Imaging-based chromatin and epigenetic age, ImAge, quantitates aging and rejuvenation.

Biomarkers of biological age that predict the risk of disease and expected lifespan better than chronological age are key to efficient and cost-effective healthcare1-3. To advance a personalized approach to healthcare, such biomarkers must reliably and accurately capture individual biology, predict biological age, and provide scalable and cost-effective measurements. We developed a novel approach - image-based chromatin and epigenetic age (ImAge) that captures intrinsic progressions of biological age, which readily emerge as principal changes in the spatial organization of chromatin and epigenetic marks in single nuclei without regression on chronological age. ImAge captured the expected acceleration or deceleration of biological age in mice treated with chemotherapy or following a caloric restriction regimen, respectively. ImAge from chronologically identical mice inversely correlated with their locomotor activity (greater activity for younger ImAge), consistent with the widely accepted role of locomotion as an aging biomarker across species. Finally, we demonstrated that ImAge is reduced following transient expression of OSKM cassette in the liver and skeletal muscles and reveals heterogeneity of in vivo reprogramming. We propose that ImAge represents the first-in-class imaging-based biomarker of aging with single-cell resolution.

Restructuring of olfactory representations in the fly brain around odor relationships in natural sources.

A core challenge of olfactory neuroscience is to understand how neural representations of odor are generated and progressively transformed across different layers of the olfactory circuit into formats that support perception and behavior. The encoding of odor by odorant receptors in the input layer of the olfactory system reflects, at least in part, the chemical relationships between odor compounds. Neural representations of odor in higher order associative olfactory areas, generated by random feedforward networks, are expected to largely preserve these input odor relationships1-3. We evaluated these ideas by examining how odors are represented at different stages of processing in the olfactory circuit of the vinegar fly D. melanogaster. We found that representations of odor in the mushroom body (MB), a third-order associative olfactory area in the fly brain, are indeed structured and invariant across flies. However, the structure of MB representational space diverged significantly from what is expected in a randomly connected network. In addition, odor relationships encoded in the MB were better correlated with a metric of the similarity of their distribution across natural sources compared to their similarity with respect to chemical features, and the converse was true for odor relationships encoded in primary olfactory receptor neurons (ORNs). Comparison of odor coding at primary, secondary, and tertiary layers of the circuit revealed that odors were significantly regrouped with respect to their representational similarity across successive stages of olfactory processing, with the largest changes occurring in the MB. The non-linear reorganization of odor relationships in the MB indicates that unappreciated structure exists in the fly olfactory circuit, and this structure may facilitate the generalization of odors with respect to their co-occurence in natural sources.

Hippocampal spatial representations exhibit a hyperbolic geometry that expands with experience.

Daily experience suggests that we perceive distances near us linearly. However, the actual geometry of spatial representation in the brain is unknown. Here we report that neurons in the CA1 region of rat hippocampus that mediate spatial perception represent space according to a non-linear hyperbolic geometry. This geometry uses an exponential scale and yields greater positional information than a linear scale. We found that the size of the representation matches the optimal predictions for the number of CA1 neurons. The representations also dynamically expanded proportional to the logarithm of time that the animal spent exploring the environment, in correspondence with the maximal mutual information that can be received. The dynamic changes tracked even small variations due to changes in the running speed of the animal. These results demonstrate how neural circuits achieve efficient representations using dynamic hyperbolic geometry.

Using Global t-SNE to Preserve Intercluster Data Structure.

The t-distributed stochastic neighbor embedding (t-SNE) method is one of the leading techniques for data visualization and clustering. This method finds lower-dimensional embedding of data points while minimizing distortions in distances between neighboring data points. By construction, t-SNE discards information about large-scale structure of the data. We show that adding a global cost function to the t-SNE cost function makes it possible to cluster the data while preserving global intercluster data structure. We test the new global t-SNE (g-SNE) method on one synthetic and two real data sets on flower shapes and human brain cells. We find that significant and meaningful global structure exists in both the plant and human brain data sets. In all cases, g-SNE outperforms t-SNE and UMAP in preserving the global structure. Topological analysis of the clustering result makes it possible to find an appropriate trade-off of data distribution across scales. We find differences in how data are distributed across scales between the two subjects that were part of the human brain data set. Thus, by striving to produce both accurate clustering and positioning between clusters, the g-SNE method can identify new aspects of data organization across scales.

Hyperbolic odorant mixtures as a basis for more efficient signaling between flowering plants and bees.

