In the perspective of building an open source simulation platform dedicated to the modelling of early biological molecular damages due to ionising radiation at the DNA scale, the general-purpose Geant4 Monte Carlo simulation toolkit has been recently extended with specific very low energy electromagnetic physics processes for liquid water medium. These processes - also called ''Geant4-DNA'' processes - simulate the physical interactions induced by electrons, hydrogen and helium atoms of different charge states. The present work reports on the energy deposit distributions obtained for incident electrons, protons and alpha particles in nanometre-size volumes comparable to those present in the genetic material of mammalian cells. The frequency distributions of the energy deposition obtained for three typical geometries of nanometre-size cylindrical targets placed in a spherical phantom are found to be in reasonable agreement with prior works. Furthermore, we present a combination of the Geant4-DNA processes with a simplified geometrical model of a cellular nucleus allowing the evaluation of energy deposits in volumes of biological interest.