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Logo of nihpaAbout Author manuscriptsSubmit a manuscriptHHS Public Access; Author Manuscript; Accepted for publication in peer reviewed journal;
 
Neuron. Author manuscript; available in PMC 2011 March 25.
Published in final edited form as:
PMCID: PMC2967021
NIHMSID: NIHMS186382

Retinal Parallel Processors: More than 100 Independent Microcircuits Operate within a Single Interneuron

SUMMARY

Most neurons are highly polarized cells with branched dendrites that receive and integrate synaptic inputs and extensive axons that deliver action potential output to distant targets. By contrast, amacrine cells, a diverse class of inhibitory interneurons in the inner retina, collect input and distribute output within the same neuritic network. The extent to which most amacrine cells integrate synaptic information and distribute their output is poorly understood. Here, we show that single A17 amacrine cells provide reciprocal feedback inhibition to presynaptic bipolar cells via hundreds of independent microcircuits operating in parallel. The A17 uses specialized morphological features, biophysical properties, and synaptic mechanisms to isolate feedback microcircuits and maximize its capacity to handle many independent processes. This example of a neuron employing distributed parallel processing rather than spatial integration provides insights into how unconventional neuronal morphology and physiology can maximize network function while minimizing wiring cost.

INTRODUCTION

A century ago, Ramon y Cajal realized the crucial relationship between neuronal morphology and function, insights that seeded our understanding of how dendritic arbors receive, filter, and integrate synaptic input and how axons form and propagate action potentials to communicate over relatively long distances. The typical morphological separation of synaptic input and output allows for extensive, specific modulation of either component but also limits the cell's capacity to handle independent processes. Exceptions to this general scheme appear in different areas of the CNS, but in many cases it remains unclear how alternative input-output arrangements afford a functional and/or physical advantage.

Cajal also described axonless interneurons in the retina that he named amacrine cells, a diverse neuron class, comprising perhaps 40 subtypes, that underlies complex spatial and temporal visual processing in the inner plexiform layer (IPL). Amacrine cells exhibit a wide range of morphologies, biophysical properties, and synaptic connectivity, but the impact of these features on their roles in network function is poorly understood. Unlike most neurons in the brain, amacrine cells typically lack morphologically distinct dendritic and axonal regions, instead mixing input and output machinery within the same “neuritic arbor.” The size and structure of these multifunctional arbors vary widely between amacrine cell subtypes but are strikingly consistent within subtypes (MacNeil and Masland, 1998), presenting a potentially rich opportunity to study how morphological and functional relationships between synaptic input and output have evolved to accomplish required computational tasks most efficiently.

In the rod pathway of the mammalian retina, adaptation at very low light levels occurs first in the inner retina at rod bipolar cell (RBC) dyad synapses (Dunn et al., 2006; Dunn and Rieke, 2008), which receive reciprocal feedback inhibition from postsynaptic A17 amacrine cells that shapes the time course of visual signaling in vivo (Dong and Hare, 2003). Each A17 soma, usually located in the inner nuclear layer (INL), extends dozens of thin, unbranched neurites into the IPL, where they express hundreds of small varicosities, each of which receives excitatory, glutamatergic input from a RBC ribbon synapse and makes a GABAergic feedback synapse onto the same RBC terminal (Zhang et al., 2002). The broad dimensions of A17 neuritic arbors (~400 μm diameter) have given rise to the idea that they may mediate long-range, “center-surround” inhibition, functionally connecting many RBC synapses (Bloomfield, 1992; Nelson and Kolb, 1985; Völgyi et al., 2002; Zhang et al., 2002). Recent work, however, has revealed synaptic and biophysical mechanisms within individual varicosities that may help to functionally isolate them from each other (Chávez et al., 2006; Grimes et al., 2009), potentially permitting synapse-specific feedback modulation that could impact the sensitivity of the rod pathway (Dunn and Rieke, 2008).

Here, we combine anatomical, physiological, and computational approaches to examine how synaptic organization, neuronal morphology, and biophysical membrane properties influence information processing within A17s in rat retina. Morphological analyses of A17 neurites and synaptic varicosities with fluorescence and serial electron microscopy (EM), together with electrotonic modeling, suggest that individual neurites are electrotonically isolated and can contain multiple, electrically independent feedback microcircuits. Biophysical properties of native Nav, Kv, and Cav conductances, derived from whole-cell patch-clamp recordings, were incorporated into an A17 model, but simulations and experiments indicated that the active conductances in A17s do not enhance membrane excitability. The effective length constant of the postsynaptic electrical response was ~50 μm, but the length constant for Cav channel activation was 4-fold less, due to the nonlinear voltage dependence of A17 L-type Cav channels, thereby further compartmentalizing microcircuit output. Two-photon imaging of synaptic Ca2+ responses in A17 neurites yielded an experimental measure of the effective length constant for Ca2+ signaling that closely matched model predictions and demonstrated that neighboring varicosities can operate nearly independently. Simulation of the relatively sparse synaptic activity that occurs under scotopic light conditions suggested that fast, local synaptic signals are rarely integrated by A17 neurites in physiologically relevant situations. Together, these results argue that a single A17 contains, on average, more than 100 independent input/output microcircuits operating in parallel and provide an example of how morphological and biophysical properties can combine to maximize a cell's capacity for independent processing while minimizing the associated tissue volume and metabolic cost.

