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New Math Method Reveals Structure of Neural Activity

A newly-developed mathematical method can detect geometric structure in neural activity in the brain. “Previously, in order to understand this structure, scientists needed to relate neural activity to some specific external stimulus,” said Vladimir Itskov, associate professor of mathematics at Penn State University. “Our method is the first to be able to reveal this structure without our knowing an external stimulus ahead of time. We’ve now shown that our new method will allow us to explore the organizational structure of neurons without knowing their function in advance.”

“The traditional methods used by researchers to analyze the relationship between the activities of neurons were adopted from physics,” said Carina Curto, associate professor of mathematics at Penn State, “but neuroscience data doesn’t necessarily play by the same rules as data from physics, so we need new tools. Our method is a first step toward developing a new mathematical toolkit to uncover the structure of neural circuits with unknown function in the brain.”

The method — clique topology — was developed by an interdisciplinary team of researchers at Penn State, the University of Pennsylvania, the Howard Hughes Medical Institute, and the University of Nebraska-Lincoln. The method is described in a paper that will be posted in the early online edition of the journal Proceedings of the National Academy of Sciences during the week ending October 23, 2015.

“We have adopted approaches from the field of algebraic topology that previously had been used primarily in the domain of pure mathematics and have applied them to experimental data on the activity of place cells — specialized neurons in the part of the brain called the hippocampus that sense the position of an animal in its environment,” said Curto.

The researchers measured the activity of place cells in the brains of rats during three different experimental conditions. They then analyzed the pairwise correlations of this activity — how the firing of each neuron was related to the firing of every other neuron.

Illustration of neurons.

This is an artist’s illustration of neurons. Credit: Benedict Campbell, Wellcome Images/CC.

In the first condition, the rats were allowed to roam freely in their environment — a behavior where the activity of place cells is directly related to the location of the animal in its environment. They searched the data to find groups of neurons, or “cliques,” in which the activity of all members of the clique was related to the activity of every other member. Their analysis of these cliques, using methods from algebraic topology, revealed an organized geometric structure. Surprisingly, the researchers found similar structure in the activities among place cells in the other two conditions they tested, wheel-running and sleep, where place cells are not expected to have geometric organization.

“Because the structure we detected was similar in all three experimental conditions, we think that we are picking up the fundamental organization of place cells in the hippocampus,” said Itskov.

About this neuroscience research

In addition to Itskov and Curto, other members of the research team include Chad Giusti at the University of Pennsylvania and Eva Pastalkova at the Howard Hughes Medical Institute.

Funding: The research was supported by the National Science Foundation (grant numbers DMS 1122519, DMS 122566, and DMS 1537228), the Alfred P. Sloan Foundation, the Defense Advanced Research Projects Agency Young Faculty Award (grant number W911NF-15-1-0084), and the Howard Hughes Medical Institute.

Source: Barbara K. Kennedy – Penn State
Image Source: The images are credited to Benedict Campbell, Wellcome Images/CC
Original Research: Full open access research for “Clique topology reveals intrinsic geometric structure in neural correlations” by Chad Giusti, Eva Pastalkova, Carina Curto, and Vladimir Itskov in PNAS. Published online August 26 2015 doi:10.1073/pnas.1506407112


Abstract

Clique topology reveals intrinsic geometric structure in neural correlations

Detecting meaningful structure in neural activity and connectivity data is challenging in the presence of hidden nonlinearities, where traditional eigenvalue-based methods may be misleading. We introduce a novel approach to matrix analysis, called clique topology, that extracts features of the data invariant under nonlinear monotone transformations. These features can be used to detect both random and geometric structure, and depend only on the relative ordering of matrix entries. We then analyzed the activity of pyramidal neurons in rat hippocampus, recorded while the animal was exploring a 2D environment, and confirmed that our method is able to detect geometric organization using only the intrinsic pattern of neural correlations. Remarkably, we found similar results during nonspatial behaviors such as wheel running and rapid eye movement (REM) sleep. This suggests that the geometric structure of correlations is shaped by the underlying hippocampal circuits and is not merely a consequence of position coding. We propose that clique topology is a powerful new tool for matrix analysis in biological settings, where the relationship of observed quantities to more meaningful variables is often nonlinear and unknown.

“Clique topology reveals intrinsic geometric structure in neural correlations” by Chad Giusti, Eva Pastalkova, Carina Curto, and Vladimir Itskov in PNAS. Published online August 26 2015 doi:10.1073/pnas.1506407112

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