Multibody System Dynamics

, Volume 33, Issue 4, pp 333–365 | Cite as

A multiscale modeling approach for biomolecular systems



This paper presents a new multiscale molecular dynamic model for investigating the effects of external interactions, such as contact and impact, during stepping and docking of motor proteins and other biomolecular systems. The model retains the mass properties ensuring that the result satisfies Newton’s second law. This idea is presented using a simple particle model to facilitate discussion of the rigid body model; however, the particle model does provide insights into particle dynamics at the nanoscale. The resulting three-dimensional model predicts a significant decrease in the effect of the random forces associated with Brownian motion. This conclusion runs contrary to the widely accepted notion that the motor protein’s movements are primarily the result of thermal effects. This work focuses on the mechanical aspects of protein locomotion; the effect ATP hydrolysis is estimated as internal forces acting on the mechanical model. In addition, the proposed model can be numerically integrated in a reasonable amount of time. Herein, the differences between the motion predicted by the old and new modeling approaches are compared using a simplified model of myosin V.


Multibody Dynamics Motor protein Multiscale Modeling Myosin V Contact 



This work was supported by National Science Foundation Grant No. MCB-1148541 and funds from the Department of Mechanical and Aerospace Engineering at the University of Texas at Arlington.


  1. 1.
    Abraham, F.F., Broughton, J.Q., Bernstein, N., Kaxiras, E.: Spanning the continuum to quantum length scales in a dynamic simulation of brittle fracture. EPL (Europhys. Lett.) 44(6), 783 (1998). Google Scholar
  2. 2.
    Acary, V., Brogliato, B.: Lecture Notes in Applied and Computational Mechanics, 1st edn., vol. 35. Springer, Berlin (2008) Google Scholar
  3. 3.
    Aksimentiev, A., Balabin, I.A., Fillingame, R.H., Schulten, K.: Insights into the molecular mechanism of rotation in the fo sector of atp synthase. Biophys. J. 86(3), 1332–1344 (2004) Google Scholar
  4. 4.
    Anderson, K., Poursina, M., Bhalerao, K.D.: On adaptive multiscale modeling of biomolecular systems with application in RNA. In: Proceedings of the Joint International Conference on Multibody System Dynamics. Lappeenranta, Finland, (2010) Google Scholar
  5. 5.
    Asenjo, A.B., Sosa, H.: A mobile kinesin-head intermediate during the ATP-waiting state. Proc. Natl. Acad. Sci. USA 106(14), 5657–5662 (2009) Google Scholar
  6. 6.
    Atzberger, P.J., Peskin, C.S.: A Brownian dynamics model of kinesin in three dimensions incorporating the force-extension profile of the coiled-coil cargo tether. Bull. Math. Biol. 68(1), 131–160 (2006) MathSciNetGoogle Scholar
  7. 7.
    Austin, R.H.: Nanoscale hydrodynamics in the cell: balancing motorized transport with diffusion. HFSP J. 2(5), 262–265 (2008) Google Scholar
  8. 8.
    Aydt, E.M., Wolff, G., Morano, I.: Molecular modeling of the myosin-S1(A1) isoform. J. Struct. Biol. 159(1), 158–163 (2007) Google Scholar
  9. 9.
    Ayton, G.S., Noid, W.G., Voth, G.A.: Multiscale modeling of biomolecular systems: in serial and in parallel. Curr. Opin. Struct. Biol. 17(2), 192–198 (2007) Google Scholar
  10. 10.
    Baruh, H.: Analytical Dynamics, 1st edn. WCB McGraw-Hill, New York (1999) Google Scholar
  11. 11.
    Ben-Ari, I., Boushaba, K., Matzavinos, A., Roitershtein, A.: Stochastic Analysis of the Motion of dna Nanomechanical Bipeds. Bulletin of Mathematical Biology (2010) Google Scholar
  12. 12.
    Bevan, D.R., Garst, J.F., Osborne, C.K., Sims, A.M.: Application of molecular modeling to analysis of inhibition of kinesin motor proteins of the BimC subfamily by monastrol and related compounds. Chem. Biodivers. 2(11), 1525–1532 (2005) Google Scholar
  13. 13.
    Bier, M.: Processive motor protein as an overdamped Brownian stepper. Phys. Rev. Lett. 91(14), 148104 (2003) Google Scholar
  14. 14.
    Bier, M.: Modelling processive motor proteins: moving on two legs in the microscopic realm. Contemp. Phys. 46(1), 41–51 (2005) MathSciNetGoogle Scholar
  15. 15.
