Research Papers

An Adaptive Multiscaling Approach for Reducing Computation Time in Simulations of Articulated Biopolymers

[+] Author and Article Information
Ashley Guy

Department of Mechanical and
Aerospace Engineering,
University of Texas at Arlington,
Arlington, TX 76019
e-mail: ashley.guy@uta.edu

Alan Bowling

The Robotics, Biomechanics, and
Dynamic Systems Laboratory Department of
Mechanical and Aerospace Engineering,
University of Texas at Arlington,
Arlington, TX 76019
e-mail: bowling@uta.edu

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received July 3, 2018; final manuscript received January 24, 2019; published online March 14, 2019. Assoc. Editor: Zdravko Terze.

J. Comput. Nonlinear Dynam 14(5), 051007 (Mar 14, 2019) (10 pages) Paper No: CND-18-1294; doi: 10.1115/1.4042691 History: Received July 03, 2018; Revised January 24, 2019

Microscale dynamic simulations can require significant computational resources to generate desired time evolutions. Microscale phenomena are often driven by even smaller scale dynamics, requiring multiscale system definitions to combine these effects. At the smallest scale, large active forces lead to large resultant accelerations, requiring small integration time steps to fully capture the motion and dictating the integration time for the entire model. Multiscale modeling techniques aim to reduce this computational cost, often by separating the system into subsystems or coarse graining to simplify calculations. A multiscale method has been previously shown to greatly reduce the time required to simulate systems in the continuum regime while generating equivalent time histories. This method identifies a portion of the active and dissipative forces that cancel and contribute little to the overall motion. The forces are then scaled to eliminate these noncontributing portions. This work extends that method to include an adaptive scaling method for forces that have large changes in magnitude across the time history. Results show that the adaptive formulation generates time histories similar to those of the unscaled truth model. Computation time reduction is consistent with the existing method.

