Dendritic Morphology of an Inhibitory Retinal Interneuron Enables Simultaneous Local and Global Synaptic Integration.

Amacrine cells, inhibitory interneurons of the retina, feature synaptic inputs and outputs in close proximity throughout their dendritic trees, making them notable exceptions to prototypical somato-dendritic integration with output transmitted via axonal action potentials. The extent of dendritic compartmentalization in amacrine cells with widely differing dendritic tree morphology, however, is largely unexplored. Combining compartmental modeling, dendritic Ca2+ imaging, targeted microiontophoresis and multielectrode patch-clamp recording (voltage and current clamp, capacitance measurement of exocytosis), we investigated integration in the AII amacrine cell, a narrow-field electrically coupled interneuron that participates in multiple, distinct microcircuits. Physiological experiments were performed with in vitro slices prepared from retinas of both male and female rats. We found that the morphology of the AII enables simultaneous local and global integration of inputs targeted to different dendritic regions. Local integration occurs within spatially restricted dendritic subunits and narrow time windows and is largely unaffected by the strength of electrical coupling. In contrast, global integration across the dendritic tree occurs over longer time periods and is markedly influenced by the strength of electrical coupling. These integrative properties enable AII amacrines to combine local control of synaptic plasticity with location-independent global integration. Dynamic inhibitory control of dendritic subunits is likely to be of general importance for amacrine cells, including cells with small dendritic trees, as well as for inhibitory interneurons in other regions of the CNS.SIGNIFICANCE STATEMENT Our understanding of synaptic integration is based on the prototypical morphology of a neuron with multiple dendrites and a single axon at opposing ends of a cell body. Many neurons, notably retinal amacrine cells, are exceptions to this arrangement, and display input and output synapses interspersed along their dendritic branches. In the large dendritic trees of some amacrine cells, such arrangements can give rise to multiple computational subunits. Other amacrine cells, with small dendritic trees, have been assumed to operate as single computational units. Here, we report the surprising result that despite a small dendritic tree, the AII amacrine cell simultaneously performs local integration of synaptic inputs (over smaller dendritic subregions) and global integration across the entire cell.

GABA-mediated tonic inhibition differentially modulates gain in functional subtypes of cortical interneurons.

The binding of GABA (γ-aminobutyric acid) to extrasynaptic GABAA receptors generates tonic inhibition that acts as a powerful modulator of cortical network activity. Despite GABA being present throughout the extracellular space of the brain, previous work has shown that GABA may differentially modulate the excitability of neuron subtypes according to variation in chloride gradient. Here, using biophysically detailed neuron models, we predict that tonic inhibition can differentially modulate the excitability of neuron subtypes according to variation in electrophysiological properties. Surprisingly, tonic inhibition increased the responsiveness (or gain) in models with features typical for somatostatin interneurons but decreased gain in models with features typical for parvalbumin interneurons. Patch-clamp recordings from cortical interneurons supported these predictions, and further in silico analysis was then performed to seek a putative mechanism underlying gain modulation. We found that gain modulation in models was dependent upon the magnitude of tonic current generated at depolarized membrane potential-a property associated with outward rectifying GABAA receptors. Furthermore, tonic inhibition produced two biophysical changes in models of relevance to neuronal excitability: 1) enhanced action potential repolarization via increased current flow into the dendritic compartment, and 2) reduced activation of voltage-dependent potassium channels. Finally, we show theoretically that reduced potassium channel activation selectively increases gain in models possessing action potential dynamics typical for somatostatin interneurons. Potassium channels in parvalbumin-type models deactivate rapidly and are unavailable for further modulation. These findings show that GABA can differentially modulate interneuron excitability and suggest a mechanism through which this occurs in silico via differences of intrinsic electrophysiological properties.

Experimentally-constrained biophysical models of tonic and burst firing modes in thalamocortical neurons.

