What does the mean mean? A simple test for neuroscience.

Trial-averaged metrics, e.g. tuning curves or population response vectors, are a ubiquitous way of characterizing neuronal activity. But how relevant are such trial-averaged responses to neuronal computation itself? Here we present a simple test to estimate whether average responses reflect aspects of neuronal activity that contribute to neuronal processing. The test probes two assumptions implicitly made whenever average metrics are treated as meaningful representations of neuronal activity: Reliability: Neuronal responses repeat consistently enough across trials that they convey a recognizable reflection of the average response to downstream regions.Behavioural relevance: If a single-trial response is more similar to the average template, it is more likely to evoke correct behavioural responses. We apply this test to two data sets: (1) Two-photon recordings in primary somatosensory cortices (S1 and S2) of mice trained to detect optogenetic stimulation in S1; and (2) Electrophysiological recordings from 71 brain areas in mice performing a contrast discrimination task. Under the highly controlled settings of Data set 1, both assumptions were largely fulfilled. In contrast, the less restrictive paradigm of Data set 2 met neither assumption. Simulations predict that the larger diversity of neuronal response preferences, rather than higher cross-trial reliability, drives the better performance of Data set 1. We conclude that when behaviour is less tightly restricted, average responses do not seem particularly relevant to neuronal computation, potentially because information is encoded more dynamically. Most importantly, we encourage researchers to apply this simple test of computational relevance whenever using trial-averaged neuronal metrics, in order to gauge how representative cross-trial averages are in a given context.

Geodesic-based distance reveals nonlinear topological features in neural activity from mouse visual cortex.

An increasingly popular approach to the analysis of neural data is to treat activity patterns as being constrained to and sampled from a manifold, which can be characterized by its topology. The persistent homology method identifies the type and number of holes in the manifold, thereby yielding functional information about the coding and dynamic properties of the underlying neural network. In this work, we give examples of highly nonlinear manifolds in which the persistent homology algorithm fails when it uses the Euclidean distance because it does not always yield a good approximation to the true distance distribution of a point cloud sampled from a manifold. To deal with this issue, we instead estimate the geodesic distance which is a better approximation of the true distance distribution and can therefore be used to successfully identify highly nonlinear features with persistent homology. To document the utility of the method, we utilize a toy model comprised of a circular manifold, built from orthogonal sinusoidal coordinate functions and show how the choice of metric determines the performance of the persistent homology algorithm. Furthermore, we explore the robustness of the method across different manifold properties, like the number of samples, curvature and amount of added noise. We point out strategies for interpreting its results as well as some possible pitfalls of its application. Subsequently, we apply this analysis to neural data coming from the Visual Coding-Neuropixels dataset recorded at the Allen Institute in mouse visual cortex in response to stimulation with drifting gratings. We find that different manifolds with a non-trivial topology can be seen across regions and stimulus properties. Finally, we interpret how these changes in manifold topology along with stimulus parameters and cortical region inform how the brain performs visual computation.

Multiple Midfrontal Thetas Revealed by Source Separation of Simultaneous MEG and EEG.

Theta-band (∼6 Hz) rhythmic activity within and over the medial PFC ("midfrontal theta") has been identified as a distinctive signature of "response conflict," the competition between multiple actions when only one action is goal-relevant. Midfrontal theta is traditionally conceptualized and analyzed under the assumption that it is a unitary signature of conflict that can be uniquely identified at one electrode (typically FCz). Here we recorded simultaneous MEG and EEG (total of 328 sensors) in 9 human subjects (7 female) and applied a feature-guided multivariate source-separation decomposition to determine whether conflict-related midfrontal theta is a unitary or multidimensional feature of the data. For each subject, a generalized eigendecomposition yielded spatial filters (components) that maximized the ratio between theta and broadband activity. Components were retained based on significance thresholding and midfrontal EEG topography. All of the subjects individually exhibited multiple (mean 5.89, SD 2.47) midfrontal components that contributed to sensor-level midfrontal theta power during the task. Component signals were temporally uncorrelated and asynchronous, suggesting that each midfrontal theta component was unique. Our findings call into question the dominant notion that midfrontal theta represents a unitary process. Instead, we suggest that midfrontal theta spans a multidimensional space, indicating multiple origins, but can manifest as a single feature at the sensor level because of signal mixing.SIGNIFICANCE STATEMENT "Midfrontal theta" is a rhythmic electrophysiological signature of the competition between multiple response options. Midfrontal theta is traditionally considered to reflect a single process. However, this assumption could be erroneous because of "mixing" (multiple sources contributing to the activity recorded at a single electrode). We investigated the dimensionality of midfrontal theta by applying advanced multivariate analysis methods to a multimodal MEG/EEG dataset. We identified multiple topographically overlapping neural sources that drove response conflict-related midfrontal theta. Midfrontal theta thus reflects multiple uncorrelated signals that manifest with similar EEG scalp projections. In addition to contributing to the cognitive control literature, we demonstrate both the feasibility and the necessity of signal demixing to understand the narrowband neural dynamics underlying cognitive processes.

