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%\textit{Our previous findings}  In a previous work \cite{bieler2014}, we performed a systematic analysis based on time-lapse imaging of circadian cycles in dividing mammalian NIH3T3 cells. We used \revalphaYFP as a transcriptional circadian reporter and detected the times of its maximal expression, or circadian peaks. For the cell cycle we detected the cell divisions via tracking and manually validated both peak and divisions times.   The study of a large collection of these times in different conditions clearly indicated that both oscillators tick in a tightly synchronized state. Moreover, contrary to our expectations, we found that the cell cycle progression exerts a unilateral influence on the circadian clock, and not the opposite. While fruitful, this analysis in term of peak and division times, implicitly assumes that the phase goes linearly between two events, and thus neglect fast components of the phase dynamic \cite{Kralemann_2008}. In addition, we estimated the parameters of a parametric form of the coupling functions via maximum likelihood. This clearly identified an acceleration of circadian phase after the division, but the stochastic nature of the problem, the large number of parameters and the particular parametric form of the coupling functions made identifying further interactions interaction  points challenging. %\textit{Our new findings}