Somatosensory thalamocortical (TC) neurons from the ventrobasal (VB) thalamus are central components in the flow of sensory information between the periphery and the cerebral cortex, and participate in the dynamic regulation of thalamocortical states including wakefulness and sleep. This property is reflected at the cellular level by the ability to generate action potentials in two distinct firing modes, called tonic firing and low-threshold bursting. Although the general properties of TC neurons are known, we still lack a detailed characterization of their morphological and electrical properties in the VB thalamus. The aim of this study was to build biophysically-detailed models of VB TC neurons explicitly constrained with experimental data from rats. We recorded the electrical activity of VB neurons (N = 49) and reconstructed morphologies in 3D (N = 50) by applying standardized protocols. After identifying distinct electrical types, we used a multi-objective optimization to fit single neuron electrical models (e-models), which yielded multiple solutions consistent with the experimental data. The models were tested for generalization using electrical stimuli and neuron morphologies not used during fitting. A local sensitivity analysis revealed that the e-models are robust to small parameter changes and that all the parameters were constrained by one or more features. The e-models, when tested in combination with different morphologies, showed that the electrical behavior is substantially preserved when changing dendritic structure and that the e-models were not overfit to a specific morphology. The models and their analysis show that automatic parameter search can be applied to capture complex firing behavior, such as co-existence of tonic firing and low-threshold bursting over a wide range of parameter sets and in combination with different neuron morphologies.

Diffusing substances during spreading depolarization: analytical expressions for propagation speed, triggering, and concentration time courses.

Spreading depolarization (SD) is an important phenomenon in stroke and migraine. However, the processes underlying the propagation of SD are still poorly understood, and an elementary model that is both physiological and quantitative is lacking. We show that, during the onset and propagation of SD, the concentration time courses of excitatory substances such as potassium and glutamate can be described with a reaction-diffusion equation. This equation contains four physiological parameters: (1) a concentration threshold for excitation; (2) a release rate; (3) a removal rate; and (4) an effective diffusion constant. Solving this equation yields expressions for the propagation velocity, concentration time courses, and the minimum stimulus that can trigger SD. This framework allows for analyzing experimental results in terms of these four parameters. The derived time courses are validated with measurements of potassium in rat brain tissue.

A neural mass model based on single cell dynamics to model pathophysiology.

Neural mass models are successful in modeling brain rhythms as observed in macroscopic measurements such as the electroencephalogram (EEG). While the synaptic current is explicitly modeled in current models, the single cell electrophysiology is not taken into account. To allow for investigations of the effects of channel pathologies, channel blockers and ion concentrations on macroscopic activity, we formulate neural mass equations explicitly incorporating the single cell dynamics by using a bottom-up approach. The mean and variance of the firing rate and synaptic input distributions are modeled. The firing rate curve (F(I)-curve) is used as link between the single cell and macroscopic dynamics. We show that this model accurately reproduces the behavior of two populations of synaptically connected Hodgkin-Huxley neurons, also in non-steady state.

Single neuron dynamics during experimentally induced anoxic depolarization.

We studied single neuron dynamics during anoxic depolarizations, which are often observed in cases of neuronal energy depletion. Anoxic and similar depolarizations play an important role in several pathologies, notably stroke, migraine, and epilepsy. One of the effects of energy depletion was experimentally simulated in slices of rat cortex by blocking the sodium-potassium pumps with ouabain. The membrane voltage of pyramidal cells was measured. Five different kinds of dynamical behavior of the membrane voltage were observed during the resulting depolarizations. Using bifurcation analysis of a single cell model, we show that these voltage dynamics all are responses of the same cell, with normally functioning ion channels, to particular courses of the intra- and extracellular concentrations of sodium and potassium.

Capacitance measurement of dendritic exocytosis in an electrically coupled inhibitory retinal interneuron: an experimental and computational study.

Exocytotic release of neurotransmitter can be quantified by electrophysiological recording from postsynaptic neurons. Alternatively, fusion of synaptic vesicles with the cell membrane can be measured as increased capacitance by recording directly from a presynaptic neuron. The "Sine + DC" technique is based on recording from an unbranched cell, represented by an electrically equivalent RC-circuit. It is challenging to extend such measurements to branching neurons where exocytosis occurs at a distance from a somatic recording electrode. The AII amacrine is an important inhibitory interneuron of the mammalian retina and there is evidence that exocytosis at presynaptic lobular dendrites increases the capacitance. Here, we combined electrophysiological recording and computer simulations with realistic compartmental models to explore capacitance measurements of rat AII amacrine cells. First, we verified the ability of the "Sine + DC" technique to detect depolarization-evoked exocytosis in physiological recordings. Next, we used compartmental modeling to demonstrate that capacitance measurements can detect increased membrane surface area at lobular dendrites. However, the accuracy declines for lobular dendrites located further from the soma due to frequency-dependent signal attenuation. For sine wave frequencies ≥1 kHz, the magnitude of the total releasable pool of synaptic vesicles will be significantly underestimated. Reducing the sine wave frequency increases overall accuracy, but when the frequency is sufficiently low that exocytosis can be detected with high accuracy from all lobular dendrites (~100 Hz), strong electrical coupling between AII amacrines compromises the measurements. These results need to be taken into account in studies with capacitance measurements from these and other electrically coupled neurons.