    Bierbaum, V., Lipowsky, R.: Chemomechanical coupling and motor cycles of myosin V. Biophys. J. 100(7), 1747–1755 (2011) Google Scholar
  16. 16.
    Block, S.M.: Kinesin motor mechanics: binding, stepping, tracking, gating, and limping. Biophys. J. 92(9), 2986–2995 (2007) Google Scholar
  17. 17.
    Bockmann, R.A., Grubmuller, H.: Nanoseconds molecular dynamics simulation of primary mechanical energy transfer steps in F1-ATP synthase. Nat. Struct. Biol. 9(3), 198–202 (2002) Google Scholar
  18. 18.
    Bolterauer, H., Tuszynski, J.A., Unger, E.: Directed binding—a novel physical mechanism that describes the directional motion of two-headed kinesin motor proteins. Cell Biochem. Biophys. 42(2), 95–119 (2005) Google Scholar
  19. 19.
    Bouzat, S., Falo, F.: The influence of direct motor–motor interaction in models for cargo transport by a single team of motors. Phys. Biol. 7(4), 046009 (2010) Google Scholar
  20. 20.
    Bowling, A., Flickinger, D.M., Harmeyer, S.: Energetically consistent simulation of simultaneous impacts and contacts in multibody systems with friction. Multibody Syst. Dyn. 22(1), 27–45 (2009) MATHMathSciNetGoogle Scholar
  21. 21.
    Bowling, A., Haghshenas-Jaryani, M.: Spatial multibody dynamics of nano-scale motor protein locomotion. In: Proceedings of the 1st International Conference on Bionics and Biomechanics (ICABB) (2010) Google Scholar
  22. 22.
    Bowling, A., Palmer, A.F.: The small mass assumption applied to the multibody dynamics of motor proteins. J. Biomech. 42(9), 1218–1223 (2009). doi: 10.1016/j.jbiomech.2009.03.017 Google Scholar
  23. 23.
    Bowling, A., Palmer, A.F., Wilhelm, L.: Contact and impact in the multibody dynamics of motor protein locomotion. Langmuir 25(22), 12974–12981 (2009). Google Scholar
  24. 24.
    Bueche, F.J.: Introduction to Physics for Scientists and Engineers, 3rd edn. McGraw-Hill Book Company, New York (1979) Google Scholar
  25. 25.
    Bulatovic, R.M.: A note on the damped vibrating systems. Theor. Appl. Mech. 33(63), 213–221 (2006) MATHMathSciNetGoogle Scholar
  26. 26.
    Bustamante, C., Keller, D., Oster, G.: The physics of molecular motors. Acc. Chem. Res. 34(6), 412–420 (2001) Google Scholar
  27. 27.
    Cappello, G., Pierobon, P., Symonds, C., Busoni, L., Gebhardt, J.C., Rief, M., Prost, J.: Myosin V stepping mechanism. Proc. Natl. Acad. Sci. USA 104(39), 15328–15333 (2007) Google Scholar
  28. 28.
    Chang, R., Ayton, G.S., Voth, G.A.: Multiscale coupling of mesoscopic- and atomistic-level lipid bilayer simulations. J. Chem. Phys. 122(24), 244716 (2005) Google Scholar
  29. 29.
    Chen, J.C., Kim, A.S.: Brownian dynamics, molecular dynamics, and Monte Carlo modeling of colloidal systems. Adv. Colloid Interface Sci. 112(1–3), 159–173 (2004) Google Scholar
  30. 30.
    Chu, J.W., Ayton, G.S., Izvekov, S., Voth, G.A.: Emerging methods for multiscale simulation of biomolecular systems. Mol. Phys. 105(2–3), 167–175 (2007) Google Scholar
  31. 31.
    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., Farmer, B.L.: MBO(N)D: a multibody method for long-time molecular dynamics simulations. J. Comput. Chem. 21(3), 159–184 (2000) Google Scholar
  32. 32.
    Ciudad, A., Sancho, J.M., Tsironis, G.P.: Kinesin as an electrostatic machine. J. Biol. Phys. 32(5), 455–463 (2006) Google Scholar
  33. 33.
    Clemen, A., Vilfan, M., Jaud, J., Zhang, J., Barmann, M., Rief, M.: Force-dependent stepping kinetics of myosin-V. Biophys. J. 88, 4402–4410 (2005) Google Scholar
  34. 34.
