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Bipolar cells (BCs) form parallel channels that carry visual signals from the outer to the inner retina. Each BC type is thought to carry a distinct visual message to select types of amacrine cells (ACs) and ganglion cells (GCs). However, the number of GC types exceeds that of BCs providing their input, suggesting that BC signals diversify on transmission to GCs. Here we explored in the salamander retina how signals from individual BCs feed into multiple GCs, and found that each BC could evoke distinct responses among GCs, differing in kinetics, adaptation, and rectification properties. This signal divergence results primarily from interactions with ACs that allow each BC to send distinct signals to its target GCs. Our results indicate that individual BC-GC connections have distinct transfer functions. This expands the number of visual channels in the inner retina and enhances the computational power and feature selectivity of early visual processing.
The visual system processes light information by encoding and separating signals into many different channels. These operations begin in the bipolar cells (BCs) of the retina1. Bipolar cells are the secondary neurons, extending their dendrites and axons towards the outer and the inner retina, respectively, and they constitute the only conduit for transmitting the signals from photoreceptors to retinal ganglion cells (GCs) and amacrine cells (ACs)2. There are ~10 types of BCs in a vertebrate retina3,4, and previous studies suggest that they form parallel channels where each BC type carries a distinct type of visual information5. Bipolar cells differ in morphology, in particular by the ramification pattern of dendrites6 and the stratification of axonal arbors3,4. They have also been divided physiologically into “ON” and “OFF” response types, and within each of these groups one further distinguishes “transient” and “sustained” types based on their visual response characteristics7. Such functional differentiation results from connections to specific photoreceptors8, the intrinsic properties of BCs such as their membrane receptors and channels9,10, and inhibitory circuitry involving ACs in the inner retina11–13.
Beyond separating the visual image into parallel channels, BCs carry out important roles through their transmission to GCs1,14. First, some BC synapses appear to be strongly rectifying — transmitting depolarization but not hyperpolarization — which leads to prominent nonlinearities in the responses of GCs, such as a pronounced sensitivity to pattern motion15–17. Other GCs respond more linearly18, presumably drawing on BC synapses with less rectification. Second, some important nonlinearities arise through the interaction with ACs at the BC terminal. For example, the direction-selectivity of GCs is largely determined by presynaptic inhibition of BC inputs19. Third, BC synapses can undergo strong activity-dependent depression20–23, and this short-term plasticity has been invoked as a mechanism for adaptation in certain GC responses14,24. Thus the function of BC-GC transmission has emerged as a key determinant of retinal computation.
The diversity of functions that have been assigned to BCs — the combination of stimulus filtering, nonlinearities, and plasticity — easily exceeds the number of distinct BC pathways. Indeed, the typical retina contains ~20 types of GCs2. Because each of the 10 BC types tiles the visual field with little overlap25, a complete coverage by GCs therefore requires divergence from individual BCs to multiple GCs. This raises the question how those BC signals become diversified.
To address this issue, we studied divergence and convergence of transmission from BCs to GCs. We gained control of individual BCs in the salamander retina with sharp electrodes; simultaneously we recorded the firing in an entire field of surrounding GCs with an extracellular multielectrode array; in addition we modulated the AC network pharmacologically and stimulated the photoreceptors with patterns of light. Here we report that individual BCs distribute very distinct signals to different GCs. Interactions with ACs were essential for diversifying the temporal dynamics and adaptation properties of the signals, but not for other characteristics such as the degree of rectification. We also found that different outputs from each BC were modulated individually by ACs; thus signals to some target GCs were suppressed while those to others were unaffected, or even enhanced by disinhibition. Taken together, the results suggest that visual information undergoes dramatic divergence and convergence during transmission in the inner retina, and that considerable computation takes place at each BC-GC connection.
To explore how each bipolar cell (BC) signal is distributed downstream, we intracellularly manipulated the activity of individual BCs in the isolated salamander retina (Fig. 1a, b), and recorded simultaneously the spiking activity of many surrounding ganglion cells (GCs; Fig. 1c, d). Frequently depolarization of a BC via current injection elicited spikes in GCs nearby (Fig. 1d), including those of different cell types (Supplementary Fig. 1). These sign-preserving responses in GCs likely arise through excitatory transmission from BCs. Other GCs were inhibited by BC depolarization, and we confirmed by pharmacological block of inhibition that this sign inversion arises from interposed amacrine cells (ACs; Supplementary Fig. 2). While it is reassuring that the actions of a single BC can be measured even across intervening neurons, the present study will focus on sign-preserving transmission to GCs.
Some of the sign-preserving responses were observed at great distances, up to ~1 mm from the stimulated BC. Given that the combined radius of BC terminal fields and GC dendritic fields is ~0.35 mm3,26,27, these effects cannot arise from a monosynaptic connection. Such long-range connections were greatly attenuated when we applied a gap junction blocker (Supplementary Data), suggesting that signals propagate laterally through electrical junctions among neurons in the inner retina26,28. To exclude such patently polysynaptic effects, we further restricted the analysis to BC-GC pairs separated by ≤0.35 mm.
