Study of the Cooperativity of Calcium Binding in Calbindin D9k using 2D Replica-Exchange Umbrella Sampling

Abstract

Department of Biochemistry and Molecular Biology, The University of Chicago, IL 60637 Argonne National Laboratory, Argonne, IL 60439 Calbindin D9k, a small protein possessing a pair of EF-hands that binds two calcium ions in a cooperative fashion, is chosen as a model system for studying the molecular mechanism of cooperativity.1 Binding is characterized in terms of a potential of mean force (PMF) as a function two variables: the distance r between the ion, and the binding pocket, and the root-mean-square deviation (RMSD) of the conformation of the EF-hand relative to its ion-bound structure. The PMF is calculated using a novel two-dimensional replica-exchange molecular dynamics (MD) umbrella sampling scheme, which is developed and implemented in the program CHARMM to increase the configuration space sampling. Using 2048 replicas on Blue Gene/P, the 2D-PMF/REMD calculation for the binding the second calcium ion converges within 800 ps, with an exchange probability of 30%. In contrast, standard umbrella sampling PMF/MD simulations without replica-exchange did not converge, even after 1.2 ns. The absolute binding free energy of a second ion to a singly occupied calbindin calculated from the 2D-PMF following the statistical mechanical formulation of noncovalent association2 is −9.4 kcal/mol, in excellent agreement with the experimental value3. The 2D-PMF/REMD simulations will be extended to provide important information about the molecular basis of calcium binding cooperativity. Footnotes 1 Marchand S. and Roux B. Protein Struct. Funct. Genet. 1998, 33, 265-284. 2 Woo H. and Roux B., PNAS, 2005, 19, 6825. 3 Linse S. et al. Biochemistry 1991, 30, 154.