發(fā)布時間：2018-06-13 14:37

  本文選題：DNA凝聚 + 彈性細桿模型�。� 參考：《南京航空航天大學》2016年博士論文

【摘要】：近年來,隨著分子生物學的飛速發(fā)展,人們將越來越多的目光集中于生物大分子這一研究領域。而DNA作為一種典型的生物大分子,其所具備的儲存和傳遞生命遺傳信息的能力使得它逐漸成為了分子生物領域的一個研究熱點。由于DNA幾何構(gòu)型的平衡與穩(wěn)定直接影響著遺傳信息的表達,因此,對于DNA平衡幾何構(gòu)型及其穩(wěn)定性的研究是了解并應用DNA分子鏈的基礎。自1953年Watson和Crick借助X射線晶體衍射技術(shù)推測出DNA的雙螺旋結(jié)構(gòu)以來,關于DNA分子鏈的理論基礎研究不斷取得突破。盡管對于DNA分子鏈的內(nèi)部分子結(jié)構(gòu)的探索屬于量子力學的研究范疇,但其在生物細胞中的宏觀幾何構(gòu)型與外力勢能作用下的力學性能的研究可以借助于經(jīng)典力學的彈性細桿模型來實現(xiàn)。由此產(chǎn)生了一個經(jīng)典彈性力學與分子生物學相互交叉的新的研究領域。其在本質(zhì)上采用連續(xù)介質(zhì)力學的概念與思路研究曲桿的幾何形態(tài)與變形,而在方法上又可運用非線性力學和分析力學對DNA分子鏈的平衡構(gòu)型與穩(wěn)定性進行分析。因此,本文在連續(xù)介質(zhì)力學的基礎上,通過建立空間彈性細桿模型,來模擬計算DNA分子鏈在溶液中的平衡幾何構(gòu)型,并對其外力作用下的彈性響應與幾何構(gòu)型的穩(wěn)定性做了研究分析。本文的第一部分簡要介紹了DNA彈性細桿的幾何描述,概述了Kirchhoff彈性桿理論的基本假定與其適用的前提條件和物理意義,給出了彈性細桿的Kirchhoff平衡方程;闡述了物質(zhì)的界面層與界面張力、界面自由能的概念,通過Young-Laplace方程推導出了固-液界面張力的表達式,將其引入Kirchhoff方程,并沿細桿截面周長對弧坐標進行積分得到了受界面牽引力作用的DNA分子鏈平衡控制方程。第二部分則基于固-液界面的吸附原理,通過Gibbs吸附方程與Langmuir吸附方程,建立起溶液濃度與固-液界面張力的關系,并推導出其具體表達式;與此同時,借助Poisson-Boltzmann理論將溶液濃度引入長分子鏈的熵彈性,得到了溶液濃度與DNA分子鏈彈性模量的直接關系式。將上述兩式代入DNA彈性細桿的平衡控制方程,應用龍格-庫塔數(shù)值算法模擬計算出以圓柱形螺旋線與橢圓柱形螺旋線為初始構(gòu)型的DNA鏈段在不同溶度濃度中的凝聚構(gòu)型,并對其進行了初步的分析。第三部分針對DNA在外力載荷作用下的邊界條件,將端部力與界面張力共同作用下的DNA鏈段的幾何構(gòu)型與彈性響應的研究歸結(jié)為求解Kirchhoff微分方程組的邊值問題,并選用打靶法給出在其不同端部力作用下的數(shù)值解,從而確定DNA鏈段的幾何構(gòu)型。同時,利用DNA鏈段兩端在主軸坐標系中的坐標計算得到不同端部力對應的末端距數(shù)值,擬合出力-末端距曲線,并分析了不同溶液濃度對DNA鏈段的力-末端距曲線的影響。第四部分從分析力學的角度出發(fā),通過Kirchhoff動力學比擬,將動力學的時間變量t置換為一維空間變量即弧坐標s,從而得到了基于弧坐標的哈密頓原理與Lagrange方程。并基于此推導出能量密度函數(shù)依賴于曲率、撓率及它們一階導數(shù)的DNA螺旋線的Euler-Lagrange方程。第五部分則通過引入截面的扭轉(zhuǎn)角及其一階導數(shù),將曲線的Euler-Lagrange方程推廣至曲桿的Euler-Lagrange方程組。在此基礎上,通過與實驗數(shù)據(jù)進行了對比,分析了采用圓截面彈性細桿模型與橢圓截面彈性細桿模型分別模擬A-,B-,Z-DNA幾何構(gòu)型的可行性,并擬合了兩種模型的r0-h曲線。同時,分析了彈性細桿截面的幾何特性對螺旋帶模型幾何構(gòu)型的影響。第六部分通過將外力勢能項引入彈性細桿的能量密度函數(shù),在彈性曲桿模型的Euler-Lagrange方程組基礎上,推導出DNA彈性細桿在端部拉伸力作用下的Euler-Lagrange方程組,并基于此對不同初始曲率與初始扭率的DNA彈性細桿模型的拉伸穩(wěn)定性進行了初步分析。
[Abstract]:In recent years, with the rapid development of molecular biology, people will focus more and more attention on the research field of biological macromolecules. As a typical biological macromolecule, DNA has the ability to store and transmit the genetic information of life, which has gradually become a hot research topic in the division of biological fields. Because of DNA geometry, it has become a research hotspot. The balance and stability of the configuration directly affect the expression of genetic information. Therefore, the study of the geometric configuration and stability of DNA is the basis for understanding and applying the DNA molecular chain. Since Watson and Crick have deduced the double helix structure of DNA with the X ray crystal diffraction technology in 1953, the theoretical foundation of the DNA molecular chain has been continuously taken. Although the exploration of the internal molecular structure of the DNA molecular chain belongs to the field of quantum mechanics, the study of the mechanical properties of the macrogeometries and the external force potential in the biological cells can be realized by the elastic thin rod model of the classical mechanics. The new research field of biology intersecting with each other. It uses the concept and thought of continuous medium mechanics to study the geometric shape and deformation of the curved rod in essence, and the method of nonlinear mechanics and analytical mechanics can be used to analyze the equilibrium configuration and stability of the DNA molecular chain. The space elastic thin bar model is established to simulate the equilibrium geometric configuration of the DNA molecular chain in the solution. The elastic response and the stability of the geometric configuration under its external force are studied and analyzed. The first part of this paper briefly introduces the geometric description of the DNA elastic rod, and summarizes the basic assumptions of the theory of the Kirchhoff elastic rod. The Kirchhoff