The way transcription factors regulate the activity of their target genes is of much interest. Several authors have recently used model based computational approaches to infer concentrations of transcription factor proteins from high throughput gene expression data ([1-3,6-7]. Here, I present an approach explicitly formulated to model periodic biological phenomena, and a least squares framework for parameter estimation of such a model. Such a computational strategy can be used to infer levels of transcription factor activities at the protein level using genes that are regulated by single transcription factors, and then to decipher “transcriptional logic” of genes under regulation by the comboined actions of multiple transcription factors.