Transcript Fast Electrostatics using Multigrid Summation

Evaluation of Fast
Electrostatics Algorithms
Alice N. Ko and Jesús A.
Izaguirre
with Thierry Matthey
Department of Computer Science and
Engineering
University of Notre Dame, USA
Department of Informatics
University of Bergen, NORWAY
Executive summary
How to choose the best among Particle Mesh Ewald
(PME), Multi-Grid (MG) summation, Ewald sum, for
molecular dynamics of biological molecules. Why
should your next simulation consider using MG?
Problem: Full Electrostatic
Energy
qi q j
1
U  
2 n i 1 j 1 ri , j ,n
'
N
N
Motivation
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Fast evaluation of full electrostatics in molecular
dynamics (MD) of biological molecules important for
accuracy in many applications
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Many methods exist to do explicit evaluation of fast
electrostatics
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Structural stability of DNA and proteins
Ionic environments
Fast Multipole Method O(N)
Greengard, 1987
Particle Mesh Ewald O(N log N) Darden, 1993
Multi-grid summation O(N)
Brandt, 1990
Skeel, 2002
Which one to use for a given system and accuracy?
Objectives
1.
Provide practical guidelines for choosing
parameters for each algorithm
2.
Evaluate competitive algorithms
3.
Evaluate suitability of MG to MD simulations
Particle Mesh Ewald
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Following Ewald, separates the
electrostatic interactions into two parts:
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Direct-space short range evaluation
Fourier-space evaluation
The Fourier term is approximated by using
fast Fourier transforms on a grid
Method parameters are grid size and
cutoff of direct-space
Multigrid I
Multigrid II
Related Work I
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Darden et al.,
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J. Chem. Phys. 2000
used FMM to compute direct part of Ewald sum
Skeel et al.,
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J. Chem. Phys. 1995
accuracy and efficiency of Particle Mesh Ewald (PME)
Krasny et al.,
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effect of varying parameters of Particle Mesh Ewald
Petersen et al.,
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J. Chem. Phys. 1993
J. Comp. Chem. 2002
study of parameters for multigrid (MG) method.
Compared MG to Fast Multipole Method (FMM).
MG faster than FMM for low accuracy
Related Work II
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Most published results
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fail to suggest how to determine the
specific values
provide general trends only
contain unknown constants in equations
that model performance
Summary
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General contributions of this study
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Practical guidelines for choosing
parameters for each algorithm, and to
choose among different algorithms
Implemented important algorithms with
reasonable efficiency in ProtoMol
 Tested algorithms for various system sizes and
accuracy
 Tested quality of these methods for MD of
solvated proteins
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Encapsulated results of this study on a tool
called MDSimAid
Experimental protocol
These methods were tested and implemented:
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1.
2.
3.
Smooth Particle Mesh Ewald
Multigrid summation
Ewald summation
Testing protocol:
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Methods (1) and (2) above were compared against (3) to
determine accuracy and relative speedup
Tested on water boxes and protein systems ranging from
1,000 to 100,000 atoms, and low and high accuracies
CHARMM used to prepare systems, NAMD and ProtoMol
used for simulations
Determined optimal parameters for each method for a
given accuracy and system size
For selected protein systems, structural and transport
properties were computed (e.g., Melittin, pdb id 2mlt, in
water, 11845 atoms)
Solvated Melittin
Results
Big picture
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Multi-grid summation is an effective
method for low accuracy computation of
full electrostatics
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For low accuracy, Multi-Grid is faster than
PME and Ewald for all system sizes tested
(from 1000 to 100,000)
For medium accuracy, Multi-Grid is faster
than PME for systems of 8,000 atoms or more
Multi-grid with low accuracy produces
correct structural and dynamic properties
Results (10-4 rPE)
Results (10-5 rPE)
RDF
Multigrid III
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Complex relationship among method
parameters:
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Cutoff and softening distances for potential
evaluation at the particle and grid levels
Grid size and interpolation order
Number of levels
Rules extracted from extensive evaluation
encapsulated in MDSimAid
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Fine tuned at run-time by running selected
tests
Makes method easier to use
Simulation Results for Melittin
PME requires about 3% of the CPU
time (17 days 20 hours) when
measured against Ewald
 MG in pbc requires only about 1%
 MG is about 66% faster than PME
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Discussion
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MG is a competitive method for low accuracy MD
simulations
Accuracy not a great concern for long time
simulations
MG would be natural choice for multiple time
stepping integrators
To choose among methods, and good parameters
for each method, MDSimAid is a useful tool
For further reference:
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http://www.nd.edu/~lcls/mdsimaid
http://www.nd.edu/~lcls/protomol
http://www.ks.uiuc.edu/development/namd
http://www.nd.edu/~izaguirr
Acknowledgements
This research was supported by an NSF Biocomplexity
grant and an NSF CAREER award