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.

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.

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.

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.

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.

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.

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.

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.

In search of the structure of human olfactory space

We analyze the responses of human observers to an ensemble of monomolecular odorants. Each odorant is characterized by a set of 146 perceptual descriptors obtained from a database of odor character profiles. Each odorant is therefore represented by a point in a highly multidimensional sensory space. In this work we study the arrangement of odorants in this perceptual space. We argue that odorants densely sample a two-dimensional curved surface embedded in the multidimensional sensory space. This surface can account for more than half of the variance of the perceptual data. We also show that only 12% of experimental variance cannot be explained by curved surfaces of substantially small dimensionality (<10). We suggest that these curved manifolds represent the relevant spaces sampled by the human olfactory system, thereby providing surrogates for olfactory sensory space. For the case of 2D approximation, we relate the two parameters on the curved surface to the physico-chemical parameters of odorant molecules. We show that one of the dimensions is related to eigenvalues of molecules’ connectivity matrix, while the other is correlated with measures of molecules’ polarity. We discuss the behavioral significance of these findings.

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.

A unifying model for activity-dependent and activity-independent mechanisms predicts complete structure of topographic maps in ephrin-A deficient mice

Axons of retinal ganglion cells establish orderly projections to the superior colliculus of the midbrain. Axons of neighboring cells terminate proximally in the superior colliculus thus forming a topographically precise representation of the visual world. Coordinate axes are encoded in retina and in the target through graded expression of chemical labels. Additional sharpening of projections is provided by electric activity, which is correlated between neighboring axons. Here we propose a quantitative model, which allows combining the effects of chemical labels and correlated activity in a single approach. Using this model we study a complete structure of two-dimensional topographic maps in mutant mice, in which the label encoding the horizontal retinal coordinate ephrin-A is reduced/eliminated. We show that topographic maps in ephrin-A deficient mice display a granular structure, with the regions of smooth mapping separated by linear discontinuities reminiscent of fractures observed in the maps of preferred orientation.

How to find decision makers in neural networks

Nervous systems often face the problem of classifying stimuli and making decisions based on these classifications. The neurons involved in these tasks can be characterized as sensory or motor, according to their correlation with sensory stimulus or motor response. In this study we define a third class of neurons responsible for making perceptual decisions. Our mathematical formalism enables the weighting of neuronal units according to their contribution to decision making, thus narrowing the field for more detailed studies of underlying mechanisms. We develop two definitions of a contribution to decision making. The first definition states that decision making activity can be found at the points of emergence for behavioral correlations in the system. The second definition involves the study of propagation of noise in the network. The latter definition is shown to be equivalent to the first one in the cases when they can be compared. Our results suggest a new approach to analyzing decision making networks.

Maps in the brain: what can we learn from them?

In mammalian visual cortex, neurons are organized according to their functional properties into multiple maps such as retinotopic, ocular dominance, orientation preference, direction of motion, and others. What determines the organization of cortical maps? We argue that cortical maps reflect neuronal connectivity in intracortical circuits. Because connecting distant neurons requires costly wiring (i.e., axons and dendrites), there is an evolutionary pressure to place connected neurons as close to each other as possible. Then, cortical maps may be viewed as solutions that minimize wiring cost for given intracortical connectivity. These solutions can help us in inferring intracortical connectivity and, ultimately, in understanding the function of the visual system.

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.

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.

Properties of synaptic transmission and the global stability of delayed activity states

The influence of synaptic channel properties on the stability of delayed activity maintained by recurrent neural networks is studied. The duration of excitatory post-synaptic current (EPSC) is shown to be essential for the global stability of the delayed response. The NMDA receptor channel is a much more reliable mediator of the reverberating activity than the AMPA receptor, due to a longer EPSC. This allows one to interpret the deterioration of the working memory observed in NMDA channel blockade experiments. The key mechanism leading to the decay of the delayed activity originates in the unreliability of synaptic transmission. The optimum fluctuation of the synaptic currents leading to the decay is identified. The decay time is calculated analytically and the result is confirmed computationally.

Orientation preference patterns in mammalian visual cortex: a wire length minimization approach

In the visual cortex of many mammals, orientation preference changes smoothly along the cortical surface, with the exception of singularities such as pinwheels and fractures. The reason for the existence of these singularities has remained elusive, suggesting that they are developmental artifacts. We show that singularities reduce the length of intracortical neuronal connections for some connection rules. Therefore, pinwheels and fractures could be evolutionary adaptations keeping cortical volume to a minimum. Wire length minimization approach suggests that interspecies differences in orientation preference maps reflect differences in intracortical neuronal circuits, thus leading to experimentally testable predictions. We discuss application of our model to direction preference maps.