Objective Morphological Classification of Neocortical Pyramidal Cells.

A consensus on the number of morphologically different types of pyramidal cells (PCs) in the neocortex has not yet been reached, despite over a century of anatomical studies, due to the lack of agreement on the subjective classifications of neuron types, which is based on expert analyses of neuronal morphologies. Even for neurons that are visually distinguishable, there is no common ground to consistently define morphological types. The objective classification of PCs can be achieved with methods from algebraic topology, and the dendritic arborization is sufficient for the reliable identification of distinct types of cortical PCs. Therefore, we objectively identify 17 types of PCs in the rat somatosensory cortex. In addition, we provide a solution to the challenging problem of whether 2 similar neurons belong to different types or to a continuum of the same type. Our topological classification does not require expert input, is stable, and helps settle the long-standing debate on whether cell-types are discrete or continuous morphological variations of each other.

On the Structure of Cortical Microcircuits Inferred from Small Sample Sizes.

The structure in cortical microcircuits deviates from what would be expected in a purely random network, which has been seen as evidence of clustering. To address this issue, we sought to reproduce the nonrandom features of cortical circuits by considering several distinct classes of network topology, including clustered networks, networks with distance-dependent connectivity, and those with broad degree distributions. To our surprise, we found that all of these qualitatively distinct topologies could account equally well for all reported nonrandom features despite being easily distinguishable from one another at the network level. This apparent paradox was a consequence of estimating network properties given only small sample sizes. In other words, networks that differ markedly in their global structure can look quite similar locally. This makes inferring network structure from small sample sizes, a necessity given the technical difficulty inherent in simultaneous intracellular recordings, problematic. We found that a network statistic called the sample degree correlation (SDC) overcomes this difficulty. The SDC depends only on parameters that can be estimated reliably given small sample sizes and is an accurate fingerprint of every topological family. We applied the SDC criterion to data from rat visual and somatosensory cortex and discovered that the connectivity was not consistent with any of these main topological classes. However, we were able to fit the experimental data with a more general network class, of which all previous topologies were special cases. The resulting network topology could be interpreted as a combination of physical spatial dependence and nonspatial, hierarchical clustering.SIGNIFICANCE STATEMENT The connectivity of cortical microcircuits exhibits features that are inconsistent with a simple random network. Here, we show that several classes of network models can account for this nonrandom structure despite qualitative differences in their global properties. This apparent paradox is a consequence of the small numbers of simultaneously recorded neurons in experiment: when inferred via small sample sizes, many networks may be indistinguishable despite being globally distinct. We develop a connectivity measure that successfully classifies networks even when estimated locally with a few neurons at a time. We show that data from rat cortex is consistent with a network in which the likelihood of a connection between neurons depends on spatial distance and on nonspatial, asymmetric clustering.

Cell type- and activity-dependent extracellular correlates of intracellular spiking.

Despite decades of extracellular action potential (EAP) recordings monitoring brain activity, the biophysical origin and inherent variability of these signals remain enigmatic. We performed whole cell patch recordings of excitatory and inhibitory neurons in rat somatosensory cortex slice while positioning a silicon probe in their vicinity to concurrently record intra- and extracellular voltages for spike frequencies under 20 Hz. We characterize biophysical events and properties (intracellular spiking, extracellular resistivity, temporal jitter, etc.) related to EAP recordings at the single-neuron level in a layer-specific manner. Notably, EAP amplitude was found to decay as the inverse of distance between the soma and the recording electrode with similar (but not identical) resistivity across layers. Furthermore, we assessed a number of EAP features and their variability with spike activity: amplitude (but not temporal) features varied substantially (∼ 30-50% compared with mean) and nonmonotonically as a function of spike frequency and spike order. Such EAP variation only partly reflects intracellular somatic spike variability and points to the plethora of processes contributing to the EAP. Also, we show that the shape of the EAP waveform is qualitatively similar to the negative of the temporal derivative to the intracellular somatic voltage, as expected from theory. Finally, we tested to what extent EAPs can impact the lowpass-filtered part of extracellular recordings, the local field potential (LFP), typically associated with synaptic activity. We found that spiking of excitatory neurons can significantly impact the LFP at frequencies as low as 20 Hz. Our results question the common assertion that the LFP acts as proxy for synaptic activity.

