Convergence among Non-Sister Dendritic Branches: An Activity-Controlled Mean to Strengthen Network Connectivity

The manner by which axons distribute synaptic connections along dendrites remains a fundamental unresolved issue in neuronal development and physiology. We found in vitro and in vivo indications that dendrites determine the density, location and strength of their synaptic inputs by controlling the distance of their branches from those of their neighbors. Such control occurs through collective branch convergence, a behavior promoted by AMPA and NMDA glutamate receptor activity. At hubs of convergence sites, the incidence of axo-dendritic contacts as well as clustering levels, pre- and post-synaptic protein content and secretion capacity of synaptic connections are higher than found elsewhere. This coupling between synaptic distribution and the pattern of dendritic overlapping results in ‘Economical Small World Network’, a network configuration that enables single axons to innervate multiple and remote dendrites using short wiring lengths. Thus, activity-mediated regulation of the proximity among dendritic branches serves to pattern and strengthen neuronal connectivity.     

Burst control: Synaptic conditions for burst generation in cortical layer 5 pyramidal neurons

The output of neocortical layer 5 pyramidal cells (L5PCs) is expressed by a train of single spikes with intermittent bursts of multiple spikes at high frequencies. The bursts are the result of nonlinear dendritic properties, including Na⁺, Ca²⁺, and NMDA spikes, that interact with the ~10,000 synapses impinging on the neuron’s dendrites. Output spike bursts are thought to implement key dendritic computations, such as coincidence detection of bottom-up inputs (arriving mostly at the basal tree) and top-down inputs (arriving mostly at the apical tree). In this study we used a detailed nonlinear model of L5PC receiving excitatory and inhibitory synaptic inputs to explore the conditions for generating bursts and for modulating their properties. We established the excitatory input conditions on the basal versus the apical tree that favor burst and show that there are two distinct types of bursts. Bursts consisting of 3 or more spikes firing at < 200 Hz, which are generated by stronger excitatory input to the basal versus the apical tree, and bursts of ~2-spikes at ~250 Hz, generated by prominent apical tuft excitation. Localized and well-timed dendritic inhibition on the apical tree differentially modulates Na⁺, Ca²⁺, and NMDA spikes and, consequently, finely controls the burst output. Finally, we explored the implications of different burst classes and respective dendritic inhibition for regulating synaptic plasticity.     

Ion Channel Gradients in the Apical Tuft Region of CA1 Pyramidal Neurons

Dendritic ion channels play a critical role in shaping synaptic input and are fundamentally important for synaptic integration and plasticity. In the hippocampal region CA1, somato-dendritic gradients of AMPA receptors and the hyperpolarization-activated cation conductance (I_h) counteract the effects of dendritic filtering on the amplitude, time-course, and temporal integration of distal Schaffer collateral (SC) synaptic inputs within stratum radiatum (SR). While ion channel gradients in CA1 distal apical trunk dendrites within SR have been well characterized, little is known about the patterns of ion channel expression in the distal apical tuft dendrites within stratum lacunosum moleculare (SLM) that receive distinct input from the entorhinal cortex via perforant path (PP) axons. Here, we measured local ion channels densities within these distal apical tuft dendrites to determine if the somato-dendritic gradients of I_h and AMPA receptors extend into distal tuft dendrites. We also determined the densities of voltage-gated sodium channels and NMDA receptors. We found that the densities of AMPA receptors, I_h, and voltage-gated sodium channels are similar in tuft dendrites in SLM when compared with distal apical dendrites in SR, while the ratio of NMDA receptors to AMPA receptors increases in tuft dendrites relative to distal apical dendrites within SR. These data indicate that the somato-dendritic gradients of I_h and AMPA receptors in apical dendrites do not extend into the distal tuft, and the relative densities of voltage-gated sodium channels and NMDA receptors are poised to support nonlinear integration of correlated SC and PP input.     

