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Figure from:LINCS: A linear constraint solver for molecular simulations

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Figure 2: The CPU time for the constraint algorithms in lysozyme plotted as a function of the accuracy, i.e. the relative deviation of the constraints averaged over 500 steps. The dashed lines show the maximum deviation and the solid lines show the r.m.s. deviation for SHAKE and for LINCS.

Figure 2 The CPU time for the constraint algorithms in lysozyme plotted as a function of the accuracy, i.e. the relative deviation of the constraints averaged over 500 steps. The dashed lines show the maximum deviation and the solid lines show the r.m.s. deviation for SHAKE and for LINCS.

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Figure 1: Schematic picture showing the three position updates needed for one timestep. The dashed line is the old bond of length d, the solid lines are the new bonds. | = dcos@ and p = (2d? — I2)3, Just like SHAKE, LINCS calculates the new constrained positions from the old po- sitions and the new unconstrained positions. Thus the same methods can be used to calculate the virial and free energy differences. However the free energy calculation for
Figure 1: Schematic picture showing the three position updates needed for one timestep. The dashed line is the old bond of length d, the solid lines are the new bonds. | = dcos@ and p = (2d? — I2)3, Just like SHAKE, LINCS calculates the new constrained positions from the old po- sitions and the new unconstrained positions. Thus the same methods can be used to calculate the virial and free energy differences. However the free energy calculation for
A large test system was used to test how the accuracy of the constraints depends on the order of expansion (22) and to compare the speed of the LINCS algorithm with the SHAKE algorithm. Results are given for 1 ps MD runs on lysozy me (129 residues, 1345 bond constraints) with the GROMACS package. The protein was solvated in a box of 4535 water molecules and 8 Cl” ions, with a Lennard-Jones cut-off of Coulomb cut-off (1 and 1.8 nm). The water is constrained with t After energy minimization and 2 ps equilibration, test runs of performed. The test runs took 1300 seconds on one processor of an Table I and figure 2 show the results for LINCS and SHAKE. Both 1 nm and a twin-range he SETTLE algorithm. 500 steps of 2 fs were R8000 PowerChallenge. routines use optimized FORTRAN code. Notice that the difference between the maximum deviation and the r.m.s. deviation is a factor 2 for SHAKE and a factor 4 for L also performed without water, giving almost the same accuracy constraint algorithms as with water (data not shown), but with seconds. NCS. Some runs were and CPU time for the a total run time of 90 Table 1: The relative deviation of the constraints in lysozyme (solvated in 4535 water molecules and 8 Cl” ions) averaged over 500 steps: the maximum and the r.m.s. deviation shown for SHAKE and for LINCS without and with rotation correction. The water was constrained with SETTLE. The second column shows the order after which expansion (22) is truncated. The last column shows the total CPU time for the constraint algorithms. The total run time is 1300 seconds. Vacuum runs give almost identical numbers for the accuracy and CPU time of the constraint algorithms. The total run time of the vacuum system is about 90 seconds.
A large test system was used to test how the accuracy of the constraints depends on the order of expansion (22) and to compare the speed of the LINCS algorithm with the SHAKE algorithm. Results are given for 1 ps MD runs on lysozy me (129 residues, 1345 bond constraints) with the GROMACS package. The protein was solvated in a box of 4535 water molecules and 8 Cl” ions, with a Lennard-Jones cut-off of Coulomb cut-off (1 and 1.8 nm). The water is constrained with t After energy minimization and 2 ps equilibration, test runs of performed. The test runs took 1300 seconds on one processor of an Table I and figure 2 show the results for LINCS and SHAKE. Both 1 nm and a twin-range he SETTLE algorithm. 500 steps of 2 fs were R8000 PowerChallenge. routines use optimized FORTRAN code. Notice that the difference between the maximum deviation and the r.m.s. deviation is a factor 2 for SHAKE and a factor 4 for L also performed without water, giving almost the same accuracy constraint algorithms as with water (data not shown), but with seconds. NCS. Some runs were and CPU time for the a total run time of 90 Table 1: The relative deviation of the constraints in lysozyme (solvated in 4535 water molecules and 8 Cl” ions) averaged over 500 steps: the maximum and the r.m.s. deviation shown for SHAKE and for LINCS without and with rotation correction. The water was constrained with SETTLE. The second column shows the order after which expansion (22) is truncated. The last column shows the total CPU time for the constraint algorithms. The total run time is 1300 seconds. Vacuum runs give almost identical numbers for the accuracy and CPU time of the constraint algorithms. The total run time of the vacuum system is about 90 seconds.
SHAKE. Table 2: The accuracy of the constraints and the total energy in a 32 residue Gaf peptide using LINCS and SHAKE. All entries are averages over 8 vacuum runs in single precision of 4 ps (2000 steps of 2 fs) with different starting structures, without temperature and pressure coupling and without cutoff. The second column shows the order after which expansion (22) is truncated. The third column shows the r.m.s. of the relative deviation of the constraints. The fourth column shows the slope of a straight line fitted to the total energy. The last columns show the r.m.s. fluctuations in the total and the kinetic energy.
SHAKE. Table 2: The accuracy of the constraints and the total energy in a 32 residue Gaf peptide using LINCS and SHAKE. All entries are averages over 8 vacuum runs in single precision of 4 ps (2000 steps of 2 fs) with different starting structures, without temperature and pressure coupling and without cutoff. The second column shows the order after which expansion (22) is truncated. The third column shows the r.m.s. of the relative deviation of the constraints. The fourth column shows the slope of a straight line fitted to the total energy. The last columns show the r.m.s. fluctuations in the total and the kinetic energy.