【作者】 张桂清；

【导师】 刘成卜；

【作者基本信息】 山东大学 ， 物理化学， 2009， 博士

【摘要】 DNA（脱氧核糖核酸Deoxyribonucleic acid）是染色体的主要成分,同时也是基因的重要组成部分。近年来,DNA中的电荷输运问题成为国际学术界研究的热点。一方面,研究发现与生命体密切相关的DNA损伤与修复过程伴随着DNA链内电荷的转移;另一方面,具有DNA结构的纳米电子元件等有重要的潜在应用价值。因此,DNA的电荷输运能力以及输运过程成为生理学、物理电子学和材料科学等多学科共同关注的课题。有关DNA的导电性问题一直存在着诸多争论。在实验上,研究者得出了迥然不同的结论:超导体、导体、半导体甚至是绝缘体。理论计算方面,由于采用的方法不同,所得结果也存在较大差异。自1993年Barton等人报道了DNA分子光诱导电荷转移实验中空穴转移距离大于4nm以来,有关DNA导电性的实验和理论研究引起人们极大的兴趣。Giese实验小组发现在GR_nG（n＜=4）组成的DNA链上,体系所负载的单位正电荷定域在单个碱基上,与晶格畸变耦合在一起形成空穴极化子,通过隧穿的方式发生转移;当n＞=4时,在热扰动的作用下,空穴极化子跃迁到桥体R_n上,在桥体上相邻碱基间无衰减的跃迁,实验进一步证明极化子在穿过3个（A:T）碱基的时间内,可以获得跳跃到（A:T）桥体上需要的热能。Barton和Schuster等人认为DNA电荷的转移距离可以多于4个（A:T）碱基对,同时证明了DNA链上的空穴是离域的,并提出了声子辅助跃迁方式;在电离势相近的片段（A:T）_n（n＞3）上,电荷输运是通过无衰减的极化子的漂移实现的。理论计算方面,Conwell小组利用紧束缚模型方法,证明了DNA链上的电荷是离域的,并基于极化子模型,很好地模拟了GG、GA碱基之间的隧穿以及A_n碱基桥上的输运过程。实验工作者对DNA分子链内的电荷转移机理提出了种种猜想,但是没有任何一种猜想能够合理解释已有的实验事实,因此,DNA电荷传输机制目前尚不清楚。鉴于这种情况,有必要开展理论研究,以便弄清DNA链中电荷的传输机理,为DNA的损伤与修复提供理论解释,同时为有关的疾病治疗、蛋白质药物研究,以及新型DNA纳米器件的设计等提供理论知识。因此,这项研究具有重要的科学意义。由于DNA分子尺寸大、结构复杂,目前的量子化学计算方法（从头算方法、密度泛函方法）处理DNA分子体系存在困难。因此,研究者发展了一系列的半经验模型方法,其中紧束缚方法由于充分考虑了DNA分子体系中电荷与格点间的耦合性质,适合于描述无外场情形以及存在外场情形下电荷的输运行为。由于紧束缚方法计算过程中用拟合参数替代复杂的从头算积分过程,从而使得该计算方法在研究大尺度体系优势非常明显。计算结果表明在成熟的参数条件下,该方法可以得到定性甚至定量的结果。本文首先介绍了DNA分子结构特征,以及常见的量子化学方法（从头算方法、密度泛函方法和半经验方法）,并指出这些方法对于处理DNA分子体系存在的困难;接着简单介绍了紧束缚方法。本文在计算过程中采用了两种紧束缚方法模型:一是紧束缚Su-Schrieffer-Heeger（SSH）模型,二是紧束缚Peyrard-Bishop-Holstein（PBH）模型。在上述两种模型中,将DNA双螺旋结构简化为两条平行链,并将每个碱基或碱基对简化为一个格点。由于DNA四种碱基或碱基对具有不同的电离势（在位能）,相对于电子或空穴而言,DNA链可以看作是由不同碱基组成的复杂的量子阱和势垒结构。在SSH模型与PBH模型中,分别考察了相邻格点间晶格畸变、互补碱基间氢键伸缩与电荷分布的耦合作用。具体研究内容与结果如下:1.无外场情形下,DNA链上电荷分布性质研究无外场作用时,体系激发掉一个电子从而带有单位正电荷,利用SSH模型考察了这种体系的静态电荷的分布性质。计算中,考虑了电荷与相邻晶格畸变的耦合作用。电荷分布与晶格畸变耦合在一起时,形成空穴极化子,净电荷定域在晶格畸变最大位置;相应地,体系的能带结构也发生了变化,出现了极化子能级和相应的低能级。通常极化子局域在在位能最低的碱基附近,但当初始的扰动比较大时,极化子会出现在初始扰动位置处。另外,利用PBH模型考察了电荷与互补碱基氢键伸缩的耦合作用下,体系静态电荷分布与氢键涨落的关系。与SSH模型得出的静态性质类似,电荷分布与氢键涨落耦合在一起,形成极化子。2.在外电场作用下,DNA链上电荷传输过程的研究以静态时电荷分布与晶格畸变为初始状态,加入外电场作用,讨论外电场作用下不同DNA链上的电荷输运性质。（1）同种链或交替链在由同种碱基和交替碱基组成的DNA链中,极化子近似保持原来的形状沿着电场方向运动,直至随着晶格涨落的加剧,最终弥散。（2）量子阱结构链当初始极化子束缚于量子阱中时,极化子在电场的作用下,会随着时间逐渐弥散;加大电场,会加速极化子弥散的速度,而无法使极化子摆脱量子阱的束缚继续沿着链向前运动。当极化子形成于DNA链的其它位置,而非束缚在量子阱中时,极化子在电场的作用下,会沿着电场的方向前进,直至掉入量子阱中。量子阱较深时,比如在A₃₀CA₆₉上,极化子始终无法摆脱量子阱的束缚,最终在阱中完全弥散;当量子阱较浅时,极化子会在短暂的弛豫之后,摆脱量子阱的束缚继续沿着电场运动,如在A₃₀TA₆₉链上。（3）势垒结构链在外电场中势垒的高度与宽度对极化子传输具有非常明显的影响。在弱电场下,空穴极化子无法穿越单势垒;而在强电场作用下,极化子可以穿过单个势垒继续沿着电场的方向运动。对于存在双势垒的情况,会有部分电荷隧穿过势垒,形成小极化子,原来的部分保持极化子形式,定域在势垒前,直至最终弥散,而小极化子会在电场的作用下继续运动,直至最终弥散。对于三个及三个以上的势垒,极化子几乎没有发生隧穿,最终弥散在势垒前;增加电场隧穿效应仍然不明显,反而增快了极化子的弥散速度。（4）（?）R_N-R′_M-R″_p（?）三嵌段结构链在电场作用下极化子仍能通过“湮灭”与“产生”的方式转移。在此过程中“湮灭”与“产生”过程是同时进行的,而且在此过程中会有双极化子,多极化子的出现。并且极化子的这种传递过程是十分迅速的,是在皮秒量级,甚至更短的时间完成的。根据电荷与晶格间的能量传递与最终达到平衡状态,推测极化子的这种新的传输方式是由以下两种耦合作用引起的:一是电荷与晶格之间的耦合作用,二是互补碱基间氢键的耦合作用。3.环境因素对电荷传输的影响理论计算忽略了环境因素的影响,为了更好地用数值方法模拟实验的结果,在本文计算中采用SSH模型,利用方形随机分布模拟了环境因素（温度、溶剂化效应等）对于静态电荷分布与电荷传输的影响。结果表明,环境因素对于体系静态电荷分布、能带结构以及电荷输运过程均产生了明显影响。总之,本文利用两种紧束缚模型（SSH模型和PBH模型）的静态和动态形式,分别考察了DNA带电体系的静态性质和在外电场作用下DNA链上电荷传输的规律。静态时,基于上述两种模型,即考虑两种不同的电荷晶格耦合作用时,分别得出了电荷分布与晶格畸变（氢键涨落）耦合在一起,形成静态极化子;加入外电场,并取DNA碱基的HOMO能量作为在位能,将由不同碱基组成的DNA链视为量子阱和能量势垒的交替,分别讨论了在两种耦合作用下,在不同DNA链上极化子的传输规律。本研究尚存在以下不足:对于模型计算,参数对计算结果的影响特别明显。由于DNA结构的复杂性,加之易于受到环境因素的影响使得其结构变得更加复杂,因此无从得到特定构型下的精确参数。求得良好的参数或者修改模型,使得模型具有更普遍的应用性是我们下一步研究的重点。上述研究过程中的极化子是定域电荷分布与晶格畸变耦合在一起,称为位置极化子,忽略了环境因素的影响。而近年来,相关的研究表明,DNA的溶剂效应对于极化子的形成起着重要的作用。研究者发现在水溶液中的DNA链存在净电荷时,极化子的束缚能约为0.5eV,该极化子不同于位置极化子,称为溶剂极化子;加之DNA链上存在较大的位置涨落,从而使得极化子变得很不稳定。在今后的研究中,对于在极性很强的水溶剂中DNA链上溶剂极化子的传输的研究也是未来工作的重要方面。更多还原

