Skeletal Muscle Atrophy Model

Abstract

Skeletal muscle atrophy occurs when there is a higher concentration of the transcription factor Forkhead box protein O1 (Foxo-1) inside the nucleus of a skeletal muscle cell than in the cytoplasm. Within a skeletal muscle cell, only dephosphorylated Foxo-1 can enter the nucleus, while only phosphorylated Foxo-1 can exit the nucleus. External stimuli such as insulin and leptomycin can activate a series of events in the cytoplasm, starting with the activation of protein kinase B (Akt) and ending with the phosphorylation of Foxo-1. Modeling the effects of these external stimuli can provide insight into how the skeletal muscle cell functions and how muscle degrades. The original model of this system was a time-dependent function with fixed parameters for the rates of phosphorylation and dephosphorylation as well as for insulin concentration. Our goal was to build on this study by shifting the fixed values of external stimuli to dynamic values and transform our time-dependent model into a dynamic model dependent on external stimuli concentration as well as time. We connected a previous model of insulin-like growth factor 1 (IGF-1) activation of Akt to our model of Akt phosphorylation of Foxo-1 in order to quantify the impact of IGF-1 on the nuclear-cytoplasmic ratio of Foxo-1. Differential equations, non-dimensional analysis, parameter optimization, and simulation conducted with MATLAB and other dynamical systems softwares were used in this study. We were able to create a functioning model that simulates the effects of IGF-1 on the nuclear-cytoplasmic ratio of Foxo-1. This research is a good foundation for future studies that may model other external stimuli nuclear translocation systems based on similar mathematical analyses.