Physiology and anatomy of synaptic connections between thick tufted pyramidal neurones in the developing rat neocortex

A model of cholinergic suppression of hippocampal ripples through disruption of balanced excitation/inhibition

Sharp wave-ripples (140-220 Hz) are patterns of brain activity observed in the local field potential of the hippocampus which are present during memory consolidation. As rodents switch from memory consolidation to memory encoding behaviors, cholinergic inputs to the hippocampus from neurons in the medial septum-diagonal band of Broca cause a marked reduction in ripple incidence. The mechanism for this disruption in ripple power is not fully understood. In isolated neurons, the major effect of cholinergic input on hippocampal neurons is depolarization of the membrane potential, which affects both hippocampal pyramidal neurons and inhibitory interneurons. Using an existing model of ripple-frequency oscillations that includes both pyramidal neurons and interneurons, we investigated the mechanism whereby depolarizing inputs to these neurons can affect ripple power and frequency. We observed that ripple power and frequency are maintained, as long as inputs to pyramidal neurons and interneurons are balanced. Preferential drive to pyramidal neurons or interneurons, however, affects ripple power and can disrupt ripple oscillations by pushing ripple frequency higher or lower. Thus, an imbalance in drive to pyramidal neurons and interneurons provides a means whereby cholinergic input can suppress hippocampal ripples.

Cortical reliability amid noise and chaos

Typical responses of cortical neurons to identical sensory stimuli appear highly variable. It has thus been proposed that the cortex primarily uses a rate code. However, other studies have argued for spike-time coding under certain conditions. The potential role of spike-time coding is directly limited by the internally generated variability of cortical circuits, which remains largely unexplored. Here, we quantify this internally generated variability using a biophysical model of rat neocortical microcircuitry with biologically realistic noise sources. We find that stochastic neurotransmitter release is a critical component of internally generated variability, causing rapidly diverging, chaotic recurrent network dynamics. Surprisingly, the same nonlinear recurrent network dynamics can transiently overcome the chaos in response to weak feed-forward thalamocortical inputs, and support reliable spike times with millisecond precision. Our model shows that the noisy and chaotic network dynamics of recurrent cortical microcircuitry are compatible with stimulus-evoked, millisecond spike-time reliability, resolving a long-standing debate.

Whisker-Mediated Touch System in Rodents: From Neuron to Behavior

A key question in systems neuroscience is to identify how sensory stimuli are represented in neuronal activity, and how the activity of sensory neurons in turn is “read out” by downstream neurons and give rise to behavior. The choice of a proper model system to address these questions, is therefore a crucial step. Over the past decade, the increasingly powerful array of experimental approaches that has become available in non-primate models (e.g., optogenetics and two-photon imaging) has spurred a renewed interest for the use of rodent models in systems neuroscience research. Here, I introduce the rodent whisker-mediated touch system as a structurally well-established and well-organized model system which, despite its simplicity, gives rise to complex behaviors. This system serves as a behaviorally efficient model system; known as nocturnal animals, along with their olfaction, rodents rely on their whisker-mediated touch system to collect information about their surrounding environment. Moreover, this system represents a well-studied circuitry with a somatotopic organization. At every stage of processing, one can identify anatomical and functional topographic maps of whiskers; “barrelettes” in the brainstem nuclei, “barreloids” in the sensory thalamus, and “barrels” in the cortex. This article provides a brief review on the basic anatomy and function of the whisker system in rodents.

Model-Based Inference of Synaptic Transmission

Synaptic computation is believed to underlie many forms of animal behavior. A correct identification of synaptic transmission properties is thus crucial for a better understanding of how the brain processes information, stores memories and learns. Recently, a number of new statistical methods for inferring synaptic transmission parameters have been introduced. Here we review and contrast these developments, with a focus on methods aimed at inferring both synaptic release statistics and synaptic dynamics. Furthermore, based on recent proposals we discuss how such methods can be applied to data across different levels of investigation: from intracellular paired experiments to in vivo network-wide recordings. Overall, these developments open the window to reliably estimating synaptic parameters in behaving animals.

Robust Associative Learning Is Sufficient to Explain the Structural and Dynamical Properties of Local Cortical Circuits

The ability of neural networks to associate successive states of network activity lies at the basis of many cognitive functions. Hence, we hypothesized that many ubiquitous structural and dynamical properties of local cortical networks result from associative learning. To test this hypothesis, we trained recurrent networks of excitatory and inhibitory neurons on memories composed of varying numbers of associations and compared the resulting network properties with those observed experimentally. We show that, when the network is robustly loaded with near-maximum amount of associations it can support, it develops properties that are consistent with the observed probabilities of excitatory and inhibitory connections, shapes of connection weight distributions, overexpression of specific 2- and 3-neuron motifs, distributions of connection numbers in clusters of 3-8 neurons, sustained, irregular, and asynchronous firing activity, and balance of excitation and inhibition. In addition, memories loaded into the network can be retrieved, even in the presence of noise that is comparable with the baseline variations in the postsynaptic potential. The confluence of these results suggests that many structural and dynamical properties of local cortical networks are simply a byproduct of associative learning. We predict that overexpression of excitatory-excitatory bidirectional connections observed in many cortical systems must be accompanied with underexpression of bidirectionally connected inhibitory-excitatory neuron pairs.SIGNIFICANCE STATEMENT Many structural and dynamical properties of local cortical networks are ubiquitously present across areas and species. Because synaptic connectivity is shaped by experience, we wondered whether continual learning, rather than genetic control, is responsible for producing such features. To answer this question, we developed a biologically constrained recurrent network of excitatory and inhibitory neurons capable of learning predefined sequences of network states. Embedding such associative memories into the network revealed that, when individual neurons are robustly loaded with a near-maximum amount of memories they can support, the network develops many properties that are consistent with experimental observations. Our findings suggest that basic structural and dynamical properties of local networks in the brain are simply a byproduct of learning and memory storage.

Multicontact Co-operativity in Spike-Timing-Dependent Structural Plasticity Stabilizes Networks

Excitatory synaptic connections in the adult neocortex consist of multiple synaptic contacts, almost exclusively formed on dendritic spines. Changes of spine volume, a correlate of synaptic strength, can be tracked in vivo for weeks. Here, we present a combined model of structural and spike-timing–dependent plasticity that explains the multicontact configuration of synapses in adult neocortical networks under steady-state and lesion-induced conditions. Our plasticity rule with Hebbian and anti-Hebbian terms stabilizes both the postsynaptic firing rate and correlations between the pre- and postsynaptic activity at an active synaptic contact. Contacts appear spontaneously at a low rate and disappear if their strength approaches zero. Many presynaptic neurons compete to make strong synaptic connections onto a postsynaptic neuron, whereas the synaptic contacts of a given presynaptic neuron co-operate via postsynaptic firing. We find that co-operation of multiple synaptic contacts is crucial for stable, long-term synaptic memories. In simulations of a simplified network model of barrel cortex, our plasticity rule reproduces whisker-trimming–induced rewiring of thalamocortical and recurrent synaptic connectivity on realistic time scales.

