Mathematical modeling of intracellular transport processes and the creatine kinase systems: a probability approach

A probability approach was used to describe mitochondrial respiration in the presence of substrates, ATP, ADP, Cr and PCr. Respiring mitochondria were considered as a three-component system, including: 1) oxidative phosphorylation reactions which provide stable ATP and ADP concentrations in the mitochondrial matrix; 2) adenine nucleotide translocase provides exchange transfer of matrix adenine nucleotides for those from outside, supplied from medium and by creatine kinase; 3) creatine kinase, starting these reactions when activated by the substrates from medium. The specific feature of this system is close proximity of creatine kinase and translocase molecules. This results in high probability of direct activation of translocase by creatine kinase-derived ADP or ATP without their leak into the medium. In turn, the activated translocase with the same high probability directly provides creatine kinase with matrix-derived ATP or ADP. The catalytic complexes of creatine kinase formed with ATP from matrix together with those formed from medium ATP provide activation of the forward creatine kinase reaction coupled to translocase activation. Simultaneously the catalytic complexes of creatine kinase formed with ADP from matrix together with those formed from medium ADP provide activation of the reverse creatine kinase reaction coupled to translocase activation. The considered probabilities were arranged into a mathematical model. The model satisfactorily simulates the available experimental data by several groups of investigators. The results allow to consider the observed kinetic and thermodynamic irregularities in behavior of structurally bound creatine kinase as a direct consequence of its tight coupling to translocase.