    Coe, J.D., Levine, B.G., Martinez, T.J.: Ab initio molecular dynamics of excited-state intramolecular proton transfer using multireference perturbation theory. J. Phys. Chem. A 111(44), 11302–11310 (2007) Google Scholar
  35. 35.
    Cordova, N.J., Ermentrout, B., Oster, G.F.: Dynamics of single-motor molecules: the thermal ratchet model. Proc. Natl. Acad. Sci. USA 89(1), 339–343 (1992) Google Scholar
  36. 36.
    Craig, E.M., Linke, H.: Mechanochemical model for myosin V. Proc. Natl. Acad. Sci. USA 106(43), 18261–18266 (2009) Google Scholar
  37. 37.
    Cressman, A., Togashi, Y., Mikhailov, A.S., Kapral, R.: Mesoscale modeling of molecular machines: cyclic dynamics and hydrodynamical fluctuations. Phys. Rev. E, Stat. Nonlinear Soft Matter Phys. 77(5 Pt 1), 050901 (2008) Google Scholar
  38. 38.
    Currie, I.G.: Foundamental Mechanics of Fluids, 3rd edn. (2007). Accel Developement Google Scholar
  39. 39.
    Cytrynbaum, E.N., Rodionov, V., Mogilner, A.: Computational model of dynein-dependent self-organization of microtubule asters. J. Cell Sci. 117(Pt 8), 1381–1397 (2004) Google Scholar
  40. 40.
    Derenyi, I., Vicsek, T.: The kinesin walk: a dynamic model with elastically coupled heads. Proc. Natl. Acad. Sci. USA 93, 6775–6779 (1996) Google Scholar
  41. 41.
    DeVille, R.E.L., Vanden-Eijnden, E.: Regular gaits and optimal velocities for motor proteins. Biophys. J. 95(6), 2681–2691 (2008) Google Scholar
  42. 42.
    Duke, T., Leibler, S.: Motor protein mechanics: a stochastic model with minimal mechanochemical coupling. Biophys. J. 71(3), 1235–1247 (1996) Google Scholar
  43. 43.
    Dunn, A.R., Spudich, J.A.: Dynamics of the unbound head during myosin V processive translocation. Nat. Struct. Mol. Biol. 14(3), 246–248 (2007) Google Scholar
  44. 44.
    Eisenberg, E., Hill, T.L.: A cross-bridge model of muscle contraction. Prog. Biophys. Mol. Biol. 33(1), 55–82 (1978) Google Scholar
  45. 45.
    Fan, D., Zheng, W., Hou, R., Li, F., Wang, Z.: Modeling motility of the kinesin dimer from molecular properties of individual monomers. Biochemistry 47(16), 4733–4742 (2008) Google Scholar
  46. 46.
    Ferreira, A.M., Bashford, D.: Model for proton transport coupled to protein conformational change: application to proton pumping in the bacteriorhodopsin photocycle. J. Am. Chem. Soc. 128(51), 16778–16790 (2006) Google Scholar
  47. 47.
    Fisher, M.E., Kolomeisky, A.B.: Simple mechanochemistry describes the dynamics of kinesin molecules. Proc. Natl. Acad. Sci. USA 98(14), 7748–7753 (2001) Google Scholar
  48. 48.
    Fricks, J., Wang, H., Elston, T.C.: A numerical algorithm for investigating the role of the motor-cargo linkage in molecular motor-driven transport. J. Theor. Biol. 239(1), 33–48 (2006) MathSciNetGoogle Scholar
  49. 49.
    Gao, Y.Q., Yang, W., Marcus, R.A., Karplus, M.: A model for the cooperative free energy transduction and kinetics of ATP hydrolysis by F1-atpase. Proc. Natl. Acad. Sci. USA 100(20), 11339–11344 (2003) Google Scholar
  50. 50.
    Gapinski, J., Szymanski, J., Wilk, A., Kohlbecher, J., Patkowski, A., Holyst, R.: Size and shape of micelles studied by means of SANS, PCS, and FCS. Langmuir 26(12), 9304–9314 (2010) Google Scholar
  51. 51.
    Gardner, M.K., Odde, D.J., Bloom, K.: Kinesin-8 molecular motors: putting the brakes on chromosome oscillations. Trends Cell Biol. 18(7), 307–310 (2008) Google Scholar
  52. 52.
    Greenberg, M.J., Moore, J.R.: The molecular basis of frictional loads in the in vitro motility assay with applications to the study of the loaded mechanochemistry of molecular motors. Cytoskeleton (Hoboken, N.J.) 67(5), 273–285 (2010) Google Scholar
  53. 53.