【Abstract】 DNA（Deoxyribonucleic acid）,the main component of chromosome and gene,is paid more attention for its physiological meanings and its potential application in nanoscale electronic devices,materials and biological synthesis.In recent years,it is found that the process of damage and repair in DNA is companied with charge transfer.Also,the potential applications in the nanoscale electronic devices are related with charge transport.So the topic of charge transfer in DNA becomes the research central in physiology,physical electronics and material science.There are many debates about the conductivity of DNA for different experimental results form superconductor,conductor,and semiconductor to insulator.However,the theoretical calculations about DNA are also different for adopted computational method.Since 1993,Barton group report that hole transfer in DNA over a distance＞4nm,a large number of experiments and theories have been advanced in the attempt to characterize the transport,mainly of a radical cation or hole.Particularly,a famous experiment was carried out by Giese on the sequence GA_nGGG,in which the hole tunnels through the first three As,then hop onto the bridge of As,where they are localized on a single A and travel further by hopping between neighboring As.Barton and Schuster groups exclaim that charge or holes can travel through more than four （A:T）s,and also holes delocalize in several bases.Meanwhile they point out that hole transport by poloraon drift in（A:T）_n（n＞3）.Conwell theory group also pay attention to charge transport in DNA and study it with tight binding method.Experiments show that charge will transfer along DNA helix;however it is not clear that how the charge transfers and what is the transport mechanism.In this paper,we will try to explain the above questions for its meaningful to DNA repair,illness treatment,protein drug design,and nano device.The theoretical calculations about DNA are difficult for the ordinary quantum chemical methods（e.g.ab initio method and Density Function Theory）can’t deal with such large scale system.So series of semiemperical methods are developed.The tight binding method is one of these methods that valuable ones to calculate complicate DNA molecules.The DNA structure and usual quantum chemistry（ab initio method,Density Function Theory and semiemperical method）methods are introduced,and then the difficulties in calculations are also pointed out.The tight binding method（TBM） can overcome the above limitations in virtue of fitted parameters which predigest multiple integral.The couplings between lattice displacements and charge distribution are focused on in SSH model and the model also explains some charge transport phenomena along DNA helix.Another important tight binding model is PBH model in which the interaction is the main one between the hydrogen bond stretching and charge distribution.These kind interactions also have visible effect on charge motion in DNA chain.1.In static state,the hole polaron will appear when one electron is excited from the DNA chain,in which charge distribution and lattice displacements are coupled together.Accordingly,the polaron energy level and the corresponding level come forth.In usual cases,polarons localize in the several bases with lowest onsite energy. Additionally,polaron forms at sites with initial structural fluctuations,but not ones with lowest onsite energy.2.Polaron motion becomes complicate when a DNA chain is put in an electric field.The polaron of the DNA chain composed by the same bases and the alternate ones can move along the chain under the suitable electric