RESULTS

Fluorescent imaging of A17 amacrine cells in acute retinal slices and 3D EM reconstructions of A17 neuritic segments revealed several distinctive morphological characteristics (Figure 1). Cells filled with the fluorescent dye Alexa 594 (40 μM) exhibited many long (typically nonbranching) neurites (22 ± 5, n = 5 cells) extending from the cell body in the INL into the deepest part of the IPL (Figure 1A), where varicose structures appeared at intervals (intervaricosity spacing = 20 ± 9 μm, n = 47; Figure 1E). The dimensions and ultrastructure of these varicosities and adjacent neurites were examined with serial EM (Figures 1B and 1C). Consistent with previous observations, excitatory inputs from RBCs, indicated by distinctive presynaptic ribbon structures, and reciprocal inhibitory synapses were colocalized to single varicosities (Ellias and Stevens, 1980; Nelson and Kolb, 1985). Most varicosities received input from only one ribbon synapse (Zhang et al., 2002), whereas each varicosity typically made two reciprocal synapses onto the same RBC terminal (Figures 1B–1D). On average, the most proximal (i.e., closest to the ribbon) of these reciprocal synapses was located only 183 ± 71 nm away (3D distance from center of ribbon synapse to edge of reciprocal synapse; n = 19), and the most distal was never more than 1 μm from the ribbon. The neurites linking feedback varicosities were very thin (132 ± 51 nm in diameter; n = 12) and devoid of synaptic input or output.

Figure 1
Quantitative Evidence for Submicron Feedback Circuits in the Inner Retina

Because input and output synapses were consistently colocalized within individual varicosities (17 of 17) that were separated by thin, asynaptic neurites, we hypothesized that each varicosity may constitute a functionally independent microcircuit. This idea counters theories that A17s may employ active membrane conductances and action potentials to mediate extensive surround inhibition (Bloomfield, 1992, 1996; Zhang et al., 2002), but it is consistent with recent evidence that local, reciprocal GABA release can be triggered locally within varicosities by Ca2+ influx through Ca2+-permeable AMPA receptors (CP-AMPARs; Chávez et al., 2006) and that membrane conductances within varicosities limit synaptic depolarization and Cav channel activation (Grimes et al., 2009). As a single A17 contains as many as 500 varicosities (Zhang et al., 2002), their independent function would represent a remarkable example of parallel processing within a single neuron.

The electrotonic spread of membrane depolarization through neuronal processes is strongly influenced by morphology (Rall, 1969). To determine the extent to which anatomy influences electrical coupling between feedback microcircuits, a passive membrane electrotonic model of an A17 amacrine cell was constructed based on anatomical measurements (Figure 1) and passive electrophysiological parameters (see Experimental Procedures; Figures 2 and S1). As expected, voltage signals were attenuated rapidly along the length of a thin (130 nm), isolated neurite with a steady-state length constant (λss) of 103 μm (Figure 2A). Adding varicosities at regular 20 μm intervals further reduced λss (to 70 μm; see also Ellias and Stevens, 1980) by a fraction that was inversely proportional to neurite diameter. The depolarization elicited by a simulated excitatory synaptic conductance (Grimes et al., 2009) at individual varicosities along a neurite of the complete “A17” model revealed the extent of local postsynaptic depolarization and electrotonic spread of the signal into neighboring varicosities and neurites (Figures 2B–2E). Local depolarizations elicited by a 200 pS conductance depended nonlinearly on distance from the soma (peaks, Figure 2C), indicating that A17 neurites are electrically compartmentalized. A synaptic depolarization in the most distal varicosity was attenuated along the neurite (effective length constant: λeff = 64 μm) and reduced by >97% at the most proximal varicosity (Figure 2D). Due to the relatively large current sink imposed by the soma, synaptic inputs onto even the most proximal varicosities did not cause significant depolarizations in neighboring neurites (Figure 2E). The model revealed that passive membrane properties and morphology alone isolate at least two independent microcircuits (in this case, the most proximal and distal varicosities) within each of the >22 neurites, corresponding to ~50 electrically independent feedback microcircuits within a single cell. Due to the probable cutting of neurites during the slicing procedure, our results likely underestimate the actual number of electrical microcircuits in an intact A17.

Figure 2
A17 Morphology Limits the Spread of Synaptically Evoked Depolarizations into Neighboring Neurites and Varicosities

In many neurons, nonlinear, active membrane conductances can locally amplify (Araya et al., 2007; Rotaru et al., 2007) or suppress (Grimes et al., 2009) synaptically evoked signals and alter the extent to which signals are attenuated over distance (Rall et al., 1992). Active conductances can enhance the integrative properties of a single neuron but may reduce the potential for parallel, independent processing. For example, a single granule cell in the olfactory bulb colocalizes synaptic inputs and outputs at hundreds of dendrodendritic synapses with mitral cells (Price and Powell, 1970; Rall et al., 1966), analogous to the arrangement between RBCs and A17s, but compact morphology, active conductances, and consequent action potentials greatly enhance cooperativity between granule cell microcircuits (Migliore and Shepherd, 2008; Schoppa, 2006a, 2006b).

