The local field potential (LFP) is the low-frequency component (below a few hundred Hertz) of the extracellular potential recorded in brain tissue that originates from transmembrane currents in the vicinity of the recording electrode (Lindén et al., 2011; Buzsáki et al., 2012; Einevoll et al., 2013; Pesaran et al., 2018; Sinha and Narayanan, 2022). While the high-frequency component of the extracellular potential, the single- or multi-unit activity (MUA), primarily reflects action potentials of one or more nearby neurons, the LFP predominantly stems from currents caused by synaptic inputs (Mitzdorf, 1985; Einevoll et al., 2007) and their associated return currents through the membranes. Thus, cortical LFPs represent aspects of neural activity that are complementary to those reflected in spikes, and as such, they can provide additional information about the underlying circuit dynamics from extracellular recordings.

Applications of LFP are diverse and include investigations of sensory processing (Rall and Shepherd, 1968; Di et al., 1990; Victor et al., 1994; Kandel and Buzsáki, 1997; Mehta et al., 2000a; Mehta et al., 2000b; Henrie and Shapley, 2005; Einevoll et al., 2007; Belitski et al., 2008; Montemurro et al., 2008; Niell and Stryker, 2008; Nauhaus et al., 2009; Bastos et al., 2015; Senzai et al., 2019), motor planning (Scherberger et al., 2005; Roux et al., 2006), navigation (Tort et al., 2008; Makarova et al., 2011; Fernández-Ruiz et al., 2012; Watrous et al., 2013; Fernández-Ruiz et al., 2017), and higher cognitive processes (Pesaran et al., 2002; Womelsdorf et al., 2006; Liu and Newsome, 2006; Kreiman et al., 2006; Liebe et al., 2012). The LFP is also a promising signal for steering neuroprosthetic devices (Mehring et al., 2003; Andersen et al., 2004; Rickert et al., 2005; Markowitz et al., 2011; Stavisky et al., 2015) and for monitoring neural activity in human recordings (Mukamel and Fried, 2012) because the LFP is more easily and stably recorded in chronic settings than spikes. Due to the vast number of neurons and multiple neural processes contributing to the LFP, however, it can be challenging to interpret (Buzsáki et al., 2012; Einevoll et al., 2013; Hagen et al., 2016). While we have extensive phenomenological understanding of the LFP, less is known about how different cell and synapse types and connection patterns contribute to the LFP or how these contributions are sculpted by different information processing streams (e.g., feedforward vs. feedback) and brain states.

One way to improve its interpretability is to calculate the current source density (CSD) from the LFP, which is a more localized measure of activity, and easier to read in terms of the underlying neural processes. The current sinks and sources indicate where positive ions flow into and out of cells, respectively, and are constrained by Kirchoff’s current law (i.e., currents sum to zero over the total membrane area of a neuron). However, the interpretation of current sinks and sources is inherently ambiguous as several processes can be the origin of a current sink or source (Buzsáki, 2006; Pettersen et al., 2006; Einevoll et al., 2007). For example, a current source may reflect an inhibitory synaptic current or an outflowing return current resulting from excitatory synaptic input elsewhere on the neuron. There is no simple way of knowing which it is from an extracellular recording alone (Buzsáki, 2006).

Another approach to uncovering the biophysical origins of current sinks and sources, and by extension the LFP, is to simulate them computationally (Pettersen et al., 2008; Einevoll et al., 2013). Following the classic work by Rall in the 1960s (Rall, 1962), a forward-modeling scheme in which extracellular potentials are calculated from neuron models with detailed morphologies using volume conduction theory under the line source approximation has been established (Holt and Koch, 1999). With this framework, we have achieved a good understanding of the biophysical origins of extracellular action potentials (Koch, 1998; Holt and Koch, 1999; Pettersen and Einevoll, 2008; Hay et al., 2011; Lindén et al., 2010). Expanding on this understanding, models composed of populations of unconnected neurons (e.g., Pettersen et al., 2008; Lindén et al., 2011; Schomburg et al., 2012; Łęski et al., 2013; Sinha and Narayanan, 2015; Hagen et al., 2017; Ness et al., 2018) and recurrent network models (e.g., Traub et al., 2005; Vierling-Claassen et al., 2010; Reimann et al., 2013; Głąbska et al., 2014; Tomsett et al., 2015; Hagen et al., 2016; Hagen et al., 2018; Chatzikalymniou and Skinner, 2018) have been used to study the neural processes underlying LFP.

While interesting insights about CSD and LFP were obtained from these computational approaches, establishing a direct relationship between the biological details of the circuit structure and the electrical signal like LFP remains a major unresolved challenge. One reason is that the amount and quality of data available for modeling the circuit architecture in detail have been limited. This situation improved substantially in recent years, and a broad range of data on the composition, connectivity, and physiology of cortical circuits have been integrated systematically (Billeh et al., 2020) in a biophysically detailed model of mouse primary visual cortex (area V1). In addition, significant improvements were achieved in experimental recordings of the LFP and the simultaneous spiking responses. In particular, the Neuropixels probes (Jun et al., 2017) record LFP and hundreds of units across the cortical depth in multiple areas, with 20 μm spacing between recording channels allowing for an unprecedented level of spatial detail. These developments provide unique opportunities to improve our understanding of circuit mechanisms that determine LFP patterns.

Here, we analyze spikes and LFP from the publicly available Allen Institute’s Visual Coding survey recorded using Neuropixels probes (https://www.brain-map.org; Siegle et al., 2021) and reproduce these using the mouse V1 model developed by Billeh et al., 2020. The model is comprised of >50,000 biophysically detailed neuron models surrounded by an annulus of almost 180,000 generalized leaky-integrate-and-fire units. The neuron models belong to 17 different cell type classes: one inhibitory class (Htr3a) in layer 1, and four classes in each of the other layers (2/3, 4, 5, and 6) where one is excitatory and three are inhibitory (Pvalb, Sst, Htr3a) in each layer. The visual coding dataset consists of simultaneous recordings from six Neuropixels 1.0 probes across a range of cortical and subcortical structures in 58 mice while they are exposed to a range of visual stimuli (about 100,000 units and 2 billion spikes over 2 hr of recording).

