The neocortical microcircuit as a tabula rasa

Mapping the matrix: the ways of neocortex

While we know that the neocortex occupies 85% of our brains and that its circuits allow an enormous flexibility and repertoire of behavior (not to mention unexplained phenomena like consciousness), a century after Cajal we have very little knowledge of the details of the cortical circuits or their mode of function. One simplifying hypothesis that has existed since Cajal is that the neocortex consists of repeated copies of the same fundamental circuit. However, finding that fundamental circuit has proved elusive, although partial drafts of a "canonical circuit" appear in many different guises of structure and function. Here, we review some critical stages in the history of this quest. In doing so, we consider the style of cortical computation in relation to the neuronal machinery that supports it. We conclude that the structure and function of cortex honors two major computational principles: "just-enough" and "just-in-time."

What can we learn from synaptic weight distributions?

Much research effort into synaptic plasticity has been motivated by the idea that modifications of synaptic weights (or strengths or efficacies) underlie learning and memory. Here, we examine the possibility of exploiting the statistics of experimentally measured synaptic weights to deduce information about the learning process. Analysing distributions of synaptic weights requires a theoretical framework to interpret the experimental measurements, but the results can be unexpectedly powerful, yielding strong constraints on possible learning theories as well as information that is difficult to obtain by other means, such as the information storage capacity of a cell. We review the available experimental and theoretical techniques as well as important open issues.

Development of GABA innervation in the cerebral and cerebellar cortices

In many areas of the vertebrate brain, such as the cerebral and cerebellar cortices, neural circuits rely on inhibition mediated by GABA (gamma-aminobutyric acid) to shape the spatiotemporal patterns of electrical signalling. The richness and subtlety of inhibition are achieved by diverse classes of interneurons that are endowed with distinct physiological properties. In addition, the axons of interneurons display highly characteristic and class-specific geometry and innervation patterns, and thereby distribute their output to discrete spatial domains, cell types and subcellular compartments in neural networks. The cellular and molecular mechanisms that specify and modify inhibitory innervation patterns are only just beginning to be understood.

Effects of Hebbian learning on the dynamics and structure of random networks with inhibitory and excitatory neurons

The aim of the present paper is to study the effects of Hebbian learning in random recurrent neural networks with biological connectivity, i.e. sparse connections and separate populations of excitatory and inhibitory neurons. We furthermore consider that the neuron dynamics may occur at a (shorter) time scale than synaptic plasticity and consider the possibility of learning rules with passive forgetting. We show that the application of such Hebbian learning leads to drastic changes in the network dynamics and structure. In particular, the learning rule contracts the norm of the weight matrix and yields a rapid decay of the dynamics complexity and entropy. In other words, the network is rewired by Hebbian learning into a new synaptic structure that emerges with learning on the basis of the correlations that progressively build up between neurons. We also observe that, within this emerging structure, the strongest synapses organize as a small-world network. The second effect of the decay of the weight matrix spectral radius consists in a rapid contraction of the spectral radius of the Jacobian matrix. This drives the system through the "edge of chaos" where sensitivity to the input pattern is maximal. Taken together, this scenario is remarkably predicted by theoretical arguments derived from dynamical systems and graph theory.

Specificity and randomness in the visual cortex

Research on the functional anatomy of visual cortical circuits has recently zoomed in from the macroscopic level to the microscopic. High-resolution functional imaging has revealed that the functional architecture of orientation maps in higher mammals is built with single-cell precision. By contrast, orientation selectivity in rodents is dispersed on visual cortex in a salt-and-pepper fashion, despite highly tuned visual responses. Recent studies of synaptic physiology indicate that there are disjoint subnetworks of interconnected cells in the rodent visual cortex. These intermingled subnetworks, described in vitro, may relate to the intermingled ensembles of cells tuned to different orientations, described in vivo. This hypothesis may soon be tested with new anatomic techniques that promise to reveal the detailed wiring diagram of cortical circuits.

