Mathematical Modeling of Mammalian Target of Rapamycin following Leucine Ingestion

Abstract

The mammalian target of rapamycin complex 1 (mTORC1) is a regulatory protein for several cell processes and is critical in the control of muscle protein synthesis and hence muscle size. Its activity is primarily regulated by nutrition (i.e., protein) and growth factors (i.e., insulin); however, how the whole-body dynamics of these factors translate into protein translational signaling in skeletal muscle cells is poorly understood. PURPOSE: The purpose of this study was to develop and analyze a simple mathematical model of the signaling controlling protein translation in human skeletal muscle following leucine ingestion. METHODS: The model was expressed as a system of ordinary differential equations (ODEs) incorporating the signaling proteins involved in the control of protein translation (e.g., IR/PI3K/AKT/mTOR axis). Intracellular biochemical reactions were represented by mass-action kinetics. We constructed the model by modifying amalgamated published models of mTOR signalling [Pezze et al. (2012) Sci Signal] and skeletal-muscle leucine kinetics [Tessari et al. (1995) Am J Physiol]. The Pezze model was specific to HeLa cells, so we calibrated the kinetic parameters using signaling data from human skeletal muscle following leucine ingestion. The ODEs were solved using the ODE23s solver in MATLAB. RESULTS: The model outputs qualitatively agreed with published time-course data for plasma leucine, plasma insulin, and phosphorylation of AktS473, mTORC1S2448, and p70S6KT389 following the ingestion of a single leucine bolus or multiple, pulsatile leucine doses. Parameter sensitivity analysis determined that mTORC1 activity was most sensitive to total mTORC1 concentration and highly sensitive to the rate of leucine transamination to alpha-ketoisocaproate. CONCLUSION: Our model represents a working quantitative hypothesis of the dynamics of protein translational control in skeletal muscle by nutritional and hormonal factors.