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In silicon and other materials with a high Peierls potential, dislocation motion takes place by nucleation and propagation of kink pairs. The rates of these unit processes are complex unknown functions of interatomic interactions in the dislocation core, stress and temperature. This work is an attempt to develop a quantitative physical description of dislocation motion in silicon based on understanding of the core structure and the energetics of core mechanisms of mobility. Atomistic simulations reveal multiple and complex kink mechanisms of dislocation translation; however, this complexity can be rationalized through the analysis of a straight kink-free dislocation, based on symmetry-breaking arguments. Further reduction is achieved by observing that the energetics of kink mechanisms is scaled by a single parameter, the energy required to break a bond in the core. To obtain accurate values of this energy we perform density functional calculations that lead us to conclude that the low mobility of the 30° dislocation results from its high bond-breaking energy. Armed with the knowledge of kink mechanisms, we develop a kinetic Monte Carlo model that makes direct use of the atomistic data as the material-defining input and predicts the dislocation velocity on the length and time scales accessible to experiments. This provides the connection between the atomistic aspects of the dislocation core and the mobility behaviour of single dislocations.