THERMODYNAMICS AND MECHANICS OF MOLECULAR MOTORS HOU RUIZHENG (Bachelor of Science, Xi’an Jiaotong University) A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSIOPHY DEPARTMENT OF PHYSICS NATIONAL UNIVERSITY OF SINGAPORE 2013 DECLARATION I hereby declare that this thesis is my original work and it has been written by me in its entirety. I have duly acknowledged all the sources of information which have been used in the thesis. This thesis has also not been submitted for any degree in any university previously. _________________ Hou Ruizheng JANUARY, 2013 Acknowledgements First and foremost, I would like to express my sincere gratitude to my supervisor Professor Wang Zhisong. Communications with him not only inspired me greatly in the academic aspect, but also led me to a profound thinking of my life. His advice will always motivate me in the future. Previous and current group members in the molecular motor lab gave me significant support. In particular, I would like to thank Artem Efremov for discussions on thermodynamics and kinetics, and Ren Jie for discussions on kinetic methods; I would like to thank Cheng Juan, Loh Iongying, Sarangapani Sreelatha and Liu Meihan for discussions on DNA motors and exchanging experiences of academic writing. Many thanks to Professor Li Baowen for providing computational resources and other resources for my studies. I would like to thank Professor Bao Weizhu and Wang Nan for our collaborations on the worm-like-chain model, and Professor Zhang Chun and Zhou Miao for our collaboration on an artificial molecular motor. Students and staffs in CCSE gave me great help in academic aspect and in daily life. In particular, I would like to thank Tao Lin, Zhu Feng, Qin Chu, Zhu Guimei, Liu Sha, Tang Qinglin, Yang Lina, Feng Ling, Zhao Qifang and Balázs Szekeres; thanks to Wang Hailong for comments on the thesis. Last but not least, I am grateful to my parents for their support and encouragement. i ii Contents Acknowledgements i Contents iii Summary ix List of Publications xi List of Figures xii ………………………………………………………… Chapter 1: Introduction 1.1 The physics perspective of molecular motors ……………………… ………………… 1.2 Bio-motors: kinesin-1 and F1-ATPase as examples 1.2.1 kinesin-1 1.2.2 F1-ATPase ………………………………………………… .… …………………………………………………… ……………………………. ……………………………………… ……………………………………… 1.3 Status quo of artificial molecular motors 1.4 Theories of molecular motors 1.4.1 Brownian motor theory 1.4.2 Cycle kinetics and thermodynamics 1.4.3 Mechanics of molecular motors ………………………… 11 ………………………………. 12 ……………………. 13 1.5 Scientific questions and objectives of the thesis Chapter 2: Energy price of microscopic direction 2.1 Introduction …………………………… 16 …………………………………………………………. 2.2 Definition of directionality based on cycle kinetics iii ………… .…… 16 17 2.3 Least energy price for directionality ……………………………… . 19 …………………… 22 2.4 Thought experiments on the least energy price 2.5 Experimental verification of the least energy price ………………… 24 2.6 Macroscopic situations and consistency with thermodynamics laws . 26 …………………………………………………… .… 27 2.7 Conclusions Chapter 3: Best efficiency of isothermal molecular motors 3.1 Introduction ……………………. 29 …………………………………………………………. 29 3.2 Motor’s efficiency and the least energy price for microscopic direction 30 3.3 Experimental phenomenology of kinesin-1 and F1-ATPase reveals . 31 a best efficiency. 3.4 Thermodynamics of molecular motors represented by cycle kinetics 34 3.5 Optimal thermodynamics underlying the F1-ATPase and kinesin-1 . 38 phenomenology 3.6 Conclusions …………………………………………………………. 43 Chapter 4: Generalized efficiency at maximum power ……………….……… . 45 4.1 Introduction ……………………………………… ……………… . 45 ………… . 46 ………………………… 46 …………………………………… 47 ……………………………………………. 49 ………………………………… 50 4.2 Generalized efficiency and efficiency-velocity trade-off 4.2.1 Definition of generalized efficiency 4.2.2 The basic kinetic diagram 4.2.3 Generalized power 4.2.4 Efficiency-velocity trade-off 4.3 Generalized efficiency at maximum generalized power 4.3.1 Equation of GEMP …………… 52 ……………………………………………. 52 4.3.2 Two upper limits of GEMP iv …………………………………… 53 4.3.3 Analytical solution at the limits ……………………….…… 54 4.3.4 Energy input constrains GEMP ………………………………. 55 4.3.5 Temperature dependence of GEMP ………………………… . 4.3.6 Generalized efficiency and power at a finite load 4.4 Discussions …………… 57 …………………………………………………………. 59 4.4.1 The concept of generalized efficiency ……………………… . 59 ……………………………… . 61 ……………… .…………………… … 61 ……………………………………… .