Understanding of dissolution processes of borosilicate glasses can shed light on mechanisms of degradation of nuclear waste forms. We have simulated structure of sodium borosilicate glass using classical molecular dynamics and calculated reaction barriers for hydrolysis reactions on the glass surface using density functional theory. The results indicate that reaction barriers in acidic conditions for dissolution of B-O-B and B-O-Si bridges are greatly reduced compared with neutral and basic conditions. We suggest barriers for B-O-B and B-O-Si hydrolysis are considerably lower than for Si-O-Si hydrolysis in acidic and neutral conditions, but less so in basic conditions. Our results suggest that at the initial stage, B-O-Si hydrolysis might contribute to the change of dissolution mechanism observed experimentally at increasing pH values.