Algorithmic Challenges in Computational Molecular Biophysics

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.

[1]  P. P. Ewald Die Berechnung optischer und elektrostatischer Gitterpotentiale , 1921 .

[2]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[3]  R W Hockney,et al.  Computer Simulation Using Particles , 1966 .

[4]  L. Verlet Computer "Experiments" on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules , 1967 .

[5]  R. Diamond A real-space refinement procedure for proteins , 1971 .

[6]  W. Stoeckenius,et al.  Bacteriorhodopsin: a light-driven proton pump in Halobacterium Halobium. , 1975, Biophysical journal.

[7]  G. Ciccotti,et al.  Numerical Integration of the Cartesian Equations of Motion of a System with Constraints: Molecular Dynamics of n-Alkanes , 1977 .

[8]  D. Tildesley,et al.  Multiple time-step methods in molecular dynamics , 1978 .

[9]  W. Vangunsteren Constrained dynamics of flexible molecules , 1980 .

[10]  H. Berendsen,et al.  Interaction Models for Water in Relation to Protein Hydration , 1981 .

[11]  Philip E. Gill,et al.  Practical optimization , 1981 .

[12]  H. C. Andersen Rattle: A “velocity” version of the shake algorithm for molecular dynamics calculations , 1983 .

[13]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[14]  H. Berendsen,et al.  Molecular dynamics with coupling to an external bath , 1984 .

[15]  H. Berendsen,et al.  A consistent empirical potential for water–protein interactions , 1984 .

[16]  W. Hendrickson Stereochemically restrained refinement of macromolecular structures. , 1985, Methods in enzymology.

[17]  M. Rossmann,et al.  The Refinement of Southern Bean Mosaic Virus in Reciprocal Space , 1984 .

[18]  Andrew W. Appel,et al.  An Efficient Program for Many-Body Simulation , 1983 .

[19]  A. Jonas Reconstitution of high-density lipoproteins. , 1986, Methods in enzymology.

[20]  Piet Hut,et al.  A hierarchical O(N log N) force-calculation algorithm , 1986, Nature.

[21]  J. Mccammon,et al.  Dynamics of Proteins and Nucleic Acids , 2018 .

[22]  Emile H. L. Aarts,et al.  Simulated Annealing: Theory and Applications , 1987, Mathematics and Its Applications.

[23]  Edward J. Haug,et al.  A Recursive Formation for Constrained Mechanical Systems Dynamics: Part I, Open Loop Systems , 1987 .

[24]  Leslie Greengard,et al.  A fast algorithm for particle simulations , 1987 .

[25]  M. Karplus,et al.  Crystallographic R Factor Refinement by Molecular Dynamics , 1987, Science.

[26]  E. Haug,et al.  A Recursive Formulation for Constrained Mechanical System Dynamics: Part II. Closed Loop Systems , 1987 .

[27]  E. Haug,et al.  A recursive formulation constrained mechanical system dynamics. I: Open loop systems , 1987 .

[28]  T. Schlick Ph.D. dissertation: Modeling and minimization techniques for predicting three-dimensional structures of large biological molecules , 1987 .

[29]  A. Brünger Crystallographic refinement by simulated annealing. Application to a 2.8 A resolution structure of aspartate aminotransferase. , 1988, Journal of molecular biology.

[30]  A. Brunger Crystallographic refinement by simulated annealing , 1988 .

[31]  M. Karplus,et al.  Proteins: A Theoretical Perspective of Dynamics, Structure, and Thermodynamics , 1988 .

[32]  J. Banavar,et al.  Computer Simulation of Liquids , 1988 .

[33]  Edward J. Haug,et al.  A Recursive Formulation for Constrained Mechanical System Dynamics: Part III. Parallel Processor Implementation , 1988 .

[34]  H. G. Petersen,et al.  An algorithm for the simulation of condensed matter which grows as the 3/2 power of the number of particles , 1988 .

[35]  B. Brooks,et al.  The effects of truncating long‐range forces on protein dynamics , 1989, Proteins.

[36]  M. Karplus,et al.  X-ray refinement of protein structures by simulated annealing: test of the method on myohemerythrin. , 1989, Acta crystallographica. Section A, Foundations of crystallography.

[37]  W. V. Gunsteren,et al.  Testing the method of crystallographic refinement using molecular dynamics , 1989 .

[38]  Helmut Grubmüller,et al.  Molecular dynamics simulations on a systolic ring of transputers. , 1990 .

[39]  R. Read Structure-factor probabilities for related structures , 1990 .

[40]  T. Ebisuzaki,et al.  A Special-Purpose Computer for Gravitational Many-Body Systems--GRAPE-2 , 1991 .