With these methods in place, we set out to characterize the diversity of signal transmission from BCs to GCs. For the reasons detailed above, we focused the approach on the following four aspects of BC-GC connections: (1) the dynamics of the GC response; (2) adaptation in GC responses across repeated BC depolarizations; (3) rectification of signal transmission to GCs; and (4) the gating of BC-GC signaling by ACs.
By examining the postsynaptic responses, we found considerable divergence and convergence of distinct BC signals. First, the same BC could evoke very different GC responses. For example, depolarization of a single BC elicited a sustained response in one GC but a sharply transient response in another GC (Fig. 2a). This indicates that the signals acquire their distinct dynamics at or after the BC-GC transmission. Second, a single GC could produce distinct responses to inputs from different BCs. After serially impaling several BCs, we encountered some GCs with a sustained response to one BC but a transient response to another BC (Fig. 2b). This indicates that the distinct dynamics arise at or before the BC-GC transmission. Apparently the transmission dynamics are specified neither by the presynaptic BCs nor by the postsynaptic GCs, but are determined at each individual BC-GC connection.
How substantial is this diversity in the output from individual BCs? To assess this quantitatively, we examined for each BC-GC connection the time course of GC firing on BC depolarization. We found that more than two-thirds of all BCs had significant variation in the peak latency among their connections to target GCs (Fig. 2c). Furthermore, the variation among the outputs from a single BC explained about two-thirds of the total variation across all the BC-GC connections. Since the BCs were sampled blindly from all cell types by the sharp electrode, it appears that the variation across cell types is less significant than the variation across the outputs of a single BC. Similarly, many GCs showed diversity among their BC inputs (Fig. 2d).
Visual signals thus differentiate in their dynamics not only at BC dendrites in the outer retina7,10 but also on transmission from BCs to GCs in the inner retina, and before they are integrated by the GCs. This may involve a combination of pre- and post-synaptic mechanisms that are private to the individual BC-GC connections. One explanation of such diversity involves the function of inhibitory interneurons. For example, the transient responses could arise as a result of feedback or feedforward inhibition via ACs11–13. Another possible explanation is that individual synapses have different pre- or post-synaptic mechanisms, for instance, by using different receptor types29,30. We distinguished these alternatives by pharmacological methods. Following a block of inhibitory transmission via γ-aminobutyric acid (GABA) and glycine, the peak evoked firing rates increased in almost all GCs (Fig. 3c), as would be expected from a general loss of inhibition. This was accompanied by changes in the dynamics of the response. Unexpectedly, however, the dynamics of transient and sustained responses were altered in opposite directions. Following the inhibitory block, the formerly transient responses peaked later (Fig. 3a), whereas the formerly sustained responses peaked earlier (Fig. 3b). Thus the overall diversity in the GC response kinetics evoked by single BCs decreased significantly after elimination of AC circuits (Fig. 3d).
How can these bidirectional changes in dynamics be explained? Given the large increase in the evoked firing rate, one would generally expect a faster decline of the response due to synaptic fatigue and thus a shorter time to peak. For example, because tonic presynaptic inhibition prevents synaptic depletion20,21,31,32, the pharmacological block of such inhibition would speed up the postsynaptic GC response to BC depolarization (Fig. 4b). But clearly this is not the only effect at work, since the formerly transient responses become more extended in time. One explanation for transient responses is that feedback or feedforward inhibition can truncate synaptic transmission shortly after onset of the GC response11–13. With such a microcircuit at the BC-GC connection, the loss of inhibition will lead to a longer peak latency (Fig. 4a, c).
Below we will elaborate on possible mechanisms that shape synaptic transmission from BCs. Regardless of the details, however, it appears that distinct microcircuits with inhibitory ACs are involved in regulating the dynamics of individual BC-GC connections, and that even a single BC engages quite different AC microcircuits at its various synapses.
Following repeated exposure to the same stimulus, many GCs change their response properties over time. Previous studies suggest that events at the BC terminal contribute to these visual adaptations in GC responses22–24. We thus examined whether GC responses evoked by single BC inputs change over consequtive trials (Fig. 5). Specifically, we alternately delivered 1 s of depolarizing and hyperpolarizing currents into individual BCs with 2 s intervals (Fig. 1d), and analyzed slow changes in the peak rate and latency of the GC responses. To avoid confusion between spontaneous and evoked spikes, we selected those GCs that had low spontaneous firing rates (≤1 Hz) and high evoked rates (≥5 Hz).
