Generalized Stein's model for anatomically complex neurons

A neuron with a large dendritic structure is considered. The number of synapses located on the dendrites is substantially higher than on the soma. The synaptic input effect on the neuronal excitability decreases with distance between a synapse ending and the trigger zone. Two areas are distinguished in accordance with the effect of synaptic input--dendritic and somatic. The dendritic area, when compared to the soma, is characterized by much higher intensity of its activation but the amplitudes of synaptically evoked changes of the membrane potential at the trigger zone are in general small. This situation is suitable for a diffusion approximation. However, on the soma, especially in the proximity of the trigger zone, the membrane potential changes are a large fraction of the threshold depolarization. The membrane potential at the trigger zone is modelled by a one-dimensional stochastic process. The diffusion Ornstein-Uhlenbeck process serves as a basis of the model; however, at the moments of somatic synapses activation its voltage changes in jumps. Their sizes represent the amplitudes of the evoked postsynaptic potentials. The unimodal histograms of interspike intervals can be explained by the model. The values of the coefficient of variation greater than one are connected with substantial inhibition.     

Syntheses of spinal cord field potentials in the terrapin

A compartmental model of a terrapin motoneuron has been set up to compute membrane potential variations associated with synaptic input at different locations or with antidromic invasion. Membrane potential distributions obtained in that way were used to compute field potentials by means of a volume conduction formalism. The model was used to simulated field potentials measured in the spinal cord in response to stimulation of a muscle nerve with the intention to discriminate between different activation hypothesis for the generation of the spinal cord potential. Extracellular potentials calculated with an excitatory input distributed over the whole dorsal dendritic tree were found to give better reconstruction when compared with excitation restricted to the distal part of the dorsal dendrites, or with somatic inhibition.     

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     

Coding with spike shapes and graded potentials in cortical networks

In cortical neurones, analogue dendritic potentials are thought to be encoded into patterns of digital spikes. According to this view, neuronal codes and computations are based on the temporal patterns of spikes: spike times, bursts or spike rates. Recently, we proposed an 'action potential waveform code' for cortical pyramidal neurones in which the spike shape carries information. Broader somatic action potentials are reliably produced in response to higher conductance input, allowing for four times more information transfer than spike times alone. This information is preserved during synaptic integration in a single neurone, as back-propagating action potentials of diverse shapes differentially shunt incoming postsynaptic potentials and so participate in the next round of spike generation. An open question has been whether the information in action potential waveforms can also survive axonal conduction and directly influence synaptic transmission to neighbouring neurones. Several new findings have now brought new light to this subject, showing cortical information processing that transcends the classical models.     

Effects of active conductance distribution over dendrites on the synaptic integration in an identified nonspiking interneuron

The synaptic integration in individual central neuron is critically affected by how active conductances are distributed over dendrites. It has been well known that the dendrites of central neurons are richly endowed with voltage- and ligand-regulated ion conductances. Nonspiking interneurons (NSIs), almost exclusively characteristic to arthropod central nervous systems, do not generate action potentials and hence lack voltage-regulated sodium channels, yet having a variety of voltage-regulated potassium conductances on their dendritic membrane including the one similar to the delayed-rectifier type potassium conductance. It remains unknown, however, how the active conductances are distributed over dendrites and how the synaptic integration is affected by those conductances in NSIs and other invertebrate neurons where the cell body is not included in the signal pathway from input synapses to output sites. In the present study, we quantitatively investigated the functional significance of active conductance distribution pattern in the spatio-temporal spread of synaptic potentials over dendrites of an identified NSI in the crayfish central nervous system by computer simulation. We systematically changed the distribution pattern of active conductances in the neuron's multicompartment model and examined how the synaptic potential waveform was affected by each distribution pattern. It was revealed that specific patterns of nonuniform distribution of potassium conductances were consistent, while other patterns were not, with the waveform of compound synaptic potentials recorded physiologically in the major input-output pathway of the cell, suggesting that the possibility of nonuniform distribution of potassium conductances over the dendrite cannot be excluded as well as the possibility of uniform distribution. Local synaptic circuits involving input and output synapses on the same branch or on the same side were found to be potentially affected under the condition of nonuniform distribution while operation of the major input-output pathway from the soma side to the one on the opposite side remained the same under both conditions of uniform and nonuniform distribution of potassium conductances over the NSI dendrite.     

