Reconstruction of Transcription Factor Profiles via Dynamic Optimization and Tikhonov Regularization

This work presents a generally-applicable technique for reconstructing transcription factor profiles from fluorescence microscopy images of GFP 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 transcription factor 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 transcription factors NF-kB 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.