……………… 62 4.4.2 GEMP and conventional EMP 4.4.3 Kinetic asymmetry 4.5 Conclusions Chapter 5: Mechanics of Kar3/Vik1: a molecular fishing effect 5.1 Introduction 5.2 Methods 57 ………………. 64 …………………………………………………………. 64 …………………………………………………………… . 67 5.2.1 Mechanical model for MT-bound states of Kar3/Vik1heterodimer 67 5.2.2 Minimization of total free energy …………………………… 5.2.3 Mechanical properties of Kar3/Vik1 necks 5.3 Results 71 ………………… . 72 ………………………………………………………………. 74 5.3.1 Stability of microtubule-bound states of Kar3/Vik1 ………… 74 5.3.2 A molecular “fishing” effect driven by ATP binding ………… 75 5.3.3 Kinesin-MT binding interface is evolved to better resist …… . 77 5.3.4 The fishing force promotes MT depolymerization ………… 80 5.3.5 Asymmetry of fishing-promoted depolymerization ………… . 81 ……………… 83 …………………………………………………………. 87 destabilizing torque 5.3.6 Inter-head strain and neck structural changes in Kar3/Vik1-MT binding 5.4 Discussions v 5.4.1 Chemomechanical cycle for Kar3/Vik1 motility based on …… 87 … 88 ……………… 89 5.4.4 The fishing is a new mechanism for head-head coordination …. 89 the ATP-driven fishing effect 5.4.2 Chemomechanical coupling ratio of fishing-based motility 5.4.3 The fishing promotes MT deploymerization by a mechanochemical effect 5.5 Conclusions …………………………………………………………. 90 Chapter 6: Proposal for an artificial nano-motor: implementation of fishing …. 92 mechanism 6.1 Introduction 6.2 Methods …………………………………………………………. 92 …………………………………………………………… . 93 6.2.1 Basic design of the motor track system ………………………. 93 6.2.2 Two methods for the motor’s operation ………………………. 95 …………………………………………… 96 …………………………………………………. 97 6.2.3 Mechanical model 6.2.4 Kinetic model 6.3 Results …………………………………………………………… 100 6.3.1 Minimal compound foot for track binding 6.3.2 Position-selective detachment 6.3.3 Two versions of the motor 6.3.4 Bias for forward binding ……………………………… . 101 …………………………………… 102 …………………………………… . 103 6.3.5 The main working cycle of the motor 6.3.6 Motor performance …………………… 100 ……………………… . 103 ………………………………………… . 104 6.3.7 Mechanistic integration and relation to motor performance 6.4 Discussions …. 109 ………………………………………………………… 111 vi energy output is determined by the directionality at zero opposing force, so directionality, in parallel to temperature for heat engine, is the key parameter to access the best efficiency. Third, maximum efficiency is usually used for evaluating performance of molecular motors, but maximum efficiency in its conventional definition does not describe performance of a moving motor but a stalemated one. A generalized efficiency is defined by counting as energy output not only the mechanical work but also the least energy price for directionality. Reported experimental data of kinesin-1 and F1-ATPase show a constant generalized efficiency over load, suggesting its relevance to molecular motors at any load. A theory is constructed to quantify thermodynamic limits to the generalized efficiency and the associated generalized power. Kinesin-1 is found to work at the generalized efficiency at maximum generalized power (GEMP), while F1-ATPase has an ideal efficiency-speed trade-off that enables the motor to maintain ~ 100% efficiency and a workable speed simultaneously. A self-closed equation for GEMP at the thermodynamic limit is derived. Solution of the equation forms a stingray-shaped surface, which is a universal thermodynamic limit for all molecular motors. In order to understand high-performing motors from biology and develop artificial mimics, it is necessary to know the molecular mechanisms by which a motor operates close to thermodynamic limits. Pure mechanical mechanisms are studied after the thermodynamics study. First, analysis on biological motor Kar3/Vik1 reveals a mechanical mechanism, referred as fishing, by which ATP binding to Kar3 consolidates Kar3 but effectively dissociates the catalytically inactive Vik1 off MT. When occurring at frayed ends of MT, the fishing channels the hydrolysis energy into depolymerization. The ATP-driven molecular fishing thus provides a common mechanistic ground for 136 Kar3’s dual functionality of motility and depolymerase. Second, based on the mechanics of bio-motor Kar3/Vik1, an artificial motor is designed and a mechanical-kinetic model is built. Both of position-selective foot detachment and biased forward binding emerge from the motor’s intrinsic mechanics. With either effect, the directionality cannot be more than 0.5. The model predicts that the directionality of the fishing motor can be very close to 1, which implies that the two mechanisms coherently support each other and enhance the motor’s performance. Moreover, based