To determine the extent to which active membrane properties influence communication between microcircuits in A17s, the native conductances were identified electrophysiologically (Figure 3) and incorporated into the electrotonic model (Figure 4). First, Nav and Kv currents, isolated pharmacologically, were recorded from A17s in acute retinal slices (Figures 3A and 3D). A series of step depolarizations revealed rapidly activating and inactivating, TTX (1 μM) -sensitive Nav currents (Figures 3A–3C). Maximal activation of this conductance (during a step from −140 to −10 mV) produced 179 ± 89 pA of TTX-sensitive current (p = 0.003; n = 6), substantially less than that exhibited by spiking neurons in the retina (~1 nA, Henne et al., 2000; Kim and Rieke, 2003). The measured midpoint of inactivation of the Nav conductance was considerably more negative (V1/2 = −98 mV) than the typical resting membrane potential of A17 (−62 ± 3 mV; n = 10), suggesting that at rest only ~5% of A17 Nav channels are available to contribute to membrane excitability (Figure 3C).

Figure 3
Biophysical Characterization of Pharmacologically Isolated Nav and Kv Conductances in A17 Amacrine Cells
Figure 4
Active Membrane Conductances Do Not Amplify EPSPs or Enhance Spatial Signaling

Similar experiments with K+-based internal solution revealed significantly larger Kv conductances in A17s that were activated at potentials more positive than −50 mV (Figures 3D–3F). The A-type Kv channel blocker 4-AP (4 mM) significantly reduced both transient (3–8 ms from onset of step; to 15% ± 47% of control at −30 mV, p = 0.016) and sustained (150–170 ms from onset of step; to 9% ± 11% of control at −30 mV, p = 0.003, n = 6) components of the outward currents for potentials ≥−30 mV. The remaining current, presumably mediated by delayed rectifiers, was sustained and activated at potentials ≥−10 mV. Comparison of the inactivating and noninactivating 4-AP-sensitive current suggested that it was mediated by inactivating A-type channels and other Kv channels that are nonspecifically blocked by 4 mM 4-AP and respond with sustained opening (Figure S2).

How and to what extent do Nav and Kv conductances actively contribute to membrane excitability and/or attenuation/compartmentalization of electrical signals in A17 neurites? To better understand their roles in integration and “global” versus “local” signaling, Nav and Kv conductances were incorporated into the electrotonic A17 model (see Experimental Procedures) to match experimentally observed values at corresponding potentials (1.8 mS/cm2 Nav conductance and 2.6 mS/cm2 Kv conductance; Figure 4A). The effects of these active conductances were evaluated by imposing the simulated synaptic conductance at individual varicosities and comparing the local excitatory postsynaptic potential (EPSP) to that in the passive model. This particular combination of active conductances actually suppressed simulated EPSPs within varicosities (by ~7%; Figure 4B) and reduced the spread of depolarization between varicosities on the same neurite (by ~12%; λeff =56 μm) when compared to the purely passive condition (Figure 4C). Similar results were observed when Nav channels were located (at higher density) exclusively in the neurites (Figures 4A–4C). These recordings and simulations suggested that A17s lack sufficient Nav current to amplify subthreshold EPSPs or fire action potentials, due to pronounced Nav channel inactivation and low channel density (also see Figure S3). Simulated synaptic input elicited dendritic action potentials only when the uniform Nav channel density was increased 70-fold (Figure 4C). Consistent with these simulation predictions, EPSPs evoked with a stimulating electrode placed in the OPL were not significantly affected by TTX, even with inhibition blocked (88% ± 17% of control, p = 0.24, n = 5; Figures 4D and 4E). The AMPAR antagonist NBQX (10 μM) completely blocked the EPSP (to −3% ± 9% control; p = 0.0037; n = 5; Figures 4D and 4E), confirming that the response was not caused by direct stimulation of the A17.

Evidence that A17s fire action potentials is inconsistent across species, with small (~10 mV) spikes evident in somatic recordings from rabbit (Bloomfield, 1996) but not cat or rat (Menger and Wässle, 2000; Nelson and Kolb, 1985). To maximize our chances to observe spikes in rat A17s, we partially relieved Nav channel inactivation by injecting a negative current step (−200 pA for 200 ms), thereby hyperpolarizing the membranes by more than 30 mV relative to rest, prior to delivering large, positive current steps (up to +1000 pA for 200 ms; Figure 4F). This protocol failed to elicit action potentials in 5 of 5 cells (Figure 4D), and subsequent bath application of TTX (1 μM) did not affect the responses significantly (data not shown). Accordingly, simulated A17s did not fire action potentials in response to injected current unless the Nav channel density was increased 70-fold (data not shown).

Taken together, these results argue that the Nav and Kv membrane conductances expressed by A17s do not amplify local synaptic events nor enhance communication between sites of synaptic feedback. Instead, they appear to increase electrical compartmentalization beyond that arising from neuronal morphology and passive properties alone.

