We present two dynamical models for the appearance of adaptive mutations, which permit a quantitative comparison with experimental observations. The models quantify two alternative pictures: The hyper-mutating sub-population picture, and the population-wide mutation picture. We find that both...

We calculate winding-angles distributions of polymer models at the θ-point in two dimensions by means of Coulomb gas techniques. Our results suggest that breaking the symmetry of the model by distinguishing between parallel and antiparallel interactions changes the universality class.