Short-Term Synaptic Depression Can Contribute to Direction Selectivity in an Elementary Reichardt Detector (A) Information from two channels (blue and red: right and left, respectively) converges on a post-synaptic cell. The blue channel exhibits short-term synaptic depression (D), which nonlinearly filters the stimulus, advancing the timing of the channel’s peak response relative to the timing of the peak of the stimulus (blue dashed lines). The red channel exhibits no depression (ND), which linearly scales the stimulus, leaving the timing of the channel’s peak response to coincide with the timing of the stimulus (red dashed lines). Differences in temporal processing interact with a spatial separation of the two channels’ receptive fields to produce direction selectivity. A moving stimulus pulse first activating the red channel leads to the summation of coincident peaks in the post-synaptic cell. A stimulus pulse moving in the opposite direction leads to the summation of disparate peaks and hence a weaker response in the post-synaptic cell. (B) A schematic outline depicting the ascending electrosensory system in Apteronotus and Eigenmannia and other Gymnotiform genera. In short, electrosensory information from receptors in the skin (RF 1 and RF 2) project topographically onto the electrosensory lateral line lobe (ELL). Neurons in the ELL in turn project topographically onto neurons in the torus semicircularis (Torus) in the midbrain via the lateral lemniscus (LL). Midbrain afferents include both depressing and nondepressing synapses that converge on to individual neurons: this convergence of information meets the requirements for the proposed elementary Reichardt motion detector. We used three categories of stimuli: global stimuli (social signals that stimulate the entire sensory surface simultaneously), a localized moving bar (shown), and a larger moving sinewave grating. doi:10.1371/journal.pcbi.0040032.g001 

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Context 1

... of animal behavior often requires the discrimination of the direction of movement of sensory images. In some behaviors, including tracking [1–5] and postural balance [6–9], animals must determine the direction of sensory slip to generate appropriate compensatory movements to stabilize the sensory image on the receptor array. For other behaviors, including prey capture [10,11], animals must respond to the direction of motion of prey relative to the sensory background. A neural correlate of these functions was described over 40 years ago: Hubel and Wiesel characterized central neurons in the mammalian visual system that exhibited preferential responses to particular directions of movement of sensory images [12–14]. Following this discovery, direction- selective response properties have been found in a diversity of animal species and across different sensory modalities, from the visual cortex of cats [12] and somatosensory cortex of monkeys [15] to the electrosensory midbrain of weakly electric fish [16,17]. Of particular interest are the direction selective responses of midbrain neurons observed in a species of weakly electric fish, Eigenmannia virescens . These neurons exhibit an unex- pected enhancement of direction selectivity by the addition of concomitant naturally occurring sensory oscillations in the gamma frequency range [17]. These oscillations strongly induce short-term synaptic depression in these midbrain neurons, and measures of this depression correlate significantly with direction selectivity [17–19]. These correlations suggest that a depression-based mechanism might underlie both the generation of direction selectivity and its enhancement by the addition of gamma-band oscillations. Here we propose a parsimonious model to describe and explore the essential features of this mechanism. The model is based on a conceptual framework for motion processing known as Reichardt detectors: information from two spatially separated channels with asymmetric temporal properties combine via a nonlinear operation on a downstream (post-synaptic) neuron to produce direction selective responses [20,21] (Figure 1). When supplied with a stimulus moving in the preferred direction, the temporal shift can compensate for the spatial separation, allowing the inputs from the two channels to interact constructively. The temporal phase shift is typically modeled as a pure delay or a low-pass filter. For direction-selective neurons in V1, Chance et al. [22] propose that the dynamical differences between synapses that exhibit short-term synaptic depression and those that do not may provide a mechanism for generating both the asym- metrical temporal properties and the nonlinear operation required by an elementary Reichardt circuit (the electrosensory midbrain of Eigenmannia also exhibit these requisite ingredients for Reichardt-style selectivity based on short- term depression [19,23].) For a depressing synapse, the magnitude of the response in the post-synaptic cell decreases during repetitive activation [24–27]. Short-term synaptic depression involves two dynamic processes with distinct time constants: the faster process, with a time-constant on the order of tens to hundreds of milliseconds, can be attributed to the depletion of the supply of readily releasable synaptic vesicles, while the slower process, with a time-constant of seconds to tens of seconds, can be attributed to the mechanisms for the replenishment of this supply [25,26]. Here we propose a parsimonious model that describes a mechanistic linkage between short-term synaptic depression and direction selectivity, based on a Reichardt-style circuit. We further test the possibility that the enhancement of direction selectivity by concomitant gamma-band oscillations may be mediated by short-term synaptic depression. Global synchronous