DNA condensation occurs in the presence of multi-valent cations and is a well-known phenomenon known since the 1970s. Since the first quantitative measurements of the inter-DNA forces during condensation, this phenomenon has attracted considerable theoretical interest and poses difficult and yet unresolved challenges. In this talk, I will give an overview of three different approaches to the study of DNA-DNA interactions to which I gave a contribution. In the first part, I will describe the mean-field electrostatic theory of Kornyshev and Leikin, that takes explicitly into account the helical patterns of charge on DNA, applied to the case of DNA supercoiling . Given the difficulty in esti-mating the parameters in this model, I will explain the importance of extracting independent results using all-atom molecular dynamics simulations, which I will detail in the second part . In the final part of my talk, I will illustrate my recent work on coarse-grained simulations of DNA condensation in single-molecule experiments .
 R. Cortini, A. Kornyshev, D.J. Lee and S. Leikin (2011) "Electrostatic braiding and homologous pairing of DNA double helices" Biophys. J. 101 875–84
 R. Cortini, X. Cheng, A. Kornyshev and J. Smith "The tilt-dependent potential of mean force of interacting DNA oligomers from all-atom molecular dynamics simulations", in preparation
 R. Cortini, B.R. Caré, J.-M. Victor and M. Barbi (2015) "Theory and simulations of toroidal and rod-like structures in single-molecule DNA condensation", J. Chem. Phys. 142 105102