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Lindorff-Larsen, K. , Piana, S. , Dror, R. O. , and Shaw, D. E. , 2011, “ How Fast-Folding Proteins Fold,” Science, 334(6055), pp. 517–520. [PubMed]
Henzler-Wildman, K. A. , Lei, M. , Thai, V. , Kerns, S. J. , Karplus, M. , and Kern, D. , 2007, “ A Hierarchy of Timescales in Protein Dynamics Is Linked to Enzyme Catalysis,” Nature, 450(7171), pp. 913–916. [PubMed]
Su, L.-C. , Xu, H. , Tran, R. T. , Tsai, Y.-T. , Tang, L. , Banerjee, S. , Yang, J. , and Nguyen, K. T. , 2014, “ In Situ Re-Endothelialization Via Multifunctional Nanoscaffolds,” ACS Nano, 8(10), pp. 10 826–10 836.
Nickolls, J. , Buck, I. , Garland, M. , and Skadron, K. , 2008, “ Scalable Parallel Programming With CUDA,” ACM Q, 6(2), pp. 40–53.
Stone, J. E. , Gohara, D. , and Shi, G. , 2010, “ Opencl: A Parallel Programming Standard for Heterogenous Computing Systems,” IEEE Des. Test, 12(3), pp. 66–73.
Meagher, D. , 1980, “ Octree Encoding: A New Technique for the Representation, Manipulation and Display of Arbitrary 3-D Objects by Computer,” Rensselaer Polytechnic Institute, Troy, NY, Report No. IPL-TR-80-111. https://searchworks.stanford.edu/view/4621957
Liu, W. , Schmidt, B. , Voss, G. , and Muller-Wittig, W. , 2008, “ Accelerating Molecular Dynamics Simulations Using Graphics Processing Units With Cuda,” Comput. Phys. Commun., 179(9), pp. 634–641.
Anderson, J. A. , Lorenz, C. D. , and Travesset, A. , 2008, “ General Purpose Molecular Dynamics Simulations Fully Implemented on Graphics Processing Units,” J. Comput. Phys., 227(10), pp. 5342–5359.
Jain, A. , Vaidehi, N. , and Rodriguez, G. A. , 1993, “ A Fast Recursive Algorithm for Molecular Dynamics Simulation,” J. Comput. Phys., 106(2), pp. 258–268.
Featherstone, R. , 1999, “ A Divide-and-Conquer Articulated-Body Algorithm for Parallel O(log(n)) Calculation of Rigid-Body-Dynamics—Part 1: Basic Algorithm,” Int. J. Robot. Res., 18(9), pp. 867–875.
Chun, H. M. , Padilla, C. E. , Chin, D. N. , Watanabe, M. , Karlov, V. I. , Alper, H. E. , Soosaar, K. , Blair, K. B. , Becker, O. M. , Caves, L. S. D. , Nagle, R. , Haney, D. N. , and Farmer, B. L. , 2000, “ MBO(N)D: A Multibody Method for Long-Time Molecular Dynamics Simulations,” J. Comp. Chem., 21(3), pp. 159–184.
Redon, S. , and Lin, M. C. , 2006, “ An Efficient, Error-Bounded Approximation Algorithm for Simulating Quasi-Statics of Complex Linkages,” Comput. Aided Des., 38(4), pp. 300–314.
Poursina, M. , Bhalerao, K. D. , Flores, S. C. , Anderson, K. S. , and Laederach, A. , 2011, “ Strategies for Articulated Multibody-Based Adaptive Coarse Grain Simulation of RNA,” Method Enzymol, 487, pp. 73–98.
Balaraman, G. S. , Park, I.-H. , Jain, A. , and Vaidehi, N. , 2011, “ Folding of Small Proteins Using Constrained Molecular Dynamics,” J. Phys. Chem., 115(23), pp. 7588–7596.
Gangupomu, V. K. , Wagner, J. R. , Park, I.-H. , Jain, A. , and Vaidehi, N. , 2013, “ Mapping Conformational Dynamics of Proteins Using Torsional Dynamics Simulations,” Biophys. J., 104(9), pp. 1999–2008. [PubMed]
Malczyk, P. , and Fraczek, J. , 2014, “ Molecular Dynamics Simulation of Simple Polymer Chain Formation Using Divide and Conquer Algorithm Based on the Augmented Lagrangian Method,” Proc. Inst. Mech. Eng. K, 229(2), pp. 116–131.
Poursina, M. , and Anderson, K. S. , 2013, “ Canonical Ensemble Simulation of Biopolymers Using a Coarse-Grained Articulated Generalized Divide-and-Conquer Scheme,” Comput. Phys. Commun., 184(3), pp. 652–660.
Deserno, M. , and Holm, C. , 1998, “ How to Mesh Up Ewald Sums—I: A Theoretical and Numerical Comparison of Various Particle Mesh Routines,” J. Chem. Phys., 109(18), pp. 7678–7693.
Voltz, K. , Trylska, J. , Tozzini, V. , Kurkal-Siebert, V. , Langowski, J. , and Smith, J. , 2008, “ Coarse-Grained Force Field for the Nucleosome From Self-Consistent Multiscaling,” J. Comput. Chem, 29(9), pp. 1429–1439. [PubMed]
Poursina, M. , and Anderson, K. S. , 2012, “ Long-Range Force and Moment Calculations in Multiresolution Simulations of Molecular Systems,” J. Comput. Phys., 231(21), pp. 7237–7254.
Poursina, M. , and Anderson, K. S. , 2014, “ An Improved Fast Multipole Method for Electrostatic Potential Calculations in a Class of Coarse-Grained Molecular Simulations,” J. Comput. Phys, 270, pp. 613–633.
Laflin, J. , and Anderson, K. S. , 2015, “ A Multibody Approach for Computing Long-Range Forces Between Rigid-Bodies Using Multipole Expansions,” J. Mech. Sci. Technol., 29(7), pp. 2671–2676.
Kremer, K. , and Muller-Plathe, F. , 2002, “ Multiscale Simulation in Polymer Science,” Mol. Simul., 28(8–9), pp. 729–750.
Broughton, J. Q. , Abraham, F. F. , Bernstein, N. , and Kaxiras, E. , 1999, “ Concurrent Coupling of Length Scales: Methodology and Application,” Phys. Rev. B, 60(4), pp. 2391–2403.
Zeng, Q. H. , Yu, A. B. , and Lu, G. Q. , 2008, “ Multiscale Modeling and Simulation of Polymer Nanocomposites,” Prog. Polym. Sci., 33(2), pp. 191–269.
Lu, G. , Tadmor, E. B. , and Kaxiras, E. , 2006, “ From Electrons to Finite Elements: A Concurrent Multiscale Approach for Metals,” Phys. Rev. B, 73(2), p. 024108.
Nielson, S. O. , Lopex, C. F. , Srinivas, G. , and Klein, M. L. , 2004, “ Coarse Grain Models and the Computer Simulation of Soft Materials,” J. Phys. Condens. Matter, 16(15), p. R481.
Shih, A. Y. , Freddolino, P. L. , Arkhipov, A. , and Schulten, K. , 2007, “ Assembly of Lipoprotein Particles Revealed by Coarse-Grained Molecular Dynamics Simulations,” J. Struct. Biol., 157(3), pp. 579–592. [PubMed]
Praprotnik, M. , Delle Site, L. , and Kremer, K. , 2005, “ Adaptive Resolution Molecular-Dynamics Simulation: Changing the Degrees of Freedom on the Fly,” J. Chem. Phys., 123(22), p. 224106. [PubMed]