A synaptic organizing principle for cortical neuronal groups.

Neuronal circuitry is often considered a clean slate that can be dynamically and arbitrarily molded by experience. However, when we investigated synaptic connectivity in groups of pyramidal neurons in the neocortex, we found that both connectivity and synaptic weights were surprisingly predictable. Synaptic weights follow very closely the number of connections in a group of neurons, saturating after only 20% of possible connections are formed between neurons in a group. When we examined the network topology of connectivity between neurons, we found that the neurons cluster into small world networks that are not scale-free, with less than 2 degrees of separation. We found a simple clustering rule where connectivity is directly proportional to the number of common neighbors, which accounts for these small world networks and accurately predicts the connection probability between any two neurons. This pyramidal neuron network clusters into multiple groups of a few dozen neurons each. The neurons composing each group are surprisingly distributed, typically more than 100 µm apart, allowing for multiple groups to be interlaced in the same space. In summary, we discovered a synaptic organizing principle that groups neurons in a manner that is common across animals and hence, independent of individual experiences. We speculate that these elementary neuronal groups are prescribed Lego-like building blocks of perception and that acquired memory relies more on combining these elementary assemblies into higher-order constructs.

Fear learning induces synaptic potentiation between engram neurons in the rat lateral amygdala.

The lateral amygdala (LA) encodes fear memories by potentiating sensory inputs associated with threats and, in the process, recruits 10-30% of its neurons per fear memory engram. However, how the local network within the LA processes this information and whether it also plays a role in storing it are still largely unknown. Here, using ex vivo 12-patch-clamp and in vivo 32-electrode electrophysiological recordings in the LA of fear-conditioned rats, in combination with activity-dependent fluorescent and optogenetic tagging and recall, we identified a sparsely connected network between principal LA neurons that is organized in clusters. Fear conditioning specifically causes potentiation of synaptic connections between learning-recruited neurons. These findings of synaptic plasticity in an autoassociative excitatory network of the LA may suggest a basic principle through which a small number of pyramidal neurons could encode a large number of memories.

Brief bursts self-inhibit and correlate the pyramidal network.

Inhibitory pathways are an essential component in the function of the neocortical microcircuitry. Despite the relatively small fraction of inhibitory neurons in the neocortex, these neurons are strongly activated due to their high connectivity rate and the intricate manner in which they interconnect with pyramidal cells (PCs). One prominent pathway is the frequency-dependent disynaptic inhibition (FDDI) formed between layer 5 PCs and mediated by Martinotti cells (MCs). Here, we show that simultaneous short bursts in four PCs are sufficient to exert FDDI in all neighboring PCs within the dimensions of a cortical column. This powerful inhibition is mediated by few interneurons, leading to strongly correlated membrane fluctuations and synchronous spiking between PCs simultaneously receiving FDDI. Somatic integration of such inhibition is independent and electrically isolated from monosynaptic excitation formed between the same PCs. FDDI is strongly shaped by I(h) in PC dendrites, which determines the effective integration time window for inhibitory and excitatory inputs. We propose a key disynaptic mechanism by which brief bursts generated by a few PCs can synchronize the activity in the pyramidal network.

Thalamic control of sensory processing and spindles in a biophysical somatosensory thalamoreticular circuit model of wakefulness and sleep.

Thalamoreticular circuitry plays a key role in arousal, attention, cognition, and sleep spindles, and is linked to several brain disorders. A detailed computational model of mouse somatosensory thalamus and thalamic reticular nucleus has been developed to capture the properties of over 14,000 neurons connected by 6 million synapses. The model recreates the biological connectivity of these neurons, and simulations of the model reproduce multiple experimental findings in different brain states. The model shows that inhibitory rebound produces frequency-selective enhancement of thalamic responses during wakefulness. We find that thalamic interactions are responsible for the characteristic waxing and waning of spindle oscillations. In addition, we find that changes in thalamic excitability control spindle frequency and their incidence. The model is made openly available to provide a new tool for studying the function and dysfunction of the thalamoreticular circuitry in various brain states.

