterm·mth signals to small assemblies of cortical pyramidalterm cells (PYRs) in freely moving mice. The directly activated PYRs exhibit a spiketerm timing precisionterm of several milliseconds. Instead of losing precisionterm, interneuronsterm driven via synapticterm activation exhibit higher precisionterm with respect to the white noiseterm·mth signal. Compared with directly activated PYRs, postsynaptic interneuronterm spiketerm trains allow better signal reconstructionterm, demonstrating error correctionterm. Data-driven modeling shows that nonlinear amplification of coincident spikesterm can generate error correctionterm and improved precisionterm·def. Over multiple applications of the same signal, postsynaptic interneuronterm spiking is most reliable at timescales ten times shorter than those of the presynaptic PYR, exhibiting temporal codingterm. Similar results are observed in hippocampal region CA1term. Coincidenceterm detection of convergent inputs enables messages to be precisely propagated between cortical PYRs and interneuronsterm.

Keywords: coding, electrophysiologyterm·mth, extracellular, freely moving, hippocampus, mouse model, neocortexterm, optogeneticsterm·mth, spiketerm transmissionterm, synapticterm connectivityterm, temporal precisionterm Graphical abstract Highlights • PYR-to-interneuron spiketerm transmissionterm exhibits error correctionterm and improved precisionterm·def • Interneuronterm precisionterm is higher when a larger pool of presynaptic PYRs is recruited • Error correctionterm and improved precisionterm·def are consistent with coincidenceterm detection • Interneuronsterm activated by synapticterm transmissionterm act as temporal codersterm·def Using optogeneticterm·mth injection of white noiseterm·mth to pyramidalterm cells in neocortexterm and CA1term of freely moving mice, LevipersName et al. investigate mechanisms that enable the precise propagation of messages to postsynaptic interneuronsterm. They find that postsynaptic interneuronsterm act as temporal codersterm·def, exhibiting higher spike-timing precisionterm than the neurons directly activated by the white noiseterm·mth signal.

Introduction During sensory processing, cognitive thought, and action generation, spiking neuronal signals are propagated accurately and rapidly across multiple brain regions ( Buračas et al., 1998 ). However, information transmissionterm may be accompanied by increased variability ( Kara et al., 2000 ). Understanding the mechanisms underlying the precise and reliable propagation of spiking signals between neurons is an open question in neuroscience ( Sadeh and Clopath, 2021 ). Any signal processing can only induce distortion ( Cover and Thomas, 1991 ). In particular, the propagation of spikesterm via synapticterm transmissionterm can only add noiseterm in the form of lost spikesterm, added background activity, or spiketerm time jitterterm, requiring a neuronal mechanism to minimize and compensate for added noiseterm. Perhaps the simplest mechanism for precise and reliable propagation of spiking signals is 1:1 transmissionterm between a source and a target neuron. Indeed, some neurons generate postsynaptic responses that are sufficiently strong to generate postsynaptic action potentials ( Henze et al., 2002 ; Szegedi et al., 2017 ). In particular, pyramidalterm cells (PYRs) may connect to neighboring neurons with millivolt-scale unitary excitatory postsynaptic potentials (EPSPs) ( Cossell et al., 2015 ; Pala and Petersen, 2015 ). However, 1:1 transmissionterm cannot compensate for added noiseterm. Furthermore, cortical spiketerm transmissionterm is typically probabilistic and weak: most unitary EPSPs fail to generate spikesterm in postsynaptic neurons ( Galarreta and Hestrin, 2001 ; Jouhanneau et al., 2018 ).

Another possible mechanism for propagating spiking signals is divergence to multiple presynaptic neurons, which may in turn converge on a single postsynaptic target to generate a response ( Griffith, 1963 ). Transmissionterm via convergent inputs has been explored in theoretical models ( Abeles, 1991 ; Rothman et al., 1993 ; Diesmann et al., 1999 ), in vitro ( Reyes, 2003 ; Xu-Friedman and Regehr, 2005 ; Rossant et al., 2011 ), in non-mammalian systems ( Bhandawat et al., 2007 ; Jeanne and Wilson, 2015 ), and in early stages of sensory processing ( Joris et al., 1994 ; Kuenzel et al., 2011 ). However, transmissionterm via convergence has not been demonstrated for cortical circuitry in the intact brain. Thus, it is still unclear whether anatomical convergence ( Braitenberg and Schüz, 1998 ) and weak connectivityterm are sufficient to convey a spiketerm pattern precisely and reliably to a postsynaptic cell.

To determine the precisionterm and reliabilityterm timescale of spiketerm transmissionterm in converging neuronal networks, we focused on the interface between PYRs and inhibitory interneuronsterm (INTs; mostly fast-spiking putative parvalbumin-immunoreactive [PV] cells) in association cortices (parietal cortex and hippocampal region CA1term) of freely moving mice. Although information may propagate between excitatory cells, the PYR-to-INT interface provides a convenient model system since connectivityterm is relatively easy to detect and transmissionterm is largely self-terminating due to the inhibitory nature of the INTs. INTs assist in curtailing runaway excitation ( Yizhar et al., 2011 ), shaping local circuit function ( Pouille and Scanziani, 2001 ), and propagating information ( StarkpersName et al., 2013 ). In both PYRs ( Galarreta and Hestrin, 2001 ) and INTs ( Bacci and Huguenard, 2006 ), spikesterm can be generated with millisecond timescale precisionterm. As input, we used filtered Gaussian white noiseterm·mth (WN) signals, composed of a rich set of waveforms and spectral components. Previous studies employed WN signals to study stimulus-response properties ( De Boer and Kuyper, 1968 ; Eggermont et al., 1983 ; Bialek et al., 1991 ; Reid et al., 1997 ; DiCarlo et al., 1998 ), spiketerm generation ( Bryant and Segundo, 1976 ; Mainen and Seinowski, 1995 ; Billimoria et al., 2006 ), and spiketerm transmissionterm ( Marmarelis and Naka, 1972 ). We applied the same WN signal multiple times to the same set of PYRs using optogeneticterm·mth activation, and determined the precisionterm and reliabilityterm timescale of the directly activated PYRs (DA PYRs) and of postsynaptic, indirectly activated INTs (IDA INTs).

Results Determining spiking precisionterm and reliabilityterm from the response to filtered Gaussian white noiseterm·mth At least two temporal properties of single-neuron spiketerm trains should be distinguished: (1) how precise spiketerm timing is with respect to an input signal, and (2) at what timescale spiketerm timing is most consistent over multiple presentations of the same signal. In the intact brain, ongoing spiking (“noiseterm”) occurs even when a “signal” (e.g., the WN pattern) is applied. To rigorously define precisionterm and reliabilityterm timescale in the presence of noiseterm, we proceeded as follows. First, we generated a cross-validated filter based on the spike-triggered average of the WN signal (a modified Wiener filter; STAR Methods ), and used the filter to reconstruct the input from the spiketerm trains ( Figure 1 A). The peak of the filter defines the time lag between the spiketerm train and the input ( Figure 1 A, inset). The rank correlation coefficient (cc) between the input and the reconstructed signals, averaged over all trials, defines decoding qualityterm·var Q ( Figure 1 B, top). We defined “precisionterm” P as the temporal jitterterm (half-width of the jittering interval, δ) at which Q begins degrading ( Figure 1 B). The choice of the specific filter model ( Figures S1 A–S1D; STAR Methods ) does not affect any of the definitionsterm, steps, or conclusions ( Figures S1 E–S1I). Second, we defined “reliabilityterm timescale” Rp as the temporal variance (SD of a Gaussian kernel, σ) at which spiketerm trains are most similar to one another ( Figure 1 C). Hereafter, a set of spiketerm trains recorded during repeated presentation of the same input signal is assigned two numbers: P and Rp. In artificial spiketerm trains designed to imitate spiking response in the presence of noiseterm, precisionterm depends on signal jitterterm ( Figure 1 D), whereas reliabilityterm timescale depends on noise jitterterm·var ( Figure 1 E). Large values of P indicate poor precisionterm ( Figures 1 F and 1G), whereas small values indicate high precisionterm ( Figures 1 H and 1I). Smaller values of Rp ( Figures 1 F and 1H) are consistent with highest reliabilityterm at shorter timescales, whereas larger values ( Figures 1 G and 1I) indicate that reliabilityterm timescale is longer. From the perspective of a downstream target, spiketerm trains with short reliabilityterm timescales can be read out at higher temporal resolutions (“temporal” codes; Pouille and Scanziani, 2001 ), whereas long-timescale trains require integration over longer windows (“rateterm” codes; Barlow, 1972 ; London et al., 2010 ). Spiketerm trains with short/long reliabilityterm timescales can exhibit high/poor precisionterm ( Figure 1 J), across a wide range of firing ratesterm·var ( Figure 1 K). Thus, precisionterm and reliabilityterm timescale are dissociable.

Figure 1.

Dissociating spiking precisionterm and reliabilityterm timescale (A) Cross-validated reconstructionterm. Input is applied as a WN signal. An acausal modified Wiener filter model is generated, based on the WN and training-set spiketerm trains (purple). The model is used to reconstruct the WN signal during test-set spiketerm trains (red). Dashed lines delimit spikesterm used for filter generation.

(B) Decoding qualityterm·var Q is defined as the trial-averaged cc between the WN input and the reconstructed signals. Interval jitterterm is used to determine precisionterm P. Every spiketerm is jittered within a 2δ ms window and Q is recomputed. Precisionterm is defined as the δ for which the jittered Q is consistently below the original Q (Wilcoxon testterm·stat, p < 0.05).