Spine calcium transients induced by synaptically-evoked action potentials can predict synapse location and establish synaptic democracy

CA1 pyramidal neurons receive hundreds of synaptic inputs at different distances from the soma. Distance-dependent synaptic scaling enables distal and proximal synapses to influence the somatic membrane equally, a phenomenon called "synaptic democracy". How this is established is unclear. The backpropagating action potential (BAP) is hypothesised to provide distance-dependent information to synapses, allowing synaptic strengths to scale accordingly. Experimental measurements show that a BAP evoked by current injection at the soma causes calcium currents in the apical shaft whose amplitudes decay with distance from the soma. However, in vivo action potentials are not induced by somatic current injection but by synaptic inputs along the dendrites, which creates a different excitable state of the dendrites. Due to technical limitations, it is not possible to study experimentally whether distance information can also be provided by synaptically-evoked BAPs. Therefore we adapted a realistic morphological and electrophysiological model to measure BAP-induced voltage and calcium signals in spines after Schaffer collateral synapse stimulation. We show that peak calcium concentration is highly correlated with soma-synapse distance under a number of physiologically-realistic suprathreshold stimulation regimes and for a range of dendritic morphologies. Peak calcium levels also predicted the attenuation of the EPSP across the dendritic tree. Furthermore, we show that peak calcium can be used to set up a synaptic democracy in a homeostatic manner, whereby synapses regulate their synaptic strength on the basis of the difference between peak calcium and a uniform target value. We conclude that information derived from synaptically-generated BAPs can indicate synapse location and can subsequently be utilised to implement a synaptic democracy.     

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.     

Remote Modulation of Current Transfer from Dendritic Glutamatergic Synapses by GABA-ergic Synapses of the Somatic Zone of Motoneurons: a Simulation Study

Until now, information concerning spatial interaction of postsynaptic excitation and inhibition in neuronal dendrites remains rather limited. In model experiments, we studied spatial effects of tonic co-activation of GABA-ergic synapses situated on the soma and axon hillock of a motoneuron and dendritic glutamatergic synapses with receptors sensitive or insensitive to N-methyl-D-aspartate. We analyzed distribution maps of the transmembrane potentials and excitatory currents transferred toward the soma over the reconstructed dendritic arborization of a rat abducens motoneuron (three-dimensional reconstruction). In the motoneuron, isolated tonic excitation of glutamatergic synapses induced two stable states of low (downstate) or high (upstate) spatially heterogeneous dendritic depolarization, which decayed with unequal rates along different dendritic paths. In this case, the local steady-state current-voltage relation of the dendritic membrane became N-shaped due to a limb of the negative slope within a certain voltage range. The upstate corresponding to plateau potentials associated with stereotyped motor activity patterns was analyzed in detail. In this state, most proximal dendritic sites were the main sources of the excitatory current reaching the soma, while the contribution from distal sites was negligible. Co-activation of GABA-synapses located at the soma and axon hillock reduced this depolarization and shifted the main excitatory current source from a perisomatic location to the middle, structurally more complex, region of the dendritic arborization. The more remote dendritic region having a greater membrane area and receiving a greater number of synaptic contacts became directly involved in the supply of the trigger zone by the excitatory current. We suggest that a special, not described earlier, operational mechanism of postsynaptic inhibition is manifested in the above spatial effects of activation of strategically located inhibitory synapses, and that the list of known crucial inhibitory mechanisms (namely hyperpolarization and shunting of the postsynaptic membrane) must be expanded.     

Synaptic modifications depend on synapse location and activity: a biophysical model of STDP

In spike-timing-dependent plasticity (STDP) the synapses are potentiated or depressed depending on the temporal order and temporal difference of the pre- and post-synaptic signals. We present a biophysical model of STDP which assumes that not only the timing, but also the shapes of these signals influence the synaptic modifications. The model is based on a Hebbian learning rule which correlates the NMDA synaptic conductance with the post-synaptic signal at synaptic location as the pre- and post-synaptic quantities. As compared to a previous paper [Saudargiene, A., Porr, B., Worgotter, F., 2004. How the shape of pre- and post-synaptic signals can influence stdp: a biophysical model. Neural Comp.], here we show that this rule reproduces the generic STDP weight change curve by using real neuronal input signals and combinations of more than two (pre- and post-synaptic) spikes. We demonstrate that the shape of the STDP curve strongly depends on the shape of the depolarising membrane potentials, which induces learning. As these potentials vary at different locations of the dendritic tree, model predicts that synaptic changes are location dependent. The model is extended to account for the patterns of more than two spikes of the pre- and post-synaptic cells. The results show that STDP weight change curve is also activity dependent.     

