Theoretical modelling of some spatial and temporal aspects of the mitochondrion/creatine kinase/myofibril system in muscle.

After discussing approaches to the modelling of mitochondrial regulation in muscle, we describe a model that takes account, in a simplified way, of some aspects of the metabolic and physical structure of the energy production/usage system. In this model, high-energy phosphates (ATP and phosphocreatine) and low energy metabolites (ADP and creatine) diffuse between the mitochondrion and the myofibrillar ATPase, and can be exchanged at any point by creatine kinase. Creatine kinase is not assumed to be at equilibrium, so explicit account can be taken of substantial changes in its activity of the sort that can now be achieved by transgenic technology in vivo. The ATPase rate is the input function. Oxidative ATP synthesis is controlled by juxtamitochondrial ADP concentration. To allow for possible functional 'coupling' between the components of creatine kinase associated with the mitochondrial adenine nucleotide translocase and the myofibrillar ATPase, we define parameters phi and psi that set the fraction of the total flux carried by ATP rather than phosphocreatine out of the mitochondrial unit and into the ATPase unit, respectively. This simplification is justified by a detailed analysis of the interplay between the mitochondrial outer membrane porin proteins, mitochondrial creatine kinase and the adenine nucleotide translocase. As both processes of possible 'coupling' are incorporated into the model as quantitative parameters, their effect on the energetics of the whole cell model can be explicitly assessed. The main findings are as follows: (1) At high creatine kinase activity, the hyperbolic relationship of oxidative ATP synthesis rate to spatially averaged ADP concentration at steady state implies also a near-linear relationship to creatine concentration, and a sigmoid relation to free energy of ATP hydrolysis. At high creatine kinase activity, the degree of functional coupling at either the mitochondrial or ATPase end has little effect on these relationships. However, lowering the creatine kinase activity raises the mean steady state ADP and creatine concentrations, and this is exaggerated when phi or psi is near unity (i.e. little coupling). (2) At high creatine kinase activity, the fraction of flow at steady state carried in the middle of the model by ATP is small, unaffected by the degree of functional coupling, but increases with ADP concentration and rate of ATP turnover. Lowering the creatine kinase activity raises this fraction, and this is exaggerated when psi or psi is near unity. (3) Both creatine and ADP concentrations show small gradients decreasing towards the mitochondrion (in the direction of their net flux), while ATP and phosphocreatine concentration show small gradients decreasing towards the myosin ATPase. Unless phi = psi = 0 (i.e. complete coupling), there is a gradient of net creatine kinase flux that results from the need to transform some of the 'adenine nucleotide flux' at the ends of the model into 'creatine flux' in the middle; the overall net flux is small, but only zero if phi = psi. A reduction in cytosolic creatine kinase activity decreases ADP concentration at the mitochondrial end and increases it at the ATPase end. (4) During work-jump transitions, spatial average responses exhibit exponential kinetics similar to those of models of mitochondrial control that assume equilibrium conditions for creatine kinase. (5) In response to a step increase in ATPase activity, concentration changes start at the ATPase end and propagate towards the mitochondrion, damped in time and space. This simplified model embodies many important features of muscle in vivo, and accommodates a range of current theories as special cases. We end by discussing its relationship to other approaches to mitochondrial regulation in muscle, and some possible extensions of the model.