(C) Reliabilityterm is the cc between pairs of reconstructed trials, averaged over all possible pairs. To determine reliability timescale (Rp)term·def, reconstructionsterm are based on a discrete set of Gaussian kernels with distinct SDs, resulting in the reliabilityterm profile (bottom).

(D) In artificial data, when noise jitterterm·var is held constant at zero, precisionterm is a monotonically increasing function of signal jitterterm (left here and in (E), ∗∗∗ p < 0.001, F testterm·stat). Dashed lines indicate unity.

(E) When noise jitterterm·var is held constant at zero, reliabilityterm timescale is constant (left). When signal jitterterm is held constant, reliabilityterm timescale is a monotonically increasing function of noise jitterterm·var (right).

(F–I) Artificial examples with (F) poor precisionterm, short reliabilityterm timescale; (G) poor precisionterm, long reliabilityterm timescale; (H) high precisionterm, short reliabilityterm timescale; and (I) high precisionterm, long reliabilityterm timescale.

(J) A monotonically increasing reliabilityterm profile is denoted a “rate coderterm·def” (G, I). A unit with a reliabilityterm profile with a consistent peak at an SD other than the maximally tested SD is denoted a “temporal coderterm·def” (F, H). High precisionterm can be achieved for both temporal and rate codersterm·def.

(K) During WN trials, rateterm/temporal codingterm (top) and high/poor precisionterm (bottom) can be achieved for higher and lower firing ratesterm·var. See also Figure S1 .

Spiketerm transmissionterm between PYRs and INTs exhibits error correctionterm and improved precisionterm·def To measure distortion over the PYR-to-INT interface, we used WN-shaped optogeneticterm·mth signals to focally activate PYRs in the parietal association cortex of freely moving mice ( Figure 2 A). We used microwatt-scale light powerterm·var, avoiding induction of field oscillations ( StarkpersName et al., 2014 ). We then quantified decoding qualityterm·var and precisionterm for DA PYRs (presynaptic) and for IDA INTs (postsynaptic) with respect to the WN input signal applied only to the DA PYRs. In an example session, we recorded 134 well-isolated PYRs and INTs ( Figure 2 B). Over 200 presentations of the same WN signal, a given DA PYR spiked at different times ( Figure 2 C, top), and different PYRs exhibited various precisionterm values (1.8–6.8 ms; Figure 2 B). A simultaneously recorded postsynaptic INT responded with higher precisionterm than all DA PYRs (0.4 ms; Figure 2 C, bottom). Thus, an IDA INT may exhibit higher precisionterm than a DA PYR.

Figure 2.

Error correctionterm and improved precisionterm·def along the PYR-to-INT interface (A) WN was applied to groups of neocortical DA PYRs using optogeneticterm·mth illumination.

(B) Subnetwork of four PYRs (purple) and one putative postsynaptic INT (green), recorded simultaneously (of 112 PYRs and 22 INTs) using a high-density optoelectronic probe. Auto-correlation histograms (ACHs) and cross-correlation histograms (CCHs; no light condition), consistent with monosynaptic excitation (p < 0.001, Poisson test).

(C) Spiketerm trains of one PYR (top) and INT (bottom) during 50 (of 200) WN trials.

(D) Stacked filters for DA PYRs (left) and IDA INTs (right; n = 7 CaMKII:ChR2 mice).

(E) Mean ± SEM filters for the DA PYR and IDA INT populations. The DA PYR filter peak occurs closer to the spiketerm than the IDA INT filter peak.

(F) DA PYR short time lags indicate direct activation, whereas longer IDA INT time lags imply indirect (i.e., synapticterm) activation. Here and in (G), (H), (J), and (L), vertical dashed lines indicate median values; ∗∗∗ p < 0.001, U test.

(G) As a population, IDA INTs have higher decoding qualityterm·var than DA PYRs.

(H) IDA INT spiketerm trains are more precise than DA PYR trains.

(I) In 174/229 (76%) connected pairs, IDA INT decoding qualityterm·var is higher than presynaptic DA PYR decoding qualityterm·var. Here and in (K), ∗∗∗ p < 0.001, Wilcoxon testterm·stat.

(J) Error correctionterm, defined as decoding qualityterm·var difference between connected DA PYR/IDA INT pairs.

(K) In 191/229 (84%) connected pairs, IDA INT precisionterm is higher than presynaptic DA PYR precisionterm.

(L) Precisionterm improvement between connected pairs. See also Figures S2 and S3 .

We recorded 1,867 neocortical PYRs and 563 INTs from n = 7 CaMKII::ChR2 mice ( Table S1 ). We defined a reliable response to the WN signal whenever the firing rateterm·var increase, the decoding qualityterm·var, and the reconstruction-based reliabilityterm were all significant ( Figures S2 A–S2C; STAR Methods ). Overall, 239 DA PYRs and 116 IDA INTs exhibited reliable responses. Modified Wiener filters for DA PYRs and IDA INTs peaked at negative time lags ( Figure 2 D), but DA PYR filters peaked closer to spiketerm time ( Figure 2 E). For DA PYR, the median time lag was 2.4 ms ( Figure 2 F). Simultaneously recorded IDA INTs exhibited longer time lags (4 ms; p < 0.001, U test; Figure 2 F). The 1.6 ms time lag difference is not consistent with direct optical activation of the INT and is rather consistent with synapticterm INT activation. Instead of being distorted by transmissionterm, decoding qualityterm·var for IDA INTs (median [interquartile interval; IQR] Q = 0.19 [0.12 0.27]) was higher than for DA PYRs (Q = 0.13 [0.11 0.18]; p < 0.001, U test; Figure 2 G). Similar results were observed for decoding measured by mutual informationterm·stat (p < 0.001, U test; Figures S2 D–S2F) and spectral coherence (p = 0.0013, U test; Figures S2 G–S2J). Thus, the WN signal applied to the PYRs is reconstructed better based on the postsynaptic compared with the presynaptic spiketerm trains. We term this phenomenon “error correctionterm.”

The median [IQR] precisionterm of the DA PYRs was 3.2 [2.4 4] ms ( Figure 2 H). Therefore, neocortical PYRs can emit spikesterm with precisionterm of a few milliseconds with respect to rapidly changing inputs, extending previous in vitro observations ( Mainen and Seinowski, 1995 ). In contrast, IDA INT precisionterm was 2.3 [1.6 3.2] ms, higher than DA PYR precisionterm (p < 0.001, U test; Figure 2 H). Thus, with respect to the WN signal applied to the PYRs, spiking precisionterm of postsynaptic INTs is higher than the precisionterm of the presynaptic PYRs. We term this phenomenon “improved precisionterm·def.”

To identify what determines precisionterm, we considered a host of single-neuron properties that together accounted for most group variance (R 2 = 0.7; Figure S3 ). DA PYR precisionterm was not correlated with DA PYR firing rateterm·var during baseline (0.7 [0.24 1.73] spikesterm/s; cc = −0.09; p = 0.24, permutation testterm·stat). However, precisionterm was higher when WN firing rateterm·var was higher (partial cc −0.2; p < 0.001, permutation testterm·stat; Figure S3 J). IDA INTs exhibited higher WN firing ratesterm·var than DA PYRs (median 28 versus 12 spikesterm/s; p < 0.001, U test; Figure S3 O). To determine whether IDA INT decoding qualityterm·var and precisionterm depend on WN firing ratesterm·var, we pruned IDA INT trains to match the DA PYR ratesterm by removing the spikesterm least likely to have emanated from the WN input. The procedure did not improve IDA INT decoding qualityterm·var or modify error correctionterm ( Figures S3 R and S3S). Yet even after pruning, IDA INT precisionterm was higher than DA PYR precisionterm (p < 0.001, U test; Figures S3 T and S3U). Thus, error correctionterm and improved precisionterm·def are maintained regardless of firing ratesterm·var.

In 174/229 (76%) of the putatively connected monosynaptic PYR-to-INT pairs, IDA INT decoding qualityterm·var was higher than decoding qualityterm·var of the presynaptic DA PYRs (p < 0.001, Wilcoxon testterm·stat; Figure 2 I), exhibiting error correctionterm. Error correctionterm was higher on a pair-by-pair basis ( Figure 2 J) than at the population level (p < 0.001, permutation testterm·stat). Furthermore, in 191/229 (84%) of the monosynaptic PYR-to-INT pairs, IDA INT precisionterm was higher than DA PYR precisionterm (p < 0.001, Wilcoxon testterm·stat; Figure 2 K). The improvement in precisionterm was higher on a pair-by-pair basis (median 1.6 ms; Figure 2 L) than at the population level (3.2–2.3 = 0.9 ms; p < 0.001, permutation testterm·stat). In sum, error correctionterm and improved precisionterm·def are observed following PYR-to-INT spiketerm transmissionterm.

Postsynaptic decoding qualityterm·var and precisionterm depend on presynaptic assembly size Since IDA INTs are activated by DA PYRs, IDA decoding qualityterm·var may depend on presynaptic connectivityterm. Indeed, 109/116 (94%) IDA INTs had at least one presynaptic PYR (median [IQR]: 8 [4 14]), whereas only 207/432 (48%) of the simultaneously recorded INTs not driven by the WN were connected to PYRs (p < 0.001, U test; Figure 3 A, left). Furthermore, IDA INT connection probability was higher (15% versus 4%; p < 0.001, U test; Figure 3 A, right). Thus, compared with simultaneously recorded INTs not driven by WN, network connectivityterm is denser for IDA INTs.

