Effects of active versus passive dendritic membranes on the transfer properties of a simulated neuron

In a simulated neuron with a dendritic tree, the relative effects of active and passive dendritic membranes on transfer properties were studied. The simulations were performed by means of a digital computer. The computations calculated the changes in transmembrane voltages of many compartments over time as a function of other biophysical variables. These variables were synaptic input intensity, critical firing threshold, rate of leakage of current across the membrane, and rate of longitudinal current spread between compartments. For both passive and active dendrites, the transfer properties of the soma studied for different rates of longitudinal current spread. With low rates of current spread, graded changes in firing threshold produced correspondingly graded changes in output discharge. With high rates of current spread, the neuron became a bistable operator where spiking was enhanced if the threshold was below a certain level and suppressed if the threshold was above that level. Since alterations in firing threshold were shown to have the same effect on firing rate as alterations in synaptic input intensity, the neuron can be said to change from graded to contrast-enhancing in its response to stimuli of different intensities. The presence or absence of dendritic spiking was found to have a significant effect on the integrative properties of the simulated neuron. In particular, contrast enhancement was considerably more pronounced in neurons with passive than with active dendrites in that somatic spike rates reached a higher maximum when dendrites were passive. With active dendrites, a less intense input was needed to initiate somatic spiking than with passive dendrites because a distal dendritic spike could easily propagate by means of longitudinal current spread to the soma. Once somatic spiking was initiated, though, spike rates tended to be lower with active than with passive dendrites because the soma recovered more slowly from its post-spike refractory period if it was also influenced by refractory periods in the dendrites. The experiment of comparing neurons with active and passive dendrites was repeated at a different, higher value of synaptic input. The same differences in transfer properties between the active and passive cases emerged as before. Spiking patterns in neurons with active dendrites were also affected by the time distribution of synaptic inputs. In a previous study, inputs had been random over both space and time, varying about a predetermined mean, whereas in the present study, inputs were random over space but uniform over time. When inputs were made uniform over time, spiking became more difficult to initiate and the transition from graded to bistable response became less sharp.     

Parallel Computational Subunits in Dentate Granule Cells Generate Multiple Place Fields

A fundamental question in understanding neuronal computations is how dendritic events influence the output of the neuron. Different forms of integration of neighbouring and distributed synaptic inputs, isolated dendritic spikes and local regulation of synaptic efficacy suggest that individual dendritic branches may function as independent computational subunits. In the present paper, we study how these local computations influence the output of the neuron. Using a simple cascade model, we demonstrate that triggering somatic firing by a relatively small dendritic branch requires the amplification of local events by dendritic spiking and synaptic plasticity. The moderately branching dendritic tree of granule cells seems optimal for this computation since larger dendritic trees favor local plasticity by isolating dendritic compartments, while reliable detection of individual dendritic spikes in the soma requires a low branch number. Finally, we demonstrate that these parallel dendritic computations could contribute to the generation of multiple independent place fields of hippocampal granule cells.     

Dendrites: bug or feature?

The integrative properties of dendrites are determined by a complex mixture of factors, including their morphology, the spatio-temporal patterning of synaptic inputs, the balance of excitation and inhibition, and neuromodulatory influences, all of which interact with the many voltage-gated conductances present in the dendritic membrane. Recent efforts to grapple with this complexity have focused on identifying functional compartments in the dendritic tree, the number and size of which depend on the aspect of dendritic function being considered. We discuss how dendritic compartments and the interactions between them help to enhance the computational power of the neuron and define the rules for the induction of synaptic plasticity.     

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.     

The Subcellular Distribution of T-Type Ca2+ Channels in Interneurons of the Lateral Geniculate Nucleus

Inhibitory interneurons (INs) in the lateral geniculate nucleus (LGN) provide both axonal and dendritic GABA output to thalamocortical relay cells (TCs). Distal parts of the IN dendrites often enter into complex arrangements known as triadic synapses, where the IN dendrite plays a dual role as postsynaptic to retinal input and presynaptic to TC dendrites. Dendritic GABA release can be triggered by retinal input, in a highly localized process that is functionally isolated from the soma, but can also be triggered by somatically elicited Ca²⁺-spikes and possibly by backpropagating action potentials. Ca²⁺-spikes in INs are predominantly mediated by T-type Ca²⁺-channels (T-channels). Due to the complex nature of the dendritic signalling, the function of the IN is likely to depend critically on how T-channels are distributed over the somatodendritic membrane (T-distribution). To study the relationship between the T-distribution and several IN response properties, we here run a series of simulations where we vary the T-distribution in a multicompartmental IN model with a realistic morphology. We find that the somatic response to somatic current injection is facilitated by a high T-channel density in the soma-region. Conversely, a high T-channel density in the distal dendritic region is found to facilitate dendritic signalling in both the outward direction (increases the response in distal dendrites to somatic input) and the inward direction (the soma responds stronger to distal synaptic input). The real T-distribution is likely to reflect a compromise between several neural functions, involving somatic response patterns and dendritic signalling.     