In the course of many repeated trials, some GCs desensitized, in that their responses became weaker and slower (Fig. 5a). By contrast, responses of other GCs did not change significantly (Fig. 5b), even though they all received inputs from the same BC. Interestingly, slow changes in the peak rate or in the latency could occur independently of each other (Fig. 5c, d). Compiling results from many such experiments, one gains a view of the broad diversity of adaptive behaviors, including both desensitization and sensitization, even in transmission from a single BC. Indeed, the variation arising among the connections of individual BCs explained most of the total variation in the adaptive behavior of the response latency, and about two-thirds for changes of the peak rate (Fig. 5e).
To examine the contribution of AC circuits, we again blocked inhibitory synaptic transmission pharmacologically. Surprisingly we found that the sensitizing or stable responses were largely turned into desensitizing ones (Fig. 5f, g): Almost all BC-GC connections now showed a gradual decline in the peak firing rate, with less diversity than prior to the block. Again, it appears that diverse AC circuits are responsible for much of the variation in behavior of BC-GC connections, even on the slow time scale of adaptation.
While the above experiments show diverse adaptive behaviors among the output connections of one BC, does the same diversity apply among the inputs of a given GC? For example, an inactivating sodium conductance contributes to slow desensitization at the level of spike generation33,34, which should affect every BC input to that GC equally. Similarly the sensitizing responses of certain GCs have been explained with a circuit model that affects all the BC inputs35. To test this notion, we drove the same GC by stimulating two different BCs intracellularly. We found multiple cases where the GC adapted to inputs from one BC but not to those from another BC (Fig. 6b), even though the nonadapting responses were sometimes stronger than the adapting ones (Fig. 6a).
To further examine if adaptation to inputs from one BC occurs independently of the other, we drove a single BC with current injection, and many other BCs with a visual stimulus presented far from the impaled BC (Fig. 6c–e). Over a 10-s train of current pulses into the single BC, most GCs desensitized strongly (Fig. 6d), and often the response vanished completely (Fig. 6c). If this adaptation originated in a general loss of sensitivity after the GC integrates its synaptic currents33,34, that should affect the response to all of the BC inputs. Instead, the GC responses to the light-evoked BC pathway did not change at all (Fig. 6e). This shows that the adaptation arises within the input pathway from a single BC. Combined with the above results on divergence from a single BC, we conclude that desensitization and sensitization are specific to a given BC-GC connection but not attributable to global changes in either the presynaptic or the postsynaptic neuron.
Under stimuli of moderate strength, BC responses can be well described by a linear function of the light intensity36,37. By contrast, many GCs show highly nonlinear responses under those same stimulus conditions15,16, and the effect has been attributed to rectification at the transmission from BCs to GCs14,17. Indeed we generally found a strong asymmetry in GC responses (e.g., Fig. 2): BC depolarization excited the GC much more than hyperpolarization inhibited it. Because many GCs had low spontaneous firing rates, however, this asymmetry could result from a cellular nonlinearity of spike generation in the GC, rather than synaptic rectification. To focus on the BC-GC transmission properties, we selected GCs with sufficiently high spontaneous firing rates (≥1 Hz) so that we could resolve a decrease as well as an increase of the firing rates. For those GCs, we examined the effects of BC currents of either polarity, and asked if the transmission was rectified or not. To this end, we used a rectification index that measures the relative efficacy of BC depolarization and hyperpolarization in changing the GC spiking activity (see Methods).
In general, BC depolarization and hyperpolarization had opposite effects on any given GC (Fig. 7); one leading to an increase of the firing rate and the other to a decrease. However, the relative strength varied over a wide range (Fig. 7b). For some GCs, only BC depolarization was effective (Fig. 7a, bottom), suggesting a rectifying transmission with the index distributed around unity. In others, depolarization and hyperpolarization had comparable effects in opposite directions (Fig. 7a, top), indicating nonrectifying transmission with the index close to zero. For nonrectifying connections, we frequently observed rebound responses — an increase in firing at the offset of BC hyperpolarization — whereas these were seen only rarely for rectifying connections (Supplementary Fig. 3). Because a given BC can make both rectifying and nonrectifying transmission to different targets (Fig. 7a), that same neuron can contribute to fundamentally different visual computations. Here we found that ~40% of the total variation of the rectification index arose from the diversity among the outputs from individual BCs (Fig. 7b).
Blocking inhibitory transmission did not affect the degree of rectification in BC-GC connections. Neither the rectification index nor the observed frequency of rectifying and nonrectifying responses changed significantly following the pharmacological block (Fig. 7b, d). Even without the contribution of ACs, the same BC could thus send both rectified and nonrectified signals to different GCs (Fig. 7c). This indicates that the signal rectification is intrinsic to individual BC-GC connections, perhaps depending on the baseline levels of calcium and vesicle release rates at the presynaptic BC terminals38,39 (Supplementary Fig. 3).
