NeuronC: a computational language for investigating functional architecture of neural circuits

Two mechanisms for direction selectivity in a model of the primate starburst amacrine cell

In a recent study, visual signals were recorded for the first time in starburst amacrine cells of the macaque retina, and, as for mouse and rabbit, a directional bias observed in calcium signals was recorded from near the dendritic tips. Stimulus motion from the soma toward the tip generated a larger calcium signal than motion from the tip toward the soma. Two mechanisms affecting the spatiotemporal summation of excitatory postsynaptic currents have been proposed to contribute to directional signaling at the dendritic tips of starbursts: (1) a "morphological" mechanism in which electrotonic propagation of excitatory synaptic currents along a dendrite sums bipolar cell inputs at the dendritic tip preferentially for stimulus motion in the centrifugal direction; (2) a "space-time" mechanism that relies on differences in the time-courses of proximal and distal bipolar cell inputs to favor centrifugal stimulus motion. To explore the contributions of these two mechanisms in the primate, we developed a realistic computational model based on connectomic reconstruction of a macaque starburst cell and the distribution of its synaptic inputs from sustained and transient bipolar cell types. Our model suggests that both mechanisms can initiate direction selectivity in starburst dendrites, but their contributions differ depending on the spatiotemporal properties of the stimulus. Specifically, the morphological mechanism dominates when small visual objects are moving at high velocities, and the space-time mechanism contributes most for large visual objects moving at low velocities.

Visual Stimulation Induces Distinct Forms of Sensitization of On-Off Direction-Selective Ganglion Cell Responses in the Dorsal and Ventral Retina

Experience-dependent modulation of neuronal responses is a key attribute in sensory processing. In the mammalian retina, the On-Off direction-selective ganglion cell (DSGC) is well known for its robust direction selectivity. However, how the On-Off DSGC light responsiveness dynamically adjusts to the changing visual environment is underexplored. Here, we report that On-Off DSGCs tuned to posterior motion direction [i.e. posterior DSGCs (pDSGCs)] in mice of both sexes can be transiently sensitized by prior stimuli. Notably, distinct sensitization patterns are found in dorsal and ventral pDSGCs. Although responses of both dorsal and ventral pDSGCs to dark stimuli (Off responses) are sensitized, only dorsal cells show the sensitization of responses to bright stimuli (On responses). Visual stimulation to the dorsal retina potentiates a sustained excitatory input from Off bipolar cells, leading to tonic depolarization of pDSGCs. Such tonic depolarization propagates from the Off to the On dendritic arbor of the pDSGC to sensitize its On response. We also identified a previously overlooked feature of DSGC dendritic architecture that can support dendritic integration between On and Off dendritic layers bypassing the soma. By contrast, ventral pDSGCs lack a sensitized tonic depolarization and thus do not exhibit sensitization of their On responses. Our results highlight a topographic difference in Off bipolar cell inputs underlying divergent sensitization patterns of dorsal and ventral pDSGCs. Moreover, substantial crossovers between dendritic layers of On-Off DSGCs suggest an interactive dendritic algorithm for processing On and Off signals before they reach the soma.SIGNIFICANCE STATEMENT Visual neuronal responses are dynamically influenced by the prior visual experience. This form of plasticity reflects the efficient coding of the naturalistic environment by the visual system. We found that a class of retinal output neurons, On-Off direction-selective ganglion cells, transiently increase their responsiveness after visual stimulation. Cells located in dorsal and ventral retinas exhibit distinct sensitization patterns because of different adaptive properties of Off bipolar cell signaling. A previously overlooked dendritic morphologic feature of the On-Off direction-selective ganglion cell is implicated in the cross talk between On and Off pathways during sensitization. Together, these findings uncover a topographic difference in the adaptive encoding of upper and lower visual fields and the underlying neural mechanism in the dorsal and ventral retinas.

Origins of direction selectivity in the primate retina

From mouse to primate, there is a striking discontinuity in our current understanding of the neural coding of motion direction. In non-primate mammals, directionally selective cell types and circuits are a signature feature of the retina, situated at the earliest stage of the visual process. In primates, by contrast, direction selectivity is a hallmark of motion processing areas in visual cortex, but has not been found in the retina, despite significant effort. Here we combined functional recordings of light-evoked responses and connectomic reconstruction to identify diverse direction-selective cell types in the macaque monkey retina with distinctive physiological properties and synaptic motifs. This circuitry includes an ON-OFF ganglion cell type, a spiking, ON-OFF polyaxonal amacrine cell and the starburst amacrine cell, all of which show direction selectivity. Moreover, we discovered that macaque starburst cells possess a strong, non-GABAergic, antagonistic surround mediated by input from excitatory bipolar cells that is critical for the generation of radial motion sensitivity in these cells. Our findings open a door to investigation of a precortical circuitry that computes motion direction in the primate visual system.