Differential contributions of synaptic and intrinsic inhibitory currents to speech segmentation via flexible phase-locking in neural oscillators

Current hypotheses suggest that speech segmentation—the initial division and grouping of the speech stream into candidate phrases, syllables, and phonemes for further linguistic processing—is executed by a hierarchy of oscillators in auditory cortex. Theta (∼3-12 Hz) rhythms play a key role by phase-locking to recurring acoustic features marking syllable boundaries. Reliable synchronization to quasi-rhythmic inputs, whose variable frequency can dip below cortical theta frequencies (down to ∼1 Hz), requires “flexible” theta oscillators whose underlying neuronal mechanisms remain unknown. Using biophysical computational models, we found that the flexibility of phase-locking in neural oscillators depended on the types of hyperpolarizing currents that paced them. Simulated cortical theta oscillators flexibly phase-locked to slow inputs when these inputs caused both (i) spiking and (ii) the subsequent buildup of outward current sufficient to delay further spiking until the next input. The greatest flexibility in phase-locking arose from a synergistic interaction between intrinsic currents that was not replicated by synaptic currents at similar timescales. Flexibility in phase-locking enabled improved entrainment to speech input, optimal at mid-vocalic channels, which in turn supported syllabic-timescale segmentation through identification of vocalic nuclei. Our results suggest that synaptic and intrinsic inhibition contribute to frequency-restricted and -flexible phase-locking in neural oscillators, respectively. Their differential deployment may enable neural oscillators to play diverse roles, from reliable internal clocking to adaptive segmentation of quasi-regular sensory inputs like speech.     

Recurrent fractal neural networks: a strategy for the exchange of local and global information processing in the brain

The regulation of biological networks relies significantly on convergent feedback signaling loops that render a global output locally accessible. Ideally, the recurrent connectivity within these systems is self-organized by a time-dependent phase-locking mechanism. This study analyzes recurrent fractal neural networks (RFNNs), which utilize a self-similar or fractal branching structure of dendrites and downstream networks for phase-locking of reciprocal feedback loops: output from outer branch nodes of the network tree enters inner branch nodes of the dendritic tree in single neurons. This structural organization enables RFNNs to amplify re-entrant input by over-the-threshold signal summation from feedback loops with equivalent signal traveling times. The columnar organization of pyramidal neurons in the neocortical layers V and III is discussed as the structural substrate for this network architecture. RFNNs self-organize spike trains and render the entire neural network output accessible to the dendritic tree of each neuron within this network. As the result of a contraction mapping operation, the local dendritic input pattern contains a downscaled version of the network output coding structure. RFNNs perform robust, fractal data compression, thus coping with a limited number of feedback loops for signal transport in convergent neural networks. This property is discussed as a significant step toward the solution of a fundamental problem in neuroscience: how is neuronal computation in separate neurons and remote brain areas unified as an instance of experience in consciousness? RFNNs are promising candidates for engaging neural networks into a coherent activity and provide a strategy for the exchange of global and local information processing in the human brain, thereby ensuring the completeness of a transformation from neuronal computation into conscious experience.     

Effects of Neural Morphology and Input Distribution on Synaptic Processing by Global and Focal NMDA-Spikes

Cortical neurons can respond to glutamatergic stimulation with regenerative N-Methyl-D-aspartic acid (NMDA)-spikes. NMDA-spikes were initially thought to depend on clustered synaptic activation. Recent work had shown however a new variety of a global NMDA-spike, which can be generated by randomly distributed inputs. Very little is known about the factors that influence the generation of these global NMDA-spikes, as well the potentially distinct rules of synaptic integration and the computational significance conferred by the two types of NMDA-spikes. Here I show that the input resistance (R_IN) plays a major role in influencing spike initiation; while the classical, focal NMDA-spike depended upon the local (dendritic) R_IN, the threshold of global NMDA-spike generation was set by the somatic R_IN. As cellular morphology can exert a large influence on R_IN, morphologically distinct neuron types can have dissimilar rules for NMDA-spikes generation. For example, cortical neurons in superficial layers were found to be generally prone to global NMDA-spike generation. In contrast, electric properties of cortical layer 5b cells clearly favor focal NMDA-spikes. These differences can translate into diverse synaptic integration rules for the different classes of cortical cells; simulated superficial layers neurons were found to exhibit strong synaptic interactions between different dendritic branches, giving rise to a single integrative compartment mediated by the global NMDA-spike. In these cells, efficiency of postsynaptic activation was relatively little dependent on synaptic distribution. By contrast, layer 5b neurons were capable of true multi-unit computation involving independent integrative compartments formed by clustered synaptic input which could trigger focal NMDA-spikes. In a sharp contrast to superficial layers neurons, randomly distributed synaptic inputs were not very effective in driving firing the layer 5b cells, indicating a possibility for different computation performed by these important cortical neurons.     