The data presented thus far suggests that ≥50 micro-feedback circuits within a single A17 can function independently with respect to electrical signaling but that neighboring varicosities along a neurite may interact. At most chemical synapses, membrane potential and transmitter release are coupled via Cav channel activation near the release site (Katz and Miledi, 1965). Although L-type Cav channels are expressed in A17 varicosities and can trigger GABA release (Grimes et al., 2009), it is not known whether they can be activated in quiescent varicosities by postsynaptic depolarization spreading from neighboring, active synapses. Simulations incorporating L-type Cav channels (Figure 4G; see Experimental Procedures) indicated that Cav channels do not enhance A17 membrane excitability (Figure 4H). These simulations also predicted a length constant for Cav channel activation that was ~4-fold less than the length constant of electrical signaling (Figure 4I), due to the nonlinear relationship between membrane potential and Cav channel activation. Similar results were also observed with larger synaptic inputs (1000 pS), corresponding to maximal release from a single ribbon synapse (Singer and Diamond, 2003; Figure S1C). In fact, this 5-fold increase in the synaptic conductance (GSyn) led to an ~25-fold increase in the local synaptically evoked Cav current but only a 9-fold increase in the neighboring varicosity, thereby decreasing the effective length constant of Cav channel activation by ~45% (from 18 to 10 μm; Figure 4I). Extensive propagation of Cav channel activation along a simulated neurite was observed only when spiking was enabled by increasing the Nav channel density 70-fold (Figure S4).

The spatial extent of Cav channel activation may be reduced further by Ca2+-activated Kv (BK) channels that operate within A17 varicosities (Grimes, et al., 2009). However, due to uncertainties regarding the detailed kinetic properties of A17 BK channels and their localization relative to Ca2+ sources within the varicosities, we have elected not to include BK channels in the present simulations.

Ca2+ signaling and GABA release from A17 neurites is further complicated by CP-AMPARs, which can trigger GABA release directly at active synapses, and Ca2+-induced Ca2+ release from intracellular stores, which boosts synaptic release from A17 varicosities (Chávez, et al., 2006). Moreover, it is unknown whether intracellular Ca2+ signals are compartmentalized between neighboring varicosities. To address these issues experimentally, intracellular Ca2+ signals were recorded at individual A17 synaptic varicosities along single neurites in response to synaptic stimulation (Figure 5). Ca2+-sensitive (Fluo-4, 200 μM) and Ca2+-insensitive (Alexa594, 40 μM) fluorophores were loaded into A17 through the somatic patch electrode (containing K+-based patch solution) via passive diffusion for a 30 min dialysis period. The duration and amplitude of the current step applied to a stimulating electrode placed in the OPL were adjusted to maximize the amplitude of EPSCs recorded under voltage clamp and test the upper limit of synaptic strength at individual RBC-A17 synapses (Grimes et al., 2009; see Experimental Procedures). Although difficult to locate, synaptically evoked Ca2+ transients were recorded in individual varicosities (blue ROIs and corresponding blue traces, i; Figures 5A and 5B). The microscope focus then was moved to the nearest neighboring varicosity, where intracellular Ca2+ signals were recorded in response to the same stimulus (ii; Figures 5A and 5B). The synaptic Ca2+ response was determined by averaging the response within each varicosity over an 80 ms coincidence window (gray boxes in Figures 5A and 5B; see Experimental Procedures). As previously observed, this protocol rarely (only 1 of 11 cases; Figure 5C) produced a detectable response under voltage clamp (>1× baseline SD; see Experimental Procedures) in the neighboring varicosity (Grimes et al., 2009), confirming that the synaptic stimulation was focused and that intracellular Ca2+ signals do not spread between varicosities (the spatial extent of Fluo-4 fluorescence likely exceeds that of free calcium under endogenous buffering conditions [Goldberg, et al., 2003]). The patch-clamp amplifier configuration then was changed to current-clamp mode to permit physiological membrane fluctuations and any consequent voltage-gated channel activation. The varicosity pair was then imaged again in response to the same synaptic stimulation (i.e., same location, duration, and amplitude), which now produced EPSPs (iii and iv; Figures 5A and 5B). Ca2+ signals in the neighboring varicosity were larger in current clamp than in voltage clamp (compare ii and iii) only when the two varicosities were separated by less than 20 μm (Figure 5B), the average distance between neighboring varicosities (V-clamp: 0.1% ± 0.2% ΔG/R, I-clamp: 1.9% ± 0.9% ΔG/R, p = 0.004, n = 6; Figure 5C). More distant (>20 μm; Figure 5A) neighbors exhibited similar Ca2+ responses in the two conditions (V-clamp: 0.1% ± 0.2% ΔG/R, I-clamp: 0.0% ± 0.4% ΔG/R, p = 0.55, n = 4; Figure 5C), indicating that local EPSPs trigger Cav channel activation over only short distances (<20 μm) but that closely neighboring microcircuits can interact. The ratios of Ca2+ responses obtained at the two locations (Δ[Ca2+]neighbor/Δ[Ca2+]synaptic) were plotted as a function of their intervaricosity distance (IVD3-D; Figure 5C), and the current-clamp data were fit with a single exponential to determine the effective length constant of Ca2+ signaling (λCa =13 μm; solid line, Figure 5C). λCa was significantly less than the effective length constant of electrical signaling predicted by the electrotonic model (λeff = 56 μm; dashed line, Figure 4C) but agreed well with model predictions for Cav activation (λCav = 10–18 μm; Figure 4I). Although relative Ca2+ responses were correlated with IVD3-D (p = 0.002), they were not significantly correlated with EPSP amplitude measured at the soma (p = 0.14; Figure 5D). This experimental measurement of the spatial extent of signaling increases our estimate of the number of functionally independent microcircuits contained within a single A17 from ~50 to >150.

