## Algorithmic challenges in computational molecular biophysics (1999)

Venue: | Journal of Computational Physics |

Citations: | 34 - 3 self |

### BibTeX

@ARTICLE{Schlick99algorithmicchallenges,

author = {Tamar Schlick and Robert D. Skeel and Axel T. Brunger and Laxmikant V. Kalé and John A. Board and Jan Hermans and Klaus Schulten},

title = {Algorithmic challenges in computational molecular biophysics},

journal = {Journal of Computational Physics},

year = {1999},

volume = {151},

pages = {9--48}

}

### OpenURL

### Abstract

A perspective of biomolecular simulations today is given, with illustrative applications and an emphasis on algorithmic challenges, as reflected by the work of a multidisciplinary team of investigators from five institutions. Included are overviews and recent descriptions of algorithmic work in long-time integration for molecular dynamics; fast electrostatic evaluation; crystallographic refinement approaches; and implementation of large, computation-intensive programs on modern architectures. Expected future developments of the field are also discussed. c ○ 1999 Academic Press Key Words: biomolecular simulations; molecular dynamics; long-time integration; fast electrostatics; crystallographic refinement; high-performance platforms.

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Citation Context ...ined dynamics [85] and the impulse–MTS method [18]. 2.7. MTS Schemes and Resonance Problems Symplectic and time-reversible MTS methods for biomolecular dynamics have been described in the early 1990s =-=[47, 126]-=-. A natural splitting for MD simulations is the following three-class hierarchy: bonded forces are considered “fast” and resolved at an inner timestep �τ; forces within a certain cutoff (e.g., 6 ˚A) a... |

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Citation Context ...ional cost of just a few percent over the cost of the multipole methods applied to an original simulation cell of size of order 10 ˚A [81]. 3.4. Ewald Methods The Ewald summation was invented in 1921 =-=[42]-=- to permit the efficient computation of lattice sums arising in solid state physics. The desirability of using periodic boundary conditions in MD simulations leads to use of Ewald methods where the en... |

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Citation Context ...ing threads, while much of the initialization code was implemented using a simple message passing style. Integrating such disparate modules in a single program was a challenge. The Converse framework =-=[71]-=- developed at the University of Illinois is used to support multiple languages and libraries in a single application. Languages and libraries such as Charm++ and PVM are implemented on top of Converse... |

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Citation Context ...nitial position in the protein and allowing the ligand to explore new contacts along its unbinding path. SMD has already been successfully applied to studies of the dissociation of biotin from avidin =-=[48, 66]-=-, the unbinding of retinal from bacteriorhodopsin [64] and of retinoic acid from its nuclear hormone receptor [77], and the extraction of lipids from membranes [91, 122]. A review of the method is pro... |

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Citation Context ..., 150, and 285 ˚A correspond, respectively, to regions I to IV defined in (a). Figure created using [61]. In the application of SMD to the force-induced unfolding of the immunoglobin domains of titin =-=[88]-=-, the starting structure for the SMD simulations was constructed on the basis of a nuclear magnetic resonance (NMR) structure of the Ig domain I27 of the cardiac titin I-band [63]. The 300-ps simulati... |

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Citation Context ...: one side of the DNA was identical to the target sequence and the other side was altered, containing two mutations in the sequence (see Fig. 2). The simulations were performed using the program NAMD =-=[97]-=- on the solvated protein/DNA complex involving approximately 36,600 atoms (Fig. 2). The 100-ps simulation required 22 days in 1996 on eight HP 735 workstations. The full electrostatic interactions are... |

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Citation Context ... half the fastest period (see Fig. 1 of [89]). The resonant timesteps are method dependent [115]. The instability problem for �t nearly equal to the half-period was later reported for the impulse–MTS =-=[12, 46]-=-. Detailed analyses of resonance artifacts in extrapolative versus impulse–MTS schemes are presented in [12, 110], where hybrid schemes are proposed to balance stability with accuracy. Resonance insta... |

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Citation Context ...imilar results were obtained for a test case at lower (2.8 ˚A) resolution and for two real cases involving new crystal structures starting with an initial model built into a poor electron density map =-=[1, 75]-=-.s42 SCHLICK ET AL. 7. FUTURE PERSPECTIVES It is impressive to look back 20 years and appreciate how rapidly the field of biomolecular modeling has progressed from the first dynamic simulation of a sm... |

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Citation Context ...for the impulse method, for LongLinearAverage, and for another mollified impulse method Equilibrium that defines A(X) to be a projection onto the equilibrium value of the bond lengths and bond angles =-=[65]-=-. (The pseudo-energy is the actual energy with Eslow(X) replaced with Eslow(A(X)).) The energy rises rapidly for the impulse method but is nearly flat for the Equilibrium version of the mollified impu... |

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Citation Context ...hods for stiff differential equations, like the implicit-Euler, for general biomolecular dynamics [116, 135]. Other approaches for integrating the equations of motion exactly in the constrained space =-=[6, 7, 68, 107]-=- are described in the context of crystallography and NMR refinement (Section 6). 2.5. Other Ways to Achieve Speedup in MD Additional ways to reap speedups from MD simulations are simplified treatments... |