Retinal horizontal cells use different synaptic sites for global feedforward and local feedback signaling

In the outer plexiform layer (OPL) of the mammalian retina, cone photoreceptors (cones) provide input to more than a dozen types of cone bipolar cells (CBCs). In the mouse, this transmission is modulated by a single horizontal cell (HC) type. HCs perform global signaling within their laterally coupled network but also provide local, cone-specific feedback. However, it is unknown how HCs provide local feedback to cones at the same time as global forward signaling to CBCs and where the underlying synapses are located. To assess how HCs simultaneously perform different modes of signaling, we reconstructed the dendritic trees of five HCs as well as cone axon terminals and CBC dendrites in a serial block-face electron microscopy volume and analyzed their connectivity. In addition to the fine HC dendritic tips invaginating cone axon terminals, we also identified "bulbs," short segments of increased dendritic diameter on the primary dendrites of HCs. These bulbs are in an OPL stratum well below the cone axon terminal base and make contacts with other HCs and CBCs. Our results from immunolabeling, electron microscopy, and glutamate imaging suggest that HC bulbs represent GABAergic synapses that do not receive any direct photoreceptor input. Together, our data suggest the existence of two synaptic strata in the mouse OPL, spatially separating cone-specific feedback and feedforward signaling to CBCs. A biophysical model of a HC dendritic branch and voltage imaging support the hypothesis that this spatial arrangement of synaptic contacts allows for simultaneous local feedback and global feedforward signaling by HCs.

Cholinergic feedback to bipolar cells contributes to motion detection in the mouse retina

Retinal bipolar cells are second-order neurons that transmit basic features of the visual scene to postsynaptic partners. However, their contribution to motion detection has not been fully appreciated. Here, we demonstrate that cholinergic feedback from starburst amacrine cells (SACs) to certain presynaptic bipolar cells via alpha-7 nicotinic acetylcholine receptors (α7-nAChRs) promotes direction-selective signaling. Patch clamp recordings reveal that distinct bipolar cell types making synapses at proximal SAC dendrites also express α7-nAChRs, producing directionally skewed excitatory inputs. Asymmetric SAC excitation contributes to motion detection in On-Off direction-selective ganglion cells (On-Off DSGCs), predicted by computational modeling of SAC dendrites and supported by patch clamp recordings from On-Off DSGCs when bipolar cell α7-nAChRs is eliminated pharmacologically or by conditional knockout. Altogether, these results show that cholinergic feedback to bipolar cells enhances direction-selective signaling in postsynaptic SACs and DSGCs, illustrating how bipolar cells provide a scaffold for postsynaptic microcircuits to cooperatively enhance retinal motion detection.

Realistic retinal modeling unravels the differential role of excitation and inhibition to starburst amacrine cells in direction selectivity

Retinal direction-selectivity originates in starburst amacrine cells (SACs), which display a centrifugal preference, responding with greater depolarization to a stimulus expanding from soma to dendrites than to a collapsing stimulus. Various mechanisms were hypothesized to underlie SAC centrifugal preference, but dissociating them is experimentally challenging and the mechanisms remain debatable. To address this issue, we developed the Retinal Stimulation Modeling Environment (RSME), a multifaceted data-driven retinal model that encompasses detailed neuronal morphology and biophysical properties, retina-tailored connectivity scheme and visual input. Using a genetic algorithm, we demonstrated that spatiotemporally diverse excitatory inputs-sustained in the proximal and transient in the distal processes-are sufficient to generate experimentally validated centrifugal preference in a single SAC. Reversing these input kinetics did not produce any centrifugal-preferring SAC. We then explored the contribution of SAC-SAC inhibitory connections in establishing the centrifugal preference. SAC inhibitory network enhanced the centrifugal preference, but failed to generate it in its absence. Embedding a direction selective ganglion cell (DSGC) in a SAC network showed that the known SAC-DSGC asymmetric connectivity by itself produces direction selectivity. Still, this selectivity is sharpened in a centrifugal-preferring SAC network. Finally, we use RSME to demonstrate the contribution of SAC-SAC inhibitory connections in mediating direction selectivity and recapitulate recent experimental findings. Thus, using RSME, we obtained a mechanistic understanding of SACs' centrifugal preference and its contribution to direction selectivity.

Preserving inhibition with a disinhibitory microcircuit in the retina

Previously, we found that in the mammalian retina, inhibitory inputs onto starburst amacrine cells (SACs) are required for robust direction selectivity of On-Off direction-selective ganglion cells (On-Off DSGCs) against noisy backgrounds (Chen et al., 2016). However, the source of the inhibitory inputs to SACs and how this inhibition confers noise resilience of DSGCs are unknown. Here, we show that when visual noise is present in the background, the motion-evoked inhibition to an On-Off DSGC is preserved by a disinhibitory motif consisting of a serially connected network of neighboring SACs presynaptic to the DSGC. This preservation of inhibition by a disinhibitory motif arises from the interaction between visually evoked network dynamics and short-term synaptic plasticity at the SAC-DSGC synapse. Although the disinhibitory microcircuit is well studied for its disinhibitory function in brain circuits, our results highlight the algorithmic flexibility of this motif beyond disinhibition due to the mutual influence between network and synaptic plasticity mechanisms.

Bayesian inference for biophysical neuron models enables stimulus optimization for retinal neuroprosthetics

While multicompartment models have long been used to study the biophysics of neurons, it is still challenging to infer the parameters of such models from data including uncertainty estimates. Here, we performed Bayesian inference for the parameters of detailed neuron models of a photoreceptor and an OFF- and an ON-cone bipolar cell from the mouse retina based on two-photon imaging data. We obtained multivariate posterior distributions specifying plausible parameter ranges consistent with the data and allowing to identify parameters poorly constrained by the data. To demonstrate the potential of such mechanistic data-driven neuron models, we created a simulation environment for external electrical stimulation of the retina and optimized stimulus waveforms to target OFF- and ON-cone bipolar cells, a current major problem of retinal neuroprosthetics.

