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## Scalable molecular dynamics with NAMD (2005)

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### Other Repositories/Bibliography

Venue: | J COMPUT CHEM |

Citations: | 848 - 63 self |

### Citations

1788 | Computer Simulation of Liquids - Allen, Tildesley - 1989 |

1516 |
Mathematical Methods of Classical Mechanics
- Arnold
- 1978
(Show Context)
Citation Context ...lap to a large degree to guarantee the desired accuracy. For example, although the hydration free energy of benzene is only 0.4 kcal/mol, insertion of a benzene molecule in bulk water constitutes too large a perturbation to fulfill the latter requirement in a single-step transformation. If such is not the case, the pathway connecting state a to state b is broken down into N intermediate, not necessarily physical states, k (a 1 0 and b N 1), so that the Helmholtz free energy difference reads: Fa3b 1 k1 N1 lnexpUr1, . . . , rN; k1 Ur1, . . . , rN; kk. (27) Here the potential energy is not only a function of the spatial coordinates, but also of the parameter that connects the reference and the target states. Perturbation of the chemical system by means of k may be achieved by scaling the relevant nonbonded force field parameters of appearing, vanishing, or changing atoms, in the spirit of turning lead into gold. In NAMD, the topologies characteristic of the initial state, a, and the final state, b, coexist, yet without interacting. This implies that, as a preamble to the free energy calculation, a hybrid topology has to be defined with an app... |

850 | Understanding Molecular Simulations: from Algorithms to Applications - Frenkel, Smit - 1996 |

416 | Numerical Initial Value Problems in Ordinary Differential Equations - Gear - 1973 |

299 | Numerical Methods - DAHLQUIST, BJÖRCK - 2003 |

117 | A Genetic Switch - Ptashne - 1992 |

80 | Statistical Physics II, Nonequilibrium Statistical Mechanics ~Springer-Verlag, - Kubo, Toda, et al. - 1998 |

34 | Computational Statistical Mechanics, - Hoover - 1991 |

30 | Tcl and the Tk Toolkit; Addison-Wesley - Ousterhout - 1994 |

12 |
Am Chem Soc
- Weiner, Kollman, et al.
- 1984
(Show Context)
Citation Context ...conditionally convergent, meaning that the result of the summation depends on the order in which it is taken. Ewald summation specifies the order as follows:12 sum over each box first, then sum over spheres of boxes of increasingly larger radii. Ewald summation is considered more reliable than a cutoff scheme,13–15 although it is noted that the artificial periodicity can lead to bias in free energy,16,17 and can artificially stabilize a protein that should have unfolded quickly.18 Dropping the prefactor 1/4 , the Ewald sum involves the following terms: EEwald Edir Erec Eself Esurface, (8) Edir 1 2 i, j1 N qiqj n r erfcri rj nr ri rj nr i, jExcluded qiqj ri rj ij , (9) Erec 1 2 V m 0 exp 2m 2/2 m 2 i1 N qiexp(2 im ri)2, (10) Eself i1 N qi 2, (11) Esurface 2 2 s 1V i1 N qiri2. (12) Here, qi and ri are the charge and position of atom i, respectively, and n r is the lattice vector. For an arbitrary simulation box defined by three independent base vectors a1, a2, a3, one defines n r n1a1 n2a2 n3a3, where n1, n2, and n3 are integers. ¥ denotes a summation over n r that exclude... |

10 | Parallel Programming using C - Kalé, Krishnan - 1996 |

8 | VRPN: Virtual Reality Peripheral Network - Taylor - 1998 |

7 | Phys Rev A - Hoover - 1986 |

6 |
Ann Phys
- Ewald
- 1921
(Show Context)
Citation Context ...radii. Ewald summation is considered more reliable than a cutoff scheme,13–15 although it is noted that the artificial periodicity can lead to bias in free energy,16,17 and can artificially stabilize a protein that should have unfolded quickly.18 Dropping the prefactor 1/4 , the Ewald sum involves the following terms: EEwald Edir Erec Eself Esurface, (8) Edir 1 2 i, j1 N qiqj n r erfcri rj nr ri rj nr i, jExcluded qiqj ri rj ij , (9) Erec 1 2 V m 0 exp 2m 2/2 m 2 i1 N qiexp(2 im ri)2, (10) Eself i1 N qi 2, (11) Esurface 2 2 s 1V i1 N qiri2. (12) Here, qi and ri are the charge and position of atom i, respectively, and n r is the lattice vector. For an arbitrary simulation box defined by three independent base vectors a1, a2, a3, one defines n r n1a1 n2a2 n3a3, where n1, n2, and n3 are integers. ¥ denotes a summation over n r that excludes the n r 0 term in the case i j; “excluded” denotes the set of atom pairs whose direct electrostatic interaction should be excluded. ij denotes the lattice vector for the (i, j) pair that minimizes ri rj ij. is a param... |

