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Multiscale Modeling in Biomechanics and Mechanobiology pp 27–61Cite as

Molecular Motors: Cooperative Phenomena of Multiple Molecular Motors

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Abstract

Transport of various types of cargoes in cells is based on molecular motors moving along the cytoskeleton. Often, these motors work in teams rather than as isolated molecules. This chapter discusses analytical and computational approaches to study the cooperation of multiple molecular motors theoretically. In particular, we focus on stochastic methods on various levels of coarse-graining and discuss how the parameters in a mesoscopic theoretical description can be determined by averaging of the underlying microscopic processes. These methods are applied toward understanding the effects of elastic coupling in a motor pair and in the cooperation of several motors pulling a bead. In addition, we review how coupling can have different effects on different motor species.

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Notes

  1. 1.

    A discussion of the origin of the quote can be found at http://quoteinvestigator.com/2011/05/13/einstein-simple/#more-2363.

  2. 2.

    For backward steps, the transition between the states \((ED)\) and \((DE)\) may also play a role [44], a picture supported by recent experiments on mutant kinesins that are more prone to backward stepping [20]. The two different mechanical transitions were also studied in Ref. [63].

  3. 3.

    Thus, we implicitly assume an exponential dwell time distribution.

  4. 4.

    The index ‘si’ is used to indicate explicitly the unbinding rate and average binding time of a single motor. The corresponding quantities for a single bound motor in a complex of several motors (e.g., in a motor pair as discussed below) are denoted by \(\epsilon _1\) and \(t_1\) respectively. These quantities are closely related to the single motor parameters, but there are some subtleties: While \(\epsilon _1=\epsilon _\mathrm{si}\), the dwell time in the 1-motor bound state (or the average duration of a 1-motor run) for cooperative motors also depends on the binding rate \(\pi \) of the second motor or any other in a system with more than 2 motors, \(t_1=(\epsilon _1+\pi )^{-1}<t_\mathrm{si}\).

  5. 5.

    It is convenient to introduce a highest state \((2,N)\) to reduce the network to a finite number of states. The state \((2,N)\) corresponds to a very large extension between the motor. Such a configuration is unlikely, because the motors typically unbind before reaching this state. Nevertheless, one has to check that the results do not depend on the choice of the value of \(N\).

  6. 6.

    There may be more parameters for nonlinear couplings.

  7. 7.

    Of course, the molecules themselves may also add a layer of complexity to the patterns of movements, for example if the motor has several different functional modes, as reported for dyneins [92].

References

  1. Ali, M.Y., Kennedy, G.G., Safer, D., Trybus, K.M., Sweeney, H.L., Warshaw, D.M.: Myosin Va and myosin VI coordinate their steps while engaged in an in vitro tug of war during cargo transport. Proc Natl Acad Sci U S A 108, E 535–541 (2011).

    Google Scholar 

  2. Ali, M.Y., Krementsova, E.B., Kennedy, G.G., Mahaffy, R., Pollard, T.D., Trybus, K.M., Warshaw, D.M.: Myosin va maneuvers through actin intersections and diffuses along microtubules. Proc Natl Acad Sci U S A 104, 4332–6 (2007).

    Google Scholar 

  3. 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, 131–60 (2006).

    Google Scholar 

  4. Barak, P., Rai, A., Rai, P., Mallik, R.: Quantitative optical trapping on single organelles in cell extract. Nat Methods 10, 68–70 (2013).

    Google Scholar 

  5. Beeg, J., Klumpp, S., Dimova, R., Gracià, R.S., Unger, E., Lipowsky, R.: Transport of beads by several kinesin motors. Biophys J 94, 532–41 (2008).

    Google Scholar 

  6. Bell, G.I.: Models for the specific adhesion of cells to cells. Science 200, 618–627 (1978).

    Google Scholar 

  7. Berger, F., Keller, C., Klumpp, S., Lipowsky, R.: Distinct transport regimes of two elastically coupled molecular motors. Phys Rev Lett 108, 208101 (2012).

    Google Scholar 

  8. Berger, F., Keller, C., Lipowsky, R., Klumpp, S.: Elastic coupling effects in cooperative transport by a pair of molecular motors. Cell Molec Bioeng 6, 48–64 (2013).