field until the polaron smears gradually for the lattices fluctuations.In the DNA chain made up of the same bases or alternate bases,the polaron can move along the chain in the direction of the electric field until smearing under the electric field.We discuss the DNA chains composed of different quantum wells and potential barriers detailedly.When polaron localizes at quantum wells,it will smear under an electric field;the polaron localizing at other sites will move forward until it localizes at the wells.The wells with deep potential energy can hold the polaron until it smears. The polaron at shallower wells will move forward further,such as in A₃₀TA₆₉.The DNA chains in which potential barriers are existed are also discussed.The results show that hole polaron can’t tunnel through single barrier under weak field,but it can go through the barrier when the electric field is enlarged.It is interested that the polaron will divided into two halves.One is small polaron and the other is the remain one.The small one will move forward and the remain one will smear under the electric field.To the case there are 3 or more barriers in a DNA chain,the tunneling can’t be observed though larger electric field.It is interested that polaron can transfer in the chains of three segments （?）R_N-R′_M-R″_p（?） by annihilating and creating.Polaron can annihilate gradually, meanwhile new polaron will be created at other sites with lowest onsite energy.The charge transport method can be finished in several picoseconds,or more rapidly. From the transport of charge and system energy,we speculate the result can be explained by two aspects:one is the coupling between charges and lattices;the other is the strong interaction of hydrogen bond of complementary bases.In the forth chapter,the environmental factors on a static polaron and a dynamic one are also simulated in SSH model.The calculations are realized based on emphasis that the environmental influences are due to structural fluctuations.The results show that the environmental factors have an effect on charge distribution,lattice displacements and energy band structure.Also,these factors can slow the polaron velocity at the same conditions,contrast to the one with no environmental effect.In brief,in virtue of polaron and quantum well theory,we investigate charge transfer in different DNA chains with SSH and PBH model.The two models are focused on adjacent space and hydrogen bond coupling with electrons respectively.They are all valuable models in our research topic.Additionally,the simulations of environmental effect on charge transport are also considered with SSH model.The next research topics are showed as following:Model calculations can give a few valuable information,but results rely on model parameters heavily.As we all known,DNA molecules are complicate and its structure are subtle when environmental factors are considered.So good parameters describing the above effect are essential in further research.The research is also relied on polaron model heavily.We can’t investigate charge transfer when polaron smears under an electric field.In our research,polaron can be named as ’space poalron’,because it forms by the interaction between electrons and lattices.In recent years,some research groups found that the tight binding energy of a polaron is about 0.5eV in water,differently form our calculated polaron model.This kind of polaron is called ’solvent polaron’.In next work,the solvent polaron should also be considered.更多还原