Disynaptic inhibition between neocortical pyramidal cells mediated by Martinotti cells

Reliable activation of inhibitory pathways is essential for maintaining the balance between excitation and inhibition during cortical activity. Little is known, however, about the activation of these pathways at the level of the local neocortical microcircuit. We report a disynaptic inhibitory pathway among neocortical pyramidal cells (PCs). Inhibitory responses were evoked in layer 5 PCs following stimulation of individual neighboring PCs with trains of action potentials. The probability for inhibition between PCs was more than twice that of direct excitation, and inhibitory responses increased as a function of rate and duration of presynaptic discharge. Simultaneous somatic and dendritic recordings indicated that inhibition originated from PC apical and tuft dendrites. Multineuron whole-cell recordings from PCs and interneurons combined with morphological reconstructions revealed the mediating interneurons as Martinotti cells. Martinotti cells received facilitating synapses from PCs and formed reliable inhibitory synapses onto dendrites of neighboring PCs. We describe this feedback pathway and propose it as a central mechanism for regulation of cortical activity.

Local potential connectivity in cat primary visual cortex

Time invariant description of synaptic connectivity in cortical circuits may be precluded by the ongoing growth and retraction of dendritic spines accompanied by the formation and elimination of synapses. On the other hand, the spatial arrangement of axonal and dendritic branches appears stable. This suggests that an invariant description of connectivity can be cast in terms of potential synapses, which are locations in the neuropil where an axon branch of one neuron is proximal to a dendritic branch of another neuron. In this paper, we attempt to reconstruct the potential connectivity in local cortical circuits of the cat primary visual cortex (V1). Based on multiple single-neuron reconstructions of axonal and dendritic arbors in 3 dimensions, we evaluate the expected number of potential synapses and the probability of potential connectivity among excitatory (pyramidal and spiny stellate) neurons and inhibitory basket cells. The results provide a quantitative description of structural organization of local cortical circuits. For excitatory neurons from different cortical layers, we compute local domains, which contain their potentially pre- and postsynaptic excitatory partners. These domains have columnar shapes with laminar specific radii and are roughly of the size of the ocular dominance column. Therefore, connections between most excitatory neurons in the ocular dominance column can be implemented by local synaptogenesis. Structural connectivity involving inhibitory basket cells is generally weaker than excitatory connectivity. Here, only nearby neurons are capable of establishing more than one potential synapse, implying that within the ocular dominance column these connections have more limited potential for circuit remodeling.

Variability v.s. synchronicity of neuronal activity in local cortical network models with different wiring topologies

Dynamical behavior of a biological neuronal network depends significantly on the spatial pattern of synaptic connections among neurons. While neuronal network dynamics has extensively been studied with simple wiring patterns, such as all-to-all or random synaptic connections, not much is known about the activity of networks with more complicated wiring topologies. Here, we examined how different wiring topologies may influence the response properties of neuronal networks, paying attention to irregular spike firing, which is known as a characteristic of in vivo cortical neurons, and spike synchronicity. We constructed a recurrent network model of realistic neurons and systematically rewired the recurrent synapses to change the network topology, from a localized regular and a "small-world" network topology to a distributed random network topology. Regular and small-world wiring patterns greatly increased the irregularity or the coefficient of variation (Cv) of output spike trains, whereas such an increase was small in random connectivity patterns. For given strength of recurrent synapses, the firing irregularity exhibited monotonous decreases from the regular to the random network topology. By contrast, the spike coherence between an arbitrary neuron pair exhibited a non-monotonous dependence on the topological wiring pattern. More precisely, the wiring pattern to maximize the spike coherence varied with the strength of recurrent synapses. In a certain range of the synaptic strength, the spike coherence was maximal in the small-world network topology, and the long-range connections introduced in this wiring changed the dependence of spike synchrony on the synaptic strength moderately. However, the effects of this network topology were not really special in other properties of network activity.