Light-evoked glutamate transporter EAAT5 activation coordinates with conventional feedback inhibition to control rod bipolar cell output

In the retina, modulation of the amplitude of dim visual signals primarily occurs at axon terminals of rod bipolar cells (RBCs). GABA and glycine inhibitory neurotransmitter receptors and the excitatory amino acid transporter 5 (EAAT5) modulate the RBC output. EAATs clear glutamate from the synapse, but they also have a glutamate-gated chloride conductance. EAAT5 acts primarily as an inhibitory glutamate-gated chloride channel. The relative role of visually evoked EAAT5 inhibition compared with GABA and glycine inhibition has not been addressed. In this study, we determine the contribution of EAAT5-mediated inhibition onto RBCs in response to light stimuli in mouse retinal slices. We find differences and similarities in the two forms of inhibition. Our results show that GABA and glycine mediate nearly all lateral inhibition onto RBCs, as EAAT5 is solely a mediator of RBC feedback inhibition. We also find that EAAT5 and conventional GABA inhibition both contribute to feedback inhibition at all stimulus intensities. Finally, our in silico modeling compares and contrasts EAAT5-mediated to GABA- and glycine-mediated feedback inhibition. Both forms of inhibition have a substantial impact on synaptic transmission to the postsynaptic AII amacrine cell. Our results suggest that the late phase EAAT5 inhibition acts with the early phase conventional, reciprocal GABA inhibition to modulate the rod signaling pathway between rod bipolar cells and their downstream synaptic targets.NEW & NOTEWORTHY Excitatory amino acid transporter 5 (EAAT5) glutamate transporters have a chloride channel that is strongly activated by glutamate, which modulates excitatory signaling. We found that EAAT5 is a major contributor to feedback inhibition on rod bipolar cells. Inhibition to rod bipolar cells is also mediated by GABA and glycine. GABA and glycine mediate the early phase of feedback inhibition, and EAAT5 mediates a more delayed inhibition. Together, inhibitory transmitters and EAAT5 coordinate to mediate feedback inhibition, controlling neuronal output.

Local Signals in Mouse Horizontal Cell Dendrites

The mouse retina contains a single type of horizontal cell, a GABAergic interneuron that samples from all cone photoreceptors within reach and modulates their glutamatergic output via parallel feedback mechanisms. Because horizontal cells form an electrically coupled network, they have been implicated in global signal processing, such as large-scale contrast enhancement. Recently, it has been proposed that horizontal cells can also act locally at the level of individual cone photoreceptors. To test this possibility physiologically, we used two-photon microscopy to record light stimulus-evoked Ca²⁺ signals in cone axon terminals and horizontal cell dendrites as well as glutamate release in the outer plexiform layer. By selectively stimulating the two mouse cone opsins with green and UV light, we assessed whether signals from individual cones remain isolated within horizontal cell dendritic tips or whether they spread across the dendritic arbor. Consistent with the mouse's opsin expression gradient, we found that the Ca²⁺ signals recorded from dendrites of dorsal horizontal cells were dominated by M-opsin and those of ventral horizontal cells by S-opsin activation. The signals measured in neighboring horizontal cell dendritic tips varied markedly in their chromatic preference, arguing against global processing. Rather, our experimental data and results from biophysically realistic modeling support the idea that horizontal cells can process cone input locally, extending the classical view of horizontal cell function. Pharmacologically removing horizontal cells from the circuitry reduced the sensitivity of the cone signal to low frequencies, suggesting that local horizontal cell feedback shapes the temporal properties of cone output.

Directional excitatory input to direction-selective ganglion cells in the rabbit retina

Directional responses in retinal ganglion cells are generated in large part by direction-selective release of γ-aminobutyric acid from starburst amacrine cells onto direction-selective ganglion cells (DSGCs). The excitatory inputs to DSGCs are also widely reported to be direction-selective, however, recent evidence suggests that glutamate release from bipolar cells is not directional, and directional excitation seen in patch-clamp analyses may be an artifact resulting from incomplete voltage control. Here, we test this voltage-clamp-artifact hypothesis in recordings from 62 ON-OFF DSGCs in the rabbit retina. The strength of the directional excitatory signal varies considerably across the sample of cells, but is not correlated with the strength of directional inhibition, as required for a voltage-clamp artifact. These results implicate additional mechanisms in generating directional excitatory inputs to DSGCs.

Time course of EPSCs in ON-type starburst amacrine cells is independent of dendritic location

KEY POINTS

Direction selectivity has been widely studied as an example of a complex neural computation. Directional GABA release from starburst amacrine cells (SBACs) is critical for generating directional signals in direction-selective ganglion cells. The mechanisms producing the directional release remain unclear. For SBACs, ordered distribution of sustained and transient bipolar cell inputs along the dendrites is proposed to generate directional GABA release. This study tests whether this hypothesis applies to ON-type SBACs. EPSCs activated at proximal and distal dendritic locations have the same time course. Therefore, the ordered arrangement of inputs from bipolar cells with different kinetic properties cannot be responsible for generating directional GABA release from ON-type SBACs.

ABSTRACT

Direction selectivity in the retina relies critically on directionally asymmetric GABA release from the dendritic tips of starburst amacrine cells (SBACs). GABA release from each radially directed dendrite is larger for motion outward from the soma toward the dendritic tips than for motion inwards toward the soma. The biophysical mechanisms generating these directional signals remain controversial. A model based on electron-microscopic reconstructions of the mouse retina proposed that an ordered arrangement of kinetically distinct bipolar cell inputs to ON- and OFF-type SBACs could produce directional GABA release. We tested this prediction by measuring the time course of EPSCs in ON-type SBACs in the mouse retina, activated by proximal and distal light stimulation. Contrary to the prediction, the kinetics of the excitatory inputs were independent of dendritic location. Computer simulations based on 3D reconstructions of SBAC dendrites demonstrated that the response kinetics of distal inputs were not significantly altered by dendritic filtering. These direct physiological measurements, do not support the hypothesis that directional signals in SBACs arise from the ordered arrangement of kinetically distinct bipolar cell inputs.

