I have 4*10 6 cells which I collected by centrifugation. Now I want to do protein extraction from it. What should be the ratio of cells: buffer to get a good quantity of protein?
This partly depends on the expression level of your protein - high expression means that you can have more buffer to cells and vice versa for low expression.
Ideally, you want to run 30-40 ug total protein if you are running a Western blot. As a benchmark, most places recommend lysing 1*10^6 cells in 100 ul RIPA buffer - therefore, you will need about 400 ul. You can then find the total protein concentration via a Bradford assay and load 30-40 ug protein. If your bands are too faint, then your protein is probably lowly expressed and you will need to use less volume. If your bands are overexposed, then you will simply need to dilute your samples.
The lowest I've gone with my ratios was 50ul of RIPA for 1.2 * 10^6 Hela cells. I needed really concentrated samples as my protein was not expressed well. It worked beautifully.
Good luck!
PS, I should add that in addition to adding RIPA, my cells went through a single freeze-thaw at -70C.