Modeling Membrane Dynamics on the Level of Organelles
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Abstract
Biological membranes are omnipresent in cells, not only enclosing organelles but also
in the form of highly dynamical structures such as tubular protrusions or complex
branched networks. Investigating the dynamics of these membranes can be a
challenging task in both experiments and computer simulations, because of the time
and length scales that need to be accessed. In this work, conformational membrane
changes are investigated by performing computer simulations using a dynamically-
triangulated membrane model, which is based on a continuum description of the
Helfrich Hamiltonian. This description is relatively general and allows to access
larger length and time scales than in typical atomistic or coarse-grained simulations.
In the first part of this thesis, the model is applied to study the formation of
tubular structures from vesicles by pulling with an external force. Our findings
are compared to theoretical approximations and minimal-energy solutions of the
Helfrich Hamiltonian, exploiting the rotational symmetry of the structures. We find
a very good agreement between the shapes found in theory and simulations. We also
simulate the formation and coalescence of several tubes protruding from a vesicle.
In the second part, we focus on the formation, energetics and stability of purely
tubular and branched structures under the action of an external field and different
global constraints. We find that both structures are unstable, when releasing the
external force, which means that in nature other types of stabilization mechanisms
must be present. We can show that when fixing the area to volume ratio of the
structure, which is a natural constraint for closed impermeable membranes, tubes
are metastable, while branches are still unstable. To stabilize these branches, an
additional constraint therefore has to be set. One possibility which we successfully
applied in this thesis is fixing the overall curvature of the system.
These findings show that tubular networks observed in biological cells need to be
stabilized by either anchoring to organelles or filaments, or by controlling the overall
curvature through curvature-inducing proteins or an area difference between the
two monolayers of the lipid bilayer. Computer simulations of biological membranes
and in particular continuum models thus provide a very valuable and useful tool
for interpreting and complementing experimental observations.