Figure 5
Experimental Evidence for Highly Compartmentalized Functional Microcircuits

The results above indicate that A17 morphology and biophysical membrane properties preserve highly localized Ca2+ signaling when a single synaptic input is activated. Synchronized activation of multiple varicosities on a single neurite, however, may boost local signals and/or enhance signal spread between varicosities. To explore these possibilities, we simulated multiple synaptic inputs in our A17 model (Figure 6). Synchronized activation of all varicosities on a single neurite (ten in total; Figure 6A) approximately doubled the average local EPSP (to 227% of the response to local stimulation only) and did not produce a significant response in neighboring neurites (Figures 6A and 6B). Local EPSPs became larger with increased numbers of synchronized inputs on the same neurite (Figure 6B). According to the model, although two synchronized inputs (separated by ~100 μm) could be processed independently in an A17 neurite (Figure 6C, top), three or more synchronized inputs would be integrated to boost local signals, thereby compromising microcircuit independence (Figure 6C).

Figure 6
Microcircuit Interactions Are Minimal under Scotopic Conditions

Although multiple, synchronized inputs could interact in A17 neurites, they are unlikely to occur under physiological conditions. A17 amacrine cells operate within the rod pathway, which transmits visual signals under low-light (scotopic) conditions, when sensitivity is high and photon absorption is infrequent in space and time. At the adaptation threshold (~0.25 Rh*/rod/s, i.e., the background light intensity at which the gain of the RBC-AII synapse begins to decrease; Dunn et al., 2006), converging, nonlinear inputs from rods give rise to ~1.25 Rh*effective/RBC/s (Field and Rieke, 2002; Dunn and Rieke, 2008), corresponding to roughly 12.5 Rh*effective/A17 neurite/s. Simulations were used to test whether A17 feedback microcircuits interact under these conditions: ten different stimulus arrays were derived to deliver randomly timed inputs to each varicosity at an average frequency approximating the adaptation threshold (1.25 Rh*effective/varicosity/s). To quantify interactions between inputs, we monitored the postsynaptic Ca2+ current at all varicosities along an entire neurite at the time that an event occurred at one centrally located varicosity (#5; ten trials; Figures 6D and 6E; see Experimental Procedures). Any deviations in the postsynaptic response at varicosity #5 from that to an isolated, single (“local only”) input (dashed line, Figures 6D and 6E) would reflect interactions between varicosities. Because EPSPs and Cav currents in A17 varicosities are fast (~7 ms halfwidth) and spatially restricted, sparse inputs rarely gave rise to interactions between varicosities (Figures 6D). In fact, the average Cav current response to inputs at varicosity #5 was nearly identical to the response to an isolated single (“local only”) input (peak: 99% local only; FWHM = 24 or 37 μm for GSyn = 1000 or 200 pS, respectively). Even at light intensities exceeding the adaptation threshold by a factor of 4, coincident activation boosted the average Cav response in varicosity #5 by only 5%–25% and increased the FWHM by 5%–12%, depending on synaptic strength (Figure 6E). These simulations suggest that one A17 amacrine cell provides highly compartmentalized feedback to hundreds of RBCs and that these input-output microcircuits rarely interact under physiological conditions.

DISCUSSION

The retina is a beautiful example of a neural network that optimizes signal processing capacity while minimizing cellular cost. The physiology of individual neurons and their synaptic connections with each other are tuned to preserve sensitivity to the absorption of single photons while remaining responsive to changes in light intensity over a billion-fold range, and volume is conserved with relatively small neurons connected by synapses that often contain multiple postsynaptic elements (Dowling and Boycott, 1965). Here, we show how a retinal interneuron, one that is likely involved in regulating sensitivity and adaptation in the rod pathway, contributes to the efficiency of the network by operating more than 150 microcircuits in parallel. We find that A17 amacrine cells combine morphological, biophysical, and synaptic properties to isolate reciprocal feedback synapses, a counterpoint to the dendritic integration performed by many neurons in the brain (Spruston, 2008). Given the diversity of amacrine cell morphology and visual processing performed in the IPL, it seems probable that different amacrine cell types may vary widely in the extent to which they integrate synaptic input (e.g., Flores-Herr, et al., 2001; Hausselt, et al., 2007). The A17 may, in this regard, represent one end of a broad spectrum.

The striking morphology of the rod pathway circuitry in the mammalian retina (Kolb and Famiglietti, 1974; Strettoi et al., 1990; Vaney, 1986; Vaney et al., 1991) provides clues about specific network requirements for reciprocal feedback onto RBC terminals. RBC axon terminals form a complete mosaic in the innermost layer of the IPL, with very little overlap between terminals of neighboring cells (Young and Vaney, 1991; Zhang et al., 2002). The terminal field of a single RBC typically spans less than 15 μm(Greferath et al., 1990; Oltedal et al., 2009; Young and Vaney, 1991), and each RBC ribbon synapse receives a reciprocal feedback synapse (Raviola and Dacheux, 1987; Strettoi et al., 1990). Because the average spacing between A17 varicosities (~20 μm; Zhang, et al., 2002; Figure 1) exceeds the average diameter of RBC axon terminals, an individual RBC usually contacts no more than a single varicosity on each A17 (Vaney, 1986; Zhang et al., 2002). Thus, it appears necessary that each ribbon synapse on a RBC terminal be controlled by an independent feedback microcircuit. Ribbon-specific feedback may be required for optimal regulation of synapse-specific gain control of RBC output (Dunn and Rieke, 2008), although it is unclear whether feedback responses at individual synapses are isolated from each other within a RBC axon terminal (Oltedal et al., 2009). One possibility is that synapse-specific inhibition at a RBC terminal could reduce variability in the observed quantal content of an elicited response (e.g., in a single AII, connected to a RBC by ~10 ribbon synapses) by reducing the chances that one ribbon synapse would be significantly more depressed than the others at a single RBC terminal. Isolation of feedback microcircuits within A17s would also limit common reciprocal feedback at neighboring RBCs, preserving independent RBC signaling (Dunn and Rieke, 2008) and minimizing interactions at rare double contacts between A17s and larger RBC terminals.

