Mechanical Properties and DNA Organization of Viruses and Bacteria
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 a...
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|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
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
This work aims to contribute to the understanding of viral mechanics
by a theoretical and numerical interpretation of the experimental
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
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.