    Google Scholar 

  9. Berger, F., Keller, C., Müller, M.J.I., Klumpp, S., Lipowsky, R.: Co-operative transport by molecular motors. Biochem Soc Trans 39, 1211–5 (2011).

    Google Scholar 

  10. Berger, F., Müller, M.J.I., Lipowsky, R.: Enhancement of the processivity of kinesin-transported cargo by myosin V. Europhys Lett 87, 28,002 (2009).

    Google Scholar 

  11. Bieling, P., Telley, I.A., Piehler, J., Surrey, T.: Processive kinesins require loose mechanical coupling for efficient collective motility. EMBO Rep 9, 1121–7 (2008).

    Google Scholar 

  12. Bierbaum, V., Lipowsky, R.: Chemomechanical coupling and motor cycles of myosin V. Biophys J 100, 1747–55 (2011).

    Google Scholar 

  13. Bierbaum, V., Lipowsky, R.: Dwell time distributions of the molecular motor myosin v. PLoS One 8, e55366 (2013).

    Google Scholar 

  14. Blehm, B.H., Schroer, T.A., Trybus, K.M., Chemla, Y.R., Selvin, P.R.: In vivo optical trapping indicates kinesin’s stall force is reduced by dynein during intracellular transport. Proc Natl Acad Sci U S A 110, 3381–6 (2013).

    Google Scholar 

  15. Block, S.M.: Kinesin motor mechanics: Binding, stepping, tracking, gating, and limping. Biophys J 92, 2986–95 (2007).

    Google Scholar 

  16. Böhm, K.J., Stracke, R., Mühlig, P., Unger, E.: Motor protein-driven unidirectional transport of micrometer-sized cargoes across isopolar microtubule arrays. Nanotechnology 12, 238–244 (2001).

    Google Scholar 

  17. 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, 046009 (2010).

    Google Scholar 

  18. Campàs, O., Kafri, Y., Zeldovich, K.B., Casademunt, J., Joanny, J.F.: Collective dynamics of interacting molecular motors. Phys Rev Lett 97, 038101 (2006).

    Google Scholar 

  19. Carter, N.J., Cross, R.A.: Mechanics of the kinesin step. Nature 435, 308–12 (2005).

    Google Scholar 

  20. Clancy B.E., Behnke-Parks W.M., Andreasson J.O.L., Rosenfeld S.S., Block S.M.: A universal pathway for kinesin stepping. Nature Struct. Mol. Biol. 18 1020–7 (2011).

    Google Scholar 

  21. Clemen, A.E.M., Vilfan, M., Jaud, J., Zhang, J., Bärmann, M., Rief, M.: Force-dependent stepping kinetics of myosin-V. Biophys J 88, 4402–10 (2005).

    Google Scholar 

  22. Constantinou, P.E., Diehl, M.R.: The mechanochemistry of integrated motor protein complexes. J Biomech 43, 31–7 (2010).

    Google Scholar 

  23. Coppin, C., Pierce, D., Hsu, L., Vale, R.: The load dependence of kinesin’s mechanical cycle. Proc Natl Acad Sci U S A 94, 8539–8544 (1997).

    Google Scholar 

  24. Crevenna, A.H., Madathil, S., Cohen, D.N., Wagenbach, M., Fahmy, K., Howard, J.: Secondary structure and compliance of a predicted flexible domain in kinesin-1 necessary for cooperation of motors. Biophys J 95, 5216–27 (2008).

    Google Scholar 

  25. Derr, N.D., Goodman, B.S., Jungmann, R., Leschziner, A.E., Shih, W.M., Reck-Peterson, S.L.: Tug-of-war in motor protein ensembles revealed with a programmable dna origami scaffold. Science 338, 662–5 (2012).

    Google Scholar 

  26. Driver, J.W., Jamison, D.K., Uppulury, K., Rogers, A.R., Kolomeisky, A.B., Diehl, M.R.: Productive cooperation among processive motors depends inversely on their mechanochemical efficiency. Biophys J 101, 386–95 (2011).

    Google Scholar 

  27. Driver, J.W., Rogers, A.R., Jamison, D.K., Das, R.K., Kolomeisky, A.B., Diehl, M.R.: Coupling between motor proteins determines dynamic behaviors of motor protein assemblies. Phys Chem Chem Phys 12, 10,398–405 (2010).