We have observed that signals from ACs can strongly affect transmission at individual BC-GC connections (Figs. 3–5). But so far these AC signals were only evoked by the intracellularly stimulated BC. In general, ACs receive stimulation from a broader region of the visual field, and multiple ACs at different locations are involved in modulating BC-GC connections14,19,40. To explore the details of this modulation, we proceeded to drive the AC circuits independently by a visual stimulus, while monitoring their effect on transmission from individual BCs.
Specifically, we projected on the retina a randomly moving grating, but excluded the receptive field center of the target BC and GCs (see Methods). The stimulus by itself did not affect the baseline activity of the GCs (Fig. 8a and Supplementary Figs. 4b and 5), indicating that they did not receive any excitatory inputs directly from the light-driven BCs, and we selected these GCs for subsequent analysis. In contrast, this visual stimulus does drive neurons in the periphery, including polyaxonal ACs whose processes are long enough to interact with the selected BC and GCs17,24,40. By combining such visual stimulation and single BC current injection, we were thus able to examine how light-driven ACs modify the GC responses to the current-driven BCs.
The background visual stimulation had diverse effects on BC-GC transmission. For some GCs the response to BC depolarization was suppressed (Fig. 8a, left), for others enhanced (Fig. 8a, right), and unaffected for the rest (Fig. 8b). Effects of opposite sign were observed even for transmission from the same BC (Fig. 8a, b). Of the total variation in these gating effects from distant stimuli, about 60% originated in diversity among connections from individual BCs (Fig. 8b). Similarly there was diversity among inputs converging onto a given GC: The same GC could experience suppression for one BC input but not for another (Fig. 8c and Supplementary Fig. 4b).
A block of inhibitory transmission from ACs eliminated these effects of peripheral visual stimulation (Fig. 8d and Supplementary Fig. 5). This means that ACs mediate both the observed suppression and enhancement of BC transmission, the latter presumably through disinhibition via serial AC connections41. We thus conclude that the gating of BC signals by distant stimuli occurs independently at each BC-GC connection, and that ACs innervate these synapses in a way that allows the selective switching of each connection.
To examine how bipolar cell (BC) signals feed into ganglion cells (GCs), we simultaneously recorded from many GCs while manipulating individual BCs intracellularly, the associated amacrine cells (ACs) pharmacologically, and the surrounding circuits visually (Fig. 1). We found considerable divergence and convergence of diverse excitatory signals from BCs to GCs, indicating that individual BC-GC connections have distinct transfer functions despite their close proximity. First, a single BC could elicit sustained responses in some GCs but sharply transient responses in others (Fig. 2). Such diverse kinetics of signal transmission resulted largely from inhibitory circuits involving ACs (Figs. 3 and and4).4). Second, distinct modes of adaptation were found in transmission from individual BCs, demonstrated by slow changes of the response amplitude and latency over time (Figs. 5 and and6).6). Again this diversity was shaped by AC circuits. Third, synapses of the same BC differ considerably in their degree of rectification. This feature appears to be intrinsic to a given BC-GC connection without the contribution of AC circuits (Fig. 7 and Supplementary Fig. 3). Finally, BC-GC connections were individually modulated by ACs; some were suppressed while others were enhanced (Fig. 8 and Supplementary Figs. 4 and 5). Taken together, our results emphasize the diverse modes of BC-GC transmission and how it may be tuned by ACs.
What are the synaptic mechanisms for this diversity among the signals from a single BC? At this point we can only speculate, but there are some plausible candidates. In most BCs, across many species, the axon branches in a tree with many synaptic terminals near the tips3,6,17,25,26 (Fig. 1b). Furthermore, ACs contact the BC specifically at its terminals, often in direct proximity to the glutamate release sites11,42. Thus it is tempting to identify the BC terminal as the key compartment that controls the BC-GC connection. This requires that different terminals be sufficiently isolated electrically or with respect to their calcium signals. Even within a terminal, there is evidence of presynaptic specializations that might differentially control transmission to different postsynaptic partners43. Alternatively, the key compartment may lie in the GC dendrite, with the transmission characteristics determined by the postsynaptic complement of transmitter receptors, local membrane dynamics, and AC innervation. Again, this would require that different parts of the GC dendrite operate independently, whereas there is some evidence that salamander GCs are electrotonically compact44. Clearly, one would like to observe directly the activity within presynaptic terminal arbors and postsynaptic dendritic trees, and new methods of targeted optical imaging may make this possible in the near future45. Here we consider in more detail possible mechanisms for our specific observations.
Regarding the diversity in transmission kinetics (Figs. 2 and and3),3), two factors mentioned above are known to affect the time course of the GC response: Presynaptic depletion of vesicles makes for a transient postsynaptic response20,21,32. Feedback/feedforward inhibition from ACs can also truncate the postsynaptic response11–13. Interestingly, these two mechanisms react in opposite ways to the block of AC activity. The removal of tonic presynaptic inhibition will enhance transmitter release, speed depletion, and thus further shorten the response. By contrast, removal of feedback/feedforward inhibition will extend the response. Simulations of BC-GC transmission showed that a combination of synaptic depression and inhibition is indeed sufficient to produce the observed bidirectional changes in the transmission dynamics (Fig. 4).
