Quantitative analysis in Förster resonance energy transfer (FRET) experiments in live cells for protein interaction studies is still a challenging issue. In a two-component system (FRET and no FRET donor species), fitting of fluorescence lifetime imaging microscopy (FLIM) data gives the fraction of donor molecules involved in FRET (f(D)) and the intrinsic transfer efficiency. But when fast FLIM acquisitions are used to monitor dynamic changes in protein-protein interactions at high spatial and temporal resolutions in living cells, photon statistics and time resolution are limited. In this case, fitting procedures are not reliable, even for single lifetime donors. We introduce the new concept of a minimal fraction of donor molecules involved in FRET (mf(D)), coming from the mathematical minimization of f(D). We find particular advantage in the use of mf(D) because it can be obtained without fitting procedures and it is derived directly from FLIM data. mf(D) constitutes an interesting quantitative parameter for live cell studies because it is related to the minimal relative concentration of interacting proteins. For multi-lifetime donors, the process of fitting complex fluorescence decays to find at least four reliable lifetimes is a near impossible task. Here, mf(D) extension for multi-lifetime donors is the only quantitative determinant. We applied this methodology for imaging the interaction between the bromodomains of TAF(II250) and acetylated histones H4 in living cells at high resolution. We show the existence of discrete acetylated chromatin domains where the minimal fraction of bromodomain interacting with acetylated H4 oscillates from 0.26 to 0.36 and whose size is smaller than half of one micron cube. We demonstrate that mf(D) by itself is a useful tool to investigate quantitatively protein interactions in live cells, especially when using fast FRET-FLIM acquisition times.