Reconstruction of transcription factor profiles from fluorescent protein reporter systems via dynamic optimization and T ikhonov regularization

This work presents a generally applicable technique for reconstructing transcription factor (TF) profiles from fluorescence microscopy images of green fluorescent protein reporter systems. The approach integrates dynamic optimization and a Tikhonov regularization to avoid over‐fitting caused by the highly ill‐conditioned structure of this inverse problem. The advantage that the presented approach has over existing methods is that no assumptions are made about the TF profile, the linearity, or lack thereof, of the dynamic model used, and the sampling time of the measurements. Moreover, the method allows to use discretization times for the model different from the measurement sampling times and can also deal with state constraints. The technique has been applied to both simulated and experimental data where the profile of the TFs NF‐κB and STAT3 are reconstructed. In both of the case studies, the presented approach exhibits excellent performance while fewer assumptions are needed than for existing techniques. © 2014 American Institute of Chemical Engineers AIChE J , 60: 3754–3761, 2014