We present a track structure model based on the local dose deposited around heavy ion tracks to explain the cross sections for single-strand and double-strand break induction in plasmid DNA in different aqueous buffers. The model is based only on measurable quantities, namely the effect distribution for inducing strand breaks after x-ray irradiation as a function of dose, and the radial dose distribution of the heavy ion track. The effect of indirect DNA damage mediated by free radicals produced in the water surrounding the DNA is accounted for by allowing the radial dose distribution to be smeared in space by an effective target size corresponding to the squared sum of the geometrical extension of the plasmid molecule and the mean free drift path of the radicals in the buffer solution. Our calculations reproduce well the measured cross sections for single-strand and double-strand break induction in SV40 plasmid DNA in various buffer solutions both as a function of the LET and of the specific energy of the heavy ion.