A17s Provide Synapse-Specific Feedback at Reduced Wiring Cost

The retina could have evolved any number of different A17 neuritic configurations to accomplish independent reciprocal feedback. Neuronal wiring optimization theory (Chklovskii, 2004) suggests reasons why A17s have adopted their characteristic wide-field morphology. In this theory, neuronal architecture evolves to fulfill the functional needs of the network while minimizing “wiring cost,” a complex accounting of the genetic, metabolic, and spatial resources required by neuronal circuitry. For example, larger neurons can distribute resources across a greater number of synaptic connections, but they require more energy for protein transport and suffer greater electrotonic signal attenuation (although this latter factor may not apply to the A17, which primarily employs distributed, parallel processing rather than integration). Fortunately, wiring cost can be reasonably approximated by a single parameter, the total cell volume required for a particular connectivity pattern (Chklovskii, 2004). This metric may be particularly relevant in the retina, because spatial acuity and dynamic range must be preserved in a biological network that is sufficiently thin and optically transparent. For example, colocalization of inputs and outputs within A17 varicosities reduces wiring cost and signaling delays by eliminating the need for separate axons and dendrites (Rushton, 1951).

This conceptual framework is useful for considering different potential implementations of synapse-specific feedback (Figure 7). The simplest configuration is one in which each A17 amacrine cell provides feedback to only a single ribbon (~36 A17s per 1 RBC), resulting in ~100,000 “single-unit processors/neurons” per square mm of retina, an exorbitant wiring cost per microcircuit (“computational cost”; Figure 7A) and an impractically large total volume (Figure 7B). An intermediate scenario is one in which each A17 provides reciprocal inhibition to all of the ribbon synapses (~36; Singer et al., 2004) on a single RBC terminal. Although each feedback varicosity would need to arise from a separate neurite to ensure biochemical and electrical compartmentalization, this “narrow field” scenario represents a significant savings in wiring cost per microcircuit (Figure 7A) and total cell volume (Figure 7B) compared with the “single-unit” arrangement. Significant cost in the “narrow field” case is expended on the 50 μm long processes connecting the soma to the varicosities in sublamina 5; this scenario is improved further by placing multiple varicosities along single neurites and spacing them sufficiently far apart to preserve functional independence (~20 μm; Figure 7A). This arrangement, reflecting the actual A17 morphology, reduces the computational cost and network volume attributed to reciprocal inhibition by a factor of four when compared with the “narrow field” case and by two orders of magnitude when compared to neurons without multiple independent microcircuits (Figure 7B).

Figure 7
Wiring Optimization/Cost Theory Provides Insight into Why Evolution Would Produce a Wide-Field Retinal Interneuron of A17's Morphology that Contains Hundreds of Parallel Microcircuits that Operate Independently

A17s Are Unlikely to Mediate Inhibitory Surround in the Rod Pathway

Previous studies in rabbit have demonstrated that center-surround inhibition in the inner retina is GABAergic and TTX sensitive (Bloomfield, 1996; Völgyi et al., 2002). Given that A17 signaling and reciprocal feedback are TTX insensitive (Figure 4; Chávez, et al., 2006), it seems likely that AII surround inhibition involves other circuit elements, perhaps a serial inhibitory network involving spiking GABAergic amacrine cells and ON cone bipolar cells (Eggers and Lukasiewicz, 2006; Flores-Herr et al., 2001). The location, morphology, and connectivity of rat A17s (Grimes et al., 2009; Menger and Wässle, 2000; Figure 1) corresponds very closely with rabbit S2 amacrine cells (Vaney, 1986; Zhang et al., 2002), so we consider these two cell types to be analogous. (We typically did not encounter larger, sparser amacrine cells, analogous to the rabbit S1 [Bloomfield, 1992; Vaney, 1986; Zhang et al., 2002], in rat retinal slices.) Most anatomical and spatial signaling studies of the rod pathway have been performed in the rabbit (Bloomfield, 1992; Strettoi et al., 1990; Vaney, 1986; Vaney et al., 1991; Völgyi et al., 2002; Young and Vaney, 1991; Zhang et al., 2002), but many parameters (e.g., synapse numbers, terminal dimensions, varicosity spacing, etc.) appear comparable in rat (Singer et al., 2004; Menger and Wässle, 2000; Figure 1). Therefore, although we present experimental evidence suggesting that rat A17s perform only local computations, we cannot exclude the possibility that a wide-field TTX-sensitive amacrine cell, perhaps analogous to S1 in rabbit retina, could provide surround inhibition to RBC terminals.