Redon, S. , Galoppo, N. , and Lin, M. C. , 2005, “ Adaptive Dynamics of Articulated Bodies,” ACM Trans. Graphic, 24(3), pp. 936–945.
Praprotnik, M. , Delle Site, L. , and Kremer, K. , 2006, “ Adaptive Resolution Scheme for Efficient Hybrid Atomistic-Mesoscale Molecular Dynamics Simulations of Dense Liquids,” Phys. Rev. E, 73(6 Pt. 2), p. 066701.
Mukherjee, R. M. , and Anderson, K. S. , 2007, “ Efficient Methodology for Multibody Simulations With Discontinuous Changes in System Definition,” Multibody Syst. Dyn., 18(2), pp. 145–168.
Rossi, R. , Isorce, M. , Morin, S. , Flocard, J. , Arumugam, K. , Crouzy, S. , Vivaudou, M. , and Redon, S. , 2007, “ Adaptive Torsion-Angle Quasi-Statics: A General Simulation Method With Applications to Protein Structure Analysis and Design,” Bioinformatics, 23(13), pp. i408–i417. [PubMed]
Poursina, M. , 2011, “ Robust Framework for the Adaptive Multiscale Modeling of Biopolymers,” Ph.D. dissertation, Rensselaer Polytechnic Institute, Troy, NY.
Poursina, M. , and Anderson, K. S. , 2013, “ Efficient Coarse-Grained Molecular Simulations in the Multibody Dynamics Scheme,” Multibody Dyn., 28, pp. 147–172.
Poursina, M. , and Anderson, K. S. , 2018, “ Optimization Problem and Efficient Partitioning Algorithm for Transitions to Finer-Scale Models in Adaptive Resolution Simulation of Articulated Biopolymers,” Multibody Syst. Dyn., 42(1), pp. 97–117.
Plimpton, S. , 1995, “ Fast Parallel Algorithms for Short-Range Molecular Dynamics,” J. Comput. Phys., 117(1), pp. 1–19.
Singh, K. K. , and Redon, S. , 2017, “ Adaptively Restrained Molecular Dynamics in LAMMPS,” Modell. Simul. Mater. Sci. Eng., 25(5), p. 055013. https://iopscience.iop.org/article/10.1088/1361-651X/aa7345/meta
Haghshenas-Jaryani, M. , Black, B. , Ghaffari, S. , Drake, J. , Bowling, A. , and Mohanty, S. , 2014, “ Dynamics of Microscopic Objects in Optical Tweezers: Experimental Determination of Underdamped Regime and Numerical Simulation Using Multiscale Analysis,” Nonlinear Dyn., 76(2), pp. 1013–1030.
Palanki, A. , and Bowling, A. , 2015, “ Dynamic Model of Estrogen Docking Using Multiscale Analysis,” Nonlinear Dyn., 79(2), pp. 1519–1534.
Haghshenas-Jaryani, M. , and Bowling, A. , 2015, “ Modeling Flexibility in Myosin V Using a Multiscale Articulated Multi-Rigid Body Approach,” ASME J. Comput. Nonlinear Dyn., 10(1), p. 011015.
Guy, A. , and Bowling, A. , 2016, “ Multiscale Modeling of Ebola Virus Glycoprotein,” ASME Paper No. NEMB2016-6028.
Guy, A. , and Bowling, A. , 2018, “ A Multiscale Formulation for Reducing Computation Time in Atomistic Simulations,” ASME J. Comput. Nonlinear Dyn., 13(5), p. 051002.
Nayfeh, A. H. , 1973, Perturbation Methods, Wiley, Weinheim, Germany.
Yakimova, R. , Syvajarvi, M. , Lockowandt, C. , and Linnarsson, M. K. , 1998, “ Silicon Carbide Grown by Liquid Phase Epitaxy in Microgravity,” J. Mater. Res., 13(7), pp. 1812–1815.
Zhou, Y. F. , Xu, J. Y. , Liu, Y. , Chen, L. D. , Huang, Y. Y. , and Huang, W. X. , 2007, “ Influence of Microgravity on Ce-Doped Bi12SiO20 Crystal Defect,” Mater. Sci. B, 30(3), pp. 211–214.
Okutani, T. , Kabeya, Y. , and Nagai, H. , 2013, “ Thermoelectric n-Type Silicon Germanium Synthesize by Unidirectional Solidification in Microgravity,” J. Alloy Compd., 551, pp. 607–615.
Bowling, A. , and Haghshenas-Jaryani, M. , 2015, “ A Multiscale Modeling Approach for Biomolecular Systems,” Multibody Syst. Dyn., 33(4), pp. 333–365.
Cornell, W. D. , Cieplak, P. , Bayly, C. I. , Gould, I. R. , Merz , K. M. , Ferguson, D. M. , Spellmeyer, D. C. , Fox, T. , Caldwell, J. W. , and Kollman, P. A. , 1995, “ A Second Generation Force Field for the Simulation of Proteins, Nucleic Acids, and Organic Molecules,” J. Am. Chem., 117(19), pp. 5179–5197.
MacKerell, A. D. , Bashford, D. , Bellott, M. , Dunbrack, R. L. , Evanseck, J. D. , Field, M. J. , Fischer, S. , Gao, J. , Guo, H. , Ha, S. , Joseph-McCarthy, D. , Kuchnir, L. , Kuczera, K. , Lau, F. T. K. , Mattos, C. , Michnick, S. , Ngo, T. , Nguyen, D. T. , Prodhom, B. , Reiher, W. E. , Roux, B. , Schlenkrich, M. , Smith, J. C. , Stote, R. , Straub, J. , Watanabe, M. , Wiorkiewicz-Kuczera, J. , Yin, D. , and Karplus, M. , 1998, “ All-Atom Empirical Potential for Molecular Modeling and Dynamics Studies of Proteins,” J. Phys. Chem., 102(18), pp. 3586–3616.
Peter, C. , and Kremer, K. , 2009, “ Multiscale Simulation of Soft Matter Systems—From the Atomistic to the Coarse-Grained Level and Back,” Soft Matter, 5(22), pp. 4357–4366.
Kroll, M. H. , Harris, T. S. , Moake, J. L. , Handin, R. I. , and Schafer, A. I. , 1991, “ Von Willebrand Factor Binding to Platelet GpIb Initiates Signals for Platelet Activation,” J. Clin. Invest., 88(5), pp. 1568–1573. [PubMed]
Kanaji, S. , Orje, J. N. , Kamikubo, Y. , Kanaji, T. , Mattson, J. , Zarpellon, A. , Fahs, S. A. , Sood, R. , Haberichter, S. L. , Ruggeri, Z. M. , and Montgomery, R. R. , 2016, “ Humanized Von Willebrand Factor-Glycoprotein Ibα Interaction in Mouse Models of Hemostasis and Thrombosis,” Blood, 128(22), p. 558. http://www.bloodjournal.org/content/128/22/558
Lu, L. , Parmar, M. B. , Kulka, M. , Kwan, P. , and Unsworth, L. D. , 2018, “ Self-Assembling Peptide Nanoscaffold That Activates Human Mast Cells,” ACS Appl. Mater. Interfaces, 10(7), pp. 6107–6117. [PubMed]
The UniProt Consortium, 2018, “ Uniprot: The Universal Protein Knowledgebase,” Nucl. Acids Res., 46(5), p. 2699.
Haghshenas-Jaryani, M. , and Bowling, A. , 2012, “ A New Switching Strategy for Addressing Euler Parameters in Dynamic Modeling and Simulation of Rigid Multibody Systems,” Multibody Syst. Dyn., 30(2), pp. 185–197.