Intrinsic Spine Dynamics Are Critical for Recurrent Network Learning in Models With and Without Autism Spectrum Disorder

It is often assumed that Hebbian synaptic plasticity forms a cell assembly, a mutually interacting group of neurons that encodes memory. However, in recurrently connected networks with pure Hebbian plasticity, cell assemblies typically diverge or fade under ongoing changes of synaptic strength. Previously assumed mechanisms that stabilize cell assemblies do not robustly reproduce the experimentally reported unimodal and long-tailed distribution of synaptic strengths. Here, we show that augmenting Hebbian plasticity with experimentally observed intrinsic spine dynamics can stabilize cell assemblies and reproduce the distribution of synaptic strengths. Moreover, we posit that strong intrinsic spine dynamics impair learning performance. Our theory explains how excessively strong spine dynamics, experimentally observed in several animal models of autism spectrum disorder, impair learning associations in the brain.

Modulation of Ion Channels in the Axon: Mechanisms and Function

The axon is responsible for integrating synaptic signals, generating action potentials (APs), propagating those APs to downstream synapses and converting them into patterns of neurotransmitter vesicle release. This process is mediated by a rich assortment of voltage-gated ion channels whose function can be affected on short and long time scales by activity. Moreover, neuromodulators control the activity of these proteins through G-protein coupled receptor signaling cascades. Here, we review cellular mechanisms and signaling pathways involved in axonal ion channel modulation and examine how changes to ion channel function affect AP initiation, AP propagation, and the release of neurotransmitter. We then examine how these mechanisms could modulate synaptic function by focusing on three key features of synaptic information transmission: synaptic strength, synaptic variability, and short-term plasticity. Viewing these cellular mechanisms of neuromodulation from a functional perspective may assist in extending these findings to theories of neural circuit function and its neuromodulation.

Multiple Two-Photon Targeted Whole-Cell Patch-Clamp Recordings From Monosynaptically Connected Neurons in vivo

Although we know a great deal about monosynaptic connectivity, transmission and integration in the mammalian nervous system from in vitro studies, very little is known in vivo. This is partly because it is technically difficult to evoke action potentials and simultaneously record small amplitude subthreshold responses in closely (<150 μm) located pairs of neurons. To address this, we have developed in vivo two-photon targeted multiple (2–4) whole-cell patch clamp recordings of nearby neurons in superficial cortical layers 1–3. Here, we describe a step-by-step guide to this approach in the anesthetized mouse primary somatosensory cortex, including: the design of the setup, surgery, preparation of pipettes, targeting and acquisition of multiple whole-cell recordings, as well as in vivo and post hoc histology. The procedure takes ~4 h from start of surgery to end of recording and allows examinations both into the electrophysiological features of unitary excitatory and inhibitory monosynaptic inputs during different brain states as well as the synaptic mechanisms of correlated neuronal activity.

Synapse loss and progress of Alzheimer's disease -A network model

We present observational evidence from studies on primary cortical cultures from AD transgenic mice, APPSwe/PS1ΔE9 (APP/PS1) mice, for significant decrease in total spine density at DIV-15 and onward. This indicates reduction in potential healthy synapses and strength of connections among neurons. Based on this, a network model of neurons is developed, that explains the consequent loss of coordinated activity and transmission efficiency among neurons that manifests over time. The critical time when structural connectivity in the brain undergoes a phase-transition, from initial robustness to irreparable breakdown, is estimated from this model. We also show how the global efficiency of signal transmission in the network decreases over time. Moreover, the number of multiple paths of high efficiency decreases rapidly as the disease progresses, indicating loss of structural plasticity and inefficiency in choosing alternate paths or desired paths for any pattern of activity. Thus loss of spines caused by β-Amyloid (Aβ) peptide results in disintegration of the neuronal network over time with consequent cognitive dysfunctions in Alzheimer’s Disease (AD).

Estrogen-Dependent Functional Spine Dynamics in Neocortical Pyramidal Neurons of the Mouse

Surgical ovariectomy has been shown to reduce spine density in hippocampal CA1 pyramidal cells of rodents, and this reduction is reversed by 17β-estradiol (E2) treatment in a model of human estrogen replacement therapy. Here, we report reduction of spine density in apical dendrites of layer 5 pyramidal neurons of several neocortical regions that is reversed by subsequent E2 treatment in ovariectomized (OVX) female Thy1M-EGFP mice. We also found that OVX-associated reduction of spine density in somatosensory cortex was accompanied by a reduction in miniature EPSC (mEPSC) frequency (but not mIPSC frequency), indicating a change in functional synapses. OVX-associated spine loss in somatosensory cortex was also rescued by an agonist of the G-protein-linked estrogen receptor (GPER) but not by agonists of the classic estrogen receptors ERα/ERβ, whereas the opposite selectivity was found in area CA1. Acute treatment of neocortical slices with E2 also rescued the OVX-associated reduction in mEPSC frequency, which could be mimicked by a GPER agonist and abolished by a GPER antagonist. Time-lapse in vivo two-photon imaging showed that OVX-associated reduction in spine density is achieved by both an increase in spine loss rate and a decrease in spine gain rate and that subsequent rescue by E2 reversed both of these processes. Crucially, the spines added after E2 rescue were no more likely to reappear at or nearby the sites of pre-OVX spines than those in control mice treated with vehicle. Thus, a model of estrogen replacement therapy, although restoring spine density and dynamics, does not entirely restore functional connectivity.SIGNIFICANCE STATEMENT Estrogen replacement therapy following menopause or surgical removal of the ovaries is a widespread medical practice, yet little is known about the consequences of such treatment for cells in the brain. Here, we show that estrogen replacement reverses some of the effects of surgical removal of the ovaries on the structure and function of brain cells in the mouse. Yet, importantly, the fine wiring of the brain is not returned to the presurgery state by estrogen treatment, suggesting lasting functional consequences.