Learning at Variable Attentional Load Requires Cooperation of Working Memory, Meta-learning, and Attention-augmented Reinforcement Learning.

Flexible learning of changing reward contingencies can be realized with different strategies. A fast learning strategy involves using working memory of recently rewarded objects to guide choices. A slower learning strategy uses prediction errors to gradually update value expectations to improve choices. How the fast and slow strategies work together in scenarios with real-world stimulus complexity is not well known. Here, we aim to disentangle their relative contributions in rhesus monkeys while they learned the relevance of object features at variable attentional load. We found that learning behavior across six monkeys is consistently best predicted with a model combining (i) fast working memory and (ii) slower reinforcement learning from differently weighted positive and negative prediction errors as well as (iii) selective suppression of nonchosen feature values and (iv) a meta-learning mechanism that enhances exploration rates based on a memory trace of recent errors. The optimal model parameter settings suggest that these mechanisms cooperate differently at low and high attentional loads. Whereas working memory was essential for efficient learning at lower attentional loads, enhanced weighting of negative prediction errors and meta-learning were essential for efficient learning at higher attentional loads. Together, these findings pinpoint a canonical set of learning mechanisms and suggest how they may cooperate when subjects flexibly adjust to environments with variable real-world attentional demands.

Flexible Frequency Switching in Adult Mouse Visual Cortex Is Mediated by Competition Between Parvalbumin and Somatostatin Expressing Interneurons.

Neuronal networks in rodent primary visual cortex (V1) can generate oscillations in different frequency bands depending on the network state and the level of visual stimulation. High-frequency gamma rhythms, for example, dominate the network's spontaneous activity in adult mice but are attenuated upon visual stimulation, during which the network switches to the beta band instead. The spontaneous local field potential (LFP) of juvenile mouse V1, however, mainly contains beta rhythms and presenting a stimulus does not elicit drastic changes in network oscillations. We study, in a spiking neuron network model, the mechanism in adult mice allowing for flexible switches between multiple frequency bands and contrast this to the network structure in juvenile mice that lack this flexibility. The model comprises excitatory pyramidal cells (PCs) and two types of interneurons: the parvalbumin-expressing (PV) and the somatostatinexpressing (SOM) interneuron. In accordance with experimental findings, the pyramidal-PV and pyramidal-SOM cell subnetworks are associated with gamma and beta oscillations, respectively. In our model, they are both generated via a pyramidal-interneuron gamma (PING) mechanism, wherein the PCs drive the oscillations. Furthermore, we demonstrate that large but not small visual stimulation activates SOM cells, which shift the frequency of resting-state gamma oscillations produced by the pyramidal-PV cell subnetwork so that beta rhythms emerge. Finally, we show that this behavior is obtained for only a subset of PV and SOM interneuron projection strengths, indicating that their influence on the PCs should be balanced so that they can compete for oscillatory control of the PCs. In sum, we propose a mechanism by which visual beta rhythms can emerge from spontaneous gamma oscillations in a network model of the mouse V1; for this mechanism to reproduce V1 dynamics in adult mice, balance between the effective strengths of PV and SOM cells is required.

Comprehensive characterization of oscillatory signatures in a model circuit with PV- and SOM-expressing interneurons.

