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Dendritic Integration and Its Role in Computing Image Velocity

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Science  18 Sep 1998:
Vol. 281, Issue 5384, pp. 1848-1850
DOI: 10.1126/science.281.5384.1848

Abstract

The mechanisms underlying visual motion detection can be studied simultaneously in different cell compartments in vivo by using calcium as a reporter of the spatiotemporal activity distribution in single motion-sensitive cells of the fly. As predicted by the Reichardt model, local dendritic calcium signals are found to indicate the direction and velocity of pattern motion but are corrupted by spatial pattern properties. The latter are canceled out by spatial integration, thus leading to a purely directional selective output signal in the axon. These findings attribute a specific computational task to the dendrites of visual interneurons and imply a functional interpretation of dendritic morphology.

In the third optic neuropile of the blowfly Calliphora erythrocephala (lobula plate), there exist about 60 different, individually identifiable tangential cells (LPTCs) (1). Located directly underneath the rear surface of the brain, they are easily accessible after the head capsule has been opened and can be imaged in vivo (2–4) while being stimulated by motion (Fig. 1A). Among the LPTCs, cells are found that respond preferentially to vertical motion like the VS cells (5) as well as cells that are best activated by horizontal motion like the HS and CH cells (6). In general, LPTCs are involved in visual course control and show direction-selective motion responses by shifting their membrane potential as well as their intracellular calcium concentration (Fig. 1B). During preferred direction motion (PD), the cells depolarize in a graded way. This depolarization, sometimes superimposed by action potentials of small and irregular amplitude (7), is accompanied by an increase in the intracellular calcium concentration. During antipreferred or null direction motion (ND), the cells hyperpolarize and the calcium concentration decreases. As has been found in nine other LPTCs, the amplitude and time course of the electrophysiological and the calcium response always show a high degree of similarity (8). In addition to detecting the direction of motion, LPTCs also encode pattern velocity in the amplitude of their electrical response (9). To examine whether this also holds true for the intracellular calcium level, we measured the correlation between the overall dendritic calcium concentration and the membrane potential when stimulating LPTCs with pattern motion of different velocities. The results indicate a fairly linear relationship between axonal membrane potential and dendritic calcium concentration (10).

Figure 1

(A) A fly is schematically shown viewing onto a moving grating beneath it. From above, after removal of one of the rear head capsules, LPTCs can be filled with calcium green and afterward be imaged by using an upright microscope and a CCD camera. (B) Calcium dynamics in a fly LPTC (VS1 cell) during visual stimulation in the cell's PD and ND with a velocity of 78° per second. Raw fluorescence and false-color images of the relative change of fluorescence (Δf/f) of the VS1 cell, during PD and ND motion, are shown above. The latter display the spatial distribution of the calcium signal in the VS1 cell during motion. The time course of the dendritic calcium signal of the cell along with the membrane potential recorded from its axon is presented below.

The LPTC response to visual motion can be formally described by the so-called Reichardt model of motion detection (11, 12). Reichardt detectors provide a direction-selective signal by correlating the luminance levels in adjacent retinal locations. They are assumed to be represented by small-field elements in the medulla, the second optic neuropile of the fly brain, impinging onto the dendrites of the LPTCs in a retinotopic way (13, 14). The output signals of the medulla elements, integrated by the LPTCs, lead to the characteristic response of the LPTCs representing the direction and velocity of pattern motion. According to the Reichardt model, a local input to the LPTCs should exhibit a two-component response: a constant shift and, superimposed on it, temporal modulations in phase with the local luminance of the pattern (12). By spatially integrating the output signals of many Reichardt detectors, the modulations are canceled, which results in a smooth graded response to constant image motion. To obtain a quantitative prediction of how strongly the dendritic membrane potential of the integrating neuron is expected to be locally modulated when fed with output signals of Reichardt-type motion detectors, we performed computer simulations on a compartmental model of a LPTC (Fig. 2). The anatomy of the cell was obtained from three-dimensional reconstructions of cobalt-stained material, and the membrane parameters were derived from current and voltage clamp experiments (15–17). If such a neuron is synaptically driven by an array of Reichardt detectors stimulated by constant motion in the cell's preferred direction (downward), the dendritic membrane potential is locally modulated around a mean excitation level, whereas the axonal membrane potential consists of a constant shift only. The amplitude of the dendritic membrane potential modulations is about 20% of the mean excitation level, and the phase varies with the location in the dendrite. This is in accordance with the retinotopic arrangement of the input elements and their responses to the local luminance changes of the pattern. The exact time course is discussed below.

Figure 2

(Top) A VS1 cell that was three-dimensionally reconstructed and used as a compartmental model to predict the spatiotemporal membrane potential distribution upon constant visual motion in the cell's PD (downward). The neuron is simulated to receive synaptic input from an array of Reichardt-type or EMDs. (Bottom) Resulting local membrane potentials in three dendritic areas indicated by the corresponding colors are shown together with the axonal membrane potential. Although the local dendritic potentials consist of a constant response superimposed by temporal modulations of identical frequency but various phase offsets, the axon potential is rather smooth.