Species-specific wiring for direction selectivity in the mammalian retina

Directionally tuned signaling in starburst amacrine cell (SAC) dendrites lies at the heart of the direction selective (DS) circuit in the mammalian retina. The relative contributions of intrinsic cellular properties and network connectivity to SAC DS remain unclear. We present a detailed connectomic reconstruction of SAC circuitry in mouse retina and describe previously unknown features of synapse distributions along SAC dendrites: 1) input and output synapses are segregated, with inputs restricted to proximal dendrites; 2) the distribution of inhibitory inputs is fundamentally different from that observed in rabbit retina. An anatomically constrained SAC network model suggests that SAC-SAC wiring differences between mouse and rabbit retina underlie distinct contributions of synaptic inhibition to velocity and contrast tuning and receptive field structure. In particular, the model indicates that mouse connectivity enables SACs to encode lower linear velocities that account for smaller eye diameter, thereby conserving angular velocity tuning. These predictions are confirmed with calcium imaging of mouse SAC dendrites in response to directional stimuli.

Systematic analysis of the contributions of stochastic voltage gated channels to neuronal noise

Electrical signaling in neurons is mediated by the opening and closing of large numbers of individual ion channels. The ion channels' state transitions are stochastic and introduce fluctuations in the macroscopic current through ion channel populations. This creates an unavoidable source of intrinsic electrical noise for the neuron, leading to fluctuations in the membrane potential and spontaneous spikes. While this effect is well known, the impact of channel noise on single neuron dynamics remains poorly understood. Most results are based on numerical simulations. There is no agreement, even in theoretical studies, on which ion channel type is the dominant noise source, nor how inclusion of additional ion channel types affects voltage noise. Here we describe a framework to calculate voltage noise directly from an arbitrary set of ion channel models, and discuss how this can be use to estimate spontaneous spike rates.

NaV1.1 channels in axon initial segments of bipolar cells augment input to magnocellular visual pathways in the primate retina

In the primate visual system, the ganglion cells of the magnocellular pathway underlie motion and flicker detection and are relatively transient, while the more sustained ganglion cells of the parvocellular pathway have comparatively lower temporal resolution, but encode higher spatial frequencies. Although it is presumed that functional differences in bipolar cells contribute to the tuning of the two pathways, the properties of the relevant bipolar cells have not yet been examined in detail. Here, by making patch-clamp recordings in acute slices of macaque retina, we show that the bipolar cells within the magnocellular pathway, but not the parvocellular pathway, exhibit voltage-gated sodium (NaV), T-type calcium (CaV), and hyperpolarization-activated, cyclic nucleotide-gated (HCN) currents, and can generate action potentials. Using immunohistochemistry in macaque and human retinae, we show that NaV1.1 is concentrated in an axon initial segment (AIS)-like region of magnocellular pathway bipolar cells, a specialization not seen in transient bipolar cells of other vertebrates. In contrast, CaV3.1 channels were localized to the somatodendritic compartment and proximal axon, but were excluded from the AIS, while HCN1 channels were concentrated in the axon terminal boutons. Simulations using a compartmental model reproduced physiological results and indicate that magnocellular pathway bipolar cells initiate spikes in the AIS. Finally, we demonstrate that NaV channels in bipolar cells augment excitatory input to parasol ganglion cells of the magnocellular pathway. Overall, the results demonstrate that selective expression of voltage-gated channels contributes to the establishment of parallel processing in the major visual pathways of the primate retina.

Neuronal morphology goes digital: a research hub for cellular and system neuroscience

The importance of neuronal morphology in brain function has been recognized for over a century. The broad applicability of "digital reconstructions" of neuron morphology across neuroscience subdisciplines has stimulated the rapid development of numerous synergistic tools for data acquisition, anatomical analysis, three-dimensional rendering, electrophysiological simulation, growth models, and data sharing. Here we discuss the processes of histological labeling, microscopic imaging, and semiautomated tracing. Moreover, we provide an annotated compilation of currently available resources in this rich research "ecosystem" as a central reference for experimental and computational neuroscience.

Directional summation in non-direction selective retinal ganglion cells

Retinal ganglion cells receive inputs from multiple bipolar cells which must be integrated before a decision to fire is made. Theoretical studies have provided clues about how this integration is accomplished but have not directly determined the rules regulating summation of closely timed inputs along single or multiple dendrites. Here we have examined dendritic summation of multiple inputs along On ganglion cell dendrites in whole mount rat retina. We activated inputs at targeted locations by uncaging glutamate sequentially to generate apparent motion along On ganglion cell dendrites in whole mount retina. Summation was directional and dependent13 on input sequence. Input moving away from the soma (centrifugal) resulted in supralinear summation, while activation sequences moving toward the soma (centripetal) were linear. Enhanced summation for centrifugal activation was robust as it was also observed in cultured retinal ganglion cells. This directional summation was dependent on hyperpolarization activated cyclic nucleotide-gated (HCN) channels as blockade with ZD7288 eliminated directionality. A computational model confirms that activation of HCN channels can override a preference for centripetal summation expected from cell anatomy. This type of direction selectivity could play a role in coding movement similar to the axial selectivity seen in locust ganglion cells which detect looming stimuli. More generally, these results suggest that non-directional retinal ganglion cells can discriminate between input sequences independent of the retina network.