on the model, thermodynamics of the motor after optimization is studied. The motor’s directionality can be optimized simultaneously for any load by adjusting the motor’s physical construction regardless of external driving. Such a universal optimality can be attained as signaled by a  factor that is stabilized around a half step size. When the motor’s directionality becomes perfect, its speed becomes infinitely slow. Such a speed-directionality trade-off is caused by an entropy crisis. These features agree with the thermodynamic theories of molecular motors described in previous chapters. The mechanical, thermodynamic and optimality studies in this thesis are open to more experimental tests and theoretical examinations in the future. For example, to what extent bio-motors other than kinesin-1 and F1-ATPase are close to the thermodynamic limits are open to future biophysical study. The thermodynamic theories are not only relevant for biological motors, but also for artificial systems. The mechanical and optimality studies provide guide lines for fabrication of artificial motors. These rationally designed artificial systems will serve as perfect model systems to test and further develop the thermodynamic theories presented in this thesis. Moreover, at present physical mechanisms of molecular motors are studied on thermodynamic level, and in the future 137 studies further on statistical mechanics level, for example to build microscopic model of molecular motors, will be scientifically meaningful explorations. 138 Bibliography 1. Szent-Gyorgyi, A., Discussion. Stud. Inst. Med. Chem. Univ. Szeged, 1941-1942. 1: p. 5. 2. Straub, B.F., Actin. Stud. Inst. Med. Chem. Univ. Szeged, 1941-1942. 2: p. 13. 3. Huxley, H. and J. Hanson, CHANGES IN THE CROSS-STRIATIONS OF MUSCLE DURING CONTRACTION AND STRETCH AND THEIR STRUCTURAL INTERPRETATION. Nature, 1954. 173(4412): p. 973-976. 4. Huxley, A.F. and R. Niedergerke, STRUCTURAL CHANGES IN MUSCLE DURING CONTRACTION - INTERFERENCE MICROSCOPY OF LIVING MUSCLE FIBRES. Nature, 1954. 173(4412): p. 971-973. 5. Huxley, H.E., THE DOUBLE ARRAY OF FILAMENTS IN CROSS-STRIATED MUSCLE. Journal of Biophysical and Biochemical Cytology, 1957. 3(5): p. 631-&. 6. Howard, J., Mechanics of motor proteins and the cytoskeleton. 2001, Sunderland, Massachusetts: Sinauer Associates, Inc. 7. Szent-Gyorgyi, A.G., Milestone in physiology - The early history of the biochemistry of muscle contraction. Journal of General Physiology, 2004. 123(6): p. 631-641. 8. Carnot, S., "Reflections on the motive power of fire, and on machines fitted to develop that power", translated by R.H.Thurston. 1977, Gloucester, Mass.: Peter Smith. 9. Schliwa, M. and G. Woehlke, Molecular motors. Nature, 2003. 422: p. 759-765. 10. Vale, R.D. and R.A. Milligan, The way things move: looking under the hood of molecular motor proteins. Science, 2000. 288: p. 88-95. 11. Vale, D., Myosin V motor proteins: marching stepwise towards a mechanism. J. Cell. Biol., 2003. 163: p. 445-450. 12. Veigel, C., et al., Load-dependent kinetics of myosin-V can explain its high processivity. Nature Cell Biology, 2005. 7: p. 861-869. 139 13. Oguchi, Y., et al., Load-dependent ADP binding to myosin V and VI: implications for subunit coordination and function. Proc. Natl. Acad. Sci. USA, 2008. 105: p. 7714-7719. 14. Vale, R.D., T.S. Reese, and M.P. Sheetz, Identification of a Novel Force-Generating Protein, Kinesin, Involved in Microtubule-Based Motility. Cell, 1985. 42: p. 39-50. 15. Burgess, S.A., et al., Dynein strcuture and power stroke. Nature, 2003. 421: p. 715-718. 16. Carter, A.P., et al., Structure and Functional Role of Dynein's Microtubule-Binding Domain. Science, 2008. 322(5908): p. 1691-1695. 17. DeWitt, M.A., et al., Cytoplasmic Dynein Moves Through Uncoordinated Stepping of the AAA+ Ring Domains. Science, 2012. 335: p. 221-225. 18. Junge, W., H. Sielaff, and S. Engelbrecht, Torque generation and elastic power transmission in the rotary F0F1-ATPase. Nature, 2009. 459: p. 364-370. 19. Lawrence, C.J., et al., A standardized kinesin nomenclature. Journal of Cell Biology, 2004. 167(1): p. 19-22. 20. Gennerich, A. and R.D. Vale, Walking the walk: how kinesin and dynein coordinate their steps. Curr. Opinion Cell. Biol., 2009. 21: p. 59-67. 21. Vale, R.D., The molecular motor toolbox for intracellular transport. Cell, 2003. 112(4): p. 467-480. 22. Howard, J. and A.A. Hyman, Dynamics and mechanics of the microtubule plus end. Nature, 2003. 422: p. 753-758. 23. McIntosh, J.R., E.L. Grishchuk, and R.R. West, Chromosome-microtubule interactions during mitosis. Annu. Rev. Cell Dev. Biol., 2002. 