equilibrium equation of the elastic thin rod is given, and the concept of interfacial tension and interfacial free energy is expounded. The expression of the solid liquid interfacial tension is derived through the Young-Laplace equation, which is introduced into the Kirchhoff equation, and the arc coordinates are integrated along the circumference of the section of the fine rod. The equilibrium control equation of DNA molecular chain is obtained by the interface traction. The second part is based on the adsorption principle of solid liquid interface. Through the Gibbs adsorption equation and the Langmuir adsorption equation, the relationship between solution concentration and solid liquid interfacial tension is established and its specific expression is derived. At the same time, the solution with the aid of Poisson-Boltzmann theory is used. The direct relation between the concentration of the solution and the elastic modulus of the DNA molecular chain is obtained by introducing the entropy elasticity of the long molecular chain. The above two formula is substituted for the equilibrium control equation of the DNA elastic thin rod, and the DNA chain of the initial configuration with the cylindrical spiral and the elliptical columnar spiral is simulated and calculated by the Runge Kutta numerical algorithm. The third part aims at the boundary conditions of DNA under the force of external force. The study of the geometric configuration and elastic response of the DNA segment under the joint action of the end force and the interfacial tension is reduced to the solution of the boundary value problem of the Kirchhoff differential equations. The numerical solution of the same end force is used to determine the geometric configuration of the DNA segment. At the same time, the end distance values corresponding to different end forces are obtained by calculating the coordinates of the two ends of the DNA segment in the spindle coordinate system, and the force - end distance curve is fitted, and the effect of different solution concentration on the force and end distance curve of the DNA segment is analyzed. The fourth part is from the analysis of the effect of the force to the end distance curve of the chain segment. Based on the analysis of mechanics, the time variable t of dynamics is replaced by a one-dimensional space variable, the arc coordinate s by Kirchhoff dynamics analogy, and the Hamilton principle and the Lagrange equation based on the arc coordinate are obtained. Based on this, the Euler of the energy density function is dependent on the curvature, the torsion and the Euler of the DNA spiral of their first derivative. In the fifth part, the fifth part, by introducing the torsional angle of the cross section and its first derivative, generalizes the Euler-Lagrange equation of the curve to the Euler-Lagrange equation set of the curved bar. On this basis, through the comparison with the experimental data, it is analyzed that the elastic thin rod model of the circular section and the elastic thin rod model of the elliptical cross section are respectively simulated, B-, and B-. The feasibility of the Z-DNA geometric configuration and the fitting of the r0-h curves of the two models are fitted. Meanwhile, the influence of the geometric characteristics of the section of the elastic thin section on the geometric configuration of the spiral belt model is analyzed. The sixth part is derived from the energy density function of the external force potential energy term to the elastic thin rod, and on the basis of the Euler-Lagrange equation set of the elastic curved bar model. The Euler-Lagrange equations of the DNA elastic thin rod under the end tensile force are given, and the tensile stability of the DNA elastic thin bar model with different initial curvature and initial torsion is preliminarily analyzed.
【學位授予單位】：南京航空航天大學
【學位級別】：博士
【學位授予年份】：2016
【分類號】：Q523