Electrotonic signal processing in AII amacrine cells: compartmental models and passive membrane properties for a gap junction-coupled retinal neuron.

Amacrine cells are critical for processing of visual signals, but little is known about their electrotonic structure and passive membrane properties. AII amacrine cells are multifunctional interneurons in the mammalian retina and essential for both rod- and cone-mediated vision. Their dendrites are the site of both input and output chemical synapses and gap junctions that form electrically coupled networks. This electrical coupling is a challenge for developing realistic computer models of single neurons. Here, we combined multiphoton microscopy and electrophysiological recording from dye-filled AII amacrine cells in rat retinal slices to develop morphologically accurate compartmental models. Passive cable properties were estimated by directly fitting the current responses of the models evoked by voltage pulses to the physiologically recorded responses, obtained after blocking electrical coupling. The average best-fit parameters (obtained at - 60 mV and ~ 25 °C) were 0.91 µF cm-2 for specific membrane capacitance, 198 Ω cm for cytoplasmic resistivity, and 30 kΩ cm2 for specific membrane resistance. We examined the passive signal transmission between the cell body and the dendrites by the electrotonic transform and quantified the frequency-dependent voltage attenuation in response to sinusoidal current stimuli. There was significant frequency-dependent attenuation, most pronounced for signals generated at the arboreal dendrites and propagating towards the soma and lobular dendrites. In addition, we explored the consequences of the electrotonic structure for interpreting currents in somatic, whole-cell voltage-clamp recordings. The results indicate that AII amacrines cannot be characterized as electrotonically compact and suggest that their morphology and passive properties can contribute significantly to signal integration and processing.

AMPA receptors at ribbon synapses in the mammalian retina: kinetic models and molecular identity.

In chemical synapses, neurotransmitter molecules released from presynaptic vesicles activate populations of postsynaptic receptors that vary in functional properties depending on their subunit composition. Differential expression and localization of specific receptor subunits are thought to play fundamental roles in signal processing, but our understanding of how that expression is adapted to the signal processing in individual synapses and microcircuits is limited. At ribbon synapses, glutamate release is independent of action potentials and characterized by a high and rapidly changing rate of release. Adequately translating such presynaptic signals into postsynaptic electrical signals poses a considerable challenge for the receptor channels in these synapses. Here, we investigated the functional properties of AMPA receptors of AII amacrine cells in rat retina that receive input at spatially segregated ribbon synapses from OFF-cone and rod bipolar cells. Using patch-clamp recording from outside-out patches, we measured the concentration dependence of response amplitude and steady-state desensitization, the single-channel conductance and the maximum open probability. The GluA4 subunit seems critical for the functional properties of AMPA receptors in AII amacrines and immunocytochemical labeling suggested that GluA4 is located at synapses made by both OFF-cone bipolar cells and rod bipolar cells. Finally, we used a series of experimental observables to develop kinetic models for AII amacrine AMPA receptors and subsequently used the models to explore the behavior of the receptors and responses generated by glutamate concentration profiles mimicking those occurring in synapses. These models will facilitate future in silico modeling of synaptic signaling and processing in AII amacrine cells.

AII amacrine cells: quantitative reconstruction and morphometric analysis of electrophysiologically identified cells in live rat retinal slices imaged with multi-photon excitation microscopy.