Diverse processing underlying frequency integration in midbrain neurons of barn owls

Emergent response properties of sensory neurons depend on circuit connectivity and somatodendritic processing. Neurons of the barn owl’s external nucleus of the inferior colliculus (ICx) display emergence of spatial selectivity. These neurons use interaural time difference (ITD) as a cue for the horizontal direction of sound sources. ITD is detected by upstream brainstem neurons with narrow frequency tuning, resulting in spatially ambiguous responses. This spatial ambiguity is resolved by ICx neurons integrating inputs over frequency, a relevant processing in sound localization across species. Previous models have predicted that ICx neurons function as point neurons that linearly integrate inputs across frequency. However, the complex dendritic trees and spines of ICx neurons raises the question of whether this prediction is accurate. Data from in vivo intracellular recordings of ICx neurons were used to address this question. Results revealed diverse frequency integration properties, where some ICx neurons showed responses consistent with the point neuron hypothesis and others with nonlinear dendritic integration. Modeling showed that varied connectivity patterns and forms of dendritic processing may underlie observed ICx neurons’ frequency integration processing. These results corroborate the ability of neurons with complex dendritic trees to implement diverse linear and nonlinear integration of synaptic inputs, of relevance for adaptive coding and learning, and supporting a fundamental mechanism in sound localization.     

NMDA receptor-mediated dendritic spikes and coincident signal amplification

Dendrites of cortical neurons possess active conductances, which contribute to the nonlinear processing of synaptic information. Recently it has been shown that basal dendrites can generate highly localized spikes mediated by NMDA receptor channels. These spikes may serve as a powerful mechanism to detect and amplify synchronously activated spatially clustered excitatory synaptic inputs in individual dendritic segments, and may enable parallel processing in several integrative dendritic subunits.     

Signal integration on the dendrites of a pyramidal neuron model

This paper studied the synaptic and dendritic integration with different spatial distributions of synapses on the dendrites of a biophysically-detailed layer 5 pyramidal neuron model. It has been observed that temporally synchronous and spatially clustered synaptic inputs make dendrites perform a highly nonlinear integration. The effect of clustering degree of synaptic distribution on neuronal responsiveness is investigated by changing the number of top apical dendrites where active synapses are allocated. The neuron shows maximum responsiveness to synaptic inputs which have an intermediate clustering degree of spatial distribution, indicating complex interactions among dendrites with the existence of nonlinear synaptic and dendritic integrations.     

Bidirectional changes in spatial dendritic integration accompanying long-term synaptic modifications

Information processing in the neuron requires spatial summation of synaptic inputs at the dendrite. In CA1 pyramidal neurons of the hippocampus, a brief period of correlated pre- and postsynaptic activity, which induces long-term potentiation (LTP) or long-term depression (LTD), results in a persistent increase or decrease in the linearity of spatial summation, respectively. Such bidirectional modification of the summation property is specific to the modified input and reflects localized dendritic changes involving I(h) channels and NMDA receptors. Thus, correlated pre- and postsynaptic activity alters not only the strength of the activated input but also its dendritic integration with other inputs.     

Computational simulation of the input-output relationship in hippocampal pyramidal cells