In our analysis of this dataset, we identified a canonical CSD pattern that captures the evoked response in mouse V1 to a full-field flash. We then modified the biophysically detailed model of mouse V1 to reproduce both the canonical CSD pattern and laminar population firing rates in V1 simultaneously. We reproduce, in a quantitative manner, the shape and timing of the pattern of current sources and sinks that have been described in considerable detail by experimentalists (e.g., Mitzdorf, 1987; Swadlow et al., 2002; Senzai et al., 2019). This shows that adjustments to synaptic parameters such as weights and placement in addition to a circuit architecture that included feedback are sufficient to reproduce experimental findings on both single-cell measures such as spikes and population-level measures such as CSD. We use this model to explain, in a highly mechanistic manner, the biophysical origins of the various ionic current sinks and sources and their location across the various layers of visual cortex.

In the process of obtaining a model that could reproduce both spikes and CSD, we discovered that the model can be modified by adjusting the synaptic weights to reproduce the experimental firing rates with only minor effects on the simulated CSD, and, conversely, that the simulated CSD can be altered with only minor effects on the firing rates by adjusting synaptic placement. Furthermore, we found that comparing the simulated CSD to the experimental CSD revealed discrepancies between model and data that were not apparent from only comparing the firing rates. Additionally, it was not until feedback from higher cortical visual areas (HVAs) was added to the model that simulations reproduced both the experimentally recorded CSD and firing rates, as opposed to only the firing rates. This bio-realistic modeling approach sheds light on specific components of the V1 circuit that contribute to the generation of the major sinks and sources of the CSD in response to abrupt visual stimulation. Our findings demonstrate that utilizing the LFP and/or the CSD in modeling can aid model configuration and implementation by revealing discrepancies between models and experiments and provide additional constraints on model parameters beyond those offered by the spiking activity. The new model obtained here is freely accessible (https://doi.org/10.5061/dryad.k3j9kd5b8) to the community to facilitate further applications of biologically detailed modeling.

Spikes and LFP were recorded across multiple brain areas, with a focus on six cortical (V1, LM, AL, RL, AM, PM) and two thalamic (LGN, LP) visual areas, using Neuropixels probes in 58 mice (Siegle et al., 2021).

A schematic of the six probes used to perform the recordings in individual mice is shown in Figure 1A, and the spikes and LFP recorded in V1 of an exemplar mouse during presentation of a full-field bright flash stimulus are displayed in Figure 1B, C. The CSD can be estimated from the LFP (averaged over 75 trials) using the delta iCSD method to obtain a more localized measure of inflowing (sinks) and outflowing currents (sources) (Pettersen et al., 2006; Einevoll et al., 2013). The biophysically detailed model of mouse V1 used to simulate the neural activity and the recorded potential in response to the full-field flash stimulus is illustrated in Figure 1E. The model contains 230,924 neurons, of which 51,978 are biophysically detailed multicompartment neurons with somatic Hodgkin–Huxley conductances and passive dendrites, and 178,946 are leaky-integrate-and-fire (LIF) neurons. These neuron models are arranged in a cylinder with a radius 845 μm and a height 860 μm. The multicompartment neurons are placed in the ‘core’ with a radius of 400 μm, while the LIF neurons form an annulus surrounding this core. Cellular models belong to 17 different classes: one excitatory class and three inhibitory (Pvalb, Sst, Htr3a) in each of layers 2/3, 4, 5 and 6, and a single Htr3a inhibitory class in layer 1. The extracellular electric field in the model was recorded on an array of simulated point electrodes (Dai et al., 2020) arranged in a straight line (Figure 1D) and separated by 20 μm, consistent with Neuropixels probes, shown in Figure 1E to scale with the model.

Figure 1

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Uncovering a canonical visually evoked CSD response

We first established a ‘typical’ experimentally recorded CSD pattern to be reproduced with the model. Though there is substantial inter-trial and inter-animal variability in the evoked CSD response, we find that most trials and animals have several salient features in common. In Figure 2A, the trial-averaged evoked CSDs from five individual mice are displayed. In the first four animals (#1–4), we observe an early transient sink arising in layer 4 (L4) ~40 ms after flash onset, followed by a sustained source starting ~60 ms, which covers L4 and parts of layers 2/3 (L2/3) and layer 5 (L5). We also observe a sustained sink covering layers 5 and 6 (L6) emerging around 50 ms, as well as a sustained sink covering layers 1 and 2/3 around 60 ms. An animal that does not fully exhibit what we term the ‘canonical’ pattern is shown in the rightmost plot (#5 in Figure 2A); it has an early L4 sink arising at 40 ms, but this sink is not followed by the sustained sinks and sources from 50 to 60 ms and onward observed in the other animals. The timing and location of sinks and sources are, overall, similar to those described earlier by Givre et al., 1994; Schroeder et al., 1998, Niell and Stryker, 2008, and Senzai et al., 2019.

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To identify the robust features across animals in this dataset, we performed principal component analysis (PCA) on the trial-averaged evoked CSD from all animals. Out of the 58 animals in the dataset, 5 did not have readable recordings of LFP in V1 during the presentation of the full-field flash stimuli, and the exact probe locations in V1 could not be recovered for 9 other animals due to fading of fluorescent dye or artifacts in the optical projection tomography (OPT) volume (see ‘Materials and methods’). The remaining 44 (out of the 58) animals in the dataset were retained for the CSD analysis. The trial-averaged CSD plots of all these 44 animals are displayed in Figure 2—figure supplement 1. The first principal component (PC 1) (Figure 2B) constitutes a sum of weighted contributions of the CSD patterns from all 44 animals and explains half (50.4%) of the variance. The salient features typically observed in individual animals are also prominent in the PC 1 CSD pattern (Figure 2B), that is, the canonical pattern. In Figure 2—figure supplement 2, the first 10 principal components cumulatively explaining 90% of the variance are plotted.