    Haghshenas-Jaryani, M., Bowling, A.: Multiscale dynamic modeling of processive motor proteins. In: Proceedings of the IEEE International Conference Robotics and Biomimetics (ROBIO), Phuket Island, Thailand, December, pp. 1403–1408 (2011) Google Scholar
  54. 54.
    Haghshenas-Jaryani, M., Bowling, A.: Spatial multibody dynamics of motor proteins. In: Proceedings of Multibody Dynamics 2011, an ECCOMAS Thematic Conference, Brussels, Belgium, July (2011) Google Scholar
  55. 55.
    Haghshenas-Jaryani, M., Bowling, A.: Multiscale dynamic modeling of flexibility in myosin V using a planar mechanical model. In: Proceedings of the IEEE International Conference Robotics and Biomimetics (ROBIO), Guangzhou, China, December, pp. 366–371 (2012) Google Scholar
  56. 56.
    Haghshenas-Jaryani, M., Bowling, A.: A new numerical strategy for handling quaternions in dynamic modeling and simulation of rigid multibody systems. In: Proceedings of the 2nd Joint International Conference on Multibody System Dynamics (IMSD), Stuttgart, Germany, May–June (2012) Google Scholar
  57. 57.
    Haghshenas-Jaryani, M., Bowling, A.: A new switching strategy for addressing Euler parameters in dynamic modeling and simulation of rigid multibody systems. Multibody Syst. Dyn. 30(2), 185–197 (2013). doi: 10.1007/s11044-012-9333-8 MathSciNetGoogle Scholar
  58. 58.
    Hancock, W.O., Howard, J.: Kinesin’s processivity results from mechanical and chemical coordination between the ATP hydrolysis cycles of the two motor domains. Proc. Natl. Acad. Sci. 96(23), 13147–13152 (1999) Google Scholar
  59. 59.
    Hayashi, K., Takano, M.: Violation of the fluctuation–dissipation theorem in a protein system. Biophys. J. 93(3), 895–901 (2007) Google Scholar
  60. 60.
    Hendricks, A., Epureanu, B., Meyhfer, E.: Mechanistic mathematical model of kinesin under time and space fluctuating loads. Nonlinear Dyn. 53(4), 303–320 (2008) MATHGoogle Scholar
  61. 61.
    Howard, J.: Motor proteins as nanomachines: the role of thermal fluctuations in generating force and motion. In: 12th Poincaré Seminar, pp. 33–44 (2009) Google Scholar
  62. 62.
    Hwang, W., Lang, M.J.: Mechanical design of translocating motor proteins. Cell Biochem. Biophys. 54(1–3), 11–22 (2009) Google Scholar
  63. 63.
    Izvekov, S., Voth, G.A.: A multiscale coarse-graining method for biomolecular systems. J. Phys. Chem. B 109(7), 2469–2473 (2005). doi: 10.1021/jp044629q Google Scholar
  64. 64.
    Jain, A., Vaidehi, N., Rodriguez, G.: A fast recursive algorithm for molecular dynamics simulation. J. Comput. Phys. 106(2), 258–268 (1993) MATHGoogle Scholar
  65. 65.
    Jamali, Y., Foulaadvand, M.E., Rafii-Tabar, H.: Computational modelling of the collective stochastic motion of kinesin nano motors. J. Theor. Comput. Nano Sci. 7, 146–152 (2010) Google Scholar
  66. 66.
    Jamali, Y., Lohrasebi, A., Rafii-Tabar, H.: Computational modelling of the stochastic dynamics of kinesin biomolecular motors. Phys. A, Stat. Mech. Appl. 381, 239–254 (2007) Google Scholar
  67. 67.
    Julicher, F., Ajdari, A., Prost, J.: Modeling molecular motors. Rev. Mod. Phys. 69(4), 1269–1282 (1997) Google Scholar
  68. 68.
    Julicher, F., Prost, J.: Spontaneous oscillations of collective molecular motors. Phys. Rev. Lett. 78(23), 4510–4513 (1997) Google Scholar
  69. 69.
    Karplus, M., McCammon, J.A.: Molecular dynamics simulations of biomolecules. Nat. Struct. Biol. 9(9), 646–652 (2002) Google Scholar
  70. 70.
    Kim, D.N., Nguyen, C.T., Bathe, M.: Conformational dynamics of supramolecular protein assemblies. J. Struct. Biol. 173(2), 261–270 (2011) Google Scholar
  71. 71.
