Immune response depends on the mathematics of the problem of narrow escape

The rough surface of a T cell means that only very small areas are in close contact with potential enemy cells. Credit: Blausen Medical

The shape of immune cells plays a key role in recognizing invaders.

The way immune cells choose their friends among their enemies can be described by a classic mathematical puzzle called "narrow escape problem".

This is one of the main conclusions of an international collaboration between biologists, immunologists and mathematicians, published in the journal Proceedings of the National Academy of Sciences.

The problem of narrow escape is a framework often applied in cell biology. It poses random moving particles trapped in a space with a tiny output and calculates the average time needed for each to escape.

"It's a new application for some known equations," says co-author Justin Tzou from Macquarie University's Department of Mathematics and Statistics.

Tzou has worked with colleagues from Oxford and Cambridge Universities in the UK, from the University of British Columbia in Canada and from the University of Skövde in Sweden to analyze how potential pathogens are detected by T cells, which identify and attack invaders. The researchers found that the equations used in the problem of narrow escape play a key role in determining the triggering of an immune response.

"The problem of narrow escape is a close cousin of the T-cell receptor situation," says Justin. "It's about determining how long a scattering particle stays in a certain area before escaping."

The unique form of T cells creates what has been called a "close contact zone" to trigger molecules called T-cell receptors. Unlike most cells, which have relatively smooth surfaces, T cells are covered flying, bumps and other protrusions.

Scientists have known for a long time that T cell receptor molecules are on the surface of cells to recognize their enemies and trigger a hostile reaction.

The receptors contain molecular patterns that mirror those found on the surface of bacteria, tumors and other dangerous intruders. But the exact operation of the recognition and triggering process – and in particular its fast and precise operation – remains a mystery.

Researchers believe that the unusually lumpy form of T cells plays a vital role.

The protuberances on the surface mean that its area of ​​contact with a potential enemy cell is very small – a few hundred nanometers only, a thousand times smaller than the width of a human hair.

And according to the new theory, T-cell receptors follow a two-second rule: if they stay longer than two seconds in the small contact zone, a chemical process starts to sound the alarm and triggers an attack .

The size of the contact area depends on the size of the lumps on the surface of the T lymphocyte.

"The smaller the area, the less likely the T-cell receptor will stay in this area, triggering an attack," Justin explains. "It seems that the size of these protuberances keeps the process sensitive to the presence of the invader."

The researchers hope their work will provide new insights into immune deficiencies and autoimmune diseases, in which the immune system turns against the body's own cells.

Reference: "A Mechanism Based on Cellular Topography for T Cell Receptor Discrimination" by Ricardo A. Fernandes, Kristina A. Ganzinger, Justin C. Tzou, Peter Jonsson, Steven F. Lee, Matthieu Palayret, Ana Mafalda Santos, Alexander R. Carr, Aleks Ponjavic, Veronica T. Chang, Charlotte Macleod, Christoffer Lagerholm, Alan E. Lindsay, Omer Dushek, Andreas Tilevik, Simon J. Davis and David Klenerman, July 20, 2019, Proceedings of the National Academy of Sciences.
DOI: 10.1073 / pnas.1817255116