A Model for Responses to Activation by Axodendritic Synapses

A simple mathematical model of synaptic activation shows that the response to synaptic activation depends inversely on the size of the subsynaptic process. This provides a theoretical foundation for: the relationship between excitability and cell size; a possible source of plasticity in nerve cell behavior; and the hypothesis that postsynaptic responses to activation at axodendritic synapses are of large amplitude. The last-mentioned idea provides for flexible nonlinear interaction in dendritic regions because the diminution of postsynaptic potentials (PSPs) by prior potential becomes significant at high levels of depolarization. Digital-computer simulations of nerve cell input-output behavior for axodendritic activation based on these ideas reveal: frequency-transfer curves for axodendritic activation saturate; activations combined on different dendritic branches sum approximately linearly while those on the same branch occlude; simultaneous activation of several synapses on a previously inactive dendritic branch results in a large “peak” response at the onset of stimulation; and such an initial peak may be markedly mitigated by a prior depolarization of the branch. The third-mentioned finding may represent a widespread mode of hypersensitivity to stimulus onset in neural systems and in particular may contribute to the “on” responses of sensory channels, and the fourth suggests that depolarizing synapses at extreme peripheries of dendritic fibers might in some cases serve an inhibitory function.     

A Biophysical Model of Neuronal Dendrites' Integrative Properties: Relations to Morphological Data

We used a biophysical model to probe the basic integrative properties of primate pallidal neurons in order to obtain a better understanding of Basal Ganglia physiology. The first results we present here deal mainly with the way dendritic morphology influences these properties. Neuronal morphology has been quantitatatively analyzed in 3D. Single fast excitatory synaptic inputs resulting in AMPA receptors activations have been simulated, without regenerative voltage dependent conductances. Dendrites of both pallidal segments (GPi and GPe) showed a strong dependence of the synaptic efficacy upon distance from soma, but even the most distal dendritic synaptic sites were able to substantially depolarize the cell body. The mean synaptic efficacy was the same in both populations, but the attenuation of propagated post-synaptic potentials was higher in GPi neurons. All these features were very dependent on the dendritic diameters which appear to constitute a key parameter in these neuronal populations both with respect to the integration of afferent information and to the differences between cells in performing this task.     

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.     

Spatial Localization of Synapses Required for Supralinear Summation of Action Potentials and EPSPs

Although the supralinear summation of synchronizing excitatory postsynaptic potentials (EPSPs) and backpropagating action potentials (APs) is important for spike-timing-dependent synaptic plasticity (STDP), the spatial conditions of the amplification in the divergent dendritic structure have yet to be analyzed. In the present study, we simulated the coincidence of APs with EPSPs at randomly determined synaptic sites of a morphologically reconstructed hippocampal CA1 pyramidal model neuron and clarified the spatial condition of the amplifying synapses. In the case of uniform conductance inputs, the amplifying synapses were localized in the middle apical dendrites and distal basal dendrites with small diameters, and the ratio of synapses was unexpectedly small: 8-16% in both apical and basal dendrites. This was because the appearance of strong amplification requires the coincidence of both APs of 3-30 mV and EPSPs of over 6 mV, both of which depend on the dendritic location of synaptic sites. We found that the localization of amplifying synapses depends on A-type K+ channel distribution because backpropagating APs depend on the A-type K+ channel distribution, and that the localizations of amplifying synapses were similar within a range of physiological synaptic conductances. We also quantified the spread of membrane amplification in dendrites, indicating that the neighboring synapses can also show the amplification. These findings allowed us to computationally illustrate the spatial localization of synapses for supralinear summation of APs and EPSPs within thin dendritic branches where patch clamp experiments cannot be easily conducted.     

