Statistical Analysis of Tract-Tracing Experiments Demonstrates a Dense, Complex Cortical Network in the Mouse.

Anatomical tract tracing methods are the gold standard for estimating the weight of axonal connectivity between a pair of pre-defined brain regions. Large studies, comprising hundreds of experiments, have become feasible by automated methods. However, this comes at the cost of positive-mean noise making it difficult to detect weak connections, which are of particular interest as recent high resolution tract-tracing studies of the macaque have identified many more weak connections, adding up to greater connection density of cortical networks, than previously recognized. We propose a statistical framework that estimates connectivity weights and credibility intervals from multiple tract-tracing experiments. We model the observed signal as a log-normal distribution generated by a combination of tracer fluorescence and positive-mean noise, also accounting for injections into multiple regions. Using anterograde viral tract-tracing data provided by the Allen Institute for Brain Sciences, we estimate the connection density of the mouse intra-hemispheric cortical network to be 73% (95% credibility interval (CI): 71%, 75%); higher than previous estimates (40%). Inter-hemispheric density was estimated to be 59% (95% CI: 54%, 62%). The weakest estimable connections (about 6 orders of magnitude weaker than the strongest connections) are likely to represent only one or a few axons. These extremely weak connections are topologically more random and longer distance than the strongest connections, which are topologically more clustered and shorter distance (spatially clustered). Weak links do not substantially contribute to the global topology of a weighted brain graph, but incrementally increased topological integration of a binary graph. The topology of weak anatomical connections in the mouse brain, rigorously estimable down to the biological limit of a single axon between cortical areas in these data, suggests that they might confer functional advantages for integrative information processing and/or they might represent a stochastic factor in the development of the mouse connectome.Netherlands Organisation for Scientific Research (Rubicon Fellowship), National Institute of Health Research (NIHR) Cambridge Biomedical Research CentreThis is the final version of the article. It first appeared from the Public Library of Science via http://dx.doi.org/10.1371/journal.pcbi.100510

Small-World Brain Networks Revisited.

It is nearly 20 years since the concept of a small-world network was first quantitatively defined, by a combination of high clustering and short path length; and about 10 years since this metric of complex network topology began to be widely applied to analysis of neuroimaging and other neuroscience data as part of the rapid growth of the new field of connectomics. Here, we review briefly the foundational concepts of graph theoretical estimation and generation of small-world networks. We take stock of some of the key developments in the field in the past decade and we consider in some detail the implications of recent studies using high-resolution tract-tracing methods to map the anatomical networks of the macaque and the mouse. In doing so, we draw attention to the important methodological distinction between topological analysis of binary or unweighted graphs, which have provided a popular but simple approach to brain network analysis in the past, and the topology of weighted graphs, which retain more biologically relevant information and are more appropriate to the increasingly sophisticated data on brain connectivity emerging from contemporary tract-tracing and other imaging studies. We conclude by highlighting some possible future trends in the further development of weighted small-worldness as part of a deeper and broader understanding of the topology and the functional value of the strong and weak links between areas of mammalian cortex.DSB acknowledges support from the John D. and Catherine T. MacArthur Foundation, the Alfred P. Sloan Foundation, the Army Research Laboratory and the Army Research Office through contract numbers W911NF-10-2-0022 and W911NF-14-1-0679, the National Institute of Health (2-R01-DC-009209-11, 1R01HD086888-01, R01-MH107235, R01-MH107703, and R21-M MH-106799), the Office of Naval Research, and the National Science Foundation (BCS-1441502, CAREER PHY-1554488, and BCS-1631550).This is the final version of the article. It first appeared from Sage at http://dx.doi.org/10.1177/1073858416667720

Greedy low-rank algorithm for spatial connectome regression

Recovering brain connectivity from tract tracing data is an important computational problem in the neurosciences. Mesoscopic connectome reconstruction was previously formulated as a structured matrix regression problem (Harris et al., 2016), but existing techniques do not scale to the whole-brain setting. The corresponding matrix equation is challenging to solve due to large scale, ill-conditioning, and a general form that lacks a convergent splitting. We propose a greedy low-rank algorithm for connectome reconstruction problem in very high dimensions. The algorithm approximates the solution by a sequence of rank-one updates which exploit the sparse and positive definite problem structure. This algorithm was described previously (Kressner and Sirkovi\'c, 2015) but never implemented for this connectome problem, leading to a number of challenges. We have had to design judicious stopping criteria and employ efficient solvers for the three main sub-problems of the algorithm, including an efficient GPU implementation that alleviates the main bottleneck for large datasets. The performance of the method is evaluated on three examples: an artificial "toy" dataset and two whole-cortex instances using data from the Allen Mouse Brain Connectivity Atlas. We find that the method is significantly faster than previous methods and that moderate ranks offer good approximation. This speedup allows for the estimation of increasingly large-scale connectomes across taxa as these data become available from tracing experiments. The data and code are available online

Cerebral organoids at the air-liquid interface generate diverse nerve tracts with functional output.