AII amacrine cells have been found in all mammalian retinas examined and play an important role for visual processing under both scotopic and photopic conditions. Whereas ultrastructural investigations have provided a detailed understanding of synaptic connectivity, there is little information available with respect to quantitative properties and variation of cellular morphology. Here, we performed whole-cell recordings from AII amacrine cells in rat retinal slices and filled the cells with fluorescent dyes. Multi-photon excitation microscopy was used to acquire image stacks and after deconvolution, we performed quantitative morphological reconstruction by computer-aided manual tracing. We reconstructed and performed morphometric analysis on 43 AII amacrine cells, with a focus on branching pattern, dendritic lengths and diameters, surface area, and number and distribution of dendritic varicosities. Compared to previous descriptions, the most surprising result was the considerable extent of branching, with the maximum branch order ranging from approximately 10-40. We found that AII amacrine cells conform to a recently described general structural design principle for neural arbors, where arbor density decreases proportionally to increasing territory size. We confirmed and quantified the bi-stratified morphology of AII amacrine cells by analyzing the arborizations as a function of retinal localization or with Sholl spheres. Principal component and cluster analysis revealed no evidence for morphological subtypes of AII amacrines. These results establish a database of morphometric properties important for studies of development, regeneration, degeneration, and disease processes, as well as a workflow compatible with compartmental modeling.

Semi-automatic 3D morphological reconstruction of neurons with densely branching morphology: Application to retinal AII amacrine cells imaged with multi-photon excitation microscopy.

BACKGROUND: Accurate reconstruction of the morphology of single neurons is important for morphometric studies and for developing compartmental models. However, manual morphological reconstruction can be extremely time-consuming and error-prone and algorithms for automatic reconstruction can be challenged when applied to neurons with a high density of extensively branching processes. NEW METHOD: We present a procedure for semi-automatic reconstruction specifically adapted for densely branching neurons such as the AII amacrine cell found in mammalian retinas. We used whole-cell recording to fill AII amacrine cells in rat retinal slices with fluorescent dyes and acquired digital image stacks with multi-photon excitation microscopy. Our reconstruction algorithm combines elements of existing procedures, with segmentation based on adaptive thresholding and reconstruction based on a minimal spanning tree. We improved this workflow with an algorithm that reconnects neuron segments that are disconnected after adaptive thresholding, using paths extracted from the image stacks with the Fast Marching method. RESULTS: By reducing the likelihood that disconnected segments were incorrectly connected to neighboring segments, our procedure generated excellent morphological reconstructions of AII amacrine cells. COMPARISON WITH EXISTING METHODS: Reconstructing an AII amacrine cell required about 2h computing time, compared to 2-4days for manual reconstruction. To evaluate the performance of our method relative to manual reconstruction, we performed detailed analysis using a measure of tree structure similarity (DIADEM score), the degree of projection area overlap (Dice coefficient), and branch statistics. CONCLUSIONS: We expect our procedure to be generally useful for morphological reconstruction of neurons filled with fluorescent dyes.

How does spreading depression spread? Physiology and modeling.

Spreading depression (SD) is a wave phenomenon in gray matter tissue. Locally, it is characterized by massive redistribution of ions across cell membranes. As a consequence, there is sustained membrane depolarization and tissue polarization that depress any normal electrical activity. Despite these dramatic events, SD remains difficult to observe in humans noninvasively, which, for long, has slowed advances in this field. The growing appreciation of its clinical importance in migraine and stroke is therefore consistent with an increasing need for computational methods that tackle the complexity of the problem at multiple levels. In this review, we focus on mathematical tools to investigate the question of spread and its two complementary aspects: What are the physiological mechanisms and what is the spatial extent of SD in the cortex? This review discusses two types of models used to study these two questions, namely, Hodgkin-Huxley type and generic activator-inhibitor models, and the recent advances in techniques to link them.

Neural dynamics during anoxia and the "wave of death".

Recent experiments in rats have shown the occurrence of a high amplitude slow brain wave in the EEG approximately 1 minute after decapitation, with a duration of 5-15 s (van Rijn et al, PLoS One 6, e16514, 2011) that was presumed to signify the death of brain neurons. We present a computational model of a single neuron and its intra- and extracellular ion concentrations, which shows the physiological mechanism for this observation. The wave is caused by membrane potential oscillations, that occur after the cessation of activity of the sodium-potassium pumps has lead to an excess of extracellular potassium. These oscillations can be described by the Hodgkin-Huxley equations for the sodium and potassium channels, and result in a sudden change in mean membrane voltage. In combination with a high-pass filter, this sudden depolarization leads to a wave in the EEG. We discuss that this process is not necessarily irreversible.