受限高分子单链动力学的格子蒙特卡罗模拟
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摘要
高分子链的动力学问题是高分子物理学中的核心问题之一。近来由于受限空间中蛋白质和DNA研究的升温,与之息息相关的受限高分子链也成为了当前研究的热点。尽管受限链物理模型简单,但是理论处理却极为复杂,存在着大量的数学近似;在实验上,纳米空间尺度的受限结构难于制备,而且受限链的特征动力学时间发生于纳秒时间尺度,也限制了大多数实验测试工具的应用。计算机模拟能够有效的反映受限空间中高分子链的动力学过程,已成为该领域的重要研究手段。
本文基于键长涨落格子模型的蒙特卡罗模拟,系统地研究了自由链、半维数限制的接枝链、一维受限的狭缝链、二维受限的管道链及三维受限的立方微腔链的特征动力学行为。其主要创新性工作可以分为以下几个部分:
(一)系统地研究了自由链和接枝链的末端环化和链内环化的平均初次接触时间的标度行为。运用已知动力学理论,我们对自由链的末端环化和链内环化行为进行了解释。而对于接枝链,我们发现由于硬墙的存在,末端环化的特征时间标度行为发生了改变,而且由于链两端的对称性遭到了破坏,接枝端基和自由端基参与的链内环化过程出现了截然不同的标度行为。
(二)系统比较了一维、二维、三维受限空间中高分子链的三种动力学特征时间的标度关系。探讨了狭缝、管道以及立方微腔中受限高分子链的三个典型动力学过程的特征时间:环化时间、旋转松弛时间和扩散时间,得到了强受限条件下一系列的标度行为,特别地,在管道强受限下,我们发现了环化时间和旋转松弛时间的指数标度行为。通过比较不同受限维数下的环化时间,我们发现三种受限情形都导致了更快的环化行为,该现象同以前球形微腔中更快的链内环化、分子伴侣笼和球形微腔中蛋白质折叠更快的现象一致;而且,随着受限维数的增加,环化时间减小,反映了更快的链内环化,从侧面应证了受限导致更快的动力学这一结论。
(三)考察了高分子链在图案化表面的吸附行为。模拟了一维周期性势能表面上自避行走链吸附的热力学行为,着重研究了链从三维空间向周期性势能平面吸附和链从横跨多个吸附条带到局域化在单个吸附条带上这两个过程。前一个过程对应着比热峰和链尺寸等热力学参量的突变,然而并非一级相变过程;而后者是个非常平缓的过程,所考察的几个参量表明该过程不存在相变行为。
在博士论文的最后阶段,本人主动要求从事实验工作以得到更全面的训练,并得到了导师的支持,从事了一种旨在作为蛋白质药物缓释载体的水凝胶微粒的研究。在实验方面的主要贡献为:(1)改进了微凝胶的制备技术。可注射性是关系到缓释体系是否为医生和病人接受的重要性质,通过改进传统的微球制备方法和后处理工艺,我们得到了粒径符合注射性的微球。此外,针对微球再分散问题,我们合成了具有不同长度的嵌段丙交酯的大单体,对其所制备得到的微球再分散性能进行了考察,找到了适合制备可注射微凝胶的大单体。(2)改进了药物包裹和体外释放的操作。我们探索了长期困扰课题组的蛋白质后包裹失活问题,考察了各种潜在因素,最终找到了失活根源。这些工作为今后该化学凝胶微球缓释体系在蛋白质药物载体方面更多的体外实验打下了基础,使得组内开发的温敏型化学凝胶朝向应用接近了一步。
Polymer dynamics is one of the core problems in polymer physics. Due to recent studies of proteins and DNAs in the confining space, the dynamics of a confined polymer chain has become a hot topic. Though the physical model of a confined polymer chain is relatively simple, the theoretical treatment is extremely complicated and the mathematical approximations must be applied in the calculations. On the other hand, the confinement structure with the nanometer spatial scale is hard to fabricate experimentally. The typical dynamical times are in the magnitude of nanosecond and thus few measurement tools can be applied in the system. As an alternative, computer simulation can effectively and has been an important and useful method in this field.
Based on lattice Monte Carlo simulations with the bond-fluctuation algorithm, we have systematically explored the characteristic dynamic behaviors of a free chain, a wall-grafted chain, and a confined chain in slit, square tube, and cubic pore confinements respectively. The main achievements and original contributions of this thesis can be summarized as follows:
(1) The scaling behavior of the mean first-passage times of the end-to-end looping associated with two reactive terminal ends and the intrachain looping associated with a terminal end and an interior monomer for a free chain and a wall-grafted chain has been studied. The end-to-end looping time and the kinetic relaxation time of the end-to-end vector for a free self-avoiding chain are in full agreement with the Rouse dynamic behavior. The simulation results of the intrachain looping collapse into a universal scaling behavior and display a maximum for different chain lengths. By testing the phantom chain, we found that the peak was not caused by the excluded-volume effect. Following the derivation of the normal modes for a Gaussian chain, we calculated the relaxation time of the end-to-interior vector, which displayed a weak maximum at nearly the same location as the looping time. Therefore, it is the internal short-time dynamic modes complicating the situation and leading to the maximum. For the wall-grafted chain, due to the confinement of the grafting point and the depletion effect of the hard wall, the characteristic time of the end-to-end looping deviated from Rouse dynamic behavior. Furthermore, just because of that, the symmetry of the two terminal ends of a polymer chain was destroyed, and thus the looping processes for the grafting terminal end and the free terminal end displayed distinct scaling behavior. For the former, the maximum caused by the complicated internal dynamic modes still existed and the numerical value was one order magnitude larger than that of a free chain. While the peak disappeared for the latter and the looping time displayed a monotonic increase.