18: p. 193-219. 24. Tanaka, K., et al., Molecular mechanisms of microtubule-dependent kinetochore transport toward spindle poles. J Cell Biol., 2007. 178: p. 269-281. 25. Maddox, P.S., et al., The Minus End-Directed Motor Kar3 Is Required for Coupling Dynamic Microtubule Plus Ends to the Cortical Shmoo Tip in Budding Yeast. Curr. Biol., 2003. 13: p. 1423-1428. 140 26. Schnitzer, M.J. and S.M. Block, Kinesin hydrolyses one ATP per 8-nm step. Nature, 1997. 388: p. 386-390. 27. Visscher, K., M.J. Schnitzer, and S.M. Block, Single kinesin molecules studied with a molecular force clamp. Nature, 1999. 400: p. 184-189. 28. Carter, N.J. and R.A. Cross, Mechanics of the kinesin step. Nature, 2005. 435(7040): p. 308-312. 29. Nishiyama, M., H. Higuchi, and T. Yanagida, Chemomechanical coupling of the forward and backward steps of single kinesin molecules. Nature Cell Biology, 2002. 4(10): p. 790-797. 30. Howard, J., The movement of kinesin along microtubules. Annual Review of Physiology, 1996. 58: p. 703-729. 31. Thorn, K.S., J.A. Ubersax, and R.D. Vale, Engineering the processive run length of the kinesin motor. Journal of Cell Biology, 2000. 151(5): p. 1093-1100. 32. Ma, Y.Z. and E.W. Taylor, Interacting head mechanism of microtubule-kinesin ATPase. Journal of Biological Chemistry, 1997. 272(2): p. 724-730. 33. Hackney, D.D., The tethered motor domain of a kinesin-microtubule complex catalyzes reversible synthesis of bound ATP. Proc. Natl. Acad. Sci. USA, 2005. 102: p. 1833818343. 34. Hua, W., et al., Coupling of kinesin steps to ATP hydrolysis. Nature, 1997. 388(6640): p. 390-393. 35. Hackney, D.D., Evidence for alternating head catalysis by kinesin during microtubulestimulated ATP hydrolysis. Proc. Natl. Acad. Sci. USA, 1994. 91: p. 6865-6869. 36. Rice, S., et al., A structural change in the kinesin motor protein that drives motility. Nature, 1999. 402(6763): p. 778-784. 37. Rice, S., et al., Thermodynamics properties of the kinesin neck-region docking to the catalytic core. Biophys. J., 2003. 84: p. 1844-1854. 141 38. Cross, R.A., The kinetic mechanism of kinesin. Trends Biochem. Sci., 2004. 29(6): p. 301-309. 39. Hyeon, C. and J.N. Onuchic, Internal strain regulates the nucleotide binding site of the kinesin leading head. Proc. Natl. Acad. Sci. USA, 2007. 104: p. 2175-2180. 40. Block, S.M., et al., Probing the kinesin reaction cycle with a 2D optical force clamp. Proc. Natl. Acad. Sci. USA, 2003. 100(5): p. 2351-2356. 41. Taniguchi, Y., et al., Entropy rectifies the Brownian steps of kinesin. Nature Chem. Biol., 2005. 1(6): p. 342-347. 42. Yajima, J., et al., Direct long-term observation of kinesin processivity at low load. Current Biology, 2002. 12(4): p. 301-306. 43. Schief, W.R., et al., Inhibition of kinesin motility by ADP and phosphate supports a handover-hand mechanism. Proc. Natl. Acad. Sci. USA, 2004. 101: p. 1183-1188. 44. Coppin, C.M., et al., The load dependence of kinesin's mechanical cycle. Proc. Natl. Acad. Sci. USA, 1997. 94: p. 8539-8544. 45. Toyabe, S., et al., Thermodynamic efficiency and mechanochemical coupling of F-1ATPase. Proceedings of the National Academy of Sciences of the United States of America, 2011. 108(44): p. 17951-17956. 46. Yasuda, R., et al., F1-ATPase is a highly efficient molecular motor that rotates with discrete 120o steps. Cell, 1998. 93: p. 1117-1124. 47. Yasuda, R., et al., Resolution of distinct rotational substeps by submillisecond kinetic analysis of F-1-ATPase. Nature, 2001. 410(6831): p. 898-904. 48. Adachi, K., et al., Coupling of rotation and catalysis in F1-ATPase revealled by singlemolecule imaging and manipulation. Cell, 2007. 130: p. 309-321. 49. Kay, E.R., D.A. Leigh, and F. Zerbetto, Synthetic molecular motors and mechanical machines. Angewandte Chemie-International Edition, 2007. 46(1-2): p. 72-191. 142 50. Hugel, T., et al., Single-molecule optomechanical cycle. Science, 2002. 296: p. 11031106. 51. Leigh, D.A., et al., Unidirectional rotation in a mechanically interlocked molecular rotor. Nature, 2003. 424(6945): p. 174-179. 52. Fletcher, S.P., et al., A reversible, unidirectional molecular rotary motor driven by chemical energy. Science, 2005. 310(5745): p. 80-82. 53. Astumian, R.D., Adiabatic operation of a molecular machine. Proc. Natl. Acad. Sci. USA, 2007. 104: p. 19715-19718. 54. Hernandez, J.V., E.R. Kay, and D.A. Leigh, A reversible synthetic rotary molecular motor. Science, 2004. 306: p. 1532-1536. 55. Sherman, W.B. and N.C. Seeman, A precisely controllable DNA biped walking devices. Nano Lett., 2004. 4: p. 1203-1207. 