Neural activity in many sensory systems is organized on low-dimensional manifolds by means of convex receptive fields. Neural codes in these areas are constrained by this organization, as not every neural code is compatible with convex receptive fields. The same codes are also constrained by the structure of the underlying neural network. In my talk I will attempt to provide answers to the following natural questions: (i) How do recurrent circuits generate codes that are compatible with the convexity of receptive fields? (ii) How can we utilize the constraints imposed by the convex receptive field to understand the underlying stimulus space. To answer question (i), we describe the combinatorics of the steady states and fixed points of recurrent networks that satisfy the Dale’s law. It turns out the combinatorics of the fixed points are completely determined by two distinct conditions: (a) the connectivity graph of the network and (b) a spectral condition on the synaptic matrix. We give a characterization of exactly which features of connectivity determine the combinatorics of the fixed points. We also find that a generic recurrent network that satisfies Dale's law outputs convex combinatorial codes. To address question (ii), I will describe methods based on ideas from topology and geometry that take advantage of the convex receptive field properties to infer the dimension of (non-linear) neural representations. I will illustrate the first method by inferring basic features of the neural representations in the mouse olfactory bulb.

We use the olfactory system and forebrain of (adult) zebrafish as a model to analyze how relevant information is extracted from sensory inputs, how information is stored in memory circuits, and how sensory inputs inform behavior. A series of recent findings provides evidence that inhibition has not only homeostatic functions in neuronal circuits but makes highly specific, instructive contributions to behaviorally relevant computations in different brain regions. These observations imply that the connectivity among excitatory and inhibitory neurons exhibits essential higher-order structure that cannot be determined without dense network reconstructions. To analyze such connectivity we developed an approach referred to as “dynamical connectomics” that combines 2-photon calcium imaging of neuronal population activity with EM-based dense neuronal circuit reconstruction. In the olfactory bulb, this approach identified specific connectivity among co-tuned cohorts of excitatory and inhibitory neurons that can account for the decorrelation and normalization (“whitening”) of odor representations in this brain region. These results provide a mechanistic explanation for a fundamental neural computation that strictly requires specific network connectivity.

I will argue that the circuit architecture of the early olfactory system provides an adaptive, efficient mechanism for compressing the vast space of odor mixtures into the responses of a small number of sensors. In this view, the olfactory sensory repertoire employs a disordered code to compress a high dimensional olfactory space into a low dimensional receptor response space while preserving distance relations between odors. The resulting representation is dynamically adapted to efficiently encode the changing environment of volatile molecules. I will show that this adaptive combinatorial code can be efficiently decoded by systematically eliminating candidate odorants that bind to silent receptors. The resulting algorithm for 'estimation by elimination' can be implemented by a neural network that is remarkably similar to the early olfactory pathway in the brain. Finally, I will discuss how diffuse feedback from the central brain to the bulb, followed by unstructured projections back to the cortex, can produce the convergence and divergence of the cortical representation of odors presented in shared or different contexts. Our theory predicts a relation between the diversity of olfactory receptors and the sparsity of their responses that matches animals from flies to humans. It also predicts specific deficits in olfactory behavior that should result from optogenetic manipulation of the olfactory bulb and cortex, and in some disease states.