(2) We have further observed the typical dynamic processes associated with three characteristic times: rotation time, diffusion time and the looping time of a self-avoiding polymer in three types of confinement: slit, square tube and cubic pore, and have discussed these three time scales in light of scaling theories. Special attention has been paid to the parameter regime where the characteristic confinement dimension is smaller than the radius of gyration of the unconfined polymer. We got a series of the scaling behavior of these three times, and in particular, for the strong tube confinement, the looping time and the rotation time displayed an exponential scaling law. Comparing the looping times under three different confinement dimensions, we found that the proper confinement lead to the faster looping dynamics, which was in agreement with the previous observations: a faster intrachain looping in the sphere pore and a faster protein folding in chaperonin and sphere. What's more, the looping time decreased with the confinement dimensions, which reflected a faster looping dynamics and proved the conclusion in another way that confinement lead to faster dynamics.
(3) We also examined the thermodynamics of the polymer adsorption on a periodic potential surface and a periodic channel-structured surface. Two processes were detected: the polymer adsorption from the free space to the periodic potential surface and the localization from two adsorbing strips to one. The former corresponds to the sharp transitions of some thermodynamic parameters such as specific heat and the chain dimensions, yet it is not a first-order phase transition. From the simulation results, however, no phase transition behavior has been observed for the localization process.
Upon basically finishing the simulations of this thesis, the author also tried to be trained experimentally and thus performed preparation of a sustained release carrier. The two contributions in the experiments are summarized as follows. (1) Microgel preparation conditions have been improved. Injectability is one of the key properties which determine whether the novel controlled release system could be accepted by the patients and the doctors. By the improvement of the traditional fabrication and post-fabrication techniques, we got the injectable microgel with small size. In addition, as to the redispersion problem of the vacuum-dried microgel, we synthesized a series of macromers with different block lengths of the lactide acid and studied the redispersion property of the microparticles fabricated from these macromers to get the most suitable one. (2) We have experimentally explored the activity loss of the released proteins from the microgel developed in our group. The potential factors have been studied and the real reason has been found finally. These investigations have laid a solid foundation for the further in-vitro and in-vivo experiments of this novel controlled release system.
本文基于键长涨落格子模型的蒙特卡罗模拟,系统地研究了自由链、半维数限制的接枝链、一维受限的狭缝链、二维受限的管道链及三维受限的立方微腔链的特征动力学行为。其主要创新性工作可以分为以下几个部分:
(一)系统地研究了自由链和接枝链的末端环化和链内环化的平均初次接触时间的标度行为。运用已知动力学理论,我们对自由链的末端环化和链内环化行为进行了解释。而对于接枝链,我们发现由于硬墙的存在,末端环化的特征时间标度行为发生了改变,而且由于链两端的对称性遭到了破坏,接枝端基和自由端基参与的链内环化过程出现了截然不同的标度行为。
(二)系统比较了一维、二维、三维受限空间中高分子链的三种动力学特征时间的标度关系。探讨了狭缝、管道以及立方微腔中受限高分子链的三个典型动力学过程的特征时间:环化时间、旋转松弛时间和扩散时间,得到了强受限条件下一系列的标度行为,特别地,在管道强受限下,我们发现了环化时间和旋转松弛时间的指数标度行为。通过比较不同受限维数下的环化时间,我们发现三种受限情形都导致了更快的环化行为,该现象同以前球形微腔中更快的链内环化、分子伴侣笼和球形微腔中蛋白质折叠更快的现象一致;而且,随着受限维数的增加,环化时间减小,反映了更快的链内环化,从侧面应证了受限导致更快的动力学这一结论。
(三)考察了高分子链在图案化表面的吸附行为。模拟了一维周期性势能表面上自避行走链吸附的热力学行为,着重研究了链从三维空间向周期性势能平面吸附和链从横跨多个吸附条带到局域化在单个吸附条带上这两个过程。前一个过程对应着比热峰和链尺寸等热力学参量的突变,然而并非一级相变过程;而后者是个非常平缓的过程,所考察的几个参量表明该过程不存在相变行为。
在博士论文的最后阶段,本人主动要求从事实验工作以得到更全面的训练,并得到了导师的支持,从事了一种旨在作为蛋白质药物缓释载体的水凝胶微粒的研究。在实验方面的主要贡献为:(1)改进了微凝胶的制备技术。可注射性是关系到缓释体系是否为医生和病人接受的重要性质,通过改进传统的微球制备方法和后处理工艺,我们得到了粒径符合注射性的微球。此外,针对微球再分散问题,我们合成了具有不同长度的嵌段丙交酯的大单体,对其所制备得到的微球再分散性能进行了考察,找到了适合制备可注射微凝胶的大单体。(2)改进了药物包裹和体外释放的操作。我们探索了长期困扰课题组的蛋白质后包裹失活问题,考察了各种潜在因素,最终找到了失活根源。这些工作为今后该化学凝胶微球缓释体系在蛋白质药物载体方面更多的体外实验打下了基础,使得组内开发的温敏型化学凝胶朝向应用接近了一步。
Polymer dynamics is one of the core problems in polymer physics. Due to recent studies of proteins and DNAs in the confining space, the dynamics of a confined polymer chain has become a hot topic. Though the physical model of a confined polymer chain is relatively simple, the theoretical treatment is extremely complicated and the mathematical approximations must be applied in the calculations. On the other hand, the confinement structure with the nanometer spatial scale is hard to fabricate experimentally. The typical dynamical times are in the magnitude of nanosecond and thus few measurement tools can be applied in the system. As an alternative, computer simulation can effectively and has been an important and useful method in this field.
