Advertisement

Modelling the Dynamic Architecture of Biomaterials Using Continuum Mechanics

  • Robin Oliver
  • Robin A. Richardson
  • Ben Hanson
  • Katherine Kendrick
  • Daniel J. Read
  • Oliver G. Harlen
  • Sarah A. Harris
Chapter

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.

Keywords

Protein Data Bank Thermal Noise Lattice Boltzmann Method Dissipative Particle Dynamic Brownian Dynamic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Meyer T et al (2010) MoDEL (molecular dynamics extended library): a database of atomistic molecular dynamics trajectories. Structure 18(11):1399–1409CrossRefGoogle Scholar
  2. 2.
    Robinson CV, Sali A, Baumeister W (2007) The molecular sociology of the cell. Nature 450(7172):973–982CrossRefGoogle Scholar
  3. 3.
    www.emdatabank.org. Emdb deposition and annotation statistics: Emdatabank. http://www.emdatabank.org/dpstn_annot_stats.html, April 2014
  4. 4.
    Marrink SJ, Tielman DP (2013) Perspective on the martini model. Chem Soc Rev 42(16):6801–6822CrossRefGoogle Scholar
  5. 5.
    Tozzini V (2010) Minimalist models for proteins: a comparative analysis. Q Rev Biophys 43(3):333–371CrossRefGoogle Scholar
  6. 6.
    Mills ZG, Mao W, Alexeev A (2013) Mesoscale modeling: solving complex flows in biology and biotechnology. Trends Biotechnol 31(7):426–434CrossRefGoogle Scholar
  7. 7.
    McLeish TC, Rodgers TL, Wilson MR (2013) Allostery without conformation change: modelling protein dynamics at multiple scales. Phys Biol 10(5):056004Google Scholar
  8. 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):886–896CrossRefGoogle Scholar
  9. 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–W614CrossRefGoogle Scholar
  10. 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):1219–1227CrossRefGoogle Scholar
  11. 11.
    Bahar I, Lezon TR, Bakan A et al (2010) Global dynamics of proteins: bridging between structure and function. Ann Rev Biophys 39:23–42CrossRefGoogle Scholar
  12. 12.
    Noid WG (2013) Perspective: coarse-grained models for biomolecular systems. J Chem Phys 139(9)Google Scholar
  13. 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. 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. 15.
    Meigh L et al (2013) CO2 directly modulates connexin 26 by formation of carbamate bridges between subunits. Elife 2:e01213Google Scholar
  16. 16.
    Kin D, Nguyen C, Bathe M (2010) Conformational dynamics of supramolecular protein assemblies. J Struc Biol 173:261–270Google Scholar
  17. 17.
    Ermak DL, Buckholz H (1980) Numerical integration of the Langevin equation: Monte carlo simulation. J Comp Phys 35(2):168–182CrossRefGoogle Scholar
  18. 18.
    Chen JC, Kim AS (2004) Brownian dynamics, molecular dynamics, and monte carlo modelling of colloidal systems. Adv Colloid Interface Sci 112(1):159–173CrossRefGoogle Scholar
  19. 19.
    Kubo R (1966) The fluctuation-dissipation theorem. Rep Prog Phys 29(1)Google Scholar
  20. 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. 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–L77CrossRefGoogle Scholar
  22. 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):1576–1584CrossRefGoogle Scholar
  23. 23.
    Joyeux M, Vreede J (2013) A model of h-ns mediated compaction of bacterial DNA. Biophys J 104(7):1615–1622CrossRefGoogle Scholar
  24. 24.
    Doi M, Edwards SF (1998) The theory of polymer dynamics. Oxford University Press, OxfordGoogle Scholar
  25. 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):1829–1838CrossRefGoogle Scholar
  26. 26.
    Groot RD, Warren PB (1997) Dissipative particle dynamics: bridging the gap between atomistic and mesoscopic simulation. J Chem Phys 107(11):4423CrossRefGoogle Scholar
  27. 27.
    Español P, Warren PB (1995) Statistical mechanics of dissipative particle dynamics. Europhys Lett 30(4):191CrossRefGoogle Scholar
  28. 28.
    Pivkin IV, Karniadakis GE (2005) A new method to impose no-slip boundary conditions in dissipative particle dynamics. J Comp Phys 207(1):114–128CrossRefGoogle Scholar
  29. 29.
    Liu F, Wu D, Kamm RD et al (2013) Analysis of nanoprobe penetration through a lipid bilayer. Biochim Biophys Acta Biomembr 1828(8):1667–1673CrossRefGoogle Scholar
  30. 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):13356–13361CrossRefGoogle Scholar
  31. 31.
    Succi S (2001) The lattice Boltzmann equation: for fluid dynamics and beyond. Oxford University Press, OxfordGoogle Scholar
  32. 32.
    Aidun C, Clausen J (2010) Lattice-boltzmann method for complex flows. Ann Rev Fluid Mech 42:439–472CrossRefGoogle Scholar
  33. 33.