Local cortical circuit model inferred from power-law distributed neuronal avalanches

How cortical neurons process information crucially depends on how their local circuits are organized. Spontaneous synchronous neuronal activity propagating through neocortical slices displays highly diverse, yet repeatable, activity patterns called "neuronal avalanches". They obey power-law distributions of the event sizes and lifetimes, presumably reflecting the structure of local circuits developed in slice cultures. However, the explicit network structure underlying the power-law statistics remains unclear. Here, we present a neuronal network model of pyramidal and inhibitory neurons that enables stable propagation of avalanche-like spiking activity. We demonstrate a neuronal wiring rule that governs the formation of mutually overlapping cell assemblies during the development of this network. The resultant network comprises a mixture of feedforward chains and recurrent circuits, in which neuronal avalanches are stable if the former structure is predominant. Interestingly, the recurrent synaptic connections formed by this wiring rule limit the number of cell assemblies embeddable in a neuron pool of given size. We investigate how the resultant power laws depend on the details of the cell-assembly formation as well as on the inhibitory feedback. Our model suggests that local cortical circuits may have a more complex topological design than has previously been thought.

Dendritic spines linearize the summation of excitatory potentials

In mammalian cortex, most excitatory inputs occur on dendritic spines, avoiding dendritic shafts. Although spines biochemically isolate inputs, nonspiny neurons can also implement biochemical compartmentalization; so, it is possible that spines have an additional function. We have recently shown that the spine neck can filter membrane potentials going into and out of the spine. To investigate the potential function of this electrical filtering, we used two-photon uncaging of glutamate and compared the integration of electrical signals in spines vs. dendritic shafts from basal dendrites of mouse layer 5 pyramidal neurons. Uncaging potentials onto spines summed linearly, whereas potentials on dendritic shafts reduced each other's effect. Linear integration of spines was maintained regardless of the amplitude of the response, distance between spines (as close as < 2 microm), distance of the spines to the soma, dendritic diameter, or spine neck length. Our findings indicate that spines serve as electrical isolators to prevent input interaction, and thus generate a linear arithmetic of excitatory inputs. Linear integration could be an essential feature of cortical and other spine-laden circuits.

Optimal Information Storage in Noisy Synapses under Resource Constraints

Experimental investigations have revealed that synapses possess interesting and, in some cases, unexpected properties. We propose a theoretical framework that accounts for three of these properties: typical central synapses are noisy, the distribution of synaptic weights among central synapses is wide, and synaptic connectivity between neurons is sparse. We also comment on the possibility that synaptic weights may vary in discrete steps. Our approach is based on maximizing information storage capacity of neural tissue under resource constraints. Based on previous experimental and theoretical work, we use volume as a limited resource and utilize the empirical relationship between volume and synaptic weight. Solutions of our constrained optimization problems are not only consistent with existing experimental measurements but also make nontrivial predictions.

Spontaneous and evoked synaptic rewiring in the neonatal neocortex

The local microcircuitry of the neocortex is structurally a tabula rasa, with the axon of each pyramidal neuron having numerous submicrometer appositions with the dendrites of all neighboring pyramidal neurons, but is functionally highly selective, with synapses formed onto only a small proportion of these targets. This design leaves a vast potential for the microcircuit to rewire without extensive axonal or dendritic growth. To examine whether rewiring does take place, we used multineuron patch-clamp recordings on 12- to 14-day-old rat neocortical slices and studied long-term changes in synaptic connectivity within clusters of neurons. We found pyramidal neurons spontaneously connecting and disconnecting from each other and that exciting the slice with glutamate greatly increases the number of new connections established. Evoked emergence of new synaptic connections requires action potential activity and activation of metabotropic glutamate receptor 5, but not NMDA receptor or group II or group III metabotropic glutamate receptor activation. We also found that it is the weaker connections that are selectively eliminated. These results provide direct evidence for spontaneous and evoked rewiring of the neocortical microcircuitry involving entire functional multisynaptic connections. We speculate that this form of microcircuit plasticity enables an evolution of the microcircuit connectivity by natural selection as a function of experience.