Visual information is coded by the output of retinal ganglion cells. Through evolution retinal ganglion cells acquired unique properties that allowed them to transmit to the brain such signals as direction of movement. The quest for the cellular mechanism of the detection of movement by retinal ganglion cells has been the holy grail of research on direction selectivity. In this study we have found a mechanism that allows individual non-direction selective On retinal ganglion cells to code sequences of excitatory inputs moving either away or toward the soma. We observed that inputs moving away from the soma resulted in enhanced, supralinear EPSP summation. Evidence from computational modeling suggests that expression of a specific set of voltage-dependent channels in dendrites introduces nonlinearities that could give a ganglion cell the ability to code looming motion. We predict that in a retinal network, such a directional tuning mechanism, together with asymmetric presynaptic inhibition, could be the building block for the development of more complex detection of visual motion.

ANCHOR — A CONNECTIONIST ARCHITECTURE FOR PARTITIONING FEATURE SPACES AND HIERARCHICAL NESTING OF NEURAL NETS

We present a novel connectionist architecture for handling arbitrarily complex neural computations. The architecture — which we call an Artificial Neural Network Compiler for Hierarchical ORganisation (ANCHOR) — facilitates network hierarchy and the partitioning of the input space into a number of small, simpler sub-mappings. This strategy is a mix of both a modular approach for reduction of the problem complexity, and an ensemble-based approach for increasing prediction accuracy. ANCHOR is implemented around the concept of a Superneuron which is a generalised view of a neuron-processing element; a superneuron is a single (or higher-order) perceptron which can be trained individually with the support of multiple learning algorithms. The indistinguishability between a superneuron, and a neuron is employed in hierarchical nesting of superneurons, up to (theoretically) infinite depth, within other superneurons as well as linear or tree-structured cascading. Hierarchical decomposition of simple boolean functions has been demonstrated as proof-of-concept. It is argued that this strategy of data-partitioning for subsequent mapping onto a hierarchical classifier reduces the learning complexity and offers better generalisation.

Fluctuations in the open time of synaptic channels: an application to noise analysis based on charge

Synaptic channels are stochastic devices. Even recording from large ensembles of channels, the fluctuations, described by Markov transition matrices, can be used to extract single channel properties. Here we study fluctuations in the open time of channels, which is proportional to the charge flowing through the channel. We use the results to implement a novel type of noise analysis that uses the charge rather than the current to extract fundamental channel parameters. We show in simulations that this charge based noise analysis is more robust if the synapse is located on the dendrites and thus subject to cable filtering. However, we also demonstrate that when multiple synapses are distributed on the dendrites, noise analysis breaks down. We finally discuss applications of our results to other biological processes.

Dendritic spikes amplify the synaptic signal to enhance detection of motion in a simulation of the direction-selective ganglion cell

The On-Off direction-selective ganglion cell (DSGC) in mammalian retinas responds most strongly to a stimulus moving in a specific direction. The DSGC initiates spikes in its dendritic tree, which are thought to propagate to the soma with high probability. Both dendritic and somatic spikes in the DSGC display strong directional tuning, whereas somatic PSPs (postsynaptic potentials) are only weakly directional, indicating that spike generation includes marked enhancement of the directional signal. We used a realistic computational model based on anatomical and physiological measurements to determine the source of the enhancement. Our results indicate that the DSGC dendritic tree is partitioned into separate electrotonic regions, each summing its local excitatory and inhibitory synaptic inputs to initiate spikes. Within each local region the local spike threshold nonlinearly amplifies the preferred response over the null response on the basis of PSP amplitude. Using inhibitory conductances previously measured in DSGCs, the simulation results showed that inhibition is only sufficient to prevent spike initiation and cannot affect spike propagation. Therefore, inhibition will only act locally within the dendritic arbor. We identified the role of three mechanisms that generate directional selectivity (DS) in the local dendritic regions. First, a mechanism for DS intrinsic to the dendritic structure of the DSGC enhances DS on the null side of the cell's dendritic tree and weakens it on the preferred side. Second, spatially offset postsynaptic inhibition generates robust DS in the isolated dendritic tips but weak DS near the soma. Third, presynaptic DS is apparently necessary because it is more robust across the dendritic tree. The pre- and postsynaptic mechanisms together can overcome the local intrinsic DS. These local dendritic mechanisms can perform independent nonlinear computations to make a decision, and there could be analogous mechanisms within cortical circuitry.

The On-Off direction-selective ganglion cell (DSGC) found in mammalian retinas generates a directional signal, responding most strongly to a stimulus moving in a specific direction. The DSGC initiates spikes in its dendritic tree which are thought to propagate to the soma and brain with high probability. Both dendritic and somatic spikes in the DSGC display strong directional tuning, whereas postsynaptic potentials (PSPs) recorded in the soma are only weakly directional, indicating that postsynaptic spike generation markedly enhances the directional signal. We constructed a realistic computational model to determine the source of the enhancement. Our results indicate that the DSGC dendritic tree is partitioned into separate computational regions. Within each region, the local spike threshold produces nonlinear amplification of the preferred response over the null response on the basis of PSP amplitude. The simulation results showed that inhibition acts locally within the dendritic arbor and will not stop dendritic spikes from propagating. We identified the role of three mechanisms that generate direction selectivity in the local dendritic regions, which suggests the origin of the previously described “non-direction-selective region,” and also suggests that the known DS in the synaptic inputs is apparently necessary for robust DS across the dendritic tree.