Quantifying CSD pattern similarity

We use the Wasserstein, or Earth Mover’s, distance (WD) to quantify the differences in CSD patterns (see ‘Materials and methods’), which can then be used to assess how well the simulated CSD matches the CSD typically observed in experiments. The WD reflects the cost of transforming one distribution into another by moving its ‘distribution mass’ around (Rubner et al., 1998; Arjovsky et al., 2017). An often-used analogy refers to the two distributions as two piles of dirt, where the WD tells us the minimal amount of work that must be done to move the mass of one pile around until its distribution matches the other pile (Rubner et al., 1998). In the context of CSD patterns, the WD reflects the cost of transforming the distribution of sinks and sources in one CSD pattern into the distribution of sinks and sources in another pattern, with larger WD indicating greater dissimilarity between CSD patterns. The WDs are computed between the sinks of two CSD patterns and between the sources of two CSD patterns independently, and then summed to form a total WD between the CSD patterns (Figure 2C). The sum of all sinks and the sum of all sources in each CSD pattern are normalized to –1 and +1, respectively, so the WD only reflects differences in patterns, and not differences in the overall amplitude. The WD scales linearly with shifts in space and time.

When computing the WDs between the evoked CSD patterns of individual animals and the canonical pattern, we find that the animals with CSD patterns that, by visual inspection, resemble the canonical pattern (Figure 2A, animals 1–4), are indeed among animals with smaller WD, while the animal with the more distinct CSD pattern (Figure 2A, animal 5) is an outlier (Figure 2D).

The onset of the evoked response is less conspicuous in the single-trial CSD due to pronounced, ongoing sinks and sources, but there is still a visible increase in magnitude from 40 to 50 ms onward (Figure 2E), compatible with the latency of spiking responses to full-field flashes in V1 (Siegle et al., 2021). An oscillation of sinks and sources with a periodicity of ~20 ms, that is, in the gamma range is apparent in the region stretching from L2/3 to the top of L5, which appears to be either partially interrupted or drowned out by more sustained sinks and sources emerging at about 60 ms. At least some of this gamma-range activity derives from the visual flash that covers the entire visual field and that drives retinal neurons and postsynaptic targets in the lateral geniculate nucleus (LGN) in an oscillatory manner (see the pronounced gamma-range oscillation in the LGN firing rate in Figure 3D).

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The inter-trial variability is roughly comparable to the inter-animal variability of the trial-averaged responses. By computing the pairwise Wasserstein distances between single trial CSDs within each animal and comparing it to the pairwise WD between the trial-averaged CSD of each animal, we find that inter-trial variability in CSD is significantly lower than the inter-animal variability in trial-averaged CSD (Kolmogorov–Smirnov distance = 0.33; p<0.001) (Figure 2F).

The majority of animals (39 out of 44) have a WD to the first principal component, PC 1, of the CSD that is less than half of the greatest WD between the CSD of individual animals and the PC 1 CSD (Figure 2D); the pairwise WDs between animals are also less than half of the maximum pairwise WD for most animals (921 out of the total 946 pairwise WDs; Figure 2E). This supports the view that most animals exhibit the canonical CSD pattern captured by the PC 1 CSD (Figure 2B). The total inter-trial variability is smaller than the inter-animal variability, both estimated by pairwise WDs (Figure 2F and G), though there are n = 5 animals for which the inter-trial WDs are larger than the inter-animal WDs (Figure 2G, marked by red stars; determined with KS tests on the distribution of pairwise WDs between animals and pairwise WDs between trials in each animal; see Figure 2—figure supplement 3).

Discrepancy between the original model and experimental observations

We simulated the response to a full-field flash stimulus with the biophysical network model of mouse primary visual cortex as presented in Billeh et al., 2020. As input to the model, we used experimentally recorded LGN spike trains (Figure 4C; see ‘Materials and methods’). A Poisson source, firing at a constant rate of 1 kHz, provides additional synaptic input to all cells, representing the influence from the rest of the brain (‘background’ input). The thalamocortical input consists of spike trains from 17,400 LGN units (Arkhipov et al., 2018; Billeh et al., 2020). The public Neuropixels data contain recordings from 1263 regular-spiking LGN neurons across 32 mice during 75 trials of full-field bright flash presentations, resulting in 94,725 spike trains. To construct the input for each of our 10 simulation trials, we randomly sampled 10 unique subsets of spike trains from this pool until all 17,400 units had been assigned a spike train in each trial.

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Figure 4A, B displays the resulting spiking pattern across all layers with its associated LFP. The inferred CSD exhibits a strong sink in the L5 and L6 region, matched by a strong source below it, both starting at ~50 ms after flash onset (Figure 4B, bottom). However, the early L4 sink, the later sustained L4 source, and the sustained L2/3 sink typically observed in the experimental CSD (Figure 2A, B) are either absent or too weak compared to the sink and source in L5 and L6. The WD from the simulated CSD to the experimental PC 1 CSD is greater than the WD between the CSD of the farthest outlier animal and the PC 1 CSD (WD = 1.84, normalized to the largest WD between CSD of individual animals and PC 1 CSD). Thus, using experimental variability as a reference, the CSD from this simulation is an outlier (Figure 4C).

The population firing rates of the model, the KS similarities and correlation between the model and the data, are plotted together with the data in Figure 4D–F. The magnitudes of the model firing rates are higher than the experimental firing rates in all populations and time windows (Figure 4H). However, the KS similarities between the model firing rates and the experimental firing rates are still within the minimum to maximum range of the boxplots for the RS L2/3, RS L4, and RS L5 cells in all time windows (Figure 4F), and during baseline for the FS cells. For RS L6 neurons, the KS similarities were among the outliers of the experiments in all time windows, while for FS neurons they were among the outliers during the peak and sustained windows (RS L2/3: KSS_b = 0.62, KSS_p = 0.63, and KSS_s = 0.54; RS L4: KSS_b = 0.77, KSS_p = 0.60, and KSS_s = 0.63; RS L5 KSS_b = 0.77, KSS_p = 0.77, and KSS_s = 0.78; RS L6: KSS_b = 0.54, KSS_p = 0.45, and KSS_s = 0.47; FS: KSS_b = 0.54, KSS_p = 0.53, and KSS_s = 0.49). The temporal profile of the model firing rates is above the minimum of the boxplots for all populations (RS L2/3: r = 0.38***, RS L4: r = 0.62***, RS L5: r = 0.75***, RS L6: r = 0.90***, FS: r = 0.80***; ***p<0.001). For RS L4 and RS L6, the model is in fact outside the experimental distribution, but it is an outlier in a positive sense; the model firing rates for these populations are more similar to the experimental average than the corresponding population firing rates in individual animals.