    Chen S, Doolen GD (1998) Lattice boltzmann method for fluid flows. Ann Rev Fluid Mech 30(1):329–364CrossRefGoogle Scholar
  34. 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):6811CrossRefGoogle Scholar
  35. 35.
    Zou Q, He X (1997) On pressure and velocity boundary conditions for the lattice boltzmann BGK model. Phys Fluids 9(6):1591–1598CrossRefGoogle Scholar
  36. 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 89:47–56CrossRefGoogle Scholar
  37. 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):47–55CrossRefGoogle Scholar
  38. 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 46:1237–1252CrossRefGoogle Scholar
  39. 39.
    Adhikari R, Stratford K, Cates ME, Wagner AJ (2005) Fluctuating lattice boltzmann. Europhys Lett 71(3):473CrossRefGoogle Scholar
  40. 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. 41.
    Fung YC (1977) A first course in continuum mechanics. Prentice-Hall Inc., Englewood CliffsGoogle Scholar
  42. 42.
    Sokolnikoff IS, Specht RD (1956) Mathematical theory of elasticity, vol 83. McGraw-Hill, New YorkGoogle Scholar
  43. 43.
    Eringen AC (1980) Mechanics of continua. Robert E. Krieger Publishing Co, MalabarGoogle Scholar
  44. 44.
    Reddy JN (2013) An Introduction to Continuum Mechanics. Cambridge University Press, CambridgeGoogle Scholar
  45. 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):35–60CrossRefGoogle Scholar
  46. 46.
    Versteeg HK, Malalasekera W (2007) An introduction to computational fluid dynamics: the finite volume method. Pearson Education, DelhiGoogle Scholar
  47. 47.
    Reddy JN (1993) An introduction to the finite element method. McGraw-Hill, New YorkGoogle Scholar
  48. 48.
    Shah S, Liu Y, Hu W, Gao J (2011) Modeling particle shape-dependent dynamics in nanomedicine. J Nanosci Nanotech 11(2):919CrossRefGoogle Scholar
  49. 49.
    Gracheva ME, Othmer HG (2004) A continuum model of motility in ameboid cells. Bull Math Biol 66(1):167–193CrossRefGoogle Scholar
  50. 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):699–712CrossRefGoogle Scholar
  51. 51.
    Bathe M (2008) A finite element framework for computation of protein normal modes and mechanical response. Proteins 70:1595–1609CrossRefGoogle Scholar
  52. 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 39:451–455CrossRefGoogle Scholar
  53. 53.
    Oliver RC, Read DJ, Harlen OG, Harris SA (2013) A stochastic finite element model for the dynamics of globular macromolecules. J Comp Phys 239:147–165CrossRefGoogle Scholar
  54. 54.
    Meyers MA, Chawla KK (2009) Mechanical behavior of materials. Cambridge University Press, CambridgeGoogle Scholar
  55. 55.
    Lai WM, Rubin DH, Rubin D, Krempl E (2009) Introduction to continuum mechanics. Butterworth-Heinemann, OxfordGoogle Scholar
  56. 56.
    Bower AF (2011) Applied mechanics of solids. CRC Press, Boca RatonGoogle Scholar
  57. 57.
    Ross CTF (1998) Advanced applied finite element methods. Woodhead Publishing, CambridgeGoogle Scholar
  58. 58.
    Dhatt G, Lefrançois E, Touzot G (2012) Finite element method. Wiley, New YorkCrossRefGoogle Scholar
  59. 59.
    Landau LD, Lifshitz EM (1959) Fluid mechanics: course of theoretical physics, vol 6. Pergamon Press, New YorkGoogle Scholar
  60. 60.
    Gere JM (2004) Mechanics of materials, 6th edn. Brookes/ColeGoogle Scholar
  61. 61.
    Burgess SA, Walker ML, Sakakibara H, Knight PJ, Oiwa K (2003) Dynein structure and powerstroke. Nature 421(6924):715–718CrossRefGoogle Scholar
  62. 62.
    Kollman JM, Pandi L, Sawaya MR, Riley M, Doolittle RF (2009) Crystal structure of human fibrinogen. Biochemistry 48(18):3877–3886CrossRefGoogle Scholar
  63. 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):1605–1612CrossRefGoogle Scholar
  64. 64.
    Schöberl J (1997) Netgen an advancing front 2d/3d-mesh generator based on abstract rules. Comput Vis Sci 1(1):41–52CrossRefGoogle Scholar
  65. 65.
    Kurland NE, Drira Z, Yadavalli VK (2012) Measurement of nanomechanical properties of biomolecules using atomic force microscopy. Micron 43(2):116–128CrossRefGoogle Scholar
  66. 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):1391–1395CrossRefGoogle Scholar
  67. 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):251–258CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Robin Oliver
    • 1
  • Robin A. Richardson
    • 2
  • Ben Hanson
    • 2
  • Katherine Kendrick
    • 2
  • Daniel J. Read
    • 3
  • Oliver G. Harlen
    • 3
  • Sarah A. Harris
    • 2
  1. 1.Sheffield UniversitySheffieldUK
  2. 2.School of Physics and Astronomy, E C Stoner BuildingUniversity of LeedsLeedsUK
  3. 3.School of MathematicsUniversity of LeedsLeedsUK

Personalised recommendations