Circuits - Computation - Models: Modeling

Modeling

<div style="text-align: justify;"><strong>Models for motion detection. a</strong> The classical Hassenstein-Rei- chardt detector. Inputs from the two photoreceptors are asym- metrically delayed by low-pass filtering and multiplied leading to a direction-selective output signal. <strong>b</strong> An elaborated scheme taking into account the split of motion detection into an ON- and an OFF-pathway. Motion detection within each pathway is computed as in <strong>a</strong>.</div> Zoom Image
Models for motion detection. a The classical Hassenstein-Rei- chardt detector. Inputs from the two photoreceptors are asym- metrically delayed by low-pass filtering and multiplied leading to a direction-selective output signal. b An elaborated scheme taking into account the split of motion detection into an ON- and an OFF-pathway. Motion detection within each pathway is computed as in a.
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The output of a single photoreceptor, capturing all light impinging on a circumscribed spot on the fly's retina, conveys no information about the direction in which an object moves. Computation is required before a visual signal becomes selective for direction. One appropriate algorithm for this operation is the elementary motion detector (EMD) as developed by Hassenstein and Reichardt based on the visual turning behavior of beetles (Hassenstein & Reichardt, 1956). Multiplying the instantaneous signal at one retinal location with the delayed signal from an adjacent receptor, and performing this operation twice in an opponent fashion with flipped inputs, achieves direction-selectivity. The signal of such a detector correlates with the direction and velocity of motion, giving positive and negative output for movement in its preferred and non-preferred direction respectively. Overwhelming experimental evidence indicates that first-order motion detection in Drosophila is mediated by EMDs of this type.

The original form of the EMD relies on purely mathematical operations: subtraction, multiplication, and linear filtering. One of the core goals in our group is understanding how a biophysical system that consists of non-linear, complex neural units operating under vastly different constraints than analogue or digital circuits implements such operations. Modeling shapes our work in at least two ways. First, it allows us to embed experimental findings in a solid theoretical framework. Second, it often yields novel predictions that guide experimental design.

Electrophysiological experiments suggested that, within the Drosophila visual system, brightness increments (ON signals) and brightness decrements (OFF signals) are handled by separate channels, starting with lamina cells L1 and L2 respectively (Joeschet al., 2010). This has important implications for the structure of the elementary motion detector. For instance, are only channel-internal interactions (ON-ON, OFF-OFF) or all four possible combinations (ON-ON, OFF-OFF, ON-OFF, OFF-ON) computed?  Modeling work from our group showed that an appropriately modified two-channel model can account for virtually all characteristics of motion detection in the fly (Eichner et al., 2011). Surprisingly, by rendering the polarity rectification slightly imperfect, this "two-quadrant" detector gains the ability to approximate sign-correct multiplication. This was initially thought to depend on the explicit interaction of ON and OFF signals. A major prediction of this model was eventually confirmed in experiments: when genetically blocking the input channels L1 and L2, results were in agreement with the properties of a two-quadrant detector in which one of the two channels was silenced (Joesch et al. 2013).

<div style="text-align: justify;"><strong>Model of fly behavior</strong>.&nbsp; The fly visual system is modeled as a superposition of a motion and a position system. The first is based on an array of Reichardt detectors, whereas the other is implemented as an array of luminance change detectors. The resulting signals are summed and low-pass filtered resulting in the turning speed of the fly. The model reproduces fly behavior in great detail.</div> Zoom Image
Model of fly behavior.  The fly visual system is modeled as a superposition of a motion and a position system. The first is based on an array of Reichardt detectors, whereas the other is implemented as an array of luminance change detectors. The resulting signals are summed and low-pass filtered resulting in the turning speed of the fly. The model reproduces fly behavior in great detail.
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Our modeling work also extends to higher-level systems such as visually driven fixation behavior (Bahl et al., 2013). Closed-loop experiments in which tethered walking flies control the position of a black stripe indicated that Drosophila employs two computed signals for keeping the object in its frontal field of view: a motion system based on Reichardt-type detectors and a position system based on spatially weighted luminance changes. A simple model of this system in which the two sub-systems are linearly combined and feed into the motor control output manages to replicate both qualitative and quantitative aspects of the experimental findings. The virtual fly is capable of fixating objects and does so with plausible dynamics and precision. Critically, the simulations confirm the observation that flies remain able to track objects when the major outputs of the motion system, cells T4 and T5, are genetically disabled. When the motion arm of the model is silenced, in silico fixation becomes weaker but stays largely intact which is in accordance with experimental data. The model thus plays a crucial role in proving the plausibility of the two-system interpretation.

Example calculation and simulation results can be downloaded via the links below.

References

Hassenstein, B. & Reichardt, W. Systemtheoretische Analyse Der Zeit, Reihenfolgen Und Vorzeichenauswertung Bei Der Bewegungsperzeption Des Rüsselkäfers Chlorophanus. Z. Naturforsch. B 11, 513–524 (1956).

Bahl, A., Ammer, G., Schilling, T. & Borst, A. Object tracking in motion-blind flies. Nat. Neurosci. 16, 730–738 (2013).

Eichner, H., Joesch, M., Schnell, B., Reiff, D. F. & Borst, A. Internal structure of the fly elementary motion detector. Neuron 70, 1155–1164 (2011).

Joesch, M., Weber, F., Eichner, H. & Borst, A. Functional specialization of parallel motion detection circuits in the fly. J. Neurosci. 33, 902–905 (2013).

Joesch, M., Schnell, B., Raghu, S. V., Reiff, D. F. & Borst, A. ON and OFF pathways in Drosophila motion vision. Nature 468, 300–304 (2010).

 
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