The mono-exponential pattern of phosphocreatine recovery after muscle exercise is a particular case of a more complex behaviour

A mathematical model is proposed showing that the mono-exponential recovery of phosphocreatine (PCr) after exercise is an approximation of a more complex pattern, which is identified by a second-order differential equation. The model predicts the possibility of three different patterns of PCr recovery: bi-exponential, oscillatory damped, and critically damped; the mono-exponential pattern being a particular case of the functions which are solutions of the differential equation. The model was tested on a sample of recovery data from 50 volunteers, checking whether the recovery patterns predicted by the model lead to a significant improvement of fit (IF) compared with the mono-exponential pattern. Results show that the IF is linked to pH. Bi-exponential solutions showed an IF in the pH range 6.65-6.85, and the oscillatory solutions at pH>6.9. Critically damped solutions displayed a poor IF. Oscillation frequencies found in the oscillatory recoveries increase at increasing pH. These results show that pH has a pivotal role on the pattern of PCr recovery and implications on the regulation of oxidative phosphorylation are discussed. (C) 2004 Elsevier B.V. All rights reserved.