6 | The lac Operon; Walter de Gruyter - Müller–Hill - 1996 |

5 | Phys Rev E - Jarzynski - 1997 |

5 | AutoIMD User’s Guide, - Cohen, Grayson - 2003 |

4 | Phys Rev Lett - Jarzynski - 1997 |

4 | Annu Rev Biochem - Hershko, Ciechanover - 1998 |

2 |
Computer Simulation Using Particles; McGraw-Hall
- Hockney, Eastwood
- 1981
(Show Context)
Citation Context ... a force of 1 N or more; t 1 ps of dynamics requires 1 s or more to compute. The interface between the haptic device and NAMD thus introduces the scaling factors Sx /x 10 8, St /t 10 12, Sf /f 10 9, (21) Multiplying the molecular equation of motion in eq. (20) by the factor SfSx/St 2 gives SfSx St 2 m d2x dt2 Sfm d2 d2 SfSx St 2 f Sx St 2 . (22) From this we can conclude SfSt 2 Sx m d2 d2 . (23) Comparison with the haptic equation of motion in eq. (20) suggests that the effective mass felt by the haptic device, and hence, by the user is SfSt 2 Sx m. (24) The molecular moieties to be moved through external forces have typical masses of (e.g., for glycerol moved through a membrane channel53) of m 180 amu or m 3 1025 kg. From eq. (21) we conclude then that the effective mass felt by the user through the haptic device is 3 kg; the user does not sense strong inertial effects, and can readily manipulate the biomolecular system. IMD can also be carried out without force feedback, using a standard mouse to steer the simulated system. To assist users of NAMD with IMD, AutoIMD89 has been developed. AutoIMD permits the researcher to use the graphic... |

2 |
Numerical Methods; Prentice Hall: Englewood Cliffs,
- Bjorck
- 1974
(Show Context)
Citation Context ...of the mechanical properties of biopolymers. Steered molecular dynamics (SMD) is the in silico complement of such studies, in which external forces are applied to molecules in a simulation to probe their mechanical properties as well as to accelerate processes that are otherwise too slow to model. This method has been reviewed in refs. 49–51. Figure 5. A symplectic method demonstrates superior long-time stability: the symplectic method used here is the symplectic Euler method ([22], Theorem 3.3), whose local error is proportional to t2; the nonsymplectic method used is the Runge–Kutta method ([30], sect. 8.3.3) whose local error is proportional to t5. The system described is a one-dimension harmonic oscillator. The equation of motion is mx m2x, with m 1, and initial conditions x 1, v 0. The exact trajectory is the unit circle. The chosen time step is t 0.5 and 10,000 steps were integrated. The trajectory of the Runge– Kutta method collapses toward the center while the symplectic Euler method maintains a stable orbit even though its trajectory is deformed into an ellipse by a larger local error. 1786 Phillips et al. • Vol. 26, No. 16 • Journal of Computational Chemistry... |

2 | Phys Rev Lett - Zhu, Li, et al. - 2008 |

1 |
Proc R Soc Lond A
- Leeuw, Perram, et al.
- 1980
(Show Context)
Citation Context ...ble than a cutoff scheme,13–15 although it is noted that the artificial periodicity can lead to bias in free energy,16,17 and can artificially stabilize a protein that should have unfolded quickly.18 Dropping the prefactor 1/4 , the Ewald sum involves the following terms: EEwald Edir Erec Eself Esurface, (8) Edir 1 2 i, j1 N qiqj n r erfcri rj nr ri rj nr i, jExcluded qiqj ri rj ij , (9) Erec 1 2 V m 0 exp 2m 2/2 m 2 i1 N qiexp(2 im ri)2, (10) Eself i1 N qi 2, (11) Esurface 2 2 s 1V i1 N qiri2. (12) Here, qi and ri are the charge and position of atom i, respectively, and n r is the lattice vector. For an arbitrary simulation box defined by three independent base vectors a1, a2, a3, one defines n r n1a1 n2a2 n3a3, where n1, n2, and n3 are integers. ¥ denotes a summation over n r that excludes the n r 0 term in the case i j; “excluded” denotes the set of atom pairs whose direct electrostatic interaction should be excluded. ij denotes the lattice vector for the (i, j) pair that minimizes ri rj ij. is a parameter adjusting the workload distribution for di... |

