Mathematical Modeling of Nuclear Trafficking of FOXO Transcription Factors

Nuclear cytoplasmic flux of Foxo transcription factors is paramount in cellular gene regulation. For example, excluding Foxo from skeletal muscle nuclei is necessary to avoid muscle wasting through elevated protein breakdown. Constructing a mathematical model of the signaling process leading to alteration of Foxo nuclear cytoplasm ratio is useful in predicting and interpreting such ratio changes. In this chapter we derive a general mathematical model for nuclear cytoplasmic flux. We apply this model to Foxo flux and take advantage of rapid phosphorylation approximation and conservation conditions to reduce the Foxo flux model. We constrain our model with data from mouse skeletal muscle with applied IGF. This procedure provides an example of what might be called the central approach of mathematical modeling: The cycling of a biological question through mathematical formulation and back to biological interpretation.