Cellular, Synaptic and Network Effects of Acetylcholine in the Neocortex

The neocortex is densely innervated by basal forebrain (BF) cholinergic neurons. Long-range axons of cholinergic neurons regulate higher-order cognitive function and dysfunction in the neocortex by releasing acetylcholine (ACh). ACh release dynamically reconfigures neocortical microcircuitry through differential spatiotemporal actions on cell-types and their synaptic connections. At the cellular level, ACh release controls neuronal excitability and firing rate, by hyperpolarizing or depolarizing target neurons. At the synaptic level, ACh impacts transmission dynamics not only by altering the presynaptic probability of release, but also the magnitude of the postsynaptic response. Despite the crucial role of ACh release in physiology and pathophysiology, a comprehensive understanding of the way it regulates the activity of diverse neocortical cell-types and synaptic connections has remained elusive. This review aims to summarize the state-of-the-art anatomical and physiological data to develop a functional map of the cellular, synaptic and microcircuit effects of ACh in the neocortex of rodents and non-human primates, and to serve as a quantitative reference for those intending to build data-driven computational models on the role of ACh in governing brain states.

Glutamate versus GABA in neuron-oligodendroglia communication

In the central nervous system (CNS), myelin sheaths around axons are formed by glial cells named oligodendrocytes (OLs). In turn, OLs are generated by oligodendrocyte precursor cells (OPCs) during postnatal development and in adults, according to a process that depends on the proliferation and differentiation of these progenitors. The maturation of OL lineage cells as well as myelination by OLs are complex and highly regulated processes in the CNS. OPCs and OLs express an array of receptors for neurotransmitters, in particular for the two main CNS neurotransmitters glutamate and GABA, and are therefore endowed with the capacity to respond to neuronal activity. Initial studies in cell cultures demonstrated that both glutamate and GABA signaling mechanisms play important roles in OL lineage cell development and function. However, much remains to be learned about the communication of glutamatergic and GABAergic neurons with oligodendroglia in vivo. This review focuses on recent major advances in our understanding of the neuron-oligodendroglia communication mediated by glutamate and GABA in the CNS, and highlights the present controversies in the field. We discuss the expression, activation modes and potential roles of synaptic and extrasynaptic receptors along OL lineage progression. We review the properties of OPC synaptic connectivity with presynaptic glutamatergic and GABAergic neurons in the brain and consider the implication of glutamate and GABA signaling in activity-driven adaptive myelination.

Leveraging heterogeneity for neural computation with fading memory in layer 2/3 cortical microcircuits

Complexity and heterogeneity are intrinsic to neurobiological systems, manifest in every process, at every scale, and are inextricably linked to the systems' emergent collective behaviours and function. However, the majority of studies addressing the dynamics and computational properties of biologically inspired cortical microcircuits tend to assume (often for the sake of analytical tractability) a great degree of homogeneity in both neuronal and synaptic/connectivity parameters. While simplification and reductionism are necessary to understand the brain's functional principles, disregarding the existence of the multiple heterogeneities in the cortical composition, which may be at the core of its computational proficiency, will inevitably fail to account for important phenomena and limit the scope and generalizability of cortical models. We address these issues by studying the individual and composite functional roles of heterogeneities in neuronal, synaptic and structural properties in a biophysically plausible layer 2/3 microcircuit model, built and constrained by multiple sources of empirical data. This approach was made possible by the emergence of large-scale, well curated databases, as well as the substantial improvements in experimental methodologies achieved over the last few years. Our results show that variability in single neuron parameters is the dominant source of functional specialization, leading to highly proficient microcircuits with much higher computational power than their homogeneous counterparts. We further show that fully heterogeneous circuits, which are closest to the biophysical reality, owe their response properties to the differential contribution of different sources of heterogeneity.

Synaptic mechanisms underlying the intense firing of neocortical layer 5B pyramidal neurons in response to cortico-cortical inputs

In the neocortex, large layer 5B pyramidal neurons implement a high-density firing code. In contrast, other subtypes of pyramidal neurons, including those in layer 2/3, are functionally characterized by their sparse firing rate. Here, we investigate the synaptic basis of this behavior by comparing the properties of the postsynaptic responses evoked by cortical inputs in layer 5B and layer 2/3 pyramidal neurons in vitro. We demonstrate that a major determinant of the larger responsiveness of layer 5B with respect to layer 2/3 pyramidal neurons is the different properties in their inhibitory postsynaptic currents (IPSCs): layer 5B pyramidal neurons have IPSCs of lower amplitude and the temporal delay between the excitatory and inhibitory synaptic components is also larger in these cells. Our data also suggest that this difference depends on the lower gain of the cortical response of layer 5 parvalbumin-positive fast-spiking (PV-FS) interneurons with respect to PV-FS cells from layer 2/3. We propose that, while superficial PV-FS interneurons are well suited to provide a powerful feed-forward inhibitory control of pyramidal neuron responses, layer 5 PV-FS interneurons are mainly engaged in a feedback inhibitory loop and only after a substantial recruitment of surrounding pyramidal cells do they respond to an external input.

Compensatory Relearning Following Stroke: Cellular and Plasticity Mechanisms in Rodents

von Monakow’s theory of diaschisis states the functional ‘standstill’ of intact brain regions that are remote from a damaged area, often implied in recovery of function. Accordingly, neural plasticity and activity patterns related to recovery are also occurring at the same regions. Recovery relies on plasticity in the periinfarct and homotopic contralesional regions and involves relearning to perform movements. Seeking evidence for a relearning mechanism following stroke, we found that rodents display many features that resemble classical learning and memory mechanisms. Compensatory relearning is likely to be accompanied by gradual shaping of these regions and pathways, with participating neurons progressively adapting cortico-striato-thalamic activity and synaptic strengths at different cortico-thalamic loops – adapting function relayed by the striatum. Motor cortex functional maps are progressively reinforced and shaped by these loops as the striatum searches for different functional actions. Several cortical and striatal cellular mechanisms that influence motor learning may also influence post-stroke compensatory relearning. Future research should focus on how different neuromodulatory systems could act before, during or after rehabilitation to improve stroke recovery.