The precise mapping of how complex patterns of synaptic inputs are integrated into specific patterns of spiking output is an essential step in the characterization of the cellular basis of network dynamics and function. Relative to other principal neurons of the hippocampus, the electrophysiology of CA1 pyramidal cells has been extensively investigated. Yet, the precise input-output relationship is to date unknown even for this neuronal class. CA1 pyramidal neurons receive laminated excitatory inputs from three distinct pathways: recurrent CA1 collaterals on basal dendrites, CA3 Schaffer collaterals, mostly on oblique and proximal apical dendrites, and entorhinal perforant pathway on distal apical dendrites. We implemented detailed computer simulations of pyramidal cell electrophysiology based on three-dimensional anatomical reconstructions and compartmental models of available biophysical properties from the experimental literature. To investigate the effect of synaptic input on axosomatic firing, we stochastically distributed a realistic number of excitatory synapses in each of the three dendritic layers. We then recorded the spiking response to different stimulation patterns. For all dendritic layers, synchronous stimuli resulted in trains of spiking output and a linear relationship between input and output firing frequencies. In contrast, asynchronous stimuli evoked non-bursting spike patterns and the corresponding firing frequency input-output function was logarithmic. The regular/irregular nature of the input synaptic intervals was only reflected in the regularity of output inter-burst intervals in response to synchronous stimulation, and never affected firing frequency. Synaptic stimulations in the basal and proximal apical trees across individual neuronal morphologies yielded remarkably similar input-output relationships. Results were also robust with respect to the detailed distributions of dendritic and synaptic conductances within a plausible range constrained by experimental evidence. In contrast, the input-output relationship in response to distal apical stimuli showed dramatic differences from the other dendritic locations as well as among neurons, and was more sensible to the exact channel densities. Action Editor: Alain Destexhe     

Computing the Local Field Potential (LFP) from Integrate-and-Fire Network Models

Leaky integrate-and-fire (LIF) network models are commonly used to study how the spiking dynamics of neural networks changes with stimuli, tasks or dynamic network states. However, neurophysiological studies in vivo often rather measure the mass activity of neuronal microcircuits with the local field potential (LFP). Given that LFPs are generated by spatially separated currents across the neuronal membrane, they cannot be computed directly from quantities defined in models of point-like LIF neurons. Here, we explore the best approximation for predicting the LFP based on standard output from point-neuron LIF networks. To search for this best “LFP proxy”, we compared LFP predictions from candidate proxies based on LIF network output (e.g, firing rates, membrane potentials, synaptic currents) with “ground-truth” LFP obtained when the LIF network synaptic input currents were injected into an analogous three-dimensional (3D) network model of multi-compartmental neurons with realistic morphology, spatial distributions of somata and synapses. We found that a specific fixed linear combination of the LIF synaptic currents provided an accurate LFP proxy, accounting for most of the variance of the LFP time course observed in the 3D network for all recording locations. This proxy performed well over a broad set of conditions, including substantial variations of the neuronal morphologies. Our results provide a simple formula for estimating the time course of the LFP from LIF network simulations in cases where a single pyramidal population dominates the LFP generation, and thereby facilitate quantitative comparison between computational models and experimental LFP recordings in vivo.     

Phasic Firing in Vasopressin Cells: Understanding Its Functional Significance through Computational Models

Vasopressin neurons, responding to input generated by osmotic pressure, use an intrinsic mechanism to shift from slow irregular firing to a distinct phasic pattern, consisting of long bursts and silences lasting tens of seconds. With increased input, bursts lengthen, eventually shifting to continuous firing. The phasic activity remains asynchronous across the cells and is not reflected in the population output signal. Here we have used a computational vasopressin neuron model to investigate the functional significance of the phasic firing pattern. We generated a concise model of the synaptic input driven spike firing mechanism that gives a close quantitative match to vasopressin neuron spike activity recorded in vivo, tested against endogenous activity and experimental interventions. The integrate-and-fire based model provides a simple physiological explanation of the phasic firing mechanism involving an activity-dependent slow depolarising afterpotential (DAP) generated by a calcium-inactivated potassium leak current. This is modulated by the slower, opposing, action of activity-dependent dendritic dynorphin release, which inactivates the DAP, the opposing effects generating successive periods of bursting and silence. Model cells are not spontaneously active, but fire when perturbed by random perturbations mimicking synaptic input. We constructed one population of such phasic neurons, and another population of similar cells but which lacked the ability to fire phasically. We then studied how these two populations differed in the way that they encoded changes in afferent inputs. By comparison with the non-phasic population, the phasic population responds linearly to increases in tonic synaptic input. Non-phasic cells respond to transient elevations in synaptic input in a way that strongly depends on background activity levels, phasic cells in a way that is independent of background levels, and show a similar strong linearization of the response. These findings show large differences in information coding between the populations, and apparent functional advantages of asynchronous phasic firing.     

