Ionizing radiation induces a variety of DNA lesions, including single and double strand breaks. Large energy deposition precisely localized along the ion track that occurs in the case of heavy ion irradiation can lead to complex types of DNA double strand breaks in exposed biological material. The formation of nuclear double strand breaks triggers phosphorylation of histone H2AX, which can be microscopically visualized as foci in the γ-H2AX assay. Studies with a carbon ion beam are being carried out at the Heavy Ion Laboratory of the University of Warsaw. The γ-H2AX assay as a method of measuring the biological response of cells irradiated with 12C ions as well as the frequency cluster size distributions obtained in the nanodosimetry experiment at HIL will be presented.