Generation Probabilities of T cell receptors: a story of Coarse Graining

The adaptive immune system operates by stochastically generating a large repertoire of unique receptors to tag foreign peptides through specific binding affinities. As a result, there is a general interest (both clinical and scientific) in being able to compute the probability of generating (Pgen) and observing a particular receptor or functionally equivalent group of receptors. Previous work has defined probabilistic models for the underlying V(D)J recombination events, however it had only been tractable to compute Pgen on the nucleotide level due to the exponential explosion of events leading to the same amino acid sequence of the receptor. Through the introduction of a novel algorithm, which leverages dynamic programming, it is now possible to compute the Pgen of amino acid sequences, as well as sequences comprised of functional motifs, quickly and efficiently. This not only provides a tool for computing the baseline generation probability of receptors, but allows statistical analysis of how the Pgen distribution changes as a result of coarse graining from recombinatorial event, to nucleotide sequence, and finally to receptor. The reduction in entropy stemming from this coarse graining suggests at a possible explanation of so-called 'public' receptors.