    Google Scholar 

  28. Erickson, R.P., Jia, Z., Gross, S.P., Yu, C.C.: How molecular motors are arranged on a cargo is important for vesicular transport. PLoS Comput Biol 7, e1002,032 (2011).

    Google Scholar 

  29. Fisher, M.E., Kolomeisky, A.B.: Simple mechanochemistry describes the dynamics of kinesin molecules. Proc Natl Acad Sci USA 98, 7748–7753 (2001).

    Google Scholar 

  30. Furuta, K., Furuta, A., Toyoshima, Y.Y., Amino, M., Oiwa, K., Kojima, H.: Measuring collective transport by defined numbers of processive and nonprocessive kinesin motors. Proc Natl Acad Sci U S A 110, 501–6 (2013).

    Google Scholar 

  31. Gagliano, J., Walb, M., Blaker, B., Macosko, J.C., Holzwarth, G.: Kinesin velocity increases with the number of motors pulling against viscoelastic drag. Eur Biophys J 39, 801–13 (2010).

    Google Scholar 

  32. Gennerich, A., Carter, A.P., Reck-Peterson, S.L., Vale, R.D.: Force-induced bidirectional stepping of cytoplasmic dynein. Cell 131, 952 (2007).

    Google Scholar 

  33. Grant, B.J., Gheorghe, D.M., Zheng, W., Alonso, M., Huber, G., Dlugosz, M., McCammon, J.A., Cross, R.A.: Electrostatically biased binding of kinesin to microtubules. PLoS Biol 9, e1001207 (2011).

    Google Scholar 

  34. Gross, S.P., Vershinin, M., Shubeita, G.T.: Cargo transport: two motors are sometimes better than one. Curr Biol 17, R478–86 (2007).

    Google Scholar 

  35. 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 USA 96, 13147–13152 (1999).

    Google Scholar 

  36. Hendricks, A.G., Perlson, E., Ross, J.L., Schroeder 3rd, H.W., Tokito, M., Holzbaur, E.L.F.: Motor coordination via a tug-of-war mechanism drives bidirectional vesicle transport. Curr Biol 20, 697–702 (2010).

    Google Scholar 

  37. Hill, T.: Free Energy Transduction in Biology. Academic Press, New York (1977).

    Google Scholar 

  38. Hill, T.L.: Interrelations between random walks on diagrams (graphs) with and without cycles. Proc Natl Acad Sci USA 85, 2879–2883 (1988).

    Google Scholar 

  39. Hill, T.L.: Number of visits to a state in a random walk, before absorption, and related topics. Proc Natl Acad Sci USA 85, 4577–4581 (1988).

    Google Scholar 

  40. Holmes, K.C.: Muscle contraction. In: L. Wolpert (ed.) The limits of reductionism in biology, Novartis Foundation Symposium 213, pp. 76–92. Wiley, Chichester (1998).

    Google Scholar 

  41. Howard, J.: Mechanics of Motor Proteins and the Cytoskeleton. Sinauer Associates, Sunderland (Mass.) (2001).

    Google Scholar 

  42. Howard, J., Hudspeth, A.J., Vale, R.D.: Movement of microtubules by single kinesin molecules. Nature 342, 154–158 (1989).

    Google Scholar 

  43. Hwang, W., Lang, M.J., Karplus, M.: Force generation in kinesin hinges on cover-neck bundle formation. Structure 16, 62–71 (2008).

    Google Scholar 

  44. Hyeon, C., Klumpp, S., Onuchic, J.N.: Kinesin’s backsteps under mechanical load. Phys Chem Chem Phys 11, 4899–910 (2009).

    Google Scholar 

  45. Hyeon, C., Onuchic, J.N.: Mechanical control of the directional stepping dynamics of the kinesin motor. Proc Natl Acad Sci U S A 104, 17,382–7 (2007).

    Google Scholar 

  46. Jülicher, F., Ajdari, A., Prost, J.: Modeling molecular motors. Rev Mod Phys 69, 1269–1281 (1997).

    Google Scholar 

  47. Keller, C.: Coupled molecular motors. Diploma thesis, Humboldt-Universität, Berlin (2009).

    Google Scholar 

  48. Keller, C.: Coupled Molecular Motors: Network Representation & Dynamics of Kinesin Motor Pairs. Ph.D. thesis, Universität Potsdam (2013).