Animals use odors in many natural contexts, for example, for finding mates or food, or signaling danger. Most analyses of natural odors search for either the most meaningful components of a natural odor mixture, or they use linear metrics to analyze the mixture compositions. However, we have recently shown that the physical space for complex mixtures is 'hyperbolic', meaning that there are certain combinations of variables that have a disproportionately large impact on perception and that these variables have specific interpretations in terms of metabolic processes taking place inside the flower and fruit that produce the odors. Here we show that the statistics of odorants and odorant mixtures produced by inflorescences (Brassica rapa) are also better described with a hyperbolic rather than a linear metric, and that combinations of odorants in the hyperbolic space are better predictors of the nectar and pollen resources sought by bee pollinators than the standard Euclidian combinations. We also show that honey bee and bumble bee antennae can detect most components of the B. rapa odor space that we tested, and the strength of responses correlates with positions of odorants in the hyperbolic space. In sum, a hyperbolic representation can be used to guide investigation of how information is represented at different levels of processing in the CNS.

The San Diego Nathan Shock Center: tackling the heterogeneity of aging.

Understanding basic mechanisms of aging holds great promise for developing interventions that prevent or delay many age-related declines and diseases simultaneously to increase human healthspan. However, a major confounding factor in aging research is the heterogeneity of the aging process itself. At the organismal level, it is clear that chronological age does not always predict biological age or susceptibility to frailty or pathology. While genetics and environment are major factors driving variable rates of aging, additional complexity arises because different organs, tissues, and cell types are intrinsically heterogeneous and exhibit different aging trajectories normally or in response to the stresses of the aging process (e.g., damage accumulation). Tackling the heterogeneity of aging requires new and specialized tools (e.g., single-cell analyses, mass spectrometry-based approaches, and advanced imaging) to identify novel signatures of aging across scales. Cutting-edge computational approaches are then needed to integrate these disparate datasets and elucidate network interactions between known aging hallmarks. There is also a need for improved, human cell-based models of aging to ensure that basic research findings are relevant to human aging and healthspan interventions. The San Diego Nathan Shock Center (SD-NSC) provides access to cutting-edge scientific resources to facilitate the study of the heterogeneity of aging in general and to promote the use of novel human cell models of aging. The center also has a robust Research Development Core that funds pilot projects on the heterogeneity of aging and organizes innovative training activities, including workshops and a personalized mentoring program, to help investigators new to the aging field succeed. Finally, the SD-NSC participates in outreach activities to educate the general community about the importance of aging research and promote the need for basic biology of aging research in particular.

How inhibitory neurons increase information transmission under threshold modulation.

Modulation of neuronal thresholds is ubiquitous in the brain. Phenomena such as figure-ground segmentation, motion detection, stimulus anticipation, and shifts in attention all involve changes in a neuron's threshold based on signals from larger scales than its primary inputs. However, this modulation reduces the accuracy with which neurons can represent their primary inputs, creating a mystery as to why threshold modulation is so widespread in the brain. We find that modulation is less detrimental than other forms of neuronal variability and that its negative effects can be nearly completely eliminated if modulation is applied selectively to sparsely responding neurons in a circuit by inhibitory neurons. We verify these predictions in the retina where we find that inhibitory amacrine cells selectively deliver modulation signals to sparsely responding ganglion cell types. Our findings elucidate the central role that inhibitory neurons play in maximizing information transmission under modulation.

Hyperbolic geometry of gene expression.

Patterns of gene expressions play a key role in determining cell state. Although correlations in gene expressions have been well documented, most of the current methods treat them as independent variables. One way to take into account gene correlations is to find a low-dimensional curved geometry that describes variation in the data. Here we develop such a method and find that gene expression across multiple cell types exhibits a low-dimensional hyperbolic structure. When more genes are taken into account, hyperbolic effects become stronger but representation remains low dimensional. The size of the hyperbolic map, which indicates the hierarchical depth of the data, was the largest for human cells, the smallest for mouse embryonic cells, and intermediate in differentiated cells from different mouse organs. We also describe how hyperbolic metric can be incorporated into the t-SNE method to improve visualizations compared with leading methods.

An argument for hyperbolic geometry in neural circuits.

This review connects several lines of research to argue that hyperbolic geometry should be broadly applicable to neural circuits as well as other biological circuits. The reason for this is that networks that conform to hyperbolic geometry are maximally responsive to external and internal perturbations. These networks also allow for efficient communication under conditions where nodes are added or removed. We will argue that one of the signatures of hyperbolic geometry is the celebrated Zipf's law (also sometimes known as the Pareto distribution) that states that the probability to observe a given pattern is inversely related to its rank. Zipf's law is observed in a variety of biological systems - from protein sequences, neural networks to economics. These observations provide further evidence for the ubiquity of networks with an underlying hyperbolic metric structure. Recent studies in neuroscience specifically point to the relevance of a three-dimensional hyperbolic space for neural signaling. The three-dimensional hyperbolic space may confer additional robustness compared to other dimensions. We illustrate how the use of hyperbolic coordinates revealed a novel topographic organization within the olfactory system. The use of such coordinates may facilitate representation of relevant signals elsewhere in the brain.

