I'm not sure I understand the question. MHCI is expressed on all cells, whereas MHC II isn't. So technically, to induce MHC II, you activate the cells that express it, such as antigen presenting cells. You can upregulate MHC II on macrophages using LPS. You call also upregulate MHC I, even though they are usually pretty high already. One of the mechanisms of innate immunity is targeted apoptosis of cells that downregulates MHC I.

Thanks for the reply. So a drug's mode of action could be linked with these underlying pathway if it shows change in MHC expression at different time points.. (ex: High MHC1 at 12 hours, then MHC2 at 48 hours.)?

It's possible. Depends on the type of cell. Usually, an increase in MHC II is related to activation status of that cell. MHC I, however, it really depends on what your baseline is.

Although remember that MHC expression is only the 1st signal... and if you want to prove increased potential for T cell activation, you need to show co-stimulatory molecule upregulation too and cytokine production.

However, MHC expression doesn't necessary mean that there is an increase in antigen presentation of the antigen of interest.

So... you have to define your hypothesis and test accordingly.