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The oxidation of dimethyl sulfide (DMS) is key for the natural sulfate aerosol formation and its climate impact. Multiphase chemistry is an important oxidation pathway but neglected in current chemistry-climate models. Here, the DMS chemistry in the aerosol-chemistry-climate model ECHAM-HAMMOZ is extended to include multiphase methane sulfonic acid (MSA) formation in deliquesced aerosol particles, parameterized by reactive uptake. First simulations agree well with observed gas-phase MSA concentrations. The implemented formation pathways are quantified to contribute up to 60% to the sulfate aerosol burden over the Southern Ocean and Arctic/Antarctic regions. While globally the impact on the aerosol radiative forcing almost levels off, a significantly more positive solar radiative forcing of up to 0.1 W m^-2 is computed in the Arctic (>60°N). The findings imply the need of both further laboratory and model studies on the atmospheric multiphase oxidation of DMS.