    Google Scholar 

  49. Keller, C., Berger, F., Liepelt, S., Lipowsky, R.: Network complexity and parametric simplicity for cargo transport by two molecular motors. J Stat Phys 150, 205–234 (2013).

    Google Scholar 

  50. King, S.J., Schroer, T.A.: Dynactin increases the processivity of the cytoplasmic dynein motor. Nat Cell Biol 2, 20 (2000).

    Google Scholar 

  51. Klumpp, S., Lipowsky, R.: Cooperative cargo transport by several molecular motors. Proc Natl Acad Sci U S A 102, 17,284–9 (2005).

    Google Scholar 

  52. Korn, C.B., Klumpp, S., Lipowsky, R., Schwarz, U.S.: Stochastic simulations of cargo transport by processive molecular motors. J Chem Phys 131, 245,107 (2009).

    Google Scholar 

  53. Kramers, H.: Brownian motion in a field of force and the diffusion model of chemical reactions. Physica 7, 284 (1940).

    Google Scholar 

  54. Kunwar, A., Mogilner, A.: Robust transport by multiple motors with nonlinear force-velocity relations and stochastic load sharing. Phys Biol 7, 16012 (2010).

    Google Scholar 

  55. Kunwar, A., Tripathy, S.K., Xu, J., Mattson, M.K., Anand, P., Sigua, R., Vershinin, M., McKenney, R.J., Yu, C.C., Mogilner, A., Gross, S.P.: Mechanical stochastic tug-of-war models cannot explain bidirectional lipid-droplet transport. Proc Natl Acad Sci U S A 108, 18960–5 (2011).

    Google Scholar 

  56. Larson, A.G., Landahl, E.C., Rice, S.E.: Mechanism of cooperative behaviour in systems of slow and fast molecular motors. Phys Chem Chem Phys 11, 4890–8 (2009).

    Google Scholar 

  57. Leduc, C., Campàs, O., Zeldovich, K.B., Roux, A., Jolimaitre, P., Bourel-Bonnet, L., Goud, B., Joanny, J.F., Bassereau, P., Prost, J.: Cooperative extraction of membrane nanotubes by molecular motors. Proc Natl Acad Sci USA 101, 17096–17101 (2004).

    Google Scholar 

  58. Leduc, C., Ruhnow, F., Howard, J., Diez, S.: Detection of fractional steps in cargo movement by the collective operation of kinesin-1 motors. Proc Natl Acad Sci USA 104, 10847–10852 (2007).

    Google Scholar 

  59. Leidel, C., Longoria, R.A., Gutierrez, F.M., Shubeita, G.T.: Measuring molecular motor forces in vivo: implications for tug-of-war models of bidirectional transport. Biophys J 103, 492–500 (2012).

    Google Scholar 

  60. Li, X., Lipowsky, R., Kierfeld, J.: Critical motor number for fractional steps of cytoskeletal filaments in gliding assays. PLoS One 7, e43219 (2012).

    Google Scholar 

  61. Liepelt, S., Lipowsky, R.: Kinesin’s network of chemomechanical motor cycles. Phys Rev Lett 98, 258102 (2007).

    Google Scholar 

  62. Liepelt, S., Lipowsky, R.: Steady-state balance conditions for molecular motor cycles and stochastic nonequilibrium processes. Europhys Lett 77, 50002 (2007).

    Google Scholar 

  63. Liepelt, S., Lipowsky, R.: Impact of slip cycles on the operation modes and efficiency of molecular motors. J Stat Phys 141, 1–16 (2010).

    Google Scholar 

  64. Lipowsky, R., Klumpp, S.: ’Life is motion’ - multiscale motility of molecular motors. Physica A 352, 53–112 (2005).

    Google Scholar 

  65. Lipowsky, R., Liepelt, S.: Chemomechanical coupling of molecular motors: Thermodynamics, network representations and balanced conditions. J Stat Phys 130, 39–67 (2008). Erratum: J Stat Phys 135, 777–778 (2009).

    Google Scholar 

  66. Lu, H., Efremov, A.K., Bookwalter, C.S., Krementsova, E.B., Driver, J.W., Trybus, K.M., Diehl, M.R.: Collective dynamics of elastically coupled myosin V motors. J Biol Chem 287, 27,753–61 (2012).

