Growing tissues: A simulation study

Tissues represent an interesting type of matter: active matter. The basic elements of tissues, the cells, divide or die, consume energy on the scale of their constituents, exert forces onto their surrounding and dissipate energy, which results in non-equilibrium systems. Tissue growth is involved in many biological processes and understanding its generic phenomena is, thus, not only important from a physical point of view. In this thesis, we are interested in the mechanics of issue growth in the context of the homeostatic pressure theory. The homeostatic pressure is defined as the pressure that has to be exerted onto a tissue, growing in a biochemically constant environment, in order to balance cell division and cell death. However, experimental observations show that tissue growth is dominated by surface effects in the sense that high division rates at the surface can compensate for an on average dying core. Thus, the homeostatic pressure is better defined as a bulk property. We study the growth with a negative homeostatic pressure, which means that without the surface growth effect such a tissue has to be kept under tension to ensure a stable steady state. A mesoscale simulation technique is used, where individual cells are represented by two point particles, interacting like soft sticky spheres. Growth is modeled by a force that repels the particles of one cell until new particles are introduced, when the cell reaches a certain size. Additionally, DPD like interactions and a constant rate of cell death concludes the active part. This approach is used to explore the dependence of the homeostatic pressure on different model parameters. Additionally, we measure the bulk growth rates of tissue spheroids under different mechanical stresses and compare our results to the data of in vitro experiments of tissue spheroids under pressure. We fit the simulations to this experimental data and extract a homeostatic pressure of the order of -1 to -2kPa. Furthermore, we find a new tissue state: a tensile membrane. In this state, the tissue forms a relatively thin sheet, where a characteristic tension develops for tissues with a negative homeostatic pressure. It is sustained by growth at the surface and death in the bulk. In addition, we study the interface dynamics of two competing tissues with a homeostatic pressure difference. In the theory of homeostatic pressure, this difference leads to a take-over of the tissue with the higher homeostatic pressure. Starting from a theoretical point of view, we solve the dynamics for the one dimensional problem without diffusion and find the interface to propagate at a constant velocity. We use the same simulation technique as above to study the interface dynamics in two dimensions and compare our results to the analytical solution. The dependence of the interface velocity on the homeostatic pressure difference between the tissues as well as the predicted stress profiles match well with the simulations. Furthermore, we analyze the scaling behavior of the interface width w, which develops initially as a power law w~t^beta and saturates depending on the system size L for later times w_sat~L^alpha. We find a growth exponent beta=0.4 and a roughness exponent alpha=0.25. While the growth exponent roughly fits into the KPZ universality class, the measured roughness exponent is substantially smaller. At last, we study divisional alignment in expanding monolayered cell sheets. We extend the simulations with a previously established motility mechanism and compare the results to the experimental data of MDCK cell sheets that invade narrow microchannels. In the experiments, we find a strong correlation between the division orientation and the emergent flow. However, cell division correlates best with the main axis of the strain rate tensor, which is related to the main axis of the stress tensor. This supports the notion that divisions are aligned by the local stress as opposed to the local velocity. Apart from boundary phenomena and a surprising flow of cells perpendicular to the main migration direction, the simulations are able to reproduce the experimentally observed quantities very well

Tissue homeostasis: A tensile state

Mechanics play a significant role during tissue development. One of the key characteristics that underlies this mechanical role is the homeostatic pressure, which is the pressure stalling growth. In this work, we explore the possibility of a negative bulk homeostatic pressure by means of a mesoscale simulation approach and experimental data of several cell lines. We show how different cell properties change the bulk homeostatic pressure, which could explain the benefit of some observed morphological changes during cancer progression. Furthermore, we study the dependence of growth on pressure and estimate the bulk homeostatic pressure of five cell lines. Four out of five result in a bulk homeostatic pressure in the order of minus one or two kPa

Alignment of cell division axes in directed epithelial cell migration

Cell division is an essential dynamic event in tissue remodeling during wound healing, cancer and embryogenesis. In collective migration, tensile stresses affect cell shape and polarity, hence, the orientation of the cell division axis is expected to depend on cellular flow patterns. Here, we study the degree of orientation of cell division axes in migrating and resting epithelial cell sheets. We use microstructured channels to create a defined scenario of directed cell invasion and compare this situation to resting but proliferating cell monolayers. In experiments, we find a strong alignment of the axis due to directed flow while resting sheets show very weak global order, but local flow gradients still correlate strongly with the cell division axis. We compare experimental results with a previously published mesoscopic particle based simulation model. Most of the observed effects are reproduced by the simulations

Interface dynamics of competing tissues

Tissues can be characterized by their homeostatic stress, i.e. the value of stress for which cell division and cell death balance. When two different tissues grow in competition, a difference of their homeostatic stresses determines which tissue grows at the expense of the second. This then leads to the propagation of the interface separating the tissues. Here, we study structural and dynamical properties of this interface by combining continuum theory with mesoscopic simulations of a cell-based model. Using a simulation box that moves with the interface, we find that a stationary state exists in which the interface has a finite width and propagates with a constant velocity. The propagation velocity in the simulations depends linearly on the homeostatic stress difference, in excellent agreement with the analytical predictions. This agreement is also seen for the stress and velocity profiles. Finally, we analyzed the interface growth and roughness as a function of time and system size. We estimated growth and roughness exponents, which differ from those previously obtained for simple tissue growt