Mathematical Modeling of Skeletal Muscle Focal Adhesion Kinase Signaling in Response to Contraction

Force is a stimulus of resistance exercise (RE) that prompts adaptations to muscle size. Force acts at the molecular level on mechanotransducers such as focal adhesion kinase (FAK), which is a tyrosine kinase that undergoes a conformational change in response to force and subsequently activates a signaling cascade that controls the rate of protein synthesis. The dynamics by which FAK signaling transduces mechanical forces into chemical signals to induce hypertrophy are unclear. PURPOSE: The purpose of this study was to develop and analyze a mathematical model of skeletal-muscle FAK signaling in response to contractions. METHODS: The model was expressed as a system of ordinary differential equations incorporating signaling proteins involved in the control of protein translation (the FAK/ERK1/2/TSC2 axis). Intracellular biochemical reactions were represented by mass-action or Michaelis-Menten kinetics. We constructed the model by amalgamating a published model of FAK signaling [Zhou et al. (2015) PLoS Comput Biol] and ERK1/2 signaling [Hatakeyama et al. (2003) Biochem J]. We calibrated the kinetic parameters of the Zhou et al. and Hatakeyama et al. models to reflect skeletal muscle cells. RESULTS: Our model outputs qualitatively agreed with published time-course data for FAK, ERK1/2, and TSC2 following the simulation of muscle force contraction profiles. Specifically, we simulated thirty contraction cycles featuring 15-pN contractions and 3 sec per contraction followed by 7 sec of rest [Ato et al. (2016) Physiol Rep], which led to increased ERK1/2 signaling lasting ~3.5 hrs. Parameter sensitivity analysis determined that the model was most sensitive to parameters that described the force-induced rate of conformational change for FAK. We also simulated various force inputs for the contraction protocol described above and observed that ERK1/2 signaling was responsive to forces between 8-15 pN, achieving a plateau for higher forces. CONCLUSION: Our model provides a working quantitative hypothesis of the dynamics of protein translational control in skeletal muscle induced by mechanical factors. Going forward we will use the model to study the effects that different RE variables (repetitions, sets, loads, rest, etc.) have on FAK signaling dynamics by simulating different contraction profiles.

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