Scaling Principles of Distributed Circuits

Effects of stochastic coding on olfactory discrimination in flies and mice

Sparse coding can improve discrimination of sensory stimuli by reducing overlap between their representations. Two factors, however, can offset sparse coding's benefits: similar sensory stimuli have significant overlap and responses vary across trials. To elucidate the effects of these 2 factors, we analyzed odor responses in the fly and mouse olfactory regions implicated in learning and discrimination-the mushroom body (MB) and the piriform cortex (PCx). We found that neuronal responses fall along a continuum from extremely reliable across trials to extremely variable or stochastic. Computationally, we show that the observed variability arises from noise within central circuits rather than sensory noise. We propose this coding scheme to be advantageous for coarse- and fine-odor discrimination. More reliable cells enable quick discrimination between dissimilar odors. For similar odors, however, these cells overlap and do not provide distinguishing information. By contrast, more unreliable cells are decorrelated for similar odors, providing distinguishing information, though these benefits only accrue with extended training with more trials. Overall, we have uncovered a conserved, stochastic coding scheme in vertebrates and invertebrates, and we identify a candidate mechanism, based on variability in a winner-take-all (WTA) inhibitory circuit, that improves discrimination with training.

High-throughput sequencing of single neuron projections reveals spatial organization in the olfactory cortex

In most sensory modalities, neuronal connectivity reflects behaviorally relevant stimulus features, such as spatial location, orientation, and sound frequency. By contrast, the prevailing view in the olfactory cortex, based on the reconstruction of dozens of neurons, is that connectivity is random. Here, we used high-throughput sequencing-based neuroanatomical techniques to analyze the projections of 5,309 mouse olfactory bulb and 30,433 piriform cortex output neurons at single-cell resolution. Surprisingly, statistical analysis of this much larger dataset revealed that the olfactory cortex connectivity is spatially structured. Single olfactory bulb neurons targeting a particular location along the anterior-posterior axis of piriform cortex also project to matched, functionally distinct, extra-piriform targets. Moreover, single neurons from the targeted piriform locus also project to the same matched extra-piriform targets, forming triadic circuit motifs. Thus, as in other sensory modalities, olfactory information is routed at early stages of processing to functionally diverse targets in a coordinated manner.

Developmental and evolutionary constraints on olfactory circuit selection

SignificanceIn this work, we explore the hypothesis that biological neural networks optimize their architecture, through evolution, for learning. We study early olfactory circuits of mammals and insects, which have relatively similar structure but a huge diversity in size. We approximate these circuits as three-layer networks and estimate, analytically, the scaling of the optimal hidden-layer size with input-layer size. We find that both longevity and information in the genome constrain the hidden-layer size, so a range of allometric scalings is possible. However, the experimentally observed allometric scalings in mammals and insects are consistent with biologically plausible values. This analysis should pave the way for a deeper understanding of both biological and artificial networks.

Connectivity and dynamics in the olfactory bulb

Dendrodendritic interactions between excitatory mitral cells and inhibitory granule cells in the olfactory bulb create a dense interaction network, reorganizing sensory representations of odors and, consequently, perception. Large-scale computational models are needed for revealing how the collective behavior of this network emerges from its global architecture. We propose an approach where we summarize anatomical information through dendritic geometry and density distributions which we use to calculate the connection probability between mitral and granule cells, while capturing activity patterns of each cell type in the neural dynamical systems theory of Izhikevich. In this way, we generate an efficient, anatomically and physiologically realistic large-scale model of the olfactory bulb network. Our model reproduces known connectivity between sister vs. non-sister mitral cells; measured patterns of lateral inhibition; and theta, beta, and gamma oscillations. The model in turn predicts testable relationships between network structure and several functional properties, including lateral inhibition, odor pattern decorrelation, and LFP oscillation frequency. We use the model to explore the influence of cortex on the olfactory bulb, demonstrating possible mechanisms by which cortical feedback to mitral cells or granule cells can influence bulbar activity, as well as how neurogenesis can improve bulbar decorrelation without requiring cell death. Our methodology provides a tractable tool for other researchers.

