GROMEX: A Scalable and Versatile Fast Multipole Method for Biomolecular Simulation

Atomistic simulations of large biomolecular systems with chemical variability such as constant pH dynamic protonation offer multiple challenges in high performance computing. One of them is the correct treatment of the involved electrostatics in an efficient and highly scalable way. Here we review and assess two of the main building blocks that will permit such simulations: (1) An electrostatics library based on the Fast Multipole Method (FMM) that treats local alternative charge distributions with minimal overhead, and (2) A λ-dynamics module working in tandem with the FMM that enables various types of chemical transitions during the simulation. Our λ-dynamics and FMM implementations do not rely on third-party libraries but are exclusively using C++ language features and they are tailored to the specific requirements of molecular dynamics simulation suites such as GROMACS. The FMM library supports fractional tree depths and allows for rigorous error control and automatic performance optimization at runtime. Near-optimal performance is achieved on various SIMD architectures and on GPUs using CUDA. For exascale systems, we expect our approach to outperform current implementations based on Particle Mesh Ewald (PME) electrostatics, because FMM avoids the communication bottlenecks caused by the parallel fast Fourier transformations needed for PME.

[1]  Charles L. Brooks,et al.  λ‐dynamics: A new approach to free energy calculations , 1996 .

[2]  Lorena A. Barba,et al.  A tuned and scalable fast multipole method as a preeminent algorithm for exascale systems , 2011, Int. J. High Perform. Comput. Appl..

[3]  Berk Hess,et al.  GROMACS 3.0: a package for molecular simulation and trajectory analysis , 2001 .

[4]  Helmut Grubmüller,et al.  Scaling of the GROMACS 4.6 molecular dynamics code on SuperMUC , 2014, PARCO.

[5]  J. Kirkwood.  Statistical Mechanics of Fluid Mixtures , 1935 .

[6]  Tamar Schlick,et al.  Scaling molecular dynamics beyond 100,000 processor cores for large‐scale biophysical simulations , 2019, J. Comput. Chem..

[7]  Martin Head-Gordon,et al.  Fractional tiers in fast multipole method calculations , 1996 .

[8]  Charles L. Brooks,et al.  Applying efficient implicit nongeometric constraints in alchemical free energy simulations , 2011, J. Comput. Chem..

[9]  Katherine A. Yelick,et al.  A Communication-Optimal N-Body Algorithm for Direct Interactions , 2013, 2013 IEEE 27th International Symposium on Parallel and Distributed Processing.

[10]  H. Grubmüller,et al.  Constant pH Molecular Dynamics in Explicit Solvent with λ-Dynamics , 2011, Journal of chemical theory and computation.

[11]  Martin Fechner,et al.  Speeding up parallel GROMACS on high‐latency networks , 2007, J. Comput. Chem..

[12]  C. Brooks,et al.  Constant pH molecular dynamics with proton tautomerism. , 2005, Biophysical journal.

[13]  William H. Press,et al.  Numerical Recipes 3rd Edition: The Art of Scientific Computing , 2007 .

[14]  Rafael C. Bernardi,et al.  Molecular dynamics simulations of large macromolecular complexes. , 2015, Current opinion in structural biology.

[15]  T. Straatsma,et al.  THE MISSING TERM IN EFFECTIVE PAIR POTENTIALS , 1987 .

[16]  Carsten Kutzner,et al.  Tackling Exascale Software Challenges in Molecular Dynamics Simulations with GROMACS , 2015, EASC.

[17]  Andreas Beckmann,et al.  Accelerating an FMM-Based Coulomb Solver with GPUs , 2016, Software for Exascale Computing.

[18]  Jana K. Shen,et al.  Charge-leveling and proper treatment of long-range electrostatics in all-atom molecular dynamics at constant pH. , 2012, The Journal of chemical physics.

[19]  Charles L. Brooks,et al.  λ‐Dynamics free energy simulation methods , 2009, J. Comput. Chem..

[20]  Helmut Grubmüller,et al.  Dynamic contact network between ribosomal subunits enables rapid large-scale rotation during spontaneous translocation , 2015, Nucleic acids research.

[21]  Berk Hess,et al.  A flexible algorithm for calculating pair interactions on SIMD architectures , 2013, Comput. Phys. Commun..