    Google Scholar 

  67. Mallik, R., Carter, B.C., Lex, S.A., King, S.J., Gross, S.: Cytoplasmic dynein functions as a gear in response to load. Nature 427, 649 (2004).

    Google Scholar 

  68. Mallik, R., Petrov, D., Lex, S.A., King, S., Gross, S.: Building complexity: An in vitro study of cytoplasmic dynein with in vivo implications. Curr Biol 15, 2075–2085 (2005).

    Google Scholar 

  69. McKenney, R.J., Vershinin, M., Kunwar, A., Vallee, R.B., Gross, S.P.: Lis1 and NudE induce a persistent dynein force-producing state. Cell 141, 304–14 (2010).

    Article  Google Scholar 

  70. Mehta, A.D., Rock, R.S., Rief, M., Spudich, J.A., Mooseker, M.S., Cheney, R.E.: Myosin-V is a processive actin-based motor. Nature 400, 590–593 (1999).

    Google Scholar 

  71. Müller, M.J.I., Klumpp, S., Lipowsky, R.: Motility states of molecular motors engaged in a stochastic tug-of-war. J Stat Phys 133, 1059–1081 (2008).

    Google Scholar 

  72. Müller, M.J.I., Klumpp, S., Lipowsky, R.: Tug-of-war as a cooperative mechanism for bidirectional cargo transport by molecular motors. Proc Natl Acad Sci USA 105, 4609–4614 (2008).

    Google Scholar 

  73. Müller, M.J.I., Klumpp, S., Lipowsky, R.: Bidirectional transport by molecular motors: enhanced processivity and response to external forces. Biophys J 98, 2610–8 (2010).

    Google Scholar 

  74. Ökten, Z., Churchman, L.S., Rock, R.S., Spudich, J.A.: Myosin VI walks hand-over-hand along actin. Nat Struct Mol Biol 11, 884 (2004).

    Google Scholar 

  75. Posta, F., D’Orsogna, M.R., Chou, T.: Enhancement of cargo processivity by cooperating molecular motors. Phys Chem Chem Phys 11, 4851–60 (2009).

    Google Scholar 

  76. Rice, S., Lin, A.W., Safer, D., Hart, C.L., Naber, N., Carragher, B.O., Cain, S.M., Pechatnikova, E., Wilson-Kubalek, E.M., Whittaker, M., Pate, E., Cooke, R., Taylor, E.W., Milligan, R.A., Vale, R.D.: A structural change in the kinesin motor protein that drives motility. Nature 402, 778–84 (1999).

    Google Scholar 

  77. Risken, H.: The Fokker-Planck Equation. Springer, Berlin Heidelberg (1996).

    Google Scholar 

  78. Rock, R.S., Rice, S.E., Wells, A.L., Purcell, T.J., Spudich, J.A., Sweeney, H.L.: Myosin VI is a processive motor with a large step size. Proc Natl Acad Sci USA 98, 13,655 (2001).

    Google Scholar 

  79. Rogers, A.R., Driver, J.W., Constantinou, P.E., Kenneth Jamison, D., Diehl, M.R.: Negative interference dominates collective transport of kinesin motors in the absence of load. Phys Chem Chem Phys 11, 4882–9 (2009).

    Google Scholar 

  80. Romberg, L., Vale, R.: Chemomechanical cycle of kinesin differs from that of myosin. Nature 361, 168–170 (1993).

    Google Scholar 

  81. Schliwa, M., Woehlke, G.: Molecular motors. Nature 422, 759–765 (2003).

    Google Scholar 

  82. Schnitzer, M.J., Visscher, K., Block, S.M.: Force production by single kinesin motors. Nature Cell Biol. 2, 718–723 (2000).

    Google Scholar 

  83. Schuster, M., Lipowsky, R., Assmann, M.A., Lenz, P., Steinberg, G.: Transient binding of dynein controls bidirectional long-range motility of early endosomes. Proc Natl Acad Sci U S A 108, 3618–23 (2011).

    Google Scholar 

  84. Soppina, V., Rai, A.K., Ramaiya, A.J., Barak, P., Mallik, R.: Tug-of-war between dissimilar teams of microtubule motors regulates transport and fission of endosomes. Proc Natl Acad Sci U S A 106, 19,381–6 (2009).

