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.

Network cloning using DNA barcodes.

The connections between neurons determine the computations performed by both artificial and biological neural networks. Recently, we have proposed SYNSeq, a method for converting the connectivity of a biological network into a form that can exploit the tremendous efficiencies of high-throughput DNA sequencing. In SYNSeq, each neuron is tagged with a random sequence of DNA-a "barcode"-and synapses are represented as barcode pairs. SYNSeq addresses the analysis problem, reducing a network into a suspension of barcode pairs. Here, we formulate a complementary synthesis problem: How can the suspension of barcode pairs be used to "clone" or copy the network back into an uninitialized tabula rasa network? Although this synthesis problem might be expected to be computationally intractable, we find that, surprisingly, this problem can be solved efficiently, using only neuron-local information. We present the "one-barcode-one-cell" (OBOC) algorithm, which forces all barcodes of a given sequence to coalesce into the same neuron, and show that it converges in a number of steps that is a power law of the network size. Rapid and reliable network cloning with single-synapse precision is thus theoretically possible.

Deconstructing Odorant Identity via Primacy in Dual Networks.

In the olfactory system, odor percepts retain their identity despite substantial variations in concentration, timing, and background. We study a novel strategy for encoding intensity-invariant stimulus identity that is based on representing relative rather than absolute values of stimulus features. For example, in what is known as the primacy coding model, odorant identities are represented by the conditions that some odorant receptors are activated more strongly than others. Because, in this scheme, odorant identity depends only on the relative amplitudes of olfactory receptor responses, identity is invariant to changes in both intensity and monotonic nonlinear transformations of its neuronal responses. Here we show that sparse vectors representing odorant mixtures can be recovered in a compressed sensing framework via elastic net loss minimization. In the primacy model, this minimization is performed under the constraint that some receptors respond to a given odorant more strongly than others. Using duality transformation, we show that this constrained optimization problem can be solved by a neural network whose Lyapunov function represents the dual Lagrangian and whose neural responses represent the Lagrange coefficients of primacy and other constraints. The connectivity in such a dual network resembles known features of connectivity in olfactory circuits. We thus propose that networks in the piriform cortex implement dual computations to compute odorant identity with the sparse activities of individual neurons representing Lagrange coefficients. More generally, we propose that sparse neuronal firing rates may represent Lagrange multipliers, which we call the dual brain hypothesis. We show such a formulation is well suited to solve problems with multiple interacting relative constraints.

Long-term memory stabilized by noise-induced rehearsal.

Cortical networks can maintain memories for decades despite the short lifetime of synaptic strengths. Can a neural network store long-lasting memories in unstable synapses? Here, we study the effects of ongoing spike-timing-dependent plasticity (STDP) on the stability of memory patterns stored in synapses of an attractor neural network. We show that certain classes of STDP rules can stabilize all stored memory patterns despite a short lifetime of synapses. In our model, unstructured neural noise, after passing through the recurrent network connections, carries the imprint of all memory patterns in temporal correlations. STDP, combined with these correlations, leads to reinforcement of all stored patterns, even those that are never explicitly visited. Our findings may provide the functional reason for irregular spiking displayed by cortical neurons and justify models of system memory consolidation. Therefore, we propose that irregular neural activity is the feature that helps cortical networks maintain stable connections.

Competition is a driving force in topographic mapping.

Topographic maps are the primary means of relaying spatial information in the brain. Understanding the mechanisms by which they form has been a goal of experimental and theoretical neuroscientists for decades. The projection of the retina to the superior colliculus (SC)/tectum has been an important model used to show that graded molecular cues and patterned retinal activity are required for topographic map formation. Additionally, interaxon competition has been suggested to play a role in topographic map formation; however, this view has been recently challenged. Here we present experimental and computational evidence demonstrating that interaxon competition for target space is necessary to establish topography. To test this hypothesis experimentally, we determined the nature of the retinocollicular projection in Math5 (Atoh7) mutant mice, which have severely reduced numbers of retinal ganglion cell inputs into the SC. We find that in these mice, retinal axons project to the anteromedialj portion of the SC where repulsion from ephrin-A ligands is minimized and where their attraction to the midline is maximized. This observation is consistent with the chemoaffinity model that relies on axon-axon competition as a mapping mechanism. We conclude that chemical labels plus neural activity cannot alone specify the retinocollicular projection; instead axon-axon competition is necessary to create a map. Finally, we present a mathematical model for topographic mapping that incorporates molecular labels, neural activity, and axon competition.