Synaptic efficacy cluster formation across the dendrite via STDP

The role of spike-timing-dependent plasticity (STDP) in shaping the strength of a synapse located on the dendritic tree has gained recent interest. Previous theoretical studies using STDP have mostly used simplified integrate-and-fire models to investigate the evolution of synaptic efficacy with time. Such studies usually show that the final weight distribution is unimodal or bimodal resulting from a multiplicative or additive STDP rule, respectively. However, very little is known about how STDP shapes the spatial organization of synaptic efficacies. Here, for the first time, we demonstrate that spatial clustering of synaptic efficacies can occur on the dendrite via STDP, where changes in synaptic efficacy are driven by timing differences between synaptic inputs and the generation of local dendritic spikes. Specifically, when the model neuron is stimulated by two independent groups of correlated afferent inputs, the synaptic efficacies from each group, are not only spatially clustered on the dendrite but also spatially complementary to each other.

Recurrent connection patterns of corticostriatal pyramidal cells in frontal cortex

Corticostriatal pyramidal cells are heterogeneous in the frontal cortex. Here, we show that subpopulations of corticostriatal neurons in the rat frontal cortex are selectively connected with each other based on their subcortical targets. Using paired recordings of retrogradely labeled cells, we investigated the synaptic connectivity between two projection cell types: those projecting to the pons [corticopontine (CPn) cell], often with collaterals to the striatum, and those projecting to both sides of the striatum but not to the pons [crossed corticostriatal (CCS) cell]. The two types were morphologically differentiated in regard to their apical tufts. The dendritic morphologies of CCS cells were correlated with their somatic depth within the cortex. CCS cells had reciprocal synaptic connections with each other and also provided synaptic input to CPn cells. However, connections from CPn to CCS cells were rarely found, even in pairs showing CCS to CPn connectivity. Additionally, CCS cells preferentially innervated the basal dendrites of other CCS cells but made contacts onto both the basal and apical dendrites of CPn cells. The amplitude of synaptic responses was to some extent correlated with the contact site number. Ratios of the EPSC amplitude to the contact number tended to be larger in the CCS to CCS connection. Therefore, our data demonstrate that these two types of corticostriatal cells distinct in their dendritic morphologies show directional and domain-dependent preferences in their synaptic connectivity.

Models and musings about them

Theories of brain function abound, and they range from Aristotle's idea that it cools the blood to the most recent conclusions deduced from fMRI scans. Today, such ideas, theories and constructs are often called models, the best of which blend the writer's laboratory data with what he or she has culled from the experiments others report. A model can therefore be viewed as the product of a unique collection of intellectual encounters with teachers-some living, some dead-at lectures and in libraries to which have been added countless unique personal experiences during experiments performed in laboratories. This essay describes some of the models I have published, naming the places where the experiments were done and some of the teachers from whom I learned what I know.

Heterogeneity in the pyramidal network of the medial prefrontal cortex

The prefrontal cortex is specially adapted to generate persistent activity that outlasts stimuli and is resistant to distractors, presumed to be the basis of working memory. The pyramidal network that supports this activity is unknown. Multineuron patch-clamp recordings in the ferret medial prefrontal cortex showed a heterogeneity of synapses interconnecting distinct subnetworks of different pyramidal cells. One subnetwork was similar to the pyramidal network commonly found in primary sensory areas, consisting of accommodating pyramidal cells interconnected with depressing synapses. The other subnetwork contained complex pyramidal cells with dual apical dendrites displaying nonaccommodating discharge patterns; these cells were hyper-reciprocally connected with facilitating synapses displaying pronounced synaptic augmentation and post-tetanic potentiation. These cellular, synaptic and network properties could amplify recurrent interactions between pyramidal neurons and support persistent activity in the prefrontal cortex.