Bilinearity in Spatiotemporal Integration of Synaptic Inputs

Neurons process information via integration of synaptic inputs from dendrites. Many experimental results demonstrate dendritic integration could be highly nonlinear, yet few theoretical analyses have been performed to obtain a precise quantitative characterization analytically. Based on asymptotic analysis of a two-compartment passive cable model, given a pair of time-dependent synaptic conductance inputs, we derive a bilinear spatiotemporal dendritic integration rule. The summed somatic potential can be well approximated by the linear summation of the two postsynaptic potentials elicited separately, plus a third additional bilinear term proportional to their product with a proportionality coefficient . The rule is valid for a pair of synaptic inputs of all types, including excitation-inhibition, excitation-excitation, and inhibition-inhibition. In addition, the rule is valid during the whole dendritic integration process for a pair of synaptic inputs with arbitrary input time differences and input locations. The coefficient is demonstrated to be nearly independent of the input strengths but is dependent on input times and input locations. This rule is then verified through simulation of a realistic pyramidal neuron model and in electrophysiological experiments of rat hippocampal CA1 neurons. The rule is further generalized to describe the spatiotemporal dendritic integration of multiple excitatory and inhibitory synaptic inputs. The integration of multiple inputs can be decomposed into the sum of all possible pairwise integration, where each paired integration obeys the bilinear rule. This decomposition leads to a graph representation of dendritic integration, which can be viewed as functionally sparse.     

Memory Maintenance in Synapses with Calcium-Based Plasticity in the Presence of Background Activity

Most models of learning and memory assume that memories are maintained in neuronal circuits by persistent synaptic modifications induced by specific patterns of pre- and postsynaptic activity. For this scenario to be viable, synaptic modifications must survive the ubiquitous ongoing activity present in neural circuits in vivo. In this paper, we investigate the time scales of memory maintenance in a calcium-based synaptic plasticity model that has been shown recently to be able to fit different experimental data-sets from hippocampal and neocortical preparations. We find that in the presence of background activity on the order of 1 Hz parameters that fit pyramidal layer 5 neocortical data lead to a very fast decay of synaptic efficacy, with time scales of minutes. We then identify two ways in which this memory time scale can be extended: (i) the extracellular calcium concentration in the experiments used to fit the model are larger than estimated concentrations in vivo. Lowering extracellular calcium concentration to in vivo levels leads to an increase in memory time scales of several orders of magnitude; (ii) adding a bistability mechanism so that each synapse has two stable states at sufficiently low background activity leads to a further boost in memory time scale, since memory decay is no longer described by an exponential decay from an initial state, but by an escape from a potential well. We argue that both features are expected to be present in synapses in vivo. These results are obtained first in a single synapse connecting two independent Poisson neurons, and then in simulations of a large network of excitatory and inhibitory integrate-and-fire neurons. Our results emphasise the need for studying plasticity at physiological extracellular calcium concentration, and highlight the role of synaptic bi- or multistability in the stability of learned synaptic structures.     

Enhanced Sensitivity to Rapid Input Fluctuations by Nonlinear Threshold Dynamics in Neocortical Pyramidal Neurons