Certain forms of contrast adaptation in the retina have been traced to a reduction of transmitter release from BCs22–24. This might be explained again by a process of presynaptic depletion20,21. Normally, the BC terminal receives tonic inhibition from ACs31, which lowers the synaptic release and thus counteracts depletion. When inhibition is blocked, the depletion effects become more pronounced, which may explain why most BC-GC synapses become desensitizing (Fig. 5g). Alternatively, the increase in GC firing may modulate the behavior of postsynaptic conductances. This could contribute to contrast adaptation of individual connections33,34, as long as their dendritic compartments are electrotonically separated.
Rectification is a well-known aspect of vesicle release at all synapses. However, the ribbon synapses at BC terminals are somewhat special; They allow for tonic release of glutamate and a continuous modulation of the release rate46. The rate increases nonlinearly with presynaptic voltage, owing largely to the voltage-dependent calcium influx38,39. The degree of rectification then depends on the BC resting potential and the voltage range during neural signaling. If the resting potential is high and the range is small, the modulation of the release rate may be essentially linear about the resting rate (Supplementary Fig. 3). In the present experiments the presynaptic voltage drive was deliberately large, and thus most BC-GC connections showed asymmetric effects of depolarization and hyperpolarization. Nevertheless, different synapses were clearly operating along different parts of the voltage-release curve (Fig. 7).
Finally, the gating of BC-GC transmission by distant visual stimuli (Fig. 8 and Supplementary Figs. 4 and 5) could be accomplished by presynaptic inhibition from polyaxonal ACs17,24,40,47. Indeed, these stimuli hyperpolarize the BC soma17 (Supplementary Fig. 4a). Since some connections from the same BC are unaffected (Fig. 8), this view requires that certain terminals receive the inhibition and others not; the hyperpolarization at the soma then reflects an average over these inputs. The morphology of polyaxonal ACs makes such a selective connectivity plausible: They carry sparse, straight and unbranched axons17,40,48. As such an axon passes through a BC terminal arbor, it can contact only a few of the terminals that lie in its path. Hence different terminals will be innervated by different polyaxonal ACs, allowing for the observed diversity in gating.
In a simple view of neural circuits, the nerve cells are treated as the active components, with fibers and synapses merely conducting signals between them. From the present work, we conclude that each connection between neurons in the inner plexiform layer is an active circuit element, whose transmission parameters are drawn from a broad palette of component options, and whose performance is controlled by its own microcircuit (Supplementary Fig. 6). These individual BC-GC connections may be the primitives of retinal computation, much as transistors form the primitives for an electronic computer.
What are the potential benefits for retinal functions of such a fine-grained control of visual signals? First, this organization permits a greater range of distinct visual computations to proceed in parallel. For an illustration of this principle beyond the current study, consider the ON-OFF direction-selective ganglion cells (DSGCs). These neurons fire selectively when a spot moves in one direction, but not for the opposite direction19. They are sensitive to tiny motions within the receptive field49, and thus the fundamental computation happens locally, in part from presynaptic inhibition of a BC terminal by a starburst amacrine cell (SAC) dendrite. The BC itself is not direction-selective, but the SAC dendrite is, and thus the BC terminal becomes a direction-selective feature detector. Our observations (Supplementary Fig. 1) suggest that each BC contributes its terminals to DSGCs with all four directional preferences, by combining with different SAC dendrites. If instead each BC had just one type of synaptic output, then each DSGC would receive input from only a quarter of the BCs. By exploiting individual BC-GC connections as elementary feature detectors, the retina thus uses its limited resources efficiently.
Second, the independent control of the various BC-GC connections shapes the way the retina adapts to prolonged visual stimulation. Among all the BC inputs feeding a GC, any given visual stimulus will drive only a subset strongly. These connections will adapt, for example owing to the synaptic depletion discussed above, and thus the sensitivity of the GC to that prolonged stimulus gradually declines. Meanwhile the cell retains high sensitivity to novel stimuli that drive the previously dormant BC inputs. For example, a GC may desensitize to persistent stimuli with a certain orientation, while retaining high sensitivity to novel stimuli of the orthogonal orientation50. In general, this organization allows the retina to implement a pattern-selective adaptation that had long been thought to arise only in higher visual areas14.