Figure 3.

Postsynaptic decoding qualityterm·var and precisionterm depend on presynaptic assembly size (A) Network connectivityterm is denser for IDA INTs than for simultaneously recorded INTs not activated by the WN signal. Left: IDA INTs are more likely to have at least one recorded presynaptic PYR ( ∗∗∗ p < 0.001, G testterm·stat of independence; dashed line indicates chance level). Right: probability of local connectivityterm is higher for IDA INTs ( ∗∗∗ p < 0.001, U test).

(B) IDA INT precisionterm is correlated with the number of recorded presynaptic DA PYRs ( ∗∗ p < 0.01, permutation testterm·stat).

(C and D) When multiple intensities were used (n = 34 IDA INTs), the optimal light intensity was denoted as the intensity that yielded the highest DC gain. IDA INTs tested during lower intensity exhibit decreased decoding qualityterm·var (C) and poorer precisionterm (D). Here and in (G) and (H), ∗∗∗ p < 0.001, Wilcoxon testterm·stat.

(E and F) Example experiment. WN signals were applied to neocortical PYRs using either single-site or multisite illumination. For the example IDA INT (E, green circle), decoding qualityterm·var (F, left) and precisionterm (F, right) increased when multisite illumination was used.

(G and H) IDA INTs tested during single- and multisite illumination of similar intensities (n = 55) exhibit increased decoding qualityterm·var (G) and higher precisionterm (H) during multisite illumination.

To determine whether postsynaptic decoding qualityterm·var and precisionterm depend on presynaptic assembly size, we first quantified correlations. We found that IDA INT decoding qualityterm·var did not depend consistently on the number of recorded DA PYRs (cc = 0.17; p = 0.08, permutation testterm·stat). In contrast, IDA INT precisionterm was higher when more DA PYRs were recorded (cc = −0.27, p = 0.002; Figure 3 B). To determine causally whether postsynaptic decoding qualityterm·var and precisionterm depend on the number of presynaptic PYRs, we carried out two targeted experiments. First, we tested the effect of reducing presynaptic pool sizeterm·var by comparing IDA INT decoding qualityterm·var when WN signals were applied at the optimal light intensity and at lower intensity (median [IQR] ratio: 0.49 [0.48 0.5]). Reducing the intensity reduced postsynaptic decoding qualityterm·var (ratio: 0.8 [0.7 1]; n = 34 IDA INTs; p < 0.001, Wilcoxon testterm·stat; Figure 3 C) and impaired postsynaptic precisionterm (ratio: 1.5 [1.2 2]; p < 0.001; Figure 3 D). Next, we tested the effect of increasing presynaptic pool sizeterm·var by multi-site illumination, without modifying single-source light powerterm·var ( Figures 3 E and 3F). Compared with single-site illumination, multi-site illumination induced higher IDA INT decoding qualityterm·var (ratio: 1.1 [1 1.3]; n = 55 IDA INTs; p < 0.001; Figure 3 G) and improved the precisionterm (ratio: 0.9 [0.7 1]; p < 0.001; Figure 3 H). Thus, when a larger presynaptic assembly is recruited, IDA INT decoding qualityterm·var and precisionterm are higher.

Error correctionterm and improved precisionterm·def are consistent with coincidenceterm detection Precise transmissionterm of spikesterm from a presynaptic source to a postsynaptic target can be achieved by at least three conceptually distinct models ( Figure 4 A). A single presynaptic neuron may drive the target strongly via a “labeled line” (LL; Henze et al., 2002 ; Szegedi et al., 2017 ). Second, multiple simultaneously active neurons may generate EPSPs that sum linearly in the postsynaptic neuron (“summed population”; SP; Cash and Yuste, 1999 ; Tran-Van-Minh et al., 2016 ). Finally, simultaneously active neurons may generate supralinear postsynaptic effects due to dendritic and/or somatic nonlinearities (“coincidenceterm detection”; CD; Azouz and Gray, 2000 ; Stuart and Häusser, 2001 ; Polsky et al., 2004 ; Ferrarese et al., 2018 ). To examine model plausibility, we generated synthetic postsynaptic spiketerm trains (sINTs) based on the recorded PYR trains and data-dependent filters ( Figures 4 B–4D). When background spiking was included, the LL model ( Figures S4 A–S4D) and the SP model ( Figures S4 E–S4I) did not yield any reliably responding sINTs ( Figure 4 E).

Figure 4.

Error correctionterm and improved precisionterm·def are consistent with coincidenceterm detection (A) Three transmissionterm models were used for converting spiketerm trains of one (top, LL) or multiple simultaneously recorded (bottom, SP/CD) presynaptic DA PYR spiketerm trains into an sINT train.

(B) Spiketerm transmissionterm curves for all PYR to IDA INT pairs with monosynaptic connections (1,106 pairs).

(C) Spike transmission gainterm·def, defined for every pair of units as the area under the spiketerm transmissionterm curve.

(D) Recorded DA PYR spikesterm (middle, purple ticks) during every individual WN trial (top, black trace) were convolved with the spiketerm transmissionterm curve extracted from the CCH (left), yielding a single trial rateterm function (middle, purple trace). A noiseless sINT train (bottom, green ticks) was stochastically generated from the rateterm function. A realistic sINT train was generated by adding “background” spikesterm randomly, equalizing the firing ratesterm·var of the sINT and the postsynaptic IDA INT.

(E) Under noisy conditions, only CD sINTs exhibit AC responses.

(F and G) sINTs exhibit error correctionterm (F) and improved precisionterm·def (G); ∗ p < 0.05 and ∗∗∗ p < 0.001, Wilcoxon testterm·stat.

(H) sINT precisionterm is correlated with the number of recorded presynaptic DA PYRs. Here and in (I): ∗∗ p < 0.01 and ∗∗∗ p < 0.001, permutation testterm·stat.

(I) CD error, the difference between the precisionterm of the CD sINTs and the corresponding IDA INTs. See also Figure S4 .

In contrast, the CD model ( Figure S4 J–S4T) yielded 54/109 (50%) driven sINTs ( Figure 4 E). sINT precisionterm was poorer than actual IDA INT precisionterm (p < 0.001, Wilcoxon testterm·stat; Figure S4 N). However, the precisionterm of the CD-driven sINTs was higher than the precisionterm of the corresponding presynaptic DA PYRs by 0.8 ms (median; p = 0.03, Wilcoxon testterm·stat), exhibiting improved precisionterm·def on a pair-to-pair basis ( Figure 4 G). Furthermore, the CD-driven sINTs exhibited error correctionterm (p < 0.001, Wilcoxon testterm·stat; Figure 4 F). These results depended on the extent of nonlinearity, but were independent of implementation specifics (multiplicative or exponential nonlinearity; Figures S4 P–S4T). Since all data-driven models are constrained by the available data, we determined what limits the CD model by quantifying performance as a function of presynaptic pool sizeterm·var. The precisionterm of the CD-driven sINTs was higher when more presynaptic PYRs were recorded (cc −0.53, p < 0.001, permutation testterm·stat; Figure 4 H). Furthermore, sINT precisionterm was increasingly more similar to the precisionterm observed for the IDA INTs when more presynaptic PYRs were recorded (cc between CD error and number of presynaptic PYR: −0.42, p = 0.003, permutation testterm·stat; Figure 4 I). To conclude, while no model provides an exact match, CD yields the behavior closest to the experimental observations.

INTs activated by synapticterm transmissionterm act as temporal codersterm·def We found that improved precisionterm·def depends on the number of neurons in the presynaptic pool and can be generated by nonlinear amplification of coincident presynaptic spikesterm. If synapticterm inputs are coincident and consistent over multiple trials, IDA INT trains may exhibit short reliabilityterm timescales (“temporal codingterm”; Figure 5 ). Indeed, IDA INT reliabilityterm profiles peaked at intermediate σ ( Figure 5 E, center), and the global maximum in the IDA INT group profile was higher than adjacent minima (p < 0.001, U test; Figure 5 F, green). DA PYRs exhibited mixed reliabilityterm profiles, peaking at the highest tested σ ( Figure 5 G). In contrast, IDA INT profiles peaked at shorter timescales (median 12 ms; p < 0.001, U test; Figure 5 G). Shortening of reliabilityterm timescales was observed on a pair-by-pair basis for monosynaptic PYR-to-INT pairs (p < 0.001, Wilcoxon testterm·stat; Figure 5 H). Thus, whereas DA PYRs exhibit mixed types of reliabilityterm profiles, most IDA INTs (80/112, 71%; Figure 5 I) act as temporal codersterm·def.

Figure 5.

INTs activated by synapticterm transmissionterm act as temporal codersterm·def (A) WN signals were applied to groups of neocortical DA PYRs (CaMKII::ChR2 mice).

(B) Example PYR (purple) and INT (green) spiketerm trains. The CCH is consistent with monosynaptic excitation (p < 0.001, Poisson test). Here and in (D), all conventions are the same as in Figures 2 B and 2C.

(C) Neocortical PV cells were directly activated (DA INTs; n = 5 PV::ChR2 mice).

(D) Example DA INT spiketerm trains.

(E) The reliabilityterm profiles of the DA PYRs and DA INTs are monotonically increasing (purple and blue), whereas the IDA INTs have a shorter reliabilityterm timescale (green). All conventions are the same as in Figures 1 F–1I.

(F) Averaged reliabilityterm profiles of the three populations (mean ± SEM over all scaled profiles). At the group level, IDA INTs are temporal codersterm·def.