Synaptic Computations within Individual A17 Microcircuits

Previous work has shown that A17 synaptic varicosities draw upon multiple sources of Ca2+ influx (Ca2+-permeable AMPARs and Cav channels; Chávez et al., 2006; Grimes et al., 2009) and activate multiple, distinct populations of GABA receptors (Eggers and Lukasiewicz, 2006; Palmer, 2006; Singer and Diamond, 2003). Our observation that most varicosities make two feedback synapses to each RBC terminal (Figure 1D) suggests a potential morphological substrate for multimodal signaling within each varicosity. The influence of Ca2+-induced Ca2+ release and Ca2+-activated membrane conductances on feedback within individual varicosities (Chávez et al., 2006; Grimes et al., 2009) suggests yet another layer of complexity. Further experiments are required to identify the specific computations performed at individual A17 feedback microcircuits, to understand how these local, independent computations regulate retinal function and to estimate the cell's total computational capacity.

EXPERIMENTAL PROCEDURES

Serial Electron Microscopy

Two isolated retinas from P18 Sprague-Dawley rats were fixed in 4% glutaraldehyde in 0.1 M cacodylate buffer (pH 7.4) at 4°C overnight. Tissue was washed for 1 hr in the same buffer and then postfixed in 1% OsO4 for 1 hr. After rinsing and dehydration, tissues were embedded in EMbed 812 resin at 50°C for 1 day, then 60°C for 2 additional days. Series of consecutive sections (35–68 sections, each 100 nm thick) were collected in Formvar-coated slot grids; some sections were counterstained with 5% uranyl acetate and 0.3% lead citrate. Series were digitally photographed at a magnification of 8000–10,000 on a JEOL-1200 EXII or JEOL-1010 EM operating at 60 or 80 kV, respectively. Serial images were aligned with Reconstruct software after the calculation of pixel size. A17 varicosities and neurites were traced through continuous sections, and synaptic inputs and outputs to and from the varicosities were marked. Structures were reconstructed in three dimensions, and quantitative analysis was performed using Reconstruct measurement tools (Fiala, 2005).

Electrophysiology

Experiments were conducted at room temperature (22°C–25°C) using light-adapted retinal slices (210 μm thick) prepared from Sprague-Dawley rats (P17–21), as previously described (Chávez et al., 2006; Singer and Diamond, 2003). Rat retinas were isolated in artificial cerebrospinal fluid (ACSF) containing (in mM) 119 NaCl, 26 NaHCO3, 1.25 Na2HPO4, 2.5 KCl, 2.5 CaCl2, 1.5 MgSO4, 10 glucose, 2 Na-pyruvate, 4 Na-lactate, and equilibrated with 95% O2/5% CO2. For synaptic experiments, unless otherwise noted, ACSF was supplemented with the group III mGluR agonist L-AP4 (10 μM) to mimic dark conditions, reduce photostimulation of the network, and quiet RBC activity. For all nonsynaptic experiments, ACSF was supplemented with the AMPAR antagonist NBQX (10 μM). Drugs were purchased from Sigma or Tocris (St. Louis, MO) with the exception of TTX (Alamone Labs, Jerusalem, Israel). All fluorescent dyes were purchased from Molecular Probes (Eugene, OR).

Unless otherwise noted, whole-cell voltage-clamp recordings were made from A17s using pipettes (~5–6 MΩ) containing (in mM) 100 Cs methanesulfonate, 20 TEA-Cl, 10 HEPES, 10 EGTA, 10 Na phosphocreatine, 4 Mg-ATP, 0.4 Na-GTP, and 0.04 Alexa-594 hydrazide (pH 7.4). Potassium-based internal for A17s contained (in mM) 100 K methanesulfonate, 20 K-Cl, 10 HEPES, 2 EGTA, 10 Na phosphocreatine, 4Mg-ATP, 0.4 Na-GTP, and 0.04 Alexa-594 hydrazide (pH 7.4). A17 access resistance was ≤30 MΩ and was left uncompensated. Recordings were made using an Axopatch 1D amplifier (Axon Instruments, Foster City, CA) controlled through an A/D board (Instrutech) by custom software written in Igor Pro (Wavemetrics). Synaptic responses recorded in A17 were elicited by electrical stimulation of bipolar cells in the OPL (~1–10 μA for 300–600 μs; FHC, Bowdoin, ME). All current responses were collected at 20 s intervals, low-pass filtered at 5 kHz and digitized at 10 kHz. Voltage steps were leak-subtracted using a P/4 subtraction protocol. Electrophysiology data were analyzed using Igor Pro and Excel (Microsoft). Step-evoked currents in Figures 3A and 3D were smoothed using the built-in Igor binomial smoothing function to emphasize kinetics of the responses. Paired, two-tailed t tests were used to compare datasets and significance was determined as *p < 0.05, **p < 0.01, or ***p < 0.001. Unless otherwise indicated, data are presented as mean ± SD and illustrated traces are averages of five to ten responses.

Mathematical Modeling

An electrotonic compartmental model of the A17 amacrine cell was built and tested using the electrotonic compartmental modeling program NEURON (Hines and Carnevale, 1997, 2001). To address specific questions about A17, anatomical measurements taken from 3D reconstructions were used to constrain the model (example cell in Figure 1A). Several assumptions were made: (1) Cmem = 1 μF/cm2, (2) all compartments have the same leak conductance and leak reversal (−65 mV), and (3) Raxial = 110 Ω*cm (Engel and Jonas, 2005; Hallermann et al., 2003; Taylor et al., 1996). The membrane resistivity was determined by adjusting the model membrane resistivity until the measured input resistance (somatic electrode) in the real A17 and the A17 electrotonic model were the same (Table 1 and Figure S1). Hodgkin and Huxley-style models for Nav, Kv and Cav were compiled in NMODL and incorporated into the membranes of the A17 model (Figure 4). For simplicity, A17 Kv conductances (i.e., delayed rectifiers, A-type, etc) were modeled as a single Kv conductance. In all cases, channel kinetics and densities were adjusted so that simulated somatic voltage-clamp recordings matched those observed experimentally.

