  Certain retroviruses, including HIV, insert their DNA in a non-random
fraction of the host genome via poorly understood selection mechanisms. Here,
we develop a biophysical model for retroviral integrations as stochastic and
quasi-equilibrium topological reconnections between polymers. We discover that
physical effects, such as DNA accessibility and elasticity, play important and
universal roles in this process. Our simulations predict that integration is
favoured within nucleosomal and flexible DNA, in line with experiments, and
that these biases arise due to competing energy barriers associated with DNA
deformations. By considering a long chromosomal region in human T-cells during
interphase, we discover that at these larger scales integration sites are
predominantly determined by chromatin accessibility. Finally, we propose and
solve a reaction-diffusion problem that recapitulates the distribution of HIV
hot-spots within T-cells. With few generic assumptions, our model can
rationalise experimental observations and identifies previously unappreciated
physical contributions to retroviral integration site selection.
