Modelling cancer cell budding in-vitro as a self-organised, non-equilibrium growth process

Predicting cancer stages from tissue energy dissipation

Understanding cancer staging in order to predict its progression is vital to determine its severity and to plan the most appropriate therapies. This task has attracted interest from different fields of science and engineering. We propose a computational model that predicts the evolution of cancer in terms of the intimate structure of the tissue, considering that this is a self-organised structure that undergoes transformations governed by non-equilibrium thermodynamics laws. Based on experimental data on the dependence of tissue configurations on their elasticity and porosity, we relate the cancerous tissue stages with the energy dissipated, showing quantitatively that tissues in more advanced stages dissipate more energy. The knowledge of this energy allows us to know the probability of observing the tissue in its different stages and the probability of transition from one stage to another. We validate our results with experimental data and statistics from the World Health Organisation. Our quantitative approach provides insights into the evolution of cancer through its different stages, important as a starting point for new and integrative research to defeat cancer.

Physical Forces in Glioblastoma Migration: A Systematic Review

The invasive capabilities of glioblastoma (GBM) define the cancer’s aggressiveness, treatment resistance, and overall mortality. The tumor microenvironment influences the molecular behavior of cells, both epigenetically and genetically. Current forces being studied include properties of the extracellular matrix (ECM), such as stiffness and “sensing” capabilities. There is currently limited data on the physical forces in GBM—both relating to how they influence their environment and how their environment influences them. This review outlines the advances that have been made in the field. It is our hope that further investigation of the physical forces involved in GBM will highlight new therapeutic options and increase patient survival. A search of the PubMed database was conducted through to 23 March 2022 with the following search terms: (glioblastoma) AND (physical forces OR pressure OR shear forces OR compression OR tension OR torsion) AND (migration OR invasion). Our review yielded 11 external/applied/mechanical forces and 2 tumor microenvironment (TME) forces that affect the ability of GBM to locally migrate and invade. Both external forces and forces within the tumor microenvironment have been implicated in GBM migration, invasion, and treatment resistance. We endorse further research in this area to target the physical forces affecting the migration and invasion of GBM.

Treatment-induced shrinking of tumour aggregates: a nonlinear volume-filling chemotactic approach

Motivated by experimental observations in 3D/organoid cultures derived from glioblastoma, we propose a novel mechano-transduction mechanism where the introduction of a chemotherapeutic treatment induces mechanical changes at the cell level. We analyse the influence of these individual mechanical changes on the properties of the aggregates obtained at the population level. We employ a nonlinear volume-filling chemotactic system of partial differential equations, where the elastic properties of the cells are taken into account through the so-called squeezing probability, which depends on the concentration of the treatment in the extracellular microenvironment. We explore two scenarios for the effect of the treatment: first, we suppose that the treatment acts only on the mechanical properties of the cells and, in the second one, we assume it also prevents cell proliferation. We perform a linear stability analysis which enables us to identify the ability of the system to create patterns and fully characterize their size. Moreover, we provide numerical simulations in 1D and 2D that illustrate the shrinking of the aggregates due to the presence of the treatment.

Physical principles of morphogenesis in mushrooms

Mushroom species display distinctive morphogenetic features. For example, Amanita muscaria and Mycena chlorophos grow in a similar manner, their caps expanding outward quickly and then turning upward. However, only the latter finally develops a central depression in the cap. Here we use a mathematical approach unraveling the interplay between physics and biology driving the emergence of these two different morphologies. The proposed growth elastic model is solved analytically, mapping their shape evolution over time. Even if biological processes in both species make their caps grow turning upward, different physical factors result in different shapes. In fact, we show how for the relatively tall and big A. muscaria a central depression may be incompatible with the physical need to maintain stability against the wind. In contrast, the relatively short and small M. chlorophos is elastically stable with respect to environmental perturbations; thus, it may physically select a central depression to maximize the cap volume and the spore exposure. This work gives fully explicit analytic solutions highlighting the effect of the growth parameters on the morphological evolution, providing useful insights for novel bio-inspired material design.