Towards a mechanistic basis of a dynamical vertex model of vascular endothelial cell morphology changes in response to wall shear stress
David Outland1,3, Daniel Seeler2,3, Nastasja Grdseloff2, Claudia Jasmin Rödel2, Charlotte Kloft3,4, Salim Abdelilah-Seyfried2, Wilhelm Huisinga1,2,3
1Institute of Mathematics, University of Potsdam, 2Institute of Biochemistry and Biology, University of Potsdam, 3Graduate Research Training Program PharMetrX: Pharmacometrics & Computational Disease Modelling, 4Clinical Pharmacy & Biochemistry, Institute of Pharmacy, Freie Universität Berlin
Objectives: The vascular system is prone to many common human diseases such as stroke, 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, which exerts forces on vessel walls. Among these forces the endothelium can sense wall shear stress (WSS) and trigger biochemical pathways that can lead to changes in endothelial cell (EC) morphology and in vessel shape [1, 2, 3]. Currently, a detailed understanding of biomechanical aspects of the vascular regulation system controlling the interaction of vessel shape, blood flow and EC morphology is lacking. Hence, our aim is to gain a deeper insight into the underlying processes focusing on the mechanisms driving EC morphology changes in response to WSS caused by blood flow. We use the zebrafish embryo as a model organism, which is highly amenable to functional molecular studies and modulating blood flow parameters. We seek to leverage existing knowledge on the cellular and subcellular WSS-response of ECs in a dynamic vertex model-based ansatz. Vertex models have been used in a biological context for example to describe cellular dynamics in apical surfaces of epithelial tissues [4, 5]. Methods: Based on vessel- and individual cell shapes we previously reconstructed from EC junctional data in zebrafish embryos [6], we performed a detailed literature review on the response of ECs to WSS reported from in vitro experiments [7, 8, 9]. We focused on the time evolution of the reaction of key molecular entities and the resulting cell morphology changes. We used this knowledge to identify key parts of a fundamental vertex model [10], which are suitable for an extension to WSS dependence. Within the model class 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: We compiled observations extracted from literature to obtain a timeline of coherent processes occurring during exposure of ECs to WSS. In static conditions, cytoskeletal actin strongly localizes to the cortex, but this localization becomes continually reduced during WSS exposure while central actin stress fibers are more strongly expressed [7, 8, 9]. Actin stress fibers are attached to focal adhesions at their ends and polymerize while reorienting in WSS direction [7]. This causes protrusions of the plasma membrane and elongated cell shapes [7]. Adherens junctions detach from the actin cortex and transiently cluster in plaques, into which the ends of actin stress fibers become inserted [7, 8]. Consequently, both adherens plaques and focal adhesions adopt a more elongated shape oriented in WSS direction [7, 8]. We were able to partially link these results to a fundamental vertex model [10] by identifying one of its components as a potential gateway for incorporating the dependence of the actin cortex on WSS. We summarized our findings in a sequence of biological sketches illustrating the main changes over time. Conclusions: We produced a qualitative model of interacting biological processes. It can form a sound basis for the development of a quantitative mechanistic mathematical model capturing the dynamic changes of EC WSS response and its underlying processes. Using such a model to assess in silico whether perturbations of particular parameters cause the system to evolve from a pathological into a physiological state can help indicate whether proteins and molecules associated with the corresponding parameters would be suited as potential drug targets.
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