【相似文獻】

相關期刊論文 前10條

1 李鴻圖;;以變尺度法優(yōu)化分子幾何構(gòu)型[J];遼寧大學學報(自然科學版);1986年01期

2 陳明旦;球烯分子的幾何構(gòu)型預測[J];廈門大學學報(自然科學版);1992年06期

3 崔淑蘭;電子對域模型與分子的空間幾何構(gòu)型[J];煙臺師范學院學報(自然科學版);1994年01期

4 李平;;一種新的分子幾何構(gòu)型理論——價電子排斥理論介紹[J];青海師范學院學報(自然科學版);1980年01期

5 費正皓;影響偶氮苯類分子幾何構(gòu)型的取代基因素[J];蘇州大學學報(自然科學);2000年03期

6 王小剛,張宏,劉洪霖;鋁中氫—空位復合體的電子結(jié)構(gòu)和幾何構(gòu)型[J];化學物理學報;1992年04期

7 袁惠英;非過渡元素共價分子的幾何構(gòu)型[J];廣州師院學報(自然科學版);1998年06期

8 張瑞勤;戴國才;關大任;蔡政亭;;具有一維和多維構(gòu)型優(yōu)化功能的CNDO/2程序[J];山東大學學報(自然科學版);1988年04期

9 韓學坤,張憲璽,劉偉,馬長勤,張鳳霞,姜建壯;酞菁在不加對稱性限制條件下的電荷分布和幾何構(gòu)型的不同半經(jīng)驗方法研究[J];山東大學學報(自然科學版);2001年04期

10 葛尚正;判斷分子空間構(gòu)型的簡便方法——價層電子對互斥理論簡述[J];山東化工;2003年01期

相關會議論文 前6條

1 高洪澤;趙亮;蘇忠民;王悅;;CIS與UDFT優(yōu)化金屬配合物的激發(fā)態(tài)構(gòu)型的比較研究[A];第11屆全國發(fā)光學學術(shù)會議論文摘要集[C];2007年

2 白紅存;;多種典型分子篩的幾何構(gòu)型與電子結(jié)構(gòu)的晶體軌道法理論研究[A];第十七屆全國分子篩學術(shù)大會會議論文集[C];2013年

3 陳義旺;;基于限制幾何構(gòu)型環(huán)烯烴配位催化聚合催化劑的合成及性能[A];中國化學會第29屆學術(shù)年會摘要集——第05分會：無機化學[C];2014年

4 王宏;武海順;;(HBNH)_n團簇的結(jié)構(gòu)和穩(wěn)定性[A];中國化學會第九屆全國量子化學學術(shù)會議暨慶祝徐光憲教授從教六十年論文摘要集[C];2005年

5 凌崗;李祝飛;姜宏亮;楊基明;;縮尺效應對高超聲速進氣道自起動性能的影響[A];中國力學大會——2013論文摘要集[C];2013年

6 李穎;王佰全;徐善生;周秀中;程正載;孫俊全;;含吡啶基側(cè)鏈限制幾何構(gòu)型鉻系催化劑的合成及催化乙烯聚合研究[A];中國化學會第十三屆金屬有機化學學術(shù)討論會論文摘要集[C];2004年

相關博士學位論文 前3條

1 王芬華;含中性吡咯配體的稀土胺基配合物、烴基配合物的合成、結(jié)構(gòu)及性能研究[D];安徽師范大學;2014年

2 蕭業(yè);基于空間彈性細桿模型的DNA平衡幾何構(gòu)型與穩(wěn)定性研究[D];南京航空航天大學;2016年

3 肖婷婷;限制幾何構(gòu)型茂金屬催化劑的合成、表征及催化烯烴聚合反應研究[D];吉林大學;2008年

相關碩士學位論文 前6條

1 楊敏敏;超聲心動圖觀察慢性間歇性低氧新西蘭兔不同左室?guī)缀螛?gòu)型左房結(jié)構(gòu)和功能的實驗研究[D];山西醫(yī)科大學;2016年

2 祁卓君;持續(xù)正壓通氣治療后阻塞性睡眠呼吸暫停綜合征患者左室?guī)缀螛?gòu)型轉(zhuǎn)變的臨床研究[D];山西醫(yī)科大學;2016年

3 陳昌;雙基正前視SAR幾何構(gòu)型與成像算法研究[D];西安電子科技大學;2014年

4 鄧小輝;金原子團簇幾何構(gòu)型和電子結(jié)構(gòu)的理論研究[D];四川大學;2007年

5 湯曉;Meso位四取代卟啉及α位四鹵代酞菁的密度泛函理論研究[D];山東大學;2008年

6 韓黨衛(wèi);硅與鋅混合團簇幾何構(gòu)型及電子結(jié)構(gòu)的研究[D];西北大學;2007年

，

本文編號：2014352