Network architecture underlying maximal separation of neuronal representations

Olfactory encoding within the insect antennal lobe: The emergence and role of higher order temporal correlations in the dynamics of antennal lobe spiking activity

In this review, we focus on the antennal lobe (AL) of three insect species - the fruit fly, sphinx moth, and locust. We first review the experimentally elucidated anatomy and physiology of the early olfactory system of each species; empirical studies of AL activity, however, often focus on assessing firing rates (averaged over time scales of about 100 ms), and hence the AL odor code is often analyzed in terms of a temporally evolving vector of firing rates. However, such a perspective necessarily misses the possibility of higher order temporal correlations in spiking activity within a single cell and across multiple cells over shorter time scales (of about 10 ms). Hence, we then review our prior theoretical work, where we constructed biophysically detailed, species-specific AL models within the fly, moth, and locust, finding that in each case higher order temporal correlations in spiking naturally emerge from model dynamics (i.e., without a prioriincorporation of elements designed to produce correlated activity). We therefore use our theoretical work to argue the perspective that temporal correlations in spiking over short time scales, which have received little experimental attention to-date, may provide valuable coding dimensions (complementing the coding dimensions provided by the vector of firing rates) that nature has exploited in the encoding of odors within the AL. We further argue that, if the AL does indeed utilize temporally correlated activity to represent odor information, such an odor code could be naturally and easily deciphered within the Mushroom Body.

Effect of Circuit Structure on Odor Representation in the Insect Olfactory System

In neuroscience, the structure of a circuit has often been used to intuit function—an inversion of Louis Kahn’s famous dictum, “Form follows function” (Kristan and Katz, 2006). However, different brain networks may use different network architectures to solve the same problem. The olfactory circuits of two insects, the locust, Schistocerca americana, and the fruit fly, Drosophila melanogaster, serve the same function—to identify and discriminate odors. The neural circuitry that achieves this shows marked structural differences. Projection neurons (PNs) in the antennal lobe innervate Kenyon cells (KCs) of the mushroom body. In locust, each KC receives inputs from ∼50% of PNs, a scheme that maximizes the difference between inputs to any two of ∼50,000 KCs. In contrast, in Drosophila, this number is only 5% and appears suboptimal. Using a computational model of the olfactory system, we show that the activity of KCs is sufficiently high-dimensional that it can separate similar odors regardless of the divergence of PN–KC connections. However, when temporal patterning encodes odor attributes, dense connectivity outperforms sparse connections. Increased separability comes at the cost of reliability. The disadvantage of sparse connectivity can be mitigated by incorporating other aspects of circuit architecture seen in Drosophila. Our simulations predict that Drosophila and locust circuits lie at different ends of a continuum where the Drosophila gives up on the ability to resolve similar odors to generalize across varying environments, while the locust separates odor representations but risks misclassifying noisy variants of the same odor.

Multiple network properties overcome random connectivity to enable stereotypic sensory responses

Connections between neuronal populations may be genetically hardwired or random. In the insect olfactory system, projection neurons of the antennal lobe connect randomly to Kenyon cells of the mushroom body. Consequently, while the odor responses of the projection neurons are stereotyped across individuals, the responses of the Kenyon cells are variable. Surprisingly, downstream of Kenyon cells, mushroom body output neurons show stereotypy in their responses. We found that the stereotypy is enabled by the convergence of inputs from many Kenyon cells onto an output neuron, and does not require learning. The stereotypy emerges in the total response of the Kenyon cell population using multiple odor-specific features of the projection neuron responses, benefits from the nonlinearity in the transfer function, depends on the convergence:randomness ratio, and is constrained by sparseness. Together, our results reveal the fundamental mechanisms and constraints with which convergence enables stereotypy in sensory responses despite random connectivity.

Optimality of sparse olfactory representations is not affected by network plasticity

The neural representation of a stimulus is repeatedly transformed as it moves from the sensory periphery to deeper layers of the nervous system. Sparsening transformations are thought to increase the separation between similar representations, encode stimuli with great specificity, maximize storage capacity of associative memories, and provide an energy efficient instantiation of information in neural circuits. In the insect olfactory system, odors are initially represented in the periphery as a combinatorial code with relatively simple temporal dynamics. Subsequently, in the antennal lobe this representation is transformed into a dense and complex spatiotemporal activity pattern. Next, in the mushroom body Kenyon cells (KCs), the representation is dramatically sparsened. Finally, in mushroom body output neurons (MBONs), the representation takes on a new dense spatiotemporal format. Here, we develop a computational model to simulate this chain of olfactory processing from the receptor neurons to MBONs. We demonstrate that representations of similar odorants are maximally separated, measured by the distance between the corresponding MBON activity vectors, when KC responses are sparse. Sparseness is maintained across variations in odor concentration by adjusting the feedback inhibition that KCs receive from an inhibitory neuron, the Giant GABAergic neuron. Different odor concentrations require different strength and timing of feedback inhibition for optimal processing. Importantly, as observed in vivo, the KC–MBON synapse is highly plastic, and, therefore, changes in synaptic strength after learning can change the balance of excitation and inhibition, potentially leading to changes in the distance between MBON activity vectors of two odorants for the same level of KC population sparseness. Thus, what is an optimal degree of sparseness before odor learning, could be rendered sub–optimal post learning. Here, we show, however, that synaptic weight changes caused by spike timing dependent plasticity increase the distance between the odor representations from the perspective of MBONs. A level of sparseness that was optimal before learning remains optimal post-learning.

Kenyon cells (KCs) of the mushroom body represent odors as a sparse code. When viewed from the perspective of follower neurons, mushroom body output neurons (MBONs) reveal an optimal level of coding sparseness that maximally separates the representations of odors. However, the KC–MBON synapse is highly plastic and may be potentiated or depressed by odor–driven experience that could, in turn, disrupt the optimality formed by pre–synaptic circuits. Contrary to this expectation, we show that synaptic plasticity based on spike timing of pre- and postsynaptic neurons improves the ability of the system to distinguish between the representations of similar odors while preserving the optimality determined by pre–synaptic circuits.

Cellular adaptation facilitates sparse and reliable coding in sensory pathways

Most neurons in peripheral sensory pathways initially respond vigorously when a preferred stimulus is presented, but adapt as stimulation continues. It is unclear how this phenomenon affects stimulus coding in the later stages of sensory processing. Here, we show that a temporally sparse and reliable stimulus representation develops naturally in sequential stages of a sensory network with adapting neurons. As a modeling framework we employ a mean-field approach together with an adaptive population density treatment, accompanied by numerical simulations of spiking neural networks. We find that cellular adaptation plays a critical role in the dynamic reduction of the trial-by-trial variability of cortical spike responses by transiently suppressing self-generated fast fluctuations in the cortical balanced network. This provides an explanation for a widespread cortical phenomenon by a simple mechanism. We further show that in the insect olfactory system cellular adaptation is sufficient to explain the emergence of the temporally sparse and reliable stimulus representation in the mushroom body. Our results reveal a generic, biophysically plausible mechanism that can explain the emergence of a temporally sparse and reliable stimulus representation within a sequential processing architecture.