Network structure and input integration in competing firing rate models for decision-making

Making a decision among numerous alternatives is a pervasive and central undertaking encountered by mammals in natural settings. While decision making for two-option tasks has been studied extensively both experimentally and theoretically, characterizing decision making in the face of a large set of alternatives remains challenging. We explore this issue by formulating a scalable mechanistic network model for decision making and analyzing the dynamics evoked given various potential network structures. In the case of a fully-connected network, we provide an analytical characterization of the model fixed points and their stability with respect to winner-take-all behavior for fair tasks. We compare several means of input integration, demonstrating a more gradual sigmoidal transfer function is likely evolutionarily advantageous relative to binary gain commonly utilized in engineered systems. We show via asymptotic analysis and numerical simulation that sigmoidal transfer functions with smaller steepness yield faster response times but depreciation in accuracy. However, in the presence of noise or degradation of connections, a sigmoidal transfer function garners significantly more robust and accurate decision-making dynamics. For fair tasks and sigmoidal gain, our model network also exhibits a stable parameter regime that produces high accuracy and persists across tasks with diverse numbers of alternatives and difficulties, satisfying physiological energetic constraints. In the case of more sparse and structured network topologies, including random, regular, and small-world connectivity, we show the high-accuracy parameter regime persists for biologically realistic connection densities. Our work shows how neural system architecture is potentially optimal in making economic, reliable, and advantageous decisions across tasks.

A simplified morphological classification scheme for pyramidal cells in six layers of primary somatosensory cortex of juvenile rats

The majority of neurons in the neocortex are excitatory pyramidal cells (PCs). Many systematic classification schemes have been proposed based the neuronal morphology, the chemical composition, and the synaptic connectivity, etc. Recently, a cortical column of primary somatosensory cortex (SSC) has been reconstruction and functionally simulated (Markram et al., 2015). Putting forward from this study, here we proposed a simplified classification scheme for PCs in all layers of the SSC by mainly identifying apical dendritic morphology based on a large data set of 3D neuron reconstructions. We used this scheme to classify three types in layer 2, two in layer 3, three in layer 4, four in layer 5, and six types in layer 6. These PC types were visually distinguished and confirmed by quantitative differences in their morphometric properties. The classes yielded using this scheme largely corresponded with PC classes that were defined previously based on other neuronal and synaptic properties such as long-range projects and synaptic innervations, further validating its applicability. Therefore, the morphology information of apical dendrites is sufficient for a simple scheme to classify a spectrum of anatomical types of PCs in the SSC.

Synaptic topography - Converging connections and emerging function

Brain circuits are constituted of individual neurons that are interconnected with a vast array of synapses. In order to understand how brain function emerges from this complex synaptic network, immense efforts have been made to trace the synaptic topography, i.e. arrangement of synaptic connections, of the network. In addition to anatomically elaborating the synaptic layout at multiple levels across brain regions, recent studies have attempted to elucidate the fundamental wiring principles that govern neural information processing in the brain, establishing a link between anatomy and function. In this review, I will discuss recent discoveries on the topographical organization of synaptic connections at the cell-to-cell and subcellular levels in the cortex and hippocampus. Accumulating evidence leads us to acknowledge the highly structured, non-random synaptic connectivity that emerges together with sensory feature preferences of neurons and synchronous neuronal activity.

Autapses enhance bursting and coincidence detection in neocortical pyramidal cells

Autapses are synaptic contacts of a neuron’s axon onto its own dendrite and soma. In the neocortex, self-inhibiting autapses in GABAergic interneurons are abundant in number and play critical roles in regulating spike precision and network activity. Here we examine whether the principal glutamatergic pyramidal cells (PCs) also form functional autapses. In patch-clamp recording from both rodent and human PCs, we isolated autaptic responses and found that these occur predominantly in layer-5 PCs projecting to subcortical regions, with very few in those projecting to contralateral prefrontal cortex and layer 2/3 PCs. Moreover, PC autapses persist during development into adulthood. Surprisingly, they produce giant postsynaptic responses (∼5 fold greater than recurrent PC-PC synapses) that are exclusively mediated by AMPA receptors. Upon activation, autapses enhance burst firing, neuronal responsiveness and coincidence detection of synaptic inputs. These findings indicate that PC autapses are functional and represent an important circuit element in the neocortex.

While autapses are synapses made by a neuron onto itself, its functional significance in pyramidal cells are not clear. Here, the authors show that in the mammalian neocortex, autapses of pyramidal cells can enhance burst firing and coincidence detection from other inputs.

Correlations between synapses in pairs of neurons slow down dynamics in randomly connected neural networks

Networks of randomly connected neurons are among the most popular models in theoretical neuroscience. The connectivity between neurons in the cortex is however not fully random, the simplest and most prominent deviation from randomness found in experimental data being the overrepresentation of bidirectional connections among pyramidal cells. Using numerical and analytical methods, we investigate the effects of partially symmetric connectivity on the dynamics in networks of rate units. We consider the two dynamical regimes exhibited by random neural networks: the weak-coupling regime, where the firing activity decays to a single fixed point unless the network is stimulated, and the strong-coupling or chaotic regime, characterized by internally generated fluctuating firing rates. In the weak-coupling regime, we compute analytically, for an arbitrary degree of symmetry, the autocorrelation of network activity in the presence of external noise. In the chaotic regime, we perform simulations to determine the timescale of the intrinsic fluctuations. In both cases, symmetry increases the characteristic asymptotic decay time of the autocorrelation function and therefore slows down the dynamics in the network.

Propagation delays determine neuronal activity and synaptic connectivity patterns emerging in plastic neuronal networks

In plastic neuronal networks, the synaptic strengths are adapted to the neuronal activity. Specifically, spike-timing-dependent plasticity (STDP) is a fundamental mechanism that modifies the synaptic strengths based on the relative timing of pre- and postsynaptic spikes, taking into account the spikes' temporal order. In many studies, propagation delays were neglected to avoid additional dynamic complexity or computational costs. So far, networks equipped with a classic STDP rule typically rule out bidirectional couplings (i.e., either loops or uncoupled states) and are, hence, not able to reproduce fundamental experimental findings. In this review paper, we consider additional features, e.g., extensions of the classic STDP rule or additional aspects like noise, in order to overcome the contradictions between theory and experiment. In addition, we review in detail recent studies showing that a classic STDP rule combined with realistic propagation patterns is able to capture relevant experimental findings. In two coupled oscillatory neurons with propagation delays, bidirectional synapses can be preserved and potentiated. This result also holds for large networks of type-II phase oscillators. In addition, not only the mean of the initial distribution of synaptic weights, but also its standard deviation crucially determines the emergent structural connectivity, i.e., the mean final synaptic weight, the number of two-neuron loops, and the symmetry of the final connectivity pattern. The latter is affected by the firing rates, where more symmetric synaptic configurations emerge at higher firing rates. Finally, we discuss these findings in the context of the computational neuroscience-based development of desynchronizing brain stimulation techniques.

