Thermodynamics and mechanics of molecular motors

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. 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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