Transient rhythmic network activity in the somatosensory cortex evoked by distributed input in vitro

The initiation and maintenance of physiological and pathophysiological oscillatory activity depends on the synaptic interactions within neuronal networks. We studied the mechanisms underlying evoked transient network oscillation in acute slices of the adolescent rat somatosensory cortex and modeled its underpinning mechanisms. Oscillations were evoked by brief spatially distributed noisy extracellular stimulation, delivered via bipolar electrodes. Evoked transient network oscillation was detected with multi-neuron patch-clamp recordings under different pharmacological conditions. The observed oscillations are in the frequency range of 2-5 Hz and consist of 4-12 mV large, 40-150 ms wide compound synaptic events with rare overlying action potentials. This evoked transient network oscillation is only weakly expressed in the somatosensory cortex and requires increased [K+]o of 6.25 mM and decreased [Ca2+]o of 1.5 mM and [Mg2+]o of 0.5 mM. A peak in the cross-correlation among membrane potential in layers II/III, IV and V neurons reflects the underlying network-driven basis of the evoked transient network oscillation. The initiation of the evoked transient network oscillation is accompanied by an increased [K+]o and can be prevented by the K+ channel blocker quinidine. In addition, a shift of the chloride reversal potential takes place during stimulation, resulting in a depolarizing type A GABA (GABAA) receptor response. Blockade of alpha-amino-3-hydroxy-5-methyl-4-isoxazole-proprionate (AMPA), N-methyl-D-aspartate (NMDA), or GABA(A) receptors as well as gap junctions prevents evoked transient network oscillation while a reduction of AMPA or GABA(A) receptor desensitization increases its duration and amplitude. The apparent reversal potential of -27 mV of the evoked transient network oscillation, its pharmacological profile, as well as the modeling results suggest a mixed contribution of glutamatergic, excitatory GABAergic, and gap junctional conductances in initiation and maintenance of this oscillatory activity. With these properties, evoked transient network oscillation resembles epileptic afterdischarges more than any other form of physiological or pathophysiological neocortical oscillatory activity.

Cochlear implants: cortical plasticity in congenital deprivation

Congenital auditory deprivation (deafness) leads to a dysfunctional intrinsic cortical microcircuitry. This chapter reviews these deficits with a particular emphasis on layer-specific activity within the primary auditory cortex. Evidence for a delay in activation of supragranular layers and reduction in activity in infragranular layers is discussed. Such deficits indicate the incompetence of the primary auditory cortex to not only properly process thalamic input and generate output within the infragranular layers, but also incorporate top-down modulations from higher order auditory cortex into the processing within primary auditory cortex. Such deficits are the consequence of a misguided postnatal development. Maturation of primary auditory cortex in deaf animals shows evidence of a developmental delay and further alterations in gross synaptic currents, spread of activation, and morphology of local field potentials recorded at the cortical surface. Additionally, degenerative changes can be observed. When hearing is initiated early in life (e.g., by chronic cochlear-implant stimulation), many of these deficits are counterbalanced. However, plasticity of the auditory cortex decreases with increasing age, so that a sensitive period for plastic adaptation can be demonstrated within the second to sixth months of life in the deaf cat. Potential molecular mechanisms of the existence of sensitive period are discussed. Data from animal research may be compared to electroencephalographic data obtained from cochlear-implanted congenitally deaf children. After cochlear implantation in humans, three phases of plastic adaptation can be observed: a fast one, taking place within the first few weeks after implantation, showing no sensitive period; a slower one, taking place within the first months after implantation (a sensitive period up to 4 years of age); and possibly a third, and the longest one, related to increasing activation of higher order cortical areas.

Segregation of the brain into gray and white matter: a design minimizing conduction delays

A ubiquitous feature of the vertebrate anatomy is the segregation of the brain into white and gray matter. Assuming that evolution maximized brain functionality, what is the reason for such segregation? To answer this question, we posit that brain functionality requires high interconnectivity and short conduction delays. Based on this assumption we searched for the optimal brain architecture by comparing different candidate designs. We found that the optimal design depends on the number of neurons, interneuronal connectivity, and axon diameter. In particular, the requirement to connect neurons with many fast axons drives the segregation of the brain into white and gray matter. These results provide a possible explanation for the structure of various regions of the vertebrate brain, such as the mammalian neocortex and neostriatum, the avian telencephalon, and the spinal cord.