Quantifying Information Conveyed by Large Neuronal Populations.

Quantifying mutual information between inputs and outputs of a large neural circuit is an important open problem in both machine learning and neuroscience. However, evaluation of the mutual information is known to be generally intractable for large systems due to the exponential growth in the number of terms that need to be evaluated. Here we show how information contained in the responses of large neural populations can be effectively computed provided the input-output functions of individual neurons can be measured and approximated by a logistic function applied to a potentially nonlinear function of the stimulus. Neural responses in this model can remain sensitive to multiple stimulus components. We show that the mutual information in this model can be effectively approximated as a sum of lower-dimensional conditional mutual information terms. The approximations become exact in the limit of large neural populations and for certain conditions on the distribution of receptive fields across the neural population. We empirically find that these approximations continue to work well even when the conditions on the receptive field distributions are not fulfilled. The computing cost for the proposed methods grows linearly in the dimension of the input and compares favorably with other approximations.

Linking neural responses to behavior with information-preserving population vectors.

All systems for processing signals, both artificial and within animals, must obey fundamental statistical laws for how information can be processed. We discuss here recent results using information theory that provide a blueprint for building circuits where signals can be read-out without information loss. Many properties that are necessary to build information-preserving circuits are actually observed in real neurons, at least approximately. One such property is the use of logistic nonlinearity for relating inputs to neural response probability. Such nonlinearities are common in neural and intracellular networks. With this nonlinearity type, there is a linear combination of neural responses that is guaranteed to preserve Shannon information contained in the response of a neural population, no matter how many neurons it contains. This read-out measure is related to a classic quantity known as the population vector that has been quite successful in relating neural responses to animal behavior in a wide variety of cases. Nevertheless, the population vector did not withstand the scrutiny of detailed information-theoretical analyses that showed that it discards substantial amounts of information contained in the responses of a neural population. We discuss recent theoretical results showing how to modify the population vector expression to make it 'information-preserving', and what is necessary in terms of neural circuit organization to allow for lossless information transfer. Implementing these strategies within artificial systems is likely to increase their efficiency, especially for brain-machine interfaces.

Hyperbolic geometry of the olfactory space.

In the natural environment, the sense of smell, or olfaction, serves to detect toxins and judge nutritional content by taking advantage of the associations between compounds as they are created in biochemical reactions. This suggests that the nervous system can classify odors based on statistics of their co-occurrence within natural mixtures rather than from the chemical structures of the ligands themselves. We show that this statistical perspective makes it possible to map odors to points in a hyperbolic space. Hyperbolic coordinates have a long but often underappreciated history of relevance to biology. For example, these coordinates approximate the distance between species computed along dendrograms and, more generally, between points within hierarchical tree-like networks. We find that both natural odors and human perceptual descriptions of smells can be described using a three-dimensional hyperbolic space. This match in geometries can avoid distortions that would otherwise arise when mapping odors to perception.

Optimal Information Transmission by Overlapping Retinal Cell Mosaics.

The retina provides an excellent system for understanding the trade-offs that influence distributed information processing across multiple neuron types. We focus here on the problem faced by the visual system of allocating a limited number neurons to encode different visual features at different spatial locations. The retina needs to solve three competing goals: 1) encode different visual features, 2) maximize spatial resolution for each feature, and 3) maximize accuracy with which each feature is encoded at each location. There is no current understanding of how these goals are optimized together. While information theory provides a platform for theoretically solving these problems, evaluating information provided by the responses of large neuronal arrays is in general challenging. Here we present a solution to this problem in the case where multi-dimensional stimuli can be decomposed into approximately independent components that are subsequently coupled by neural responses. Using this approach we quantify information transmission by multiple overlapping retinal ganglion cell mosaics. In the retina, translation invariance of input signals makes it possible to use Fourier basis as a set of independent components. The results reveal a transition where one high-density mosaic becomes less informative than two or more overlapping lower-density mosaics. The results explain differences in the fractions of multiple cell types, predict the existence of new retinal ganglion cell subtypes, relative distribution of neurons among cell types and differences in their nonlinear and dynamical response properties.

On texture, form, and fixational eye movements.

Recent studies show that small movements of the eye that occur during fixation are controlled in the brain by similar neural mechanisms as large eye movements. Information theory has been successful in explaining many properties of large eye movements. Could it also help us understand the smaller eye movements that are much more difficult to study experimentally? Here I describe new predictions for how small amplitude fixational eye movements should be modulated by visual context in order to improve visual perception. In particular, the amplitude of fixational eye movements is predicted to differ when localizing edges defined by changes in texture or luminance.

