Determining transcription factor profiles from fluorescent reporter systems involving regularization of inverse problems

The availability and quality of experimental data pose challenges for identifying the role of individual proteins in signal transduction pathways. To address this issue, this paper formulates and solves an inverse problem to determine the dynamics of transcription factors, i.e., one important class of proteins, from fluorescence intensity measurements of green fluorescent protein (GFP) reporter systems. In the presented approach, a model describing transcription and translation of GFP is discretized and concentrations of transcription factor are estimated at discrete time points. Unlike previous works, this approach has no restrictions with regard to a particular shape of the profiles. However, the resulting inverse problem is ill-conditioned and requires the use of regularization techniques. Two regularization methods - truncated singular value decomposition and Tikhonov regularization - are investigated in this work and the characteristics of the results obtained are discussed in detail.