The original model studied in Figure 4 produced firing rates and orientation and direction tuning consistent with recordings in vivo (Billeh et al., 2020) with some shortcomings, such as relatively slow responses of V1 to the onset of visual stimuli (Arkhipov et al., 2018; Billeh et al., 2020). Here, we see even more inconsistencies reflected clearly in the CSD pattern. This demonstrates the importance of multi-modal characterization of such biologically detailed models. To investigate the properties of the cortical circuit that sculpt the CSD, we manipulated the model and observed how both the CSD and firing rate responses were improved to match the experimental data.

Adjusting the model to fit experimental firing rates

Due to the discrepancy between the magnitudes of the model firing rates and the experimental firing rates, especially with respect to the outliers of the modeled RS L6 and FS neurons, we selectively adjusted the recurrent synaptic weights. We left the synaptic weights between LGN and the V1 model unchanged since they were well constrained by data (Billeh et al., 2020).

We first reduced the synaptic weights from all excitatory populations to the FS PV-neurons by 30% to bring their firing rates closer to the average firing rate in this population in the experiments. This resulted in increased firing rates in all other (RS) populations due to the reduced activity of the inhibitory Pvalb-neurons (Figure 4—figure supplement 1). Therefore, we further applied reductions in the synaptic weights from all excitatory neurons to RS neurons and increases in the synaptic weights from inhibitory neurons to the RS neurons to bring their firing rates closer to the experimental average firing rates. We multiplied the recurrent synaptic weights with factors in the [0.2, 2.5] range until we arrived at a set of weights where none of the model firing rates were among the experimental outliers in any time window (KSS_b = 0.73, KSS_p = 0.77, and KSS_s = 0.70; average across RS populations and the FS population) and temporal profiles (RS L2/3: r = 0.49***, RS L4: r = 0.63***, RS L5: r = 0.71***, RS L6: r = 0.87***, FS: r = 0.86***; *** p<0.001) (Figure 5A–C).

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The resulting pattern (but not the magnitude) of the CSD, however, was largely unchanged (Figure 5D) compared to the original CSD (Figure 4B). The overall magnitude was reduced, and there were some traces of a sink arising at 40 ms after flash onset, and a L2/3 (and L1) sink after 60 ms, but they were substantially weaker relative to the L5/L6 dipole than they were in the experiments. Furthermore, the large and sustained L4 source after 60 ms was still either absent or too weak to be visible. The WD between the CSD from this version of the model and the experimental PC 1 CSD remained among the outliers of the animals (Figure 5E) (normalized WD = 1.26).

Effects of feedback from higher visual areas to the model

Hartmann et al., 2019 found that feedback from higher visual areas (HVAs) can exert a powerful influence on the magnitude of the evoked LFP response recorded in V1 of macaque monkeys, particularly in the period 80–100 ms after stimulus onset. The sustained L2/3 sink and L4 source we observe in the experimental CSD emerge at 60 ms (Figure 2A and B), which roughly coincides with the peak firing rates in the latero-medial (LM), rostro-lateral (RL), antero-lateral (AL), and postero-medial (PM) cortical areas (Figure 3C). Furthermore, anatomical data indicate that synapses from HVAs terminate on L1 and L2/3 apical dendrites of pyramidal cells (whose cell bodies reside in L2/3 or L5) (Glickfeld and Olsen, 2017; Marques et al., 2018; Hartmann et al., 2019; Keller et al., 2020; Shen et al., 2020). Together, these observations suggest that the sustained L2/3 sink and L4 source might, in part, be induced by feedback from HVAs, where the sink is generated from the input to the apical tufts in L1 and L2/3, and the source may be the return currents of this input.

Of these HVAs, the feedback from LM to V1 is best characterized (Marques et al., 2018; Keller et al., 2020; Shen et al., 2020) and has the highest connection density to V1 (Harris et al., 2019). Based on these considerations, we decided to test the hypothesis that the large sinks and sources in the upper layers were caused, at least in part, by feedback from LM. In addition to the earlier feedforward LGN input and the background input representing the influence of the rest of the brain, we introduced a feedback input constructed from experimentally recorded spike trains in LM. In total, the public Neuropixels dataset has 2075 neurons recorded in LM (simultaneously with the recordings in LGN, V1, and other visual areas) from 42 animals during presentations of the full-field flash stimulus. 1823 of the 2075 neurons were classified as RS, and spike trains from these were used to generate the feedback input to the model (Figure 6A).

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The synapses from this LM source were placed on the apical dendrites of L2/3 excitatory neurons (within 150 μm from the soma), on the apical tufts (>300 μm from the soma) and the basal dendrites (within 150 μm from the soma) of L5 excitatory neurons, and on the somata and basal dendrites of L2/3, and L5 inhibitory (Pvalb and Sst) neurons (at any distance from the soma). The input onto L2/3 excitatory neurons did generate a sink in L1 and L2/3 and a source below in L4 (Figure 6B–E).

The synaptic weights from LM to the populations targeted by the feedback were initialized at high values (see ‘Materials and methods’), and then adjusted (decreased) by multiplying them with factors in the range [0.05, 0.5] (see ‘Materials and methods’). The weights from the background to the feedback-targeted populations were also multiplied by factors in the range [0.2, 0.5], and the weights of connections from Pvalb neurons to L2/3 excitatory and L5 excitatory neurons were multiplied by factors in the range [0.8, 1.2]. This weight scaling was done until the population firing rates were within the experimental variability. Additionally, the synapses from excitatory populations onto L6 excitatory cells were restricted to be within 150 μm from the soma to reduce the magnitude of the L5/L6 dipole (Figure 6—figure supplement 1; see ‘Materials and methods’). Greater separation between a sink and a source in a dipole moment increases its magnitude, so restricting the range within which synapses can be placed should diminish the L5/L6 dipole’s dominance.