The problem of colliding networks and its relation to cell fusion and cancer.

Cell fusion, a process that merges two or more cells into one, is required for normal development and has been explored as a tool for stem cell therapy. It has also been proposed that cell fusion causes cancer and contributes to its progression. These functions rely on a poorly understood ability of cell fusion to create new cell types. We suggest that this ability can be understood by considering cells as attractor networks whose basic property is to adopt a set of distinct, stable, self-maintaining states called attractors. According to this view, fusion of two cell types is a collision of two networks that have adopted distinct attractors. To learn how these networks reach a consensus, we model cell fusion computationally. To do so, we simulate patterns of gene activities using a formalism developed to simulate patterns of memory in neural networks. We find that the hybrid networks can assume attractors that are unrelated to parental attractors, implying that cell fusion can create new cell types by nearly instantaneously moving cells between attractors. We also show that hybrid networks are prone to assume spurious attractors, which are emergent and sporadic network states. This finding means that cell fusion can produce abnormal cell types, including cancerous types, by placing cells into normally inaccessible spurious states. Finally, we suggest that the problem of colliding networks has general significance in many processes represented by attractor networks, including biological, social, and political phenomena.

An exactly solvable model of random site-specific recombinations.

Cre-lox and other systems are used as genetic tools to control site-specific recombination (SSR) events in genomic DNA. If multiple recombination sites are organized in a compact cluster within the same genome, a series of random recombination events may generate substantial cell specific genomic diversity. This diversity is used, for example, to distinguish neurons in the brain of the same multicellular mosaic organism, within the brainbow approach to neuronal connectome. In this paper, we study an exactly solvable statistical model for SSR operating on a cluster of recombination sites. We consider two types of recombination events: inversions and excisions. Both of these events are available in the Cre-lox system. We derive three properties of the sequences generated by multiple recombination events. First, we describe the set of sequences that can in principle be generated by multiple inversions operating on the given initial sequence. We call this description the ergodicity theorem. On the basis of this description, we calculate the number of sequences that can be generated from an initial sequence. This number of sequences is experimentally testable. Second, we demonstrate that after a large number of random inversions every sequence that can be generated is generated with equal probability. Lastly, we derive the equations for the probability to find a sequence as a function of time in the limit when excisions are much less frequent than inversions, such as in shufflon sequences.

Spatiotemporal 3D image registration for mesoscale studies of brain development.

Comparison of brain samples representing different developmental stages often necessitates registering the samples to common coordinates. Although the available software tools are successful in registering 3D images of adult brains, registration of perinatal brains remains challenging due to rapid growth-dependent morphological changes and variations in developmental pace between animals. To address these challenges, we introduce CORGI (Customizable Object Registration for Groups of Images), an algorithm for the registration of perinatal brains. First, we optimized image preprocessing to increase the algorithm's sensitivity to mismatches in registered images. Second, we developed an attention-gated simulated annealing procedure capable of focusing on the differences between perinatal brains. Third, we applied classical multidimensional scaling (CMDS) to align ("synchronize") brain samples in time, accounting for individual development paces. We tested CORGI on 28 samples of whole-mounted perinatal mouse brains (P0-P9) and compared its accuracy with other registration algorithms. Our algorithm offers a runtime of several minutes per brain on a laptop and automates such brain registration tasks as mapping brain data to atlases, comparing experimental groups, and monitoring brain development dynamics.

Correlated connectivity and the distribution of firing rates in the neocortex.

