Statistical Mechanics of Two-Way Recognition

Molecular recognition, the selective interaction between the elements of two different populations, plays a central role in regulating key processes in biology as, for example, immune responses where T cell receptors have the task of recognizing peptide antigens. Despite advances in sequencing technologies, predicting whether a TCR-antigen pair will bind remains a major challenge due to the experimental limitations in data collection. Data-driven approaches exploiting neural networks have shown to be promising in this regard, therefore understanding the amount and type of data on interacting partners necessary for generalisation is a question of great interest. In this thesis we translate this problem into the language of statistical physics and study two different settings of data collection exploiting the well-known teacher-student model and replica trick. In the first model we demonstrate the interesting equivalence between the particular setting in which we have few orthogonal elements from one population tested against many elements from the other and the case of multiple independent perceptrons. The second model features many paired elements from both populations, we analyse the behaviour of the overlap parameters and observe how the volume of the space of interaction matrices decreases as a function of the amount of training data. These results offer theoretical insights into data requirements of learning in molecular recognition tasks and may inform future experimental strategies and design of neural models for biological applications.