    Kim, T., Kao, M.T., Hasselbrink, E.F., Meyhofer, E.: Nanomechanical model of microtubule translocation in the presence of electric fields. Biophys. J. 94(10), 3880–3892 (2008) Google Scholar
  72. 72.
    Kolomeisky, A.B., Fisher, M.E.: A simple kinetic model describes the processivity of myosin-V. Biophys. J. 84, 1642–1650 (2003) Google Scholar
  73. 73.
    Kolomeisky, A.B., Fisher, M.E.: Molecular motors: a theorist’s perspective. Annu. Rev. Phys. Chem. 58, 675–695 (2007) Google Scholar
  74. 74.
    Korn, C.B., Klumpp, S., Lipowsky, R., Schwarz, U.S.: Stochastic simulations of cargo transport by processive molecular motors. J. Chem. Phys. 131(24), 245107 (2009) Google Scholar
  75. 75.
    Kuznetsov, A.V., Avramenko, A.A., Blinov, D.G.: Numerical modeling of molecular-motor-assisted transport of adenoviral vectors in a spherical cell. Comput. Methods Biomech. Biomed. Eng. 11(3), 215–222 (2008) Google Scholar
  76. 76.
    Lan, G., Sun, S.X.: Dynamics of myosin-V processivity. Biophys. J. 88(2), 999–1008 (2005) Google Scholar
  77. 77.
    Lan, G., Sun, S.X.: Flexible light-chain and helical structure of F-actin explain the movement and step size of myosin-VI. Biophys. J. 91, 4002–4013 (2006) Google Scholar
  78. 78.
    Lei, U., Yang, C.Y., Wu, K.C.: Viscous torque on a sphere under arbitrary rotation. Appl. Phys. Lett. 89(18), 181908 (2006). doi: 10.1063/1.2372704 Google Scholar
  79. 79.
    Leibler, S., Huse, D.A.: Porters versus rowers: a unified stochastic model of motor proteins. J. Cell Biol. 121(6), 1357–1368 (1993) Google Scholar
  80. 80.
    Levin, Y.: Dynamics of myosin-V processivity. Rep. Prog. Phys. 65(11), 1577–1632 (2002) Google Scholar
  81. 81.
    Lin, C.T., Meyhofer, E., Kurabayashi, K.: Predicting the stochastic guiding of kinesin-driven microtubules in microfabricated tracks: a statistical-mechanics-based modeling approach. Phys. Rev. E, Stat. Nonlinear Soft Matter Phys. 81(1 Pt 1), 011919 (2010) Google Scholar
  82. 82.
    Lipowsky, R., Liepelt, S.: Chemomechanical coupling of molecular motors: thermodynamics, network representations, and balance conditions. J. Stat. Phys. 130(1), 39–67 (2008) MATHMathSciNetGoogle Scholar
  83. 83.
    Liu, J., Taylor, D.W., Krementsova, E.B., Trybus, K.M., Taylor, K.A.: Three-dimensional structure of the myosin V inhibited state by cryoelectron tomography. Nature 442(13), 208–211 (2006) Google Scholar
  84. 84.
    Lohrasebi, A., Jamali, Y., Rafii-Tabar, H.: Modeling the effect of external electric field and current on the stochastic dynamics of atpase nano-biomolecular motors. Phys. A, Stat. Mech. Appl. 387, 5466–5476 (2007) Google Scholar
  85. 85.
    Masuda, T.: A simulation model of the conventional kinesin based on the driven-by-detachment mechanism. Biosystems 97(2), 121–126 (2009) MathSciNetGoogle Scholar
  86. 86.
    Mateos, J.L.: Walking on ratchets with two Brownian motors. Fluct. Noise Lett. 4(1), L161–L170 (2004) Google Scholar
  87. 87.
    Mather, W.H., Fox, R.F.: Kinesin’s biased stepping mechanism: amplification of neck linker zippering. Biophys. J. 91(7), 2416–2426 (2006) Google Scholar
  88. 88.
    Miller, R., Tadmor, E.: The quasicontinuum method: overview, applications and current directions. J. Comput.-Aided Mater. Des. 9, 203–239 (2002). Google Scholar
  89. 89.
    Mukherjee, R.M., Crozier, P.S., Plimpton, S.J., Anderson, K.S.: Substructured molecular dynamics using multibody dynamics algorithms. Int. J. Non-Linear Mech. 43(10), 1040–1055 (2008) MATHGoogle Scholar
  90. 90.