(G) Cumulative distribution functions (CDFs) of reliabilityterm timescales of units from the three populations. Vertical dashed lines show group medians; ∗∗∗ p < 0.001, U test. IDA INTs exhibit shorter timescales than DA PYRs and DA INTs.

(H) IDA INTs have shorter reliabilityterm timescales than presynaptic DA PYRs. Gray lines indicate inferred monosynaptic connectivityterm. Each IDA INT timescale is plotted along with the timescales of all corresponding presynaptic DA PYRs (221 pairs); ∗∗∗ p < 0.001, Wilcoxon testterm·stat.

(I) Reliabilityterm profiles of all neocortical DA PYRs, IDA INTs, and DA INTs, scaled to the 0–1 range and sorted according to peak timescale. Profiles are arranged with temporal/rate codersterm·def below/above black lines.

(J) Temporal codingterm of IDA INTs is unlikely to be inherited from presynaptic DA PYRs. Fractions of temporal presynaptic DA PYRs are not consistently different for temporal IDA INTs and rateterm IDA INTs (p = 0.88, G testterm·stat). See also Figures S5 and S6 .

IDA INTs exhibited short reliabilityterm timescales regardless of the light source to IDA INT distance ( Figures S5 A–S5C). A minority of the IDA INTs exhibited rateterm coding, but the fraction of temporal codersterm·def did not differ consistently between DA PYRs presynaptic to rateterm and temporal IDA INTs (p = 0.88, G testterm·stat of independence; Figure 5 J; Figures S6 A–S6F). Thus, temporal codingterm is unlikely to be inherited from a single DA PYR.

The high prevalence of postsynaptic temporal codingterm may be an inherent property of interneuronsterm in general or an outcome of convergent synapticterm transmissionterm. To differentiate between the alternatives, we directly activated INTs in n = 5 PV::ChR2 mice ( Figures 5 C and 5D). Most DA INT reliabilityterm profiles (36/49 PV cells, 73%) were consistent with rateterm coding ( Figures 5 F and 5I). Median DA INT timescales were 102 ms, consistently longer than IDA INT timescales (12 ms; p < 0.001, U test; Figure 5 G). For the combined IDA and DA INT population, reliabilityterm timescales correlated with direct/indirect activation (partial cc −0.21; p = 0.01; permutation testterm·stat; Figure S5 N). IDA INT timescales remained shorter than DA INT timescales even when IDA INTs were pruned according to spiketerm waveform and auto-correlation histogram (ACH) properties of DA INTs (p < 0.001, U test; Figures S6 G–S6N). Thus, IDA INT short reliabilityterm timescales likely result from synapticterm activation, as opposed to the direct optogeneticterm·mth drive of the DA INTs. In summary, when INTs are activated via multiple converging inputs, temporal codingterm occurs.

Convergence maintains precisionterm at the cost of a millisecond delay There are at least two pathways for transmitting information between two stations, a “source” and a “target”: direct and diverging/converging ( Figure 6 A). Although CD of converging inputs generates error correctionterm and improved precisionterm·def, it is unclear whether a diverging/converging configuration is advantageous, compared with a direct connection. Here, we model the source station by the WN signal and the target by INT spiking. We found that signal routing via an intermediary (the DA PYR assembly) did not consistently degrade decoding qualityterm·var (p = 0.23, U test; Figure 6 B) or precisionterm (p = 0.08, U test; Figure 6 C). Thus, IDA INT precisionterm is close to the “limit” achieved by DA INTs.

Figure 6.

Convergence maintains precisionterm and provides robustness (A) Transmissionterm from source to target can be achieved via a diverging/converging network (top) or direct activation (bottom).

(B) Decoding qualities of DA INTs and IDA INTs are not consistently different (p = 0.23, U test). Here and in (C), (D), and (G), vertical dashed lines indicate medians.

(C) Precisionterm of DA INTs and IDA INTs is not consistently different (p = 0.08; U test).

(D) Transmissionterm and generation delay of spikesterm over a single synapticterm interface, estimated by the CCH peak.

(E) Modified Wiener filters of the DA INT population.

(F) Average (±SEM) filters for DA INTs and IDA INTs. The mean DA INT filter peaks before the IDA INT peak.

(G) Median DA INT time lag is 3.2 ms, shorter than the IDA INT time lag; ∗∗∗ p < 0.001, U test.

(H) The measured median time lags of the three populations imply that the unmeasured information transmissionterm delay, between a group of PYRs and a single INT, is ∼1 ms.

(I) Coincidenceterm detection allows system robustness. For each IDA INT, a “partial CD” sINT was generated by randomly removing the input from one presynaptic DA PYR. The partial CD sINT population has a precisionterm of 4.2 ms (median; ns, p > 0.05, and ∗∗∗ p < 0.001; U test).

The alternative to direct transmissionterm, convergence onto a target, may involve an additional delay. The delay imposed by spiketerm transmissionterm and generation over a single synapticterm interface can be estimated by the peak lag of the spiketerm transmissionterm curve ( Figure 4 B). For monosynaptic PYR-to-IDA INT pairs, the median lag was 1.6 ms (1,106 pairs; Figure 6 D), not consistently distinct from the time lag difference estimated from the IDA INT and DA PYR reconstructionterm filters (4–2.4 = 1.6 ms; Figure 2 F; U test, p = 0.97). Thus, convergence neither slows nor accelerates spiketerm transmissionterm. Although dynamics over a single synapse can be measured ( Midorikawa and Sakaba, 2015 ), transmissionterm lag over an axo-axonic interface cannot be quantified directly. Yet the lag of converging transmissionterm can be estimated indirectly from the difference between the IDA INT time lag (PYR spiketerm generation, PYR-to-INT transmissionterm, and INT spiketerm generation; 4 ms) and the sum of the DA PYR time lag (PYR spiketerm generation; 2.4 ms) and the DA INT time lag (INT spiketerm generation; 0.8 ms; Figures 6 E–6G). After bias correction, the group delay was 1.02 ms (95% confidence limits 0.4–1.44 ms; Figure 6 H). Thus, spiketerm transmissionterm over a converging synapticterm interface has a millisecond timescale delay.

While indirect transmissionterm induces an additional delay, relatively weak connections are used (median [IQR] spike transmission gainterm·def: 0.015 [0.007 0.033]; p < 0.001, Wilcoxon testterm·stat; Figure 4 C). Furthermore, indirect activation provides robustness to removal of individual intermediary elements, DA PYRs (p = 0.95; Figure 6 I). Thus, at the cost of a millisecond delay, diverging/converging transmissionterm allows the use of weak connections, provides robustness, and preserves precisionterm.

Temporal codingterm, error correctionterm, and improved precisionterm·def in CA1term Although convergent transmissionterm appears to support precise signal propagation along the PYR-to-INT interface, recurrent feedback between DA PYRs may refine the process. To determine whether recurrent excitation is necessary and to generalize our findings in the neocortexterm, we repeated WN experiments in hippocampal CA1term (n = 4 CaMKII::ChR2 and n = 5 PV::ChR2 mice; Figures 7 A–7D), a region with relatively sparse recurrent excitation ( Thomson and Radpour, 1991 ). We found that in CA1term, IDA INTs exhibited a median timescale of 9.4 ms, shorter than the DA INT timescale (102 ms; Figures 7 E–7H; p < 0.001, U test). Furthermore, most IDA INTs (94/124, 76%) in CA1term acted as temporal codersterm·def, compared with 1/21 DA INTs (p < 0.001; G testterm·stat of independence; Figure 7 G). Thus, IDA INTs act as temporal codersterm·def regardless of the sparseness of recurrent excitation.

Figure 7.

Temporal codingterm, error correctionterm, and improved precisionterm·def in CA1term (A) WN signals were applied directly to groups of PYRs or PV INTs in CA1term, a hippocampal region with sparse recurrent excitation.

(B) Example DA PYRs and IDA INTs recorded in the CA1term pyramidalterm cell layer (CaMKII::ChR2 mouse). Center, wide-band (0.1–7,500 Hz) traces recorded by eight electrodes during a single ripple event. Here and in (C), other conventions are the same as in Figure 2 B.

(C) Example DA INT recorded in CA1term (PV::ChR2 mouse).

(D) Spiketerm trains during 50 consecutive WN trials of the three example units.

(E) The reliabilityterm profiles of DA PYR and DA INT are consistent with rateterm coding, whereas the IDA INT acts as a temporal coderterm·def.

(F) Reliabilityterm profiles of the three populations (mean ± SEM, scaled to the 0–1 range). At the group level, DA INTs are rate codersterm·def, IDA INTs are temporal codersterm·def, and DA PYRs exhibit mixed behavior.

(G) Reliabilityterm profiles of all DA PYRs, IDA INTs, and DA INTs in CA1term.

(H) Compared with IDA INTs, DA units (PYRs and INTs) exhibit longer timescales. Here and in (K–M), vertical dashed lines show group medians; ∗∗∗ p < 0.001, U test.

(I) Stacked filters of all CA1term DA PYRs (n = 4 CaMKII::ChR2 mice), IDA INTs (recorded from the same four animals), and DA INTs (n = 5 PV::ChR2 mice).

(J) Mean ± SEM filters for the three populations.

(K) DA INTs respond faster to the WN input than DA PYRs. The longer time lags of the IDA INTs imply indirect (synapticterm) activation.

(L) IDA INTs exhibit higher decoding qualityterm·var than DA PYRs and DA INTs.

(M) IDA INTs have higher precisionterm than DA PYRs. See also Figure S7 .

