One possible explanation for this is southwest injury or sun scald. The idea is that sudden changes in temperature can destroy cells just under the bark. The sun is quite often involved in this effect due to radiated heat. The result is that the cambium layer is destroyed but not all around the trunk or branch, and good tissues can spread back over the wound to repair it but leaving a somewhat disfigured visible effect. Some tree species are affected more than others including mulberry.
In your pictures it is the tops of the branches that are affected. This could be caused by overhead sun at a time when the tree is flush with sap, the sun is strong and changes take place so rapidly the tree can't keep up. Trunks are more often subject to this because they are unprotected, but branches further up in the tree are often hidden from the direct sun.
Measures to protect the tree from this effect are laborious, perhaps painting exposed branches white to reflect the sun's heat. The tree will be able to repair itself over time, but there is a risk in horizontal branches that the top sides will be weakened and subject to breakage in high winds for example. Continuing care is to ensure that the canopy is as full and compact as possible, an even suit of armour against the varying effects of the strong sun.