Algorithmic Challenges in Computational Molecular Biophysics

Schlick, Tamar; Skeel, Robert D.; Brünger, A.T.; Kalé, Laxmikant V.; Board, John A.; Hermans, Jan; Schulten, Klaus

doi:10.1006/jcph.1998.6182

Cited by 173 publications

(137 citation statements)

References 128 publications

(199 reference statements)

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“…During the simulations, the system was kept at constant temperature (300 K) using Langevin damping coefficient of 5 ps Ϫ1 and constant pressure (1 atm) using a Nosé-Hoover Langevin piston (56) with an oscillation timescale of 200 fs and damping time scale of 100 fs. 2-fs integration time steps were used under a multiple time stepping scheme (57), where bonded and short-range interactions were computed every time step and long-range electrostatic interactions every third time step. A cutoff of 12 Å for van der Waals and shortrange electrostatic interactions was used.…”

Section: Methodsmentioning

confidence: 99%

A Novel Structural Unit in the N-terminal Region of Filamins

Sethi

Seppälä

Tossavainen

et al. 2014

Journal of Biological Chemistry

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Section: Methodsmentioning

confidence: 99%

A Novel Structural Unit in the N-terminal Region of Filamins

Sethi

Seppälä

Tossavainen

et al. 2014

Journal of Biological Chemistry

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“…The asymptotic improvement in efficiency comes, however, with great increases in the complexity of the coding, especially when distributed on multiprocessor computers. The numerical prefactors in these scaling laws are uncomfortably high: Despite the great effort put into optimizing the electrostatic loop, it is found that in the simulation of a large biomolecule (with N ∼ 10 5 ) the great majority of the CPU time is still used in the Coulomb loop [6] in even the most sophisticated numerical codes. Most of these "fast" methods can only be used efficiently in molecular dynamics simulations; there are many occasions where one would like to perform efficient Monte-Carlo simulations due to the stability and simplicity of the method.…”

mentioning

confidence: 99%

“…(2) allows one to perform field updates far more rarely than particle updates leading to additional acceleration of the algorithm. Such multiple time step ideas have been applied to conventional electrostatic solvers but in molecular dynamics are sometimes prone to numerical instabilities [6].…”

mentioning

confidence: 99%

Local Simulation Algorithms for Coulomb Interactions

Maggs

Rossetto²

2002

Phys. Rev. Lett.

115

178

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Long ranged electrostatic interactions are time consuming to calculate in molecular dynamics and MonteCarlo simulations. We introduce an algorithmic framework for simulating charged particles which modifies the dynamics so as to allow equilibration using a local Hamiltonian. The method introduces an auxiliary field with constrained dynamics so that the equilibrium distribution is determined by the Coulomb interaction. We demonstrate the efficiency of the method by simulating a simple, charged lattice gas. PACS numbers: 71.15.Pd, 07.05.Tp, 61.20.Ja, 72.20.Jv The electrostatic interaction between two point charges in a medium with uniform dielectric constant ǫ 0 varies as e 1 e 2 /4πǫ 0 r. The large numerical value of this energy together with its long range are such that it is very often the most costly component in the simulation of charged condensed matter systems. Naive evaluation of the electrostatic energies in molecular dynamics and Monte-Carlo algorithms leads to inner loops where the summation over all pairs takes a time which scales as O(N 2 ) for a single step in which all N particles are updated.Many methods are used to improve this poor scaling: The optimized Ewald algorithm splits the summation between real and Fourier space and has a complexity of O(N 3/2 ) [1, 2]. By interpolation of the charge distribution onto a grid, fast Fourier transform methods allow a scaling in O(N log(N )) [3]. Finally, a popular method in very large simulations is an expansion of the charge distribution using hierarchical multipoles [4,5]. The asymptotic improvement in efficiency comes, however, with great increases in the complexity of the coding, especially when distributed on multiprocessor computers. The numerical prefactors in these scaling laws are uncomfortably high: Despite the great effort put into optimizing the electrostatic loop, it is found that in the simulation of a large biomolecule (with N ∼ 10 5 ) the great majority of the CPU time is still used in the Coulomb loop [6] in even the most sophisticated numerical codes. Most of these "fast" methods can only be used efficiently in molecular dynamics simulations; there are many occasions where one would like to perform efficient Monte-Carlo simulations due to the stability and simplicity of the method.The classical methods for treating charged systems have another disadvantage, their inability to treat systems with inhomogeneous dielectric constants. Dielectric inhomogeneities have drastic effects on material properties. For instance the dielectric contrast between water and the core of proteins leads to expulsion of counter-ions from a 3A thick hydration layer [7]. To treat charging effects in proteins quite arbitrary, uncontrolled approximations are made [8] on effective electrostatic interactions in the vicinity of a protein in order to reduce interactions to effective pair-wise additive potentials. Similarly much work [9] has been performed on the phase structure of charged synthetic polymers while neglecting the large dielectric contrasts between water...

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“…A cutoff of 12 Å (switching function starting at 10 Å ) for van der Waals interactions was assumed. An integration time step of 2 fs was used, permitting a multiple timestepping algorithm [31,32] to be employed, in which interactions involving covalent bonds were computed every time step. Shortrange non-bonded interactions were computed every two-time step, and long-range electrostatic forces were computed every four-time steps.…”

Section: Molecular Dynamics Studiesmentioning

confidence: 99%