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Modelling the Dynamic Architecture of Biomaterials Using Continuum Mechanics

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Book cover Protein Modelling

Abstract

While computer simulations that model biomacromolecules at the quantum mechanical and atomistic levels are well established, mesoscale methods that access longer length scales (\( {\sim} 10 - 500\,{\text{nm}} \)) are less mature. Simulation techniques originally developed for materials modelling, such as dissipative particle dynamics, lattice Boltzmann and finite element analysis, have however recently been applied to biomolecules, and provide access to time and length-scale far greater than those accessible with quantum or atomistic simulations, with the caveat that there is a significant reduction in the level of detail in which structures are represented during the calculations. We provide an overview of these mesoscale methods, explaining the underlying physical principles and comment on their advantages and limitations, with an emphasis on their potential for biomolecular simulation.

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References

  1. Meyer T et al (2010) MoDEL (molecular dynamics extended library): a database of atomistic molecular dynamics trajectories. Structure 18(11):1399–1409

    Article  CAS  Google Scholar 

  2. Robinson CV, Sali A, Baumeister W (2007) The molecular sociology of the cell. Nature 450(7172):973–982

    Article  CAS  Google Scholar 

  3. www.emdatabank.org. Emdb deposition and annotation statistics: Emdatabank. http://www.emdatabank.org/dpstn_annot_stats.html, April 2014

  4. Marrink SJ, Tielman DP (2013) Perspective on the martini model. Chem Soc Rev 42(16):6801–6822

    Article  CAS  Google Scholar 

  5. Tozzini V (2010) Minimalist models for proteins: a comparative analysis. Q Rev Biophys 43(3):333–371

    Article  CAS  Google Scholar 

  6. Mills ZG, Mao W, Alexeev A (2013) Mesoscale modeling: solving complex flows in biology and biotechnology. Trends Biotechnol 31(7):426–434

    Article  CAS  Google Scholar 

  7. McLeish TC, Rodgers TL, Wilson MR (2013) Allostery without conformation change: modelling protein dynamics at multiple scales. Phys Biol 10(5):056004

    Google Scholar 

  8. Zheng W, Liao JC, Brooks BR, Doniach S (2007) Toward the mechanism of dynamical couplings and translocation in hepatitis c virus ns3 helicase using elastic network model. Proteins Struct Funct Bioinf 67(4):886–896

    Article  CAS  Google Scholar 

  9. Suhre K, Sanejouand YH (2004) Elnémo: a normal mode web server for protein movement analysis and the generation of templates for molecular replacement. Nucleic Acids Res 32(2):W610–W614

    Article  CAS  Google Scholar 

  10. Emekli U, SchneidmanDuhovny D, Wolfson HJ, Nussinov R, Haliloglu T (2008) Hingeprot: automated prediction of hinges in protein structures. Proteins Struct Funct Bioinf 70(4):1219–1227

    Article  CAS  Google Scholar 

  11. Bahar I, Lezon TR, Bakan A et al (2010) Global dynamics of proteins: bridging between structure and function. Ann Rev Biophys 39:23–42

    Article  CAS  Google Scholar 

  12. Noid WG (2013) Perspective: coarse-grained models for biomolecular systems. J Chem Phys 139(9)

    Google Scholar 

  13. Gur M, Zomot E, Bahar I (2013) Global motions exhibited by proteins in micro- to milliseconds simulations concur with anisotropic network model predictions. J Chem Phys 139(12)

    Google Scholar 

  14. Rodgers TL, Townsend PD, Burnell D et al (2013) Modulation of global low-frequency motions underlies allosteric regulation: demonstration in CRP/FNR family transcription factors. PLOS Biol 11(9)

    Google Scholar 

  15. Meigh L et al (2013) CO2 directly modulates connexin 26 by formation of carbamate bridges between subunits. Elife 2:e01213

    Google Scholar 

  16. Kin D, Nguyen C, Bathe M (2010) Conformational dynamics of supramolecular protein assemblies. J Struc Biol 173:261–270

    Google Scholar 

  17. Ermak DL, Buckholz H (1980) Numerical integration of the Langevin equation: Monte carlo simulation. J Comp Phys 35(2):168–182

    Article  Google Scholar 

  18. Chen JC, Kim AS (2004) Brownian dynamics, molecular dynamics, and monte carlo modelling of colloidal systems. Adv Colloid Interface Sci 112(1):159–173

    Article  CAS  Google Scholar 

  19. Kubo R (1966) The fluctuation-dissipation theorem. Rep Prog Phys 29(1)

    Google Scholar 

  20. McGuffee SR, Elcock AH (2010) Diffusion, crowding and protein stability in a dynamic molecular model of the bacterial cytoplasm. PLOS Comp Biol 6(3)

    Google Scholar 

  21. Frembgen-Kesner T, Elcock AH (2010) Absolute protein-protein association rate constants from flexible, coarse-grained brownian dynamics simulations: the role of intermolecular hydrodynamic interactions in barnase-barstar association. Biophys J 99(9):L75–L77

