Regulation of the energy metabolism of the muscle – a modeling approach

The present paper is an excerpt (chapter 4) from the monograph “Laktat: Stoffwechselgrundlagen, Leistungsdiagnostik, Trainingssteuerung“ ("Lactate: Metabolic Basics, Performance Diagnostics, Training Control") (2022) by Hermann Heck, Ulrich Bartmus and Volker Grabow. 

Chapter 4 essentially contains a detailed description of the so-called Mader model of muscular energy metabolism, which was first described in Alois Mader's postdoctoral thesis in 1984. Unfortunately, the book is only available in German. The authors would like to thank Springer-Verlag for their permission to provide an English version of the chapter to those interested in the subject.

Chapter 4 contains the following core messages:
Regulation of muscular energy metabolism is essentially dependent on the state of the ATP/PCr system (ATP, PCr, P_i) and the adenylic acid system (ATP, ADP, AMP). High concentrations of ATP inhibit ATP synthesis, increasing concentrations of ADP, AMP and Pi increase ATP synthesis by activating enzymes of citrate cycle and respiratory chain as well as glycogenolysis and glycolytic enzymes

• As a result of different activation characteristics of oxidation and glycolysis in relation to the free ADP concentration of the muscle, different load dependent proportions of glucose and fatty acids are used as substrates of ATP resynthesis. At low loads, glycolytic rate and therefore lactate formation rate are lower than the load-related demand of substrate of the citrate cycle. This deficit is covered by activating the breakdown of fatty acids. However, as the activation characteristic curve of glycolysis is steeper than that of oxidation, the difference decreases with increasing load and ultimately reaches the point at which the lactate formation rate and oxidative elimination rate are equal (crossing point, limit lactate steady state).

• The quasi-exponential increase in blood lactate concentration with increasing exertion (ramp-shaped or gradually increasing) can therefore be explained by differences in activation of glycolysis and oxidative ATP resynthesis. Increases in lactate do not necessarily require a muscular oxygen deficiency. Like numerous other factors, a muscular oxygen deficiency merely has a modulating function on the lactate response.

The simulation of energy metabolism using the Mader model enables to demonstrate effects of differences in V̇O₂max and ν_Lamax as well as constants of the mathematical description on time-dependent lactate responses. For example, the following findings can be substantiated:

• the increase in blood lactate without oxygen deficiency in the muscles

• the occurrence of a maximum lactate steady state (MLSS) as the beginning of the partial anaerobic-lactic energy metabolism of the muscle cell providing the biochemical basis of numerous concepts of the lactate threshold.

• the right or left shift of the lactate performance curve as a result of the increase or decrease in maximum oxygen uptake

• the right or left shift of the lactate performance curve with unchanged maximum oxygen uptake by reducing or increasing the maximum glycolytic rate

• the increase or decrease in the relative maximum lactate steady state (%V̇O₂max) as a function of maximum oxygen uptake and maximum lactate formation rate.

The two-compartment model includes muscle plus extra-muscular lactate space. It allows the analysis of muscular energy metabolism in a closed control loop, additionally including loads that are above the V̇O₂max. It simulates not only the muscle lactate but also the time- and load-dependent blood lactate concentration.