56. Shin, J.S. and N.A. Pierce, A synthetic DNA walker for molecular transport. J. Am. Chem. Soc., 2004. 126: p. 10834-10835. 57. Yin, P., et al., A unidirectional DNA walker that moves autonomously along a track. Angew. Chem. Int. Ed., 2004. 43: p. 4906-4911. 58. Bath, J., S.J. Green, and A.J. Turberfield, A free-running DNA motor powered by a nicking enzyme. Angew. Chem. Int. Ed., 2005. 44: p. 4358-4361. 59. Tian, Y., et al., A DNAzyme that walks processiviely and autonomously along a onedimensional track. Angew. Chem. Int. Ed., 2005. 44: p. 4355-4358. 60. Yin, P., et al., Programming biomolecular self-assembly pathways. Nature, 2008. 451: p. 318-322. 61. Green, S.J., J. Bath, and A.J. Turberfield, Coordinated chemomechanical cycles: a mechanism for autonomous molecular motion. Phys. Rev. Lett., 2008. 101: p. 238101(14). 143 62. Omabegho, T., R. Sha, and N.C. Seeman, A bipedal DNA Brownian motor with coordinated legs. Science, 2009. 324: p. 67-71. 63. von Delius, M., E.M. Geertsema, and D.A. Leigh, A synthetic small molecule that can walk down a track. Nature Chemistry, 2010. 2(2): p. 96-101. 64. Bath, J., et al., Mechanism for a Directional, Processive, and Reversible DNA Motor. Small, 2009. 5: p. 1513-1516. 65. Wickham, S.F.J., et al., Direct observation of stepwise movement of a synthetic molecular transporter. Nature Nanotechnology, 2011. 6: p. 166-169. 66. You, M.X., et al., An Autonomous and Controllable Light-Driven DNA Walking Device. Angewandte Chemie-International Edition, 2012. 51(10): p. 2457-2460. 67. Gu, H., et al., A proximity-based programmable DNA nanoscale assembly line. Nature, 2010. 465: p. 202-206. 68. Lund, K., et al., Molecular robots guided by prescriptive landscapes. Nature, 2010. 465: p. 206-210. 69. He, Y. and D.R. Liu, Autonomous multistep organic synthesis in a single isothermal solution mediated by a DNA walker. Nat. Nanotechnology, 2010. 5: p. 778-782. 70. Wang, Z.S., Synergic mechanism and fabrication target for bipedal nanomotors. Proc. Natl. Acad. Sci. USA, 2007. 104: p. 17921-17926. 71. Juan, C., et al., Bipedal Nanowalker by Pure Physical Mechansims. Physical Review Letters, 2012. 109: p. 5. 72. Smoluchowski, M.v., Experimentell nachweisbare, der ublichen Thermodynamik widersprechende Molekular phanomene. Physikalische Zeitschrift, 1912. 13: p. 12. 73. Julicher, F., A. Ajdari, and J. Prost, Modeling molecular motors. Reviews of Modern Physics, 1997. 69(4): p. 1269-1281. 74. Reimann, P., Brownian motors: noisy transport far from equilibrium. Physics Reports, 2002. 361: p. 57-265. 144 75. Astumian, R.D. and P. Hanggi, Brownian motors. Physics Today, 2002. 55(11): p. 33-39. 76. Hanggi, P. and F. Marchesoni, Artificial Brownian motors: Controlling transport on the nanoscale. Reviews of Modern Physics, 2009. 81(1): p. 387-442. 77. Magnasco, M.O., Forced thermal ratchets. Phys. Rev. Lett., 1993. 71: p. 1477-1481. 78. Rousselet, J., et al., DIRECTIONAL MOTION OF BROWNIAN PARTICLES INDUCED BY A PERIODIC ASYMMETRIC POTENTIAL. Nature, 1994. 370(6489): p. 446-448. 79. Faucheux, L.P., et al., Optical thermal ratchet. Phys. Rev. Lett., 1995. 74: p. 1504-1507. 80. Julicher, F. and J. Prost, COOPERATIVE MOLECULAR MOTORS. Physical Review Letters, 1995. 75(13): p. 2618-2621. 81. Hanggi, P. and R. Bartussek, Lecture Notes in Physics. 1996. 476. 82. Astumian, R.D., Thermodynamics and kinetics of a Brownian motor. Science, 1997. 276: p. 917-922. 83. Astumian, R.D. and I. Derenyi, A chemically reversible Brownian motor: application to kinesin and Ncd. Biophys. J., 1999. 77: p. 993-1002. 84. Kanada, R. and K. Sasaki, Theoretical model for motility and processivity of two-headed molecular motors. Phys. Rev., 2003. E 67: p. 061917 (1-13). 85. Dan, D., A.M. Jayannavar, and G.I. Menon, A biologically inspired ratchet model of two coupled Brownian motors. Physica A, 2003. 318: p. 40-47. 86. Downton, M.T., et al., Single-polymer Brwonian motor: a simulation study. Phys. Rev., 2006. E 73: p. 011909. 87. Munarriz, J., J.J. Mazo, and F. Falo, Model for hand-over-hand motion of molecular motors. Phys. Rev., 2008. E 77: p. 031915(7). 88. Efremov, A. and Z.S. Wang, Maximum directionality and systematic classification of molecular motors. Phys. Chem. Chem. Phys., 2011. 13: p. 5159-5170. 89. Parrondo, J.M.R. and B.J. De Cisneros, Energetics of Brownian motors: a review. Applied Physics a-Materials Science & Processing, 2002. 75(2): p. 179-191. 145 90. Parrondo, J.M.R., et al., Efficiency of Brownian motors Europhys. Lett., 1998. 43: p. 248254. 