The Mader model of muscle energy metabolism simulates key metabolic exercise phenomena

Abstract

Energy metabolism matches adenosine triphosphate (ATP) resynthesis to hydrolysis even during abrupt transitions such as exercise onset. In 1984, Alois Mader proposed a mechanistic model that captures this regulation through 33 coupled differential equations linking oxidative phosphorylation, glycolysis, and the phosphocreatine shuttle via adenosine diphosphate (ADP), phosphate, and pH feedback. Despite its potential, broader adoption has been limited by closed-source implementations and key publications available only in German. Here, we present MetaboliSim, an open-source software tool that simulates muscle energy metabolism in a virtual human parameterized by four physiological inputs: V̇O 2 max (oxidative capacity), v Lamax (glycolytic capacity), body mass, and active muscle mass. Using MetaboliSim, we test Mader’s equations against 10 experimentally established phenomena of exercise metabolism, including ATP homeostasis under fatigue, transient pH alkalinization, glycogen-dependent lactate thresholds, intensity-dependent fat oxidation, the V̇O 2 slow component, and work-rate-dependent exhaustion, without altering any equation or constant within the model. Mader’s model qualitatively reproduces all 10 phenomena, generating similarly shaped response curves; absolute values depend on individual parameterization rather than being universally matched. The characteristic inverted-U of fat oxidation and the exercise intensity-dependent V̇O 2 kinetics, for example, both emerge from the same equation system. A Sobol sensitivity analysis (S01) reveals a calibration hierarchy: V̇O 2 max and body mass drive power predictions; v Lamax and buffer capacity drive metabolite predictions. That a compact, 40-year-old equation system accounts for this breadth of metabolic phenomena suggests that a small number of regulatory feedback loops may suffice to explain a wide range of metabolic responses to exercise. MetaboliSim is freely available to enable independent testing, empirical calibration, and refinement.

The authors' abstract, as published at the source. Proceedings of the National Academy of Sciences, 2026 · DOI ↗