Neural circuits contain a wide variety of interneuron types, which differ in their biophysical properties and connectivity patterns. The two most common interneuron types, parvalbumin-expressing and somatostatin-expressing cells, have been shown to be differentially involved in many cognitive functions. These cell types also show different relationships with the power and phase of oscillations in local field potentials. The mechanisms that underlie the emergence of different oscillatory rhythms in neural circuits with more than one interneuron subtype, and the roles specific interneurons play in those mechanisms, are not fully understood. Here, we present a comprehensive analysis of all possible circuit motifs and input regimes that can be achieved in circuits comprised of excitatory cells, PV-like fast-spiking interneurons and SOM-like low-threshold spiking interneurons. We identify 18 unique motifs and simulate their dynamics over a range of input strengths. Using several characteristics, such as oscillation frequency, firing rates, phase of firing and burst fraction, we cluster the resulting circuit dynamics across motifs in order to identify patterns of activity and compare these patterns to behaviors that were generated in circuits with one interneuron type. In addition to the well-known PING and ING gamma oscillations and an asynchronous state, our analysis identified three oscillatory behaviors that were generated by the three-cell-type motifs only: theta-nested gamma oscillations, stable beta oscillations and theta-locked bursting behavior, which have also been observed in experiments. Our characterization provides a map to interpret experimental activity patterns and suggests pharmacological manipulations or optogenetics approaches to validate these conclusions.

Sensitivity to Stimulus Irregularity Is Inherent in Neural Networks.

Behavior is controlled by complex neural networks in which neurons process thousands of inputs. However, even short spike trains evoked in a single cortical neuron were demonstrated to be sufficient to influence behavior in vivo. Specifically, irregular sequences of interspike intervals (ISIs) had a more reliable influence on behavior despite their resemblance to stochastic activity. Similarly, irregular tactile stimulation led to higher rates of behavioral responses. In this study, we identify the mechanisms enabling this sensitivity to stimulus irregularity (SSI) on the neuronal and network levels using simulated spiking neural networks. Matching in vivo experiments, we find that irregular stimulation elicits more detectable network events (bursts) than regular stimulation. Dissecting the stimuli, we identify short ISIs-occurring more frequently in irregular stimulations-as the main drivers of SSI rather than complex irregularity per se. In addition, we find that short-term plasticity modulates SSI. We subsequently eliminate the different mechanisms in turn to assess their role in generating SSI. Removing inhibitory interneurons, we find that SSI is retained, suggesting that SSI is not dependent on inhibition. Removing recurrency, we find that SSI is retained due to the ability of individual neurons to integrate activity over short timescales ("cell memory"). Removing single-neuron dynamics, we find that SSI is retained based on the short-term retention of activity within the recurrent network structure ("network memory"). Finally, using a further simplified probabilistic model, we find that local network structure is not required for SSI. Hence, SSI is identified as a general property that we hypothesize to be ubiquitous in neural networks with different structures and biophysical properties. Irregular sequences contain shorter ISIs, which are the main drivers underlying SSI. The experimentally observed SSI should thus generalize to other systems, suggesting a functional role for irregular activity in cortex.

Characterization of network structure in stereoEEG data using consensus-based partial coherence.

Coherence is a widely used measure to determine the frequency-resolved functional connectivity between pairs of recording sites, but this measure is confounded by shared inputs to the pair. To remove shared inputs, the 'partial coherence' can be computed by conditioning the spectral matrices of the pair on all other recorded channels, which involves the calculation of a matrix (pseudo-) inverse. It has so far remained a challenge to use the time-resolved partial coherence to analyze intracranial recordings with a large number of recording sites. For instance, calculating the partial coherence using a pseudoinverse method produces a high number of false positives when it is applied to a large number of channels. To address this challenge, we developed a new method that randomly aggregated channels into a smaller number of effective channels on which the calculation of partial coherence was based. We obtained a 'consensus' partial coherence (cPCOH) by repeating this approach for several random aggregations of channels (permutations) and only accepting those activations in time and frequency with a high enough consensus. Using model data we show that the cPCOH method effectively filters out the effect of shared inputs and performs substantially better than the pseudo-inverse. We successfully applied the cPCOH procedure to human stereotactic EEG data and demonstrated three key advantages of this method relative to alternative procedures. First, it reduces the number of false positives relative to the pseudo-inverse method. Second, it allows for titration of the amount of false positives relative to the false negatives by adjusting the consensus threshold, thus allowing the data-analyst to prioritize one over the other to meet specific analysis demands. Third, it substantially reduced the number of identified interactions compared to coherence, providing a sparser network of connections from which clear spatial patterns emerged. These patterns can serve as a starting point of further analyses that provide insight into network dynamics during cognitive processes. These advantages likely generalize to other modalities in which shared inputs introduce confounds, such as electroencephalography (EEG) and magneto-encephalography (MEG).

