Understanding and predicting the dissolution kinetics of borosilicate glasses is of primary importance for nuclear waste immobilization applications. However, our ability to predict the kinetics of dissolution is limited by (i) the lack of knowledge regarding the rate-limiting mechanism of glass corrosion, (ii) uncertainties regarding the atomic structure of oxide glasses, (iii) the large number of intrinsic (e.g., glass composition) and extrinsic (e.g., solution chemistry, pH, temperature, etc.) features at play, and (iv) the vast compositional envelope accessible to borosilicate glasses. Here, based on vertical scanning interferometry (VSI), we study the stage I dissolution of borosilicate glasses under several values of pH. We demonstrate that the kinetics of the dissolution is controlled by the topology of the atomic network. We propose a topological model of dissolution, which is shown to offer realistic predictions of the activation energy of dissolution for a wide selection range of silicate glasses and crystals.