    Google Scholar 

  85. Svoboda, K., Block, S.M.: Force and velocity measured for single kinesin molecules. Cell 77, 773 (1994).

    Google Scholar 

  86. Svoboda, K., Schmidt, C.F., Schnapp, B.J., Block, S.M.: Direct observation of kinesin stepping by optical trapping interferometry. Nature 365, 721–727 (1993).

    Google Scholar 

  87. Toba, S., Watanabe, T.M., Yamaguchi-Okimoto, L., Toyoshima, Y.Y., Higuchi, H.: Overlapping hand-over-hand mechanism of single molecular motility of cytoplasmic dynein. Proc Natl Acad Sci USA 103, 5741 (2006).

    Google Scholar 

  88. van Kampen, N.: Stochastic Processes in Physics and Chemistry. Elsevier, Amsterdam (1992).

    Google Scholar 

  89. Veigel, C., Coluccio, L.M., Jontes, J.D., Sparrow, J.C., Milligan, R.D., Molloy, J.E.: The motor protein myosin-I produces its working stroke in two steps. Nature 398, 530–533 (1999).

    Google Scholar 

  90. Vershinin, M., Carter, B.C., Razafsky, D.S., King, S.J., Gross, S.P.: Multiple-motor based transport and its regulation by tau. Proc Natl Acad Sci U S A 104, 87–92 (2007).

    Google Scholar 

  91. Visscher, K., Schnitzer, M.J., Block, S.M.: Single kinesin molecules studied with a molecular force clamp. Nature 400, 184 (1999).

    Google Scholar 

  92. Walter, W.J., Koonce, M.P., Brenner, B., Steffen, W.: Two independent switches regulate cytoplasmic dynein’s processivity and directionality. Proc Natl Acad Sci U S A 109, 5289–93 (2012).

    Google Scholar 

  93. Wang, Z., Li, M.: Force-velocity relations for multiple-molecular-motor transport. Phys Rev E 80, 041923 (2009).

    Google Scholar 

  94. Welte, M.A.: Bidirectional transport along microtubules. Curr Biol 14, R525–37 (2004).

    Google Scholar 

  95. Welte, M.A., Gross, S.P.: Molecular motors: a traffic cop within? HFSP J 2, 178–82 (2008).

    Google Scholar 

  96. Xu, J., Shu, Z., King, S.J., Gross, S.P.: Tuning multiple motor travel via single motor velocity. Traffic 13, 1198–205 (2012).

    Google Scholar 

  97. Yildiz, A., Forkey, J.N., McKinney, S.A., Ha, T., Goldman, Y.E., Selvin, P.R.: Myosin V walks hand-over-hand: Single fluorophore imaging with 1.5-nm localization. Science 300, 2061–2065 (2003).

    Google Scholar 

  98. Yildiz, A., Selvin, P.R.: Fluorescence imaging with one nanometer accuracy: application to molecular motors. Acc Chem Res 38, 574–82 (2005).

    Google Scholar 

  99. Yildiz, A., Tomishige, M., Gennerich, A., Vale, R.D.: Intramolecular strain coordinates kinesin stepping behaviour along microtubules. Cell 134, 1030–1040 (2008).

    Google Scholar 

  100. Yildiz, A., Tomishige, M., Vale, R.D., Selvin, P.R.: Kinesin walks hand-over-hand. Science 303, 676–678 (2004).

    Google Scholar 

  101. Zhang, Y.: Cargo transport by several motors. Phys Rev E 83, 011909 (2011).

    Google Scholar 

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  1. Max Planck Institute of Colloids and Interfaces, Science Park Golm, 14424, Potsdam, Germany

    Stefan Klumpp, Corina Keller, Florian Berger & Reinhard Lipowsky

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  1. Dept. of Mechanical, Aerospace & Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, New York, USA

    Suvranu De

  2. Dept. of Biomedical Engineering, Texas A&M University, College Station, Texas, USA

    Wonmuk Hwang

  3. Dept.of Mechanical Engineering Bioengineering & Cardiothoracic Surgery, Stanford University, Stanford, California, USA

    Ellen Kuhl

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Klumpp, S., Keller, C., Berger, F., Lipowsky, R. (2015). Molecular Motors: Cooperative Phenomena of Multiple Molecular Motors. In: De, S., Hwang, W., Kuhl, E. (eds) Multiscale Modeling in Biomechanics and Mechanobiology. Springer, London. https://doi.org/10.1007/978-1-4471-6599-6_3

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