Thin dendrites of cerebellar interneurons confer sublinear synaptic integration and a gradient of short-term plasticity

Interneurons are critical for neuronal circuit function, but how their dendritic morphologies and membrane properties influence information flow within neuronal circuits is largely unknown. We studied the spatiotemporal profile of synaptic integration and short-term plasticity in dendrites of mature cerebellar stellate cells by combining two-photon guided electrical stimulation, glutamate uncaging, electron microscopy, and modeling. Synaptic activation within thin (0.4?μm) dendrites produced somatic responses that became smaller and slower with increasing distance from the soma, sublinear subthreshold input-output relationships, and a somatodendritic gradient of short-term plasticity. Unlike most studies showing that neurons employ active dendritic mechanisms, we found that passive cable properties of thin dendrites determine the sublinear integration and plasticity gradient, which both result from large?dendritic depolarizations that reduce synaptic driving force. These integrative properties allow stellate cells to act as spatiotemporal filters of synaptic input patterns, thereby biasing their output in favor of sparse presynaptic activity.     

The influences of somatic and dendritic inhibition on bursting patterns in a neuronal circuit model

The balance between inhibition and excitation plays a crucial role in the generation of synchronous bursting activity in neuronal circuits. In human and animal models of epilepsy, changes in both excitatory and inhibitory synaptic inputs are known to occur. Locations and distribution of these excitatory and inhibitory synaptic inputs on pyramidal cells play a role in the integrative properties of neuronal activity, e.g., epileptiform activity. Thus the location and distribution of the inputs onto pyramidal cells are important parameters that influence neuronal activity in epilepsy. However, the location and distribution of inhibitory synapses converging onto pyramidal cells have not been fully studied. The objectives of this study are to investigate the roles of the relative location of inhibitory synapses on the dendritic tree and soma in the generation of bursting activity. We investigate influences of somatic and dendritic inhibition on bursting activity patterns in several paradigms of potential connections using a simplified multicompartmental model. We also investigate the effects of distribution of fast and slow components of GABAergic inhibition in pyramidal cells. Interspike interval (ISI) analysis is used for examination of bursting patterns. Simulations show that the inhibitory interneuron regulates neuronal bursting activity. Bursting behavior patterns depend on the synaptic weight and delay of the inhibitory connection as well as the location of the synapse. When the inhibitory interneuron synapses on the pyramidal neuron, inhibitory action is stronger if the inhibitory synapse is close to the soma. Alterations of synaptic weight of the interneuron can be compensatory for changes in the location of synaptic input. The relative changes in these parameters exert a considerable influence on whether synchronous bursting activity is facilitated or reduced. Additional simulations show that the slow GABAergic inhibitory component is more effective than the fast component in distal dendrites. Taken together, these findings illustrate the potential for GABAergic inhibition in the soma and dendritic tree to play an important modulatory role in bursting activity patterns.     

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     

Temporal sub units in dendritic trees

This simulation study examines the possibility that dendritic sub units can be defined according to temporal aspects in the timing of populations of synaptic inputs. A two cell model with passive dendritic trees is used, which is subject to both common and independent synaptic inputs, the presence of common synaptic input results in a tendency for correlated firing in the two cell model. The strength of this correlation is used to measure the efficacy of the common synaptic inputs in modulating the output discharge of each neurone. Our results suggest that a small fraction of the total synaptic input can effectively modulate the timing of output spikes, this phenomenon is not dependent on the physical location of the inputs on the dendritic tree. This phenomenon depends on the presence of temporal correlation between the pre-synaptic spike trains that provide the common input. We propose to refer to these as temporal sub units.     

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.     

