分子马达定向运动机制的研究
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摘要
分子马达是具有马达功能的蛋白质大分子，广泛存在于生物体细胞内，是一类可以高效率的将储存在ATP中的化学能直接转化为机械能的蛋白质。生物体的一切生命活动，都离不开分子马达做功的推动。分子马达通过催化ATP水解获得能量，从而产生宏观运动，在这个过程中，伴随着ATP水解的化学过程而产生的运动的动力学机制是我们关注的焦点问题。
由于在分子尺度上，蛋白质马达布朗运动的特征十分明显，因而在不考虑分子马达构象变化的情况下，通常把分子马达抽象为布朗粒子，利用非平衡态统计理论解释分子马达在介质中的运动机制。周围环境的影响被简化为某种特定形式噪声的激励作用，分子马达与轨道之间的相互作用可以用特定的势函数来表示。
论文中首先简单地介绍了几种经典的马达蛋白的生物结构和催化ATP水解的工作机制；接着，介绍在描述分子马达定向运动机制中常用的主方程和Langevin方程，详细介绍了数值求解Langevin方程的Runge-Kutta算法和Monte Carlo模拟方法，并结合简单具体模型进行了讨论。在第三部分，介绍了一些特殊的布朗马达模型。第四章中我们提出了二维闪烁布朗马达型，分析了在白噪声作用下和非恒定外部驱动力下的分子马达各个参量的对稳态流J的影响。
Molecular motors are cellular proteins able of converting chemical energy of ATP into mechanical force with high efficiency. Most of the life activities depend on the motor protein and mechanical work it does. The energy source of the cell is hydrolization of ATP, thereby generating directional motion. In this procedure, molecular dynamical mechanics which adjoint with hydrolization of ATP received extensive interests.
In the scale of molecule, the movement of the proteins has the features of Brownian movement. So we can take molecular motor as a Brownian particle in the case of ignoring the conformational changes. We can use nonequilibrium statistical theory to explain the working mechanics of molecular motor in the realm of physics. The effect of the environment can be simplified as a noise while the interactions between molecular motor and its tracks can be described by a special potential.
At first, in the thesis of ours, the structures of several kinds of well known motors and their cycle of ATP hydrolization were introduced briefly. Secondly, we give out the Master Equation and Langevin Equation which were commonly used to explain the work mechanics of molecular motor. Then we discussed two numerical methods to solve stochastic differential equation: Runge-Kutta algorithms and Monte Carlo Simulations, with these we give out a simple example to display how to use them. In part three, we introduce some special model of molecular motors. Finally, we give out the two dimensions flashing potential model under white noise, we analysis the current behaviors under different environment variables.
由于在分子尺度上，蛋白质马达布朗运动的特征十分明显，因而在不考虑分子马达构象变化的情况下，通常把分子马达抽象为布朗粒子，利用非平衡态统计理论解释分子马达在介质中的运动机制。周围环境的影响被简化为某种特定形式噪声的激励作用，分子马达与轨道之间的相互作用可以用特定的势函数来表示。
论文中首先简单地介绍了几种经典的马达蛋白的生物结构和催化ATP水解的工作机制；接着，介绍在描述分子马达定向运动机制中常用的主方程和Langevin方程，详细介绍了数值求解Langevin方程的Runge-Kutta算法和Monte Carlo模拟方法，并结合简单具体模型进行了讨论。在第三部分，介绍了一些特殊的布朗马达模型。第四章中我们提出了二维闪烁布朗马达型，分析了在白噪声作用下和非恒定外部驱动力下的分子马达各个参量的对稳态流J的影响。
Molecular motors are cellular proteins able of converting chemical energy of ATP into mechanical force with high efficiency. Most of the life activities depend on the motor protein and mechanical work it does. The energy source of the cell is hydrolization of ATP, thereby generating directional motion. In this procedure, molecular dynamical mechanics which adjoint with hydrolization of ATP received extensive interests.
In the scale of molecule, the movement of the proteins has the features of Brownian movement. So we can take molecular motor as a Brownian particle in the case of ignoring the conformational changes. We can use nonequilibrium statistical theory to explain the working mechanics of molecular motor in the realm of physics. The effect of the environment can be simplified as a noise while the interactions between molecular motor and its tracks can be described by a special potential.
