The cellular response to ionizing radiation continues to be of significant research interest in cancer radiotherapy, and DNA is recognized as the critical target for the biologic effects of radiation. Incident particles can cause initial DNA damages through the physical and chemical interactions within a short time scale. The initial DNA damage can be repaired via different pathways available at different stages of the cell cycle. The misrepair of DNA damage results in genomic rearrangement and causes mutation and chromosome aberrations which can drive cell death. This work presents an integrated study of cellular response after irradiation of protons with energies of 0.5 -500 MeV. A model of a whole nucleus with fractal DNA geometry was implemented in TOPAS-nBio for initial DNA damage simulations. The default physics and chemistry models in TOPAS-nBio were used to describe interactions of primaries, secondaries, and the radiolysis within the nucleus. The initial DNA double strand break (DSB) yield was found to increase from 6.5 DSB/Gy/Gbp at low linear energy transfer (LET) to 21.2 DSB/Gy/Gbp at high LET. A mechanistic repair model was applied to predict the characteristics of DNA damage repair and dose response of chromosome aberrations. It was found that 90% of the DSBs are repaired within the first 24 hours and up to 11.2% of the DSBs remain unrepaired after 24 hours. The dicentric and acentric fragment yields and the probability of micronuclei formation after proton irradiation were calculated and compared with experimental results.