34 |
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Citation Context ...d every �t = k2tm = k1�τ, the outermost timestep. The ratio r = k1k2 = �t/�τ determines the overall speedup, since the majority of the work in the total force evaluation stems from the slow component =-=[11]-=-. Typical timestep regimes are �τ = 0.5 fs, �tm around 1 or 2 fs, and �t = 4 fs. The requirement of symplecticness unfortunately necessitates the merging of the slow forces with remaining terms via pe... |

31 |
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Citation Context ...more closely (see Fig. 6). This suggests that the parameter γ should be kept as small as possible, just sufficient to guarantee numerical stability of the method. An estimate for such a γ is given in =-=[12]-=- and refined ins24 SCHLICK ET AL. FIG. 6. BPTI spectral densities derived from the cosine Fourier transforms of the velocity autocorrelation function for all atoms for LN versus the Verlet generalizat... |

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28 |
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Citation Context ...ortant in force-splitting approaches, which update forces in different classes at varying, appropriately chosen frequencies. Such multiple-timestep (MTS) schemes were suggested two decades ago for MD =-=[123]-=- and have recently become popular in biomolecular dynamics simulations with the introduction of symplectic variants. 2.6. Symplectic Integrators Important mathematical contributions regarding symplect... |

27 |
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Citation Context ...tials, where all interactions past a certain distance were simply ignored. Though acceptable for some simulation experiments, this cutoff approximation leads to unphysical behavior in many situations =-=[131]-=-. An alternative “brute force” quadratic method tailored to specialized parallel hardware [25, 62] increased the size of systems that could be simulated “exactly,” but the quadratic complexity eventua... |

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Citation Context ...amework of iterative nonlinear-system solvers such as SOR, an analogy which helps explain convergence properties, as well as improve convergence via introduction of an additional relaxation parameter =-=[9]-=-. Unfortunately, the SHAKE approach cannot be extended to freeze the next fastest vibrational mode, heavy-atom bond angles, because the overall motion is altered significantly [10, 53]. This strong vi... |

25 |
Dangers of multiple-time-step methods
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Citation Context ...s spread quickly to the computational chemistry community. It was shown that the popular Verlet method is symplectic, as are the RATTLE scheme for constrained dynamics [85] and the impulse–MTS method =-=[18]-=-. 2.7. MTS Schemes and Resonance Problems Symplectic and time-reversible MTS methods for biomolecular dynamics have been described in the early 1990s [47, 126]. A natural splitting for MD simulations ... |

25 |
G.: A fast recursive algorithm for molecular dynamics simulation
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Citation Context ...hods for stiff differential equations, like the implicit-Euler, for general biomolecular dynamics [116, 135]. Other approaches for integrating the equations of motion exactly in the constrained space =-=[6, 7, 68, 107]-=- are described in the context of crystallography and NMR refinement (Section 6). 2.5. Other Ways to Achieve Speedup in MD Additional ways to reap speedups from MD simulations are simplified treatments... |

24 |
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Citation Context ...Greengard and Rokhlin appeared in 1987, placing this class of algorithms on a more rigorous theoretical footing [50]. The FMA was soon adapted to the needs of electrostatic particle simulation for MD =-=[23, 118]-=-. The multipole-accelerated algorithms overcome the O(N 2 ) complexity of the N-body problem by using a hierarchy of approximations to represent the effect of increasingly distant groups of charged pa... |

24 |
Torsion angle dynamics: reduced variable conformational sampling enhances crystallographic structure refinement. Proteins: Struct
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Citation Context ...hods for stiff differential equations, like the implicit-Euler, for general biomolecular dynamics [116, 135]. Other approaches for integrating the equations of motion exactly in the constrained space =-=[6, 7, 68, 107]-=- are described in the context of crystallography and NMR refinement (Section 6). 2.5. Other Ways to Achieve Speedup in MD Additional ways to reap speedups from MD simulations are simplified treatments... |

24 |
New spherical-cutoff methods for long-range forces in macromolecular simulation
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Citation Context ...tion 3). The rapidly decaying van der Waals forces can still be treated by cutoff techniques, though more sophisticated schemes than straightforward truncation—smooth switching and shifting functions =-=[121]-=-— are needed to tame the artifacts that might otherwise result from abrupt changes in energy. Another practical procedure for cutting the work per MD timestep is to use a nonbonded pairlist and update... |

23 | Difficulties with multiple timestepping and the fast multipole algorithm in molecular dynamics
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(Show Context)
Citation Context ...ot explained by resonance in the papers which first applied these MTS variants to biomolecules [60, 130], large energy growth has been reported beyond this threshold; see also recent illustrations in =-=[19]-=-. Barth and Schlick found that the introduction of stochasticity into MTS schemes delays resonance artifacts of impulse–MTS to an outer timestep near the period (10 fs) rather than half-period; see vi... |