Top-down control of cortical gamma-band communication via pulvinar induced phase shifts in the alpha rhythm.

Selective routing of information between cortical areas is required in order to combine different sources of information according to cognitive demand. Recent experiments have suggested that alpha band activity originating from the pulvinar coordinates this inter-areal cortical communication. Using a computer model we investigated whether top-down induced shifts in the relative alpha phase between two cortical areas could modulate cortical communication, quantified in terms of changes in gamma band coherence between them. The network model was comprised of two uni-directionally connected neuronal populations of spiking neurons, each representing a cortical area. We find that the phase difference of the alpha oscillations modulating the two neuronal populations strongly affected the interregional gamma-band neuronal coherence. We confirmed that a higher gamma band coherence also resulted in more efficient transmission of spiking information between cortical areas, thereby confirming the value of gamma coherence as a proxy for cortical information transmission. In a model where both neuronal populations were connected bi-directionally, the relative alpha phase determined the directionality of communication between the populations. Our results show the feasibility of a physiological realistic mechanism for routing information in the brain based on coupled oscillations. Our model results in a set of testable predictions regarding phase shifts in alpha oscillations under different task demands requiring experimental quantification of neuronal oscillations in different regions in e.g. attention paradigms.

The missing link: Predicting connectomes from noisy and partially observed tract tracing data.

Our understanding of the wiring map of the brain, known as the connectome, has increased greatly in the last decade, mostly due to technological advancements in neuroimaging techniques and improvements in computational tools to interpret the vast amount of available data. Despite this, with the exception of the C. elegans roundworm, no definitive connectome has been established for any species. In order to obtain this, tracer studies are particularly appealing, as these have proven highly reliable. The downside of tract tracing is that it is costly to perform, and can only be applied ex vivo. In this paper, we suggest that instead of probing all possible connections, hitherto unknown connections may be predicted from the data that is already available. Our approach uses a 'latent space model' that embeds the connectivity in an abstract physical space. Regions that are close in the latent space have a high chance of being connected, while regions far apart are most likely disconnected in the connectome. After learning the latent embedding from the connections that we did observe, the latent space allows us to predict connections that have not been probed previously. We apply the methodology to two connectivity data sets of the macaque, where we demonstrate that the latent space model is successful in predicting unobserved connectivity, outperforming two baselines and an alternative model in nearly all cases. Furthermore, we show how the latent spatial embedding may be used to integrate multimodal observations (i.e. anterograde and retrograde tracers) for the mouse neocortex. Finally, our probabilistic approach enables us to make explicit which connections are easy to predict and which prove difficult, allowing for informed follow-up studies.

Correction: The missing link: Predicting connectomes from noisy and partially observed tract tracing data.

[This corrects the article DOI: 10.1371/journal.pcbi.1005374.].

Temporally precise control of single-neuron spiking by juxtacellular nanostimulation.

Temporal patterns of action potentials influence a variety of activity-dependent intra- and intercellular processes and play an important role in theories of neural coding. Elucidating the mechanisms underlying these phenomena requires imposing spike trains with precisely defined patterns, but this has been challenging due to the limitations of existing stimulation techniques. Here we present a new nanostimulation method providing control over the action potential output of individual cortical neurons. Spikes are elicited through the juxtacellular application of short-duration fluctuating currents ("kurzpulses"), allowing for the sub-millisecond precise and reproducible induction of arbitrary patterns of action potentials at all physiologically relevant firing frequencies (<120 Hz), including minute-long spike trains recorded in freely moving animals. We systematically compared our method to whole cell current injection, as well as optogenetic stimulation, and show that nanostimulation performance compares favorably with these techniques. This new nanostimulation approach is easily applied, can be readily performed in awake behaving animals, and thus promises to be a powerful tool for systematic investigations into the temporal elements of neural codes, as well as the mechanisms underlying a wide variety of activity-dependent cellular processes.NEW & NOTEWORTHY Assessing the impact of temporal features of neuronal spike trains requires imposing arbitrary patterns of spiking on individual neurons during behavior, but this has been difficult to achieve due to limitations of existing stimulation methods. We present a technique that overcomes these limitations by using carefully designed short-duration fluctuating juxtacellular current injections, which allow for the precise and reliable evocation of arbitrary patterns of neuronal spikes in single neurons in vivo.

