When 4 cells are all touching each other, the maximum sum of their digits is 45. So, when for example each cell has a sum of 11 (so they have a total sum of 44) all digits except the 1 should be in those 4 cells.

When 2 touching cells both have a sum of 4 then one cell should contain a 4 and the other a 1 and a 3. That means that all cells that touch both cells can't contain a 1, 3 and 4.