Postsynaptic calcium feedback between rods and rod bipolar cells in the mouse retina

Light-evoked currents were recorded from rod bipolar cells in a dark-adapted mouse retinal slice preparation. Low-intensity light steps evoked a sustained inward current. Saturating light steps evoked an inward current with an initial peak that inactivated, with a time constant of about 60-70 ms, to a steady plateau level that was maintained for the duration of the step. The inactivation was strongest at hyperpolarized potentials, and absent at positive potentials. Inactivation was mediated by an increase in the intracellular calcium concentration, as it was abolished in cells dialyzed with 10 mM BAPTA, but was present in cells dialyzed with 1 mM EGTA. Moreover, responses to brief flashes of light were broader in the presence of intracellular BAPTA indicating that the calcium feedback actively shapes the time course of the light responses. Recovery from inactivation observed for paired-pulse stimuli occurred with a time constant of about 375 ms. Calcium feedback could act to increase the dynamic range of the bipolar cells, and to reduce variability in the amplitude and duration of the single-photon signal. This may be important for nonlinear processing at downstream sites of convergence from rod bipolar cells to AII amacrine cells. A model in which intracellular calcium rapidly binds to the light-gated channel and reduces the conductance can account for the results.

Direction selectivity in a model of the starburst amacrine cell

The starburst amacrine cell (SBAC), found in all mammalian retinas, is thought to provide the directional inhibitory input recorded in On–Off direction-selective ganglion cells (DSGCs). While voltage recordings from the somas of SBACs have not shown robust direction selectivity (DS), the dendritic tips of these cells display direction-selective calcium signals, even when γ-aminobutyric acid (GABAa,c) channels are blocked, implying that inhibition is not necessary to generate DS. This suggested that the distinctive morphology of the SBAC could generate a DS signal at the dendritic tips, where most of its synaptic output is located. To explore this possibility, we constructed a compartmental model incorporating realistic morphological structure, passive membrane properties, and excitatory inputs. We found robust DS at the dendritic tips but not at the soma. Two-spot apparent motion and annulus radial motion produced weak DS, but thin bars produced robust DS. For these stimuli, DS was caused by the interaction of a local synaptic input signal with a temporally delayed “global” signal, that is, an excitatory postsynaptic potential (EPSP) that spread from the activated inputs into the soma and throughout the dendritic tree. In the preferred direction the signals in the dendritic tips coincided, allowing summation, whereas in the null direction the local signal preceded the global signal, preventing summation. Sine-wave grating stimuli produced the greatest amount of DS, especially at high velocities and low spatial frequencies. The sine-wave DS responses could be accounted for by a simple mathematical model, which summed phase-shifted signals from soma and dendritic tip. By testing different artificial morphologies, we discovered DS was relatively independent of the morphological details, but depended on having a sufficient number of inputs at the distal tips and a limited electrotonic isolation. Adding voltage-gated calcium channels to the model showed that their threshold effect can amplify DS in the intracellular calcium signal.

Effects of noise on the spike timing precision of retinal ganglion cells

Information in a spike train is limited by variability in the spike timing. This variability is caused by noise from several sources including synapses and membrane channels; but how deleterious each noise source is and how they affect spike train coding is unknown. Combining physiology and a multicompartment model, we studied the effect of synaptic input noise and voltage-gated channel noise on spike train reliability for a mammalian ganglion cell. For tonic stimuli, the SD of the interspike intervals increased supralinearly with increasing interspike interval. When the cell was driven by current injection, voltage-gated channel noise and background synaptic noise caused fluctuations in the interspike interval of comparable amplitude. Spikes initiated on the dendrites could cause additional spike timing fluctuations. For transient stimuli, synaptic noise was dominant and spontaneous background activity strongly increased fluctuations in spike timing but decreased the latency of the first spike.

Cost of cone coupling to trichromacy in primate fovea

Cone synaptic terminals couple electrically to their neighbors. This reduces the amplitude of temporally uncorrelated voltage differences between neighbors. For an achromatic stimulus coarser than the cone mosaic, the uncorrelated voltage difference between neighbors represents mostly noise; so noise is reduced more than the signal. Here coupling improves signal-to-noise ratio and enhances contrast sensitivity. But for a chromatic stimulus the uncorrelated voltage difference between neighbors of different spectral type represents mostly signal; so signal would be reduced more than the noise. This cost of cone coupling to encoding chromatic signals was evaluated using a compartmental model of the foveal cone array. When cones sensitive to middle (M) and long (L) wavelengths alternated regularly, and the conductance between a cone and all of its immediate neighbors was 1,000 pS (approximately 2 connexons/cone pair), coupling reduced the difference between the L and M action spectra by nearly fivefold, from about 38% to 8%. However, L and M cones distribute randomly in the mosaic, forming small patches of like type, and within a patch the responses to a chromatic stimulus are correlated. In such a mosaic, coupling still reduced the difference between the L and M action spectra, but only by 2.4-fold, to about 18%. This result is independent of the L/M ratio. Thus "patchiness" of the L/M mosaic allows cone coupling to improve achromatic contrast sensitivity while minimizing the cost to chromatic sensitivity.

