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<h1 class="ltx_title_section">Introduction</h1><div>Positioned 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&nbsp;<cite class="ltx_cite raw v1">\cite{Turner-Evans2016}</cite>.  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&nbsp;<cite class="ltx_cite raw v1">\cite{Heinze_2007a,26305929}</cite>, and extracellular recordings from the  cockroach  have found sensory and motor correlates throughout the region&nbsp;<cite class="ltx_cite raw v1">\cite{Bender_2010,Guo_2012,Roy_2012}</cite>.  More recently, calcium imaging experiments in behaving&nbsp;<i>Drosophila</i> have shown that both visual and motor cues can update a fly's internal representation of heading&nbsp;<cite class="ltx_cite raw v1">\cite{Seelig_2015}</cite>. 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&nbsp;<cite class="ltx_cite raw v1">\cite{Poeck_2008}</cite>, visual memory&nbsp;<cite class="ltx_cite raw v1">\cite{16452971}</cite>, sensory-motor adaptation&nbsp;<cite class="ltx_cite raw v1">\cite{Triphan_2010}</cite>, and short- and long-term spatial memory&nbsp;<cite class="ltx_cite raw v1">\cite{Neuser_2008,Ofstad_2011}</cite>. 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 of neurons in the fly central complex— and the ease of genetic  access to individual cell types in&nbsp;<i>Drosophila melanogaster</i>, make this circuit tractable  with existing theoretical and experimental methods. Detailed light level anatomy&nbsp;<cite class="ltx_cite raw v1">\cite{Hanesch1989,Wolff2015,Lin2013}</cite> of a significant fraction of the cell types, along with the availability of tools to genetically target these neurons by type&nbsp;<cite class="ltx_cite raw v1">\cite{Wolff2015}</cite>, have given rise to the first mechanistic investigations of how the circuit constructs a stable heading representation&nbsp;<cite class="ltx_cite raw v1">\cite{Kim2017}</cite>, and how this representation updates as the animal turns  in darkness&nbsp;<cite class="ltx_cite raw v1">\cite{Turner-Evans2017,Green2017}</cite>. 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&nbsp;<cite class="ltx_cite raw v1">\cite{kakaria_ring_2017,givon_generating_2017,chang_topographical_2017,Cope_2017,Su_2017,Fiore_2017,Kim2017,Stone2017,Turner-Evans2017}</cite>. 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,&nbsp; which are suggestive of  pre- and post-synaptic specializations respectively. To go beyond those anatomical approaches, we constructed 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, &nbsp;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.</div><div></div><div>The quest to obtain circuit diagrams date back to  Cajal and Golgi&nbsp;<cite class="ltx_cite raw v1">\cite{Ram_n_y_Cajal_1894,Pannese_1999}</cite>, who used sparse labeling techniques to reveal neuron morphology and 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&nbsp;<cite class="ltx_cite raw v1">\cite{Livet_2007,Hampel_2011,Nern_2015,Lee_2001,Chiang2011}</cite>&nbsp;and photoactivatable fluorophores&nbsp;<cite class="ltx_cite raw v1">\cite{Patterson_2002,Ruta_2010}</cite>. These methods allow the extraction of the detailed anatomy of individual neurons. But even when used in combination with synaptic markers&nbsp;<cite class="ltx_cite raw v1">\cite{Nicolai_2010,8229205,Zhang_2002,Fouquet_2009}</cite>, 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&nbsp;<cite class="ltx_cite raw v1">\cite{Talay_2017,Huang_2017}</cite> 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.&nbsp;</div><div></div><div>More recently,  electron microscopy (EM) reconstruction has become the gold standard for connectomics&nbsp;<cite class="ltx_cite raw v1">\cite{Briggman_2012,Zheng2017,Schneider_Mizell_2016}</cite>. 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&nbsp;<cite class="ltx_cite raw v1">\cite{Zheng2017}</cite>. 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. </div><div></div><div>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&nbsp;<cite class="ltx_cite raw v1">\cite{Salvador_2004,Stam_2004}</cite> and with multi-electrode recordings in monkeys and rodents (for example,&nbsp;<cite class="ltx_cite raw v1">\citealt{Gerhard_2011}</cite>). &nbsp;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&nbsp;<cite class="ltx_cite raw v1">\cite{Heinze_2009a,Heinze_2014}</cite>. However, such functional methods are correlative and do not provide a causal basis for the inferred connectivity.</div><div></div><div>To obtain a causal description of functional connectivity —sometimes termed effective connectivity— it is necessary 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 approach of this class is  paired patch-clamp recording, which identifies connected pairs and their functional properties with a high level of detail&nbsp;<cite class="ltx_cite raw v1">\cite{Huang_2010,Yaksi2010,Fişek2014}</cite>, but can only be performed at low throughput&nbsp;<cite class="ltx_cite raw v1">\cite{Jiang_2015}</cite>. In&nbsp; recent years, the development of optogenetics has expanded the toolkit for simultaneous stimulation and recording experiments&nbsp;<cite class="ltx_cite raw v1">\cite{17435752}</cite>. In&nbsp;<i>Drosophila</i>, the ease of use of genetic reagents renders such approaches particularly attractive. Combinations of P2X2 and GCaMP&nbsp;<cite class="ltx_cite raw v1">\cite{yao_analysis_2012}</cite>, P2X2 and patch-clamp recordings&nbsp;<cite class="ltx_cite raw v1">\cite{hu_functional_2010}</cite>, Channelrhodopsin-2 and patch-clamp&nbsp;<cite class="ltx_cite raw v1">\cite{gruntman_integration_2013}</cite> and CsChrimson and GCaMP (<cite><a href="#hampel_neural_2015">Hampel et al., 2015;</a>&nbsp;<a href="#zhou_central_2015">Zhou et al., 2015;</a>&nbsp;<a href="#ohyama_multilevel_2015">Ohyama et al., 2015</a></cite>) have been used in individual studies to investigate a small number of connections.&nbsp;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. These methods cannot definitively distinguish  connections that are direct from those that might involve several  synapses   (but see Results/Discussion) and are limited by the sensitivity of the calcium sensors used. Despite these shortcomings, such methods constitute a good compromise as they still provide 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.</div><div></div><h2 data-label="946238" class="ltx_title_subsection">Cell types and hypothetical information flow in the central complex</h2>