摘要
生物膜结构不仅是细胞结构的组织形式，也是生命活动的主要结构基础。许多生命过程，如能量转换、物质运输、信息识别与传递、细胞发育与分化，以及神经传导、激素作用等都与生物膜有密切关系。然而，由于真实的细胞膜十分复杂，人们必须寻找合适的模型。幸运的是，理论和实验均表明由两亲性分子所形成的囊泡(vesicle)是细胞膜最为简单有效的模型。因此，本论文围绕生物膜开展了四个方面的研究工作：锚泊有聚合物链的囊泡；刚棒／柔性高分子锚泊流体膜；多层囊泡的复杂形状；耗散粒子动力学对多组分膜相分离的动力学研究。
第一部分：锚泊聚合物链的囊泡。生物膜通常被蛋白质、胆固醇、糖类等生物大分子所“修饰”。作为生物膜的简化模型，聚合物链锚泊囊泡的研究具有极其重要的生物学意义。我们将多组分聚合物体系的自洽平均场理论和囊泡的膜弯曲弹性理论拓展至聚合物链锚泊囊泡体系。我们引入聚合物链不能穿透囊泡膜的限制条件，考虑了高分子链段和囊泡膜的相互作用，以及高分子链段和溶剂的相互作用，重新推导出新的膜平衡的形状方程。聚合物锚泊囊泡和单纯囊泡体系的主要差别是，由于囊泡膜对聚合物链的几何空间限制，聚合物链段对囊泡表面施加不均匀的熵压，诱发了聚合物锚泊囊泡的不对称性。当高分子链段和囊泡表面存在相互作用时，聚合物链不仅对囊泡表面施加外压，还改变了囊泡的表面张力。而压力和表面张力的改变大小和相互作用参数、聚合物链段的浓度分布息息相关。当囊泡膜和高分子链段的相互作用从排斥变为强吸附时，聚合物的浓度分布也实现从“mushroom”至“pancake”的转变。溶剂对囊泡形状的影响不显含在我们推导的形变方程中，而是通过改变聚合物链段的浓度分布来实现囊泡形状的改变。聚合物链对囊泡的影响随着囊泡的弯曲刚性的降低而变得显著。锚泊聚合物链的链长对囊泡的形状的影响很小，而在高分子链段和囊泡膜存在相互作用时，锚泊聚合物链链长的变化则对囊泡的形状有着显著的影响。这是因为囊泡膜表面高分子链段的浓度分布受锚泊高分子链链长、膜和链段相互作用强度、锚泊高分子链数目等参数的共同影响。不同于聚合物锚泊流体膜体系，聚合物锚泊囊泡形状的变化要考虑囊泡的全局因素，因此囊泡形状的变化非常复杂，难以用单纯囊泡的对称性给以描述。我们利用新拓展的理论研究了聚合物锚泊囊泡形状的变化。此外，我们的理论还可以拓展到多组分、不同拓扑结构的聚合物链锚泊囊泡体系，从而为将来研究细胞的生命活动提供一种方法。
第二部分：刚棒／柔性高分子锚泊的流体膜。我们依然运用高分子的自洽场理论和膜弹性理论结合的方法，研究柔性链或刚棒锚泊流体膜的复合体系。由于膜的不可穿透性，减少了高分子链的活动空间，为了使高分子获得更高的构象熵，膜发生弯曲远离高分子。在锚泊点附近，柔性链和刚棒浓度分布不同，导致膜在锚泊点附近变形的趋势也不同。尤为重要的是，由于刚棒的取向和膜曲率的连续性之间的矛盾，导致刚棒和膜之间存在有限距离。膜和高分子之间相互吸附作用会影响高分子的行为：对于柔性链，吸附强度从弱到强，其构象分布发生从“mushroom”至“pancake”的转变；对于刚棒的分布则发生“扇形”至“锥形”的转变，且“扇形”的半径和刚棒的长度保持一致。如果膜和柔性链之间没有相互作用时，链长的增加不会对膜对形状产生明显的作用，但当膜和柔性链之间有吸附作用时，链长的增大会加剧膜的形变。而对于刚棒，甚至在膜和刚棒没有任何相互作用时，由于其在膜上的覆盖面积和链长呈正比，随着链长的增加，增大了链的末端距，刚棒在膜施加熵压的接触点增大了，导致膜会随着链长的增加而进一步远离刚棒。此外，膜本身的弯曲刚性和表面张力也会影响膜的形变。
第三部分：多膜囊泡的复杂形状。一些细胞器，如线粒体等，均具有双层膜的构造。对于含有双层膜构造的细胞器，细胞器外、双层膜间区和双层膜内各区的压力差别将导致非常复杂的形态。为了对这类细胞器的形态提供理论模型，我们采用离散空间变分的方法研究了多层囊泡的复杂形状问题，即单层囊泡置于可变形的受限环境下的形状。我们主要讨论了双层囊泡之间的面积比、弯曲刚性模量、各部分几何空间压力比、以及静电相互作用对多层囊泡的复杂形状的影响。当内膜的面积大于外膜面积时，内膜主要以皱褶的形式存在于外膜空间；当内膜面积小于外膜面积时，每层膜的形状和其所处空间的势差(压力)有关，如果膜所包围的空间的压力大于此膜外部空间的压力，膜的形状大部分以圆的形式存在。外膜和内膜的弯曲刚性模量在各部分空间压力不同时，其对多层囊泡形状的影响也不同。不均匀的长程静电相互作用的存在可使内膜形成的管状皱褶均匀分布在外膜所包围的几何空间。双层囊泡根据各部分自由能的贡献的大小调整外膜和内膜形状，以及每层囊泡所包围空间体积。这些结果将对于理解诸如线粒体之类细胞器的形态具有积极的意义。
第四部分：耗散粒子动力学研究多组分膜的相分离过程。在适当的温度或其他条件下，两亲性脂类分子通常不均匀地分布在双分子层生物膜中，膜的侧向上存在着复杂的微区，这些微区在膜内移动，与细胞中的蛋白质输送及细胞内信息传递等功能的实现有密切关系。我们通过介观的模拟方法—耗散粒子动力学(DPD)的方法研究了单组分聚集体的形成过程和条件，结果表明可得到各种聚集体，如胶束、柱状、球形的囊泡；用同样的方法，我们还研究了多组分膜相分离过程中，聚集体会表现出两亲性分子的扩散、微区之间的合并以及囊泡形状的变化(出芽和分裂)等行为。本论文中，采用耗散粒子动力学方法对多组分膜体系的形变和相分离的研究只是一个初步的探索，为进一步深入研究囊泡在受限环境下的流动行为、囊泡和基板相互作用以及囊泡和囊泡相互作用等提供有益的启示。
Biological membrane is not only the basic unit of the cell structure, but also the structural foundation to provide the life activity. Biological membrane is in close related with many life process, such as signal recognisee and transduction, cell growth and differentiation, energy transformation, substance transportation etc.. Because of the complexity of the real biological membrane, the appropriate model is developed. Fortunately, vesicle which is consisted of am-phiphilic is the simple and effective model of the biological membrane. Then, in this thesis, we have studies four parts of the project surrounded in the biological membrane: polymer anchored vesicle, rigid rod/flexible chain anchored the infinite membrane, the complicated shapes of the membrane confined in the outer membrane, phase separation dynamics study of two-component membrane.