    Mullner, F.E., Syed, S., Selvin, P.R., Sigworth, F.J.: Improved hidden Markov models for molecular motors, part 1: Basic theory. Biophys. J. 99(11), 3684–3695 (2010) Google Scholar
  91. 91.
    Nayfeh, A.H.: Perturbation Methods. Wiley, New York (1973) MATHGoogle Scholar
  92. 92.
    Neto, N., Bellucci, L.: A new algorithm for rigid body molecular dynamics. Chem. Phys. 328(1–3), 259–268 (2006) Google Scholar
  93. 93.
    Parker, D., Bryant, Z., Delp, S.L.: Coarse-grained structural modeling of molecular motors using multibody dynamics. Cell. Mol. Bioeng. 2(3), 366–374 (2009) Google Scholar
  94. 94.
    Pavliotis, G.A., Stuart, A.M.: Periodic homogenization for inertial particles. Phys. D, Nonlinear Phenom. 2004(3–4), 161–187 (2005) MathSciNetGoogle Scholar
  95. 95.
    Peskin, C.S., Odell, G.M., Oster, G.F.: Cellular motions and thermal fluctuations: the Brownian ratchet. Biophys. J. 65(1), 316–324 (1993) Google Scholar
  96. 96.
    Peskin, C.S., Oster, G.: Coordinated hydrolysis explains the mechanical behavior of kinesin. Biophys. J. 68(4 Suppl), 202S–210S (1995). Discussion, 210S–211S Google Scholar
  97. 97.
    Ping, X., Shuo-Xing, D., Peng-Ye, W.: A model for processivity of molecular motors. Chin. Phys. 13(9), 1569–2863 (2004) Google Scholar
  98. 98.
    Poursina, M., Anderson, K.S.: Canonical ensemble simulation of biopolymers using a coarse-grained articulated generalized divide-and-conquer scheme. Comput. Phys. Commun. 184(3), 652–660 (2013) MATHMathSciNetGoogle Scholar
  99. 99.
    Poursina, M., Anderson, K.S.: Efficient coarse-grained molecular simulations in the multibody dynamics scheme. Multibody Dyn. 28, 147–172 (2013) MathSciNetGoogle Scholar
  100. 100.
    Poursina, M., Bhalerao, K.D., Flores, S.C., Anderson, K.S., Laederach, A.: Strategies for articulated multibody-based adaptive coarse grain simulation of rna. Methods Enzymol. 487, 73–98 (2011) Google Scholar
  101. 101.
    Praprotnik, M., Site, L.D., Kremer, K.: Adaptive resolution molecular-dynamics simulation: changing the degrees of freedom on the fly. J. Chem. Phys. 123(22) (2005) Google Scholar
  102. 102.
    Pratt, C., Cornely, K.: Essential Biochemistry. Wiley, New York (2004) Google Scholar
  103. 103.
    Purcell, T.J., Sweeney, H.L., Spudich, J.A.: A force-dependent state controls the coordination of processive myosin V. Proc. Natl. Acad. Sci. 102(39), 13873–13878 (2005) Google Scholar
  104. 104.
    Rafii-Tabar, H., Jamali, Y., Lohrasebi, A.: Computational modelling of the stochastic dynamics of kinesin biomolecular motors. Physica A 381, 239–254 (2007) Google Scholar
  105. 105.
    Reif, F.: Fundamentals of Statistical and Thermal Physics. McGraw Hill, New York (1965) Google Scholar
  106. 106.
    Reimann, P.: Brownian motors: noisy transport far from equilibrium. Phys. Rep. 361(2–4), 57–265 (2002) MATHMathSciNetGoogle Scholar
  107. 107.
    Rice, S.E., Purcell, T.J., Spudich, J.A.: Building and using optical traps to study properties of molecular motors. Methods Enzymol. 361, 112–133 (2003) Google Scholar
  108. 108.
    Rief, M., Rock, R.S., Mehta, A.D., Mooseker, M.S., Cheney, R.E., Spudich, J.A.: Myosin-V stepping kinetics: a molecular model for processivity. Proc. Natl. Acad. Sci. 97(17), 9482–9486 (2000) Google Scholar
  109. 109.
    Rossi, R., Isorce, M., Morin, S., Flocard, J., Arumugam, K., Crouzy, S., Vivaudou, M., Redon, S.: Adaptive torsion-angle quasi-statics: a general simulation method with applications to protein structure analysis and design. Bioinformatics 23(13), i408–417 (2007) Google Scholar
  110. 110.
