T cells are like the special ops forces of the immune system; detecting and killing infected cells. When a new threat is the cells ramp up from just a few sentry cells to a full platoon. But how does the immune system make just the right amount of T cells, when the starting populations of T cells vary?. Now a team from Princeton has provided insight into this question using mathematical modeling.
The team found that the most important factors in how T cells expand the starting amount of infectious agent and the affinity of the cells for that agent. The Princeton team became intrigued by this question after a recent study by another team found that this ramp-up follows a predictable pattern: If the initial number of T cells is small; the ramp-up is large, but if the beginning number of T cells is large, the ramp-up is small.

## The amount of T cell

This relationship follows a mathematical “power law,” which states that the amount of T cell expansion depends inversely as a power of the initial number of T cells. “The significance of this observed relationship is that even though the immune system is very complicated and has all sorts of feedback mechanisms, you see a kind of regularity; meaning there is likely to some sort of simple underlying mechanism at work.

The upshot of this relationship is that, whether there were few or many T cells; to begin with, the final number ready to fight infection is neither too large nor too small. This makes sense for the organism fighting the infection, but the Princeton team wondered what is happening in the immune system to make this selective ramp-up possible. First author Andreas Mayer and the team used mathematical modeling to explore how T cells respond when an infection occurs.

## The T-cell receptors

T cells are dotted with receptors capable of detecting bits of infectious agents; known as antigens, on the surface of infected cells. When the T-cell receptors stick to antigens on the surface of these cells; the T cells are spurred to clone themselves to make an infection-fighting army. Early in a new infection, antigen-presenting cells display lots of antigens on their surfaces; but this presentation wanes over time, especially if the infection is successfully fought by the immune system.

The team found that these warning levels of antigen provide a simple mechanism which can explain the power-law relationship. The idea is that T cells amplify at their maximum rate until the decreasing number of antigens means that the T cells are no longer able to find antigens. “If you start off with a low number of T cells; you get to expand for longer until you reach the decreasing level of antigens. “But if you start off with a larger number of T cells, then relatively quickly you run out of antigens.”

T cells that cannot find antigens eventually stop dividing. These relationships suggest lessons for vaccine developers; Wingreen said. Vaccines involve the use of antigens to stimulate the production of immune system cells. Mathematical models may help researchers figure out how much antigen is to achieve an optimal immune response. The study, “Regulation of T cell expansion by antigen presentation dynamics,”