The first part predicates shapes of polymer anchored vesicles. In biological systems, lipid bilayers or membrane are often "decorated" by a large number of macromolecules, such as protein, cytoskeleton and glycocalix. As the simplified model of such biological membrane, it is important for biology to study the shapes of polymer anchored vesicles. Shape transformations have been extensively predicted in such fluid vesicles/polymer compound system by the method combined self-consistent-field theory (SCFT) for the polymer with Helfrich curvature energy for the vesicle. With the impenetrability of the membrane to the polymer, we obtain the new shape equation of the membrane, taking account of the interaction potential of membrane/polymer and polymer/solvents. The main difference between the ordinary shape equation and polymer anchored vesicle's is that the surface of the vesicle is exerted the inhomogeneous entropic pressure because of the confined available space. The asymmetric shape of polymer anchored vesicle is induced because of the inhomogeneous entropic pressure. With the interaction potential between the membrane and the chain segments, the anchored segments changed not only the exerted pressure, but also the surface tension of the vesicle. However, the extents of the alterative pressure and surface tension are in close related with the interaction parameter between the polymer and the vesicle, the polymer segments distribution on the surface of the vesicle. In repulsive or weak adsorption between the membrane and segments, the anchored polymer forms "mushroom", in which the configuration entropy dominates over the interactive energy. However, when the interaction play a dominated role in the state of strong adsorption, polymer prone to form the "pancake" to broaden much more surface contacts with the membrane, which seriously enhance the inhomogeneous spatial distribution of the polymer on the surface of the vesicle. The term concerned with the interaction between the polymer and
solvents is not explicitly appearing in the shape equation. However, the shape of the vesicle is only influenced with the help of the polymer distribution in the solvent molecules. Since the segment concentrations near the membrane will be not increased in relation to the larger size of chain length anchoring, as well as in the good solvent, shape transformations have much less dependence on chain length of the anchored polymer and good solvent in such systems. At the weak adsorption, the effect of chain length is to some extent augmented because the chain segments' densities have been seriously increased adjacent the membrane surface, which can augment the exerted entropic pressure and stretched the tensile stress on the membrane. Also, larger bending rigidity of the membrane can strongly resist fluctuation arising from both the pressure and tensile stress, that is, suppressing the degree of shape transformation irrespective of short or long-ranged interaction. The shape of the polymer anchored vesicle is transformed based on the global factors, and can not be described by the simple symmetric characteristics. Moreover, extension of this method to more complicated systems, such as chain stiffness, different chain architectures, multi-components and chain systems, is straightforward, which provide one method to study the life science of cell.
