AbstractThe central complex is a highly conserved insect brain region composed of morphologically stereotyped neurons that arborize in distinctively shaped substructures. The region has been implicated in a wide range of behaviors, including navigation, motor control and sleep, and has been the subject of several modeling studies exploring the underlying circuit mechanisms. Most studies so far have relied on assumptions about connectivity between neurons in the region based on their overlap in light-level microscopic images. Here, we present an extensive functional connectome of Drosophila melanogaster's central complex at cell-type resolution. Using simultaneous optogenetic stimulation and GCaMP recordings and pharmacology, we tested the connectivity between over 70 presynaptic-to-postsynaptic cell-type pairs. The results reveal a range of inputs to the central complex, some of which had not been previously described, and suggest that the central complex has a limited number of output channels. Despite the high degree of recurrence in the circuit, network connectivity appears to be sparser than anticipated from light-level images. Finally, the connectivity matrix we obtained highlights the potentially critical role of a class of bottleneck interneurons of the protocerebral bridge known as the Δ7 neurons. All data is provided for interactive exploration in a website with the capacity to accommodate additional connectivity information as it becomes available.IntroductionPositioned in the middle of the insect brain, the central complex provides a unique opportunity to obtain mechanistic insights into the way brains build and use abstract representations. Studies in a variety of insects, including locusts, dung beetles and monarch butterflies, have used intracellular recordings to chart maps of polarized light E-vectors in substructures of the region \cite{Heinze_2007a,26305929}, and extracellular recordings from the cockroach have found sensory and motor correlates throughout the region \cite{Bender_2010,Guo_2012,Roy_2012}. More recently, experiments in behaving Drosophila have shown that both visual and motor cues can update a fly's internal representation of heading \cite{Seelig_2015}. Independently, neurogenetic studies have used disruptions of the normal physiology of the structure to highlight its involvement in a variety of functions, including motor coordination \cite{Poeck_2008}, visual memory \cite{16452971}, sensory-motor adaptation \cite{Triphan_2010}, and short- and long-term spatial memory \cite{Neuser_2008,Ofstad_2011}. It is likely that these tasks rely on the correct establishment and use of an internal representation of heading. Moreover, the scale of the network —a few thousands neurons in the fly— and the ease of genetic access to individual cell types in Drosophila melanogaster, make this circuit tractable with existing theoretical and experimental methods. Detailed light level anatomy \cite{Hanesch_1989,Lin_2013,Wolff_2015} of a significant fraction of the cell types, along with the availability of tools to genetically target these neurons by type \cite{Wolff_2015}, have given rise to the first mechanistic investigations of how the circuit constructs a stable heading representation \cite{Kim_2017}, and how this representation updates as the animal turns in darkness \cite{Turner_Evans_2017,Green_2017}. Such results and related findings from other insects have also inspired a number of modeling studies aimed at predicting or reproducing physiologically and behaviorally relevant response patterns \cite{kakaria_ring_2017,givon_generating_2017,chang_topographical_2017,Turner_Evans_2017,Cope_2017,Su_2017,Fiore_2017,Kim2017,Stone2017}. Many of these models make assumptions about connectivity within the central complex based on the degree of overlap at the light microscopy level between processes that look bouton-like and those that seem spiny,  which are suggestive of pre- and post-synaptic specializations respectively. We aimed to construct a connectivity map based on functional data, which includes information about whether connections are effectively excitatory or inhibitory. This map will help dissect the function of the central complex by constraining large-scale models and aiding the formulation and testing of new hypotheses. Given the likely number of existing and undiscovered cell types in the central complex,  the diversity of neurotransmitters and receptors they express, the mixture of pre- and post-synaptic specializations in their arbors, and the dense recurrence of the network, we see this map as an initial scaffold, which will allow new information to be incorporated as it becomes available.The quest to obtain circuit diagrams can be dated back to the work of Cajal and Golgi \cite{Ram_n_y_Cajal_1894,Pannese_1999}, who used sparse labeling techniques to reveal circuit architectures. Anatomical methods based on marking a discrete subset of neurons and imaging them with light microscopy have recently been revived in the form of techniques relying on stochastic genetic labeling \cite{Livet_2007,Hampel_2011,Nern_2015,Lee_2001,Chiang_2011} and photoactivatable fluorophores \cite{Patterson_2002,Ruta_2010}. These methods allow the