oscillations in activity may arise endogenously, as occurs in cortical and other circuits [28], or exogenously, as occurs in weakly electric fish from the interaction of the electric fields of nearby conspecifics [29] and the jamming avoidance response [30]. In the model, these oscillations induce depression, which can lead to an enhancement of direction selectivity to moving objects. We systematically explore the effects of variations of biologically relevant parameters of the model and evaluate the results in relation to electrophysiological data from a population of motion- sensitive electrosensory neurons in the midbrain of weakly electric fish [17]. Information from two spatially separated receptive fields converges onto a post-synaptic neuron via dynamically different synapses: one that exhibits short-term synaptic depression and the other that does not (Figure 1). The spatial separation of the receptive fields combined with the differences in temporal dynamics of the synaptic inputs satisfies the requirements for an elementary Reichardt motion detector. In this model, only the depressing synapse contributes state to the model, which consists of one or two variables whose dynamic evolution is governed by uncoupled and identical (up to parameters) nonlinear ordinary differential equations. We have found that the one-state model, which includes only the fast process of short-term synaptic depression, exhibits direction selectivity (Figure 2A). Since short-term synaptic depression creates a phase advance in the synapse, a moving stimulus that first passes through the nondepressing area leads to a simultaneous arrival (a constructive combina- tion) of signals from both synapses (Figure 2A, blue). Movement in the opposite direction leads to asynchronous arrival of information (Figure 2A, red). These results are similar to those reported previously [22]. The response to the sine-wave grating is nearly identical from cycle to cycle over time. In this case, the time constant of depression is fast relative to the period of the stimulation so that the depressing synapse has sufficient time to return to its initial state during the dark phase of each cycle. In the two-state model, which includes both the fast and slow processes associated with short-term synaptic depression, neurons exhibit direction selectivity that enhances from cycle to cycle of a sustained sine wave grating (Figure 2B). In the first cycle, the response is nearly identical to the response of the one-state model. However, in each subsequent cycle there is a total reduction in the probability of firing and in the total number of spikes for both directions of motion. This reduction in probability of firing is asymptotic. This overall reduction in firing nonetheless increases the direction index (reported in the caption to Figure 2 and defined in Model) by increasing the relative difference between the responses to the preferred and non-preferred directions of movement. Intracellularly, this enhancement effect will occur as long as the stimulus is maintained even if the depression limits the PSPs so that they do not reach the spiking threshold. In extracellular recordings, however, there is a possibility that the depression could lead to a complete elimination of spiking responses to the moving stimulus. The sine-wave gratings that we used are sustained stimuli— such stimuli that might arise during image-stabilization tasks. In contrast, many behaviors, such as prey capture, involve spatiotemporally localized, or intermittent stimuli. We have examined the performance of the model to this class of stimuli. Our intermittent stimulus consists of the temporal sequence defined by Equation 2, which is a 1.5 cycle sine-wave pulse. Prior to the arrival of the stimulus, we initialized the system with at least 3 seconds of a spatially homogeneous stimulus of intermediate intensity, which we call 50% grey (see Model). At the arrival of the pulse, the model lies in approximately the same state as it does for the first cycle of the sine grating. As a result, the responses to the first cycle of the grating and to the intermittent stimulus are nearly identical (compare Figures 2B and 3A). For the same parameter values, the responses differ only because the stimuli are subtly different: the sine grating stimulus appears in both receptive fields at the same time, but at different phases, whereas the 1.5 cycle pulse first appears in one receptive field then moves to the other and disappears. We also tested the model’s response to an intermittent stimulus that was initialized not with a uniform background but rather with global synchronous gamma-band oscillations. These sorts of oscillations occur exogenously in groups of weakly electric fish [29] and endogenously in many CNS circuits [28]. In the model, the gamma-band oscillations drive activity simultaneously in both afferents which activates both the fast (0 , D ( t ) ( 1) and slow (0 , S ( t ) ( 1) processes in the depressing synapse (see Model). The response of the model to the moving pulse after 3 seconds of global stimulation compares to its asymptotic response to a persistent sine grating (compare Figures 2B and 3B). The response in this condition is more ‘‘ sparse ’’ than in the grey-initialized condition—the responses are reduced due to the activation of the slow process associated with short- term synaptic depression. The code is more sparse in that fewer spikes more reliably encode information—the direction of movement. Depending on the values of the parameters, this reduction in spiking can lead to an enhancement of direction selectivity (Figure 3A versus 3B) or a reduction of the direction selectivity (Figure 3C versus 3D). We varied the contributions of the depressing and nondepressing synapses in the model and measured the response to the moving pulse ...

