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‘Multi-dimensional universe’ in brain networks

‘Multi-dimensional universe’ in brain networks

Researchers were able to identify architectural patterns that arise when the brain had to comprehend information before disintegrating into nothing by utilizing a sophisticated mathematical method.

The discovery showed that the brain is full of multi-dimensional geometrical structures operating in as many as 11 dimensions.

A team of researchers from the Blue Brain Project, a Swiss research effort dedicated to constructing a supercomputer-powered recreation of the human brain, created this brain model.

The team employed algebraic topology, a field of mathematics used to explain the characteristics of objects and spaces independent of their form change. This is the first time this branch of math has been applied to neuroscience.

“Algebraic topology is like a telescope and microscope at the same time. It can zoom into networks to find hidden structures—the trees in the forest—and see the empty spaces—the clearings—all at the same time,” said study author Kathryn Hess.

In the study, researchers ran a series of experiments on virtual brain tissue to identify brain structures that would never emerge by chance. They then repeated the trials on actual brain tissue to validate their virtual findings. They observed that when they stimulated the virtual tissue, clusters of neurons formed a clique. To generate a precise geometric object, each neuron links to every other neuron in a very particular way. The greater the dimensions, the more neurons in a clique.

(A) Thin (10 μm) slice of in silico reconstructed tissue. Red: A clique formed by five pyramidal cells in layer 5. (B1) Full connection matrix of a reconstructed microcircuit with 31,146 neurons. Neurons are sorted by cortical layer and morphological type within each layer. Pre-/postsynaptic neurons along the vertical/horizontal axis. Each grayscale pixel indicates the connections between two groups of 62 neurons each, ranging from white (no connections) to black (≥8% connected pairs). (B2) Zoom into the connectivity between two groups of 434 neurons each in layer 5, i.e., 7 by 7 pixels in (A), followed by a further zoom into the clique of 5 neurons shown in (A). Black indicates presence, and white absence of a connection. (B3) Zoom into the somata of the clique in (A) and representation of their connectivity as a directed graph.

A 4-clique in the undirected connectivity graph has one of 729 configurations in the directed graph. (A2) Configurations containing bidirectional connections are resolved by considering all sub-graphs without bidirectional connections. (A3) Without bidirectional connections, 64 possible configurations remain, 24 of which are acyclic, with a clear sink-source structure (directed simplices, in this case of dimension 3). (B) Number of simplices in each dimension in the Bio-M reconstruction (shaded area: standard deviation of seven statistical instantiations) and in three types of random control networks. (C) Examples of neurons forming high-dimensional simplices in the reconstruction. Bottom: Their representation as directed graphs. (D) (Left) Number of directed simplices of various dimensions found in 55 in vitro patch-clamp experiments sampling groups of pyramidal cells in layer 5. (Right) Number of simplices of various dimensions found in 100,000 in silico experiments mimicking the patch-clamp procedure of (B).

“We found a world that we had never imagined,” said lead resercher, neuroscientist Henry Markram from the EPFL institute in Switzerland. “There are tens of millions of these objects even in a small speck of the brain, up through seven dimensions. In some networks, we even found structures with up to 11 dimensions.”

Virtual experiments on Blue Brain’s digital reconstruction of a microcircuit in the rat brain, a computer model consisting of 31 000 neurons – and a whopping 8 million connections – all based on physiological data © Blue Brain Project
The left shows a digital copy of a part of the neocortex, the most evolved part of the brain. On the right is a representation of the structures with different dimensions. The black hole in the middle symbolizes a complex of multi-dimensional spaces, or cavities. © Blue Brain Project

“The appearance of high-dimensional cavities when the brain is processing information means that the neurons in the network react to stimuli in an extremely organized manner,” said one of the researchers, Ran Levi.

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“It is as if the brain reacts to a stimulus by building then razing a tower of multi-dimensional blocks, starting with rods (1D), then planks (2D), then cubes (3D), and then more complex geometries with 4D, 5D, etc. The progression of activity through the brain resembles a multi-dimensional sandcastle that materializes out of the sand and then disintegrates,” he said.

These findings offer a tantalizing new picture of how the brain processes information, but the researchers point out that it is still unclear what causes the cliques and holes to develop in such particular ways. More research will be required to discover how the intricacy of these multidimensional geometric patterns generated by our neurons corresponds with the difficulty of different cognitive activities.

Cliques of Neurons Bound into Cavities Provide a Missing Link between Structure and Function, Michael W. Reimann, Max Nolte, Martina Scolamiero, Katharine Turner, Rodrigo Perin, Giuseppe Chindemi, Paweł Dłotko, Ran Levi, Kathryn Hess and Henry Markram

Published: June 2017

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