When the model received this feedback input together with the LGN input, the resulting CSD pattern reproduced the main features observed in the experiments (Figure 6C). The WD between the model CSD and the experimental PC 1 CSD was also no longer an outlier (Normalized WD = 0.41; Figure 6D), and the population firing rates remained within the minimum and maximum value of the experimental boxplots for the firing rates in all windows and all populations, both with respect to magnitudes (KSS_b = 0.77, KSS_p = 0.70, and KSS_s = 0.68; average across all populations) and temporal profiles (RS L2/3: r = 0.36***, RS L4: r = 0.64***, RS L5: r = 0.69***, RS L6: r = 0.87***, FS: r = 0.77***, ***p<0.001) (Figure 6F and G). Thus, when average responses to the full-field flash are considered, this final adjusted model exhibits both the CSD and firing rate patterns that are consistent with the experimental observations and are well within animal variability (Figure 6F–H).

Furthermore, we investigated whether the model could reproduce the stereotypical features of the single-unit firing response observed in experiments. To this end, we computed the moments of the distribution of peak firing rates as well as the distribution of latencies to the peak across cells both for individual animals and for the model versions (Figure 6—figure supplements 2 and 3). The original model was an outlier for the first moment of the peak firing rate distributions of RS L2/3, L4, L6, and FS populations, while the intermediate model was within the experimental variability for all populations, and the final model was within the experimental variability for all populations except RS L2/3, where it was just outside the maximum value of the experimental boxplot (Figure 6—figure supplement 2A). All three model versions were outside the experimental variability of the third moment (skewness) of the peak firing rate distributions for the RS L2/3 population, and the original model was just outside for the RS L5 and FS populations as well (Figure 6—figure supplement 2C). Otherwise, all model versions were within the experimental variability for all moments that we considered and for all populations.

With respect to the distribution of latencies to the peak firing rates, all model versions were within the experimental variability for all populations and all moments except the fourth moment (kurtosis) of the FS population, where all model versions were outside the experimental variability. We also computed the relative change in firing rates between neighboring populations (Figure 6—figure supplement 4) and the distributions of greatest curvature of the firing rate across cells (Figure 6—figure supplement 5), and found that all model versions were within the experimental variability on both of these metrics too. Thus, as with the analysis of population firing rates, the original model is an outlier when compared to the experiments on the features of unit firing, while the intermediate and final model versions reproduce most features observed in the experiments.

To check if the model continued to exhibit appropriate orientation and direction tuning after the adjustments made, we ran a simulation with the final model configuration and the same drifting grating stimulus that was utilized in Billeh et al., 2020. We found that the model still displayed firing rates at preferred directions and direction and orientation selectivity indices comparable to those observed experimentally (Figure 6—figure supplement 6).

Identifying the biophysical origins of the canonical CSD

With the canonical CSD (Figure 2B) reproduced, we can use the model to probe the biophysical origins of its sinks and sources. We began by removing all recurrent connections and only feeding the LGN input to the model to find the contribution from the thalamocortical synapses onto excitatory and inhibitory neurons (Figure 7A). The main thalamic contribution to the CSD is from synapses onto excitatory neurons, in line with the expectation that neurons with a spatial separation between synaptic input currents and the return currents dominate the cortical LFP generation (Einevoll et al., 2013). (Neurons without apical dendrites will have largely overlapping synaptic input currents and return currents, resulting in a cancellation of current sinks and sources.).

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We further observed that the early L4 and the sustained L5/L6 sinks are present in the CSD contributions of excitatory neurons, though the magnitude of the L5/L6 sink is substantially reduced compared to its magnitude when the model is configured with recurrent synapses intact (Figures 4B—6). The sustained L2/3 sink and L4 source, on the other hand, were not visible. This suggests that the early L4 sink and the L5/L6 sink are at least partly generated by thalamocortical synapses. However, the substantially diminished magnitude of the L5/L6 sink indicates that recurrent synapses also contribute significantly to the generation of this sink.

We then removed the LGN input and added the feedback (while keeping the recurrent connections cut), which resulted in a prominent upper layer dipole, with the sink residing in L1 and L2/3, and the source residing in L4 (Figure 7B). Together with their absence when input came from LGN only (Figure 7A), this suggests that the sustained L2/3 sink and the L4 source in the canonical pattern originate at least in part from the feedback synapses onto the apical dendrites of L2/3 and L5 pyramidal cells and the activity this input generates.

To assess the extent to which active channels at the somata contributed to the CSD pattern, we compared the CSD resulting from a simulation with both LGN and feedback input (where the recurrent connections were still cut) when we included or excluded the active channels (NaT, NaP, NaV, h, Kd, Kv2like, Kv3_1, K_T, Im_v2, SK, Ca_HVA, Ca_LVA; only at the soma [see supplementary information in Gouwens et al., 2018 for definitions]) on all neurons in the model. The most prominent discrepancy between the CSD with and without active channels is the magnitude of the L4 source and the L2/3 sink (Figure 7C). In this all-passive setting, the L4 source is significantly attenuated, and the L2/3 sink is either absent or dominated by a source in the same region.

We explored whether the contributions from currents in recurrent connections come primarily from excitatory or inhibitory synapses by removing all connections from inhibitory (Pvalb, Sst, Htr3a) neurons to all other neurons, so that all postsynaptic currents stem from excitatory thalamocortical synapses, excitatory synapses from HVAs, or recurrent excitatory synapses in V1 (Figure 7D and Figure 7—figure supplement 1). Note that inhibitory synaptic currents give rise to sources, while excitatory synaptic currents give rise to a sink. Of course, without inhibition, the network is unbalanced, which limits the conclusions that can be drawn from this simulation. However, the fact that the major sinks and sources are still present is an indication that the currents from excitatory input account for the majority of the sinks and sources observed in the experimental CSD.

The contributions from each population to the total CSD in the final model (Figure 6D) with both LGN and feedback input and intact recurrent connections are displayed in Figure 7D. From this, it is apparent that the L5/L6 dipole is mainly generated by L6 excitatory cells, the L2/3 sink stems from sinks at the apical tufts of the L2/3 and L5 excitatory cells, the L4 sink from both the L4 excitatory and inhibitory cells, while the L4 source is a mix of sources from mainly L2/3, L4, and L5 excitatory cells, as well as the L4 inhibitory cells. (The magnitude of the CSD contribution from L4 inhibitory cells is greater than anticipated. Given their lack of apical dendrites, we would expect their postsynaptic current sinks and sources to largely cancel [Einevoll et al., 2013]. Their contribution can be reduced by scrambling the 3-D orientation of these cells [Figure 7—figure supplement 2]. However, we cannot rule out that L4 inhibitory cells can have a contribution comparable in magnitude to the excitatory cells with the data we have available. We therefore let the L4 inhibitory cells keep their original orientation here.)