Two recent experimental observations pose a challenge to many cortical models. First, the activity in the auditory cortex is sparse, and firing rates can be described by a lognormal distribution. Second, the distribution of nonzero synaptic strengths between nearby cortical neurons can also be described by a lognormal distribution. Here we use a simple model of cortical activity to reconcile these observations. The model makes the experimentally testable prediction that synaptic efficacies onto a given cortical neuron are statistically correlated, i.e., it predicts that some neurons receive stronger synapses than other neurons. We propose a simple Hebb-like learning rule that gives rise to such correlations and yields both lognormal firing rates and synaptic efficacies. Our results represent a first step toward reconciling sparse activity and sparse connectivity in cortical networks.

Sperry versus Hebb: topographic mapping in Isl2/EphA3 mutant mice.

BACKGROUND: In wild-type mice, axons of retinal ganglion cells establish topographically precise projection to the superior colliculus of the midbrain. This means that axons of neighboring retinal ganglion cells project to the proximal locations in the target. The precision of topographic projection is a result of combined effects of molecular labels, such as Eph receptors and ephrins, and correlated neural activity. In the Isl2/EphA3 mutant mice the expression levels of molecular labels are changed. As a result the topographic projection is rewired so that the neighborhood relationships between retinal cell axons are disrupted. RESULTS: Here we study the computational model for retinocollicular connectivity formation that combines the effects of molecular labels and correlated neural activity. We argue that the effects of correlated activity presenting themselves in the form of Hebbian learning rules can facilitate the restoration of the topographic connectivity even when the molecular labels carry conflicting instructions. This occurs because the correlations in electric activity carry information about retinal cells' origin that is independent on molecular labels. We argue therefore that partial restoration of the topographic property of the retinocollicular projection observed in Isl2/EphA3 heterozygous knockin mice may be explained by the effects of correlated neural activity. We address the maps observed in Isl2/EphA3 knockin/EphA4 knockout mice in which the levels of retinal labels are uniformly reduced. These maps can be explained by either the saturation of EphA receptor mapping leading to the relative signaling model or by the reverse signaling conveyed by ephrin-As expressed by retinal axons. CONCLUSION: According to our model, experiments in Isl2/EphA3 knock-in mice test the interactions between effects of molecular labels and correlated activity during the development of neural connectivity. Correlated activity can partially restore topographic order even when molecular labels carry conflicting information.

Neural Networks With Motivation.

Animals rely on internal motivational states to make decisions. The role of motivational salience in decision making is in early stages of mathematical understanding. Here, we propose a reinforcement learning framework that relies on neural networks to learn optimal ongoing behavior for dynamically changing motivation values. First, we show that neural networks implementing Q-learning with motivational salience can navigate in environment with dynamic rewards without adjustments in synaptic strengths when the needs of an agent shift. In this setting, our networks may display elements of addictive behaviors. Second, we use a similar framework in hierarchical manager-agent system to implement a reinforcement learning algorithm with motivation that both infers motivational states and behaves. Finally, we show that, when trained in the Pavlovian conditioning setting, the responses of the neurons in our model resemble previously published neuronal recordings in the ventral pallidum, a basal ganglia structure involved in motivated behaviors. We conclude that motivation allows Q-learning networks to quickly adapt their behavior to conditions when expected reward is modulated by agent's dynamic needs. Our approach addresses the algorithmic rationale of motivation and makes a step toward better interpretability of behavioral data via inference of motivational dynamics in the brain.

Mosaic representations of odors in the input and output layers of the mouse olfactory bulb.

The elementary stimulus features encoded by the olfactory system remain poorly understood. We examined the relationship between 1,666 physical-chemical descriptors of odors and the activity of olfactory bulb inputs and outputs in awake mice. Glomerular and mitral and tufted cell responses were sparse and locally heterogeneous, with only a weak dependence of their positions on physical-chemical properties. Odor features represented by ensembles of mitral and tufted cells were overlapping but distinct from those represented in glomeruli, which is consistent with an extensive interplay between feedforward and feedback inputs to the bulb. This reformatting was well described as a rotation in odor space. The physical-chemical descriptors accounted for a small fraction in response variance, and the similarity of odors in the physical-chemical space was a poor predictor of similarity in neuronal representations. Our results suggest that commonly used physical-chemical properties are not systematically represented in bulbar activity and encourage further searches for better descriptors of odor space.