    Article  CAS  Google Scholar 

  22. Balbo J, Mereghetti P, Herten D, Wade RC (2013) The shape of protein crowders is a major determinant of protein diffusion. Biophys J 104(7):1576–1584

    Article  CAS  Google Scholar 

  23. Joyeux M, Vreede J (2013) A model of h-ns mediated compaction of bacterial DNA. Biophys J 104(7):1615–1622

    Article  CAS  Google Scholar 

  24. Doi M, Edwards SF (1998) The theory of polymer dynamics. Oxford University Press, Oxford

    Google Scholar 

  25. Hajjoul H, Mathon J, Ranchon H et al (2013) High-throughput chromatin motion tracking in living yeast reveals the flexibility of the fiber throughout the genome. Genome Res 23(11):1829–1838

    Article  CAS  Google Scholar 

  26. Groot RD, Warren PB (1997) Dissipative particle dynamics: bridging the gap between atomistic and mesoscopic simulation. J Chem Phys 107(11):4423

    Article  CAS  Google Scholar 

  27. Español P, Warren PB (1995) Statistical mechanics of dissipative particle dynamics. Europhys Lett 30(4):191

    Article  Google Scholar 

  28. Pivkin IV, Karniadakis GE (2005) A new method to impose no-slip boundary conditions in dissipative particle dynamics. J Comp Phys 207(1):114–128

    Article  Google Scholar 

  29. Liu F, Wu D, Kamm RD et al (2013) Analysis of nanoprobe penetration through a lipid bilayer. Biochim Biophys Acta Biomembr 1828(8):1667–1673

    Article  CAS  Google Scholar 

  30. Peng Z, Li X, Pivkin I, Dao M, Karniadakis G, Suresh S (2013) Lipid bilayer and cytoskeletal interactions in a red blood cell. Proc Natl Acad Sci USA 110(33):13356–13361

    Article  CAS  Google Scholar 

  31. Succi S (2001) The lattice Boltzmann equation: for fluid dynamics and beyond. Oxford University Press, Oxford

    Google Scholar 

  32. Aidun C, Clausen J (2010) Lattice-boltzmann method for complex flows. Ann Rev Fluid Mech 42:439–472

    Article  Google Scholar 

  33. Chen S, Doolen GD (1998) Lattice boltzmann method for fluid flows. Ann Rev Fluid Mech 30(1):329–364

    Article  Google Scholar 

  34. He X, Luo LS (1997) Theory of the lattice boltzmann method: from the boltzmann equation to the lattice boltzmann equation. Phys Rev E 56(6):6811

    Article  CAS  Google Scholar 

  35. Zou Q, He X (1997) On pressure and velocity boundary conditions for the lattice boltzmann BGK model. Phys Fluids 9(6):1591–1598

    Article  CAS  Google Scholar 

  36. Yin X, Thomas T, Zhang J (2013) Multiple red blood cell flows through microvascular bifurcations: cell free layer, cell trajectory, and hematocrit separation. Microvasc Res 89:47–56

    Article  Google Scholar 

  37. Zhang J, Johnson PC, Popel AS (2008) Red blood cell aggregation and dissociation in shear flows simulated by lattice boltzmann method. J Biomech 41(1):47–55

    Article  Google Scholar 

  38. Liu Y, Zhang L, Wang X, Liu WK (2004) Coupling of navierstokes equations with protein molecular dynamics and its application to hemodynamics. Int J Numer Methods Fluids 46:1237–1252

    Article  CAS  Google Scholar 

  39. Adhikari R, Stratford K, Cates ME, Wagner AJ (2005) Fluctuating lattice boltzmann. Europhys Lett 71(3):473

    Article  CAS  Google Scholar 

  40. Gross M, Adhikari R, Cates ME, Varnik F (2010) Thermal fluctuations in the lattice boltzmann method for nonideal fluids. Phys Rev E 82(5)

    Google Scholar 

  41. Fung YC (1977) A first course in continuum mechanics. Prentice-Hall Inc., Englewood Cliffs

    Google Scholar 

  42. Sokolnikoff IS, Specht RD (1956) Mathematical theory of elasticity, vol 83. McGraw-Hill, New York

    Google Scholar 

  43. Eringen AC (1980) Mechanics of continua. Robert E. Krieger Publishing Co, Malabar

    Google Scholar 

  44. Reddy JN (2013) An Introduction to Continuum Mechanics. Cambridge University Press, Cambridge

    Google Scholar 

  45. Fadlun EA, Verzicco R, Orlandi P, Mohd-Yusof J (2000) Combined immersed-boundary finite-difference methods for three-dimensional complex flow simulations. J Comp Phys 161(1):35–60

    Article  Google Scholar 

  46. Versteeg HK, Malalasekera W (2007) An introduction to computational fluid dynamics: the finite volume method. Pearson Education, Delhi

    Google Scholar 

  47. Reddy JN (1993) An introduction to the finite element method. McGraw-Hill, New York

    Google Scholar 

  48. Shah S, Liu Y, Hu W, Gao J (2011) Modeling particle shape-dependent dynamics in nanomedicine. J Nanosci Nanotech 11(2):919