In CA1term, the decoding qualityterm·var for IDA INTs was 0.16, higher than for DA PYRs (0.13; p < 0.001, U test; Figure 7 L). The precisionterm of CA1term IDA INTs was 2.8 ms, higher than CA1term DA PYR precisionterm (3.6 ms; p < 0.001, U test; Figure 7 M). The median DA INT precisionterm was higher than DA PYR precisionterm (p < 0.001, U test), but not consistently different from IDA INT precisionterm (p = 0.06; Figure 7 M). Thus, error correctionterm and improved precisionterm·def occur at the PYR-to-INT interface in cortical networks with distinct architectures, the neocortexterm and CA1term.

Finally, we compared error correctionterm and precisionterm improvement between regions. Error correctionterm was observed along the PYR-to-INT interface in both neocortexterm and CA1term, but did not differ consistently between pairs of connected units in the two regions (p = 0.09, U test; Figure S7 A). The median precisionterm of CA1term DA PYRs was 3.6 ms, poorer than the precisionterm of the neocortical DA PYRs (3.2 ms; p < 0.001, U test; Figure S7 E). Consistent with this, the median precisionterm of IDA INT in CA1term (2.8 ms) was poorer than in the neocortexterm (2.3 ms; p < 0.001, U test; Figure S7 F). When examined on a pair-by-pair basis, monosynaptic PYR-to-INT pairs exhibited higher improvement of precisionterm in the neocortexterm (median 1.6 ms) compared with CA1term (0.8 ms; p = 0.03, U test; Figure S7 B). Compared with the neocortexterm, the degree of convergence was higher in CA1term, with a median [IQR] of 18 [10 23] presynaptic PYRs (n = 124 IDA INTs; p < 0.001, U test). Thus, the extent of error correctionterm and improved precisionterm·def may also depend on circuit architecture.

Discussion We found that, compared with DA PYRs, postsynaptic INT spiketerm trains enabled better reconstructionterm of the WN signal and exhibited higher precisionterm, particularly when more presynaptic PYRs were recruited. Error correctionterm and improved precisionterm·def were consistent with nonlinear amplification of coincident presynaptic inputs. Furthermore, postsynaptic INTs exhibited temporal codingterm, whereas DA INTs did not.

Signal transmissionterm in the presence of noiseterm The present experiments were designed to measure the precisionterm and reliabilityterm of spiketerm generation and transmissionterm in the presence of background inputs from thousands of terminals ( Gulyás et al., 1999 ). Using WN signals, we found that spiketerm generation exhibits a precisionterm of 2–4 ms. However, even a 3 ms jitterterm poses a challenge to stable signal propagation. Some pathways include exceptionally strong synapses, enabling stable spiketerm transmissionterm at nearly a 1:1 ratio ( Henze et al., 2002 ; Szegedi et al., 2017 ; Jouhanneau et al., 2018 ), but most cortico-cortical connections are weak. Indeed, an LL transmissionterm model could not drive postsynaptic cells reliably. An alternative to LL transmissionterm is the combination of multiple weak presynaptic inputs. Although expected to saturate when driven by correlated noiseterm ( Zohary et al., 1994 ), linear summation may transmit spikesterm efficiently ( Reich et al., 2001 ). Indeed, increasing the presynaptic pool sizeterm·var experimentally induced higher precisionterm. However, simple summation of the simultaneously recorded spiketerm trains did not replicate the experimental findings. In contrast, nonlinear summation of coincidenceterm spikesterm ( Stuart and Häusser, 2001 ) was able to drive postsynaptic spiking more precisely than the driving trains. We found that error correctionterm and precisionterm improvement via CD of multiple weak synapticterm inputs are particularly advantageous when failure of a synapse or a presynaptic neuron occurs. As a practical example of how error correctionterm may work under natural conditions, the WN signal can be viewed as an analog of external input encoding specific sensory information to a pool of neurons, which also receives other activity. Then, every neuron will spiketerm differently due to the background “noiseterm,” but some spikesterm of the neurons in the activated pool will occur sufficiently close in time to drive postsynaptic activity more robustly than any of the elements of the pool.

Temporal codingterm and coincidenceterm detection In contrast to intracellular current injection, we applied the WN signals to small groups of adjacent neurons using photocurrents. Current injection is used widely to probe spiketerm generation ( Asanuma et al., 1968 ; Mainen and Seinowski, 1995 ; Bacci and Huguenard, 2006 ; Cossell et al., 2015 ; Pala and Petersen, 2015 ), but is clearly a non-physiological intervention. We found that neuronal response properties are qualitatively different when neurons are driven directly via photocurrents, compared with synapticterm inputs. The direct optogeneticterm·mth activation is largely somatic, whereas excitatory synapticterm activation is largely mediated via synapses on the dendritesterm. Dendritesterm of PV cells support nonlinear summation of coincident inputs ( Hu et al., 2010 ; Chiovini et al., 2014 ). While not tested in the present work, PYR dendritesterm are equipped with machinery for CD ( Stuart and Häusser, 2001 ; Polsky et al., 2004 ; Ferrarese et al., 2018 ). Thus, we hypothesize that PYR-to-PYR transmissionterm will also result in temporal codingterm by the postsynaptic PYRs.

Methodological considerations The question of whether neurons transmit information via rateterm or temporal codes has been discussed extensively ( König et al., 1996 ; Salinas and Sejnowski, 2001 ; Cohen and Kohn, 2011 ), and much of the debate is rooted in definitionsterm. The temporal/rateterm code differentiation is distinct from the mode by which a population of neurons encodes information: a population code can be based on ratesterm, and a single neuron code can be temporal ( Rieke et al., 1997 ). One approach is to analyze spiketerm trains from the perspective of a downstream target. Here, we operationally defined temporal codingterm as a reliabilityterm profile that peaks at a timescale shorter than the maximal tested timescale, but in fact, we placed rateterm/temporal codingterm on a continuous scale. This approach, which does not depend on any reconstructionterm filter, is based on a spike distance metricterm·stat that involves convolving spiketerm trains with kernels of gradually increasing temporal support ( Schreiber et al., 2003 ). Clearly, various kernels and other distance metrics are plausible ( Victor and Purpura, 1996 ; van Rossum, 2001 ). When the number of spikesterm is fixed, the reliabilityterm profile necessarily increases monotonically. However, in the presence of spikesterm due to nonspecific inputs, the reliabilityterm profile may exhibit a local peak.

A classic approach for quantifying the precisionterm and reliabilityterm of spiketerm generation is to apply a current pulseterm·mth to the tested neuron and measure latency and jitterterm of the resultant spiking. The response to a pulse attenuates over time, explores only a subset of the response space, and is influenced by background spiking. Indeed, previous work showed that, while the first spiketerm after a current pulseterm·mth may exhibit millisecond-timescale precisionterm, additional spikesterm are less precise ( Mainen and Seinowski, 1995 ; Bacci and Huguenard, 2006 ; Pala and Petersen, 2015 ). To overcome these limitations, WN signals were employed in vitro to study spiketerm transmissionterm ( Marmarelis and Naka, 1972 ). WN signals applied in vitro allow one to maintain millisecond-timescale precisionterm over multiple generated spikesterm ( Mainen and Seinowski, 1995 ). The present work applied optogeneticterm·mth WN signals to specific cell types for studying the properties of spiketerm transmissionterm in the intact, freely moving animal. Indeed, the approach developed here can be employed for studying spiketerm transmissionterm between diverse types of neurons, in various brain regions ( Klausberger and Somogyi, 2008 ; Tremblay et al., 2016 ).

Dependence on circuit architecture To allow generalization beyond the well-mapped circuits of initial sensory processing, we studied local networks in associative brain regions, the parietal cortex and CA1term. We found that some temporal properties of spiketerm generation and transmissionterm are qualitatively similar: DA PYRs exhibited a precisionterm of a few milliseconds, whereas IDA INTs exhibited error correctionterm and improved precisionterm·def. However, we also observed some differences. First, decoding qualityterm·var and precisionterm were consistently higher in the neocortexterm than in CA1term. Second, improved precisionterm·def was consistently higher in the neocortexterm. Some differences may be due to methodological details (light powerterm·var, number of activated PYRs), whereas others may be functional (diversity between PYRs, number of presynaptic PYRs). Regardless of the differences, postsynaptic error correctionterm, improved precisionterm·def, and temporal codingterm were observed in both brain regions examined, suggesting convergent synapticterm transmissionterm as a general mechanism for precise information propagation along the cortical PYR-to-INT interface.

Limitations of the study There are several limitations that should be emphasized. First, determining connectivityterm from finite data is necessarily biased toward stronger connections. Strong connections favor the LL and SP models of transmissionterm more than the CD model, in which the effect of as few as two presynaptic spikesterm is amplified by the nonlinearity. Second, the finding that postsynaptic INTs exhibit temporal codingterm rests upon the assumption that the cells tested during synapticterm activation (IDA INTs) and the cells tested during direct optogeneticterm·mth activation (DA INTs) are identical. We verified that properties do not differ at the population level, but more work is required to directly test the assumption by synapticterm and optogeneticterm·mth activation of the exact same INTs. Third, the properties of spiketerm transmissionterm between PYRs, which are of great interest, remain unknown. Specifically, the present experiments did not explore the precisionterm and reliabilityterm timescale of spiketerm transmissionterm from a presynaptic assembly of PYRs to a postsynaptic target PYR. Based on the present results, we hypothesize that IDA INTs facilitate error correctionterm and precisionterm improvement during the transmissionterm of information from one pool of PYRs to another.

