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.

Borders are important as they demarcate developing tissue into distinct functional units. A key challenge is the discovery of mechanisms that can convert morphogen gradients into tissue borders. While mechanisms that produce ultrasensitive cellular responses provide a solution, how extracellular morphogens drive such mechanisms remains poorly understood. Here, we show how Bone Morphogenetic Protein (BMP) and Fibroblast Growth Factor (FGF) pathways interact to generate ultrasensitivity and borders in the dorsal telencephalon. BMP and FGF signaling manipulations in explants produced border defects suggestive of cross inhibition within single cells, which was confirmed in dissociated cultures. Using mathematical modeling, we designed experiments that ruled out alternative cross inhibition mechanisms and identified a cross-inhibitory positive feedback (CIPF) mechanism, or "toggle switch", which acts upstream of transcriptional targets in dorsal telencephalic cells. CIPF explained several cellular phenomena important for border formation such as threshold tuning, ultrasensitivity, and hysteresis. CIPF explicitly links graded morphogen signaling in the telencephalon to switch-like cellular responses and has the ability to form multiple borders and scale pattern to size. These benefits may apply to other developmental systems.

Distributed circuits wherein connections between subcircuit components seem randomly distributed are common to the olfactory circuit, hippocampus, and cerebellum. In such circuits, activation patterns seem random too, showing no detectable spatial preference, and contrast with regions that have topographic connections between subcircuits and topographic activation patterns. Quantitative studies of topographic circuits in the neocortex have yielded common principles of organization. Whether distributed circuits share similar principles of organization is unknown because similar quantitative information is missing and understanding the way they encode information remains a challenge. We addressed these needs by providing a quantitative description of the mouse piriform cortex, a paleocortical distributed circuit that subserves olfaction. The quantitative information provided two insights. First, with a nearly parameter-free model of the olfactory circuit, we show that the piriform cortex robustly maintains odor information and discrimination ability present in the olfactory bulb. Second, the paleocortex is quantitatively different from the neocortex: it has a lower surface area density, which decreases from the anterior to posterior paleocortex contrasting with the uniform neuronal density of the neocortex. These insights might also apply to other distributed circuits.

The Xenopus left-right organizer (LRO) breaks symmetry along the left-right axis of the early embryo by producing and sensing directed ciliary flow as a patterning cue. To carry out this process, the LRO contains different ciliated cell types that vary in cilia length, whether they are motile or sensory, and how they position their cilia along the anterior-posterior (A-P) planar axis. Here, we show that these different cilia features are specified in the prospective LRO during gastrulation, based on anisotropic mechanical strain that is oriented along the A-P axis, and graded in levels along the medial-lateral axis. Strain instructs ciliated cell differentiation by acting on a mesodermal prepattern present at blastula stages, involving foxj1. We propose that differential strain is a graded, developmental cue, linking the establishment of an A-P planar axis to cilia length, motility, and planar location during formation of the Xenopus LRO.

Identifying shared quantitative features of a neural circuit across species is important for 3 reasons. Often expressed in the form of power laws and called scaling relationships [1, 2], they reveal organizational principles of circuits, make insights gleaned from model systems widely applicable, and explain circuit performance and function, e.g., visual circuits [3, 4]. The visual circuit is topographic [5, 6], wherein retinal neurons target and activate predictable spatial loci in primary visual cortex. The brain, however, contains many circuits, where neuronal targets and activity are unpredictable and distributed throughout the circuit, e.g., olfactory circuits, in which glomeruli (or mitral cells) in the olfactory bulb synapse with neurons distributed throughout the piriform cortex [7-10]. It is unknown whether such circuits, which we term distributed circuits, are scalable. To determine whether distributed circuits scale, we obtained quantitative descriptions of the olfactory bulb and piriform cortex in six mammals using stereology techniques and light microscopy. Two conserved features provide evidence of scalability. First, the number of piriform neurons n and bulb glomeruli g scale as n∼g3/2. Second, the average number of synapses between a bulb glomerulus and piriform neuron is invariant at one. Using theory and modeling, we show that these two features preserve the discriminatory ability and precision of odor information across the olfactory circuit. As both abilities depend on circuit size, manipulating size provides evolution with a way to adapt a species to its niche without designing developmental programs de novo. These principles might apply to other distributed circuits like the hippocampus.