Dendritic solutions to the credit assignment problem

Guaranteeing that synaptic plasticity leads to effective learning requires a means for assigning credit to each neuron for its contribution to behavior. The 'credit assignment problem' refers to the fact that credit assignment is non-trivial in hierarchical networks with multiple stages of processing. One difficulty is that if credit signals are integrated with other inputs, then it is hard for synaptic plasticity rules to distinguish credit-related activity from non-credit-related activity. A potential solution is to use the spatial layout and non-linear properties of dendrites to distinguish credit signals from other inputs. In cortical pyramidal neurons, evidence hints that top-down feedback signals are integrated in the distal apical dendrites and have a distinct impact on spike-firing and synaptic plasticity. This suggests that the distal apical dendrites of pyramidal neurons help the brain to solve the credit assignment problem.

The impact of spike-frequency adaptation on balanced network dynamics

A dynamic balance between strong excitatory and inhibitory neuronal inputs is hypothesized to play a pivotal role in information processing in the brain. While there is evidence of the existence of a balanced operating regime in several cortical areas and idealized neuronal network models, it is important for the theory of balanced networks to be reconciled with more physiological neuronal modeling assumptions. In this work, we examine the impact of spike-frequency adaptation, observed widely across neurons in the brain, on balanced dynamics. We incorporate adaptation into binary and integrate-and-fire neuronal network models, analyzing the theoretical effect of adaptation in the large network limit and performing an extensive numerical investigation of the model adaptation parameter space. Our analysis demonstrates that balance is well preserved for moderate adaptation strength even if the entire network exhibits adaptation. In the common physiological case in which only excitatory neurons undergo adaptation, we show that the balanced operating regime in fact widens relative to the non-adaptive case. We hypothesize that spike-frequency adaptation may have been selected through evolution to robustly facilitate balanced dynamics across diverse cognitive operating states.

FluoEM, virtual labeling of axons in three-dimensional electron microscopy data for long-range connectomics

The labeling and identification of long-range axonal inputs from multiple sources within densely reconstructed electron microscopy (EM) datasets from mammalian brains has been notoriously difficult because of the limited color label space of EM. Here, we report FluoEM for the identification of multi-color fluorescently labeled axons in dense EM data without the need for artificial fiducial marks or chemical label conversion. The approach is based on correlated tissue imaging and computational matching of neurite reconstructions, amounting to a virtual color labeling of axons in dense EM circuit data. We show that the identification of fluorescent light- microscopically (LM) imaged axons in 3D EM data from mouse cortex is faithfully possible as soon as the EM dataset is about 40-50 µm in extent, relying on the unique trajectories of axons in dense mammalian neuropil. The method is exemplified for the identification of long-distance axonal input into layer 1 of the mouse cerebral cortex.

Delay-Induced Multistability and Loop Formation in Neuronal Networks with Spike-Timing-Dependent Plasticity

Spike-timing-dependent plasticity (STDP) adjusts synaptic strengths according to the precise timing of pre- and postsynaptic spike pairs. Theoretical and computational studies have revealed that STDP may contribute to the emergence of a variety of structural and dynamical states in plastic neuronal populations. In this manuscript, we show that by incorporating dendritic and axonal propagation delays in recurrent networks of oscillatory neurons, the asymptotic connectivity displays multistability, where different structures emerge depending on the initial distribution of the synaptic strengths. In particular, we show that the standard deviation of the initial distribution of synaptic weights, besides its mean, determines the main properties of the emergent structural connectivity such as the mean final synaptic weight, the number of two-neuron loops and the symmetry of the final structure. We also show that the firing rates of the neurons affect the evolution of the network, and a more symmetric configuration of the synapses emerges at higher firing rates. We justify the network results based on a two-neuron framework and show how the results translate to large recurrent networks.

Structural Properties of Synaptic Transmission and Temporal Dynamics at Excitatory Layer 5B Synapses in the Adult Rat Somatosensory Cortex

Cortical computations rely on functionally diverse and highly dynamic synapses. How their structural composition affects synaptic transmission and plasticity and whether they support functional diversity remains rather unclear. Here, synaptic boutons on layer 5B (L5B) pyramidal neurons in the adult rat barrel cortex were investigated. Simultaneous patch-clamp recordings from synaptically connected L5B pyramidal neurons revealed great heterogeneity in amplitudes, coefficients of variation (CVs), and failures (F%) of EPSPs. Quantal analysis indicated multivesicular release as a likely source of this variability. Trains of EPSPs decayed with fast and slow time constants, presumably representing release from small readily releasable (RRP; 5.40 ± 1.24 synaptic vesicles) and large recycling (RP; 74 ± 21 synaptic vesicles) pools that were independent and highly variable at individual synaptic contacts (RRP range 1.2–12.8 synaptic vesicles; RP range 3.4–204 synaptic vesicles). Most presynaptic boutons (~85%) had a single, often perforated active zone (AZ) with a ~2 to 5-fold larger pre- (0.29 ± 0.19 μm²) and postsynaptic density (0.31 ± 0.21 μm²) when compared with even larger CNS synaptic boutons. They contained 200–3400 vesicles (mean ~800). At the AZ, ~4 and ~12 vesicles were located within a perimeter of 10 and 20 nm, reflecting docked and readily releasable vesicles of a putative RRP. Vesicles (~160) at 60–200 nm constituting the structural estimate of the presumed RP were ~2-fold larger than our functional estimate of the RP although both with a high variability. The remaining constituted a presumed large resting pool. Multivariate analysis revealed two clusters of L5B synaptic boutons distinguished by the size of their resting pool. Our functional and ultrastructural analyses closely link stationary properties, temporal dynamics and endurance of synaptic transmission to vesicular content and distribution within the presynaptic boutons suggesting that functional diversity of L5B synapses is enhanced by their structural heterogeneity.

Criteria on Balance, Stability, and Excitability in Cortical Networks for Constraining Computational Models

During ongoing and Up state activity, cortical circuits manifest a set of dynamical features that are conserved across these states. The present work systematizes these phenomena by three notions: excitability, the ability to sustain activity without external input; balance, precise coordination of excitatory and inhibitory neuronal inputs; and stability, maintenance of activity at a steady level. Slice preparations exhibiting Up states demonstrate that balanced activity can be maintained by small local circuits. While computational models of cortical circuits have included different combinations of excitability, balance, and stability, they have done so without a systematic quantitative comparison with experimental data. Our study provides quantitative criteria for this purpose, by analyzing in-vitro and in-vivo neuronal activity and characterizing the dynamics on the neuronal and population levels. The criteria are defined with a tolerance that allows for differences between experiments, yet are sufficient to capture commonalities between persistently depolarized cortical network states and to help validate computational models of cortex. As test cases for the derived set of criteria, we analyze three widely used models of cortical circuits and find that each model possesses some of the experimentally observed features, but none satisfies all criteria simultaneously, showing that the criteria are able to identify weak spots in computational models. The criteria described here form a starting point for the systematic validation of cortical neuronal network models, which will help improve the reliability of future models, and render them better building blocks for larger models of the brain.