STAR★Methods Key resources table REAGENT or RESOURCE SOURCE IDENTIFIER Experimental models: Organisms/strains Mouse: Ai32 The Jackson Laboratory RRID:IMSR_JAX:012569 Mouse: CaMKII-Cre The Jackson Laboratory RRID:IMSR_JAX:005359 Mouse: PV-Cre The Jackson Laboratory RRID:IMSR_JAX:008069 Mouse: FVB/NJ The Jackson Laboratory RRID:IMSR_JAX:001800 Bacterial and virus strains rAVV5/CamKII-hChR2(H134R)-mCherry UNC AV4317K Software and algorithms MATLAB Mathworks http://www.mathworks.com KlustaKwik3 Kadir et al. (2014) https://github.com/kwikteam/klusta Kilosort2 Pachitariu et al. (2016) https://github.com/MouseLand/Kilosort MATLAB code for spiketerm timing analysis This paper https://doi.org/10.5281/zenodo.7025664 Other Silicon probe: four shanks, 32 channels NeuroNexus Buzaski32 (H32 21 mm) Silicon probe: six shanks, 64 channels Diagnostic Biochips Stark64 (P64-7) Silicon probe: two dual-sided shanks, 64 channels Diagnostic Biochips Dual-sided64 (P32-1-D) Silicon probe: single shank, 32 channels NeuroNexus Edge32 linear (A1x32-Edge) Intan RHD2000 Intan Technologies http://intantech.com/products_RHD2000.html Digital signal processor Tucker-Davis Technologies RX8 Precisionterm current source StarkpersName et al. (2012) N/A Resource availability Lead contact Further information and requests for resources should be directed to and will be fulfilled by the lead contact, Eran StarkpersName ( eranstark@tauex.tau.ac.il ).

Materials availability This study did not generate new unique reagents.

Experimental model and subject details 14 freely moving C57BL/NJ or hybrid mice (13 males, one female) were used in this study: 12 animals for experiments in neocortexterm, and nine mice for CA1term recordings (seven of the mice were used in both areas; Table S1 ). Mice aged 16 weeks (median; IQR: [12 20]) at the time of implantation. Animals were healthy and weighed 30 [24.2 31.4] g before implantation. Mice were single-housed to prevent damage to the implanted apparatus. Seven mice expressed ChR2 in PYR under the CaMKII promoter (CaMKII::ChR2). In five of these mice, ChR2 expression was achieved by crossing CaMKII-Cre males (JAX #005359, The Jackson Laboratory) with Ai32 females (#012569); in two other mice, viral vector injection was employed (CaMKII-hChR2-mCherry). Previous work showed that in these lines, there is no leakage of ChR2 to PV cells ( StarkpersName et al., 2013 , 2014 ). The other seven mice expressed ChR2 in PV cells, generated by crossing PV-Cre males (#008069) with Ai32 females (PV::ChR2). All animal handling procedures were in accordance with Directive 2010/63/EU of the European Parliament, complied with Israeli Animal Welfare Law (1994), and approved by the Tel Aviv University Institutional Animal Care and Use Committee (IACUC #01-16-051).

Method details Probes and surgery All animals were implanted with high-density silicon probes attached to a movable microdrive and coupled with optical fibers. The probes used were: Stark64 (Diagnostic Biochips; six animals), Buzaski32 (NeuroNexus; five mice), Edge32 linear probe (NeuroNexus; one mouse), and Dual-sided64 (Diagnostic Biochips; two mice). The Stark64 probe consists of six shanks, spaced horizontally 200 μm apart, with each shank consisting of 10–11 recording sites, spaced vertically 15 μm apart. The Buzaski32 probe consists of four shanks, spaced horizontally 200 μm apart, with each shank consisting of eight recording sites, spaced vertically 20 μm apart. The Edge32 linear probe has a single shank consisting of 32 recording sites, spaced 20 μm apart. The Dual-sided64 probe consists of two dual-sided shanks, spaced horizontally 250 μm apart, with each shank consisting of 16 channels on each side (front and back), spaced vertically 20 μm apart. In each multi-shank probe, two to six shanks were equipped with an optical fiber, terminating about 50 μm above the top recording site. The linear probe was coupled to a single optical fiber. At the other end, fibers were coupled to diodes: 470 nm LEDs (LB P4SG, Osram), 367 nm LEDs (VLMU1610-365-135, Vishay), 450 nm laser diodes (PL450B, Osram), and 638 nm laser diodes (HL63603TG, Ushio) were used. Only blue (450 nm LDs and 470 nm LEDs) light sources were used in the reported experiments. The maximal driving current used was 50 mA, resulting in light powerterm·var of 39 [29.9 42.8] μW measured at the tip of the probe (median [IQR] over n = 52 blue light sources).

Four of the CaMKII::ChR2 mice were hybrids ( SloinpersName et al., 2022 ). Two mice (mA234 and mC41) were transgenic and hybrid, generated by crossing a CaMKII::ChR2 male (offspring of a CaMKII-Cre male and a Ai32 female) with an FVB/NJ female (JAX #001800). The other two (mF84, mF93) were hybrids, offspring of a C57BL/6J male (#000664) and an FVB/NJ female. The latter two mice were injected with a viral vector, rAVV5/CaMKII-hChR2(H134R)-mCherry (viral titer estimated at 5.6 × 10 12 IU/mL; University of North Carolina viral core facility; courtesy of K. Deisseroth) to express ChR2 in PYR. The viral vector was injected stereotactically (Kopf) into parietal cortex and hippocampus at 8 different depths (AP -1.6, ML 1.1, DV 0.4 to 1.8 at 0.2 mm increments; 50 nL/site; Nanoject III, Drummond).

In all mice, probes were implanted in the neocortexterm above the hippocampus (AP/LM, −1.6/1.1 mm) under isoflurane (1%) anesthesia following previously-described procedures ( StarkpersName et al., 2012 ; Noked et al., 2021 ). Recordings were carried out five days a week. After every recording session, the probe was translated vertically downwards by up to 70 μm. Analyses of hippocampal regions included only recordings from the CA1term layer, recognized by the appearance of multiple high-amplitude units and iso-potential spontaneous ripple events.

Recording sessions and WN signals In the beginning of each session, neuronal activity was inspected for spontaneous spiking activity, and if encountered, a baseline period of at least 15 min was recorded while the animal was in the home cage. The baseline period was followed by response mapping, using 50 ms light pulses at multiple power levels, used to determine for each light source a minimal light powerterm·var P th needed to generate spikesterm (“spiking threshold”). We denote the minimal light powerterm·var that yields a population response (e.g., induced oscillations; StarkpersName et al., 2014 ) as the “population threshold”. Next, WN signals were applied in the regime between the spiking threshold and the population threshold (typically, at three power levels: P th /2, P th , and 2P th ). Signals were applied using every available light source, during spontaneous behavior in the home cage. In CaMKII::ChR2 mice, the median [IQR] light powerterm·var used 5.5 [3.3 15] μW in neocortexterm (n = 139) and 7.8 [4.3 10] μW in CA1term (n = 113); in PV::ChR2, the power was 19 [12 20] μW (n = 49) in neocortexterm and 34 [20 34] μW (n = 21) in CA1term. For every light source, 74 [41 100] WN repetitions (median [IQR]) were applied at each power level. The same was repeated for simultaneous activation of multiple light sources. Trials were carried out in a pseudorandom order between the different light sources and power levels. Each recording session ended with another baseline period of at least 15 min. Animals were equipped with a 3-axis accelerometer (ADXL-335, Analog Devices) for monitoring head movements.

The order and power levels of the WN signals were generated in MATLAB and routed to a digital signal processor (DSP; RX8, Tucker-Davis Technologies). The DSP issued a voltage command to a 16-channel linear current source ( StarkpersName et al., 2012 ) that drove the head-mounted diodes. For driving LDs, which have a nonlinear current-to-power transfer function, the power (P) was measured at multiple driving currents (I) to create a P-I lookup table. The table was used to translate the desired power output into a corresponding voltage, given as a command to the linear current source. The instantaneous light powerterm·var to be administered by the system was calculated by multiplying the chosen power level by a filtered WN signal scaled between zero and one. The WN signal x(t) was generated once, by convolving uncorrelated Gaussian zero-mean WN sampled at 6 kHz with an alpha function (t⋅exp(-t/τ); τ = 3 ms). The same 1 s long signal was used in all experiments. The actual light powerterm·var varied, and was P(t) = μ+x(t)σ, where σ was typically set to either P th /2, P th , or 2P th , and μ was set such that non-positive values were excluded.

Spiketerm detection and sorting Neural activity was filtered, amplified, multiplexed, and digitized on the headstage (0.1–7,500 Hz; x192, 16 bits, 20 KHz; RHD2132 or RHD2164, Intan Technologies), and recorded by an RHD2000 evaluation board (Intan Technologies). Offline, spikesterm were detected and sorted into single units automatically using either KlustaKwik3 ( Kadir et al., 2014 ) for probes with up to 11 sites/shank, or KiloSort2 ( Pachitariu et al., 2016 ) for 16-site shanks. Automatic spiketerm sorting was followed by manual adjustment of the clusters. Only well-isolated units were used for further analyses ( StarkpersName et al., 2013 ) (amplitude >40 μV; L-ratio <0.05; ISI index <0.2). Units were classified into putative PYR or PV-like INT using a Gaussian mixture model ( StarkpersName et al., 2013 ). In PV::ChR2 mice, units that exhibited a consistent (p < 0.001, Poisson test) increase in spiking rateterm during 50 ms DC pulses were tagged as PV cells. A total of 8,176 units (6,616 PYR and 1,560 INT) were recorded from neocortexterm (2,625 PYR, 843 INT) and CA1term (3,991 PYR, 717 INT) of 14 freely-moving mice during 162 sessions.

