A dynamical system for the IGF1-AKT signaling pathway in skeletal muscle adaptation

Physical activity produces a change in skeletal-muscle size by activating synthesis or degradation of protein, which are outcomes of stimulating the IGF1-AKT signaling pathway. In this work, we propose a mathematical model that predicts the variation in muscle size under different activity conditions. The IGF1-AKT pathway was modeled using its 4 main molecules as variables in a dynamical system. We checked the stability of the system; we defined exercise training as a function of intensity, duration, and frequency; and we tested the model under four scenarios: first, we considered the daily low-intensity activity that should not promote atrophy nor hypertrophy (steady state); second, we simulated the effects of physical therapy in spinal cord injury patients (atrophy); third, we simulated exercise training in healthy subjects (hypertrophy); and fourth, we considered the effects of suspending a training program in healthy subjects (recovery after hypertrophy). Results showed that: protein synthesis and degradation are inactive, thus the size of the muscle stays stable in the first scenario; the muscle decreases only 10% of its initial size after 84 days of therapy every two days in the second scenario; training frequency produces rapid hypertrophy (11% after 25 days) when training every day, to no hypertrophy when training every 5 days in the third scenario; and a reduction of 50% the gain of the training program in the fourth scenario. By comparing our results to experimental reports, we found a remarkable agreement; therefore, our model is suitable for the development of training and therapeutic protocols.