Anti-correlations in the degree distribution increase stimulus detection performance in noisy spiking neural networks.

Neuronal circuits in the rodent barrel cortex are characterized by stable low firing rates. However, recent experiments show that short spike trains elicited by electrical stimulation in single neurons can induce behavioral responses. Hence, the underlying neural networks provide stability against internal fluctuations in the firing rate, while simultaneously making the circuits sensitive to small external perturbations. Here we studied whether stability and sensitivity are affected by the connectivity structure in recurrently connected spiking networks. We found that anti-correlation between the number of afferent (in-degree) and efferent (out-degree) synaptic connections of neurons increases stability against pathological bursting, relative to networks where the degrees were either positively correlated or uncorrelated. In the stable network state, stimulation of a few cells could lead to a detectable change in the firing rate. To quantify the ability of networks to detect the stimulation, we used a receiver operating characteristic (ROC) analysis. For a given level of background noise, networks with anti-correlated degrees displayed the lowest false positive rates, and consequently had the highest stimulus detection performance. We propose that anti-correlation in the degree distribution may be a computational strategy employed by sensory cortices to increase the detectability of external stimuli. We show that networks with anti-correlated degrees can in principle be formed by applying learning rules comprised of a combination of spike-timing dependent plasticity, homeostatic plasticity and pruning to networks with uncorrelated degrees. To test our prediction we suggest a novel experimental method to estimate correlations in the degree distribution.

A Developmental Switch for Hebbian Plasticity.

Hebbian forms of synaptic plasticity are required for the orderly development of sensory circuits in the brain and are powerful modulators of learning and memory in adulthood. During development, emergence of Hebbian plasticity leads to formation of functional circuits. By modeling the dynamics of neurotransmitter release during early postnatal cortical development we show that a developmentally regulated switch in vesicle exocytosis mode triggers associative (i.e. Hebbian) plasticity. Early in development spontaneous vesicle exocytosis (SVE), often considered as 'synaptic noise', is important for homogenization of synaptic weights and maintenance of synaptic weights in the appropriate dynamic range. Our results demonstrate that SVE has a permissive, whereas subsequent evoked vesicle exocytosis (EVE) has an instructive role in the expression of Hebbian plasticity. A timed onset for Hebbian plasticity can be achieved by switching from SVE to EVE and the balance between SVE and EVE can control the effective rate of Hebbian plasticity. We further show that this developmental switch in neurotransmitter release mode enables maturation of spike-timing dependent plasticity. A mis-timed or inadequate SVE to EVE switch may lead to malformation of brain networks thereby contributing to the etiology of neurodevelopmental disorders.

How to detect the Granger-causal flow direction in the presence of additive noise?

Granger-causality metrics have become increasingly popular tools to identify directed interactions between brain areas. However, it is known that additive noise can strongly affect Granger-causality metrics, which can lead to spurious conclusions about neuronal interactions. To solve this problem, previous studies have proposed the detection of Granger-causal directionality, i.e. the dominant Granger-causal flow, using either the slope of the coherency (Phase Slope Index; PSI), or by comparing Granger-causality values between original and time-reversed signals (reversed Granger testing). We show that for ensembles of vector autoregressive (VAR) models encompassing bidirectionally coupled sources, these alternative methods do not correctly measure Granger-causal directionality for a substantial fraction of VAR models, even in the absence of noise. We then demonstrate that uncorrelated noise has fundamentally different effects on directed connectivity metrics than linearly mixed noise, where the latter may result as a consequence of electric volume conduction. Uncorrelated noise only weakly affects the detection of Granger-causal directionality, whereas linearly mixed noise causes a large fraction of false positives for standard Granger-causality metrics and PSI, but not for reversed Granger testing. We further show that we can reliably identify cases where linearly mixed noise causes a large fraction of false positives by examining the magnitude of the instantaneous influence coefficient in a structural VAR model. By rejecting cases with strong instantaneous influence, we obtain an improved detection of Granger-causal flow between neuronal sources in the presence of additive noise. These techniques are applicable to real data, which we demonstrate using actual area V1 and area V4 LFP data, recorded from the awake monkey performing a visual attention task.