The way in which single neurons transform input into output spike trains has fundamental consequences for network coding. Theories and modeling studies based on standard Integrate-and-Fire models implicitly assume that, in response to increasingly strong inputs, neurons modify their coding strategy by progressively reducing their selective sensitivity to rapid input fluctuations. Combining mathematical modeling with in vitro experiments, we demonstrate that, in L5 pyramidal neurons, the firing threshold dynamics adaptively adjust the effective timescale of somatic integration in order to preserve sensitivity to rapid signals over a broad range of input statistics. For that, a new Generalized Integrate-and-Fire model featuring nonlinear firing threshold dynamics and conductance-based adaptation is introduced that outperforms state-of-the-art neuron models in predicting the spiking activity of neurons responding to a variety of in vivo-like fluctuating currents. Our model allows for efficient parameter extraction and can be analytically mapped to a Generalized Linear Model in which both the input filter—describing somatic integration—and the spike-history filter—accounting for spike-frequency adaptation—dynamically adapt to the input statistics, as experimentally observed. Overall, our results provide new insights on the computational role of different biophysical processes known to underlie adaptive coding in single neurons and support previous theoretical findings indicating that the nonlinear dynamics of the firing threshold due to Na⁺-channel inactivation regulate the sensitivity to rapid input fluctuations.     

Encoding of spatio-temporal input characteristics by a CA1 pyramidal neuron model

The in vivo activity of CA1 pyramidal neurons alternates between regular spiking and bursting, but how these changes affect information processing remains unclear. Using a detailed CA1 pyramidal neuron model, we investigate how timing and spatial arrangement variations in synaptic inputs to the distal and proximal dendritic layers influence the information content of model responses. We find that the temporal delay between activation of the two layers acts as a switch between excitability modes: short delays induce bursting while long delays decrease firing. For long delays, the average firing frequency of the model response discriminates spatially clustered from diffused inputs to the distal dendritic tree. For short delays, the onset latency and inter-spike-interval succession of model responses can accurately classify input signals as temporally close or distant and spatially clustered or diffused across different stimulation protocols. These findings suggest that a CA1 pyramidal neuron may be capable of encoding and transmitting presynaptic spatiotemporal information about the activity of the entorhinal cortex-hippocampal network to higher brain regions via the selective use of either a temporal or a rate code.     

Hippocampal Feedforward Inhibition Focuses Excitatory Synaptic Signals into Distinct Dendritic Compartments

Feedforward inhibition controls the time window for synaptic integration and ensures temporal precision in cortical circuits. There is little information whether feedforward inhibition affects neurons uniformly, or whether it contributes to computational refinement within the dendritic tree. Here we demonstrate that feedforward inhibition crucially shapes the integration of synaptic signals in pyramidal cell dendrites. Using voltage-sensitive dye imaging we studied the transmembrane voltage patterns in CA1 pyramidal neurons after Schaffer collateral stimulation in acute brain slices from mice. We observed a high degree of variability in the excitation-inhibition ratio between different branches of the dendritic tree. Many dendritic segments showed no depolarizing signal at all, especially the basal dendrites that received predominantly inhibitory signals. Application of the GABA_A receptor antagonist bicuculline resulted in the spread of depolarizing signals throughout the dendritic tree. Tetanic stimulation of Schaffer collateral inputs induced significant alterations in the patterns of excitation/inhibition, indicating that they are modified by synaptic plasticity. In summary, we show that feedforward inhibition restricts the occurrence of depolarizing signals within the dendritic tree of CA1 pyramidal neurons and thus refines signal integration spatially.     

Moderate AMPA receptor clustering on the nanoscale can efficiently potentiate synaptic current

The prevailing view at present is that postsynaptic expression of the classical NMDA receptor-dependent long-term potentiation relies on an increase in the numbers of local AMPA receptors (AMPARs). This is thought to parallel an expansion of postsynaptic cell specializations, for instance dendritic spine heads, which accommodate synaptic receptor proteins. However, glutamate released into the synaptic cleft can normally activate only a hotspot of low-affinity AMPARs that occur in the vicinity of the release site. How the enlargement of the AMPAR pool is causally related to the potentiated AMPAR current remains therefore poorly understood. To understand possible scenarios of postsynaptic potentiation, here we explore a detailed Monte Carlo model of the typical small excitatory synapse. Simulations suggest that approximately 50% increase in the synaptic AMPAR current could be provided by expanding the existing AMPAR pool at the expense of 100–200% new AMPARs added at the same packing density. Alternatively, reducing the inter-receptor distances by only 30–35% could achieve a similar level of current potentiation without any changes in the receptor numbers. The NMDA receptor current also appears sensitive to the NMDA receptor crowding. Our observations provide a quantitative framework for understanding the ‘resource-efficient’ ways to enact use-dependent changes in the architecture of central synapses.     

