Gold Nanoparticles (GNPs) have recently gained a lot of attention due to their potential benefit to improve the efficacy of X-ray radiotherapy. Owing to their high atomic number, GNPs are able to absorb higher quantities of incident radiation with respect to the surrounding tissue, producing, in particular, photoelectrons and low energy Auger electrons. These additional low energy electrons increase the local energy deposition in the region surrounding the GNP. Monte Carlo simulations play a key role in the investigation of GNP radio-enhancement and it is widely recognised that track structure physics models are the state-of-the-art for nano-scale studies. In 2016, we have developed track structure physics models for the Geant4-DNA toolkit allowing electron transport for microscopic bulk gold (Geant4_DNA_AU_2016) and we have recently improved them in the low energy domain (Geant4_DNA_AU_2018). In this paper, we report the benchmarking of these newly developed physics models when calculating the physical dose and the Dose Enhancement Factor (DEF) around a GNP. We demonstrate that Geant4_DNA_AU_2018 models give similar azimuthal distribution of two dimensional absorbed dose around a single GNP, but result in larger absorbed dose and DEF than Geant4_DNA_AU_2016 models. In parallel, we investigated the performance of a newly developed multiple scattering model in Geant4 based on the Goudsmit-Saunderson (GS) model, when used together with the electromagnetic physics models with the Geant4 Livermore condensed-history approach. Our results show that the GS model does not affect the results of the simulations when studying GNP radio-enhancement with a condensed-history approach.