91. Parmeggiani, A., et al., Energy transduction of isothermal ratchets: generic aspects and specific examples close to and far from equilibirum. Phys. Rev., 1999. E 60: p. 21272140. 92. Onsager, L., Reciprocal relations in irreversible processes. I. Physical Review, 1931. 37(4): p. 405-426. 93. Jarzynski, C., Nonequilibrium equality for free energy differences. Phys. Rev. Lett., 1997. 78: p. 2690-2693. 94. Crooks, G.E., Nonequilibrium measurements of free energy differences for microscopically reversible Markovian systems. Journal of Statistical Physics, 1998. 90(56): p. 1481-1487. 95. Schnakenberg, J., NETWORK THEORY OF MICROSCOPIC AND MACROSCOPIC BEHAVIOR OF MASTER EQUATION SYSTEMS. Reviews of Modern Physics, 1976. 48(4): p. 571-585. 96. Hill, T.L., Theoretical formalism for the sliding filament model of contraction of striated muscle Part I. Progress in Biophysics and Molecular Biology, 1974. 28: p. 74. 97. Hill, T.L., Free Energy Transduction and Biochemical Cycle Kinetics 1989: (Springer, New York). 98. Fisher, M.E. and A.B. Kolomeisky, The force exerted by a molecular motor. Proc. Natl. Acad. Sci. USA, 1999. 96(12): p. 6597-6602. 99. Lipowsky, R., Universal Aspects of the Chemomechanical Coupling for Molecular Motors. Phys. Rev. Lett., 2000. 85: p. 4401-4404. 100. Fox, R.F. and M.H. Choi, Rectified Brownian motion and kinesin motion along microtubules. Phys. Rev. E, 2001. 63: p. 051901. 146 101. Liepelt, S. and R. Lipowsky, Kinesin's network of chemomechanical motor cycles. Phys. Rev. Lett., 2007. 98: p. 258102. 102. Liepelt, S. and R. Lipowsky, Impact of Slip Cycles on the Operation Modes and Efficiency of Molecular Motors. J. Stat. Phys., 2010. 141: p. 1-16. 103. Wang, Z.S., et al., Kinesin is an evolutionarily fine-tuned molecular ratchet-and-pawl device of decisively locked directionality. Biophys. J., 2007. 93: p. 3363-3372. 104. Fan, D.G., et al., Modelling motility of the kinesin dimer from molecular properties of individual monomers. Biochemistry (USA), 2008. 47: p. 4733-4742. 105. Zheng, W.W., et al., Load-resisting capacity of kinesin. Physical Biology, 2009. 6: p. 036002. 106. Seifert, U., Entropy Production along a Stochastic Trajectory and an Integral Fluctuation Theorem. Phys. Rev. Lett., 2005. 95: p. 040602. 107. Seifert, U., Fluctuation theorem for a single enzym or molecular motor. Europhysics Letters, 2005. 70(1): p. 36-41. 108. Astumian, R.D., Thermodynamics and Kinetics of Molecular Motors. Biophys. J., 2010. 98: p. 2401-2409. 109. Efremov, A. and Z.S. Wang, Universal optimal working cycles of molecular motors. Phys. Chem. Chem. Phys., 2011. 13: p. 6223-6233. 110. Schnitzer, M.J., K. Visscher, and S.M. Block, Force production by single kinesin motors. Nat. Cell. Biol., 2000. 2: p. 718-723. 111. Uemura, S., et al., Kinesin-microtubule binding depends on both nucleotide state and loading direction. Proc. Natl. Acad. Sci. USA, 2002. 99(9): p. 5977-5981. 112. Lan, G.H. and S.X. Sun, Dynamics of myosin-V processivity. Biophysical Journal, 2005. 88(2): p. 999-1008. 113. Schwaiger, I., et al., The myosin coiled-coil is a truly elastic protein structure. Nature Materials, 2002. 1(4): p. 232-235. 147 114. Case, R.B., et al., The directional preference of kinesin motors is specified by an element outside of the motor catalytic domain. Cell, 1997. 90(5): p. 959-966. 115. Xu, Y. and Z.S. Wang, Comprehensive physical mechanism of two-headed biomotor myosin V. J Chem Phys, 2009. 131: p. 245104(9). 116. Allingham, J.S., et al., Vik1 modulates microtubule-kar3 interactions through a motor domain that lacks an active site. Cell, 2007. 128: p. 1161-1172. 117. Manning, B.D., et al., Differential Regulation of the Kar3p Kinesin-related Protein by Two Associated Proteins, Cik1p and Vik1p. J Cell Biol., 1999. 144: p. 1219-1233. 118. Sproul, L.R., et al., Cik1 targets the minus-end kinesin depolymerase Kar3 to microtubule plus end. Curr. Biol., 2005. 15: p. 1420-1427. 119. Woehlke, G. and M. Schliwa, Kinesin Kar3 and Vik1 go head to head. Cell, 2007. 128: p. 1033-1034. 120. Mackey, A.T. and S.P. Gilbert, The ATPase cross-bridge cycle of the Kar3 motor domain. J Biol. Chem., 2003. 278: p. 3527-3535. 121. Derenyi, I., O. Bieri, and R.D. Astumian, Generalized efficiency and its application to microscopic engines. Phys. Rev. Lett., 1999. 83: p. 903-906. 122. Oster, G. and H. Wang, Reverse engineering a protein: the mechanochemistry of ATP synthase. Biochim. Biophys. Acta, 2000. 1458: p. 482-510. 123. Lau, A.W.C., D. Lacoste, and K. Mallick, Nonequilibrium fluctuations and mechanochemical couplings of a molecular motor. Phys. Rev. Lett., 2007. 99: p. 158102. 