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Model simulations indicate that the response of growing cell populations on mechanical stress follows the same functional relationship and is predictable over different cell lines and growth conditions despite the response curves look largely different. We develop a hybrid model strategy in which cells are represented by coarse-grained individual units calibrated with a high resolution cell model and parameterized measurable biophysical and cell-biological parameters. Cell cycle progression in our model is controlled by volumetric strain, the latter being derived from a bio-mechanical relation between applied pressure and cell compressibility. After parameter calibration from experiments with mouse colon carcinoma cells growing against the resistance of an elastic alginate capsule, the model adequately predicts the growth curve in i) soft and rigid capsules, ii) in different experimental conditions where the mechanical stress is generated by osmosis via a high molecular weight dextran solution, and iii) for other cell types with varying doubling times. Our model simulation results suggest that the growth response of cell population upon externally applied mechanical stress is the same, as it can be quantitatively predicted using the same growth progression function.Author summaryThe effect of mechanical resistance on the growth of tumor cells remains today largely unquantified. We studied data from two different experimental setups that monitor the growth of tumor cells under mechanical compression. The existing data in the first experiment examined growing CT26 cells in an elastic permeable capsule. In the second experiment, growth of tumor cells under osmotic stress of the same cell line as well as other cell lines were studied. We have developed and agent-based model with measurable biophysical and cell-biological parameters that can simulate both experiments. Cell cycle progression in our model is a Hill function of cell volumetric strain, derived from a bio-mechanical relation between applied pressure and cell compressibility. After calibration of the model parameters within the data of the first experiment, we are able predict the growth rates in the second experiment. We show that that the growth response of cell populations upon externally applied mechanical stress in the two different experiments and over different cell lines can be predicted using the same growth progression function once the growth kinetics of the cell lines in abscence of mechanical stress is known.

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. Electronic supplementary material The online version of this article (10.1007/s10237-019-01204-7) contains supplementary material, which is available to authorized users.

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. The focus in this paper is to study the regeneration of liver after drug-induced depletion of hepatocytes, in which surviving dividing and migrating hepatocytes must squeeze through a blood vessel network to fill the emerged lesions. Here, the cells’ response to mechanical stress might significantly impact on the regeneration process. We present a 3D high-resolution cell-based model integrating information from measurements in order to obtain a refined quantitative understanding of the cell-biomechanical impact on the closure of drug-induced lesions in liver. Our model represents each cell individually, constructed as a 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 infer the nature of their mechanical elements and their parameters 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 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. This effect is expected to be even more present in chronic liver disease, where tissue stiffens and excess collagen narrows pores for cells to squeeze through.

Model simulations indicate that the response of growing cell populations on mechanical stress follows the same functional relationship and is predictable over different cell lines and growth conditions despite experimental response curves look largely different. We develop a hybrid model strategy in which cells are represented by coarse-grained individual units calibrated with a high resolution cell model and parameterized by measurable biophysical and cell-biological parameters. Cell cycle progression in our model is controlled by volumetric strain, the latter being derived from a bio-mechanical relation between applied pressure and cell compressibility. After parameter calibration from experiments with mouse colon carcinoma cells growing against the resistance of an elastic alginate capsule, the model adequately predicts the growth curve in i) soft and rigid capsules, ii) in different experimental conditions where the mechanical stress is generated by osmosis via a high molecular weight dextran solution, and iii) for other cell types with different growth kinetics from the growth kinetics in absence of external stress. Our model simulation results suggest a generic, even quantitatively same, growth response of cell populations upon externally applied mechanical stress, as it can be quantitatively predicted using the same growth progression function., Author summary The effect of mechanical resistance on the growth of tumor cells remains today largely unquantified. We studied data from two different experimental setups that monitor the growth of tumor cells under mechanical compression. The existing data in the first experiment examined growing CT26 cells in an elastic permeable capsule. In the second experiment, growth of tumor cells under osmotic stress of the same cell line as well as other cell lines were studied. We have developed an agent-based model with measurable biophysical and cell-biological parameters that can simulate both experiments. Cell cycle progression in our model is a Hill-type function of cell volumetric strain, derived from a bio-mechanical relation between applied pressure and cell compressibility. After calibration of the model parameters within the data of the first experiment, we are able predict the growth rates in the second experiment. We show that that the growth response of cell populations upon externally applied mechanical stress in the two different experiments and over different cell lines can be predicted using the same growth progression function once the growth kinetics of the cell lines in abscence of mechanical stress is known.

Motivation: TiQuant is a modular software tool for efficient quantification of biological tissues based on volume data obtained by biomedical image modalities. It includes a number of versatile image and volume processing chains tailored to the analysis of different tissue types which have been experimentally verified. TiQuant implements a novel method for the reconstruction of three-dimensional surfaces of biological systems, data that often cannot be obtained experimentally but which is of utmost importance for tissue modelling in systems biology. Availability: TiQuant is freely available for non-commercial use at msysbio.com/tiquant. Windows, OSX and Linux are supported., 6 pages, 4 figures