Detailed-history Monte-Carlo code is used to study the energy deposition from proton and alpha particle tracks at the sub-cellular level. Inelastic cross sections for both the vapour and liquid phases of water have been implemented into the code in order to explore the influence of non-linear density effects associated with the condensed-phase cellular environment. Results of energy deposition and its straggling for 0.5 to 5 MeV amu(-1) protons and alpha particles traversing or passing near spherical volumes of 2-200 nm in diameter relevant to DNA- and chromosome-size targets are presented. It is shown that the explicit account of delta-ray transport reduces the dose by as much as 10-60%, whereas stochastic fluctuations lead to a relative uncertainty ranging from 20% to more than 100%. Protons and alpha particles of the same velocity exhibit a similar delta-ray effect, whereas the relative uncertainty of the alphas is almost half that of protons. The effect of the phase is noticeable (10-15%) mainly through differences on the transport of delta-rays, which in liquid water have higher penetration distances. It is expected that the implementation of such results into multi-scale biophysical models of radiation effects will lead to a more realistic predictions on the efficacy of new radiotherapeutic modalities that employ either external proton beam irradiation or internal alpha-emitting radionuclides.