Finally, the gain of a given BC-GC connection is not only a function of its recent activity, but can be controlled by presynaptic AC circuits (Fig. 8). When this modulation affects different synapses in opposite directions, the selectivity of the receiving GC may be altered dramatically. For example, for some GCs the polarity of the light response can switch from Off-type to On-type, depending on the activity in distant ACs40. This suggests a flexible routing of signals from different BC pathways into one GC, and similarly from the same BC to different GCs (Fig. 8). Such fine-scale routing is an essential feature of artificial computing machines, and its full implications for neuronal circuits remain to be explored.
Simultaneous intracellular and multielectrode recording was performed as described previously17, following protocols approved by the Institutional Animal Care and Use Committee at Harvard University. In short, the dark-adapted retina of a tiger salamander (Ambystoma tigrinum; both sexes; age unspecified but in the larval stage) was isolated and placed on a flat array of 61 extracellular electrodes with the ganglion cell (GC) side down (Fig. 1a). The retina was superfused with oxygenated Ringer’s medium (in mM: NaCl, 110; NaHCO3, 22; KCl, 2.5; MgCl2, 1.6; CaCl2, 1; and D-glucose, 10; equilibrated with 95% O2 and 5% CO2 gas) at room temperature. Sharp intracellular microelectrodes were filled with 2 M potassium acetate and 3% Rhodamine Dextran 10,000 MW (fluorescent dye; Molecular Probes) with a final impedance of 150–250 MΩ, and blindly inserted into various cells until one with visual response characteristics matching those of bipolar cells (BCs) was found37. We sampled the signals from each extra- and intra-cellular electrode at 10 kHz, and used an Axoclamp 2B amplifier (Molecular Devices, Palo Alto, CA) in bridge mode for intracellular recordings and current injection into BCs. In all experiments, we alternately delivered depolarizing and hyperpolarizing square pulse currents (500 pA; 1 s each) into BCs with 2 s intervals (Fig. 1d). Each trial of this protocol thus lasted for 6 s, and each BC was typically examined with 30–100 trials. In some experiments, we also used a train of square-wave pulse currents (±500 pA; 1 Hz; 10 s) to deplete transmission from the intracellularly stimulated BC (10–15 trials with 10 s intervals; Fig. 6c–e).
Visual stimuli were displayed on a gamma-corrected cathode-ray tube monitor (DELL E773c; frame rate 100 Hz; mean luminance ~18 mW m−2) and projected on the photoreceptor layer of the retina as described previously17. Bipolar cells were identified during the experiment by their responses to center spot (~200 μm diameter), annulus ring (~500 μm inner diameter, ~1,000 μm outer diameter), and full-field flash stimuli. The spatio-temporal receptive fields of BCs and GCs were mapped using flickering checkerboard stimuli51 for 10–15 minutes, with square fields 20–100 μm in width, each modulated independently by white noise (e.g., Supplementary Fig. 1).
To characterize how GC responses adapt to BC inputs (Fig. 6c–e), we stimulated the GCs in two ways: one by single BC current injection to induce adaptation in one BC pathway, and the other by visual stimulation to probe the effects on other BC pathways. The visual stimulus was comprised of black and white stripes (80 μm width) confined to an annulus region (outer diameter, 1,000 μm; inner diameter, 500 μm; centered at the BC soma), and its contrast was inverted twice (with 0.5 s interval) 3 s before and immediately after repetitive intracellular stimulation of a single BC (see above). Note that this visual stimulus did not change its mean intensity, and that it intersected with the receptive field center of the GC but not that of the current-stimulated BC.
To examine how amacrine cells (ACs) gate the synaptic transmission between BCs and GCs (Fig. 8 and Supplementary Figs. 4 and 5), the entire visual field (6,400×4,800 μm) was covered by a grating of black and white stripes (80 μm width) and divided into a circular center region (1,000 μm in diameter, centered at the BC soma) and the surrounding background region17,24. In combination with the current injection into a BC, the surrounding grating was then either shifted by a half period every 200 ms or jittered on every 10 ms frame update (Gaussian random motion with a standard deviation of 2 mm s−1, corresponding to a step size of 2 pixels per frame) to recruit inputs from polyaxonal ACs17,40. The center region remained static so as not to visually stimulate the current-stimulated BC or GCs nearby. In the former shifting case, every current injection trial was delayed by 50 ms in order to vary the relative timing between the onset of square pulse currents and that of background stimulus motion. We also inverted the contrast of the center and surrounding gratings in or out of phase to examine the BC response characteristics17 (Supplementary Fig. 4a).
For extracellular recordings, spike trains from individual GCs were extracted from raw voltage traces by a semi-automated spike-sorting algorithm written in Igor (Wave Metrics). In total we identified 4,236 GCs (mean spontaneous firing rate, 1.0 Hz; standard deviation, 2.2 Hz; median, 0.20 Hz), of which 965 GCs showed significant responses to single BC stimulation and thus were used for subsequent analyses. Note that the GC layer also contains some displaced ACs, but their action potentials are expected to be below the noise level of the multielectrode recordings and are attenuated further by signal filtering prior to spike sorting52. The extracted spike timing data and intracellular data traces were then analyzed in Matlab (Mathworks).
