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Fixation has two functions. First, it preserves the cells by preventing lysis and autolytic degradation. Second, it makes the cells permeable and thus their DNA accessible to impermeant DNA-binding dyes.
Precipitating fixatives (methanol, ethanol, acetone) are preferred for single color cell cycle staining. Disadvantages include some epitpoes are destroyed and there is more cell aggregation.
Crosslinking fixitves (-aldehydes) can have a harmful effect on stoichiometry of DNA staining, but fewer epitpoes are destroyed and less cell aggregation is induced. Although inferior in terms of stabilization & preservation of low molecular weight constituents within the cell, they adequately stabilize undamaged DNA.
You will need to choose the best fixation method for your application. Or you may use a cell-permeant dye such as the Vybrant DyeCycle stains or UV-excited Hoechst 33342 for cell cycle in living cells.