[41]  Klaus Schulten,et al.  Generalized Verlet Algorithm for Efficient Molecular Dynamics Simulations with Long-range Interactions , 1991 .

[42]  G. Bricogne A multisolution method of phase determination by combined maximization of entropy and likelihood. III. Extension to powder diffraction data , 1991 .

[43]  B. Matthews,et al.  A cavity-containing mutant of T4 lysozyme is stabilized by buried benzene , 1993, Nature.

[44]  Christopher R. Anderson,et al.  An Implementation of the Fast Multipole Method without Multipoles , 1992, SIAM J. Sci. Comput..

[45]  W. Goddard,et al.  The reduced cell multipole method for Coulomb interactions in periodic systems with million-atom unit cells , 1992 .

[46]  A. Brunger Free R value: a novel statistical quantity for assessing the accuracy of crystal structures. , 1992 .

[47]  Mark E. Tuckerman,et al.  Reversible multiple time scale molecular dynamics , 1992 .

[48]  J. W. Causey,et al.  Accelerated molecular dynamics simulation with the parallel fast multipole algorithm , 1992 .

[49]  A. Brünger Free R value: a novel statistical quantity for assessing the accuracy of crystal structures , 1992, Nature.

[50]  T. Darden,et al.  The effect of long‐range electrostatic interactions in simulations of macromolecular crystals: A comparison of the Ewald and truncated list methods , 1993 .

[51]  Robert D. Skeel,et al.  Dangers of multiple time step methods , 1993 .

[52]  Abhinandan Jain,et al.  A fast recursive algorithm for molecular dynamics simulation , 1993 .

[53]  Tamar Schlick,et al.  LIN: A new algorithm to simulate the dynamics of biomolecules by combining implicit‐integration and normal mode techniques , 1993, J. Comput. Chem..

[54]  T. Darden,et al.  Particle mesh Ewald: An N⋅log(N) method for Ewald sums in large systems , 1993 .

[55]  Michael S. Warren,et al.  A parallel hashed oct-tree N-body algorithm , 1993, Supercomputing '93. Proceedings.

[56]  Abhinandan Jain,et al.  Protein simulations using techniques suitable for very large systems: The cell multipole method for nonbond interactions and the Newton‐Euler inverse mass operator method for internal coordinate dynamics , 1994, Proteins.

[57]  Bernard R. Brooks,et al.  New spherical‐cutoff methods for long‐range forces in macromolecular simulation , 1994, J. Comput. Chem..

[58]  J. M. Sanz-Serna,et al.  Numerical Hamiltonian Problems , 1994 .

[59]  B. Berne,et al.  A Multiple-Time-Step Molecular Dynamics Algorithm for Macromolecules , 1994 .

[60]  B. Leimkuhler,et al.  Symplectic Numerical Integrators in Constrained Hamiltonian Systems , 1994 .

[61]  L.V. Kale,et al.  Modeling biomolecules: larger scales, longer durations , 1994, IEEE Computational Science and Engineering.

[62]  Jiro Shimada,et al.  Performance of fast multipole methods for calculating electrostatic interactions in biomacromolecular simulations , 1994, J. Comput. Chem..

[63]  T. Schlick,et al.  The Langevin/implicit‐Euler/normal‐mode scheme for molecular dynamics at large time steps , 1994 .

[64]  A. Brünger,et al.  Torsion angle dynamics: Reduced variable conformational sampling enhances crystallographic structure refinement , 1994, Proteins.

[65]  T. Darden,et al.  Atomic-level accuracy in simulations of large protein crystals. , 1994, Proceedings of the National Academy of Sciences of the United States of America.

[66]  William Dewey Elliott Multipole algorithms for molecular dynamics simulation on high performance computers , 1995 .

[67]  Z. S. Hakura,et al.  Scalable Variants of Multipole-accelerated Algorithms for Molecular Dynamics Applications , 1995 .

[68]  K. Schulten,et al.  Molecular Dynamics Studies of Bacteriorhodopsin's Photocycles , 1995 .

[69]  T. Schlick,et al.  Comment on ‘‘Backward Euler and other methods for simulating molecular fluids’’ [J. Chem. Phys. 103, 3718 (1995)] , 1995 .

[70]  T. Darden,et al.  MOLECULAR DYNAMICS SIMULATION STUDIES OF A HIGH RESOLUTION Z-DNA CRYSTAL , 1995 .

[71]  T. Darden,et al.  Accurate crystal molecular dynamics simulations using particle-mesh-Ewald: RNA dinucleotides — ApU and GpC , 1995 .

[72]  K. Esselink A comparison of algorithms for long-range interactions , 1995 .