    Rudd, R.E., Broughton, J.Q.: Coarse-grained molecular dynamics and the atomic limit of finite elements. Phys. Rev. B 58(10), R5893–R5896 (1998). doi: 10.1103/PhysRevB.58.R5893 Google Scholar
  111. 111.
    Schief, W.R., Howard, J.: Conformational changes during kinesin motility. Curr. Opin. Cell Biol. 13(1), 19–28 (2001) Google Scholar
  112. 112.
    Schuyler, A.D., Chirikjian, G.S.: Normal mode analysis of proteins: a comparison of rigid cluster modes with cα coarse graining. J. Mol. Graph. Model. 22(3), 183–193 (2004) Google Scholar
  113. 113.
    Schuyler, A.D., Chirikjian, G.S.: Efficient determination of low-frequency normal modes of large protein structures by cluster-nma. J. Mol. Graph. Model. 24(1), 46–58 (2005) Google Scholar
  114. 114.
    Schwieters, C.D., Clore, G.M.: A physical picture of atomic motions within the Dickerson DNA dodecamer in solution derived from joint ensemble refinement against NMR and large-angle X-ray scattering data. Biochemistry 46(5), 1152–1166 (2007) Google Scholar
  115. 115.
    Shao, Q., Gao, Y.Q.: On the hand-over-hand mechanism of kinesin. Proc. Natl. Acad. Sci. USA 103(21), 8072–8077 (2006) Google Scholar
  116. 116.
    Shiroguchi, K., Kinosita, K.: Myosin V walks by lever action and Brownian motion. Science 316(5828), 1208–1212 (2007) Google Scholar
  117. 117.
    Simon, S.M., Peskin, C.S., Oster, G.F.: What drives the translocation of proteins? Proc. Natl. Acad. Sci. 89(9), 3770–3774 (1992) Google Scholar
  118. 118.
    Singh, M.P., Mallik, R., Gross, S.P., Yu, C.C.: Monte Carlo modeling of single-molecule cytoplasmic dynein. Proc. Natl. Acad. Sci. USA 102(34), 12059–12064 (2005) Google Scholar
  119. 119.
    Skau, K.I., Hoyle, R.B., Turner, M.S.: A kinetic model describing the processivity of myosin-V. Biophys. J. 91, 2475–2489 (2006) Google Scholar
  120. 120.
    Sosa, H., Peterman, E.J.G., Moerner, W.E., Goldstein, L.S.B.: ADP-induced rocking of the kinesin motor domain revealed by single-molecule fluorescence polarization microscopy. Nat. Struct. Biol. 8(6), 540–544 (2001) Google Scholar
  121. 121.
    Stratopoulos, G.N., Dialynas, T.E., Tsironis, G.P.: Directional Newtonian motion and reversals of molecular motors. Phys. Lett. A 252(3–4), 151–156 (1999) Google Scholar
  122. 122.
    Szymanski, J., Patkowski, A., Wilk, A., Garstecki, P., Holyst, R.: Diffusion and viscosity in a crowded environment: from nano- to macroscale. Phys. Chem. Lett. B 110, 25593–25597 (2006) Google Scholar
  123. 123.
    Tsygankov, D., Fisher, M.E.: Kinetic models for mechanoenzymes: structural aspects under large loads. J. Chem. Phys. 128(1), 015102 (2008) Google Scholar
  124. 124.
    Vaidehi, N., Jain, A., Goddard, W.A.: Constant temperature constrained molecular dynamics: the Newton–Euler inverse mass operator method. J. Phys. Chem. 100(25), 10508–10517 (1996). doi: 10.1021/jp953043o Google Scholar
  125. 125.
    Vale, R.D.: Myosin V motor proteins: marching stepwise towards a mechanism. J. Cell Biol. 163(3), 445–450 (2003) Google Scholar
  126. 126.
    Veigel, C., Wang, F., Bartoo, M.L., Sellers, J.R., Molloy, J.E.: The gated gait of the processive molecular motor, myosin V. Nat. Cell Biol. 4(1), 59–65 (2002) Google Scholar
  127. 127.
    Vilfan, A.: Elastic lever-arm model for myosin V. Biophys. J. 88, 3792–3805 (2005) Google Scholar
  128. 128.
    Vilfan, A.: Five models for myosin V. Front. Biosci. 14, 2269–2284 (2009) Google Scholar
  129. 129.