Odor memories are exceptionally robust and essential for the survival of many species. In rodents, the olfactory cortex shows features of an autoassociative memory network and plays a key role in the retrieval of olfactory memories (Meissner-Bernard et al., 2019). Interestingly, the telencephalic area Dp, the zebrafish homolog of olfactory cortex, transiently enters a state of precise balance during the presentation of an odor (Rupprecht and Friedrich, 2018). This state is characterized by large synaptic conductances (relative to the resting conductance) and by co-tuning of excitation and inhibition in odor space and in time at the level of individual neurons. Our aim is to understand how this precise synaptic balance affects memory function. For this purpose, we build a simplified, yet biologically plausible spiking neural network model of Dp using experimental observations as constraints: besides precise balance, key features of Dp dynamics include low firing rates, odor-specific population activity and a dominance of recurrent inputs from Dp neurons relative to afferent inputs from neurons in the olfactory bulb. To achieve co-tuning of excitation and inhibition, we introduce structured connectivity by increasing connection probabilities and/or strength among ensembles of excitatory and inhibitory neurons. These ensembles are therefore structural memories of activity patterns representing specific odors. They form functional inhibitory-stabilized subnetworks, as identified by the “paradoxical effect” signature (Tsodyks et al., 1997): inhibition of inhibitory “memory” neurons leads to an increase of their activity. We investigate the benefits of co-tuning for olfactory and memory processing, by comparing inhibitory-stabilized networks with and without co-tuning. We find that co-tuned excitation and inhibition improves robustness to noise, pattern completion and pattern separation. In other words, retrieval of stored information from partial or degraded sensory inputs is enhanced, which is relevant in light of the instability of the olfactory environment. Furthermore, in co-tuned networks, odor-evoked activation of stored patterns does not persist after removal of the stimulus and may therefore subserve fast pattern classification. These findings provide valuable insights into the computations performed by the olfactory cortex, and into general effects of balanced state dynamics in associative memory networks.

Can alterations in experience trigger different plastic modifications in neuronal structure and function, and if so, how do they integrate at the cellular level? To address this question, we interrogated circuitry in the mouse olfactory bulb responsible for the earliest steps in odor processing. We induced experience-dependent plasticity in mice of either sex by blocking one nostril for one day, a minimally invasive manipulation that leaves the sensory organ undamaged and is akin to the natural transient blockage suffered during common mild rhinal infections. We found that such brief sensory deprivation produced structural and functional plasticity in one highly specialized bulbar cell type: axon-bearing dopaminergic neurons in the glomerular layer. After 24 h naris occlusion, the axon initial segment (AIS) in bulbar dopaminergic neurons became significantly shorter, a structural modification that was also associated with a decrease in intrinsic excitability. These effects were specific to the AIS-positive dopaminergic subpopulation because no experience-dependent alterations in intrinsic excitability were observed in AIS-negative dopaminergic cells. Moreover, 24 h naris occlusion produced no structural changes at the AIS of bulbar excitatory neurons, mitral/tufted and external tufted cells, nor did it alter their intrinsic excitability. By targeting excitability in one specialized dopaminergic subpopulation, experience-dependent plasticity in early olfactory networks might act to fine-tune sensory processing in the face of continually fluctuating inputs. (https://www.jneurosci.org/content/41/10/2135)

Neural stem cells reside in the adult mammalian brain. The ventricular-subventricular zone (V-SVZ) gives rise to olfactory bulb neurons, as well as small numbers of glia throughout life. Adult V-SVZ neural stem cells dynamically integrate intrinsic and extrinsic signals to either maintain the quiescent state or to become activated to divide and generate progeny. I will present our recent findings highlighting adult neural stem cell heterogeneity, including the identification of novel gliogenic domains and cell types, and the key roles of physiological state and long-range signals in the regulation of regionally distinct pools of adult neural stem cells.

In the olfactory system, cholinergic modulation has been associated with contrast modulation and changes in receptive fields in the olfactory bulb, as well the learning of odor associations in the olfactory cortex. Computational modeling and behavioral studies suggest that cholinergic modulation could improve sensory processing and learning while preventing pro-active interference when task demands are high. However, how sensory inputs and/or learning regulate incoming modulation has not yet been elucidated. We here use a computational model of the olfactory bulb, piriform cortex (PC) and horizontal limb of the diagonal band of Broca (HDB) to explore how olfactory learning could regulate cholinergic inputs to the system in a closed feedback loop. In our model, the novelty of an odor is reflected in firing rates and sparseness of cortical neurons in response to that odor and these firing rates can directly regulate learning in the system by modifying cholinergic inputs to the system.