We investigated what would happen if we turned the feedback off again at 60 ms for the final model version (Figure 7—figure supplement 3). Most notably, we found that the sustained L4 source was replaced by a sink, and that the sustained L2/3 sink turned more transient as it was significantly reduced in magnitude after about 70 ms. This CSD pattern serves as a prediction that can be tested experimentally, for example, by optogenetic silencing of the HVAs in the sustained periods of the evoked response (e.g., see Keller et al., 2020).

We summarize the main contributions to the canonical CSD in Figure 7F. Before the onset of the evoked response (0–35 ms) there is, on average, no significant net inflow or outflow of current to any neurons. Around 40 ms, an inflow of current from excitatory thalamocortical synapses onto all excitatory neurons and all Pvalb inhibitory neurons appears, with the largest current coming from the synapses targeting basal and apical dendrites of L4 excitatory cells. This is the primary origin of the L4 sink. Following this initial L4 sink, there is a sustained sink in L5/L6 arising at ~50 ms, which originates partly from thalamocortical synapses onto L6 excitatory cells and partly from recurrent synapses from excitatory populations in V1 onto L6 excitatory cells. At ~60 ms, a sustained sink emerges in L1 and L2/3, which partly originates in synapses from HVAs targeting apical tufts of L2/3 and L5 excitatory cells. This feedback results in a stronger return current at the soma and basal dendrites of L2/3 excitatory cells and L5 excitatory cells.

In the present study, we analyzed experimentally recorded spikes and LFP during presentation of full-field flashes from a large-scale visual coding dataset derived from mouse visual cortex (Siegle et al., 2021) and simulated the same experimental protocol using a biophysically detailed model of mouse V1 (Billeh et al., 2020). Our analysis of the experimental data focused on the responses in LGN and cortical visual areas V1 and HVAs. We found that the evoked CSD in V1, computed from the LFP, is captured by a canonical pattern of sinks and sources during the first 100 ms after stimulus onset (Figure 2B). This canonical CSD, in response to a flashed, bright field pattern, explains half (50.4 %) of the variance in the trial-averaged CSD responses across animals.

Both the early L4 sink with concurrent sources above and below and the L5/L6 sink with a source below were observed with a similar timing by Senzai et al., 2019. The L4 source and L2/3 sink were also observed in that study but emerge somewhat later than in our data – just after 100ms as opposed to ~60 ms in our canonical pattern. This discrepancy in onset might simply be due to differences in stimuli. In Senzai et al., 2019, the animals were exposed to 100 ms light pulses, while the animals in our data were presented with 250 ms whole-field flashes of a white screen. Nonetheless, the canonical CSD pattern exhibits good overall agreement with the pattern seen in Senzai et al., 2019. Studies in non-human primates where the animals were exposed to flashes also demonstrate good spatio-temporal agreement with the CSD observed here, with sinks and sources occurring not only in the same layers and in the same order, but also at the same time after stimulus presentation (Givre et al., 1994; Schroeder et al., 1998).

We introduced the WD as a method to evaluate the difference between two CSD patterns and used it to quantify the variability in trial-averaged CSD between animals (Figure 2D), the trial-to-trial variability in CSD within animals (Figure 2F and G), and the difference between the model CSD, the trial-averaged CSD of individual animals, and the canonical CSD pattern. This application of the WD to compare CSD patterns comes with certain considerations that are important to note. First, although we compute WD for sinks and sources separately, sinks and sources do not arise independently. Current leaving the extracellular space in one place leads to current entering the extracellular space in another place, so current sinks and sources are inter-dependent. Second, the cost of shifting a sink or a source in space relative to shifting it in time is determined by the relative resolution in space vs. time. This relative cost does not necessarily correspond to the actual cost of changing the underlying physiology such that two distributions of sinks or sources match spatially vs. temporally. Determining the most appropriate relative cost of moving sinks and sources in space vs. time would require more detailed data than currently available and is beyond the scope of this study.

For the firing rate analysis, we utilized KS similarity and correlation to quantify experimental variability and model performance with regard to magnitude and temporal profile, respectively. We also investigated the statistics of unit spike firing by computing the moments of the distributions across cells in each population of peak firing and latencies to peak firing for both individual animals and model versions (Figure 6—figure supplements 2 and 3). Systematic use of quantitative metrics for biophysical modeling at this scale is still relatively uncommon, and our work establishes a set of measures for testing the model on LFP and spiking simultaneously, which can be useful for future studies in the field. Of course, there may well be other metrics that are equally or more suitable, and a systematic investigation into what would be the optimal metrics to apply is an important avenue for future work.

Our aim was to simultaneously reproduce experimentally recorded spikes and the CSD in our simulations. The original model captured spiking responses to gratings well (reproducing, e.g., direction selectivity distributions for different neuronal populations) with variable success when applied to other visual stimuli (Billeh et al., 2020). It was not originally tested on LFP/CSD. We found that, for the full-field flash stimulus, this model did not reproduce the CSD pattern in the upper layers of V1, and the spiking responses for this stimulus also exhibited a number of discrepancies.

After making selective adjustments to the recurrent synaptic weights, the model could reproduce the experimental firing rates (Figure 5A–C), though the discrepancy between the model CSD and the canonical CSD remained (Figure 5D and E), with only minor differences relative to the CSD of the original model (Figure 4B). The fact that the model can capture the experimental firing rates without capturing the experimental CSD and that adjustments to the synaptic weights yielded significant alterations in firing rates with only small changes in the CSD supports the point that LFP/CSD reflects aspects of circuit dynamics that are complementary to those reflected in locally recorded spikes.

