Dokument

Summary:
Viruses are an important subject to biological research. In particular their astonishing ability to replicate without proper metabolic system and to assemble complex shells arrests great scientific interest. This interest has even increased in the past years due to possible nano-technolocgical applications. The outstanding robustness of viral capsids aginst external forces and internal pressure has inspired a recent series of SFM experiments. In these studies the mechanical limits of capsids are quantitatively explored. Thereby they shed light on the nature of protein bindings within the shell and give insight into the process of viral self-assembly. This work aims to contribute to the understanding of viral mechanics by a theoretical and numerical interpretation of the experimental results. The work starts with a discussion of the foundation of viral mechanics. Here, we focus on the inner structure of capsids. Capsids consist of a small number of large protein clusters, so called capsomers. This viral shells have a discrete structure. In particular the presence of topological defects has a strong influence on the elasticity of capsids. In the first chapter we derive exact shape equations for arbitrarily shaped, continuous shells subjected to small deformations. In particular they allow the analytical treatment of icosahedral shells. We restrict their evaluation to the analytically tractable case of spherical shells. We obtain results for the reversible elastic regime as well as for the rupture behavior. The response of spherical shells to large deformations is qualitatively investigated in a scaling analysis. The second and third chapter are concerned with the numerical analysis of capsid stability. There, we extend an approach developed for the investigation of vesicles. First, we focus on empty capsids. In our simulations, we systematically vary the elastic moduli and geometry of the capsids and probe their mechanical response to external deformations. This allows the systematic study of rupture of mechanical shells. The simulations provide insights into the geometry-dependence of viral stability and allow us to relate the observed macroscopic elasticity to the strength of capsomer bindings and the underlying capsid design. By comparing our numerical results with experimental data we are able to give reasonable estimates for the bulk elastic moduli. In our simulations we can even access features which are not observable in experiments, such as e.g., the local strain. We determine the distribution of strain and rupture forces across capsid surfaces. By comparing with ensemble rupture measurements these rupture maps offer the possibility to draw conclusions about the spatial variation of protein binding strength. The sta bility of filled capsids is discussed in the fourth chapter. The DNA is taken into account by an appropriate pressure contribution to the total energy of the capsid. This allows us to simulate nano-indentation experiments on loaded phage heads with high internal pressure. In this context, we will also discuss the influence of anisotropic packing. We extend our numerical scheme to study the stability under extreme internal pressure. These results can be related to osmotic shock experiments in which capsids are osmotically swollen. In the fifth chapter we finally study random configurations of the bacterial genome in Monte Carlo simulations. We extend random walk methods known from polymer physics to cope with the geometrical constraints imposed by the bacterial cell. These simulations indicate to which extend active mechanisms are involved in DNA compaction.

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