A Canonical Circuit for Generating Phase-Amplitude Coupling

‘Phase amplitude coupling’ (PAC) in oscillatory neural activity describes a phenomenon whereby the amplitude of higher frequency activity is modulated by the phase of lower frequency activity. Such coupled oscillatory activity – also referred to as ‘cross-frequency coupling’ or ‘nested rhythms’ – has been shown to occur in a number of brain regions and at behaviorally relevant time points during cognitive tasks; this suggests functional relevance, but the circuit mechanisms of PAC generation remain unclear. In this paper we present a model of a canonical circuit for generating PAC activity, showing how interconnected excitatory and inhibitory neural populations can be periodically shifted in to and out of oscillatory firing patterns by afferent drive, hence generating higher frequency oscillations phase-locked to a lower frequency, oscillating input signal. Since many brain regions contain mutually connected excitatory-inhibitory populations receiving oscillatory input, the simplicity of the mechanism generating PAC in such networks may explain the ubiquity of PAC across diverse neural systems and behaviors. Analytic treatment of this circuit as a nonlinear dynamical system demonstrates how connection strengths and inputs to the populations can be varied in order to change the extent and nature of PAC activity, importantly which phase of the lower frequency rhythm the higher frequency activity is locked to. Consequently, this model can inform attempts to associate distinct types of PAC with different network topologies and physiologies in real data.     

Dendritic enlightenment: using patterned two-photon uncaging to reveal the secrets of the brain's smallest dendrites

It has been a longstanding challenge for experimentalists to manipulate precisely the spatial and temporal patterns of synaptic input to the dendritic tree in order to mimic activity occurring in the intact brain and determine their importance for synaptic integration. In this issue of Neuron, Losonczy and Magee have used rapid multisite two-photon uncaging of glutamate to define patterns of synaptic input on a submillisecond and micron scale to investigate the rules for summation of synaptic inputs in the fine oblique dendrites of pyramidal neurons.     

Ablation of NMDA Receptors Enhances the Excitability of Hippocampal CA3 Neurons

Synchronized discharges in the hippocampal CA3 recurrent network are supposed to underlie network oscillations, memory formation and seizure generation. In the hippocampal CA3 network, NMDA receptors are abundant at the recurrent synapses but scarce at the mossy fiber synapses. We generated mutant mice in which NMDA receptors were abolished in hippocampal CA3 pyramidal neurons by postnatal day 14. The histological and cytological organizations of the hippocampal CA3 region were indistinguishable between control and mutant mice. We found that mutant mice lacking NMDA receptors selectively in CA3 pyramidal neurons became more susceptible to kainate-induced seizures. Consistently, mutant mice showed characteristic large EEG spikes associated with multiple unit activities (MUA), suggesting enhanced synchronous firing of CA3 neurons. The electrophysiological balance between fast excitatory and inhibitory synaptic transmission was comparable between control and mutant pyramidal neurons in the hippocampal CA3 region, while the NMDA receptor-slow AHP coupling was diminished in the mutant neurons. In the adult brain, inducible ablation of NMDA receptors in the hippocampal CA3 region by the viral expression vector for Cre recombinase also induced similar large EEG spikes. Furthermore, pharmacological blockade of CA3 NMDA receptors enhanced the susceptibility to kainate-induced seizures. These results raise an intriguing possibility that hippocampal CA3 NMDA receptors may suppress the excitability of the recurrent network as a whole in vivo by restricting synchronous firing of CA3 neurons.