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.Author Summary: Tract-tracing depends on active axonal transport of tracers between nerve cells, indicating the anatomical connectivity between areas of the brain. Recent advances in tract-tracing technology have enabled reconstruction of the connectome or wiring diagram of mammalian cerebral cortex. Here, we propose a novel statistical model to account for the noise arising from automation of tract-tracing measurements and from injections of tracer into multiple cortical areas simultaneously. On this basis, we find that the strength of anatomical connectivity in the mouse brain varies over six orders of magnitude, with the weakest links between regions approximately representing a few axons. Including all weak links above the statistical noise thresholds, we find that the connection density of the mouse connectome (73%) is greater than previously reported. Many of the complex topological and spatial properties of the mouse brain network emerge on the basis of the strongest axonal projections, whereas the weakest links have a more random organization. We conclude that inter-areal connections mediated by a few axons can be rigorously distinguished from experimental sources of noise in contemporary tract tracing data. Such weak links could support integrated functions of the mouse brain network and/or could represent an element of randomness in its formation.