Computational Modeling of Vesicle-Mediated Cell Transport
Final Report Abstract
The present project deals with the numerical simulation of the viral uptake into a cell. This phenomenon is concerned with the diffusion of receptors over the cells surface. However, the process is significantly influenced by the cells interior actin filament structure and plays an important role when conforming its local shape in the contact area to the virus ones. The concepts developed within the project make it possible to obtain information about the viral uptake in various scenarios. By fitting the virus specific quantities, such as receptor density and radius, the uptake can be investigated throughout the whole process, which is not otherwise accessible when using current experimental methods. Thus, the required process time and its limiting behavior can be investigated. In particular, the models developed in the project deal with specific tasks which complement each other in the overall uptake process. Therefore, the formulations are chosen in such a way, that they provide distinct interfaces to incorporate the information of other models and additional phenomena. The models developed in the project combine several approaches. Firstly, the mechanical response of the actin filament network utilize a dimensionless force in order to express the derivatives of a potential, which is not explicitly formulated. The multiscale FEM is utilized as an important simulation technique to describe the fine network structure. Numerical results indicate, that both the filament density as well as their direction contribute significantly to the effective mechanical behavior. Furthermore, they indicate that the filaments total length acts as a threshold for the deformation which has to be exceeded in order to activate their influence on the mechanical response. The multiscale FEM has also proved to be an effective method to simulate the influence of actin filament network alterations onto the diffusion properties and the transport time of vesicles inside the cell. The numerical simulations, in this case predicted a 35% increase in transport time due to a uniformly distributed four-fold increase of the total filament amount. Moreover, a hypothetically reduced expression of filament cross-linking proteins led to sparser filament networks and, thus, a speed up of the vesicle transport. Secondly, the boundary value problem yields a formulation for the tracking of the adhesion front purely depending on physical quantities. The framework incorporates two boundary conditions in order to solve the diffusion equation. The energetic description of the processes involved in the front movement provides an efficient interface to add additional phenomena by enhancing the corresponding energy term. Even though, the numerical studies were focused on the vesicle-mediated cell transport, the developed concepts and achieved experience are expected to be useful for the simulation of alternative intracellular diffusion processes which are necessary to ensure the optimal functionality of eukaryotic cells. The models applied show some important advantages: On one hand, they investigate the state of the underlying process throughout the whole uptake, for a variety of parameters typical for several viruses. On the other hand, embedded in the finite element method, they offer time efficient solutions especially compared to purely stochastic ones. The results achieved within the project confirm the great potential of numerical approaches for studying the cell activity, however, they also identify the coupling to the experimental investigations for the purpose of evaluation of process parameters as the major challenge for the future work.
Publications
- (2018). Multiscale FEM simulations of cross-linked actin network embedded in cytosol with the focus on the filament orientation. Int. J. Numer. Method. Biomed. Eng., 34, 7, e2993
S. Klinge, S. Aygün, R. P. Gilbert and G. A. Holzapfel
(See online at https://doi.org/10.1002/cnm.2993) - 2018 Viscoelasticity of Cross-Linked Actin Network Embedded in Cytosol, PAMM, 18, 1, e201800151
T. Wiegold, S. Klinge, S. Aygün, R. P. Gilbert, G. A. Holzapfel
(See online at https://doi.org/10.1002/pamm.201800151) - 2019 Computational modeling of adhesive contact between a virus and a cell during receptor driven endocytosis, PAMM, 19, 1, e201900161
T. Wiegold, S. Klinge, R. P. Gilbert and G. A. Holzapfel
(See online at https://doi.org/10.1002/pamm.201900161) - 2019 Numerical simulation of the viral entry into a cell by receptor driven endocytosis, Proceedings of 8th GACM Colloquium on Computational Mechanics, 401-404
T. Wiegold, S. Klinge, R. P. Gilbert and G. A. Holzapfel
- 2020 On the modeling of cell components, PAMM, 20, 1, e202000129
S. Klinge, T. Wiegold, S. Aygün, R. P. Gilbert and G. A. Holzapfel
(See online at https://doi.org/10.1002/pamm.202000129) - (2021). Numerical analysis of the impact of cytoskeletal actin filament density alterations onto the diffusive vesicle-mediated cell transport. PLoS Comput. Biol., 17(5)
D. Haspinger, S. Klinge and G. A. Holzapfel
(See online at https://doi.org/10.1371/journal.pcbi.1008784) - (2021). Numerical simulation of the viral entry into a cell driven by the receptor diffusion. Comput. Math. Appl., 84, 224-243
T. Wiegold, S. Klinge, R. P. Gilbert and G. A. Holzapfel
(See online at https://doi.org/10.1016/j.camwa.2020.12.012)
