Figure 1.
Inverse approach applied to wide-field motion integration.
The morphology and physiology of VS cells are well described. We formulate a hypothesis based on the biological data and express this hypothesis in a formula, i.e., the fitness function. Subsequently, we generate model neurons (from a model specification) and assess their performance according to the fitness function. Based on the assessment, the model specification is optimized using a genetic algorithm until models are found that perform the desired function. Afterwards, these optimized model neurons are analyzed for matches with real VS cells. Matches support the notion that the hypothesized function is indeed carried out by these neurons. Details in the methods. (Fly photograph by M. Turney, Wikimedia Commons, VS cell morphology after [5] and voltage data by H. Cuntz.)
Figure 2.
The rows correspond to the different models: (A) shows the reference model while the best optimized passive and active model neurons are shown in (B) and (C), respectively. The left column illustrates the dendritic tree of the model neuron and its synapses (red dots). The right column shows the membrane potential at the beginning of the axon in rest (green) and upon stimulation in preferred-direction (red) and null-direction (blue). The distinctive characteristics as evaluated in the fitness function such as the variance of the signal and the amplitude of the membrane shift can be observed from these traces.
Figure 3.
Comparison of optimized performance to real VS cell performance.
Response of a real VS cell (A) and two optimized model neurons (B, C) to a similar stimulation protocol is shown. The protocol consists of no motion, preferred-direction motion and null-direction motion. The responses of the models neurons and the real VS cell are similar. We did not directly optimize for this similarity and the high resemblance is an emergent property corroborating the hypothesis of VS performing wide-field motion integration. (Voltage data in A by H. Cuntz.)
Figure 4.
Different morphologies when optimizing for wiring-constraints only.
We optimized morphologies without the terms for wide-field motion integration, once with only the overall size as constraint and once with the overall size and average path length as constraint. The morphology with the lowest overall size (A) and combined size and path length (B) are shown. The morphology in A deviates substantially from the morphologies found originally, while the morphology in B shares the same blueprint as originally optimized models and VS cells. Both neurons have a significantly lower performance as wide-field motion integrators than the originally optimized passive model neurons.
Figure 5.
Required conductance distributions to perform wide-field motion integration.
All successfully optimized active model neurons showed the same blueprint for the conductance distributions, namely a high density of (A) and a low density of
(B) in the dendrites. The distribution of
(C) is less constrained and more variable (over different optimized models) because the lack of
channels. The colors are scaled to the minimum and maximum density allowed in the optimization,
,
and
for
,
and
, respectively.
Figure 6.
Role of active conductances in balancing depolarization- and hyperpolarization amplitudes.
Passive models can only achieve a hyperpolarizing shift of of the depolarization due to different driving forces caused by the synaptic reversal potentials. We optimized passive and active models as before but demanded a balance between the depolarization and hyperpolarization shifts so that the depolarization amplitude had to be
of the hyperpolarization amplitude. None of the optimized passive models exhibited the desired membrane shifts (typical model illustrated in A), while all active models exhibited the demanded membrane shifts (typical model illustrated in B). Therefore, this result follows our hypotheses that active conductances are required in VS cells to achieve biologically realistic balancing between responses in preferred- and null-direction.
Figure 7.
Comparison of the intrinsic dynamics of the reference model and optimized models.
Intrinsic physiology is here determined in a current-clamp simulation. Injected currents are (in steps of 1) from to
nA in the reference model (A) and from
to
nA in the optimized models (B: passive model, C: active mode). The optimized models show the same qualitative dynamics as the reference model: (i) outward rectification, (ii) a dampening oscillation after
injection, and (iii) strong after-depolarization. Note that the dynamics are not optimized explicitly but emergent, corroborating the hypothesis of wide-field motion integration in VS cells. B: *In the passive model, active conductances were inserted as in the reference model, after optimization with passive properties only.
Figure 8.
Mechanism of wide-field motion integration by VS cells.
Left: full model neuron. Center: Passive mechanism for wide-field motion integration is twofold: electronic distance is similar for each input thus achieving ‘equal weight, equal delay’-summation of temporally shifted inputs in the axon (B), and temporal smoothing by voltage attenuation (C, schematic). Right: Active mechanism that employs Na-currents to boost the smoothed signal in the axon (D) and the strong K-currents in the dendrites which reduce lower the amplitude of individual inputs (E). Color coding of the traces as the locations in (A) indicate.
Figure 9.
Overview of the model used in this study.
The stimulus is external and the subsequent processing is done in two stages. The first stage is small-field motion detection and corresponds to the signal transformation in the lamina and medulla of fly. The second stage corresponds to the wide-field motion integration. In this model, small-field motion detection is performed by Reichardt detectors. The outputs of the small-field motion detectors are projected onto the integrator cell in a biologically accurate way as illustrated. Each small-field motion detector is connected to the integrator cell through an excitatory and inhibitory ribbon synapse that convey graded potentials. Illustrated is a random cell with its connections. The number of detectors shown in the figure is reduced from the actual 20 to 4 for the sake of clarity.