The development of local circuits in the neocortex: recent lessons from the mouse visual cortex

Precise synaptic connections among neurons in the neocortex generate the circuits that underlie a broad repertoire of cortical functions including perception, learning and memory, and complex problem solving. The specific patterns and properties of these synaptic connections are fundamental to the computations cortical neurons perform. How such specificity arises in cortical circuits has remained elusive. Here, we first consider the cell-type, subcellular and synaptic specificity required for generating mature patterns of cortical connectivity and responses. Next, we focus on recent progress in understanding how the synaptic connections among excitatory cortical projection neurons are established during development using the primary visual cortex of the mouse as a model.

Attractor Dynamics in Networks with Learning Rules Inferred from In Vivo Data

The attractor neural network scenario is a popular scenario for memory storage in the association cortex, but there is still a large gap between models based on this scenario and experimental data. We study a recurrent network model in which both learning rules and distribution of stored patterns are inferred from distributions of visual responses for novel and familiar images in the inferior temporal cortex (ITC). Unlike classical attractor neural network models, our model exhibits graded activity in retrieval states, with distributions of firing rates that are close to lognormal. Inferred learning rules are close to maximizing the number of stored patterns within a family of unsupervised Hebbian learning rules, suggesting that learning rules in ITC are optimized to store a large number of attractor states. Finally, we show that there exist two types of retrieval states: one in which firing rates are constant in time and another in which firing rates fluctuate chaotically.

Redundancy in synaptic connections enables neurons to learn optimally

Recent experimental studies suggest that, in cortical microcircuits of the mammalian brain, the majority of neuron-to-neuron connections are realized by multiple synapses. However, it is not known whether such redundant synaptic connections provide any functional benefit. Here, we show that redundant synaptic connections enable near-optimal learning in cooperation with synaptic rewiring. By constructing a simple dendritic neuron model, we demonstrate that with multisynaptic connections synaptic plasticity approximates a sample-based Bayesian filtering algorithm known as particle filtering, and wiring plasticity implements its resampling process. Extending the proposed framework to a detailed single-neuron model of perceptual learning in the primary visual cortex, we show that the model accounts for many experimental observations. In particular, the proposed model reproduces the dendritic position dependence of spike-timing-dependent plasticity and the functional synaptic organization on the dendritic tree based on the stimulus selectivity of presynaptic neurons. Our study provides a conceptual framework for synaptic plasticity and rewiring.

Human Cortical Pyramidal Neurons: From Spines to Spikes via Models

We present detailed models of pyramidal cells from human neocortex, including models on their excitatory synapses, dendritic spines, dendritic NMDA- and somatic/axonal Na⁺ spikes that provided new insights into signal processing and computational capabilities of these principal cells. Six human layer 2 and layer 3 pyramidal cells (HL2/L3 PCs) were modeled, integrating detailed anatomical and physiological data from both fresh and postmortem tissues from human temporal cortex. The models predicted particularly large AMPA- and NMDA-conductances per synaptic contact (0.88 and 1.31 nS, respectively) and a steep dependence of the NMDA-conductance on voltage. These estimates were based on intracellular recordings from synaptically-connected HL2/L3 pairs, combined with extra-cellular current injections and use of synaptic blockers, and the assumption of five contacts per synaptic connection. A large dataset of high-resolution reconstructed HL2/L3 dendritic spines provided estimates for the EPSPs at the spine head (12.7 ± 4.6 mV), spine base (9.7 ± 5.0 mV), and soma (0.3 ± 0.1 mV), and for the spine neck resistance (50–80 MΩ). Matching the shape and firing pattern of experimental somatic Na⁺-spikes provided estimates for the density of the somatic/axonal excitable membrane ion channels, predicting that 134 ± 28 simultaneously activated HL2/L3-HL2/L3 synapses are required for generating (with 50% probability) a somatic Na⁺ spike. Dendritic NMDA spikes were triggered in the model when 20 ± 10 excitatory spinous synapses were simultaneously activated on individual dendritic branches. The particularly large number of basal dendrites in HL2/L3 PCs and the distinctive cable elongation of their terminals imply that ~25 NMDA-spikes could be generated independently and simultaneously in these cells, as compared to ~14 in L2/3 PCs from the rat somatosensory cortex. These multi-sites non-linear signals, together with the large (~30,000) excitatory synapses/cell, equip human L2/L3 PCs with enhanced computational capabilities. Our study provides the most comprehensive model of any human neuron to-date demonstrating the biophysical and computational distinctiveness of human cortical neurons.

Morphological Diversity Strongly Constrains Synaptic Connectivity and Plasticity

Synaptic connectivity between neurons is naturally constrained by the anatomical overlap of neuronal arbors, the space on the axon available for synapses, and by physiological mechanisms that form synapses at a subset of potential synapse locations. What is not known is how these constraints impact emergent connectivity in a circuit with diverse morphologies. We investigated the role of morphological diversity within and across neuronal types on emergent connectivity in a model of neocortical microcircuitry. We found that the average overlap between the dendritic and axonal arbors of different types of neurons determines neuron-type specific patterns of distance-dependent connectivity, severely constraining the space of possible connectomes. However, higher order connectivity motifs depend on the diverse branching patterns of individual arbors of neurons belonging to the same type. Morphological diversity across neuronal types, therefore, imposes a specific structure on first order connectivity, and morphological diversity within neuronal types imposes a higher order structure of connectivity. We estimate that the morphological constraints resulting from diversity within and across neuron types together lead to a 10-fold reduction of the entropy of possible connectivity configurations, revealing an upper bound on the space explored by structural plasticity.

3D morphology-based clustering and simulation of human pyramidal cell dendritic spines

The dendritic spines of pyramidal neurons are the targets of most excitatory synapses in the cerebral cortex. They have a wide variety of morphologies, and their morphology appears to be critical from the functional point of view. To further characterize dendritic spine geometry, we used in this paper over 7,000 individually 3D reconstructed dendritic spines from human cortical pyramidal neurons to group dendritic spines using model-based clustering. This approach uncovered six separate groups of human dendritic spines. To better understand the differences between these groups, the discriminative characteristics of each group were identified as a set of rules. Model-based clustering was also useful for simulating accurate 3D virtual representations of spines that matched the morphological definitions of each cluster. This mathematical approach could provide a useful tool for theoretical predictions on the functional features of human pyramidal neurons based on the morphology of dendritic spines.

