Serum starvation of cells before treatment removes the knowns and the unknowns, reduces analytical interference, and provides more reproducible experimental conditions. Moreover, it reduces basal cellular activity and makes the population of proliferating cells more homogenous, since they withdraw from the cell cycle to enter the quiescent G0/G1 phase.
Serum starvation therefore helps to induce cell cycle synchronization. Please note that serum starvation for too long will also lead to reduced cell survival and increased apoptosis.
So, you could use 0.5% - 1% serum in culture medium so that the cells remain healthy but do not proliferate.