Can the Immune System Perform a t-Test?

Abstract

The self-nonself discrimination hypothesis remains a landmark concept in immunology. It proposes that tolerance breaks down in the presence of nonself antigens. In strike contrast, in statistics, occurrence of nonself elements in a sample (i.e., outliers) is not obligatory to violate the null hypothesis. Very often, what is crucial is the combination of (self) elements in a sample. The two views on how to detect a change seem challengingly different and it could seem difficult to conceive how immunological cellular interactions could trigger responses with a precision comparable to some statistical tests. Here it is shown that frustrated cellular interactions reconcile the two views within a plausible immunological setting. It is proposed that the adaptive immune system can be promptly activated either when nonself ligands are detected or self-ligands occur in abnormal combinations. In particular we show that cellular populations behaving in this way could perform location statistical tests, with performances comparable to t or KS tests, or even more general data mining tests such as support vector machines or random forests. In more general terms, this work claims that plausible immunological models should provide accurate detection mechanisms for host protection and, furthermore, that investigation on mechanisms leading to improved detection in “in silico” models can help unveil how the real immune system works.

Cellular frustration algorithms for anomaly detection applications

“…Following our previous work [43], it will be assumed that each agent can only perceive a binary signal, b , from the information displayed by agents of the opposite type. This simplifies considerably ILists and their orderings.…”

“…To achieve accurate anomaly detection, cellular frustrated systems (CFSs) must first undergo a training stage (also called repertoire education) during which detector ILists are changed to increasingly frustrate the overall dynamics and reach a maximally frustrated state. To understand how this guarantees accurate anomaly detection, it is important to take into consideration the mechanisms involved, thoroughly discussed in [3] and [43]. So far it has been found that CFSs can detect 3 types of anomalous patterns: 1) the presence of outliers, i.e., signals never (or rarely) displayed during training; 2) the absence of an abnormally large number of frequently displayed signals (as compared to what is observed during training); 3) the absence of combinations of signals frequently displayed during training.…”

“…The detection mechanisms discussed above require an algorithm for ordering ILists. In [3, 43] it was proposed that the education of cells in the immune system is accomplished through a negative selection mechanism operating on the duration of pairings. Following inspiration from what is known in immunology, it was proposed that each T cell (or detector agent) establishing one of the longest pairings would be replaced by a new incoming cell, with randomly ordered IList.…”

“…Testing the anomaly detection performance of the algorithm follows closely that outlined in [43]. First it undergoes a calibration stage, to extract typical properties from the frustrated dynamics.…”

“…However, since accessing directly pairing lifetimes is difficult, the CFF proposes measuring the fraction of pairs lasting for a certain amount of time, τ , which is an indirect measure of the pairing lifetime. Indeed, it was hypothesized that the important function of positive selection—a training stage in the adaptive immune system that eliminates T cells that stay alone for too long—is to normalize the distribution of pairing durations so that by measuring a pairing duration, pairing lifetimes can be implicitly measured [3, 43].…”