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).

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 Ca_v 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 (λ_ss) of 103 μm (Figure 2A). Adding varicosities at regular 20 μm intervals further reduced λ_ss (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: λ_eff = 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.

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, Na_v and K_v 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 Na_v 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 Na_v conductance was considerably more negative (V_1/2 = −98 mV) than the typical resting membrane potential of A17 (−62 ± 3 mV; n = 10), suggesting that at rest only ~5% of A17 Na_v channels are available to contribute to membrane excitability (Figure 3C).

Similar experiments with K⁺-based internal solution revealed significantly larger K_v conductances in A17s that were activated at potentials more positive than −50 mV (Figures 3D–3F). The A-type K_v 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 K_v channels that are nonspecifically blocked by 4 mM 4-AP and respond with sustained opening (Figure S2).

How and to what extent do Na_v and K_v 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, Na_v and K_v conductances were incorporated into the electrotonic A17 model (see Experimental Procedures) to match experimentally observed values at corresponding potentials (1.8 mS/cm² Na_v conductance and 2.6 mS/cm² K_v 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%; λ_eff =56 μm) when compared to the purely passive condition (Figure 4C). Similar results were observed when Na_v channels were located (at higher density) exclusively in the neurites (Figures 4A–4C). These recordings and simulations suggested that A17s lack sufficient Na_v current to amplify subthreshold EPSPs or fire action potentials, due to pronounced Na_v channel inactivation and low channel density (also see Figure S3). Simulated synaptic input elicited dendritic action potentials only when the uniform Na_v 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 Na_v 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 Na_v channel density was increased 70-fold (data not shown).

Taken together, these results argue that the Na_v and K_v 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 Ca_v channel activation near the release site (Katz and Miledi, 1965). Although L-type Ca_v 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 Ca_v channels (Figure 4G; see Experimental Procedures) indicated that Ca_v channels do not enhance A17 membrane excitability (Figure 4H). These simulations also predicted a length constant for Ca_v 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 Ca_v 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 (G_Syn) led to an ~25-fold increase in the local synaptically evoked Ca_v current but only a 9-fold increase in the neighboring varicosity, thereby decreasing the effective length constant of Ca_v channel activation by ~45% (from 18 to 10 μm; Figure 4I). Extensive propagation of Ca_v channel activation along a simulated neurite was observed only when spiking was enabled by increasing the Na_v channel density 70-fold (Figure S4).

The spatial extent of Ca_v channel activation may be reduced further by Ca²⁺-activated K_v (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 Ca_v 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 (IVD_3-D; Figure 5C), and the current-clamp data were fit with a single exponential to determine the effective length constant of Ca²⁺ signaling (λ_Ca =13 μm; solid line, Figure 5C). λ_Ca was significantly less than the effective length constant of electrical signaling predicted by the electrotonic model (λ_eff = 56 μm; dashed line, Figure 4C) but agreed well with model predictions for Ca_v activation (λ_Cav = 10–18 μm; Figure 4I). Although relative Ca²⁺ responses were correlated with IVD_3-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.

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).

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.

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