Based on lattice Monte Carlo simulations with the bond-fluctuation algorithm, we have systematically explored the characteristic dynamic behaviors of a free chain, a wall-grafted chain, and a confined chain in slit, square tube, and cubic pore confinements respectively. The main achievements and original contributions of this thesis can be summarized as follows:
(1) The scaling behavior of the mean first-passage times of the end-to-end looping associated with two reactive terminal ends and the intrachain looping associated with a terminal end and an interior monomer for a free chain and a wall-grafted chain has been studied. The end-to-end looping time and the kinetic relaxation time of the end-to-end vector for a free self-avoiding chain are in full agreement with the Rouse dynamic behavior. The simulation results of the intrachain looping collapse into a universal scaling behavior and display a maximum for different chain lengths. By testing the phantom chain, we found that the peak was not caused by the excluded-volume effect. Following the derivation of the normal modes for a Gaussian chain, we calculated the relaxation time of the end-to-interior vector, which displayed a weak maximum at nearly the same location as the looping time. Therefore, it is the internal short-time dynamic modes complicating the situation and leading to the maximum. For the wall-grafted chain, due to the confinement of the grafting point and the depletion effect of the hard wall, the characteristic time of the end-to-end looping deviated from Rouse dynamic behavior. Furthermore, just because of that, the symmetry of the two terminal ends of a polymer chain was destroyed, and thus the looping processes for the grafting terminal end and the free terminal end displayed distinct scaling behavior. For the former, the maximum caused by the complicated internal dynamic modes still existed and the numerical value was one order magnitude larger than that of a free chain. While the peak disappeared for the latter and the looping time displayed a monotonic increase.
(2) We have further observed the typical dynamic processes associated with three characteristic times: rotation time, diffusion time and the looping time of a self-avoiding polymer in three types of confinement: slit, square tube and cubic pore, and have discussed these three time scales in light of scaling theories. Special attention has been paid to the parameter regime where the characteristic confinement dimension is smaller than the radius of gyration of the unconfined polymer. We got a series of the scaling behavior of these three times, and in particular, for the strong tube confinement, the looping time and the rotation time displayed an exponential scaling law. Comparing the looping times under three different confinement dimensions, we found that the proper confinement lead to the faster looping dynamics, which was in agreement with the previous observations: a faster intrachain looping in the sphere pore and a faster protein folding in chaperonin and sphere. What's more, the looping time decreased with the confinement dimensions, which reflected a faster looping dynamics and proved the conclusion in another way that confinement lead to faster dynamics.
(3) We also examined the thermodynamics of the polymer adsorption on a periodic potential surface and a periodic channel-structured surface. Two processes were detected: the polymer adsorption from the free space to the periodic potential surface and the localization from two adsorbing strips to one. The former corresponds to the sharp transitions of some thermodynamic parameters such as specific heat and the chain dimensions, yet it is not a first-order phase transition. From the simulation results, however, no phase transition behavior has been observed for the localization process.
Upon basically finishing the simulations of this thesis, the author also tried to be trained experimentally and thus performed preparation of a sustained release carrier. The two contributions in the experiments are summarized as follows. (1) Microgel preparation conditions have been improved. Injectability is one of the key properties which determine whether the novel controlled release system could be accepted by the patients and the doctors. By the improvement of the traditional fabrication and post-fabrication techniques, we got the injectable microgel with small size. In addition, as to the redispersion problem of the vacuum-dried microgel, we synthesized a series of macromers with different block lengths of the lactide acid and studied the redispersion property of the microparticles fabricated from these macromers to get the most suitable one. (2) We have experimentally explored the activity loss of the released proteins from the microgel developed in our group. The potential factors have been studied and the real reason has been found finally. These investigations have laid a solid foundation for the further in-vitro and in-vivo experiments of this novel controlled release system.
引文
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