Three propagation schemes for rigid structures in dynamics. In SHAKE and SHAPE schemes, the unconstrained positions of individual particles are iteratively corrected to reach a rigid structure. In constrained dynamics, the constrained forces, c, are calculated to maintain a rigid structure. Alternatively, the Cartesian coordinates of a rigid body can be represented by position and rotation variables, which can be used to propagate the rigid structure to the next time step.
Model systems, the rigid bodies are shown in ball and stick mode: (a) 126 water molecules box, the rigid water molecule is labeled; (b) Trp-case protein, two separate rigid bodies are labeled; (c) matrix metalloproteinase 2 with substrate, the single rigid body is enlarged in inset; (d) nine-residue β-hairpin peptide, peptide bonds as treated as individual rigid structures, Cα carbons shared by adjacent rigid structures are shown in black. The solvent molecules are not shown in (b), (c), or (d).
The RMSD of whole water box of system a between two trajectories comparing SHAKE to SHAPE to implement rigid water constraints are plotted for the first 1000 MD steps. The unit of RMSD value is in Å.
Total energies (in kcal/mol) and standard deviation of model systems from simulations using different time steps.
RMSD (Å) of rigid bodies in model systems from simulations using different time steps.a
A nine-residue β-hairpin peptide as model system d for outer loop of SHAPE algorithm.
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