Modeling

Comparison between the Hassenstein-Reichardt model and responses from a large tangential cell of the blow fly. (A) Steady-state response as a function of grating speed, for four different spatial wavelengths (B) Transient response to grating being at rest until time 0 and then being stepped to a temporal frequency of 5 Hz. (C) Temporal frequency–response functions for Gaussian velocity profiles with three different half-widths.

The so-called "Hassenstein-Reichardt-Detector" represents a purely algorithmic model of motion detection. Here, the signal from one image location is fed through a temporal low-pass filter and subsequently multiplied by the high-pass filtered signal from a neighboring image pixel. This is done twice in a mirror-symmetrical way. The output of both multipliers finally become subtracted to deliver a directionally selective signal. Pooling these signals across the moving image leads to a good agreement with many experimental results obtained from lobula plate tangential cells (reviewed in Borst, 2014).

Compared to T4 and T5 cells, however, the Hassenstein-Reichardt-Detector reveals a smaller degree of direction-selectivity. In order to model their behavior, preferred direction enhancement and null direction suppression needs to be combined in a single stage, where the central signal is multiplied by the low-pass signal from one side and divided by the low-pass signal from the other side (Arenz et al, 2017). But how are these operations realized in real neurons, what is the biophysical basis of multiplication and division? To explore these mechanisms, we replace the T4 cells by an electrical equivalent circuit of a neural membrane and have the input signals change ionic conductances (Borst, 2018). With the knowledge about the transmitter receptors and the feasibility to electrically record from T4 and T5 cells (Gruntman et al, 2018), such models become within reach and, once confirmed experimentally, will tell us how neurons in the fly visual system compute the direction of motion at the level of the biophysical membrane properties.

(A) Three-arm motion detector, as proposed in Haag et al, eLife, 2016. (B) Biophysical implementation of the same model (from Borst, 2018). (C) Comparison of model performance (left) and experimental data from T4 cells (right).

References

Arenz A, Drews MS, Richter FG, Ammer G, Borst A (2017) The temporal tuning of the Drosophila motion detectors is determined by the dynamics of their input elements. Curr Biol 27: 929-944.

Borst A (2014) Neural circuits for elementary motion detection. J Neurogenet 28: 361-373.

Borst A (2018) A biophysical mechanism for preferred direction enhancement in fly motion vision. PLoS Comput Biol 14: e1006240.

Gruntman E, Tomani S, Reiser MB (2018) Simple integration of fast excitation and offset, delayed inhibition computes directional selectivity in Drosophila. Nat Neurosci 21: 250-257.

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