Context 2

... of animal behavior often requires the discrimination of the direction of movement of sensory images. In some behaviors, including tracking [1–5] and postural balance [6–9], animals must determine the direction of sensory slip to generate appropriate compensatory movements to stabilize the sensory image on the receptor array. For other behaviors, including prey capture [10,11], animals must respond to the direction of motion of prey relative to the sensory background. A neural correlate of these functions was described over 40 years ago: Hubel and Wiesel characterized central neurons in the mammalian visual system that exhibited preferential responses to particular directions of movement of sensory images [12–14]. Following this discovery, direction- selective response properties have been found in a diversity of animal species and across different sensory modalities, from the visual cortex of cats [12] and somatosensory cortex of monkeys [15] to the electrosensory midbrain of weakly electric fish [16,17]. Of particular interest are the direction selective responses of midbrain neurons observed in a species of weakly electric fish, Eigenmannia virescens . These neurons exhibit an unex- pected enhancement of direction selectivity by the addition of concomitant naturally occurring sensory oscillations in the gamma frequency range [17]. These oscillations strongly induce short-term synaptic depression in these midbrain neurons, and measures of this depression correlate significantly with direction selectivity [17–19]. These correlations suggest that a depression-based mechanism might underlie both the generation of direction selectivity and its enhancement by the addition of gamma-band oscillations. Here we propose a parsimonious model to describe and explore the essential features of this mechanism. The model is based on a conceptual framework for motion processing known as Reichardt detectors: information from two spatially separated channels with asymmetric temporal properties combine via a nonlinear operation on a downstream (post-synaptic) neuron to produce direction selective responses [20,21] (Figure 1). When supplied with a stimulus moving in the preferred direction, the temporal shift can compensate for the spatial separation, allowing the inputs from the two channels to interact constructively. The temporal phase shift is typically modeled as a pure delay or a low-pass filter. For direction-selective neurons in V1, Chance et al. [22] propose that the dynamical differences between synapses that exhibit short-term synaptic depression and those that do not may provide a mechanism for generating both the asym- metrical temporal properties and the nonlinear operation required by an elementary Reichardt circuit (the electrosensory midbrain of Eigenmannia also exhibit these requisite ingredients for Reichardt-style selectivity based on short- term depression [19,23].) For a depressing synapse, the magnitude of the response in the post-synaptic cell decreases during repetitive activation [24–27]. Short-term synaptic depression involves two dynamic processes with distinct time constants: the faster process, with a time-constant on the order of tens to hundreds of milliseconds, can be attributed to the depletion of the supply of readily releasable synaptic vesicles, while the slower process, with a time-constant of seconds to tens of seconds, can be attributed to the mechanisms for the replenishment of this supply [25,26]. Here we propose a parsimonious model that describes a mechanistic linkage between short-term synaptic depression and direction selectivity, based on a Reichardt-style circuit. We further test the possibility that the enhancement of direction selectivity by concomitant gamma-band oscillations may be mediated by short-term synaptic depression. Global synchronous oscillations in activity may arise endogenously, as occurs in cortical and other circuits [28], or exogenously, as occurs in weakly electric fish from the interaction of the electric fields of nearby conspecifics [29] and the jamming avoidance response [30]. In the model, these oscillations induce depression, which can lead to an enhancement of direction selectivity to moving objects. We systematically explore the effects of variations of biologically relevant parameters of the model and evaluate the results in relation to electrophysiological data from a population of motion- sensitive electrosensory neurons in the midbrain of weakly electric fish [17]. Information from two spatially separated receptive fields converges onto a post-synaptic neuron via dynamically different synapses: one that exhibits short-term synaptic depression and the other that does not (Figure 1). The spatial separation of the receptive fields combined with the differences in temporal dynamics of the synaptic inputs satisfies the requirements for an elementary Reichardt motion detector. In this model, only the depressing synapse contributes state to the model, which consists of one or two variables whose dynamic evolution is governed by uncoupled and identical (up to parameters) nonlinear ordinary differential equations. We have found that the one-state model, which includes only the fast process of short-term synaptic depression, exhibits direction selectivity (Figure 2A). Since short-term synaptic depression creates a phase advance in the synapse, a moving stimulus that first passes through the nondepressing area leads to a simultaneous arrival (a constructive combina- tion) of signals from both synapses (Figure 2A, blue). Movement in the opposite direction leads to asynchronous arrival of information (Figure 2A, red). These results are similar to those reported previously [22]. The response to the sine-wave grating is nearly identical from cycle to cycle over time. In this case, the time constant of depression is fast relative to the period of the stimulation so that the depressing synapse has sufficient time to return to its initial state during the dark phase of each cycle. In the two-state model, which includes both the fast and slow processes associated with short-term synaptic depression, neurons exhibit direction selectivity that enhances from cycle to cycle of a sustained sine wave grating (Figure 2B). In the first cycle, the response is nearly identical to the response of the one-state model. However, in each subsequent cycle there is a total reduction in the probability of firing and in the total number of spikes for both directions of motion. This reduction in probability of firing is asymptotic. This overall reduction in firing nonetheless increases the direction index (reported in the caption to Figure 2 and defined in Model) by increasing the relative difference between the responses to the preferred and non-preferred directions of movement. Intracellularly, this enhancement effect will occur as long as the stimulus is maintained even if the depression limits the PSPs so that they do not reach the spiking threshold. In extracellular recordings, however, there is a possibility that the depression could lead to a complete elimination of ...