[73]  B. Berne,et al.  A new molecular dynamics method combining the reference system propagator algorithm with a fast multipole method for simulating proteins and other complex systems , 1995 .

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

[75]  T. Schlick,et al.  Resonance in the dynamics of chemical systems simulated by the implicit midpoint scheme , 1995 .

[76]  H. G. Petersen Accuracy and efficiency of the particle mesh Ewald method , 1995 .

[77]  John A. Board,et al.  Scalable Variants of Multipole-based Algorithms for Molecular Dynamics Applications , 1995, PPSC.

[78]  T. Darden,et al.  Toward the Accurate Modeling of DNA: The Importance of Long-Range Electrostatics , 1995 .

[79]  Eric Barth,et al.  Algorithms for constrained molecular dynamics , 1995, J. Comput. Chem..

[80]  B. Matthews,et al.  Energetic origins of specificity of ligand binding in an interior nonpolar cavity of T4 lysozyme. , 1995, Biochemistry.

[81]  M. Karplus,et al.  SIMULATIONS OF MACROMOLECULES BY MULTIPLE TIME-STEP METHODS , 1995 .

[82]  B. Matthews,et al.  Protein flexibility and adaptability seen in 25 crystal forms of T4 lysozyme. , 1995, Journal of molecular biology.

[83]  John A. Board,et al.  A portable distributed implementation of the parallel multipole tree algorithm , 1995, Proceedings of the Fourth IEEE International Symposium on High Performance Distributed Computing.

[84]  T. Darden,et al.  A Multipole-Based Algorithm for Efficient Calculation of Forces and Potentials in Macroscopic Period , 1996 .

[85]  P. Tavan,et al.  Ligand Binding: Molecular Mechanics Calculation of the Streptavidin-Biotin Rupture Force , 1996, Science.

[86]  K. Schulten,et al.  The crystal structure of the light-harvesting complex II (B800-850) from Rhodospirillum molischianum. , 1996, Structure.

[87]  A. Leach Molecular Modelling: Principles and Applications , 1996 .

[88]  Laxmikant V. Kalé,et al.  Converse: an interoperable framework for parallel programming , 1996, Proceedings of International Conference on Parallel Processing.

[89]  K Schulten,et al.  VMD: visual molecular dynamics. , 1996, Journal of molecular graphics.

[90]  T. Schlick,et al.  A Multigrid Tutorial with Applications to Molecular Dynamics , 1996, IEEE Computational Science and Engineering.

[91]  G. Scuseria,et al.  Kohn-Sham analytic energy second derivatives with the Gaussian very fast multipole method (GvFMM) , 1996 .

[92]  G. Kleywegt,et al.  Checking your imagination: applications of the free R value. , 1996, Structure.

[93]  Berend Smit,et al.  Understanding molecular simulation: from algorithms to applications , 1996 .

[94]  John A. Board,et al.  Distributed P trticle-Mesh Ewald: A Parallel Ewald Summation Method , 1996, PDPTA.

[95]  J. Board,et al.  Ewald summation techniques in perspective: a survey , 1996 .

[96]  R. Read,et al.  Improved Structure Refinement Through Maximum Likelihood , 1996 .

[97]  Laxmikant V. Kalé,et al.  NAMD: a Parallel, Object-Oriented Molecular Dynamics Program , 1996, Int. J. High Perform. Comput. Appl..

[98]  A. Pastore,et al.  Immunoglobulin-like modules from titin I-band: extensible components of muscle elasticity. , 1996, Structure.

[99]  B. Matthews,et al.  Binding of small electron-dense ligands in large protein cavities , 1996 .

[100]  P. Procacci,et al.  Taming the Ewald sum in molecular dynamics simulations of solvated proteins via a multiple time step algorithm , 1996 .

[101]  H. Y. Wang,et al.  An efficient fast‐multipole algorithm based on an expansion in the solid harmonics , 1996 .

[102]  K. Schulten,et al.  Binding pathway of retinal to bacterio-opsin: a prediction by molecular dynamics simulations. , 1997, Biophysical journal.

[103]  P. Gill A new expansion of the Coulomb interaction , 1997 .

[104]  R. Levine,et al.  Molecular Collision Dynamics on Several Electronic States , 1997 .

[105]  K. Schulten,et al.  Binding of the estrogen receptor to DNA. The role of waters. , 1997, Biophysical journal.

[106]  James C. Phillips,et al.  Predicting the structure of apolipoprotein A-I in reconstituted high-density lipoprotein disks. , 1997, Biophysical journal.

[107]  B. Berne,et al.  Large scale simulation of macromolecules in solution: Combining the periodic fast multipole method with multiple time step integrators , 1997 .