Synaptic pathways in neural microcircuits

The functions performed by different neural microcircuits depend on the anatomical and physiological properties of the various synaptic pathways connecting neurons. Neural microcircuits across various species and brain regions are similar in terms of their repertoire of neurotransmitters, their synaptic kinetics, their short-term and long-term plasticity, and the target-specificity of their synaptic connections. However, microcircuits can be fundamentally different in terms of the precise recurrent design used to achieve a specific functionality. In this review, which is part of the TINS Microcircuits Special Feature, we compare the connectivity designs in spinal, hippocampal, neocortical and cerebellar microcircuits, and discuss the different computational challenges that each microcircuit faces.

The human connectome: A structural description of the human brain

The connection matrix of the human brain (the human "connectome") represents an indispensable foundation for basic and applied neurobiological research. However, the network of anatomical connections linking the neuronal elements of the human brain is still largely unknown. While some databases or collations of large-scale anatomical connection patterns exist for other mammalian species, there is currently no connection matrix of the human brain, nor is there a coordinated research effort to collect, archive, and disseminate this important information. We propose a research strategy to achieve this goal, and discuss its potential impact.

Dendritic branch typing and spine expression patterns in cortical nonpyramidal cells

To understand the dendritic differentiation in various types of cortical nonpyramidal cells, we analyzed quantitatively their dendritic branching and spine expression. The dendritic internode and interspine interval obeyed exponential distributions with type-specific decay constants. The initial branching pattern, internode interval and spine density at the light microscopic level divided nonpyramidal cells into three dendritic types, correlated with axonal, neurochemical and firing types. The initial branching pattern determined the overall vertical spread of dendrites. Basket cell subtypes with different firing and chemical expression patterns were distinct in the vertical and horizontal spatial spread, providing diverse input territories. Internode densities of dendritic spines, as well as those of axonal synaptic boutons, did not correlate with the tortuosities and intervals, suggesting a tendency to distribute synapses homogeneously over the arbor. Dendritic spines identified at the electron microscopic level were different in length and shape among subtypes. Although the density was lower than that of pyramidal cells, spines themselves were also composed of several morphological types such as mushroom and multihead ones, which were expressed differentially among subtypes. Correlation of dendritic branching characteristics with differences in spine structure suggests distinct ways to receive specific inputs among the subtypes.

Diverse modes of axon elaboration in the developing neocortex

The development of axonal arbors is a critical step in the establishment of precise neural circuits, but relatively little is known about the mechanisms of axonal elaboration in the neocortex. We used in vivo two-photon time-lapse microscopy to image axons in the neocortex of green fluorescent protein-transgenic mice over the first 3 wk of postnatal development. This period spans the elaboration of thalamocortical (TC) and Cajal-Retzius (CR) axons and cortical synaptogenesis. Layer 1 collaterals of TC and CR axons were imaged repeatedly over time scales ranging from minutes up to days, and their growth and pruning were analyzed. The structure and dynamics of TC and CR axons differed profoundly. Branches of TC axons terminated in small, bulbous growth cones, while CR axon branch tips had large growth cones with numerous long filopodia. TC axons grew rapidly in straight paths, with frequent interstitial branch additions, while CR axons grew more slowly along tortuous paths. For both types of axon, new branches appeared at interstitial sites along the axon shaft and did not involve growth cone splitting. Pruning occurred via retraction of small axon branches (tens of microns, at both CR and TC axons) or degeneration of large portions of the arbor (hundreds of microns, for TC axons only). The balance between growth and retraction favored overall growth, but only by a slight margin. Given the identical layer 1 territory upon which CR and TC axons grow, the differences in their structure and dynamics likely reflect distinct intrinsic growth programs for axons of long projection neurons versus local interneurons.

