Abstract
Mathematical models are increasingly designed to guide experiments in biology, biotechnology, as well as to assist in medical decision making. They are in particular important to understand emergent collective cell behavior. For this purpose, the models, despite still abstractions of reality, need to be quantitative in all aspects relevant for the question of interest. This paper considers as showcase example the regeneration of liver after drug-induced depletion of hepatocytes, in which the surviving and dividing hepatocytes must squeeze in between the blood vessels of a network to refill the emerged lesions. Here, the cells’ response to mechanical stress might significantly impact the regeneration process. We present a 3D high-resolution cell-based model integrating information from measurements in order to obtain a refined and quantitative understanding of the impact of cell-biomechanical effects on the closure of drug-induced lesions in liver. Our model represents each cell individually and is constructed by a discrete, physically scalable network of viscoelastic elements, capable of mimicking realistic cell deformation and supplying information at subcellular scales. The cells have the capability to migrate, grow, and divide, and the nature and parameters of their mechanical elements can be inferred from comparisons with optical stretcher experiments. Due to triangulation of the cell surface, interactions of cells with arbitrarily shaped (triangulated) structures such as blood vessels can be captured naturally. Comparing our simulations with those of so-called center-based models, in which cells have a largely rigid shape and forces are exerted between cell centers, we find that the migration forces a cell needs to exert on its environment to close a tissue lesion, is much smaller than predicted by center-based models. To stress generality of the approach, the liver simulations were complemented by monolayer and multicellular spheroid growth simulations. In summary, our model can give quantitative insight in many tissue organization processes, permits hypothesis testing in silico, and guide experiments in situations in which cell mechanics is considered important.
Highlights
Driven by the insight that multicellular organization cannot be explained from the viewpoint of biochemical processes alone and flanked by recent development of methods in imaging and probing of physical forces at small scales, the role of mechanics in the interplay of cell and multicellular dynamics is moving into the main focus of biological research (Fletcher and Mullins 2010)
The cells were approximated as spheres, while the forces between them are simulated as forces between the cell centers, which is why these models are often termed “center-based model” (CBM)
The deformable cell model (DCM) can be used to verify the systems behavior of the CBM for small cell populations, while the CBM can be used to simulate large cell populations. We demonstrate this by direct comparison of a CBM and a DCM in the same liver lobule
Summary
Driven by the insight that multicellular organization cannot be explained from the viewpoint of biochemical processes alone and flanked by recent development of methods in imaging and probing of physical forces at small scales, the role of mechanics in the interplay of cell and multicellular dynamics is moving into the main focus of biological research (Fletcher and Mullins 2010). Simulations with quasi-incompressible cells characterized by a Poisson ratio of ≈ 0.5 can lead to unrealistic multicellular arrangements and to false predictions Such situation may occur during liver regeneration after APAP or CCl4 intoxication where many cells enter the cell cycle almost at the same time close the drug-induced lesion. To ensure that the center-based model behaves “on average” as the DCM, which is a priori not the case due to the shortcomings of the CBM approach as discussed above, we here propose a simple correction scheme in which the interaction forces of the CBM are calibrated from simulations with the DCM In this way, the DCM can be used to verify the systems behavior of the CBM for small cell populations, while the CBM can be used to simulate large cell populations. The elastic properties of emergent tissues simulated with the model can be compared to elastographic images (Sack et al 2013)
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