[108]  Christophe G. Lambert,et al.  Ewald and Multipole Methods for Periodic N-body Problems , 1997, PPSC.

[109]  M. Rief,et al.  Reversible unfolding of individual titin immunoglobulin domains by AFM. , 1997, Science.

[110]  K. Schulten,et al.  Extraction of Lipids from Phospholipid Membranes by Steered Molecular Dynamics , 1997 .

[111]  P. Weiner,et al.  Computer Simulation of Biomolecular Systems , 1997 .

[112]  K. Schulten,et al.  Difficulties with multiple time stepping and fast multipole algorithm in molecular dynamics , 1997 .

[113]  T. Schlick,et al.  A separating framework for increasing the timestep in molecular dynamics , 1997 .

[114]  J. Marko Twist and shout (and pull): molecular chiropractors undo DNA. , 1997, Proceedings of the National Academy of Sciences of the United States of America.

[115]  P. Adams,et al.  New applications of simulated annealing in X-ray crystallography and solution NMR. , 1997, Structure.

[116]  T. Schlick Modeling and simulating biomolecules , 1997 .

[117]  K. Schulten,et al.  Molecular dynamics study of unbinding of the avidin-biotin complex. , 1997, Biophysical journal.

[118]  R. Read,et al.  Cross-validated maximum likelihood enhances crystallographic simulated annealing refinement. , 1997, Proceedings of the National Academy of Sciences of the United States of America.

[119]  O. Berger,et al.  Adhesion forces of lipids in a phospholipid membrane studied by molecular dynamics simulations. , 1998, Biophysical journal.

[120]  J. C. Phillips,et al.  Quantum dynamics of the femtosecond photoisomerization of retinal in bacteriorhodopsin. , 1998, Faraday discussions.

[121]  P. Kollman,et al.  Pathways to a protein folding intermediate observed in a 1-microsecond simulation in aqueous solution. , 1998, Science.

[122]  T. Ohwada Higher Order Approximation Methods for the Boltzmann Equation , 1998 .

[123]  H. Berendsen,et al.  Domain motions in bacteriophage T4 lysozyme: A comparison between molecular dynamics and crystallographic data , 1998, Proteins.

[124]  R. Skeel,et al.  Nonlinear Resonance Artifacts in Molecular Dynamics Simulations , 1998 .

[125]  T. Schlick,et al.  Extrapolation versus impulse in multiple-timestepping schemes. II. Linear analysis and applications to Newtonian and Langevin dynamics , 1998 .

[126]  K. Schulten,et al.  Unfolding of titin immunoglobulin domains by steered molecular dynamics simulation. , 1998, Biophysical journal.

[127]  T. Schlick,et al.  Overcoming stability limitations in biomolecular dynamics. I. Combining force splitting via extrapolation with Langevin dynamics in LN , 1998 .

[128]  S. W. Leeuw,et al.  An Iterative PPPM Method for Simulating Coulombic Systems on Distributed Memory Parallel Computers , 1998 .

[129]  Robert D. Skeel,et al.  Long-Time-Step Methods for Oscillatory Differential Equations , 1998, SIAM J. Sci. Comput..

[130]  T. Martínez,et al.  Nonadiabatic molecular dynamics: Validation of the multiple spawning method for a multidimensional problem , 1998 .

[131]  T. Schlick,et al.  Masking Resonance Artifacts in Force-Splitting Methods for Biomolecular Simulations by Extrapolative Langevin Dynamics , 1999 .

[132]  Laxmikant V. Kale,et al.  NAMD2: Greater Scalability for Parallel Molecular Dynamics , 1999 .

[133]  Klaus Schulten,et al.  Steered Molecular Dynamics , 1999, Computational Molecular Dynamics.

[134]  K. Schulten,et al.  Reconstructing Potentials of Mean Force through Time Series Analysis of Steered Molecular Dynamics Simulations , 1999 .

[135]  Jesús A. Izaguirre,et al.  The Five Femtosecond Time Step Barrier , 1999, Computational Molecular Dynamics.

[136]  Michael Dellnitz,et al.  Computation of Essential Molecular Dynamics by Subdivision Techniques , 1996, Computational Molecular Dynamics.

[137]  K. Schulten,et al.  Unbinding of retinoic acid from its receptor studied by steered molecular dynamics. , 1999, Biophysical journal.

[138]  Tamar Schlick,et al.  Some Failures and Successes of Long-Timestep Approaches to Biomolecular Simulations , 1999, Computational Molecular Dynamics.

[139]  J. Izaguirre Longer Time Steps for Molecular Dynamics , 1999 .