Patterns of Impulsation Generated by Abducens Motoneurons with Active Reconstructed Dendrites: a Simulation Study

Mathematical models of abducens motoneurons with reconstructed dendritic arborizations were investigated. The two types of models differed from each other in electrical properties of the dendrites, either passive (model group 1) or active and non-linear (model group 2). The relations between morphology of the dendrites, their electrical transfer characteristics, and formation of impulse patterns at the cell output were studied under conditions of tonic activation of glutamatergic (NMDA-type) excitatory synapses homogeneously distributed over the dendrites. For reconstructed dendritic arborizations, their morphometric characteristics (size, complexity, and metrical asymmetry) and electrical ones (somatopetal current transfer effectiveness function and sensitivity of the latter to variations of the homogeneous membrane conductivity) were computed. Changes in the membrane potential were also studied in different parts of the dendritic arborization during generation of various patterns of discharges of action potentials (APs) at the neuronal output under different intensities of synaptic activation; this allowed us to reveal “spatial signatures” of the above-mentioned temporal patterns. The output patterns and their “spatial signatures” changed in a certain manner with increase in the intensity of synaptic activation. A simple periodical discharge of low-frequency APs with constant interspike intervals was replaced by a complex periodical or nonperiodical (stochastic) bursting pattern, which then was replaced again by a simple rhythmic but high-frequency discharge. Simple periodical patterns were associated with generation of synchronous oscillatory dendritic depolarizations phase-shifted in metrically asymmetrical parts of the arborization. In the case of generation of complex periodical or stochastic patterns, depolarization processes in asymmetrical dendritic parts were asynchronous and differed from each other in their amplitude and duration. Such a structure-dependent repertoire of output discharge patterns was quite compatible with that observed earlier in examined simulated neocortical pyramidal and cerebellar Purkinje neurons. This fact is indicative of a possible similarity of the rules governing the formation of specific output patterns in neurons with active membrane properties of the dendrites based on intrinsic mophological/functional features of the dendritic arborization of a given neuron.     

Selective regulation of neurite extension and synapse formation by the beta but not the alpha isoform of CaMKII

Neurite extension and branching are important neuronal plasticity mechanisms that can lead to the addition of synaptic contacts in developing neurons and changes in the number of synapses in mature neurons. Here we show that Ca2+/calmodulin-dependent protein kinase II (CaMKII) regulates movement, extension, and branching of filopodia and fine dendrites as well as the number of synapses in hippocampal neurons. Only CaMKIIbeta, which peaks in expression early in development, but not CaMKIIalpha, has this morphogenic activity. A small insert in CaMKIIbeta, which is absent in CaMKIIalpha, confers regulated F-actin localization to the enzyme and enables selective upregulation of dendritic motility. These results show that the two main neuronal CaMKII isoforms have markedly different roles in neuronal plasticity, with CaMKIIalpha regulating synaptic strength and CaMKIIbeta controlling the dendritic morphology and number of synapses.     

Principles governing the operation of synaptic inhibition in dendrites

Synaptic inhibition plays a key role in shaping the dynamics of neuronal networks and selecting cell assemblies. Typically, an inhibitory axon contacts a particular dendritic subdomain of its target neuron, where it often makes 10-20 synapses, sometimes on very distal branches. The functional implications of such a connectivity pattern are not well understood. Our experimentally based theoretical study highlights several new and counterintuitive principles for dendritic inhibition. We show that distal "off-path" rather than proximal "on-path" inhibition effectively dampens proximal excitable dendritic "hotspots," thus powerfully controlling the neuron's output. Additionally, with multiple synaptic contacts, inhibition operates globally, spreading centripetally hundreds of micrometers from the inhibitory synapses. Consequently, inhibition in regions lacking inhibitory synapses may exceed that at the synaptic sites themselves. These results offer new insights into the synergetic effect of dendritic inhibition in controlling dendritic excitability and plasticity and in dynamically molding functional dendritic subdomains and their output.     

Somatic motoneurones in amphioxus larvae: cell types, cell position and innervation patterns

Serial transmission electron microscopy and 3D reconstruction were used to document cell morphology and position of the motoneurones innervating somites 1 and 2 of a 12.5-day amphioxus larva, of Branchiostoma floridae , and also those innervating the dorsal compartment of somites 3 through 6 of an 8-day larva. Motoneurones supplying the ventral and dorsal compartments can be distinguished from one another on a number of morphological criteria. The ventral compartment motoneurones are neither symmetrical nor particularly ordered in arrangement. Their cilia are short and point forward or obliquely across the central canal; their axons run along the basal lamina adjacent to processes from muscle fibres, with which they make extended linear series of synapses containing 45–60 nm synaptic vesicles. The dorsal compartment motoneurones are paired and tend to be positioned at or near the junctions between somites. Their cilia are longer and project caudally; their axons are large, filled with mitochondria and 30–45 nm synaptic vesicles, and make synapses only at specific, segmentally repeated sites.
  An unusual feature of both cell types is that synaptic input occurs all along the axon, either by direct axo-axonal synapses or via slender dendritic processes. This allows for redundancy and multiple inputs, and is possible only because amphioxus somatic motor axons lie entirely within the nerve cord, which is itself an unusual feature among chordates. The possible significance of dual somatic innervation is discussed in relation to the dual innervation of the head in vertebrates, which has separate sets of somatic and visceral/branchiomotor nerves.     