A calcium-based plasticity model for predicting long-term potentiation and depression in the neocortex.

Pyramidal cells (PCs) form the backbone of the layered structure of the neocortex, and plasticity of their synapses is thought to underlie learning in the brain. However, such long-term synaptic changes have been experimentally characterized between only a few types of PCs, posing a significant barrier for studying neocortical learning mechanisms. Here we introduce a model of synaptic plasticity based on data-constrained postsynaptic calcium dynamics, and show in a neocortical microcircuit model that a single parameter set is sufficient to unify the available experimental findings on long-term potentiation (LTP) and long-term depression (LTD) of PC connections. In particular, we find that the diverse plasticity outcomes across the different PC types can be explained by cell-type-specific synaptic physiology, cell morphology and innervation patterns, without requiring type-specific plasticity. Generalizing the model to in vivo extracellular calcium concentrations, we predict qualitatively different plasticity dynamics from those observed in vitro. This work provides a first comprehensive null model for LTP/LTD between neocortical PC types in vivo, and an open framework for further developing models of cortical synaptic plasticity.

Frequency-dependent disynaptic inhibition in the pyramidal network: a ubiquitous pathway in the developing rat neocortex.

The general structure of the mammalian neocortex is remarkably similar across different cortical areas. Despite certain cytoarchitectural specializations and deviations from the general blueprint, the principal organization of the neocortex is relatively uniform. It is not known, however, to what extent stereotypic synaptic pathways resemble each other between cortical areas, and how far they might reflect possible functional uniformity or specialization. Here, we show that frequency-dependent disynaptic inhibition (FDDI) is a generic circuit motif that is present in all neocortical areas we investigated (primary somatosensory, auditory and motor cortex, secondary visual cortex and medial prefrontal cortex of the developing rat). We did find, however, area-specific differences in occurrence and kinetics of FDDI and the short-term dynamics of monosynaptic connections between pyramidal cells (PCs). Connectivity between PCs, both monosynaptic and via FDDI, is higher in primary cortices. The long-term effectiveness of FDDI is likely to be limited by an activity-dependent attenuation of the PC-interneuron synaptic transmission. Our results suggest that the basic construction of neocortical synaptic pathways follows principles that are independent of modality or hierarchical order within the neocortex.

Estimating the Readily-Releasable Vesicle Pool Size at Synaptic Connections in the Neocortex.

Previous studies based on the 'Quantal Model' for synaptic transmission suggest that neurotransmitter release is mediated by a single release site at individual synaptic contacts in the neocortex. However, recent studies seem to contradict this hypothesis and indicate that multi-vesicular release (MVR) could better explain the synaptic response variability observed in vitro. In this study we present a novel method to estimate the number of release sites per synapse, also known as the size of the readily releasable pool (NRRP), from paired whole-cell recordings of connections between layer 5 thick tufted pyramidal cell (L5_TTPC) in the juvenile rat somatosensory cortex. Our approach extends the work of Loebel et al. (2009) by leveraging a recently published data-driven biophysical model of neocortical tissue. Using this approach, we estimated NRRP to be between two to three for synaptic connections between L5_TTPCs. To constrain NRRP values for other connections in the microcircuit, we developed and validated a generalization approach using published data on the coefficient of variation (CV) of the amplitudes of post-synaptic potentials (PSPs) from literature and comparing them against in silico experiments. Our study predicts that transmitter release at synaptic connections in the neocortex could be mediated by MVR and provides a data-driven approach to constrain the MVR model parameters in the microcircuit.

Cliques of Neurons Bound into Cavities Provide a Missing Link between Structure and Function.

The lack of a formal link between neural network structure and its emergent function has hampered our understanding of how the brain processes information. We have now come closer to describing such a link by taking the direction of synaptic transmission into account, constructing graphs of a network that reflect the direction of information flow, and analyzing these directed graphs using algebraic topology. Applying this approach to a local network of neurons in the neocortex revealed a remarkably intricate and previously unseen topology of synaptic connectivity. The synaptic network contains an abundance of cliques of neurons bound into cavities that guide the emergence of correlated activity. In response to stimuli, correlated activity binds synaptically connected neurons into functional cliques and cavities that evolve in a stereotypical sequence toward peak complexity. We propose that the brain processes stimuli by forming increasingly complex functional cliques and cavities.

