David Outland (1, 3), Daniel Seeler (2,3), Nastasja Grdseloff (2), Claudia Jasmin Rödel (2), Charlotte Kloft (4), Salim Abdelilah-Seyfried (2), Wilhelm Huisinga (1, 2)
(1) Institute of Mathematics, University of Potsdam, Germany, (2) Institute of Biochemistry and Biology, University of Potsdam, Germany, (3) Graduate Research Training Program PharMetrX: Pharmacometrics & Computational Disease Modelling, Berlin/Potsdam, Germany, (4) Clinical Pharmacy & Biochemistry, Freie Universität Berlin, Germany
Objectives: The vascular system is prone to many common human diseases such as stroke, cardiac malfunction and arrest, thrombosis, hypertension as well as rarer diseases such as cerebral cavernous malformations. Beyond potentially perturbed intracellular processes, a central factor in these diseases is blood flow with the forces it acts on the vessel wall. The endothelium can sense these forces and trigger biochemical pathways that can lead to changes in endothelial cell morphology and in vessel shape [1, 2, 3]. A detailed understanding of mechanical aspects of the vascular regulation system however is currently lacking. Our aim is to gain a deeper insight into the underlying processes. In approaching this problem, we focus on endothelial cells as the interface between mechanical and biochemical processes and use the zebrafish embryo as a model organism. We describe endothelial cells using a vertex model based ansatz. Two-dimensional vertex models have been used in a biological context for example to describe cellular dynamics in apical surfaces of epithelial tissues [4, 5]. We deem endothelial cells as a special squamous type of epithelial cells suited for the description with models based on this methodology.
Methods: We obtained experimental data through confocal microscopy of dorsal aorta segments of zebrafish embryos. As zebrafish embryos in early developmental stages are transparent [6], we obtained 3D endothelial cell junctional data using live imaging [7]. This allowed to resolve different cell morphologies occurring during development of the embryo [7]. We reconstructed smooth vessel geometries and individual cell shapes from this data. We conceptualized a mechanical model of endothelial cell morphology in a community of cells which through its dynamic character accounts for shape changes of endothelial cells in response to mechanical stimuli. We base the model on the methodology of vertex models. Cells are considered as connected polygons, the shapes of which are determined by the positions and connectivity of their vertices [4, 5].
Results: Based on the vertex model approach we conceptualized a model explicitly considering cell-cell interfaces and their dynamics. Cell junctions are modeled as connected vertices. Here, triple-points at which three cells meet through their connectivity define the adjacency relations of the cells. Cell interfaces consist of cell junctions between two triple-points. Cytoskeletal elements such as stress fibers which are suspected to play a central role in force transduction [8] are modeled as intracellular connections of the vertices. The morphology of the cells in the tissue is mainly determined by the positions of the vertices and triple-points, which in turn are determined by the balance of forces from the cytoskeletal elements which can be modeled as spring-like elastic structures [9] and effective forces caused by the viscous drag of the blood flow. The sensing of mechanical forces from blood flow by the endothelial cells and their consequential active change in morphology is considered by a dependence of the orientation and stiffness of the modelled cytoskeletal elements on the viscous drag experienced locally by the corresponding endothelial cell.
Conclusions: This ansatz is a first step towards better understanding mechanical aspects of the vascular regulation system. In the long term, we plan to implement the model and identify physiological and pathological states by calibrating model-based simulations with experimental data. Assessing in silico whether perturbations of particular parameters cause the system to evolve from a pathological into a physiological state would then help indicate whether molecules associated with the corresponding parameters would be suited as potential drug targets.
References:
[1] Roux, Etienne, et al. “Fluid shear stress sensing by the endothelial layer.” Frontiers in Physiology 11 (2020): 861.
[2] Sugden, Wade W., et al. “Endoglin controls blood vessel diameter through endothelial cell shape changes in response to haemodynamic cues.” Nature cell biology 19.6 (2017): 653-665.
[3] Baeyens, Nicolas, and Martin A. Schwartz. “Biomechanics of vascular mechanosensation and remodeling.” Molecular biology of the cell 27.1 (2016): 7-11.
[4] Fletcher, Alexander G., et al. “Vertex models of epithelial morphogenesis.” Biophysical journal 106.11 (2014): 2291-2304.
[5] Alt, Silvanus, Poulami Ganguly, and Guillaume Salbreux. “Vertex models: from cell mechanics to tissue morphogenesis.” Philosophical Transactions of the Royal Society B: Biological Sciences 372.1720 (2017): 20150520.
[6] Kimmel, Charles B., et al. “Stages of embryonic development of the zebrafish.” Developmental dynamics 203.3 (1995): 253-310.
[7] Seeler, Daniel, et al. “Novel mathematical morphology model identifies dorsal-ventral asymmetry of endothelial cell morphology in dorsal aorta of wild-type and Endoglin-deficient zebrafish embryos.” bioRxiv (2024): 2024-02.
[8] Civelekoglu-Scholey, G., et al. “Model of coupled transient changes of Rac, Rho, adhesions and stress fibers alignment in endothelial cells responding to shear stress.” Journal of theoretical biology 232.4 (2005): 569-585.
[9] Pakravan, H. A., M. S. Saidi, and B. Firoozabadi. “A mechanical model for morphological response of endothelial cells under combined wall shear stress and cyclic stretch loadings.” Biomechanics and modeling in mechanobiology 15 (2016): 1229-1243.
Reference: PAGE 32 (2024) Abstr 11156 [www.page-meeting.org/?abstract=11156]
Poster: Drug/Disease Modelling - Other Topics