A phenomenological theory of spatially structured local synaptic connectivity

The structure of local synaptic circuits is the key to understanding cortical function and how neuronal functional modules such as cortical columns are formed. The central problem in deciphering cortical microcircuits is the quantification of synaptic connectivity between neuron pairs. I present a theoretical model that accounts for the axon and dendrite morphologies of pre- and postsynaptic cells and provides the average number of synaptic contacts formed between them as a function of their relative locations in three-dimensional space. An important aspect of the current approach is the representation of a complex structure of an axonal/dendritic arbor as a superposition of basic structures—synaptic clouds. Each cloud has three structural parameters that can be directly estimated from two-dimensional drawings of the underlying arbor. Using empirical data available in literature, I applied this theory to three morphologically different types of cell pairs. I found that, within a wide range of cell separations, the theory is in very good agreement with empirical data on (i) axonal–dendritic contacts of pyramidal cells and (ii) somatic synapses formed by the axons of inhibitory interneurons. Since for many types of neurons plane arborization drawings are available from literature, this theory can provide a practical means for quantitatively deriving local synaptic circuits based on the actual observed densities of specific types of neurons and their morphologies. It can also have significant implications for computational models of cortical networks by making it possible to wire up simulated neural networks in a realistic fashion.

Each neuron communicates signals via synaptic connections simultaneously to several hundreds of neighboring neurons forming a synaptic circuit. Determining the pattern of synaptic connections between local neurons is crucial for understanding a specific cortical function implemented by a synaptic circuit. The connectivity between a pair of neurons is affected by their axonal/dendritic morphologies and relative spatial locations. Although neuroscientists have precise tools to measure neuronal activity caused by the flow of signals between circuit neurons, there are still considerable difficulties in the direct experimental measurement of local synaptic connectivity, which actually determines the underlying activity. This paper presents a theoretical approach to synaptic connectivity accounting for the morphologies of pre- and postsynaptic neurons and providing the average number of synaptic contacts formed between them as a function of their relative locations. An important aspect is the decomposition of the complex structure of an axonal/dendritic arbor into a small number of basic structures. The theory is in very good agreement, within a wide range of cell separations, with empirical data on axonal–dendritic contacts of pyramidal cells and somatic synapses formed by the axons of inhibitory interneurons. The current approach can provide a practical means for quantitatively deriving local synaptic circuits based on the actual observed densities of specific types of neurons and their morphologies.

The cortex as a central pattern generator

Vertebrate spinal cord and brainstem central pattern generator (CPG) circuits share profound similarities with neocortical circuits. CPGs can produce meaningful functional output in the absence of sensory inputs. Neocortical circuits could be considered analogous to CPGs as they have rich spontaneous dynamics that, similar to CPGs, are powerfully modulated or engaged by sensory inputs, but can also generate output in their absence. We find compelling evidence for this argument at the anatomical, biophysical, developmental, dynamic and pathological levels of analysis. Although it is possible that cortical circuits are particularly plastic types of CPG ('learning CPGs'), we argue that present knowledge about CPGs is likely to foretell the basic principles of the organization and dynamic function of cortical circuits.

Geometric and functional organization of cortical circuits

Can neuronal morphology predict functional synaptic circuits? In the rat barrel cortex, 'barrels' and 'septa' delineate an orderly matrix of cortical columns. Using quantitative laser scanning photostimulation we measured the strength of excitatory projections from layer 4 (L4) and L5A to L2/3 pyramidal cells in barrel- and septum-related columns. From morphological reconstructions of excitatory neurons we computed the geometric circuit predicted by axodendritic overlap. Within most individual projections, functional inputs were predicted by geometry and a single scale factor, the synaptic strength per potential synapse. This factor, however, varied between projections and, in one case, even within a projection, up to 20-fold. Relationships between geometric overlap and synaptic strength thus depend on the laminar and columnar locations of both the pre- and postsynaptic neurons, even for neurons of the same type. A large plasticity potential appears to be incorporated into these circuits, allowing for functional 'tuning' with fixed axonal and dendritic arbor geometry.