Grahic Jump Location
Fig. 1

(top) 3D model of GP1b protein and vWF receptor; image taken from the modeling tools on Ref. [55]; (bottom) model of GP1b coarse grain approximation; dashed lines correlate to the plotted bodies in Figs. 2 and 6

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Fig. 2

Locations of the eight GP1b proteins on the nanoparticle

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Fig. 3

Plots of initial and final positions of the nanoparticle. Bang-bang and hyperbolic shown as Adaptive.

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Fig. 4

Nanoparticle position in N̂1 direction over time

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Fig. 5

Trajectories of centers of mass

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Fig. 6

GP1b proteins approximately 0.3 μs after adaptive scaling enabled

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Fig. 7

Bang-bang controlled system energy. W denotes the work done by friction (subscript d), potential (p), stochastic (s), and conformational (c) forces. T denotes kinetic energy.

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Fig. 8

Hyperbolic controlled system energy

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Fig. 9

Unscaled system energy

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Fig. 10

Force magnitudes from the bang-bang (top) and hyperbolic (bottom) systems. Forces shown are damping (subscript d), conformational (c), potential (p), and stochastic (s). Dashed vertical line denotes time when adaptive scaling is activated.

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Fig. 11

Adaptive scaling factor a2* over time

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Fig. 12

Kinetic energy over time. Dashed vertical line denotes time when bang-bang controller is activated.



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