Table 1
A17 Electronic Model Parameters (Unless Otherwise Noted)

An alpha function

equation M1
(1)

provided the synaptic conductance, where gmax is the maximum conductance (referred to as GSyn in the Results). gmax was set to either 200 pS (corresponding to the opening of ~20 AMPARs) to mimic either the postsynaptic response to the release of a single synaptic vesicle or 1000 pS to mimic the avid multivesicular release observed at RBC-A17 synapses (five to ten vesicles released within 1–2 ms; Singer, et al., 2004). The larger conductance, at a varicosity <100 μm from the soma, elicited a 12.5 pA EPSC in the soma (Figure S1), similar to that evoked in A17s by maximal stimulation of a single RBC-A17 synapse (Singer and Diamond, 2003). τ was chosen to create a synaptic conductance with a time course of decay of ~3 ms, which is similar to experimentally observed EPSCs recorded from A17s with a patch electrode (Grimes et al., 2009; Singer and Diamond, 2003) and likely represent an upper limit to the time course of the synaptic currents actually occurring in the feedback varicosities. Electrotonic model parameters are indicated in Table 1 unless otherwise indicated in the text. Simulations were run using 25 μs time steps, and all results were analyzed using IGOR pro.

Simulated light experiments were used to test for coincident activity and independence along simulated neurites under physiological conditions. All ten varicosities received simultaneous input from different random arrays of events corresponding to photon absorption rates of 0.25 or 1 Rh*/rod/s. After accounting for an ~20:1 convergence of rods to RBCs and the nonlinearity occurring at individual inputs that rejects ~75% of events, each varicosity received input at a rate 1.25 or 5 Rh*effective/varicosity/s. Each of the ten random event arrays (for ten trials) were created by extracting the number of events to occur within the simulation time (2 s) from a poisson distribution (for the appropriate Rh*effective/varicosity/s) and assigning each event a random time during the simulation. Summation between microcircuit signals was observed as changes in the average response at a central varicosity (#5), a location with a high probability of interacting with coincident events within the neurite. Postsynaptic signals for each trial (in response to events occurring at varicosity #5; 1st event for each trial after the first 100 ms) were taken as the peak Cav current response occurring within each varicosity along the neurite within 8 ms of the varicosity #5 stimulus onset.

Wiring cost was equated to the total A17 volume for a particular wiring configuration. The general expression for the “single unit” through “narrow field” cellular volume was simply the spherical volume of a cell body (12 μm diameter) plus the volume of the neurite (initial segment: cylinder, 130 nm diameter, 50 μm length and varicosity: sphere, 0.9 μm radius) times the number of neurites. The computational cost or wiring cost per microcircuit was taken as the total cellular volume divided by the number of independent microcircuits contained within.

Two-Photon Ca2+ Imaging

Intracellular Ca2+ dynamics were observed by replacing the standard intracellular Ca2+ chelator, EGTA, with a high-affinity fluorescent chelator (200 μM Fluo-4), whose emissions dramatically increase upon binding Ca2+ions (Grynkiewicz et al., 1985). Whole-cell recordings were allowed to dialyze for ~30 min before imaging to allow for equilibration of the dye. Fluorescence was acquired from individual compartments of A17s using a modified Zeiss LSM 510 two-photon microscope. For these experiments the excitation source consisted of a computer-controlled Chameleon infrared laser (λ = 810 nm; Coherent). For time-dependent imaging of varicosities, a 40× objective (1.0 NA, Zeiss) and digitized zoom were used to collect 1–2 s of the fluorescence from individual varicosities in frame scan mode (~162 pixels) at ~50 Hz. At each image location along the neurite, three to five responses were acquired for each condition and averaged before amplitude measurements were taken. Background fluorescence was corrected for the varicosity-containing regions of interest (ROIs) by measuring average red and green signals at nearby regions not containing the dye-filled dendrite. This approach has the advantage of a larger denominator (Alexas have a higher quantum yield than the Fluo family), which is insensitive to changes in intracellular calcium, therefore providing a more robust measurement of relative influx (Yasuda et al., 2004). Because inputs from multiple neurites sum linearly at the somatic recording electrode (Figure S1C), it is estimated that the stimulus protocol for experiments presented in Figure 5 reflect activation of one to five neurites. Imaging data were analyzed using custom Matlab scripts. Intervaricosity distance was measured using Zeiss image analysis software. Additional neurites contained within the reconstructed volume of the specific neurites imaged in Figures 5A and 5B were digitally removed from each image before reconstructing to allow for a better view of the neurite used for calcium imaging.

Supplementary Material

ACKNOWLEDGMENTS

This work was supported by the NINDS and NIDCD Intramural Research Programs.

Footnotes

SUPPLEMENTAL INFORMATION Supplemental Information includes three figures and can be found with this article online at doi:10.1016/j.neuron.2010.02.028.

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