    Wagner, G.J., Liu, W.K.: Coupling of atomistic and continuum simulations using a bridging scale decomposition. J. Comput. Phys. 190(1), 249–274 (2003) MATHGoogle Scholar
  130. 130.
    Walcott, S., Warshaw, D.M.: Modeling smooth muscle myosin’s two heads: long-lived enzymatic roles and phosphorylation-dependent equilibria. Biophys. J. 99(4), 1129–1138 (2010) Google Scholar
  131. 131.
    Wang, H.: Mathematical theory of molecular motors and a new approach for uncovering motor mechanism. IEE Proc. Nanobiotechnol. 150(3), 127–133 (2003) Google Scholar
  132. 132.
    Wang, H., Elston, T.C.: Mathematical and computational methods for studying energy transduction in protein motors. J. Stat. Phys. 128(1–2), 35–76 (2007) MATHMathSciNetGoogle Scholar
  133. 133.
    Warshaw, D.M., Kennedy, G.G., Work, S.S., Krementsova, E.B., Beck, S.: Differential labeling of myosin V heads with quantum dots allows direct visualization of hand-over-hand processivity. Biophys. J. 88(5), L30–L32 (2005) Google Scholar
  134. 134.
    Wereley, S.T., Meinhart, C.D.: Recent advances in micro-particle image velocimetry. Annu. Rev. Fluid Mech. 42, 557–576 (2010) Google Scholar
  135. 135.
    Wu, Y., Gao, Y.Q., Karplus, M.: A kinetic model of coordinated myosin V. Biochemistry 46, 6318–6330 (2007) Google Scholar
  136. 136.
    Xiao, S.P., Belytschko, T.: A bridging domain method for coupling continua with molecular dynamics. Comput. Methods Appl. Mech. Eng. 193(17–20), 1645–1669 (2004) MATHMathSciNetGoogle Scholar
  137. 137.
    Xie, P.: Stepping behavior of two-headed kinesin motors. Biochim. Biophys. Acta (BBA), Bioenerg. 1777(9), 1195–1202 (2008) Google Scholar
  138. 138.
    Xing, J., Wang, H., Oster, G.: From continuum Fokker–Planck models to discrete kinetic models. Biophys. J. 89(3), 1551–1563 (2005) Google Scholar
  139. 139.
    Yamada, M.D., Maruta, S., Yasuda, S., Kondo, K., Maeda, H., Arata, T.: Conformational dynamics of loops l11 and l12 of kinesin as revealed by spin-labeling EPR. Biochem. Biophys. Res. Commun. 364(3), 620–626 (2007) Google Scholar
  140. 140.
    Yildiz, A., Tomishige, M., Vale, R.D., Selvin, P.R.: Kinesin walks hand-over-hand. Langmuir 20(12), 4892–4897 (2004) Google Scholar
  141. 141.
    Yu, H., Ma, L., Yang, Y., Cui, Q.: Mechanochemical coupling in the myosin motor domain. I. Insights from equilibrium active-site simulations. PLoS Comput. Biol. 3(2), e21 (2007) Google Scholar
  142. 142.
    Yu, H., Ma, L., Yang, Y., Cui, Q.: Mechanochemical coupling in the myosin motor domain. II. Analysis of critical residues. PLoS Comput. Biol. 3(2), e23 (2007) Google Scholar
  143. 143.
    Yu, J., Ha, T., Schulten, K.: Structure-based model of the stepping motor of PcrA helicase. Biophys. J. 91(6), 2097–2114 (2006) Google Scholar
  144. 144.
    Zeldovich, K.B., Joanny, J.F., Prost, J.: Motor proteins transporting cargos. Eur. Phys. J. E 17(2), 155–163 (2005) Google Scholar
  145. 145.
    Zhang, J., Li, W., Wang, J., Qin, M., Wu, L., Yan, Z., Xu, W., Zuo, G., Wang, W.: Protein folding simulations: from coarse-grained model to all-atom model. IUBMB Life 61(6), 627–643 (2009) Google Scholar
  146. 146.
    Zheng, W.: Multiscale modeling of structural dynamics underlying force generation and product release in actomyosin complex. Proteins 78(3), 638–660 (2010) Google Scholar
  147. 147.
    Zheng, W., Doniach, S.: A comparative study of motor-protein motions by using a simple elastic-network model. Proc. Natl. Acad. Sci. 100(23), 13253–13258 (2003) Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Department of Mechanical and Aerospace EngineeringThe University of Texas at ArlingtonArlingtonUSA

Personalised recommendations