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Associative memory in the Mushroom Body of the fruit fly brain depends on the encoding and processing of odorants in the first three stages of the Early Olfactory System: the Antenna, the Antennal Lobe and the Mushroom Body Calyx. The Kenyon Cells (KCs) of the Calyx provide the Mushroom Body compartments the identity of pure and odorant mixtures encoded as a train of spikes. Characterizing the code underlying the KC spike trains is a major challenge in neuroscience. To address this challenge we start by explicitly modeling the space of odorants using constructs of both semantic and syntactic information. Odorant semantics concerns the identity of odorants while odorant syntactics pertains to their concentration amplitude. These odorant attributes are multiplicatively coupled in the process of olfactory transduction. A key question that early olfactory systems must address is how to disentangle the odorant semantic information from the odorant syntactic information. To address the untanglement we devised an Odorant Encoding Machine (OEM) modeling the first three stages of early olfactory processing in the fruit fly brain. Each processing stage is modeled by Divisive Normalization Processors (DNPs). DNPs are spatio-temporal models of canonical computation of brain circuits. The end-to-end OEM is constructed as cascaded DNPs. By extensively modeling and characterizing the processing of pure and odorant mixtures in the Calyx, we seek to answer the question of its functional significance. We demonstrate that the DNP circuits in the OEM combinedly reduce the variability of the Calyx response to odorant concentration, thereby separating odorant semantic information from syntactic information. We then advance a code, called first spike sequence code, that the KCs make available at the output of the Calyx. We show that the semantics of odorants can be represented by this code in the spike domain and is ready for easy memory access in the Mushroom Body compartments. 

Recent advances in molecular transduction of odorants in the Olfactory Sensory Neurons (OSNs) of theDrosophilaAntenna have shown that theodorant object identityis multiplicatively coupled with theodorant concentration waveform. The resulting combinatorial neural code is a confounding representation of odorant semantic information (identity) and syntactic information (concentration). To distill the functional logic of odor information processing in the Antennal Lobe (AL) a number of challenges need to be addressed including 1) how is the odorantsemantic informationdecoupled from thesyntactic informationat the level of the AL, 2) how are these two information streams processed by the diverse AL Local Neurons (LNs) and 3) what is the end-to-end functional logic of the AL? By analyzing single-channel physiology recordings at the output of the AL, we found that the Projection Neuron responses can be decomposed into aconcentration-invariantcomponent, and two transient components boosting the positive/negative concentration contrast that indicate onset/offset timing information of the odorant object. We hypothesized that the concentration-invariant component, in the multi-channel context, is the recovered odorant identity vector presented between onset/offset timing events. We developed a model of LN pathways in the Antennal Lobe termed the differential Divisive Normalization Processors (DNPs), which robustly extract thesemantics(the identity of the odorant object) and the ON/OFF semantic timing events indicating the presence/absence of an odorant object. For real-time processing with spiking PN models, we showed that the phase-space of the biological spike generator of the PN offers an intuit perspective for the representation of recovered odorant semantics and examined the dynamics induced by the odorant semantic timing events. Finally, we provided theoretical and computational evidence for the functional logic of the AL as a robustON-OFF odorant object identity recovery processoracross odorant identities, concentration amplitudes and waveform profiles.