Previous simulation studies demonstrated the importance of synaptic placement in shaping the LFP and CSD signature (Einevoll et al., 2007; Pettersen et al., 2008; Lindén et al., 2010; Lindén et al., 2011; Łęski et al., 2013; Hagen et al., 2017; Ness et al., 2018). To uncover the model adjustments that capture firing rates and CSD simultaneously, we explored the effects of changes in the synaptic positioning. In one case, we placed all excitatory synapses onto only basal or apical dendrites of L4 excitatory cells, as opposed to their original placement on both apical and basal dendrites. Moving all excitatory synapses onto basal dendrites resulted in substantial changes in both the pattern and magnitude of the CSD contribution from these L4 excitatory cells, with only minor changes to their firing rates (Figure 5F and G and Figure 5—figure supplement 1). Placing all excitatory synapses on apical dendrites led to somewhat larger changes in firing rates, though still similar to the firing rate of the original model, and to even bigger changes in the CSD magnitude. Performing the same manipulations of synaptic placement on L2/3 or L5 excitatory cells resulted in a similar decoupling of CSD and firing rates (Figure 5—figure supplements 3 and 4). It should, however, be noted that the decoupling is neither perfect nor universal.

This demonstrates a two-way dissociation of the firing rates and the pattern of sinks and sources in the CSD: The firing rates can be substantially altered with small effects on the CSD by adjusting the synaptic weights, and the CSD can be substantially altered with only small effects on the firing rates by adjusting synaptic placement. These results align with findings in, for example, Schroeder et al., 1998 and Leszczyński et al., 2020, where a lack of correlation between MUA and CSD in the upper layers of V1 during flash exposure to non-human primates suggested that these signals can sometimes be decoupled. Our findings imply that the LFP can reveal deficiencies in the model architecture that would not be evident from the firing rates alone, and that, to a certain extent, models can be optimized for firing rates and CSD independently.

Past studies have suggested that LFP can be modulated by attention through feedback during evoked responses (Mehta et al., 2000a; Mehta et al., 2000b). However, their findings indicated that V1 was not significantly affected by this modulation until the period 250 ms or later after stimulus onset. A recent study showed that feedback from higher visual areas can in fact exert a strong influence on the magnitude of LFP already at around 80 ms after stimulus onset (Hartmann et al., 2019). To investigate whether such cortico-cortical influence can contribute to the sinks and sources in the later stages (>50 ms) of the canonical CSD pattern, we added feedback consisting of experimentally recorded spikes from the higher cortical visual area LM (Siegle et al., 2021) impinging on synapses placed onto V1 neurons in our model, using anatomical data (Glickfeld and Olsen, 2017; Marques et al., 2018; Hartmann et al., 2019; Keller et al., 2020; Shen et al., 2020).

We found that the feedback can play a significant role in shaping the sustained sinks and sources (Figure 6B–E). The resulting model CSD reproduced the major sinks and sources identified in the canonical CSD pattern and was no longer among the outliers compared to the experimental variability (Figure 6D). Interestingly, absence of the feedback was not apparent from analysis of the firing rates alone, as the firing rates were already within the experimental variability before adding the feedback, further underscoring the utility of the LFP in illuminating structure–function relations in the circuit. Contributions from other visual cortical areas were not included, even though they too impinge upon neurons in V1 (Harris et al., 2019; Siegle et al., 2021), due to the lack of data characterizing such connections. This awaits future work. Finally, turning off the feedback from LM at 60ms disrupted the CSD pattern in layers 2/3 and 4 during the sustained period (Figure 7—figure supplement 3), which serves as a prediction for what will be observed if HVAs, and particularly LM, are silenced in this period of an evoked flash response. Our findings accord with the view that basal dendrites are the main targets for feedforward input, while the tufts of apical dendrites are the main targets for feedback input, even though basal dendrites can also receive input from long-range feedback connections and apical dendrites receive input from feedforward connections (Aru et al., 2020).

In our analyses, we aligned the CSD plots to depths obtained from histology and provided in Allen Common Coordinate Framework (CCF) coordinates. An alternative approach is to align the CSD to landmarks in the data (Senzai et al., 2019). In Figure 6—figure supplement 7, we explored whether utilizing landmarks rather than histology for alignment would affect our results. We found that this approach did not change our conclusion as the final model CSD was still within the experimental variability while the original and intermediate model CSD were outliers both when using the first principal component and when using the plain average as the target (Figure 6—figure supplements 7B and C and 8). Lastly, using the plain average rather than the first principal component as the target did not significantly affect our results when we aligned to histology (Figure 6—figure supplement 9).

With the major sinks and sources of the canonical CSD pattern reproduced, we explored their biophysical origins. We found that the initial L4 sink originates in the thalamocortical input to L4 excitatory cells, which aligns with suggestions made in Mitzdorf, 1987, Swadlow et al., 2002, and Senzai et al., 2019. The sustained L5/L6 sink comes from postsynaptic currents in L6 excitatory cells triggered by a combination of thalamocortical and recurrent excitatory inputs. The sustained L2/3 sink stems, in part, from input from LM onto the apical tufts of L2/3 and L5 excitatory cells. The sustained L4 source has its origins in a mixture of return currents from L2/3 and L5 excitatory cells resulting from the abovementioned feedback onto the apical dendrites of these cells, as well as contributions from L4 excitatory and inhibitory cells (Figure 7A, B, D and E).

In line with observations made by Reimann et al., 2013, we found that the somatic voltage-dependent membrane currents significantly shape the CSD signature (Figures 5H and 7C). Even so, our findings still emphasize the importance of synaptic inputs in sculpting the CSD, as the addition of synaptic input (Figure 6A–E) and changes to synaptic placement (Figure 5F) substantially altered the CSD pattern.

Recent investigations into the unitary LFP (the LFP generated by a single neuron) from inhibitory and excitatory synapses have suggested that inhibitory inputs exert a greater influence on LFP than excitatory input (Bazelot et al., 2010; Teleńczuk et al., 2017; Telenczuk et al., 2020). While this may be true of unitary effects, the total effect of excitatory input can still be greater if there are significantly more excitatory than inhibitory cells, and, correspondingly, significantly more excitatory synapses. In this V1 model, inhibitory cells make up about 15% and excitatory cells about 85% of the total number of cells, reflecting the cellular composition in mouse V1. Whether the pronounced dominance of excitatory cells is enough to make up for the reduced unitary influence of excitatory cells is an interesting area for further research.