Olfactory dysfunction in aging and neurodegenerative diseases

Alterations in olfactory functions are proposed to be early biomarkers for neurodegeneration. Many neurodegenerative diseases are age-related, including two of the most common, Parkinson's disease (PD) and Alzheimer's disease (AD). The establishment of biomarkers that promote early risk identification is critical for the implementation of early treatment to postpone or avert pathological development. Olfactory dysfunction (OD) is seen in 90% of early-stage PD patients and 85% of patients with early-stage AD, which makes it an attractive biomarker for early diagnosis of these diseases. Here, we systematically review widely applied smelling tests available for humans as well as olfaction assessments performed in some animal models and the relationships between OD and normal aging, PD, AD, and other conditions. The utility of OD as a biomarker for neurodegenerative disease diagnosis and future research directions are also discussed.

What the odor is not: Estimation by elimination

Olfactory systems use a small number of broadly sensitive receptors to combinatorially encode a vast number of odors. We propose a method of decoding such distributed representations by exploiting a statistical fact: Receptors that do not respond to an odor carry more information than receptors that do because they signal the absence of all odorants that bind to them. Thus, it is easier to identify what the odor is not rather than what the odor is. For realistic numbers of receptors, response functions, and odor complexity, this method of elimination turns an underconstrained decoding problem into a solvable one, allowing accurate determination of odorants in a mixture and their concentrations. We construct a neural network realization of our algorithm based on the structure of the olfactory pathway.

The unreasonable effectiveness of deep learning in artificial intelligence

Deep learning networks have been trained to recognize speech, caption photographs, and translate text between languages at high levels of performance. Although applications of deep learning networks to real-world problems have become ubiquitous, our understanding of why they are so effective is lacking. These empirical results should not be possible according to sample complexity in statistics and nonconvex optimization theory. However, paradoxes in the training and effectiveness of deep learning networks are being investigated and insights are being found in the geometry of high-dimensional spaces. A mathematical theory of deep learning would illuminate how they function, allow us to assess the strengths and weaknesses of different network architectures, and lead to major improvements. Deep learning has provided natural ways for humans to communicate with digital devices and is foundational for building artificial general intelligence. Deep learning was inspired by the architecture of the cerebral cortex and insights into autonomy and general intelligence may be found in other brain regions that are essential for planning and survival, but major breakthroughs will be needed to achieve these goals.

Closing the gap from transcription to the structural connectome enhances the study of connections in the human brain

The brain is composed of a complex web of networks but we have yet to map the structural connections of the human brain in detail. Diffusion MR imaging is a high-throughput method that relies on the principle of diffusion to reconstruct tracts (ie, pathways) across the brain. Although diffusion MR tractography is an exciting method to explore the structural connectivity of the brain in development and across species, the tractography has at times led to questionable interpretations. There are at present few if any alternative methods to trace structural pathways in the human brain. Given these limitations and the potential of diffusion MR imaging to map the human connectome, it is imperative that we develop new approaches to validate neuroimaging techniques. I discuss our recent studies integrating neuroimaging with transcriptional and anatomical variation across humans and other species over the course of development and in adulthood. Developing a novel framework to harness the potential of diffusion MR tractography provides new and exciting opportunities to study the evolution of developmental mechanisms generating variation in connections and bridge the gap between model systems to humans.

Odor coding in piriform cortex: mechanistic insights into distributed coding

Olfaction facilitates a large variety of animal behaviors such as feeding, mating, and communication. Recent work has begun to reveal the logic of odor transformations that occur throughout the olfactory system to form the odor percept. In this review, we describe the coding principles and mechanisms by which the piriform cortex and other olfactory areas encode three key odor features: odor identity, intensity, and valence. We argue that the piriform cortex produces a multiplexed odor code that allows non-interfering representations of distinct features of the odor stimulus to facilitate odor recognition and learning, which ultimately drives behavior.