A computer-assisted multi-electrode patch-clamp system.

The patch-clamp technique is today the most well-established method for recording electrical activity from individual neurons or their subcellular compartments. Nevertheless, achieving stable recordings, even from individual cells, remains a time-consuming procedure of considerable complexity. Automation of many steps in conjunction with efficient information display can greatly assist experimentalists in performing a larger number of recordings with greater reliability and in less time. In order to achieve large-scale recordings we concluded the most efficient approach is not to fully automatize the process but to simplify the experimental steps and reduce the chances of human error while efficiently incorporating the experimenter's experience and visual feedback. With these goals in mind we developed a computer-assisted system which centralizes all the controls necessary for a multi-electrode patch-clamp experiment in a single interface, a commercially available wireless gamepad, while displaying experiment related information and guidance cues on the computer screen. Here we describe the different components of the system which allowed us to reduce the time required for achieving the recording configuration and substantially increase the chances of successfully recording large numbers of neurons simultaneously.

Computing the size and number of neuronal clusters in local circuits.

The organization of connectivity in neuronal networks is fundamental to understanding the activity and function of neural networks and information processing in the brain. Recent studies show that the neocortex is not only organized in columns and layers but also, within these, into synaptically connected clusters of neurons (Ko et al., 2011; Perin et al., 2011). The recently discovered common neighbor rule, according to which the probability of any two neurons being synaptically connected grows with the number of their common neighbors, is an organizing principle for this local clustering. Here we investigated the theoretical constraints for how the spatial extent of neuronal axonal and dendritic arborization, heretofore described by morphological reach, the density of neurons and the size of the network determine cluster size and numbers within neural networks constructed according to the common neighbor rule. In the formulation we developed, morphological reach, cell density, and network size are sufficient to estimate how many neurons, on average, occur in a cluster and how many clusters exist in a given network. We find that cluster sizes do not grow indefinitely as network parameters increase, but tend to characteristic limiting values.

A biophysically detailed model of neocortical local field potentials predicts the critical role of active membrane currents.

Brain activity generates extracellular voltage fluctuations recorded as local field potentials (LFPs). It is known that the relevant microvariables, the ionic currents across membranes, jointly generate the macrovariables, the extracellular voltage, but neither the detailed biophysical knowledge nor the required computational power have been available to model these processes. We simulated the LFP in a model of the rodent neocortical column composed of >12,000 reconstructed, multicompartmental, and spiking cortical layer 4 and 5 pyramidal neurons and basket cells, including five million dendritic and somatic compartments with voltage- and ion-dependent currents, realistic connectivity, and probabilistic AMPA, NMDA, and GABA synapses. We found that, depending on a number of factors, the LFP reflects local and cross-layer processing. Active currents dominate the generation of LFPs, not synaptic ones. Spike-related currents impact the LFP not only at higher frequencies but below 50 Hz. This work calls for re-evaluating the genesis of LFPs.

Ephaptic coupling of cortical neurons.

The electrochemical processes that underlie neural function manifest themselves in ceaseless spatiotemporal field fluctuations. However, extracellular fields feed back onto the electric potential across the neuronal membrane via ephaptic coupling, independent of synapses. The extent to which such ephaptic coupling alters the functioning of neurons under physiological conditions remains unclear. To address this question, we stimulated and recorded from rat cortical pyramidal neurons in slices with a 12-electrode setup. We found that extracellular fields induced ephaptically mediated changes in the somatic membrane potential that were less than 0.5 mV under subthreshold conditions. Despite their small size, these fields could strongly entrain action potentials, particularly for slow (<8 Hz) fluctuations of the extracellular field. Finally, we simultaneously measured from up to four patched neurons located proximally to each other. Our findings indicate that endogenous brain activity can causally affect neural function through field effects under physiological conditions.