The kinetics of a chemical model of Ca 2+ transport and coupled ATPase activity in sarcoplasmic reticulum membranes were solved for the transient-state of simulated reactions, using a numerical integration procedure. The simulation conditions reproduced in vitro experiments using either fragmented membranes or vesicles with Ca -'+ accumulating ability. The results yielded the concentrations of all the ligands and intermediates of the enzymatic cycle as a function of the reaction time. These results were applied to calculations of several thermodynamic variables: (1) the step by step profile of the standard free energy change of the cycle. (2) The step by step profile of the actual free energy change of the cycle, and its evolution with the reaction time. (3) The separate contributions of ATP hydrolysis and Ca 2+ transport to the overall free energy change along the reaction. (4) The dependence of the velocity of the free energy change with the reaction time. (5) The efficiency of the transport system, and its change with the reaction time. (6) The separate contributions of the Ca 2+ gradient and some enzymatic intermediates as free energy stores.
The main findings are: (1) the step by step diagrams of the free energy change calculated from the results of the kinetic analysis better describe the thermodynamic profile of the cycle than previously reported diagrams of the standard free energy and basic free energy changes. The relative contribution of each partial step to the driving force of the whole reactions, as well as their changes upon the advancement of the reactions, are derived from the diagrams. (2) Free energy yielded by ATP hydrolysis is stored by the system, not only as a Ca 2+ gradient, but also as enzymatic intermediates of the reaction. The progressive increase of both free energy pools upon the advancement of the reaction is quantitated.