Functional architecture of primate cone and rod axons

The cone axon is nearly four times thicker than the rod axon (1.6 vs 0.45 microns diameter). To assess how signal transfer and integration at the terminal depend on cable dimensions, a transducer (cone = ohmic conductance, rod = current source) coupled via passive cable to a sphere with a chloride conductance (representing GABAA receptor) was modelled. For a small signal in peripheral cone with a short axon, steady photosignal transfers independently of axon diameter despite a significant chloride conductance at the cone terminal. Temporally varying photosignal also transfers independently of axon diameter up to 20 Hz and is attenuated only 20% at 50 Hz. Thus, to accomplish the basic electrical functions of a peripheral cone, a thin axon would suffice. For a foveal cone with a long axon steady photosignal transfers independently of axon diameter, but temporally varying photosignal is attenuated 5-fold at 50 Hz for a thick axon and 10-fold for a thin axon. This might contribute to the lower sensitivity of central retina to high temporal frequencies. The cone axon contains 14-fold more microtubules than the rod axon, and its terminal contains at least 20-fold more ribbon synapses than the rod's. Since ribbon synapses sustain high rates of exocytosis, the additional microtubules (which require a thicker axon) may be needed to support a greater flux of synaptic vesicle components.

Syncytial integration by a network of coupled bipolar cells in the retina

A model system for syncytial integration is the outer vertebrate retina, where graded signals or electrotonic potentials interact laterally via gap junctions to form an integrated response that is relayed by chemical synapses to the next layer of interconnected cells. Morphological and physiological experiments confirm that bipolar cells form quasisyncytial lattices, and so this review will aim to address two important issues: the function of coupling in visual information processing and the construction of a robust mathematical model that can adequately simulate signal spread in the bipolar cell syncytium. It is shown that the role of coupling in bipolar cells differs from that associated in the presynaptic networks, namely, loss in spatial resolution in order to increase the signal-to-noise ratio. The intrinsic membrane properties of bipolar cells which give rise to voltage-dependent currents are inactive over the normal in vivo operating range of membrane potential and may be shunted as a direct result of electrotonic coupling, suppressing any possibility of action potential propagation in the bipolar cell syncytium. It is therefore speculated that the mechanisms underlying processing of information in bipolar networks are dependent on the structure of bipolar cells and in particular, on the presence of gap junctions. It is proposed that a three-dimensional model which incorporates the spatial properties of each bipolar cell in the network in the form of a leaky cable is the most likely model to simulate signal spread in the bipolar cell syncytium in vivo. This is because discrete network models represent each bipolar cell in the syncytium as isopotential units without any spatial structure, and thus are unable to reproduce the temporal characteristics of electrotonic potential spread within the central receptive field of bipolar cells.

A general computational framework for modeling cellular structure and function

The "Virtual Cell" provides a general system for testing cell biological mechanisms and creates a framework for encapsulating the burgeoning knowledge base comprising the distribution and dynamics of intracellular biochemical processes. It approaches the problem by associating biochemical and electrophysiological data describing individual reactions with experimental microscopic image data describing their subcellular localizations. Individual processes are collected within a physical and computational infrastructure that accommodates any molecular mechanism expressible as rate equations or membrane fluxes. An illustration of the method is provided by a dynamic simulation of IP3-mediated Ca2+ release from endoplasmic reticulum in a neuronal cell. The results can be directly compared to experimental observations and provide insight into the role of experimentally inaccessible components of the overall mechanism.

Effects of horizontal cell network architecture on signal spread in the turtle outer retina. Experiments and simulations

In the Pseudemys turtle retina five functionally distinct, electrically coupled networks of horizontal cells distribute signals in the outer plexiform layer. These networks differ significantly in their architecture, as determined by intracellular labeling with Neurobiotin after physiological recording and identification. The density of H1 horizontal cells is highest, ranging around 1800 cells/mm2 at approximately 2.3 mm eccentricity. H1 horizontal cell somata are connected via 6-10 thin, short dendrites. The H1 horizontal cell axon terminal network is composed of thick axon terminals, forming a three-dimensional, sheath-like structure. Networks of coupled H2 and H3 horizontal cells have cell densities of around 210 cells/mm2 and 350 cells/mm2, respectively, at the same eccentricity of 2.3 mm. Cell bodies are connected with 6-12 long, thin dendrites. Here we report for the first time H4 horizontal cell networks. Cell density is approximately 970 cells/mm2 at 2 mm eccentricity, and cell bodies are connected with 6-10 thin, short dendrites. General properties of passive voltage spread were compared for three of these horizontal cell networks using NeuronC. Realistic network architectures were obtained by digitizing the intracellularly labeled networks, respectively. One network obtained from coupled H1 horizontal cell bodies, one from coupled H1 horizontal cell axon terminals, and one from H2 horizontal cells were simulated. These three realistic networks were compared with an artificial, electrically coupled regular triangular network. Passive signal spread in these networks strongly depended on the exact network architecture using otherwise identical parameters. Changes in coupling strength affected signal spread in these networks differently. As in the experimental situation, changes in synaptic conductance influenced signal spread. Some principal effects of extensively coupled horizontal cells on photoreceptor signal processing were simulated with one type of photoreceptor connected by telodendria, synapsing onto an underlying triangular network and receiving feedback synapses. Under certain conditions, spatial information is coded in single photoreceptors. This was also the case in the experimental situation. In the simulation, spatial filter adjustment for optimal spatial coding in photoreceptors can be achieved by changing coupling strength in the horizontal cell network.