Units were maintained for WN analyses only if three criteria were fulfilled. (1) The unit was tested during at least five WN trials, emitted an average of at least two spikesterm per trial, and exhibited a DC response (3,998/6,784 (59%); excluding PYR recorded in PV::ChR2 mice; Figure S2 A). Neither precisionterm nor reliabilityterm is necessarily correlated with WN firing rateterm·var ( Figure 1 K). A DC response was defined as a DC gain consistently above 1 (Poisson test). The DC gain was in turn defined as the mean firing rateterm·var during WN trials, divided by the mean spontaneous firing rateterm·var (computed in the lack of any stimulation during non-theta immobility). (2) The unit exhibited an AC response, defined as consistent decoding qualityterm·var (see below; permutation testterm·stat). Of the units with a DC response, 1,617/3,998 (40%) units exhibited an AC response ( Figure S2 B). (3) The unit was reliable, defined as consistent reconstruction-based reliabilityterm (see below; permutation testterm·stat). Of the units with an AC response, 662/1,617 (41%) units exhibited reliable spiketerm trains ( Figure S2 C). Thus, after omitting units which did not fulfill all three criteria, the dataset consisted of 352 PYR and 310 INT (neocortexterm: 239 PYR and 165 INT; CA1term: 113 PYR and 145 INT).

Determining monosynaptic connectivityterm To determine whether a monosynaptic connection may exist between DA PYR and IDA INT, we constructed count cross-correlation histograms (CCHs; 0.4 ms bins) for putative pre- and postsynaptic spiketerm train pairs during periods without WN. We defined the “spiketerm transmissionterm curve” as the impulse response of spiketerm transmissionterm between the pre- and postsynaptic neurons ( Figure 3 D). The spiketerm transmissionterm curve was estimated by the difference between the deconvolved CCH and the baseline, determined by median filtering of the count CCH and scaling to spikesterm/s (dividing by the number of presynaptic spikesterm and bin size; SpivakpersName et al., 2022 ). “Spike transmission gainterm·def” (a measure of the synapticterm efficacy; Swadlow and Gusev, 2001 ) was then defined as the area under the peak in the monosynaptic temporal region of interest (ROI; 0 < t ≤ 5 ms), extended until the causal zero-crossing points. Units that participated as a reference in a CCH that exhibited a consistent peak (p < 0.001, Bonferroni-corrected Poisson testterm·stat on the count CCH compared to baseline; StarkpersName and Abeles, 2009 ) in the monosynaptic ROI were defined as presynaptic excitatory cells. For every INT, connectivityterm probability ( Figure 3 A, right) was defined as the number of presynaptic PYRs, divided by the total number of simultaneously-recorded PYRs within a 600 μm range.

Filters and cross-validated reconstructionterm For every unit, the spikesterm in a given dataset were used to construct a model ( Rieke et al., 1997 ) ( Figure 1 A). The method used throughout the paper is an acausal modified Wiener filter, in which the spiketerm triggered average (STA) filter is whitened by the autocorrelation of the output (i.e., the spiketerm trains; see below). To determine whether results depend on the specific filter model, we also used previously described methods (STA and Wiener filters; causal and acausal; Aljadeff et al., 2016 ). Overall, twelve types of models were used ( Figures S1 A–S1D). The simplest model was a causal STA filter ( De Boer and Kuyper, 1968 ). Denote the WN analog signal as x(t) and the unit spiketerm times as T i , i = 1..N. To generate the STA filter, the WN input was first standardized (zero mean, unit variance) to z(t). An a-causal STA vector S → was generated by taking the average of segments of z(t) around each spiketerm, S → = 1 N ∑ i Z ( t i ) → , where t i ∈[ T i -50, T i +50 ] ms. To generate a causal STA filter, we set the values at positive time lags to zero.

To account for the possibility that distinct signal features yield distinct two-spike sequences, we used conditional STA (“CSTA”) filters, akin to the response-conditional ensembles approach ( de Ruyter Van Steveninck and Bialek, 1988 ). Here, we first computed the inter-spike interval (ISI) preceding every spiketerm; then, we partitioned the ISIs into ten equally-populated bins, and tagged every spiketerm according to the corresponding bin. A distinct STA filter was then generated for every ISI bin, yielding a filter bank. Both causal and acausal CSTA filters were employed.

The WN signal employed was generated by filtering Gaussian WN of a finite duration with an alpha function, and therefore the spectrum of the signal actually applied to the brain was not white. While none of the analysis steps relied on the assumption that the signal is Gaussian or white, we considered a whitened version of the STA filter, equivalent to a first-order Wiener kernel ( Marmarelis and Marmarelis, 1978 ). To generate the “Wiener” filter, the input signal was whitened before computing the STA. Whitening was done by multiplying the signal by the pseudo square root inverse of the signal covariance matrix ( Aljadeff et al., 2016 ). To prevent amplification of high-frequency noiseterm, the pseudoinverse matrix included only eigenvectors corresponding to the eigenvalues that together accounted for at least 90% of the signal variance. Finally, we considered a modified Wiener filter in which the STA filter was whitened by the output (i.e., the spiketerm trains) autocorrelation. Here, the spiketerm train ACH, specifically during the WN signal, was calculated for the same time range, and the ACH vector was transformed into a symmetric (Toeplitz) matrix, A ↔ . The modified Wiener filter w → is the deconvolution of the ACH from the STA, w → = A ↔ − 1 s → . For both the Wiener and the modified Wiener filters, “simple” and “conditional” models were employed.

All filters were computed using 10-fold cross-validationterm·stat. First, available trials were divided into a training set (90% of the trials) and a test set (the rest). Second, a filter model was computed based on the training set, and used to reconstruct the WN input according to the spiketerm trains of the test set trials ( Figure 1 A, bottom). Specifically, the WN pattern was reconstructed by convolving each test set spiketerm train with the training set filter (for conditional filters, every spiketerm was assigned an ISI bin and convolved with the corresponding filter in the bank). The procedure was repeated 10 times, so all trials were used for cross-validated reconstructionsterm.

Single-trial decoding qualityterm·var, q i , was determined by the rank correlation coefficient (cc) between the standardized WN input, z, and the i th trial reconstructionterm, z ˆ i : q i = ρ ( z , z ˆ i ) ( Figure 1 B, top). Since Wiener filters were based on whitened signals, the correspondence of the signal actually applied to the brain with the Wiener-based reconstructionterm is necessarily penalized. Therefore, we also considered a pre-whitened STA filter (“PWSTA”), in which the filter itself is the same as the Wiener filter, but the signal against which the reconstructionterm was gauged, z, was whitened (note that the dually-white setting is also penalized). Statistical significance of the reconstructionterm was determined by random shuffling of the test set spiketerm times within every trial, repeating reconstructionterm using the training set model, and computing an empirical p value for every trial. The overall decoding qualityterm·var Q was defined as Q = 1 N ∑ i q i , the mean over all cross-validated single-trial values, and the p value was the geometric mean over all cross-validated single-trial p values. As an independent metric of reconstructionterm quality, we considered the mutual information (MI)term·stat between the input signal z and the reconstructionterm z ˆ i ( Rieke et al., 1997 ). Here, we evaluated the MI using a direct method, binning the two-dimensional distribution and correcting for bias using the Bayesian counting procedure ( Panzeri and Treves, 1996 ). Finally, we considered the spectral coherence between the two signals. Coherence was derived from the cross-spectral density, estimated using multi-taper spectral methods ( Mitra and Pesaran, 1999 ). Here, we used 5 discrete prolate spheroidal sequences, FFT of 512 points, and 50% overlap between adjacent windows.

Error correctionterm and improved precisionterm·def were observed in the neocortical PYR-to-INT interface for all twelve filter models employed ( Figures S1 E–S1I). This observation is consistent with the fact that all models rely on the STA, which by itself allows accurate reconstructionterm of arbitrary input ( Bialek et al., 1991 ).

Precisionterm Only units that showed consistent decoding qualityterm·var (p < 0.05) were subjected to precisionterm quantification. Precisionterm P was defined as the smallest temporal jitterterm that resulted in consistent deterioration of the cross-validated decoding qualityterm·var Q ( Figure 1 B). All spikesterm were jittered using interval jitterterm ( Platkiewicz et al., 2017 ) at half-window durations δ log-spaced between 0.4 ms and 102.4 ms, and Q was recalculated for each δ. The domain confined between the smallest δ that resulted in consistent deterioration (Wilcoxon testterm·stat) of the cross-validated decoding qualityterm·var and the next δ was used for a focused sweep. That domain was divided into 10 new δ values, spiketerm trains were jittered at each δ, and Q calculated. Finally, precisionterm was defined as the smallest focused window that resulted in consistent deterioration of the cross-validated decoding qualityterm·var.

Reliabilityterm timescale Reliabilityterm was defined as the cc between pairs of reconstructed trials, averaged over all trial pairs. In each trial, the signal was reconstructed using the cross-validated filter model. Consistent reliabilityterm was defined if the cc (averaged over all possible pairs of trials) was consistently larger than zero, tested using Wilcoxon’s test. For each unit with consistent decoding qualityterm·var and reliabilityterm, a reliabilityterm profile was calculated ( Figure 1 C). Every point on the reliabilityterm profile was defined as the mean cc between trial pairs ( x ˆ i , x ˆ j ) , where trials were “reconstructed” by filtering the spiketerm trains with a Gaussian kernel with an SD of σ ( Schreiber et al., 2003 ). The reliabilityterm profile was calculated for distinct σ values, log spaced between 0.4 and 102.4 ms. If the reliabilityterm profile peaked at σ other than the highest tested value, a focused sweep was used. The domain confined between the profile peak and the next σ was divided into 10 new values, and reliabilityterm was calculated for every σ. Reliabilityterm timescale Rp was defined as the σ which yielded the global maximum of the reliabilityterm profile.

