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ND physicist models brain’s network structure

Henry Gens | Monday, October 14, 2013

Perhaps social media websites like Facebook are always on our minds because our brains are structured in a way similar to these ubiquitous social networks. A recently published study by Notre Dame physics professor Zoltan Toroczkai on the fundamental wiring of the neurons that make up the complex structure of the brain suggests this may be the case.

Toroczkai, an expert in the study of large-scale networks said he uses his unconventional background  as a physicist to investigate the structure and dynamics of a wide range of networks.

“Social systems, such as Facebook, are an example complex networks,” Toroczkai said. “With technological advances we are even more connected, more information is flowing.

“So you can think of the social network as another large network that evolves due to the information in it. From a top-level perspective, this is not different from what happens in the primate brain.”

The challenge to Toroczkai lies in adapting the statistical methods of the physicist to interpreting and understanding the underlying phenomena in these systems.

 “In the brain, the neurons can almost arbitrarily be connected, humans can almost arbitrarily be connected – the connections between real-world networks, such as social networks and neuronal networks, are not like the ones in a crystalline solid,” Toroczkai said. “They are much more complicated. So there is a challenge for a physicist to develop the methods that we use to study regular materials and apply them to different types of networks.”

In his recent finding, Toroczkai said he collaborated with a group of researchers, including biologists from France, to analyze a wealth of data obtained from thorough retrograde tracing experiments on Macaque monkey cortexes. They injected a chemical dye into the brain of the monke, and after affew weeks, the tissues are dissected to reveal the path that the tracer took through the dense network of neurons, which allows one to make some sense of the structure, he said.

“The primate brain has an extremely large number of elements,” Toroczkai said. “If you think about the neocortex, which is basically a couple-millimeter-thick sheet that is lining your brain, it’s about the size of a napkin in the typical primate brain. It’s very small, and yet it has about 100 billion neurons and they are not isolated.
tThey are interconnected in a very complicated network-it is estimated that there are about 100 trillion connections in this area.”

This complicated network in the cortex can be divided into 29 functional areas, such as those controlling motion and sensory perception, in order construct a model, Toroczkai said. In doing so, he said he noticed that certain patterns emerged from the data related to density of connections and distance.   

“We said that this network should be subject to a physical constraint,” Toroczkai said. “I mean that when the brain develops, the neuron is growing these axons, and there’s a growth process that eventually stops.

“The longer you want to grow, the more effort you have to put in. These neurons are grown chemically during development, so I said that there should be some sort of exponential cost-some grow long and some grow short. And the simplest model you could think of, if you’re a modeler, is exponential decay. And that’s exactly what it was. So we used this wiring along with the geometry of the cortex to come up with this simple model.”

The result, Toroczkai said, was very surprising-the model turned out to be extremely simple, yet it largely explained much of the structural interconnectivity between the different functional areas of the cortex.

“It has only one parameter, which you also get from the data, and you get a network that looks very much like the one in the brain,” he said. “It tells you that the large-scale network between the different areas of the brain can be explained by physical principles, based on entropic cost of wiring.”

The next step in further elucidating the workings of the brain would be to look at dynamic processes, such as neuronal signaling and resulting behaviors, Toroczkai said. To that end, he said he will loos forward to future cross-disciplinary collaborations to which he can add his unconventional approaches and insights.

“Here we had a collaboration between biologists and physicists,” Toroczkai said. “As a physicist our goal is usually to simplify a problem-to reduce it to the essential components. We are not looking for the differences between things in the world, we’re are looking for things that are common, invariant.”

Contact Henry Gens at hgens@nd.edu