The demonstration of a linear relationship between membrane voltage and intracellular calcium concentration suggests that the intracellular calcium concentration of LPTCs is controlled by membrane voltage. For that reason we used calcium green as a reporter of dendritic activity to compare the behavior of the simulated cell with the behavior of a real cell (Fig. 3). Evaluating the time course of local calcium changes in small dendritic areas during constant PD motion, we found that the calcium signal in these areas was permanently increased and, in addition, modulated with the temporal frequency of the stimulus. In different areas of the dendrite, these modulations had a different phase offset. Similar results were obtained in 10 other experiments. The calcium modulations indicate local modulations of dendritic activity that are in phase with the retinal luminance level at the corresponding locations. In contrast to the activity modulations in the dendrite, the calcium signal in the axon showed a smooth time course, corresponding to the smooth axonal membrane potential. These data confirm the predictions derived from the Reichardt scheme of motion detection and closely match the results of the compartmental model simulations (Fig. 2).

Figure 3

Dendritic calcium modulations in a VS1 cell observed during constant image motion of a periodic grating in the cell's PD (downward). Image velocity was 13° per second, resulting in a temporal frequency of 0.5 Hz. (Top) One Δf/f image of the cell is shown indicating the overall calcium response and the five areas in which the time course of relative fluorescence changes were evaluated. These time courses are displayed on the bottom in the corresponding colors together with the membrane potential. The fluorescence traces are modulated with the temporal frequency of the moving pattern and are phase shifted according to the location of the respective areas in the dendritic tree.

The local dendritic calcium modulations unambiguously demonstrate local activity modulations in the dendrite. However, whether they reflect synaptic input activity only or local changes of postsynaptic membrane potential as well remains a question. Although the existence of voltage-activated calcium channels (VACCs) in the dendrites of LPTCs has been demonstrated (4), an additional calcium flux through transmitter-gated channels during synaptic stimulation cannot be excluded. This possibility must be considered in particular because nicotinic acetylcholine receptors (nAChRs) have been demonstrated on LPTCs (14), which, in vertebrates, are known to be permeable for calcium (18). Yet, for insect nAChRs, calcium permeability has not been tested (19). To decide whether the local calcium modulations in the dendritic tips are caused by VACCs and therefore directly represent local membrane modulations or whether the calcium signals represent modulated synaptic input activity only, we applied the same stimulus protocol as in Fig. 3 with one modification: after 10 s of PD motion, a negative current ramp was applied simultaneously to the continuing PD motion stimulus. If nAChRs are the only gate for calcium to enter the cell, then the amplitude of the modulation should increase by hyperpolarization of the cell. If, however, calcium is entering the cell via VACCs, the amplitude of the modulation should become reduced during hyperpolarization. The result from such an experiment performed on an HS cell is shown in Fig. 4. During the first 10 s of PD motion, the cell shows the typical dendritic calcium modulations. After the onset of the negative current ramp, the modulations become smaller with increasing amplitude of the hyperpolarizing current. We conclude that dendritic calcium modulations in LPTCs during PD motion are largely mediated by VACCs. Therefore, local calcium modulations observed during constant image motion (Fig. 3) are likely to reflect local dendritic membrane potential modulations.

Figure 4

Dendritic calcium modulations in an HS cell observed during constant image motion of a periodic grating in the cell's PD (from the front to the back of the animal). All the stimulus parameters were identical to the experiment shown in Fig. 3. In addition, a negative current ramp (0 to −14 nA) was applied in the second half of the stimulation interval. This led to a decreased amplitude of the calcium modulations.

Knowing the origin of the dendritic calcium response allows for a quantitative comparison of the simulation results (Fig. 2) and the local calcium measurements (Fig. 3). In both cases, close inspection of the dendritic signals' time courses reveals that, in addition to the constant response and the first harmonic, a second harmonic is also present. In general, second harmonics arise from the multiplicative nature of the correlation process and depend in amplitude on the imbalance between excitatory and inhibitory motion detectors, as biophysically realized by their different driving forces. Assuming an effective pattern contrast of 3 (12) leads to a quantitative match of the amplitude relations in the simulations and the experimental data (20).

In conclusion, local motion signals as represented by the synaptic inputs to fly LPTCs are corrupted by temporal modulations in phase with the local luminance of the pattern. Information about image velocity thus is represented with high fidelity only globally after spatial integration by the dendrite. Interestingly, effective spatial integration by the LPTC dendrites is almost independent of their electrotonic properties (21) but depends critically on their particular geometry. Whereas VS cells extend their dendritic arbors mainly along the dorsoventral axis of the lobula plate, dendrites of horizontal-sensitive HS and CH cells are much more oriented along the medial-lateral axis. Because the orientation of the dendritic arbor is aligned with that direction of motion where temporal modulations are phase offset, the modulations are optimally canceled by spatial integration. The respective geometries of the LPTC dendrites thus appear to support the specific computational task of the neurons in visual course control.

  • * To whom correspondence should be addressed. E-mail: alexander.borst{at}tuebingen.mpg.de

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