Marija Vucelja (University of Virginia), Applied Mathematics Colloquium

Title:  Modelling the emergence of clones in populations (by drawing analogies with the physics of glasses) and the adaptive immune system of bacteria (called CRISPR)

Abstract:  I will describe about two examples where drawing analogies with physics has been pivotal to our understanding of the population genetics phenomena. First, I will talk about the emergence of clones in populations. Recombination reshuffles genetic material, while selection amplifies the fittest genotypes. If recombination is more rapid than selection, a population consists of a diverse mixture of many genotypes. In the opposite regime selection can amplify individual genotypes into large clones causing the “clonal condensation”. I will point out the similarity between clonal condensation and the freezing transition in the Random Energy Model of spin glasses. I will derive one of the key quantities of interest: the probability that two individuals are genetically identical. As my second example I will speak about the CRISPR mechanism which serves as an adaptive defense mechanism of bacteria against phages. It takes parts of genomic sequences from the ”invaders” and in this way builds up a memory of past infections. With a new encounter of an invading sequence, this memory is accessed, and in a successful outcome, the invader is neutralized. I will introduce a population dynamics model where immunity can be both acquired and lost. Two key parameters of the model are the ease of acquisition and the effectiveness in conferring immunity.