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Volume electron microscopy together with computer-based image analysis are yielding neural circuit diagrams of ever larger regions of the brain. These datasets are usually represented in a cell-to-cell connectivity matrix and contain important information about prevalent circuit motifs allowing to directly test various theories on the computation in that brain structure. Of particular interest are the detection of cell assemblies and the quantification of feedback, which can profoundly change circuit properties. While the ordering of cells along the rows and columns doesn't change the connectivity, it can make special connectivity patterns recognizable. For example, ordering the cells along the flow of information, feedback and feedforward connections are segregated above and below the main matrix diagonal, respectively. Different algorithms are used to renumber matrices such as to minimize a given cost function, but either their performance becomes unsatisfying at a given size of the circuit or the CPU time needed to compute them scales in an unfavorable way with increasing number of neurons. Based on previous ideas, I describe an algorithm which is effective in matrix reordering with respect to both its performance as well as to its scaling in computing time. Rather than trying to reorder the matrix in discrete steps, the algorithm transiently relaxes the integer program by assigning a real-valued parameter to each cell describing its location on a continuous axis ('smooth-index') and finds the parameter set that minimizes the cost. I find that the smooth-index algorithm outperforms all algorithms I compared it to, including those based on topological sorting.

The visual system must make predictions to compensate for inherent delays in its processing. Yet little is known, mechanistically, about how prediction aids natural behaviors. Here, we show that despite a 20-30ms intrinsic processing delay, the vertical motion sensitive (VS) network of the blowfly achieves maximally efficient prediction. This prediction enables the fly to fine-tune its complex, yet brief, evasive flight maneuvers according to its initial ego-rotation at the time of detection of the visual threat. Combining a rich database of behavioral recordings with detailed compartmental modeling of the VS network, we further show that the VS network has axonal gap junctions that are critical for optimal prediction. During evasive maneuvers, a VS subpopulation that directly innervates the neck motor center can convey predictive information about the fly's future ego-rotation, potentially crucial for ongoing flight control. These results suggest a novel sensory-motor pathway that links sensory prediction to behavior.

Seeing the direction of motion is essential for survival of all sighted animals. Consequently, nerve cells that respond to visual stimuli moving in one but not in the opposite direction, so-called 'direction-selective' neurons, are found abundantly. In general, direction selectivity can arise by either signal amplification for stimuli moving in the cell's preferred direction ('preferred direction enhancement'), signal suppression for stimuli moving along the opposite direction ('null direction suppression'), or a combination of both. While signal suppression can be readily implemented in biophysical terms by a hyperpolarization followed by a rectification corresponding to the nonlinear voltage-dependence of the Calcium channel, the biophysical mechanism for signal amplification has remained unclear so far. Taking inspiration from the fly, I analyze a neural circuit where a direction-selective ON-cell receives inhibitory input from an OFF cell on the preferred side of the dendrite, while excitatory ON-cells contact the dendrite centrally. This way, an ON edge moving along the cell's preferred direction suppresses the inhibitory input, leading to a release from inhibition in the postsynaptic cell. The benefit of such a two-fold signal inversion lies in the resulting increase of the postsynaptic cell's input resistance, amplifying its response to a subsequent excitatory input signal even with a passive dendrite, i.e. without voltage-gated ion channels. A motion detector implementing this mechanism together with null direction suppression shows a high degree of direction selectivity over a large range of temporal frequency, narrow directional tuning, and a large signal-to-noise ratio.