The spatio-temporal receptive fields of BCs and GCs were estimated by reverse-correlation methods17,51. Using the random flicker stimulus, we computed the response-weighted average of the stimulus waveform, where the weight is the measured membrane voltage for BCs (e.g., Supplementary Fig. 1a), and spike number for GCs (e.g., Supplementary Fig. 1b–e). To display the receptive field locations, we computed two-dimensional Gaussian fits to the spatial receptive field and assigned the cell’s location to the center of that profile (e.g., Fig. 1c).
To quantify transmission from BCs to GCs, we first computed the peri-stimulus time histogram (PSTH; 0.1 s bin width) of GC spiking activity while manipulating BC activity intracellularly. For those GCs that had significantly different firing rates from their spontaneous activity (rspont; based on the activity 1 s before the onset of current injection) in at least one bin during the current injection periods (significance level, 0.05; two-tailed with Bonferroni correction), we calculated the average firing rates for the 1 s periods of BC depolarization and hyperpolarization: rdep and rhyp, respectively. If the difference (rdep − rhyp) was significantly above or below zero, then we considered that the BC had sign-preserving or sign-inverting effects on the GC activity, respectively. The confidence interval was estimated by bootstrap resampling methods over trials (10,000 repeats). The effective strength of the BC-GC connection was then defined as:
where sdep and shyp are the standard deviation of the GC firing rates across trials upon BC depolarization and hyperpolarization, respectively.
This standardized measure (called the “effect size” in statistics) does not depend on the data length (number of trials), unlike the p-values in the significance tests. Changes in ES[dep;hyp] were thus used as a measure of the effects of background visual stimulation on BC-GC connections (Fig. 8b–d). Estimation of statistical significance follows the confidence intervals of ES[dep;hyp] in the presence and absence of the background stimulation. The Levene’s test (for the equality of variance) and χ2-test (for the independence of the observed frequencies of the significant changes in ES[dep;hyp]) were used to judge the effects of the drug application across the population (Fig. 8d).
To quantify the divergence of BC signals, we partitioned the total variation of GC response characteristics into the sum of the variation within inputs from individual BCs and the variation across different BCs, much as in the analysis of variance. Formally,
where xij is any given response property of interest for j-th GC in response to i-th BC stimulation (for i = 1, …, n and j = 1, …, mi), and xi. and x.. indicate the average over j and over all cell pairs, respectively. The fraction of the total variation due to the variation within inputs from individual BCs was then computed as the ratio of the “variation within BCs” to the “total variation” from Eq.(2).
To analyze the dynamics of BC-GC connectivity, we fit the PSTHs of GCs in response to BC depolarization with the following unimodal function: f(t) = αtβ exp(−t/γ) + rspont, where α, β, and γ denote the free parameters, t (>0) indicates the time after the onset of current injection, and rspont is the spontaneous firing rate. The peak latency was then computed as tpeak = β γ and the peak firing rate as rpeak = f(tpeak) − rspont. Confidence intervals on the fit parameters were used for judging if significant variation exists among different BC-GC connections (Fig. 2c, d). The sign test was used to examine the changes in rpeak before and after drug application (Fig. 3c), and the Levene’s test was used to assess the changes in the distribution of tpeak (Fig. 3d).
For those GCs with low spontaneous firing rates (rspont ≤ 1 Hz) but high peak rates (rpeak ≥ 5 Hz), we analyzed the variation of the peak rate and latency across trials to examine adaptive changes in BC-GC transmission over time (Figs. 5 and and6).6). We first computed the peak rate and latency using a moving window of 10 trials, and performed a linear regression over trials. We then considered that the peak rate showed desensitization or sensitization if the slope was significantly below or above zero, respectively. For the peak latency, significant decrease or increase over trials indicates sensitization or desensitization, respectively. Note that the rate adaptation did not necessarily coincide with the latency adaptation (Fig. 5c, d). These slope values were used for the divergence analysis (Fig. 5e), and the χ2-test was used for examining the effects of the inhibitory transmission blockers (Fig. 5g).
To address whether the adaptation arises before or after GCs integrate their synaptic inputs from BCs (Fig. 6), we examined if adaptation in one BC pathway (driven by single BC current injection) affects the GC responses to inputs from other BC pathways (driven by a visual stimulus). A single exponential function was used to fit the time course of GC responses to repetitive intracellular stimulation of single BCs (Fig. 6c, d). The sign test was used to compare the GC visual responses before and after the adaptation by the current injection (rbefore and rafter, respectively, using the spike counts during the 1 s visual stimulation periods; Fig. 6e).