Stochastic Ion Channel Gating in Dendritic Neurons: Morphology Dependence and Probabilistic Synaptic Activation of Dendritic Spikes

Neuronal activity is mediated through changes in the probability of stochastic transitions between open and closed states of ion channels. While differences in morphology define neuronal cell types and may underlie neurological disorders, very little is known about influences of stochastic ion channel gating in neurons with complex morphology. We introduce and validate new computational tools that enable efficient generation and simulation of models containing stochastic ion channels distributed across dendritic and axonal membranes. Comparison of five morphologically distinct neuronal cell types reveals that when all simulated neurons contain identical densities of stochastic ion channels, the amplitude of stochastic membrane potential fluctuations differs between cell types and depends on sub-cellular location. For typical neurons, the amplitude of membrane potential fluctuations depends on channel kinetics as well as open probability. Using a detailed model of a hippocampal CA1 pyramidal neuron, we show that when intrinsic ion channels gate stochastically, the probability of initiation of dendritic or somatic spikes by dendritic synaptic input varies continuously between zero and one, whereas when ion channels gate deterministically, the probability is either zero or one. At physiological firing rates, stochastic gating of dendritic ion channels almost completely accounts for probabilistic somatic and dendritic spikes generated by the fully stochastic model. These results suggest that the consequences of stochastic ion channel gating differ globally between neuronal cell-types and locally between neuronal compartments. Whereas dendritic neurons are often assumed to behave deterministically, our simulations suggest that a direct consequence of stochastic gating of intrinsic ion channels is that spike output may instead be a probabilistic function of patterns of synaptic input to dendrites.     

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.     

Emerging methodologies for the study of hypothalamic gonadotropin-releasing-hormone (GnRH) neurons

Gonadotropin-releasing-hormone (GnRH) neurons form part of a central neural oscillator that controls sexual reproduction through intermittent release of the GnRH peptide. Activity of GnRH neurons, and by extension release of GnRH, has been proposed to reflect intrinsic properties and synaptic input of GnRH neurons. To study GnRH neurons, we used traditional electrophysiology and computational methods. These emerging methodologies enhance the elucidation of processing in GnRH neurons. We used dynamic current-clamping to understand how living GnRH somata process input from glutamate and GABA, two key neurotransmitters in the neuroendocrine hypothalamus. In order to study the impact of synaptic integration in dendrites and neuronal morphology, we have developed full-morphology models of GnRH neurons. Using dynamic clamping, we have demonstrated that small-amplitude glutamatergic currents can drive repetitive firing in GnRH neurons. Furthermore, application of simulated GABAergic synapses with a depolarized reversal potential have revealed two functional subpopulations of GnRH neurons: one population in which GABA chronically depolarizes membrane potential (without inducing action potentials) and a second population in which GABAergic excitation results in slow spiking. Finally, when AMPA-type and GABA-type simulated inputs are applied together, action potentials occur when the AMPA-type conductance occurs during the descending phase of GABAergic excitation and at the nadir of GABAergic inhibition. Compartmental computer models have shown that excitatory synapses at >300 microns from somtata are unable to drive spiking with purely passive dendrites. In models with active dendrites, distal synapses are more efficient at driving spiking than somatic inputs. We then used our models to extend the results from dynamic current clamping at GnRH somata to distribute synaptic inputs along the dendrite. We show that propagation delays for dendritic synapses alter synaptic integration in GnRH neurons by widening the temporal window of interaction for the generation of action potentials. Finally, we have shown that changes in dendrite morphology can modulate the output of GnRH neurons by altering the efficacy of action potential generation in response to after-depolarization potentials (ADPs). Taken together, the methodologies of dynamic current clamping and multi-compartmental modeling can make major contributions to the study of synaptic integration and structure-function relationships in hypothalamic GnRH neurons. Use of these methodological approaches will continue to provide keen insights leading to conceptual advances in our understanding of reproductive hormone secretion in normal and pathological physiology and open the door to understanding whether the mechanisms of pulsatile GnRH release are conserved across species.