124. Rahav, S., J. Horowitz, and C. Jarzynski, Direct flow in nonadiabatic stochastic pumping. Phys. Rev. Lett., 2008. 101: p. 140602(1-4). 125. Chernyak, V.Y. and N.A. Sinitsyn, Pumping restrcition theorem for stochastic networks. Phys. Rev. Lett., 2008. 101: p. 160601(1-4). 126. Seifert, U., Efficiency of autonomous soft nanomachines at maximum power. Phys. Rev. Lett., 2011. 106: p. 020601. 148 127. Van den Broeck, C., N. Kumar, and K. Lindenberg, Efficiency of Isothermal Molecular Machines at Maximum Power. Physical Review Letters, 2012. 108(21). 128. Squires, T.M. and S.R. Quake, Microfluidics: Fluid physics at the nanoliter scale. Reviews of Modern Physics, 2005. 77(3): p. 977-1026. 129. Gennerich, A., et al., Force-induced bidirectional stepping of cytoplasmic dynein. Cell, 2007. 131: p. 952-965. 130. Scanlon, J.A.B., et al., Determination of the partial reactions of rotational catalysis in F1-ATPase. Biochemistry, 2007. 46: p. 8785-8797. 131. Curzon, F.L. and B. Ahlborn, Efficiency of a Carnot engine at maximum power output. American Journal of Physics, 1975. 43: p. 22-24. 132. Van den Broeck, C., Thermodynamic efficiency at maximum power. Physical Review Letters, 2005. 95(19). 133. Esposito, M., et al., Efficiency at Maximum Power of Low-Dissipation Carnot Engines. Physical Review Letters, 2010. 105(15). 134. Madbox, P.S., Microtubules: Kar3 eats up the track. Curr. Biol., 2005. 15: p. R622-R624. 135. Gulick, A.M., et al., X-ray crystal structure of the yeast Kar3 motor domain complexed with Mg.ADP to 2.3 A resolution. Biochemistry, 1998. 37: p. 1769-1776. 136. Hirose, K., et al., Large conformational changes in a kinesin motor catalyzed by interaction with microtubules. Molecular Cell, 2006. 23: p. 913-923. 137. Mackey, A.T., et al., Mechanistic analysis of the Saccharomyces cerevisiae kinesin Kar3. J Biol. Chem., 2004. 279: p. 51354-51361. 138. Sablin, E.P., et al., Direction determination in the minus-end-directed kinesin motor ncd. Nature, 1998. 395: p. 813-816. 139. Wendt, T.G., et al., Microscopic evidence for a minus-end-directed power stroke in the kinesin motor ncd. Embo Journal, 2002. 21: p. 5969-5978. 149 140. Endres, N.F., et al., A lever-arm rotation drives motility of the minus-end-directed kinesin Ncd. Nature, 2006. 439(7078): p. 875-878. 141. Wang, Z.S., K.W. Plaxco, and D.E. Makarov, Influence of local and residual structures on the scaling behavior and dimensions of unfolded proteins. Biopolymers, 2007. 86: p. 321-328. 142. Wang, Z.S. and D.E. Makarov, Rate of intramolecular contact formation in peptides: the loop length dependence. J. Chem. Phys, 2002. 117: p. 4591-4593. 143. Tripet, B. and R.S. Hodges, Helix capping interactions stabilizing the N-terminus of the kinesin neck coiled-coil. J Struct. Biol., 2002. 137: p. 220-235. 144. Kawaguchi, I. and S. Ishiwata, Nucleotide-dependent single- to double-headed binding of kinesin. Science, 2001. 291(5504): p. 667-669. 145. Molodtsov, M.I., et al., Force production by depolymerizing microtubules: a theoretical study. Proc. Natl. Acad. Sci. USA, 2005. 102: p. 4353-4358. 146. Endow, S.A., et al., Yeast Kar3 is a minus-end microtubule motor protein that destabilizes microtubules preferentially at the minus ends. EMBO J, 1994. 13: p. 27082713. 147. Hoenger, A., et al., A new look at the microtubule binding patterns of dimeric kinesins. J. Mol. Biol., 2000. 297: p. 1087-1103. 148. Ogawa, T., et al., A common mechanism for microtubule destabilizers-M type kinesins stabilize curling of the protofilament using the class-specific neck and loops. Cell, 2004. 116: p. 591-602. 149. Wang, Z.S., Bio-inspired track-walking molecular motors. BioInterphases, 2010. 5: p. FA63-FA68. 150. Liang, X., T. Mochizuki, and H. Asanuma, A supra-photoswitch involving sandwiched DNA base pairs and azobenzenes for light-driven nanostructures and nanodevices. Small, 2009. 5: p. 1761-1768. 150 151. Li, D., D. Fan, and Z.S. Wang, General mechanism for inchworm nanoscale track walkers: Analytical theory and realistic simulation. J Chem Phys, 2007. 126: p. 24510511. 152. Howard, J., Protein power strokes. Curr. Biol., 2006. 16: p. R517-R519. 153. Mather, W.H. and R.F. Fox, Kinesin's biased stepping mechanism: amplification of neck linker zippering. Biophys. J., 2006. 91: p. 2416-2426. 154. Kuwada, N.J., et al., Tuning the performance of an artificial protein motor. Phys. Rev. E, 2011. 84: p. 031922. 155. Hill, T.L., Discrete-time random-walks on diagrams (graphs) with cycles. Proc. Natl. Acad. Sci. USA, 1988. 85: p. 5345-5349. 151 [...]