Activity-driven tissue alignment in proliferating spheroids
Liam Ruske & Julia Yeomans
We extend the continuum theory of active nematic fluids to study cell flows and tissue dynamics inside multicellular spheroids, spherical, self-assembled aggregates of cells that are widely used as model systems to study tumour dynamics. Cells near the surface of spheroids have better access to nutrients and therefore proliferate more rapidly than those in the resource-depleted core. Using both analytical arguments and three-dimensional simulations, we find that the proliferation gradients result in flows and in gradients of activity both of which can align the orientation axis of cells inside the aggregates. Depending on environmental conditions and the intrinsic tissue properties, we identify three distinct alignment regimes: spheroids in which all the cells align either radially or tangentially to the surface throughout the aggregate and spheroids with angular cell orientation close to the surface and radial alignment in the core. The continuum description of tissue dynamics inside spheroids not only allows us to infer dynamic cell parameters from experimentally measured cell alignment profiles, but more generally motivates novel mechanisms for controlling the alignment of cells within aggregates which has been shown to influence the mechanical properties and invasive capabilities of tumors.
Multicellular spheroids are self-assembled balls of cells, typically hunderds of microns in diameter. They are important model systems for high throughput screening of the effects of mechanical or oxidative stress on tumors and for testing the efficacy of anti-cancer drugs. Gradients in metabolite concentration and the cell division rate across spheroids lead to gradients in activity, the rate at which the cells use energy to generate forces. This results in cell ordering and flows that can be described using the theories of active nematics. By comparing cell alignment profiles in experiments to model predictions, we can extract dynamical tissue parameters which are difficult to measure directly, thus establishing a link between 3D active fluids and the tissue-scale organization in biological systems.
Between the 1st and the 19th of August 2022 Liam participated in the Nordita workshop Current and Future Themes in Soft & Biological Active Matter. In his talk titled “Modelling the Dynamics of 3D cell aggregates” he motivated how cell divisions and death act as a source of active forces in cellular aggregates and how these processes can be incorporated into continuum models of tissues. Applying this model to 3D living cell aggregates (spheroids) not only allows the inference of dynamic cell parameters from experimentally measured cell alignment profiles, but more generally motivates novel mechanisms for controlling the alignment of cells within aggregates which has been shown to influence the mechanical properties and invasive capabilities of tumors.
Activity gradients in two- and three-dimensional active nematics
Liam Ruske & Julia Yeomans
Soft Matter 18 5654-5661 (2022)
We numerically investigate how spatial variations of extensile or contractile active stress affect bulk active nematic systems in two and three dimensions. In the absence of defects, activity gradients drive flows which re-orient the nematic director field and thus act as an effective anchoring force. At high activity, defects are created and the system transitions into active turbulence, a chaotic flow state characterized by strong vorticity. We find that in two-dimensional (2D) systems active torques robustly align +1/2 defects parallel to activity gradients, with defect heads pointing towards contractile regions. In three-dimensional (3D) active nematics disclination lines preferentially lie in the plane perpendicular to activity gradients due to active torques acting on line segments. The average orientation of the defect structures in the plane perpendicular to the line tangent depends on the defect type, where wedge-like +1/2 defects align parallel to activity gradients, while twist defects are aligned anti-parallel. Understanding the response of active nematic fluids to activity gradients is an important step towards applying physical theories to biology, where spatial variations of active stress impact morphogenetic processes in developing embryos and affect flows and deformations in growing cell aggregates, such as tumours.
Between the 26th of June and the 1st of July 2022 Liam participated in the Active and Intelligent Living Matter conference on Sicily, where he presented a poster summarizing several of his research projects about active continuum theories and their application to biological systems.
Between the 23rd and the 27th of May 2022 Liam participated in the CECAM workshop on Computational methods and tools for complex suspensions to present some of his work. In his talk titled “Modelling biological matter as active nematic fluids” he highlighted how numerical simulations of active fluids can be used to study the self-organization of three-dimensional tissues in a variety of biological systems, where a continuous influx of energy on a single-cell level drives striking collective behaviour at the tissue scale.
Abstract: We numerically investigate the morphology and disclination line dynamics of active nematic droplets in three dimensions. Although our model incorporates only the simplest possible form of achiral active stress, active nematic droplets display an unprecedented range of complex morphologies. For extensile activity, fingerlike protrusions grow at points where disclination lines intersect the droplet surface. For contractile activity, however, the activity field drives cup-shaped droplet invagination, run-and-tumble motion, or the formation of surface wrinkles. This diversity of behavior is explained in terms of an interplay between active anchoring, active flows, and the dynamics of the motile disclination lines. We discuss our findings in the light of biological processes such as morphogenesis, collective cancer invasion, and the shape control of biomembranes, suggesting that some biological systems may share the same underlying mechanisms as active nematic droplets.
A lot is understood about the ways in which single cells move, but there are still many questions about the motion and organisation of cell aggregates where cells coupled through intercellular junctions show a range of collective behaviours.
This work, which has been recently published Phys. Rev. X 11, 021001 (2021), shows the potential of active nematic continuum models to describe collective cell motion in a three dimensional environment.
Active matter describes systems—living and synthetic—where a continuous influx of energy at the level of individual components leads to striking collective behavior among the individual components, such as self-organizing bacteria colonies, bird flocks, or polymers in the cytoskeleton of cells. Understanding their behavior has attracted interest for studies of biological systems—from the spread of cancer to the development of organisms—as well the development of mesoscopic engines. Here, we numerically investigate 3D droplets composed of active matter and the ways in which their shapes change in response to the continuous input of energy.
One striking observation is the continuous formation of fingerlike protrusions, reminiscent of the collective motion of invading cancer cells. By changing the mechanical properties of the drop or the activity level, we find several different dynamical responses: For example, the droplet surface can wrinkle in a way that resembles a walnut or the active forces can drive a dimple in the droplet to grow, leading to a cup shape. Such invagination is reminiscent of patterns seen during morphogenesis.
Understanding the behavior of model systems, here a continuum model of active material, is an important step toward the goal of understanding the role of physical theories in the life sciences.
It is increasingly becoming apparent that the physical concepts of forces and flows play an important role in understanding biological processes, from the spread of cancers to morphogenesis, thedevelopment of organisms. However, biological systems, such as cells, probe new ideas in that theyoperate out of thermodynamic equilibrium continually taking chemical energy from their surroundings, and using it to move and self-organise.
The term active matter has come to describe models of living systems where such a continuous influx of energy leads to striking collective behaviour like the chaotic flow patterns of active turbulence seen in collections of bacteria and self-propelled topological defects which are now thought to be relevant to some modes of biofilm formation. This paper is a numerical investigation of three-dimensional droplets composed of active matter and the ways in which their shapes change in response to the continuous input of energy. One striking observation is the continuous formation of finger-like protrusions, reminiscent of the collective motion of invading cancer cells. By changing the mechanical properties of the drop or the activity level, we find several different dynamical responses: for example the droplet surface can wrinkle in a way that resembles a walnut or the active forces can drive a dimple in the droplet to grow, leading to a cup-shape: such invagination is reminiscent of patterns seen during morphogenesis.
Understanding the behaviour of model systems, here a continuum model of active material, is an important step towards the goal of understanding the role of physical theories in the life sciences.
The first major meeting between the ESRs and PIs in our network took place on 10 September. On that occasion Liam Ruske, ESR from the University of Oxford, gave a brief introduction to the field of active fluids in the form of a short presentation.
Why not take a moment to learn about why active liquid crystals surprisingly exhibit turbulence at small Reynolds numbers and how the study of active nematics can help us to better understand collective dynamics in biological systems.