[22]  Emmanuel Agullo,et al.  Task-Based FMM for Multicore Architectures , 2014, SIAM J. Sci. Comput..

[23]  H. Grubmüller,et al.  Charge-Neutral Constant pH Molecular Dynamics Simulations Using a Parsimonious Proton Buffer. , 2016, Journal of chemical theory and computation.

[24]  L. Greengard,et al.  A new version of the Fast Multipole Method for the Laplace equation in three dimensions , 1997, Acta Numerica.

[25]  Helmut Grubmüller,et al.  Microtubule assembly governed by tubulin allosteric gain in flexibility and lattice induced fit , 2018, eLife.

[26]  John Mongan,et al.  Biomolecular simulations at constant pH. , 2005, Current opinion in structural biology.

[27]  B. Montgomery Pettitt,et al.  Molecular Dynamics At a Constant pH , 1994, Int. J. High Perform. Comput. Appl..

[28]  Holger Dachsel,et al.  Corrected article: "An error-controlled fast multipole method" [J. Chem. Phys. 131, 244102 (2009)]. , 2010, The Journal of chemical physics.

[29]  Benjamin Lindner,et al.  Scaling of Multimillion-Atom Biological Molecular Dynamics Simulation on a Petascale Supercomputer. , 2009, Journal of chemical theory and computation.

[30]  Bert L de Groot,et al.  Protein thermostability calculations using alchemical free energy simulations. , 2010, Biophysical journal.

[31]  Michael L. Scott,et al.  Algorithms for scalable synchronization on shared-memory multiprocessors , 1991, TOCS.

[32]  Ross C. Walker,et al.  Fast and Flexible GPU Accelerated Binding Free Energy Calculations within the AMBER Molecular Dynamics Package , 2018, bioRxiv.

[33]  Michael Hofmann,et al.  Comparison of scalable fast methods for long-range interactions. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[34]  C. Brooks,et al.  Constant‐pH molecular dynamics using continuous titration coordinates , 2004, Proteins.

[35]  David L. Mobley,et al.  Chapter 4 Alchemical Free Energy Calculations: Ready for Prime Time? , 2007 .

[36]  Charles L. Brooks,et al.  Efficient and Flexible Algorithm for Free Energy Calculations Using the λ-Dynamics Approach , 1998 .

[37]  C. Brooks,et al.  Constant pH molecular dynamics of proteins in explicit solvent with proton tautomerism , 2014, Proteins.

[38]  David L Mobley,et al.  Perspective: Alchemical free energy calculations for drug discovery. , 2012, The Journal of chemical physics.

[39]  Carsten Kutzner,et al.  GROMACS 4:  Algorithms for Highly Efficient, Load-Balanced, and Scalable Molecular Simulation. , 2008, Journal of chemical theory and computation.

[40]  David L. Mobley,et al.  Alchemical Free Energy Calculations : Ready for Prime Time ? , 2016 .

[41]  Jennifer L. Knight,et al.  Constant pH Molecular Dynamics Simulations of Nucleic Acids in Explicit Solvent. , 2012, Journal of chemical theory and computation.

[42]  Holger Dachsel,et al.  An error-controlled fast multipole method. , 2009, The Journal of chemical physics.

[43]  Martin Fechner,et al.  Best bang for your buck: GPU nodes for GROMACS biomolecular simulations , 2015, J. Comput. Chem..

[44]  Helmut Grubmüller,et al.  Accurate Three States Model for Amino Acids with Two Chemically Coupled Titrating Sites in Explicit Solvent Atomistic Constant pH Simulations and pK(a) Calculations. , 2017, Journal of chemical theory and computation.

[45]  T. Darden,et al.  A smooth particle mesh Ewald method , 1995 .

[46]  Jana K. Shen,et al.  All-Atom Continuous Constant pH Molecular Dynamics With Particle Mesh Ewald and Titratable Water. , 2016, Journal of chemical theory and computation.

[47]  Helmut Grubmüller,et al.  Quantifying Artifacts in Ewald Simulations of Inhomogeneous Systems with a Net Charge. , 2014, Journal of chemical theory and computation.

[48]  Martin Fechner,et al.  More bang for your buck: Improved use of GPU nodes for GROMACS 2018 , 2019, J. Comput. Chem..