The remarkable ability of tardigrades to withstand a wide range of physical and chemical extremes has attracted a considerable interest in these small invertebrates, with a particular focus on the protective roles of proteins expressed during such conditions. The discovery that a tardigrade-unique protein named Dsup (damage suppressor) protects DNA from damage produced by radiation and radicals, has raised expectations concerning its potential applications in biotechnology and medicine. We present in this paper what might be dubbed a "computational experiment" on the Dsup-DNA system. By means of molecular modelling, calculations of electrostatic potentials and electric fields, and all-atom molecular dynamics simulations, we obtained a dynamic picture of the Dsup-DNA interaction. Our results suggest that the protein is intrinsically disordered, which enables Dsup to adjust its structure to fit DNA shape. Strong electrostatic attractions and high protein flexibility drive the formation of a molecular aggregate in which Dsup shields DNA. While the precise mechanism of DNA protection conferred by Dsup remains to be elucidated, our study provides some molecular clues of their association that could be of interest for further investigation in this line.