Neural organoids have the potential to improve our understanding of human brain development and neurological disorders. However, it remains to be seen whether these tissues can model circuit formation with functional neuronal output. Here we have adapted air-liquid interface culture to cerebral organoids, leading to improved neuronal survival and axon outgrowth. The resulting thick axon tracts display various morphologies, including long-range projection within and away from the organoid, growth-cone turning, and decussation. Single-cell RNA sequencing reveals various cortical neuronal identities, and retrograde tracing demonstrates tract morphologies that match proper molecular identities. These cultures exhibit active neuronal networks, and subcortical projecting tracts can innervate mouse spinal cord explants and evoke contractions of adjacent muscle in a manner dependent on intact organoid-derived innervating tracts. Overall, these results reveal a remarkable self-organization of corticofugal and callosal tracts with a functional output, providing new opportunities to examine relevant aspects of human CNS development and disease

The missing link: Predicting connectomes from noisy and partially observed tract tracing data

Our understanding of the wiring map of the brain, known as the connectome, has increased greatly in the last decade, mostly due to technological advancements in neuroimaging techniques and improvements in computational tools to interpret the vast amount of available data. Despite this, with the exception of the C. elegans roundworm, no definitive connectome has been established for any species. In order to obtain this, tracer studies are particularly appealing, as these have proven highly reliable. The downside of tract tracing is that it is costly to perform, and can only be applied ex vivo. In this paper, we suggest that instead of probing all possible connections, hitherto unknown connections may be predicted from the data that is already available. Our approach uses a 'latent space model' that embeds the connectivity in an abstract physical space. Regions that are close in the latent space have a high chance of being connected, while regions far apart are most likely disconnected in the connectome. After learning the latent embedding from the connections that we did observe, the latent space allows us to predict connections that have not been probed previously. We apply the methodology to two connectivity data sets of the macaque, where we demonstrate that the latent space model is successful in predicting unobserved connectivity, outperforming two baselines and an alternative model in nearly all cases. Furthermore, we show how the latent spatial embedding may be used to integrate multimodal observations (i.e. anterograde and retrograde tracers) for the mouse neocortex. Finally, our probabilistic approach enables us to make explicit which connections are easy to predict and which prove difficult, allowing for informed follow-up studies

Spatial embedding and wiring cost constrain the functional layout of the cortical network of rodents and primates

Mammals show a wide range of brain sizes, reflecting adaptation to diverse habitats. Comparing interareal cortical networks across brains of different sizes and mammalian orders provides robust information on evolutionarily preserved features and species-specific processing modalities. However, these networks are spatially embedded, directed, and weighted, making comparisons challenging. Using tract tracing data from macaque and mouse, we show the existence of a general organizational principle based on an exponential distance rule (EDR) and cortical geometry, enabling network comparisons within the same model framework. These comparisons reveal the existence of network invariants between mouse and macaque, exemplified in graph motif profiles and connection similarity indices, but also significant differences, such as fractionally smaller and much weaker long-distance connections in the macaque than in mouse. The latter lends credence to the prediction that long-distance cortico-cortical connections could be very weak in the much-expanded human cortex, implying an increased susceptibility to disconnection syndromes such as Alzheimer disease and schizophrenia. Finally, our data from tracer experiments involving only gray matter connections in the primary visual areas of both species show that an EDR holds at local scales as well (within 1.5 mm), supporting the hypothesis that it is a universally valid property across all scales and, possibly, across the mammalian class

Remodeling of Axonal Connections Contributes to Recovery in an Animal Model of Multiple Sclerosis

In multiple sclerosis (MS), inflammation in the central nervous system (CNS) leads to damage of axons and myelin. Early during the clinical course, patients can compensate this damage, but little is known about the changes that underlie this improvement of neurological function. To study axonal changes that may contribute to recovery, we made use of an animal model of MS, which allows us to target inflammatory lesions to the corticospinal tract (CST), a major descending motor pathway. We demonstrate that axons remodel at multiple levels in response to a single neuroinflammatory lesion as follows: (a) surrounding the lesion, local interneurons show regenerative sprouting; (b) above the lesion, descending CST axons extend new collaterals that establish a “detour” circuit to the lumbar target area, whereas below the lesion, spared CST axons increase their terminal branching; and (c) in the motor cortex, the distribution of projection neurons is remodeled, and new neurons are recruited to the cortical motor pool. Behavioral tests directly show the importance of these changes for recovery. This paper provides evidence for a highly plastic response of the motor system to a single neuroinflammatory lesion. This framework will help to understand the endogenous repair capacity of the CNS and to develop therapeutic strategies to support it

Synaptic properties of parabigeminal circuits.

Subcortical structures of the visual system have been the subject of intense study in recent years, but there remain some important unanswered questions regarding the synaptic relationships linking the nuclei that comprise this important sensory network within the brain. In these studies, we use several modern and traditional approaches, including viral tract tracing, in vitro slice physiology, immunohistochemistry, optogenetics, and electron microscopy to characterize the circuits linking the superior colliculus (SC), parabigeminal nucleus (PBG), and lateral geniculate nucleus (LGN), with particular focus on GABAergic and cholinergic cell types. We found that the SC, an important visuomotor structure with connections to the LGN, PBG, pretectum, and pulvinar nucleus (among others), hosts a large and diverse population of GABAergic neurons that is composed primarily of interneurons labeled in the GAD67-GFP reporter mouse. Among these GABAergic cells residing within stratum griseum superficiale (SGS) of the SC, we found that GABAergic projection cells targeting the PBG exhibit unique characteristics, distinguishing them from other GABAergic projection populations as well as parvalbumin positive SC-PBG cells that exert opposing effects on postsynaptic cells in the PBG. Utilizing optogenetics in conjunction with whole-cell patch-clamp slice physiology, we additionally demonstrate a high degree of convergence between these opposing tectal inputs onto PBG neurons. Our electron microscopy experiments and lightlevel immunohistochemistry in GAD67 reporter mice also revealed a previously unidentified extra-tectal souce of GABAergic input to the PBG, where these inhibitory synapses were observed to account for almost half of its inputs. Finally, using MATH5-/- mutant mice that lack retinofugal projections, we identify the largely cholinergic inputs from the PBG as the likely source of “retinal replacement terminals” observed in the LGN in previous studies utilizing animal models of retinofugal input loss

Transient Neuronal Populations Are Required to Guide Callosal Axons: A Role for Semaphorin 3C

Neurons, glia, and callosal axons operate as a “ménage à trois” in the development of the corpus callosum