Model for a robust neural integrator.

Integrator circuits in the brain show persistent firing that reflects the sum of previous excitatory and inhibitory inputs from external sources. Integrator circuits have been implicated in parametric working memory, decision making and motor control. Previous work has shown that stable integrator function can be achieved by an excitatory recurrent neural circuit, provided synaptic strengths are tuned with extreme precision (better than 1% accuracy). Here we show that integrator circuits can function without fine tuning if the neuronal units have bistable properties. Two specific mechanisms of bistability are analyzed, one based on local recurrent excitation, and the other on the voltage-dependence of the NMDA (N-methyl-D-aspartate) channel. Neither circuit requires fine tuning to perform robust integration, and the latter actually exploits the variability of neuronal conductances.

Spatial geometry of stem cell proliferation in the adult hippocampus.

The modes of stem cell divisions (e.g., symmetric vs. asymmetric) can have a profound impact on the number of progeny and tissue growth, repair, and function. This is particularly relevant for adult neural stem cells, since stem cell-derived neurons affect cognitive and mental states, resistance to stress and disease, and response to therapies. Here we show that although dividing stem cells in the adult hippocampus display a certain bias towards paired distribution (which could imply the prevalence of symmetric divisions), this bias already exists in the distribution of the general population of stem cells and may be responsible for the perceived occurrence of symmetric stem cell divisions. Remarkably, the bias in the distribution of stem cells decreases with age. Our results argue that the preexisting bias in stem cell distribution may affect current assumptions regarding stem cell division and fate as well as conjectures on the prospects of brain repair and rejuvenation.

A primacy code for odor identity.

Humans can identify visual objects independently of view angle and lighting, words independently of volume and pitch, and smells independently of concentration. The computational principles underlying invariant object recognition remain mostly unknown. Here we propose that, in olfaction, a small and relatively stable set comprised of the earliest activated receptors forms a code for concentration-invariant odor identity. One prediction of this "primacy coding" scheme is that decisions based on odor identity can be made solely using early odor-evoked neural activity. Using an optogenetic masking paradigm, we define the sensory integration time necessary for odor identification and demonstrate that animals can use information occurring <100 ms after inhalation onset to identify odors. Using multi-electrode array recordings of odor responses in the olfactory bulb, we find that concentration-invariant units respond earliest and at latencies that are within this behaviorally-defined time window. We propose a computational model demonstrating how such a code can be read by neural circuits of the olfactory system.

DALMATIAN: An Algorithm for Automatic Cell Detection and Counting in 3D.

Current 3D imaging methods, including optical projection tomography, light-sheet microscopy, block-face imaging, and serial two photon tomography enable visualization of large samples of biological tissue. Large volumes of data obtained at high resolution require development of automatic image processing techniques, such as algorithms for automatic cell detection or, more generally, point-like object detection. Current approaches to automated cell detection suffer from difficulties originating from detection of particular cell types, cell populations of different brightness, non-uniformly stained, and overlapping cells. In this study, we present a set of algorithms for robust automatic cell detection in 3D. Our algorithms are suitable for, but not limited to, whole brain regions and individual brain sections. We used watershed procedure to split regional maxima representing overlapping cells. We developed a bootstrap Gaussian fit procedure to evaluate the statistical significance of detected cells. We compared cell detection quality of our algorithm and other software using 42 samples, representing 6 staining and imaging techniques. The results provided by our algorithm matched manual expert quantification with signal-to-noise dependent confidence, including samples with cells of different brightness, non-uniformly stained, and overlapping cells for whole brain regions and individual tissue sections. Our algorithm provided the best cell detection quality among tested free and commercial software.

Mathematical Model of Evolution of Brain Parcellation.