At first, in the thesis of ours, the structures of several kinds of well known motors and their cycle of ATP hydrolization were introduced briefly. Secondly, we give out the Master Equation and Langevin Equation which were commonly used to explain the work mechanics of molecular motor. Then we discussed two numerical methods to solve stochastic differential equation: Runge-Kutta algorithms and Monte Carlo Simulations, with these we give out a simple example to display how to use them. In part three, we introduce some special model of molecular motors. Finally, we give out the two dimensions flashing potential model under white noise, we analysis the current behaviors under different environment variables.
引文
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[2] 刘建峰，分子马达简介，中学生物学，2005，21(11)：5．
[3] George Oster and Hongyun Wang, Rotary protein motors, Trends in Cell Biology Vol. 13. No. 3 March 2003.
[4] 郑燕，展永，韩英荣等，神奇的生物酶-旋转分子马达，现代物理知识，2006，18(6)：28．
[5] 蒋怀伟，王石刚，徐威等．纳米生物机器人研究与进展．机器ROBOT，2005，26(6)：572
[6] Manson MD, Tedesco P, Berg HC, et al. A protonmotive force drives bacterial Flagella. Proc Natl Acad Sci USA, 1997, 74(7): 3060～3064.
[7] Imae Y Atsumi. Na+-driven bacterial flagella motors. J Bioenerg Biomembr, 1989, 21(6): 705～716.
[8] J. M. Berg, J. L. Tymoczko, L. Stryer and N. D. Clarke. Biochemistry. New York: W. H. Freeman and Co: 2002.
[9] Lloyd S A, Blair D ECharged residues of the rotor Protein FliG essential for torque generation in the flagellar motor of Escherichia coli. J Mol Biol, 1997, 266(4): 733～744.
[10] Khan IH, Rease T S, Khan S. The cytoplasmic component of the bacterial flagellar motor. Proc Natl Acad Sci USA, 1992, 89(13): 5959～5960.
[11] C. V. Gabel and H. C. Berg, PNAS. 100. 8748(2003).
[12] Kubo S, Magariyama Y, Aizawa S, Abrupt changes in flagellar rotation observed by aser dark-field microscopy. Nature, 1990, 346(6285): 677～680.
[13] RD. Vale, RA. Milligan Operational model for the coupling of ATP hydrolysis to movement of myosin along an actin filament. 2002, Science 288: 88.
[14] Ahmet Yildiz, MichioTomishige, RonaldD. Vale, Paul R. Selvin, Kinesin Walks Hand-Over-Hand Science 2004 303: 676～678.
[15] 王丹，邓迎春．Tilting Ratchet肌动蛋白双足运动模型的研究．湖南城市学院学报．2006，15(4)：32．
[16] Hua W, Chung J, Gelles J, Distinguishing inchworm and hand-over-hand processsive kinesin Movement by neck rotation measurements, Science, 2002, 295, 844～848.
[17] Boyer P, Biochem. Biophys. Acta 1140, 215 (1993).
[18] WANG Xian-ju, AI Bao-quan, LIU Liang-gang. Review on Modeling Molecular Motor. 中山大学学报．2001．40(2)：42-44．
[19] Qian H, A Simple Theory of Motor Protein Kinesin and Energetics[J]. Biophys. Chem. 1997,67:263-267.
[20] Kolomeisky A.B, Widom B. A Simplified "Ratchet" Model of Molecular Motors. [J]. J. Stat.Phys. 1998,93:633-645.
[21] Fisher M E, Kolomeisky A.B.The Force Exerted by a Molecular Motor[J]. Pro.Natl. Acad.Sci.USA, 1999,96:6597-6602.
[22] Derrida B, Velocity and Diffusion Constant of a Periodic One-Dimensional Hopping Model. J. Stat. Phys, 1983,31:433-450.
[23] 冯娟，卓益忠，应用主方程方法研究分子马达的定向运动．生物物理学报，2002，18(4)：418
[24] 冯娟，卓益忠等．分子马达的三态周期跳跃模型．化学物理学报．2002，15(5)，379-386．
[25] 卓益忠，赵同军，展永，分子马达与布朗马达，物理，2000，29，(12)：712-718．
[26] 展永，赵同军，卓益忠等，布朗马达的定向输运模型，物理学报，1997，46：1880．
[27] J.D.Bao, Y.Z.Zhuo and X.Z.Wu, Diffusion Current for a System in a Periodic Potential Driven by Mutiplicative Colored Noise.Phys Lett, 1996,A215:154-159.
