Mathematical modeling reveals modulation of both nuclear influx and efflux of Foxo1 by the IGF-I/PI3K/Akt pathway in skeletal muscle fibers.

Foxo family transcription factors contribute to muscle atrophy by promoting transcription of the ubiquitin ligases muscle-specific RING finger protein and muscle atrophy F-box/atrogin-1. Foxo transcriptional effectiveness is largely determined by its nuclear-cytoplasmic distribution, with unphosphorylated Foxo1 transported into nuclei and phosphorylated Foxo1 transported out of nuclei. We expressed the fluorescent fusion protein Foxo1-green fluorescent protein (GFP) in cultured adult mouse flexor digitorum brevis muscle fibers and tracked the time course of the nuclear-to-cytoplasmic Foxo1-GFP mean pixel fluorescence ratio (N/C) in living fibers by confocal imaging. We previously showed that IGF-I, which activates the Foxo kinase Akt/PKB, caused a rapid marked decline in N/C, whereas inhibition of Akt caused a modest increase in N/C. Here we develop a two-state mathematical model for Foxo1 nuclear-cytoplasmic redistribution, where Foxo phosphorylation/dephosphorylation is assumed to be fast compared with nuclear influx and efflux. Cytoplasmic Foxo1-GFP mean pixel fluorescence is constant due to the much larger cytoplasmic than nuclear volume. Analysis of N/C time courses reveals that IGF-I strongly increased unidirectional nuclear efflux, indicating similarly increased fractional phosphorylation of Foxo1 within nuclei, and decreased unidirectional nuclear influx, indicating increased cytoplasmic fractional phosphorylation of Foxo1. Inhibition of Akt increased Foxo1 unidirectional nuclear influx, consistent with block of Foxo1 cytoplasmic phosphorylation, but did not decrease Foxo1 unidirectional nuclear efflux, indicating that Akt may not be involved in Foxo1 nuclear efflux under control conditions. New media change experiments show that cultured fibers release IGF-I-like factors, which maintain low nuclear Foxo1 in the medium. This study demonstrates the power of quantitative modeling of observed nuclear fluxes.