Rare event simulation for T cells recognising foreign antigens
by
Florian Lipsmeier
Bielefeld University
Coauthors: Ellen Baake (Bielefeld University)

We reconsider the problem of foreign-self distinction in immunobiology, namely, the discrimination of foreign antigens against a background of the body's own molecules. As is well known, the precise mechanism, though one of the major tasks of the immune system, continues to be a fundamental puzzle. We reconsider it here as a problem of statistical recognition as recently formulated by van den Berg, Rand and Burroughs [1], who modelled the probabilistic nature of the interaction between T cells and antigen-presenting cells (APC's). Here, the stochasticity is due to the random sample of antigens present on the surface of every APC, and to the random receptor type that characterises individual T cells. It has been shown previously [1, 2] that this model, though highly idealised, is capable of reproducing important aspects of the recognition phenomenon, and of explaining them on the basis of stochastic rare events. The `rare events' come into play here because the probability that a randomly chosen T cell will be activated by a randomly chosen APC is very low, whether the APC carries foreign antigens or not. It is therefore adequate to use large deviations theory, which characterises tail events. However, the results obtained so far are asymptotic in nature; simulations have been restricted to the straightforward simple sampling approach, which does not allow for sample sizes large enough to address more detailed questions. Building on the available large deviation results, we develop an importance sampling technique here that allows for a convenient exploration of the relevant tail events by means of simulation [3]. With its help, we investigate the mechanism of statistical recognition in some depth. In particular, we illustrate how a foreign antigen can `stand out' against the self background if it is present in sufficiently many copies, although no a priori difference between self and nonself is built into the model. This method will also allow to tackle models that are more realistic than the basic caricature considered so far.

References:

[1] Van Den Berg, H.A., Rand, D.A., Burroughs, N.J.: A reliable and safe T cell repertoire based on low-affinity T cell receptors. J Theor Biol 209(4), 465-486 (2001)

[2] Zint, N., Baake, E., den Hollander, F.: How T-cells use large deviations to recognize foreign antigens. J Math Biol., in press

[3] Lipsmeier, F. , Baake, E. Rare event simulation for T cells, in preparation

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Date received: May 8, 2008