Grain boundaries (GBs) can move in response to an applied stress in a plasticity mechanism known as shear coupled GB migration (SCGBM). On the nanoscale, this movement is faciliated by dislocation-like defects (“disconnections”) on the GB, which are line defects characterized by a Burgers vector b and step height h. Grain boundaries can undergo phase-like transitions, known as 'complexion transitions', in which their structure, composition, and properties change discontinuously at critical values of thermodynamic parameters such as temperature, pressure and chemical potential. In the Σ19 and Σ37 ⟨111⟩ tilt GBs of Cu, two congruent complexions varying in atomic structure, named “pearl” and “domino”,  were experimentally observed. Here, we study how the different GB structures influence the GB mobility using molecular dynamics simulations.