    Article  CAS  Google Scholar 

  49. Gracheva ME, Othmer HG (2004) A continuum model of motility in ameboid cells. Bull Math Biol 66(1):167–193

    Article  Google Scholar 

  50. De Hart J, Baaijens FPT, Peters GWM, Schreurs PJG (2003) A computational fluid-structure interaction analysis of a fiber-reinforced stentless aortic valve. J Biomech 36(5):699–712

    Article  Google Scholar 

  51. Bathe M (2008) A finite element framework for computation of protein normal modes and mechanical response. Proteins 70:1595–1609

    Article  CAS  Google Scholar 

  52. Kim D, Altschuler J, Strong C, McGill G, Bathe M (2011) Conformational dynamics data bank: a database for conformational dynamics of proteins and supramolecular protein assemblies. Nucleic Acids Res 39:451–455

    Article  Google Scholar 

  53. Oliver RC, Read DJ, Harlen OG, Harris SA (2013) A stochastic finite element model for the dynamics of globular macromolecules. J Comp Phys 239:147–165

    Article  CAS  Google Scholar 

  54. Meyers MA, Chawla KK (2009) Mechanical behavior of materials. Cambridge University Press, Cambridge

    Google Scholar 

  55. Lai WM, Rubin DH, Rubin D, Krempl E (2009) Introduction to continuum mechanics. Butterworth-Heinemann, Oxford

    Google Scholar 

  56. Bower AF (2011) Applied mechanics of solids. CRC Press, Boca Raton

    Google Scholar 

  57. Ross CTF (1998) Advanced applied finite element methods. Woodhead Publishing, Cambridge

    Google Scholar 

  58. Dhatt G, Lefrançois E, Touzot G (2012) Finite element method. Wiley, New York

    Book  Google Scholar 

  59. Landau LD, Lifshitz EM (1959) Fluid mechanics: course of theoretical physics, vol 6. Pergamon Press, New York

    Google Scholar 

  60. Gere JM (2004) Mechanics of materials, 6th edn. Brookes/Cole

    Google Scholar 

  61. Burgess SA, Walker ML, Sakakibara H, Knight PJ, Oiwa K (2003) Dynein structure and powerstroke. Nature 421(6924):715–718

    Article  CAS  Google Scholar 

  62. Kollman JM, Pandi L, Sawaya MR, Riley M, Doolittle RF (2009) Crystal structure of human fibrinogen. Biochemistry 48(18):3877–3886

    Article  CAS  Google Scholar 

  63. Pettersen EF, Goddard TD, Huang CC, Couch GS, Greenblatt DM, Meng EC, Ferrin TE (2004) UCSF chimera—a visualization system for exploratory research and analysis. J Comp Chem 25(13):1605–1612

    Article  CAS  Google Scholar 

  64. Schöberl J (1997) Netgen an advancing front 2d/3d-mesh generator based on abstract rules. Comput Vis Sci 1(1):41–52

    Article  Google Scholar 

  65. Kurland NE, Drira Z, Yadavalli VK (2012) Measurement of nanomechanical properties of biomolecules using atomic force microscopy. Micron 43(2):116–128

    Article  CAS  Google Scholar 

  66. Desfossee A, Goret G, Estrozi LF, Ruigrok RWH, Gutsche I (2011) Nucleo-protein-rna orientation in the measles virus nucleocapsid by three-dimensional electron microscopy. J Virology 85(3):1391–1395

    Article  Google Scholar 

  67. Meyer T, Ferrer-Costa C, Perez A, Rueda M, Bidon-Chanal A, Luque F, Laughton CA, Orozco M (2006) Essential dynamics: a tool for efficient trajectory compression and management. J Chem Theory Comput 2(2):251–258

    Article  CAS  Google Scholar 

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Authors and Affiliations

  1. Sheffield University, Hicks Building Hounsfield Road, Sheffield, S3 7RH, UK

    Robin Oliver

  2. School of Physics and Astronomy, E C Stoner Building, University of Leeds, Leeds, LS2 9JT, UK

    Robin A. Richardson, Ben Hanson, Katherine Kendrick & Sarah A. Harris

  3. School of Mathematics, University of Leeds, Leeds, LS2 9JT, UK

    Daniel J. Read & Oliver G. Harlen

Authors
  1. Robin Oliver
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  2. Robin A. Richardson
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  3. Ben Hanson
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  4. Katherine Kendrick
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  5. Daniel J. Read
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  6. Oliver G. Harlen
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  7. Sarah A. Harris
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Corresponding author

Correspondence to Sarah A. Harris .

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Editors and Affiliations

  1. Chemistry Department, Eotvos Lorand University, Budapest, Hungary

    Gábor Náray-Szabó

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Oliver, R. et al. (2014). Modelling the Dynamic Architecture of Biomaterials Using Continuum Mechanics. In: Náray-Szabó, G. (eds) Protein Modelling. Springer, Cham. https://doi.org/10.1007/978-3-319-09976-7_8

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