Whether it is in radiobiology to identify DNA lesions or in medicine to adapt the radiotherapeutic protocols, a detailed understanding of the radiation-induced interactions in living matter is required. Monte Carlo track-structure codes have been successfully developed to describe these interactions and predict the radiation-induced energy deposits at the nanoscale level in the medium of interest. In this work, the quantum-mechanically based Monte Carlo track-structure code TILDA-V has been used to compute the slowing-down of protons in water and DNA. Stopping power and range are then reported and compared with existing data. Then, a first application of TILDA-V to cellular irradiations is also reported in order to highlight the absolute necessity of taking into account a realistic description of the cellular environment in microdosimetry.