Which condition will prevent any migration of proteins across an electrophoretic support medium?

The condition that will prevent any migration of proteins across an electrophoretic support medium is the loss of contact with the buffer. The buffer solution provides the necessary ions that carry the electric current during electrophoresis. It ensures that the protein molecules are in a conductive medium where they can migrate in response to the applied electric field. If there is a loss of contact with the buffer, the proteins will no longer be able to migrate because they are not in an environment that allows for the movement of ions and the flow of current.

In contrast, while using too high a voltage or excessive current can affect the quality of the separation and may cause overheating or distortions in the bands, it does not completely halt the migration of proteins. Evaporation of solvent can also influence the concentration of the buffer and the overall setup, but it does not entirely prevent migration as long as the proteins remain in contact with some liquid medium. Therefore, loss of contact with the buffer is the critical condition that completely stops protein migration.