The AII amacrine network: coupling can increase correlated activity

Retinal ganglion cells in the cat respond to single rhodopsin isomerizations with one to three spikes. This quantal signal is transmitted in the retina by the rod bipolar pathway: rod-->rod bipolar-->AII-->cone bipolar-->ganglion cell. The two-dimensional circuit underlying this pathway includes extensive convergence from rods to an AII amacrine cell, divergence from a rod to several AII and ganglion cells, and coupling between the AII amacrine cells. In this study we explored the function of coupling by reconstructing several AII amacrine cells and the gap junctions between them from electron micrographs; and simulating the AII network with and without coupling. The simulation showed that coupling in the AII network can: (1) improve the signal/noise ratio in the AII network; (2) improve the signal/noise ratio for a single rhodopsin isomerization striking in the periphery of the ganglion cell receptive field center, and therefore in most ganglion cells responding to a single isomerization; (3) expand the AII and ganglion cells' receptive field center; and (4) expand the "correlation field". All of these effects have one major outcome: an increase in correlation between ganglion cell activity. Well correlated activity between the ganglion cells could improve the brain's ability to discriminate few absorbed external photons from the high background of spontaneous thermal isomerizations. Based on the possible benefits of coupling in the AII network, we suggest that coupling occurs at low scotopic luminances.

Parallel cone bipolar to on-beta ganglion cell pathways in the cat retina: spatial responses, spatial aliasing, and spatial variance

An important issue in understanding the retina is finding candidate functional roles for different cell pathways and the details of their anatomy and physiology. We consider various spatial properties of the three main cone ==> cone bipolar cell ==> on-beta ganglion cell pathways in the cat retina and possible roles for the particulars of their anatomy. The cone bipolar cells in these pathways have distinct morphologies and modest differences in their convergence, divergence, densities, and synaptic weighting; and it is unclear whether the pathways differ in their spatial properties or in some other manner. Since differences in spatial processing of cells are best studied on a systemwide level, we developed the multirate filter-based method of retinal modeling, a technique for relating the anatomy of multiple cell layers to its systemic effects. We demonstrate that (1) despite the anatomic distinctions among the three main cone bipolar cell pathways, their spatial responses are essentially identical; (2) despite the spatial averaging in the pathways, there is essentially no filtering of the nonaliasing signal components after the cone layer; (3) instead, this averaging combined with prefiltering by the eye's optics and cone gap junctions prevents spatial aliasing; and (4) the averaging and prefiltering combined allow cell responses to be similar despite significant cell-to-cell anatomic differences.

Simulation of the AII amacrine cell of mammalian retina: functional consequences of electrical coupling and regenerative membrane properties

The AII amacrine cell of mammalian retina collects signals from several hundred rods and is hypothesized to transmit quantal "single-photon" signals at scotopic (starlight) intensities. One problem for this theory is that the quantal signal from one rod when summed with noise from neighboring rods would be lost if some mechanism did not exist for removing the noise. Several features of the AII might together accomplish such a noise removal operation: The AII is interconnected into a syncytial network by gap junctions, suggesting a noise-averaging function, and a quantal signal from one rod appears in five AII cells due to anatomical divergence. Furthermore, the AII contains voltage-gated Na+ and K+ channels and fires slow action potentials in vitro, suggesting that it could selectively amplify quantal photon signals embedded in uncorrelated noise. To test this hypothesis, we simulated a square array of AII somas (Rm = 25,000 Ohm-cm2) interconnected by gap junctions using a compartmental model. Simulated noisy inputs to the AII produced noise (3.5 mV) uncorrelated between adjacent cells, and a gap junction conductance of 200 pS reduced the noise by a factor of 2.5, consistent with theory. Voltage-gated Na+ and K+ channels (Na+: 4 nS, K+: 0.4 nS) produced slow action potentials similar to those found in vitro in the presence of noise. For a narrow range of Na+ and coupling conductance, quantal photon events (approximately 5-10 mV) were amplified nonlinearly by subthreshold regenerative events in the presence of noise. A lower coupling conductance produced spurious action potentials, and a greater conductance reduced amplification. Since the presence of noise in the weakly coupled circuit readily initiates action potentials that tend to spread throughout the AII network, we speculate that this tendency might be controlled in a negative feedback loop by up-modulating coupling or other synaptic conductances in response to spiking activity.

Simulation of an anatomically defined local circuit: the cone-horizontal cell network in cat retina

The outer plexiform layer of the retina contains a neural circuit in which cone synaptic terminals are electrically coupled and release glutamate onto wide-field and narrow-field horizontal cells. These are also electrically coupled and feed back through a GABAergic synapse to cones. In cat this circuit's structure is known in some detail, and much of the chemical architecture and neural responses are also known, yet there has been no attempt to synthesize this knowledge. We constructed a large-scale compartmental model (up to 50,000 compartments) to incorporate the known anatomical and biophysical facts. The goal was to discover how the various circuit components interact to form the cone receptive field, and thereby what possible function is implied. The simulation reproduced many features known from intracellular recordings: (1) linear response of cone and horizontal cell to intensity, (2) some aspects of temporal responses of cone and horizontal cell, (3) broad receptive field of the wide-field horizontal cell, and (4) center-surround cone receptive field (derived from a "deconvolution model"). With the network calibrated in this manner, we determined which of its features are necessary to give the cone receptive field a Gaussian center-surround shape. A Gaussian-like center that matches the center derived from the ganglion cell requires both optical blur and cone coupling: blur alone is too narrow, coupling alone gives an exponential shape without a central dome-shaped peak. A Gaussian-like surround requires both types of horizontal cell: the narrow-field type for the deep, proximal region and the wide-field type for the shallow, distal region. These results suggest that the function of the cone-horizontal cell circuit is to reduce the influence of noise by spatio-temporally filtering the cone signal before it passes through the first chemical synapse on the pathway to the brain.