Dendritic spines of pyramidal neurons are the targets of most excitatory synapses in the cerebral cortex and their morphology appears to be critical from the functional point of view. Thus, characterizing this morphology is necessary to link structural and functional spine data and thus interpret and make them more meaningful. We have used a large database of more than 7,000 individually 3D reconstructed dendritic spines from human cortical pyramidal neurons that is first transformed into a set of 54 quantitative features characterizing spine geometry mathematically. The resulting data set is grouped into spine clusters based on a probabilistic model with Gaussian finite mixtures. We uncover six groups of spines whose discriminative characteristics are identified with machine learning methods as a set of rules. The clustering model allows us to simulate accurate spines from human pyramidal neurons to suggest new hypotheses of the functional organization of these cells.

Single synaptic inputs drive high-precision action potentials in parvalbumin expressing GABA-ergic cortical neurons in vivo

A defining feature of cortical layer 2/3 excitatory neurons is their sparse activity, often firing in singlets of action potentials. Local inhibitory neurons are thought to play a major role in regulating sparseness, but which cell types are recruited by single excitatory synaptic inputs is unknown. Using multiple, targeted, in vivo whole-cell recordings, we show that single _uEPSPs have little effect on the firing rates of excitatory neurons and somatostatin-expressing GABA-ergic inhibitory neurons but evoke precisely timed action potentials in parvalbumin-expressing inhibitory neurons. Despite a _uEPSP decay time of 7.8 ms, the evoked action potentials were almost completely restricted to the _uEPSP rising phase (~0.5 ms). Evoked parvalbumin-expressing neuron action potentials go on to inhibit the local excitatory network, thus providing a pathway for single spike evoked disynaptic inhibition which may enforce sparse and precisely timed cortical signaling.

Long-term potentiation expands information content of hippocampal dentate gyrus synapses

An approach combining signal detection theory and precise 3D reconstructions from serial section electron microscopy (3DEM) was used to investigate synaptic plasticity and information storage capacity at medial perforant path synapses in adult hippocampal dentate gyrus in vivo. Induction of long-term potentiation (LTP) markedly increased the frequencies of both small and large spines measured 30 minutes later. This bidirectional expansion resulted in heterosynaptic counterbalancing of total synaptic area per unit length of granule cell dendrite. Control hemispheres exhibited 6.5 distinct spine sizes for 2.7 bits of storage capacity while LTP resulted in 12.9 distinct spine sizes (3.7 bits). In contrast, control hippocampal CA1 synapses exhibited 4.7 bits with much greater synaptic precision than either control or potentiated dentate gyrus synapses. Thus, synaptic plasticity altered total capacity, yet hippocampal subregions differed dramatically in their synaptic information storage capacity, reflecting their diverse functions and activation histories.

Translaminar circuits formed by the pyramidal cells in the superficial layers of cat visual cortex

Pyramidal cells in the superficial layers of the neocortex provide a major excitatory projection to layer 5, which contains the pyramidal cells that project to subcortical motor-related targets. Both structurally and functionally rather little is known about this interlaminar pathway, especially in higher mammals. Here, we made sparse ultrastructural reconstructions of the projection to layer 5 of three pyramidal neurons from layer 3 in cat V1 whose morphology, physiology, and synaptic connections with layers 2 and 3 were known. The dominant targets of the 74 identified synapses in layer 5 were the dendritic spines of pyramidal cells. The fractions of target spiny dendrites were 59, 61, and 84% for the three cells, with the remaining targets being dendrites of smooth neurons. These fractions were similar to the distribution of targets of unlabeled asymmetric synapses in the surrounding neuropil. Serial section reconstructions revealed that the target dendrites were heterogenous in morphology, indicating that different cell types are innervated. This new evidence indicates that the descending projection from the superficial layer pyramidal cells does not simply drive the output pyramidal cells that project to cortical and subcortical targets, but participates in the complex circuitry of the deep cortical layers.

Functional consequences of pre- and postsynaptic expression of synaptic plasticity

Growing experimental evidence shows that both homeostatic and Hebbian synaptic plasticity can be expressed presynaptically as well as postsynaptically. In this review, we start by discussing this evidence and methods used to determine expression loci. Next, we discuss the functional consequences of this diversity in pre- and postsynaptic expression of both homeostatic and Hebbian synaptic plasticity. In particular, we explore the functional consequences of a biologically tuned model of pre- and postsynaptically expressed spike-timing-dependent plasticity complemented with postsynaptic homeostatic control. The pre- and postsynaptic expression in this model predicts (i) more reliable receptive fields and sensory perception, (ii) rapid recovery of forgotten information (memory savings), and (iii) reduced response latencies, compared with a model with postsynaptic expression only. Finally, we discuss open questions that will require a considerable research effort to better elucidate how the specific locus of expression of homeostatic and Hebbian plasticity alters synaptic and network computations.This article is part of the themed issue 'Integrating Hebbian and homeostatic plasticity'.

Long Synfire Chains Emerge by Spike-Timing Dependent Plasticity Modulated by Population Activity

Sequences of precisely timed neuronal activity are observed in many brain areas in various species. Synfire chains are a well-established model that can explain such sequences. However, it is unknown under which conditions synfire chains can develop in initially unstructured networks by self-organization. This work shows that with spike-timing dependent plasticity (STDP), modulated by global population activity, long synfire chains emerge in sparse random networks. The learning rule fosters neurons to participate multiple times in the chain or in multiple chains. Such reuse of neurons has been experimentally observed and is necessary for high capacity. Sparse networks prevent the chains from being short and cyclic and show that the formation of specific synapses is not essential for chain formation. Analysis of the learning rule in a simple network of binary threshold neurons reveals the asymptotically optimal length of the emerging chains. The theoretical results generalize to simulated networks of conductance-based leaky integrate-and-fire (LIF) neurons. As an application of the emerged chain, we propose a one-shot memory for sequences of precisely timed neuronal activity.

Dendritic small conductance calcium-activated potassium channels activated by action potentials suppress EPSPs and gate spike-timing dependent synaptic plasticity

Small conductance calcium-activated potassium channels (SK channels) are present in spines and can be activated by backpropagating action potentials (APs). This suggests they may play a critical role in spike-timing dependent synaptic plasticity (STDP). Consistent with this idea, EPSPs in both cortical and hippocampal pyramidal neurons were suppressed by preceding APs in an SK-dependent manner. In cortical pyramidal neurons EPSP suppression by preceding APs depended on their precise timing as well as the distance of activated synapses from the soma, was dendritic in origin, and involved SK-dependent suppression of NMDA receptor activation. As a result SK channel activation by backpropagating APs gated STDP induction during low-frequency AP-EPSP pairing, with both LTP and LTD absent under control conditions but present after SK channel block. These findings indicate that activation of SK channels in spines by backpropagating APs plays a key role in regulating both EPSP amplitude and STDP induction.