... parts Overall thermodynamics of molecular motors is only understood to a very limited degree, and few physical guidelines are in hand for designing artificial motors The main objective of this thesis is to study thermodynamics and mechanics of molecular motors The methods of cycle kinetics and mechanical modeling are applied to analyze thermodynamics and working mechanisms of molecular motors The focus... several types of biomolecular motors have been discovered from biology, and a few types of artificial motors have been synthesized in laboratory The science behind the biomolecular motors remains largely unclear, and the artificial ones are still far poorer in performance than the biological counterparts This thesis studies thermodynamics and mechanics of molecular motors in the hope of revealing their... performing motors like kinesin-1 and F1-ATPase The directionality based analysis is an inspiration for the thermodynamic study in this thesis 1.4.3 Mechanics of molecular motors A motor’s molecular construction determines its thermodynamics and performance Mechanics in the molecular constructions plays an important role in motors physical 12 mechanisms Hence mechanical study of molecular motors will... biological nanomotors … 48 kinesin and F1-ATPase 4.3 Generalized efficiency and generalized power of molecular motors ………… 51 4.4 Maximum power and corresponding generalized efficiency versus ………… 56 energy input and temperature 4.5 Generalized power versus generalized efficiency of kinesin and F1-ATPase … 58 at different loads ……………………………………… 66 5.1 Mechanics and energies of Kar3/Vik1 5.2 Molecular fishing... motion of molecular motors is a main part of this thesis For this purpose, analyses on experimental data of high-performing biological motors and theoretical formulation are especially necessary Below we will review experimental and theoretical studies of molecular motors from biology as well as manmade nanotechnology 2 1.2 Bio -motors: kinesin-1 and F1-ATPase as examples Since the discovery of muscle... experimental data of two bio -motors, kinesin-1 and F1-ATPase, for fuel-induced motion and external force-induced motion Based on the least energy price, a thermodynamic theory of molecular motors is formulated While the 2nd law of thermodynamics decides the efficiency limit of macroscopic heat engine, it is unclear whether the 2nd law remains a primary constraint on efficiency of molecular motors Based... biological motors The inner working mechanisms of these artificial molecular motors are likely far inferior to the biological motors 1.4 Theories of molecular motors 1.4.1 Brownian motor theory A molecular motor displays self-induced directional motion, which is related to nonequilibrium thermodynamics Before molecular motors are known, non-equilibrium transport effects have had attention of physicists... of how to design and fabricate a high-performance motor, and also may help to understand the relation between thermodynamics and performance of motors An analysis based on experimental data indicated that the energy consumption rate of kinesin-1 is reduced by external load, and the load dependence follows a form of Boltzmann’s law [110] There exists experimental evidence that the gating mechanism of. .. important for the study of molecular motors, because 11 their inner working is always cyclic In 1999, Fisher and Kolomeisky analyzed the force exerted by molecular motors based on a discrete jump model [98] In 2000, Lipowsky introduced a network diagram to describe motion of molecular motors [99] In 2001, Fox and Choi introduced a simple cycle diagram to analyze the motion of kinesin-1, and also considered... chapter 3, the best efficiency of isothermal molecular motors allowed by the 2nd law of thermodynamics is formulated, and the signatures predicted by the theory are confronted with the experiment data of kinesin-1 and F1ATPase In chapter 4, two new quantities, i.e generalized efficiency and generalized power, are introduced; thermodynamics limits of the two quantities for ideal motors are derived The limits . THERMODYNAMICS AND MECHANICS OF MOLECULAR MOTORS HOU RUIZHENG (Bachelor of Science, Xi’an Jiaotong University) A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSIOPHY. Status quo of artificial molecular motors ……………………………. 7 1.4 Theories of molecular motors ……………………………………… 9 1.4.1 Brownian motor theory ……………………………………… 9 1.4.2 Cycle kinetics and thermodynamics. several types of biomolecular motors have been discovered from biology, and a few types of artificial motors have been synthesized in laboratory. The science behind the biomolecular motors remains