We study the distribution of brain and cortical area sizes [parcellation units (PUs)] obtained for three species: mouse, macaque, and human. We find that the distribution of PU sizes is close to lognormal. We propose the mathematical model of evolution of brain parcellation based on iterative fragmentation and specialization. In this model, each existing PU has a probability to be split that depends on PU size only. This model suggests that the same evolutionary process may have led to brain parcellation in these three species. Within our model, region-to-region (macro) connectivity is given by the outer product form. We show that most experimental data on non-zero macaque cortex macroscopic-level connections can be explained by the outer product power-law form suggested by our model (62% for area V1). We propose a multiplicative Hebbian learning rule for the macroconnectome that could yield the correct scaling of connection strengths between areas. We thus propose an evolutionary model that may have contributed to both brain parcellation and mesoscopic level connectivity in mammals.

A stochastic model for retinocollicular map development.

BACKGROUND: We examine results of gain-of-function experiments on retinocollicular maps in knock-in mice [Brown et al. (2000) Cell 102:77]. In wild-type mice the temporal-nasal axis of retina is mapped to the rostral-caudal axis of superior colliculus. The established map is single-valued, which implies that each point in retina maps to a unique termination zone in superior colliculus. In homozygous Isl2/EphA3 knock-in mice the map is double-valued, which means that each point on retina maps to two termination zones in superior colliculus. This is because about 50 percent of cells in retina express Isl2, and two types of projections, wild-type and Isl2/EphA3 positive, form two branches of the map. In heterozygous Isl2/EphA3 knock-ins the map is intermediate between the homozygous and wild-type: it is single-valued in temporal and double-valued in the nasal parts of retina. In this study we address possible reasons for such a bifurcation of the map. RESULTS: We study the map formation using stochastic model based on Markov chains. In our model the map undergoes a series of reconstructions with probabilities dependent upon a set of chemical cues. Our model suggests that the map in heterozygotes is single-valued in temporal region of retina for two reasons. First, the inhomogeneous gradient of endogenous receptor in retina makes the impact of exogenous receptor less significant in temporal retina. Second, the gradient of ephrin in the corresponding region of superior colliculus is smaller, which reduces the chemical signal-to-noise ratio. We predict that if gradient of ephrin is reduced by a genetic manipulation, the single-valued region of the map should extend to a larger portion of temporal retina, i.e. the point of transition between single-and double-valued maps should move to a more nasal position in Isl2-EphA3 heterozygotes. CONCLUSIONS: We present a theoretical model for retinocollicular map development, which can account for intriguing behaviors observed in gain-of-function experiments by Brown et al., including bifurcation in heterozygous Isl2/EphA3 knock-ins. The model is based on known chemical labels, axonal repulsion/competition, and stochasticity. Possible mapping in Isl2/EphB knock-ins is also discussed.

Orbitofrontal cortex is required for optimal waiting based on decision confidence.

Confidence judgments are a central example of metacognition-knowledge about one's own cognitive processes. According to this metacognitive view, confidence reports are generated by a second-order monitoring process based on the quality of internal representations about beliefs. Although neural correlates of decision confidence have been recently identified in humans and other animals, it is not well understood whether there are brain areas specifically important for confidence monitoring. To address this issue, we designed a postdecision temporal wagering task in which rats expressed choice confidence by the amount of time they were willing to wait for reward. We found that orbitofrontal cortex inactivation disrupts waiting-based confidence reports without affecting decision accuracy. Furthermore, we show that a normative model can quantitatively account for waiting times based on the computation of decision confidence. These results establish an anatomical locus for a metacognitive report, confidence judgment, distinct from the processes required for perceptual decisions.

Sparse incomplete representations: a potential role of olfactory granule cells.

Mitral/tufted cells of the olfactory bulb receive odorant information from receptor neurons and transmit this information to the cortex. Studies in awake behaving animals have found that sustained responses of mitral cells to odorants are rare, suggesting sparse combinatorial representation of the odorants. Careful alignment of mitral cell firing with the phase of the respiration cycle revealed brief transient activity in the larger population of mitral cells, which respond to odorants during a small fraction of the respiration cycle. Responses of these cells are therefore temporally sparse. Here, we propose a mathematical model for the olfactory bulb network that can reproduce both combinatorially and temporally sparse mitral cell codes. We argue that sparse codes emerge as a result of the balance between mitral cells' excitatory inputs and inhibition provided by the granule cells. Our model suggests functional significance for the dendrodendritic synapses mediating interactions between mitral and granule cells.