Biophysical Chemistry, 38 (1990) 179-183 Elsevier 179 BIOCHE 01518 Electrostatic contributions to the binding of Ca2’ in calbindin mutants A Monte Carlo study Bo Svensson, Bo Jthsson and Clifford Woodward Physical Chemisfty 2, Chemical Centre, PO Box 124, S-22100 Lund, Sweden Received 8 May 1990 Accepted 28 June 1990 Dielectric continuum: Simulation; Widom technique; Screening; Protein model Monte Carlo simulation is used to calculate the free energy of binding of calcium ions to the native and several mutant forms of bovine calbindin D,, in salt solution. Tbe simulations are performed in the canonical ensemble wherein free energies are calculated with a modified Widom method. The protein is modelled as a set of fixed hard spheres of fractional or unit charge with the surrounding solution as a dielectric continuum containing counterions and added salt particles. The interior of the protein is assumed to have the same dielectric perrnittivity as the solvent, which turns out to be an excellent approximation., indeed, this simple model is able to predict accurately experimentally measured shifts in the calcium binding constants of up to five orders of magnitude, due to mutations and added salt. 1. Introduction Molecular dynamics simulation has become a major tool in theoretical biochemistry during the last decade [l]. With a priori knowledge of a biomolecule’s molecular makeup, these simula- tions provide a detailed description of local dy- namics, even in aqueous solution. Furthermore, structural information, for example, on interfacial water and the organization of side chains and other small groups [2], may also be extracted. The validity of these results obtained is dependent upon the accuracy of the intermolecular potentials used and also on the length of time the system is simulated. Indeed, it is often impractical to run these generally large simulations to complete con- vergence. Correspondence address: B. Svensson, Physical Chemistry 2, Chemical Centre, PO Box 124, S-22100 Lund, Sweden. Free energies associated, for example, with the binding of substrates to enzymes, are usually more interesting for the biochemist than local struc- tures. However, they are also much more difficult to calculate in simulations. Perturbation methods have. recently been applied to this problem with variable success [3] and not unexpected conver- gence problems appear when substrate binding induces large structural changes. The potential utility of these methods is enormous, but their future development is intrinsically tied to that of fast computers. On the, other hand, one may ex- pect that changes in binding free energies, upon variation in some property of the system, should be more readily calculable if structural changes induced by binding are relatively constant over the varied conditions. In this communication we use Monte Carlo (rather than molecular dynamics) simulations to calculate free energy differences associated with 0301~4622/90/$03.50 Q 1990 Elsevier Science Publishers B.V. (Biomedical Division)