The second part is the infinite membrane anchored by rigid rod/flexible chain. We investigate the shape deformation of such systems, which the density of rigid rod/flexible chains is calculated with the self-consistent field theory (SCFT) and the shape of the membrane is predicted by the Helfrich membrane elasticity theory. It is found that the membrane bends away from polymer, so that the polymer decrease the entropic reduction due to the restriction of the available space. Close to the anchoring position, the polymer distribution is different between the rod and flexible chain, resulting in different shape behaviors of the membrane. Importantly, an evident gap is found between the membrane and the rigid rod because the membrane's curvature has to be continuous. Also, the interaction between the membrane and the polymer will influence the shapes of the membrane. When the interaction between the membrane and the polymer increase from the weak to the strong adsorption, the distribution of the flexible changes from "mushroom" to "pancake", while that of the rigid rod change from "fan" to "cone" and the radius of the "fan" is equal to the chain length of the rod. Without the interaction between the membrane and the flexible chain, the shape of the membrane is almost independent of the chain length; with the interaction, the shape transformation of the membrane is seriously augmented as the chain length increases. Even without the interaction, the shape of the membrane will much bend away from the membrane as the rod length increase, because the end-to-end distance of the rod and the coverage area of the membrane are in proportion to the rod length. Moreover, the bending rigidity and surface tension of the membrane are also one of the factors
for the shape transformation of the membrane.
The third part studies the shape problem of the double layer vesicle with the discrete-spatial variation method, that is, the complicated shape of the inner vesicle confined in the soft and outer environment. We focus on the factors of the complicated shape: the area ratio between the outer and inner vesicle, the bending rigidity parameter between the outer and inner vesicle, the pressure of different space and the electrostatic interaction among the inner vesicle. When the area of the inner vesicle is larger than that of the outer vesicle, the inner is prone to form the cristae in the confined space of the outer vesicle. When the area of the inner membrane is less than that of the outer vesicle, the shapes of the divided vesicle concern with the pressure of different space: the shape of the vesicle is circle if the pressure of the outer space is much less than that of the inner space for each vesicle. The bending rigidity of the outer and inner vesicle impacts the shapes of the double layer vesicle according to the different space pressure. Inhomogeneous electrostatic interaction among the inner vesicle can cause the cristae uniformly distributed in the confined space. The double vesicle adjusts its complicated shape to minimize its whole energy. These results would provide the significant basis to understand the shapes of the organelle, such as mitochondria.
The last part studies phase separation dynamics of two-component membrane by means of Dissipative particle dynamics. In biological membrane, amphiphilic is usually inhomogeneous distributed in the bilayers under certain experiment condition. Many complicated domains, which can laterally diffuse on the surface of the membrane, are extensively found on the surface of the membrane. All these phenomena are related to the cell function, such as protein diffusion. We use the mesoscopic model called dissipative particle dynamics to study the spontaneous aggregation formation of amphiphilic molecules in aqueous solution, for example micelles, rod shapes and vesicles. Also, we study the phase separation dynamics of two-component aggregations. Under appropriate conditions, typical shape transformations of aggregations, such as budding, fission, domain diffusion, are observed. We also wish to develop this method to simulate more complicated systems, such as the floating behavior of the vesicle in the confined tube, the interaction between the cell and the base plane, the interaction between the cell and the cell.
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