Each system (protein + membrane + water + ions, and protein + membrane in the absence of water) was energy minimized by 1,000 steps using the steepest descent method followed by conjugate gradient method for thousands of additional steps until the root mean square of the energy gradient (GRMS) fell below 10−4 kcal/mol.Å−1.

The energy-minimized structures, E1.Mg2+:SLN and E1.Mg2+, were considered as starting systems to calculate normal modes. Because of the large number of atoms in each system (>70,000 atoms) the DIMB method (Diagonalization in a Mixed Basis) (Mouawad and Perahia, 1993; Perahia and Mouawad, 1995) was used in program CHARMM. DIMB is an iterative method in which the Hessian matrix to be diagonalized is divided into small-size Hessian matrices expressed in a mixed basis of intermediate NMs and Cartesian coordinates. By an iterative process of diagonalizations, the modes converge to those that would be obtained from the diagonalization of the entire Hessian matrix. However, to be able to perform the calculations in a reasonable time (<10 days), we accelerated this method by making it work on a GPU system, in a home-made adaptation of CHARMM. This adaptation was tested beforehand on small proteins to ensure that the results were the same as those obtained on CPU. For each system 206 modes were calculated, the 6 trivial global translation-rotation modes with null frequencies, and 200 non-trivial modes (modes 7 to 206), sorted according to the ascending order of their frequencies. The modes were considered as converged when the maximum eigenvectors convergence was <0.03.

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