Even the mildest form of a traumatic brain injury, better known as a concussion, can cause permanent, irreparable damage. Now, an interdisciplinary team of University of Pennsylvania researchers is improving their mathematical model of how this injury happens on the molecular scale.

A better understanding of why the rapid acceleration and deceleration associated with football hits, car crashes, and bomb blasts are particularly dangerous could provide insights into potential preventative measures and treatments for concussions.

The team consists of Vivek Shenoy, a professor of materials science and engineering in the School of Engineering and Applied Science, Hossein Ahmadzadeh, a member of Shenoy’s lab, and Douglas Smith, professor of neurosurgery in the Perelman School of Medicine and director of the Penn Center for Brain Injury and Repair.

They published their results in Biophysical Journal.

Previous modeling work by the team investigated the properties of a critical brain protein and its role in the elasticity of axons, the long, tendril-like part of brain cells. This protein, known as tau, helps explain the apparent contradiction this elasticity presents: If axons are so stretchy, why do they break under the strain of a traumatic brain injury?

Microtubules run down the length of axons in bundles that are linked by tau. The team’s first model incorporated the fact that tau is viscoelastic. Like Silly Putty, which is soft and stretchy but will shatter when hit by a hammer, the rate at which strain is applied determines how far tau can stretch without breaking.

The researchers‘ new model gets closer to the molecular mechanisms behind this phenomenon.

“In our earlier study,” Shenoy said, “we just had the tau as a viscoelastic link between two microtubules, but it’s actually more complicated than that. Our new model is more realistic, because it incorporates the fact that there are two tau proteins in each link.”

The heads of the tau proteins are bound to the microtubules, while their tails meet in the space between them and are bound to one another. The bonds between two individual tau proteins aren’t permanent, however. Normal motion in the brain causes them to detach from one another and reattach to new partners.

“These taus are always jumping from one point to another,” Ahmadzadeh said. “The average time they are sitting in one spot is only four seconds. This dynamic element needed to be in our models if we were going to understand tau’s role.”

This unbinding and rebinding allows microtubules to slide relative to one another without damage, enabling the axon to stretch up to twice its original length. The rapid jolt caused by a concussive tackle or blast doesn’t allow for this process to take place.

“When you pull the microtubules very slowly,” Ahmadzadeh said, “you’re giving more time for the tau to untangle and the bonds between the two break. When you pull them very fast, that bond doesn’t break and the forces gets exerted on the microtubule itself. That’s what’s causing the damage in a traumatic brain injury.”

“Another interesting aspect of the model,” Smith said, “is that it shows tau protein at the center axon damage in concussion. Notably, aggregation of the very same tau protein is also implicated in chronic traumatic encephalopathy, which is found in some athletes with a history of multiple concussions. Looking forward, the model may allow us to examine the role of axon damage and the development of tau pathologies in concussions.”

The research was supported by the National Institute of Biomedical Imaging and Bioengineering under award number R01EB017753, National Science Foundation grant CMMI-1312392, National Institutes of Health grants R01-NS038104, R01 NS092389 and P01-NS056202, and Department of Defense grant PT110785.