[28] YuHui, ZhaoTongjun, Ji Qing, Song Yanli,Wang Yonghong,Zhan Yong, Dipole-Dipole Interaction and the Directional Motion of Brownian Motors. Common Theor Phys, (Beijing China), 2002,37:381-384.
[29] Zhan Yong, ZhaoTongjun, Ji Qing, Song Yanli.Transport Properties under the Influence of Finite Friction China Phy. (Beijing China), 2002,6.
[30] J.D.Bao, Y.Z.Zhuo and X.Z.Wu.Effects of Mutiplicative Noise on Fluctuation-induced Transport. Phys Lett, 1996,A 217:241-247.
[31] 赵同军，分子马达输运和能量转化效率的动力学，吉林大学博士毕业论文1999
[32] Rebecca L Honeycutt, Stochastic Runge-Kutta Algorithms. I. White Noise. APS. 1992, 45:600～603.
[33] N.G Van Kampen, Stochastic Processes in Physics and Chemistry (North-Holland, Amster-dam, 1981).
[34] W.H Press, B.P. Flannery, S.A.Teukosky, and W.T.Vetterling, Numerical Recipes: The Art of Scientific Computing(Cambridge University Press, New York,1986).
[35] 许淑艳，P．Frobrich．Langevin方程的蒙特卡罗模拟．计算物理．1989．6(2)：205～214
[36] 包景东，许淑艳，卓益忠．Monte Carlo方法模拟Langevin方程中的时间步长问题．计算物理．1989．6(2)：241～247
[37] 王梓坤，概率论基础及其应用(1976)．
[38] G.N. Milstein, Approximate Integration of stochastic differential equations, Theory Probab. Appl. 1974.19(3): 557～562.
[39] R.Mannella, V.Palleschi, Fast and precise algorothm for computer simulation of stochastic differential equations, Phys.Rev. 1989,40. 3381～3386.
[40] Bao J D, Zhuo Y Z. Wu X Z. Effects of multiplicative noise on fluctuation-induced transport. Phys Lett, 1996,A 217:241。
[41] 包景东，卓益忠．分子马达单向梯跳运动的偏压涨落模型，科学通报．1998．43(14)：1493
[42] 徐荣归，分子马达运动机制的动力学研究，东华大学硕士学位论文．2006：30
[43] Schnitzer.MJ,Block.SM, Kinesin hydrolyzes one ATP per 8-nm step, Nature,1997,388, 386-330
[44] Peter Reimann, Brownian motors: noisy transport far from equilibrium, Phys. Rep. 361, 57 (2002).
[45] Zhan Yong, Zhao Tongjun, Ji Qing, et al.Research progressing on molecular motors theories. Journal of Hebei University of Technology.2004,33(2):41～45.
[46] 周继平，分子马达理论及人工合成研究进展，学信息手术学分册，200619(2)：60
[47] B.Trpisova and A.Tuszynski,Phys.Rev.E 55(1997) 3288
[48] M.V.Sataric,J.A.Tuszynski and R.BZakula, Phys.Rev.E 48(1993) 589
[49] Yu-XiaoLi. Brownian motors possessing internal degree of freedom. Physica A,251 (1998) 382
[50] E.P. Jansons,G.D.Lythe,Phys.Rev.Lett.81 (1998) 3136
[51] H. Risken,The Fokker-Planck Equation, Springer, Berlin,(1984).
[52] N. Madras and G. Slade, The Self-Avoiding Walk (Birkhauser, Boston, 1992).
[53] J. Mai, I.M. Sokolov, and A. Blumen, Directed particle diffusion under burnt bridge condition Phys. Rev. E 64, 011102 (2001).
[54] T. Antal and P.L. Krapivsky.A Burnt Bridge Brownian Ratchet. Phys. Rev. E 72, 046104 (2005)
[55] J.Howard, Mechanics of Motor Proteins and the Cytoskeleton (Sinauer Associates, Sunderland,MA,2001).
[56] R.Fox, Phys .Rev. E 57, 2177-2203 (1998).
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