Understanding the computational implications of specific synaptic connectivity patterns is a fundamental goal in neuroscience. In particular, the computational role of ubiquitous electrical synapses operating via gap junctions remains elusive. In the fly visual system, the cells in the vertical-system network, which play a key role in visual processing, primarily connect to each other via axonal gap junctions. This network therefore provides a unique opportunity to explore the functional role of gap junctions in sensory information processing. Our information theoretical analysis of a realistic VS network model shows that within 10 ms following the onset of the visual input, the presence of axonal gap junctions enables the VS system to efficiently encode the axis of rotation, θ, of the fly's ego motion. This encoding efficiency, measured in bits, is near-optimal with respect to the physical limits of performance determined by the statistical structure of the visual input itself. The VS network is known to be connected to downstream pathways via a subset of triplets of the vertical system cells; we found that because of the axonal gap junctions, the efficiency of this subpopulation in encoding θ is superior to that of the whole vertical system network and is robust to a wide range of signal to noise ratios. We further demonstrate that this efficient encoding of motion by this subpopulation is necessary for the fly's visually guided behavior, such as banked turns in evasive maneuvers. Because gap junctions are formed among the axons of the vertical system cells, they only impact the system's readout, while maintaining the dendritic input intact, suggesting that the computational principles implemented by neural circuitries may be much richer than previously appreciated based on point neuron models. Our study provides new insights as to how specific network connectivity leads to efficient encoding of sensory stimuli.

Understanding the principles governing axonal and dendritic branching is essential for unravelling the functionality of single neurons and the way in which they connect. Nevertheless, no formalism has yet been described which can capture the general features of neuronal branching. Here we propose such a formalism, which is derived from the expression of dendritic arborizations as locally optimized graphs. Inspired by Ramón y Cajal's laws of conservation of cytoplasm and conduction time in neural circuitry, we show that this graphical representation can be used to optimize these variables. This approach allows us to generate synthetic branching geometries which replicate morphological features of any tested neuron. The essential structure of a neuronal tree is thereby captured by the density profile of its spanning field and by a single parameter, a balancing factor weighing the costs for material and conduction time. This balancing factor determines a neuron's electrotonic compartmentalization. Additions to this rule, when required in the construction process, can be directly attributed to developmental processes or a neuron's computational role within its neural circuit. The simulations presented here are implemented in an open-source software package, the "TREES toolbox," which provides a general set of tools for analyzing, manipulating, and generating dendritic structure, including a tool to create synthetic members of any particular cell group and an approach for a model-based supervised automatic morphological reconstruction from fluorescent image stacks. These approaches provide new insights into the constraints governing dendritic architectures. They also provide a novel framework for modelling and analyzing neuronal branching structures and for constructing realistic synthetic neural networks.

To comprehend the principles underlying sensory information processing, it is important to understand how the nervous system deals with various sources of perturbation. Here, we analyze how the representation of motion information in the fly's nervous system changes with temperature and luminance. Although these two environmental variables have a considerable impact on the fly's nervous system, they do not impede the fly to behave suitably over a wide range of conditions. We recorded responses from a motion-sensitive neuron, the H1-cell, to a time-varying stimulus at many different combinations of temperature and luminance. We found that the mean firing rate, but not firing precision, changes with temperature, while both were affected by mean luminance. Because we also found that information rate and coding efficiency are mainly set by the mean firing rate, our results suggest that, in the face of environmental perturbations, the coding efficiency is improved by an increase in the mean firing rate, rather than by an increased firing precision.

Dendrite morphology, a neuron's anatomical fingerprint, is a neuroscientist's asset in unveiling organizational principles in the brain. However, the genetic program encoding the morphological identity of a single dendrite remains a mystery. In order to obtain a formal understanding of dendritic branching, we studied distributions of morphological parameters in a group of four individually identifiable neurons of the fly visual system. We found that parameters relating to the branching topology were similar throughout all cells. Only parameters relating to the area covered by the dendrite were cell type specific. With these areas, artificial dendrites were grown based on optimization principles minimizing the amount of wiring and maximizing synaptic democracy. Although the same branching rule was used for all cells, this yielded dendritic structures virtually indistinguishable from their real counterparts. From these principles we derived a fully-automated model-based neuron reconstruction procedure validating the artificial branching rule. In conclusion, we suggest that the genetic program implementing neuronal branching could be constant in all cells whereas the one responsible for the dendrite spanning field should be cell specific.