THEORETICAL MODELING OF SOME SPATIAL AND TEMPORAL ASPECTS OF THE MITOCHONDRION CREATINE-KINASE MYOFIBRIL SYSTEM IN MUSCLE

After discussing approaches to the modelling of mitochondrial regulati on in muscle, we describe a model that takes account, in a simplified way, of some aspects of the metabolic and physical structure of the en ergy production/usage system. In this model, high-energy phosphates (A TP 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 subs tantial changes in its activity of the sort that can now be achieved b y transgenic technology in vivo. The ATPase rate is the input function . Oxidative ATP synthesis is controlled by juxtamitochondrial ADP conc entration. To allow for possible functional 'coupling' between the com ponents of creatine kinase associated with the mitochondrial adenine n ucleotide translocase and the myofibrillar ATPase, we define parameter s phi and psi that set the fraction of the total flux carried by ATP r ather than phosphocreatine out of the mitochondrial unit and into the ATPase unit, respectively. This simplification is justified by a detai led analysis of the interplay between the mitochondrial outer membrane porin proteins, mitochondrial creatine kinase and the adenine nucleot ide translocase. As both processes of possible 'coupling' are incorpor ated into the model as quantitative parameters, their effect on the en ergetics of the whole cell model can be explicitly assessed. The main findings are as follows: (1) At high creatine kinase activity, the hyp erbolic relationship of oxidative ATP synthesis rate to spatially aver aged ADP concentration at steady state implies also a near-linear rela tionship to creatine concentration, and a sigmoid relation to free ene rgy of ATP hydrolysis. At high creatine kinase activity, the degree of functional coupling at either the mitochondrial or ATPase end has lit tle effect on these relationships. However, lowering the creatine kina se activity raises the mean steady state ADP and creatine concentratio ns, 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, u naffected 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 phi or psi is near unity. (3) Both creatine and ADP concentrations show small gr adients decreasing towards the mitochondrion (in the direction of thei r net flux), while ATP and phosphocreatine concentration show small gr adients decreasing towards the myosin ATPase. Unless phi = psi approxi mate to 0 (i.e. complete coupling), there is a gradient of net creatin e kinase flux that results from the need to transform some of the 'ade nine 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 conc entration at the mitochondrial end and increases it at the ATPase end. (4) During work-jump transitions, spatial average responses exhibit e xponential kinetics similar to those of models of mitochondrial contro l that assume equilibrium conditions for creatine kinase. (5) In respo nse 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 sp ecial cases. We end by discussing its relationship to other approaches to mitochondrial regulation in muscle, and some possible extensions o f the model.