Synaptic Transmission Optimization Predicts Expression Loci of Long-Term Plasticity

Long-term modifications of neuronal connections are critical for reliable memory storage in the brain. However, their locus of expression-pre- or postsynaptic-is highly variable. Here we introduce a theoretical framework in which long-term plasticity performs an optimization of the postsynaptic response statistics toward a given mean with minimal variance. Consequently, the state of the synapse at the time of plasticity induction determines the ratio of pre- and postsynaptic modifications. Our theory explains the experimentally observed expression loci of the hippocampal and neocortical synaptic potentiation studies we examined. Moreover, the theory predicts presynaptic expression of long-term depression, consistent with experimental observations. At inhibitory synapses, the theory suggests a statistically efficient excitatory-inhibitory balance in which changes in inhibitory postsynaptic response statistics specifically target the mean excitation. Our results provide a unifying theory for understanding the expression mechanisms and functions of long-term synaptic transmission plasticity.

Whole-Cell Recording of Neuronal Membrane Potential during Behavior

Neuronal membrane potential is of fundamental importance for the mechanistic understanding of brain function. This review discusses progress in whole-cell patch-clamp recordings for low-noise measurement of neuronal membrane potential in awake behaving animals. Whole-cell recordings can be combined with two-photon microscopy to target fluorescently labeled neurons, revealing cell-type-specific membrane potential dynamics of retrogradely or genetically labeled neurons. Dual whole-cell recordings reveal behavioral modulation of membrane potential synchrony and properties of synaptic transmission in vivo. Optogenetic manipulations are also readily integrated with whole-cell recordings, providing detailed information about the effect of specific perturbations on the membrane potential of diverse types of neurons. Exciting developments for future behavioral experiments include dendritic whole-cell recordings and imaging, and use of the whole-cell recording pipette for single-cell delivery of drugs and DNA, as well as RNA expression profiling. Whole-cell recordings therefore offer unique opportunities for investigating the neuronal circuits and synaptic mechanisms driving membrane potential dynamics during behavior.

Modeling somatic and dendritic spike mediated plasticity at the single neuron and network level

Synaptic plasticity is thought to be the principal neuronal mechanism underlying learning. Models of plastic networks typically combine point neurons with spike-timing-dependent plasticity (STDP) as the learning rule. However, a point neuron does not capture the local non-linear processing of synaptic inputs allowed for by dendrites. Furthermore, experimental evidence suggests that STDP is not the only learning rule available to neurons. By implementing biophysically realistic neuron models, we study how dendrites enable multiple synaptic plasticity mechanisms to coexist in a single cell. In these models, we compare the conditions for STDP and for synaptic strengthening by local dendritic spikes. We also explore how the connectivity between two cells is affected by these plasticity rules and by different synaptic distributions. Finally, we show that how memory retention during associative learning can be prolonged in networks of neurons by including dendrites.

Synaptic plasticity is the neuronal mechanism underlying learning. Here the authors construct biophysical models of pyramidal neurons that reproduce observed plasticity gradients along the dendrite and show that dendritic spike dependent LTP which is predominant in distal sections can prolong memory retention.

Following Spinal Cord Injury Transected Reticulospinal Tract Axons Develop New Collateral Inputs to Spinal Interneurons in Parallel with Locomotor Recovery

The reticulospinal tract (RtST) descends from the reticular formation and terminates in the spinal cord. The RtST drives the initiation of locomotion and postural control. RtST axons form new contacts with propriospinal interneurons (PrINs) after incomplete spinal cord injury (SCI); however, it is unclear if injured or uninjured axons make these connections. We completely transected all traced RtST axons in rats using a staggered model, where a hemisection SCI at vertebra T10 is followed by a contralateral hemisection at vertebra T7. In one group of the animals, the T7 SCI was performed 2 weeks after the T10 SCI (delayed; dSTAG), and in another group, the T10 and T7 SCIs were concomitant (cSTAG). dSTAG animals had significantly more RtST-PrIN contacts in the grey matter compared to cSTAG animals (p < 0.05). These results were accompanied by enhanced locomotor recovery with dSTAG animals significantly outperforming cSTAG animals (BBB test; p < 0.05). This difference suggests that activity in neuronal networks below the first SCI may contribute to enhanced recovery, because dSTAG rats recovered locomotor ability before the second hemisection. In conclusion, our findings support the hypothesis that the injured RtST forms new connections and is a key player in the recovery of locomotion post-SCI.

Latching dynamics in neural networks with synaptic depression

Prediction is the ability of the brain to quickly activate a target concept in response to a related stimulus (prime). Experiments point to the existence of an overlap between the populations of the neurons coding for different stimuli, and other experiments show that prime-target relations arise in the process of long term memory formation. The classical modelling paradigm is that long term memories correspond to stable steady states of a Hopfield network with Hebbian connectivity. Experiments show that short term synaptic depression plays an important role in the processing of memories. This leads naturally to a computational model of priming, called latching dynamics; a stable state (prime) can become unstable and the system may converge to another transiently stable steady state (target). Hopfield network models of latching dynamics have been studied by means of numerical simulation, however the conditions for the existence of this dynamics have not been elucidated. In this work we use a combination of analytic and numerical approaches to confirm that latching dynamics can exist in the context of a symmetric Hebbian learning rule, however lacks robustness and imposes a number of biologically unrealistic restrictions on the model. In particular our work shows that the symmetry of the Hebbian rule is not an obstruction to the existence of latching dynamics, however fine tuning of the parameters of the model is needed.

Note on the coefficient of variations of neuronal spike trains

It is known that many neurons in the brain show spike trains with a coefficient of variation (CV) of the interspike times of approximately 1, thus resembling the properties of Poisson spike trains. Computational studies have been able to reproduce this phenomenon. However, the underlying models were too complex to be examined analytically. In this paper, we offer a simple model that shows the same effect but is accessible to an analytic treatment. The model is a random walk model with a reflecting barrier; we give explicit formulas for the CV in the regime of excess inhibition. We also analyze the effect of probabilistic synapses in our model and show that it resembles previous findings that were obtained by simulation.