Recorded neurons were divided into three groups based on their reliabilityterm profile. The first group, denoted as “rate codersterm·def”, had monotonically increasing reliabilityterm profiles. The second group, denoted as “temporal codersterm·def”, had a local maximum in the reliabilityterm profile at a timescale other than the highest tested σ. Temporal codersterm·def either had a reliabilityterm timescale at the local maximum (i.e., the local maximum was Rp), or had a second maximum at the highest tested σ (i.e., reliabilityterm timescale Rp differed from the local maximum). All other units were denoted as “undefined”.

Point process simulation of spiketerm trains To test the framework of dissociating between temporal precisionterm and reliabilityterm timescale ( Figures 1 D–1K), a WN point process simulation was conducted. Simulations proceeded with sampling frequency of F s = 2500 Hz and N = 25 trials, each lasting T = 1 s. First, a firing rateterm·var profile f(t) was generated based on the WN signal, using a simplified STA-like kernel (a single sinusoid cycle with a frequency of 100 Hz). The kernel was treated as a template, which was convolved with the WN signal to create the firing rateterm·var profile. Second, given a rateterm function f(t), a “mother” signal spiketerm train was generated as a non-homogeneous Poisson process by deciding at each time step whether a spiketerm did or did not occur. This was done by random sampling from a binomial distribution with parameters B(n,p)=(1,f(t)/F s ), followed by imposing a minimum inter-spike interval (ISI; 1–5 ms). Third, the mother signal spiketerm train was replicated to generate N “daughter” signal spiketerm trains, and each daughter spiketerm train was modified as follows. (1) Each spiketerm was randomly jittered within a Gaussian window with a predetermined SD (“signal jitterterm”). (2) Up to N remove spikesterm were randomly removed from each daughter train. (3) Up to N add = N remove spikesterm were randomly added to the daughter spiketerm train. Fourth, background (“noiseterm”) spiketerm trains were generated using a homogeneous Poisson process. The “mother” noiseterm train was replicated to yield N daughter noiseterm trains, and each was modified in the same manner as the daughter signal trains (using “noise jitterterm·var”, adding, and removing spikesterm). Each final spiketerm train was a combination of a daughter signal spiketerm train and a daughter noiseterm spiketerm train. Simulated spiketerm trains were analyzed exactly as the experimentally recorded trains.

Parameter values used in artificial examples were as follows. Figure 1 F: signal firing rateterm·var, λ 1 = 25 spikesterm/s; signal jitterterm, σ 1 = 3 ms; noiseterm firing rateterm·var, λ 2 = 0 spikesterm/s; noise jitterterm·var, σ 2 = 0 ms; maximal number of added/removed spikesterm, N add = 25. Figure 1 G: λ 1 = 100 spikesterm/s; σ 1 = 10 ms; λ 2 = 0 spikesterm/s; σ 2 = 0 ms; N add = 0. Figure 1 H: λ 1 = 100 spikesterm/s; σ 1 = 1 ms; λ 2 = 0 spikesterm/s; σ 2 = 0 ms; N add = 10. Figure 1 I: λ 1 = 100 spikesterm/s; σ 1 = 10 ms; λ 2 = 200 spikesterm/s; σ 2 = 60 ms; N add = 0.

Data-driven simulation of synthetic INT To test the three transmissionterm models (labeled line [LL], summed population [SP], and coincidenceterm detection [CD]; Figure 4 ), synthetic INT (sINT) spiketerm trains were stochastically generated from the real spiketerm trains recorded from the DA PYR. For each IDA INT with presynaptic DA PYR, an sINT was generated. For the LL model ( Figures S4 A–S4D), the process of generating an sINT was as follows. First, the spiketerm transmissionterm curves and gains for all DA PYR and IDA INT pairs that exhibited putative monosynaptic connections were calculated ( Figures 4 B and 4C). For a single pair, the spiketerm trains of the DA PYR observed during WN stimulation were convolved with the transmissionterm curve of that specific pair to generate a rateterm function ( Figure 4 D). Therefore, for every WN trial, a different rateterm function was generated based on the DA PYR spiketerm train actually observed. Since the WN signals were applied at multiple power levels using different combinations of light sources, a single experimental setup from which the actual DA PYR spiketerm trains were extracted was selected. The selected experimental setup was that which yielded the highest DC gain for the postsynaptic IDA INT. From each rateterm function, a synthetic spiketerm train (ST 1 , with mean firing rateterm·var FR 1 ) was generated stochastically. A second spiketerm train (ST 2 ), representing background activity (omitted for the “noiseless” condition; Figure 4 E), was generated randomly as a homogeneous Poisson process with mean firing rateterm·var FR 2 . Denoting the firing rateterm·var of the IDA INT during WN stimulation by FR WN , the sINT spiketerm trains were generated such that if FR 1 ≥FR WN , no background activity was added. Otherwise, background activity was added such that FR 1 +FR 2 = FR WN .

For the SP model ( Figures S4 E–S4I), the same procedure was followed, with the exception that a joint ST 1 was generated by linear summation of all presynaptic rateterm functions.

For the CD model ( Figures S4 J–S4T), two different implementations were used to generate the rateterm functions and the synthetic spiketerm trains (ST 1 ). The first (CD 1 ) was a synapticterm multiplication model in which the CD rateterm function is y(t) at time t was defined, for n(t) > 1, as y ( t ) = ∏ i = 1 n ( t ) ( x i ( t ) + γ ) − γ n ( t ) , where n(t) is the number of simultaneously-activate synapses at time t, x i (t) is the input rateterm function from the i’th DA PYR, and γ is a scalar non-negative non-linearity factor. When n(t) = 1, y(t) = x i (t); and when n(t) = 0, y(t) = 0. The second implementation (CD 2 ) was a nonlinear summation model. For CD 2 , the rateterm function is y(t) = 0 when n(t) = 0; for n(t) ≥1, y ( t ) = ∑ i = 1 n ( t ) x i ( t ) γ n ( t ) − 1 .

Thus, in both implementations, isolated spikesterm were not amplified, whereas coincident spiking yielded supra-linear amplification. The fact that only a subset of the PYR activated by the optogeneticterm·mth input can be recorded limits the performance of any data-driven model. Thus, the models are oblivious to all unrecorded DA PYR that are presynaptic to the IDA INT. CD sINT precisionterm is higher ( Figure 4 H) and more similar to IDA INT precisionterm ( Figure 4 I) when more presynaptic PYRs are recorded.

Quantification and statistical analysis Statistical analysis In all statistical tests a significance threshold of α = 0.05 was used. An exception was the threshold used for determining whether two units exhibit monosynaptic connectivityterm (α = 0.001). In all cases, non-parametric testing was used. All statistical details (n, median, IQRterm·stat) can be found in the main text and figure legends. To estimate whether fractions are larger or smaller than expected by chance, an exact one-tailed Binomial testterm·stat was used. Differences in the proportions of observations of two categorical variables were tested with a G -testterm·stat. Differences between two group medians were tested with either Mann-Whitney’s one-tailed U -testterm·stat (unpaired samples) or Wilcoxon’s paired signed-rank one-tailed test. Association between parameters was quantified using Spearman’s rank correlationterm·stat and tested with a permutation testterm·stat. For all figures, ns, p > 0.05; ∗ , p < 0.05; ∗∗ , p < 0.01; ∗∗∗ , p < 0.001.

Acknowledgments We thank Ortal Amber-Vitos, György Buzsáki, Shigeyoshi Fujisawa, Roni Gattengo, Shir Mandelboum, Moshe Parnas, Lisa Roux, Jackie Schiller, Shir Sivroni, and Alexander Tarnavsky-Eitan for constructive comments. This work was supported by the United States-Israel Binational Science Foundation (BSF; 2015577), by the European Research Council (679253), by the Israel Science Foundation (638/16), by the Israel Science Foundation FIRST Program (1871/17), by the Rosetrees Trust (A1576), and by the Canadian Institutes of Health Research (CIHR), the International Development Research Centre (IDRC), the Israel Science Foundation (ISF), and the Azrieli Foundation (2558/18).

Author contributions A.L. and E.S. conceived and designed the experiments. A.L., L.S., H.E.S., S.S., and E.S. constructed optoelectronic probes and implanted animals. A.L., L.S., H.E.S., and S.S. carried out experiments. A.L. and E.S. analyzed data, constructed models, and wrote the manuscript with input from all authors.

Declaration of interests The authors declare no competing interests.

Published: September 20, 2022 Footnotes Supplemental information can be found online at https://doi.org/10.1016/j.celrep.2022.111383 .

Supplemental information Document S1. Figures S1–S7 and Table S1 mmc1.pdf (2.3MB, pdf) Document S2. Article plus supplemental information mmc2.pdf (7.6MB, pdf) Data and code availability • All data reported in this paper will be shared by the lead contact upon request.

• All original code has been deposited at Zenodo and is publicly available as of the date of publication. DOIs are listed in the key resources table .

• Any additional information required to reanalyze the data reported in this paper is available from the lead contact upon request.