For those GCs with sufficiently high spontaneous firing rates (rspont ≥ 1 Hz), we investigated if the BC-GC synaptic transmission was rectified or not (Fig. 7). Specifically, we used bootstrap resampling methods over trials (10,000 repeats) to analyze the differences of rdep and rhyp from rspont. We considered that the synaptic transmission was rectified if either rdep or rhyp was significantly different from rspont, and nonrectified if both rdep and rhyp were significantly different from rspont. The rectification index was defined as:
where ES[dep;spont] and ES[spont;hyp] from Eq.(1) indicate the effective strength of BC depolarization and hyperpolarization, respectively (Fig. 7b, d). Note that ES[dep;spont] > 0 for an increase in GC spiking activity on BC depolarization, while ES[spont;hyp] > 0 for a decrease in GC spiking activity on BC hyperpolarization. The index is thus close to unity for rectifying excitatory transmission because ES[dep;spont] > 0 and ES[spont;hyp] ≈ 0, whereas the index is near zero for nonrectifying transmission because ES[dep;spont] ≈ ES[spont;hyp]. The rank-sum test (for the equality of median rectification indices) and the χ2-test (for the independence of the observed frequencies of rectifying and nonrectifying BC-GC connections) were used to judge the effects of blocking inhibitory AC circuits (Fig. 7d).
To examine the contributions of different AC circuits to the transmission dynamics from BCs to GCs (Fig. 3), we incorporated the following four types of AC inputs into a phenomenological model of the synaptic transmission53 (Fig. 4 and Supplementary Fig. 7); tonic presynaptic inhibition (αpre > 0), tonic postsynaptic inhibition (αpost > 0), feedback presynaptic inhibition (βpre > 0), and feedforward postsynaptic inhibition (βpost > 0). Specifically, the presynaptic side was modeled by the dynamics of the vesicle pool x [0,1] and release rate u [0,1]:
where τd and τf are the recovery constants of depression and facilitation, respectively. The release rate u works as a driving force of vesicle release, reflecting, for example, the fraction of opened calcium channels20,32; u0 and k indicate the baseline and the change rate of u, respectively. The effective presynaptic membrane potential Vm = V(I) − αpre − Bpre changes upon receiving input current I with current-voltage transform V. When Vm > 0, neurotransmitters are released by the amount v = [uxVm]+ as in Eq.(4), where [·]+ is a half-wave rectification function, and the release rate u increases because a fraction of closed calcium channels (1 − u) opens as in Eq.(5). With time constant τ, the released vesicles v recruit feedback or feedforward inhibition: dB*/dt = −B*/τ + vβ*, where “*” is either “pre” or “post”, respectively. The postsynaptic dynamics were then simulated by the firing rate r = [v − θ]+, where θ = θ0 + αpost + Bpost is the effective spiking threshold with a baseline of θ0. Note that GCs in the salamander retina are thought to be electrotonically compact for excitatory input44; and that voltage-dependent processing in the dendrites contributes little to signal integration33.
The simulation was done at time steps of 1 ms using the following parameter values. For simplicity, we ignored the nonlinear effects of current-voltage transform in BCs54 and assumed V(I) = IRin + V0 with an input resistance Rin = 100 MΩ and a baseline potential V0 = 0 mV. In accord with our experimental protocol, we used I = 500 pA for t [0,1], otherwise 0 A. Previous studies suggest that recovery from synaptic depression after a sustained depolarization is slow32, whereas the calcium dynamics are relatively fast and facilitatory55 and the time course of retinal inhibition is even faster56. Thus we used τd = 5 s, τf = 0.5 s, u0 = k = 0.01, and τ = 0.1 s. For the postsynaptic side, we set θ0 = 0.8 so that the normalized firing rate r decays within ~0.5 s in the absence of inhibition (Fig. 3). For the inhibition parameters, we used αpre [0,3]; αpost [0,0.18]; βpre [0,0.75]; and βpost [0,1.5] (normalized in Fig. 4 for display purposes). A stronger inhibition led to no firing responses in the postsynaptic side. We obtained qualitatively similar results over many different sets of the parameters, confirming that the model is robust in accounting for the effects of AC circuitry.
To examine how the rectification arises (Fig. 7), we also simulated the transmitter release v at different baseline potentials V0 (Supplementary Fig. 3). Specifically, we used V0 = 0, 7.5, and 15 mV with the injected current I following the protocol of Fig. 1d, and ran the simulation with the same parameter values as described above but with no inhibition (αpre = αpost = βpre = βpost = 0).
We gratefully acknowledge Ed Soucy for his extensive help in experiments, as well as all the members of the Meister laboratory for many useful discussions.
Grants: This work was supported by a JSPS Postdoctoral Fellowship for Research Abroad (H.A.) and grants from NIH (M.M.).
Author contributions: H.A. and M.M. designed the study and wrote the manuscript. H.A. performed experiments and analysis.
Competing interests: The authors declare no competing financial interests.