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. We developed an Agent-Based 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. 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 growth response of cell populations upon externally applied mechanical stress, as it can be quantitatively predicted using the same growth progression function.

During early embryonic development, cells organize into multicellular arrangements of epithelial tissue that continuously grows and deforms without losing tissue integrity. The embryo shape changes depend on the interplay between stress acting on or within the epithelial sheet and the ability of the epithelium to remodel, i.e. tissue rheological properties. Cell divisions appear to play a fundamental role in this process, since it not only drives tissue growth, but can also affect tissue mechanical stress and tissue remodeling by cell mitotic rounding [1], and the forces generated during cytokinesis. In turn, mechanical forces regulate the rate and orientation of cell division through mechanosensitive feedback processes [2]. A well-known mechanism is contact inhibition of proliferation where high cell density surpresses cell division. Defects in these feedback loops can result in uncontrolled tissue growth and loss of tissue integrity and epithelial structure, commonly observed during tumor growth.

Understanding the dynamics and mechanics of epithelial tissues during embryonic development requires computational modeling from the single-cell perspective. Therefore, we developed a 3D deformable cell model that accurately describes cell mechanical properties, cell-cell interactions and its accompanied shape changes before and during cell divisions. In this model, a cell is represented as a fluid-filled, viscous vesicle under active tension with adhesive cell-cell interactions analogous to a bubble inside a foam. Finally, cytokinesis is driven by an elastic contractile furrow ring [3].

In this work, we implement a mechanosensitive feedback loop between cell growth and division, and mechanical stress perceived by the individual cell inside the tissue. Next, this model is applied to study the tissue steady-state (homeostatic) mechanical state such as tissue stress, cell density,… in function of single-cell mechanical properties such as cell-cell adhesive interactions, cell cortex contractility and cell growth pressure. Doing so, allows us to unravel the interplay between cell growth, division and epithelial integrity.

References

[1] Petridou N., et al. (2019). Fluidization-mediated tissue spreading by mitotic cell rounding and non-canonical Wnt signalling. Nature Cell Biology. Vol 21

[2] Godard, B., Heisenberg C. (2019). Cell Division and tissue mechanics. Current Opinion in Cell Biology

[3] Cuvelier, M., et al. (2022). Stability of asymmetric cell division under confinement: A deformable cell model of cytokinesis applied to C. elegans development. bioRxiv

One of the main challenges in improving the efficacy of conventional chemotherapeutic drugs is that they do not reach the cancer cells at sufficiently high doses, while at the same time affecting healthy tissue and causing significant side effects and suffering in cancer patients. To overcome this deficiency, magnetic nanoparticle-based drugs have emerged as a promising approach to achieve more specific tumour targeting. Nanoparticles are nano-sized organic or inorganic materials that can be equipped with various biological and medical functions and designed with different physicochemical properties: a chemotherapeutic agent can be encapsulated in the nanoparticles or attached to their surface, and magnetic nanoparticles can be directed to the target tissue by applying an external magnetic field. However, the geometry and position of the magnet are critical to the effective delivery of the drug to the tumour.

We therefore present a computational model for the magnetic targeting of nanoparticles that are designed to deliver therapeutic agents to the tumour: our model includes the interstitial flow around the tumour, the magnetic forces that guide the nanoparticles, and the transport within the tumour. We show how a model for the transport of magnetic nanoparticles in an external magnetic field can be integrated with a multiphase tumour growth model based on porous media. Tumour spheroids as model systems are on the scale of a few hundred micrometres, whereas nanoparticles are several orders of magnitude smaller. While it is possible to computationally study the movement of individual particles, the computational burden is enormous when thousands of particles are involved at the scale of an entire tumour, and we hence use a homogenised approach at the macroscale.

Such a computational model allows studying the influence of the geometry and position of the magnet on the accumulation of nanoparticles in the tumour, which is essential for successful cancer therapy. The ultimate goal of any cancer therapy is to optimise the effectiveness of the treatment strategy, and to this end we also show how probabilistic Bayesian methods can be used to optimise magnetic drug targeting. Our entire approach is based on the underlying physical mechanisms, not just on big data or artificial intelligence. It can therefore provide crucial insights into mechanisms that cannot be studied conclusively in vivo or in vitro alone. Model development, in vivo or in vitro experiments, and clinical trials must complement each other in a feedback loop to achieve more personalised treatment strategies that improve therapeutic outcomes and limit adverse effects for cancer patients.

A short remaining life expectancy and high mortality characterise brain tumours as a particularly dangerous disease. Simulations of the relevant processes of tumour growth and regression in brain tissue are realised by embedding a continuum-mechanical model in the framework of the Theory of Porous Media (TPM) into a data-integrated workflow. This workflow is based on suitable patient-specific data, that is basically available, e. g. from magnetic resonance images (MRI). Preparing the data by a set of tools, for example using a convolutional neural network in a shape of an U-Net, result in the segmented position and composition of the tumour and provide the referential geometry of an initial boundary value problem (IBVP). Furthermore, relevant information, e. g. about heterogenities or flow properties, are collected by image-processing tools. A more cost effective surrogate model based on the ratio of the composition of the tumour compartments is developed and calibrated with simulations of the TPM model. These modularly arranged components of the developed data-integrated approach are processed using the finite-element framework FEniCS and allow to study relevant clinical questions.

Cancer cell mechanics dictates cellular force generation, intra- and inter-cellular force transmission, cell morphology, cell migration and cell metastatic potential. The mechanics is a function of organization and dynamics of several cytoskeletal elements such as actin, microtubule and intermediate filaments, molecular motors interacting with these filaments, filament cross-linkers and other associated proteins that guide filaments polymerization, branching and depolymerization. These elements are further influenced by the activity of various enzymes, metabolites and small molecule effectors. The biochemical signaling networks upstream of a cell’s cytoskeletal elements can be complex with competing interactions, vary based on cellular genotype and phenotype, and consequently drive diverse mechanical behaviors in cells in response to microenvironmental signals. We map this extensive cytoskeletal signaling network, develop a new Boolean-Hybrid-Modular model to solve this signaling network and use it to predict changes in cytoskeletal elements and their organization in response to external and internal signals. We further connect these changes in cytoskeletal elements with existing cell-mechanics based models of traction force generation and migration to understand how a confluence of various micro-environmental signals and cell phenotypes drive disparate cancer cell behaviors.

Bacteria predominantly reside in multicellular communities, called biofilms, rather than as independent planktonic organisms. These biofilms are encompassed by a self-produced extracellular matrix that provides mechanical support and serves as a barrier for external stressors such as antimicrobial treatments. Hence, biofilms are notoriously hard to treat and eradicate and consequently confer a large societal and medical toll. Although the overall protective effects of extracellular matrix production are well-known, it remains unclear how the production of matrix at single-cell level can shape the structure, and hence the protection, of the bacteria and matrix. Using a combination of individual-cell based modeling and in vitro single-cell level characterization of Salmonella biofilms, we aim to elucidate the emergence of biofilm structure in function of matrix productivity. In silico, we model growth-driven biofilm formation where matrix production is represented through the modulation of cell-cell adhesion and friction. We find that increases in cell-cell adhesion result in more aligned and densely packed biofilms, whereas increases in cell-cell friction decrease orientational order and density. As such, increases in matrix production can potentially result in more porous biofilms, and, contrary to the current paradigm, less protection against antimicrobial treatment.