1.6.1 The Hassenstein-Reichardt Detector
A single photoreceptor only reacts to light increments or decrements, but not to the direction of an input signal. Direction sensitive cells have to compare the light changes detected from at least two photoreceptors. Two algorithmic models describe such a basic motion detection: correlation and gradient detectors (Borst, 2007). The motion detection of a gradient detector arises from dividing the temporal gradient of local luminance by the spatial gradient. A correlation model compares the luminance change at one location with the delayed change at a neighboring location.
To obtain insights into the underlying algorithm, W. Reichardt and B. Hassenstein measured
the optomotor response of the beetleChlorophanus as left-right decisions in response to motion
stimuli (described in 1.4.1). They found a temporal frequency optimum of the response, which can not be explained by a gradient detector model. To describe the optomotor response properties of the beetle, Hassenstein and Reichardt proposed a correlation detector model in which inputs of two neighboring photoreceptors are multiplied after one of them has passed a low-pass filter with a time
constantτ (Fig. 1.21 a) (Hassenstein, 1951; Hassenstein and Reichardt, 1956; Hassenstein, 1961).
Subsequently, two mirror-symmetric subunits with an opposite preferred direction are subtracted from each other, resulting in a positive response to preferred direction and a negative response to null direction stimulation.
Figure 1.21: A Comparison of Different Correlation Detectors.
aThe Hassenstein-Reichardt half achieves direction selectivity by multiplication of a delayed input
signal with a fast signal. The arrow points towards the preferred direction of the detector. Photos
from Stadtarchiev Kiel and Bundesarchiv, B145. b The Barlow Levick inhibits a response to the
null direction by dividing a fast signal by a delayed signal. The arrow points towards the preferred
direction of the detector. c 2-Quadrant Hassenstein-Reichardt detector with ON and OFF inputs.
Subtraction of the output from to half detectors induces direction selectivity. ON-ON or OFF-OFF inputs are processed in two independent subunits.
Barlow and Levick (1965) developed another version of a correlation model. The Barlow-Levick model suppresses the response to null direction stimulation using a division of a fast input signal by a delayed signal (Fig. 1.21 b). Therefore, the Barlow-Levick detector results in an inhibition of null direction responses, in contrast to the Hassenstein-Reichardt detector which enhances the preferred direction response. It should be noted that the Barlow-Levick detector explains the direction-selectivity of retinal ganglion cells inadequately, since these cells receive already direction- selective input from starburst amacrine cells(Euler et al., 2002).
The Hassenstein-Reichardt detector takes into account both positive and negative signals at the input stage. However, the fly visual system is subdivided into an ON (sensitive to light increments) and an OFF (sensitive to light decrements) pathway (Joesch et al., 2010; Clark et al., 2011). Blocking the two main input cells to the ON and the OFF pathway, while recording the response of lobula plate tangential cells to apparent motion stimuli with different ON/OFF combinations, revealed that both pathways are separated from each other and feed input to the lobula plate independently (Joesch et al., 2013). This can be simulated by a 2-Quadrant Hassenstein-Reichardt detector with two components multiplying ON-ON and OFF-OFF inputs, thereby the inputs to both subunits are processed by a half-wave rectification resulting in only non-negative signals (Fig. 1.21 c) (Eichner et al., 2011). Since lobula plate tangential cells respond to apparent motion stimuli with several seconds in between stimulation, the model uses a proportion of the input signal
as a tonic (or DC) signal. This also results in an incomplete separation of the ON and OFF pathway, otherwise the two pathways are processed independently. The cellular implementation of the multiplication step was supposed to be the T4/T5 cells, while the dendrites of lobula plate tangential cells represent the summation step (Joesch et al., 2013).
1.6.2 Looming Detectors
Avoidance behavior like escape jumps and avoidance turns, but also the landing response depend on the detection of expansion stimuli. Neurons which are tuned to looming motion should specifically detect nonlinear expansion rather than overall luminance changes or whole-field motion. Such a
looming sensing neuron of another insect species, the locust Schistocerca americana, is studied
in detail. The descending contralateral motion detector neuron (DCMD) is important for gliding (Santer et al., 2008), an escape behavior during flight, and involved in the timing of escape jumps (Simmons et al., 2010). Its input neuron is the lobula giant movement detector (LGMD), which has two dendritic branches in the lobula. DCMD as well as the LGMD are looming sensitive and act as a size threshold detector: after a fixed delay when the looming object reaches an angular threshold size on the retina, the neurons fire maximally (Gabbiani et al., 1999). A model that describes the activity of the LGMD neuron multiplies the logarithm of the angular velocity with an inhibitory input related to the angular size of the looming object (Gabbiani et al., 2002, 2005). On a cellular level, the smaller dendritic branch of the LGMD receives the feed-forward inhibition related to the angular size (Wang et al., 2018), whereas the bigger branch receives excitatory information proportional to the angular velocity (Zhu et al., 2018) (Fig. 1.22 a). The excitatory input is enhanced by lateral excitation in the presynaptic network and receives global, normalizing inhibition. Stimulating single ommatidia of the locust’s eye indicated that the input elements of the LGMD do not perform a Reichardt detector like computation, but rather signal the rate of luminance change on individual photoreceptors (Jones and Gabbiani, 2010). The sensitivity of the LGMD inputs to edge acceleration tune this neuron to looming stimuli.
In theDrosophila brain, one comparable neuron detecting expansion stimuli is described. The
giant fiber, a descending neuron connecting the central brain with motor neurons in the thoracic ganglion, responds to expansion and looming stimuli (Sherman et al., 2004) and is involved in escape behavior (King and Wyman, 1980; Zhang et al., 2007). This neuron was shown to have a peak response at a critical retinal size of the approaching stimulus object (von Reyn et al., 2014). The giant fiber receives two main visual inputs. LC4 neurons provide an excitatory input proportional to the angular velocity of a looming object (Fig. 1.22 b) (von Reyn et al., 2017). The second main input cells to the giant fiber are LPLC2 neurons. These cells provide excitation input to the giant fiber dependent on the angular size of the looming stimulus (Ache et al., 2019). Blocking both LC4 and LPCL2 neurons while recording from the giant fiber revealed an additional input, which inhibits the giant fiber at large disc sizes. A model using a supralinear summation of the LC4 and LPLC2 input, together with the large size inhibition, can predict the giant fiber
Figure 1.22: Looming Detection Models.
aModel of the looming sensitive LGMD neuron from the locustSchistocerca americana. It multi-
plies an excitatory input proportional to angular velocity of the looming object with a feed-forward
inhibition related to angular size. Picture modified from Gabbiani et al. (2002). b Model of the
Drosophila giant fiber sensing looming by a supralinear summation of two excitatory inputs. While LC4 provides input proportional to the angular velocity, LPLC2 encodes the angular size of the looming object. In addition, an unknown input inhibits the giant fiber at a larger stimulus size. Image modified from Ache et al. (2019).
response properties for different looming velocities and also expansion with constant velocity (Ache et al., 2019).