Dependence of V2 illusory contour response on V1 cell properties and topographic organization.

An illusory contour is an image that is perceived as a contour in the absence of typical contour characteristics, such as a change in luminance or chromaticity across the stimulus. In cats and primates, cells that respond to illusory contours are sparse in cortical area V1, but are found in greater numbers in cortical area V2. We propose a model capable of illusory contour detection that is based on a realistic topographic organization of V1 cells, which reproduces the responses of individual cell types measured experimentally. The model allows us to explain several experimentally observed properties of V2 cells including variability in orientation tuning and inducer spacing preference. As a practical application, the model can be used to estimate the relationship between the severity of a cortical injury in the primary visual cortex and the deterioration of V2 cell responses to real and illusory contours.

Analyzing Thalamocortical Tract-Tracing Experiments in a Common Reference Space.

Current mesoscale connectivity atlases provide limited information about the organization of thalamocortical projections in the mouse brain. Labeling the projections of spatially restricted neuron populations in thalamus can provide a functionally relevant level of connectomic analysis, but these need to be integrated within the same common reference space. Here, we present a pipeline for the segmentation, registration, integration and analysis of multiple tract-tracing experiments. The key difference with other workflows is that the data is transformed to fit the reference template. As a test-case, we investigated the axonal projections and intranuclear arrangement of seven neuronal populations of the ventral posteromedial nucleus of the thalamus (VPM), which we labeled with an anterograde tracer. Their soma positions corresponded, from dorsal to ventral, to cortical representations of the whiskers, nose and mouth. They strongly targeted layer 4, with the majority exclusively targeting one cortical area and the ones in ventrolateral VPM branching to multiple somatosensory areas. We found that our experiments were more topographically precise than similar experiments from the Allen Institute and projections to the primary somatosensory area were in agreement with single-neuron morphological reconstructions from publicly available databases. This pilot study sets the basis for a shared virtual connectivity atlas that could be enriched with additional data for studying the topographical organization of different thalamic nuclei. The pipeline is accessible with only minimal programming skills via a Jupyter Notebook, and offers multiple visualization tools such as cortical flatmaps, subcortical plots and 3D renderings and can be used with custom anatomical delineations.

Anterior Cingulate Cortex Causally Supports Meta-Learning.

In dynamic environments with volatile rewards the anterior cingulate cortex (ACC) is believed to determine whether a visual object is relevant and should be chosen. The ACC may achieve this by integrating reward information over time to estimate which objects are worth to explore and which objects should be avoided. Such a higher-order meta-awareness about which objects should be explored predicts that the ACC causally contributes to choices when the reward values of objects are unknown and must be inferred from ongoing exploration. We tested this suggestion in nonhuman primates using a learning task that varied the number of object features that could be relevant, and by controlling the motivational value of choosing objects. During learning the ACC was transiently micro-stimulated when subjects foveated the to-be-chosen stimulus. We found that stimulation selectively impaired learning when feature uncertainty and motivational value of choices were high, which was linked to a deficit in using reward outcomes for feature-specific credit assignment. Application of an adaptive reinforcement learning model confirmed a primary deficit in weighting prediction errors that led to a meta-learning impairment to adaptively increase exploration during learning and to an impaired use of working memory to support learning. These findings provide causal evidence that the reward history traces in ACC are essential for meta-adjusting the exploration-exploitation balance and the strength of working memory of object values during adaptive behavior.

Regulation of spike timing in visual cortical circuits.

A train of action potentials (a spike train) can carry information in both the average firing rate and the pattern of spikes in the train. But can such a spike-pattern code be supported by cortical circuits? Neurons in vitro produce a spike pattern in response to the injection of a fluctuating current. However, cortical neurons in vivo are modulated by local oscillatory neuronal activity and by top-down inputs. In a cortical circuit, precise spike patterns thus reflect the interaction between internally generated activity and sensory information encoded by input spike trains. We review the evidence for precise and reliable spike timing in the cortex and discuss its computational role.