Modeling the steady-state behavior of the Ca2+ -Mg2+ -ATPase pump of sarcoplasmic reticulum

A FORTRAN computer program capable of calculating the steady-state behavior of the Ca2+ -Mg2+-ATPase pump of skeletal sarcoplasmic reticulum under all conditions of reactant and product concentrations is described. The model describes the behavior of the enzyme in terms of occupation of three binding sites: (a) a translocator site which can bind Ca2+, K+, H+, or Mg2+, (b) an ATP/ADP binding site, and (c) a phosphorylation and phosphate binding site. The translocator site can move across the membrane in the Ca2+-laden and K+ + H+-laden form, thereby accomplishing Ca2+ for K+ + H+ countertransport. The rate constants for ion binding and the translocation reactions vary as a function of translocator orientation, ATP and ADP occupancy, phosphorylation, and phosphate binding. Rate constants for the binding and the reactant and product concentrations and association reactions and other transformations between states of the enzyme are entered and the computer program solves for the steady-state concentrations of all states of the enzyme and for the turnover number of the enzyme. The program contains a matrix of differential equations for creation and destruction of all states of the enzyme using the steady-state assumption together with the rule of conservation of the total enzyme. The matrix of equations and states is solved by Gaussian elimination. The program presents the distribution of enzyme states in histogram fashion and is capable of presenting the concentration of a particular state or the rate of turnover as a function of any of the reactant or product concentrations. Three demonstrations of the utility of the program and predictive power of the model are given.