1 |
Mol Simulat
- Grubmuller, Heller, et al.
- 1991
(Show Context)
Citation Context ...atom pairs whose direct electrostatic interaction should be excluded. ij denotes the lattice vector for the (i, j) pair that minimizes ri rj ij. is a parameter adjusting the workload distribution for direct and reciprocal sums. s is the dielectric constant of the surroundings of the simulation box, which is water for most biomolecular systems. V is the volume of the simulation box. m is the reciprocal vector defined as m m1b1 m2b2 m3b3, where m1, m2, m3 are integers, and the reciprocal base vectors b1, b2, b3 are defined so that a b , , 1, 2, 3. (13) The complementary error function erfc( x) in eq. (9) is erfcx 2 x et 2 dt. (14) The Ewald sum in eq. (8) has four terms: direct sum Edir, reciprocal sum Erec, self-energy Eself, and surface energy Esurface. The self-energy term is a trivial constant, while the surface term is usually neglected by assuming the “tin-foil” boundary condition s , which is partly due to the dielectric constant of water ( s 80) being much larger than 1. The Ewald sum has a freely chosen parameter , which can shift the computational load between the direct sum and the reciprocal sum. For a given accuracy, th... |

1 |
Proteins Struct Funct Genet
- Loncharich, Brooks
- 1989
(Show Context)
Citation Context ...he lattice vector for the (i, j) pair that minimizes ri rj ij. is a parameter adjusting the workload distribution for direct and reciprocal sums. s is the dielectric constant of the surroundings of the simulation box, which is water for most biomolecular systems. V is the volume of the simulation box. m is the reciprocal vector defined as m m1b1 m2b2 m3b3, where m1, m2, m3 are integers, and the reciprocal base vectors b1, b2, b3 are defined so that a b , , 1, 2, 3. (13) The complementary error function erfc( x) in eq. (9) is erfcx 2 x et 2 dt. (14) The Ewald sum in eq. (8) has four terms: direct sum Edir, reciprocal sum Erec, self-energy Eself, and surface energy Esurface. The self-energy term is a trivial constant, while the surface term is usually neglected by assuming the “tin-foil” boundary condition s , which is partly due to the dielectric constant of water ( s 80) being much larger than 1. The Ewald sum has a freely chosen parameter , which can shift the computational load between the direct sum and the reciprocal sum. For a given accuracy, the computationally optimal choice of the parameter leads to a cost proportional to N3/... |

1 |
Mol Phys
- Perram, Petersen, et al.
- 1988
(Show Context)
Citation Context ...system can be deduced from nonequilibrium simulations was given by Jarzynski.76,77 The second law of thermodynamics states that the average work W done through a nonequilibrium process that changes a parameter of a system from 0 at time zero to t at time t is greater than or equal to the equilibrium free energy difference between the two states specified through the final and initial values of : F Ft F0 W, (18) where the equality holds only if the process is quasi-static. Jarzynski76 discovered an equality that holds regardless of the speed of the process: e F eW, (19) where (kBT) 1. The Jarzynski equality provides a way to extract equilibrium information, such as free energy differences, from averaging over nonequilibrium processes,76 a method that has been tested against computer simulations77 and experiments.78 A major difficulty that arises with the application of eq. (19) is that the average of exponential work appearing in Jarzynski’s equality is dominated by trajectories corresponding to small work values that arise only rarely. Hence, an accurate estimate of free energy requires suitable sampling of such rare trajectories, and thus the accuracy... |

1 |
Proteins Struct Funct Genet
- Harvey
- 1989
(Show Context)
Citation Context ...rence arising from this perturbation is equal to G2 mutation 2 G1 mutation. Each leg of the thermodynamic cycle consists of 50 intermediate states and a total MD sampling of 6 ns. For clarity, the environment of the -helical dimer, formed by a dodecane slab in equilibrium between two lamellae of water, is not shown. [Color figure can be viewed in the online issue, which is available at www.interscience.wiley.com.] Scalable Molecular Dynamics with NAMD 1791 acting on , F, is evaluated from an unconstrained MD simulation:93 dA d U(r1, . . . , rN) 1 lnJ F, (29) where J denotes the determinant of the Jacobian for the transformation from Cartesian to generalized coordinates, which is a necessary modification of metric, given that {r1, . . . , rN} and are not independent variables. The specific form of J is an inherent function of the coordinate, , chosen to advance the system. In the course of the simulation in NAMD, the force, F, acting along the ordering parameter, , is accrued in small bins, thereby supplying an estimate of the derivative dA()/d. The so called adaptive biasing force (ABF), F ABF Fr, is determined in such a w... |

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