This investigation into the biophysical origins of sinks and sources is limited by the fact that the contributions from recurrent connections are difficult to estimate precisely due to the nonlinear effects of these connections. That is, their contribution cannot simply be found by subtracting the CSD from thalamocortical and feedback synapses with all recurrent connections removed (Figure 7A and B) from the total CSD with the same input and recurrent connections intact (Figure 6C, right). Still, this analysis provides an initial estimate into the biophysical origins of the sinks and sources observed experimentally and demonstrates the insights that can be obtained from modeling of extracellular signals.

There is ample evidence that firing rates and LFP are modulated by the behavioral state of the animal, including measures like the pupil size (considered to be a proxy for arousal level) or running speed (Niell and Stryker, 2010; McGinley et al., 2015; Vinck et al., 2015; Saleem et al., 2017). In this study, the responses averaged over all trials have been the target for the modeling, without regard to any state-dependence of the responses. Our understanding of the state-dependent responses could benefit from the potential to probe the biophysical origins of extracellular signals. Therefore, reproducing these state-dependent responses is an important avenue for future research.

Note that the set of synaptic weights and other parameters that can reproduce the experimental firing rates and CSD is unlikely to be unique. This is a consequence of the degeneracy inherent to biological neural networks, known from both simulation and experimental studies, as many different parameterizations of neuronal networks can perform the same functions (Prinz et al., 2004; Marder and Goaillard, 2006; Drion et al., 2015; O’Leary, 2018). Thus, our network should only be considered an example of a circuit model that can produce firing rates and CSD that match the experimental observations. Obtaining multiple solutions and characterizing their diversity using automatic searches of the parameter space will be an interesting direction for future work. We did not utilize such an approach here because the number of simulations required (typically, many thousands or more for automatic optimization approaches) would currently be prohibitively expensive on a model of this scale and level of complexity: running a 1 s simulation with this model takes ~90 min on 384 CPU-cores (Billeh et al., 2020); a single trial in this study simulates 0.75 s of activity.

The original model used as a starting point here produced firing rates and direction and orientation tuning consistent with recordings during presentations of drifting gratings (Arkhipov et al., 2018; Billeh et al., 2020). In this study, we focused on the analysis and modeling of the response to full-field flashes, but when the final model was tested with the drifting gratings stimulus utilized in Billeh et al., 2020, we found that the present, revised model continued to exhibit orientation and direction tuning even though the adjustments were made with the aim to reproduce the observed CSD and population firing rates during full-field flashes (Figure 6—figure supplement 6). Ideally, the model should reproduce both firing rates and LFP simultaneously not only for flashes or drifting gratings, but for any visual stimulus (out-class generalization). This is a long-term goal and can be called ‘the holy grail’ of visual system modeling.

In this study, we developed a systematic framework to quantify experimental variability in both LFP/CSD and spikes and to evaluate model performance. We identified a canonical CSD pattern observed during presentations of full-field flash stimuli and obtained a bio-realistic model that reproduced both the canonical CSD pattern and spikes simultaneously. This model thus reproduces, in a quantitative manner, the shape and timing of current sinks and sources observed experimentally. We utilized this validated model to explain, mechanistically, the biophysical origins of the various current sinks and sources and their location across the layers of visual cortex. Our models are freely shared and should be useful for future studies disentangling the mechanisms underlying spiking dynamics and electrogenesis in the cortex.

The files necessary to run simulations of the different model versions presented in the paper as well as data resulting from simulations of those model versions are publicly available in Dryad: https://doi.org/10.5061/dryad.k3j9kd5b8. The experimental data set utilized is publicly available at: https://portal.brain-map.org/explore/circuits/visual-coding-neuropixels. The code generated for data analysis and producing the figures in this manuscript is publicly available at: https://github.com/atleer/CINPLA_Allen_V1_analysis.git (copy archived at Rimehaug, 2023).

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Author details

1. Atle E Rimehaug

   Department of Informatics, University of Oslo, Oslo, Norway

   Contribution

   Conceptualization, Software, Formal analysis, Investigation, Visualization, Methodology, Writing – original draft, Writing – review and editing

   For correspondence

   atleeri@ifi.uio.no

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-8312-9875

2. Alexander J Stasik

   Department of Physics, University of Oslo, Oslo, Norway

   Contribution

   Conceptualization, Software, Formal analysis, Investigation, Visualization, Methodology

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0003-1646-2472

3. Espen Hagen

   1. Department of Physics, University of Oslo, Oslo, Norway
   2. Department of Data Science, Norwegian University of Life Sciences, Ås, Norway

   Contribution

   Conceptualization, Resources, Software, Formal analysis, Investigation, Methodology, Writing – review and editing

   Competing interests

   No competing interests declared

4. Yazan N Billeh

   MindScope Program, Allen Institute, Seattle, United States

   Contribution

   Conceptualization, Software, Methodology

   Competing interests

   No competing interests declared

5. Josh H Siegle

   MindScope Program, Allen Institute, Seattle, United States

   Contribution

   Data curation, Investigation, Visualization, Writing – review and editing

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-7736-4844

6. Kael Dai

   MindScope Program, Allen Institute, Seattle, United States

   Contribution

   Resources, Software, Methodology

   Competing interests

   No competing interests declared

7. Shawn R Olsen

   MindScope Program, Allen Institute, Seattle, United States

   Contribution

   Resources, Supervision

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-9568-7057

8. Christof Koch

   MindScope Program, Allen Institute, Seattle, United States

   Contribution

   Conceptualization, Resources, Supervision, Funding acquisition, Methodology, Project administration, Writing – review and editing

   Competing interests

   No competing interests declared

9. Gaute T Einevoll

   1. Department of Physics, University of Oslo, Oslo, Norway
   2. Department of Physics, Norwegian University of Life Sciences, Ås, Norway

   Contribution

   Conceptualization, Resources, Supervision, Funding acquisition, Methodology, Project administration, Writing – review and editing

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-5425-5012

10. Anton Arkhipov

    MindScope Program, Allen Institute, Seattle, United States

    Contribution

    Conceptualization, Resources, Supervision, Funding acquisition, Methodology, Project administration, Writing – review and editing

    For correspondence

    antona@alleninstitute.org

    Competing interests

    No competing interests declared

    Additional information

    Lead contact

    "This ORCID iD identifies the author of this article:" 0000-0003-1106-8310

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