Equilibrium and steady state thermodynamics of active transport systems studied on simple models simulating Ca2+...

Equilibrium and steady state conditions of primary active transport systems are analyzed in models simulating well known characteristics of calcium transport through sarcoplasmic reticulum membranes. The model for the equilibrium simulations is a closed system with two compartments and a vectorial chemical reaction coupling Ca transport and ATP breakdown. The chemical potential difference for Ca (delta mu Ca) is calculated as a function of the total amount of Ca (Cat) and nucleotides (Nt) in the system. Results are obtained by successive approximations along the thermodynamic pathway of the reaction, up to minimizing free energy of the system, since the solution of the explicit equations cannot be obtained with computers of current precision for data within physiological ranges. delta mu Ca and [Caout] are extremely dependent on Cat and Nt for certain combinations of the variables, i.e. [Caout] can be raised from 10(-8) to 10(-6) M when Cat varies from 0.998 to 1.002 mM, therefore, the running force of the spontaneous reaction is largely shifted by tiny changes in the parameters of the system. For steady state simulations, ATP supply to the system, ADP and Pi drainage, and Ca diffusion through the barrier, are assumed. Again, conditions within physiological ranges can be found where tiny changes in Cat, the rate of ATP supply, diffusion, the ratio between the volumes of the compartments, or a relative uncoupling between the transport and hydrolytic reactions, largely shifts delta mu Ca and [Caout], thus making the steady state highly unstable and therefore well designed to operate as an amplifier of physiological signals. The equilibrium model describes some physicochemical characteristics of the system; the steady state model is more useful to simulate several physiological situations.