extraction of the detailed anatomy of individual neurons. But even when used in combination with synaptic markers \cite{Nicolai_2010,8229205,Zhang_2002,Fouquet_2009}, such methods do not offer definitive evidence of synaptic connections, as they rely solely on the proximity of putative pre- and post-synaptic compartments. Recently, promising trans-synaptic genetic tagging systems \cite{Talay_2017,Huang_2017} have been developed to address some of these issues. However, none of these approaches provide any insight into the functional properties of potential connections. Despite such shortcomings, light-level imaging constitutes a good starting point by constraining the search for possible connections within large populations of neurons —at the simplest level, if putative pre- and post-synaptic compartments do not overlap in light microscopy images, they cannot be in synaptic contact. More recently, electron microscopy (EM) reconstruction has become the gold standard for connectomics \cite{Briggman_2012,Zheng2017,Schneider_Mizell_2016}. Under ideal conditions, it permits the unambiguous identification of synapses between all neurons in a given volume. As game-changing as this capability is, the technique also suffers from a few limitations. Acquiring, processing and analyzing the data is still time-consuming. As a result, connectomes from EM data are typically based on data from a single animal. In addition, EM does not permit the identification of neurotransmitter types at a given synapse, nor does it detect gap-junctions in invertebrate tissue, at least at present \cite{Zheng_2017}. Finally, it can be challenging to assess the strengths of connections between two neurons, because it is not yet clear whether the number of synapses predicts the functional strength of the connection. Functional methods address some of these drawbacks. Simple measures of activity have been used to assess a form of functional connectivity: regions or neurons whose simultaneously recorded activity is correlated —either spontaneously or during a given task— are deemed connected. This has been used with EEG, fMRI and MEG recordings in humans to establish maps at the brain region level \cite{Salvador_2004,Stam_2004} and with multi-electrode recordings in monkeys and rodents (for example, \citealt{Gerhard_2011}).  Functional connectivity has also been inferred from correlations or graded changes in the response properties of neurons recorded in different animals, usually in cases where the neurons have overlapping arbors when examined with light microscopy. This approach has been employed to suggest polarized light processing pathways in the central complex of the locust and monarch butterfly \cite{Heinze_2009a,Heinze_2014}. However, such functional methods are correlative and do not provide a causal basis for the inferred connectivity.To obtain a causal description of functional connectivity —sometimes termed effective connectivity— one needs to either stimulate one node of the network while recording from another one, or record both at sufficiently high resolution as to detect hallmarks of direct connectivity. The most reliable application of such an idea is paired patch-clamp recording, which identifies connected pairs and their functional properties with a high level of detail \cite{Huang_2010,Yaksi2010,Fişek2014}, but can only be performed at low throughput \cite{Jiang_2015}. In  recent years, the development of optogenetics has expanded the toolkit for simultaneous stimulation and recording experiments \cite{17435752}. In Drosophila, the ease of use of genetic reagents renders such approaches particularly attractive. Combinations of P2X2 and GCaMP \cite{yao_analysis_2012}, P2X2 and patch-clamp recordings \cite{hu_functional_2010}, Channelrhodopsin-2 and patch-clamp \cite{gruntman_integration_2013} and CsChrimson and GCaMP (Hampel et al., 2015; Zhou et al., 2015; Ohyama et al., 2015) have been used in individual studies to investigate a small number of connections. Methods that rely on the genetic expression of calcium indicators to detect potential post-synaptic responses operate at a lower resolution than paired-recordings since they usually establish connectivity between cell types, as defined by the genetic driver lines used, rather than between individual neurons. They are also ambiguous as far as the directness of discovered connections, which are not precluded from being several synapses away from the stimulated neuron (but see Results/Discussion) and are limited by the sensitivity of the calcium sensors used. Despite these shortcomings, these methods constitute a good compromise as they still provides a causal measure of functional connectivity, and at a much higher throughput than double patch recordings. It is also worth noting that the advantages and limitations of these techniques complement those of serial EM reconstructions. We chose to apply this combination of optogenetics and calcium imaging on a large scale by systematically testing genetically defined pairs of central complex cell types, therefore building a large and extensible map of functional connections in the structure at cell-type resolution.Cell types and information flow in the central complex