Transient kinetics of thermodynamic buffering

The transient response of mitochondrial ATP production towards perturbations was studied by analyzing the trajectories leading from arbitrary initial conditions of the adenine nucleotide pool to the final steady state. These trajectories were calculated from differential equations based on linear relations between flows and thermodynamic forces of the adenylate kinase system including oxidative phosphorylation. The motion of the system along the trajectories consists of two phases: (1) a rapid phase leading from initial states to a common relaxation curve; and (2) a slow phase leading along the relaxation curve to the final steady state. The first phase corresponds to a motion close to the loci of constant adenylic energy charge. In line with this observation is the finding that the energy charge is a constant of motion of the adenylate kinase reaction. The second phase corresponds to a motion along a relaxation curve characterized by minimal Lyapunov exponents in the concentration space of the adenine nucleotides. Thus, both phases of the transient kinetics can be approximated in terms of thermodynamic functions to a high degree of precision. Incubations with isolated rat liver mitochondria were in excellent agreement with the theoretical predictions. In summary, these studies show that the adenylate kinase system not only optimizes the efficiency of oxidative phosphorylation through thermodynamic buffering but, in addition, also deeply influences the transient response of the whole system.