How T-cells use large deviations to recognize foreign antigens

Occam's razor: from Ockham's via moderna to modern data science

The principle of parsimony, also known as 'Occam's razor', is a heuristic dictum that is thoroughly familiar to virtually all practitioners of science: Aristotle, Newton, and many others have enunciated it in some form or other. Even though the principle is not difficult to comprehend as a general heuristic guideline, it has proved surprisingly resistant to being put on a rigorous footing - a difficulty that has become more pressing and topical with the 'big data' explosion. We review the significance of Occam's razor in the philosophical and theological writings of William of Ockham, and survey modern developments of parsimony in data science.

Chemodetection in fluctuating environments: receptor coupling, buffering, and antagonism

Variability in the chemical composition of the extracellular environment can significantly degrade the ability of cells to detect rare cognate ligands. Using concepts from statistical detection theory, we formalize the generic problem of detection of small concentrations of ligands in a fluctuating background of biochemically similar ligands binding to the same receptors. We discover that in contrast with expectations arising from considerations of signal amplification, inhibitory interactions between receptors can improve detection performance in the presence of substantial environmental variability, providing an adaptive interpretation to the phenomenon of ligand antagonism. Our results suggest that the structure of signaling pathways responsible for chemodetection in fluctuating and heterogeneous environments might be optimized with respect to the statistics and dynamics of environmental composition. The developed formalism stresses the importance of characterizing nonspecific interactions to understand function in signaling pathways.

Modulation of T-cell receptor functional sensitivity via the opposing actions of protein tyrosine kinases and phosphatases: a mathematical model

Combining receptor kinetics and stochastic modelling of receptor activation, we show that a T-cell can specifically augment its functional sensitivity to one particular peptide ligand while simultaneously decreasing its sensitivity to other ligands, by coordinating the expression levels of the co-receptor CD8 and the relative activities of kinases and phosphatases in the vicinity of the T-cell receptor (TCR). We propose that this focusable degeneracy of epitope recognition allows a TCR to have a wide range of potential ligands but be specifically sensitive to only one or a few of these at any one time, which resolves the paradox of how a relatively small number of clones (∼10(6)) can maintain the potential to respond to a vast space of ligands (∼20(9)) whilst avoiding auto-immunity. We validate the model against experimental data and predict shifts in functional sensitivity following a shift in the kinase/phosphatase balance (which could in principle be induced by experimental means). Moreover, we propose that in vivo, the T-cell gauges ligand quality by monitoring changes in TCR triggering rate concomitant with shifts in this balance, for instance as the immunological synapse matures.

Stochastic modelling of T-cell activation

We investigate a specific part of the human immune system, namely the activation of T-cells, using stochastic tools, especially sharp large deviation results. T-cells have to distinguish reliably between foreign and self peptides which are both presented to them by antigen presenting cells. Our work is based on a model studied by Zint et al. (J Math Bio 57(6):841-861, 2008). We are able to dispense with some restrictive distribution assumptions that were used previously, i.e., we establish a higher robustness of the model. A central issue is the analysis of two new perspectives to the scenario (two different quenched systems) in detail. This means that we do not only analyse the total probability of a T-cell activation (the annealed case) but also consider the probability of an activation of one certain clonotype and the probability of a T-cell activation by a certain antigen presentation profile (the quenched cases). Finally, we see analytically that the probability of T-cell activation increases with the number of presented foreign peptides in all three cases.

Specific T-cell activation in an unspecific T-cell repertoire

T-cells are a vital type of white blood cell that circulate around our bodies, scanning for cellular abnormalities and infections. They recognise disease-associated antigens via a surface receptor called the T-cell antigen receptor (TCR). If there were a specific TCR for every single antigen, no mammal could possibly contain all the T-cells it needs. This is clearly absurd and suggests that T-cell recognition must, to the contrary, be highly degenerate. Yet highly promiscuous TCRs would appear to be equally impossible: they are bound to recognise self as well as non-self antigens. We review how contributions from mathematical analysis have helped to resolve the paradox of the promiscuous TCR. Combined experimental and theoretical work shows that TCR degeneracy is essentially dynamical in nature, and that the T-cell can differentially adjust its functional sensitivity to the salient epitope, "tuning up" sensitivity to the antigen associated with disease and "tuning down" sensitivity to antigens associated with healthy conditions. This paradigm of continual modulation affords the TCR repertoire, despite its limited numerical diversity, the flexibility to respond to almost any antigenic challenge while avoiding autoimmunity.