Long-term potentiation in rat hippocampal neurons is accompanied by spatially widespread changes in intrinsic oscillatory dynamics and excitability

Oscillations in neural activity are a prominent feature of many brain states. Individual hippocampal neurons exhibit intrinsic membrane potential oscillations and intrinsic resonance in the theta frequency range. We found that the subthreshold resonance frequency of CA1 pyramidal neurons was location dependent, varying more than 3-fold between the soma and the distal dendrites. Furthermore, activity- and NMDA-receptor-dependent long-term plasticity increased this resonance frequency through changes in h channel properties. The increase in resonance frequency and an associated reduction in excitability were nearly identical in the soma and the first 300 mum of the apical dendrites. These spatially widespread changes accompanying long-term synaptic potentiation also reduced the neuron's ability to elicit spikes evoked through a nonpotentiated synaptic pathway. Our results suggest that the frequency response of these neurons depends on the dendritic location of their inputs and that activity can regulate their response dynamics within an oscillating neural network.     

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.     

Synaptic integration in dendritic trees

Most neurons have elaborate dendritic trees that receive tens of thousands of synaptic inputs. Because postsynaptic responses to individual synaptic events are usually small and transient, the integration of many synaptic responses is needed to depolarize most neurons to action potential threshold. Over the past decade, advances in electrical and optical recording techniques have led to new insights into how synaptic responses propagate and interact within dendritic trees. In addition to their passive electrical and morphological properties, dendrites express active conductances that shape individual synaptic responses and influence synaptic integration locally within dendrites. Dendritic voltage-gated Na(+) and Ca(2+) channels support action potential backpropagation into the dendritic tree and local initiation of dendritic spikes, whereas K(+) conductances act to dampen dendritic excitability. While all dendrites investigated to date express active conductances, different neuronal types show specific patterns of dendritic channel expression leading to cell-specific differences in the way synaptic responses are integrated within dendritic trees. This review explores the way active and passive dendritic properties shape synaptic responses in the dendrites of central neurons, and emphasizes their role in synaptic integration.     

Role of active dendritic conductances in subthreshold input integration

Dendrites of many types of neurons contain voltage-dependent conductances that are active at subthreshold membrane potentials. To understand the computations neurons perform it is key to understand the role of active dendrites in the subthreshold processing of synaptic inputs. We examine systematically how active dendritic conductances affect the time course of postsynaptic potentials propagating along dendrites, and how they affect the interaction between such signals. Voltage-dependent currents can be classified into two types that have qualitatively different effects on subthreshold input responses: regenerative dendritic currents boost and broaden EPSPs, while restorative currents attenuate and narrow EPSPs. Importantly, the effects of active dendritic currents on EPSP shape increase as the EPSP travels along the dendrite. The effectiveness of active currents in modulating the EPSP shape is determined by their activation time constant: the faster it is, the stronger the effect on EPSP amplitude, while the largest effects on EPSP width occur when it is comparable to the membrane time constant. We finally demonstrate that the two current types can differentially improve precision and robustness of neural computations: restorative currents enhance coincidence detection of dendritic inputs, whereas direction selectivity to sequences of dendritic inputs is enhanced by regenerative dendritic currents.     

Advantages and Limitations of the Use of Optogenetic Approach in Studying Fast-Scale Spike Encoding

Understanding single-neuron computations and encoding performed by spike-generation mechanisms of cortical neurons is one of the central challenges for cell electrophysiology and computational neuroscience. An established paradigm to study spike encoding in controlled conditions in vitro uses intracellular injection of a mixture of signals with fluctuating currents that mimic in vivo-like background activity. However this technique has two serious limitations: it uses current injection, while synaptic activation leads to changes of conductance, and current injection is technically most feasible in the soma, while the vast majority of synaptic inputs are located on the dendrites. Recent progress in optogenetics provides an opportunity to circumvent these limitations. Transgenic expression of light-activated ionic channels, such as Channelrhodopsin2 (ChR2), allows induction of controlled conductance changes even in thin distant dendrites. Here we show that photostimulation provides a useful extension of the tools to study neuronal encoding, but it has its own limitations. Optically induced fluctuating currents have a low cutoff (~70Hz), thus limiting the dynamic range of frequency response of cortical neurons. This leads to severe underestimation of the ability of neurons to phase-lock their firing to high frequency components of the input. This limitation could be worked around by using short (2 ms) light stimuli which produce membrane potential responses resembling EPSPs by their fast onset and prolonged decay kinetics. We show that combining application of short light stimuli to different parts of dendritic tree for mimicking distant EPSCs with somatic injection of fluctuating current that mimics fluctuations of membrane potential in vivo, allowed us to study fast encoding of artificial EPSPs photoinduced at different distances from the soma. We conclude that dendritic photostimulation of ChR2 with short light pulses provides a powerful tool to investigate population encoding of simulated synaptic potentials generated in dendrites at different distances from the soma.