Pattern formation on self deforming materials is playing an increasingly vital role in the study of many biological processes. An example is the cell cortex, a network of interlinked actin filaments connected to the inside of the cell membrane. The stiffness of these filaments makes the cortex rigid and gives the cortex a strong influence in the shape of the cell. Additionally, molecular turnover and motor proteins allow shape changes necessary for the cell to divide and to adapt to its environment. Due to the incredible number of proteins that make up the cell cortex, simulation of the molecular dynamics for the entire cortex is impossible. However, when considering a larger scale, these dynamics can be approximated, making it possible to model the cortex as an active viscoelastic surface. To implement this, we use the surface equivalent of a Maxwell material, additionally distinguishing between shear and dilational stress. The motor proteins are modelled by an advection diffusion equation on the surface combined with a concentration dependent surface tension. Surrounding the surface is a fluid modelled by the Navier-Stokes equations. We study the formation of patterns both analytically and numerically. In the analytical study the 2-dimensional curved surface is reduced to a flat 2-dimensional surface with periodic boundary conditions
and no surrounding fluid. We then show, that despite the minimal complexity of this model, spatiotemporal patterns can develop on a viscoelastic surface if the relaxation times are different. For the numerical study the Arbitrary Lagrangian Eulerian method (ALE) is applied. The equations for the surface and bulk are solved separately, but this partial method is numerically unstable for dominantly viscous surfaces. With that in mind, we also implemented a monolithic model for viscous surfaces, solving the bulk and surface equations simultaneously. As a special case the influence of a chiral flow field on a sphere is studied. These chiral flows have been observed in biological experiments and are hypothesised to originate from the small scale torques caused
by the helix structure of the actin filaments. We found that a high shear elastic modulus in combination with a chiral force field can induce neck formation. Additionally, for a concentration dependent chiral force field combined with active surface tension and a high dilational elastic modulus, the chiral forces can stabilise a contractile ring. These results provide mechanistic evidence that chiral flows can play a
role during cell division.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:90674 |
| Date | 04 April 2024 |
| Creators | de Kinkelder, Eloy Merlijn |
| Contributors | Aland, Sebastian, Fischer-Friedrich, Elisabeth, Technische Universität Bergakademie Freiberg |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/publishedVersion, doc-type:doctoralThesis, info:eu-repo/semantics/doctoralThesis, doc-type:Text |
| Rights | info:eu-repo/semantics/openAccess |
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