A Low-Rank Method for Characterizing High-Level Neural Computations.

The signal transformations that take place in high-level sensory regions of the brain remain enigmatic because of the many nonlinear transformations that separate responses of these neurons from the input stimuli. One would like to have dimensionality reduction methods that can describe responses of such neurons in terms of operations on a large but still manageable set of relevant input features. A number of methods have been developed for this purpose, but often these methods rely on the expansion of the input space to capture as many relevant stimulus components as statistically possible. This expansion leads to a lower effective sampling thereby reducing the accuracy of the estimated components. Alternatively, so-called low-rank methods explicitly search for a small number of components in the hope of achieving higher estimation accuracy. Even with these methods, however, noise in the neural responses can force the models to estimate more components than necessary, again reducing the methods' accuracy. Here we describe how a flexible regularization procedure, together with an explicit rank constraint, can strongly improve the estimation accuracy compared to previous methods suitable for characterizing neural responses to natural stimuli. Applying the proposed low-rank method to responses of auditory neurons in the songbird brain, we find multiple relevant components making up the receptive field for each neuron and characterize their computations in terms of logical OR and AND computations. The results highlight potential differences in how invariances are constructed in visual and auditory systems.

Multidimensional receptive field processing by cat primary auditory cortical neurons.

The receptive fields of many auditory cortical neurons are multidimensional and are best represented by more than one stimulus feature. The number of these dimensions, their characteristics, and how they differ with stimulus context have been relatively unexplored. Standard methods that are often used to characterize multidimensional stimulus selectivity, such as spike-triggered covariance (STC) or maximally informative dimensions (MIDs), are either limited to Gaussian stimuli or are only able to recover a small number of stimulus features due to data limitations. An information theoretic extension of STC, the maximum noise entropy (MNE) model, can be used with non-Gaussian stimulus distributions to find an arbitrary number of stimulus dimensions. When we applied the MNE model to auditory cortical neurons, we often found more than two stimulus features that influenced neuronal firing. Excitatory and suppressive features coded different acoustic contexts: excitatory features encoded higher temporal and spectral modulations, while suppressive features had lower modulation frequency preferences. We found that the excitatory and suppressive features themselves were sensitive to stimulus context when we employed two stimuli that differed only in their short-term correlation structure: while the linear features were similar, the secondary features were strongly affected by stimulus statistics. These results show that multidimensional receptive field processing is influenced by feature type and stimulus context.

Optimizing Neural Information Capacity through Discretization.

Discretization in neural circuits occurs on many levels, from the generation of action potentials and dendritic integration, to neuropeptide signaling and processing of signals from multiple neurons, to behavioral decisions. It is clear that discretization, when implemented properly, can convey many benefits. However, the optimal solutions depend on both the level of noise and how it impacts a particular computation. This Perspective discusses how current physiological data could potentially be integrated into one theoretical framework based on maximizing information. Key experiments for testing that framework are discussed.

Cross-orientation suppression in visual area V2.

Object recognition relies on a series of transformations among which only the first cortical stage is relatively well understood. Already at the second stage, the visual area V2, the complexity of the transformation precludes a clear understanding of what specifically this area computes. Previous work has found multiple types of V2 neurons, with neurons of each type selective for multi-edge features. Here we analyse responses of V2 neurons to natural stimuli and find three organizing principles. First, the relevant edges for V2 neurons can be grouped into quadrature pairs, indicating invariance to local translation. Second, the excitatory edges have nearby suppressive edges with orthogonal orientations. Third, the resulting multi-edge patterns are repeated in space to form textures or texture boundaries. The cross-orientation suppression increases the sparseness of responses to natural images based on these complex forms of feature selectivity while allowing for multiple scales of position invariance.

Eigenvalue spectra of large correlated random matrices.

Using the diagrammatic method, we derive a set of self-consistent equations that describe eigenvalue distributions of large correlated asymmetric random matrices. The matrix elements can have different variances and be correlated with each other. The analytical results are confirmed by numerical simulations. The results have implications for the dynamics of neural and other biological networks where plasticity induces correlations in the connection strengths within the network. We find that the presence of correlations can have a major impact on network stability.

Plasticity to the Rescue.

The balance between excitatory and inhibitory inputs is critical for the proper functioning of neural circuits. Landau and colleagues show that, in the presence of cell-type-specific connectivity, this balance is difficult to achieve without either synaptic plasticity or spike-frequency adaptation to fine-tune the connection strengths.