Multicellular aggregates: a model system for tissue rheology

Local Yield and Compliance in Active Cell Monolayers

The rheology of biological tissue plays an important role in many processes, from organ formation to cancer invasion. Here, we use a multiphase field model of motile cells to simulate active microrheology within a tissue monolayer. When unperturbed, the tissue exhibits a transition between a solidlike state and a fluidlike state tuned by cell motility and deformability-the ratio of the energetic costs of steric cell-cell repulsion and cell-edge tension. When perturbed, solid tissues exhibit local yield-stress behavior, with a threshold force for the onset of motion of a probe particle that vanishes upon approaching the solid-to-liquid transition. This onset of motion is qualitatively different in the low and high deformability regimes. At high deformability, the tissue is amorphous when solid, it responds compliantly to deformations, and the probe transition to motion is smooth. At low deformability, the monolayer is more ordered translationally and stiffer, and the onset of motion appears discontinuous. Our results suggest that cellular or nanoparticle transport in different types of tissues can be fundamentally different and point to ways in which it can be controlled.

Mapping cell cortex rheology to tissue rheology and vice versa

The mechanics of biological tissues mainly proceeds from the cell cortex rheology. A direct, explicit link between cortex rheology and tissue rheology remains lacking, yet would be instrumental in understanding how modulations of cortical mechanics may impact tissue mechanical behavior. Using an ordered geometry built on 3D hexagonal, incompressible cells, we build a mapping relating the cortical rheology to the monolayer tissue rheology. Our approach shows that the tissue low-frequency elastic modulus is proportional to the rest tension of the cortex, as expected from the physics of liquid foams as well as of tensegrity structures. A fractional visco-contractile cortex rheology is predicted to yield a high-frequency fractional visco-elastic monolayer rheology, where such a fractional behavior has been recently observed experimentally at each scale separately. In particular cases, the mapping may be inverted, allowing to derive from a given tissue rheology the underlying cortex rheology. Interestingly, applying the same approach to a 2D hexagonal tiling fails, which suggests that the 2D character of planar cell cortex-based models may be unsuitable to account for realistic monolayer rheologies. We provide quantitative predictions, amenable to experimental tests through standard perturbation assays of cortex constituents, and hope to foster new, challenging mechanical experiments on cell monolayers.

All-in-one rheometry and nonlinear rheology of multicellular aggregates

Tissues are generally subjected to external stresses, a potential stimulus for their differentiation or remodeling. While single-cell rheology has been extensively studied leading to controversial results about nonlinear response, mechanical tissue behavior under external stress is still poorly understood, in particular, the way individual cell properties translate at the tissue level. Herein, using magnetic cells we were able to form perfectly monitored cellular aggregates (magnetic molding) and to deform them under controlled applied stresses over a wide range of timescales and amplitudes (magnetic rheometer). We explore the rheology of these minimal tissue models using both standard assays (creep and oscillatory response) as well as an innovative broad spectrum solicitation coupled with inference analysis thus being able to determine in a single experiment the best rheological model. We find that multicellular aggregates exhibit a power-law response with nonlinearities leading to tissue stiffening at high stress. Moreover, we reveal the contribution of intracellular (actin network) and intercellular components (cell-cell adhesions) in this aggregate rheology.

Compression of a pressurized spherical shell by a spherical or flat probe

Measuring the mechanical properties of cells and tissues often involves indentation with a sphere or compression between two plates. Different theoretical approaches have been developed to retrieve material parameters (e.g., elastic modulus) or state variables (e.g., pressure) from such experiments. Here, we extend previous theoretical work on indentation of a spherical pressurized shell by a point force to cover indentation by a spherical probe or a plate. We provide formulae that enable the modulus or pressure to be deduced from experimental results with realistic contact geometries, giving different results that are applicable depending on pressure level. We expect our results to be broadly useful when investigating biomechanics or mechanobiology of cells and tissues.

A three dimensional model of multicellular aggregate compression

Multicellular aggregates are an excellent model system to explore the role of tissue biomechanics, which has been demonstrated to play a crucial role in many physiological and pathological processes. In this paper, we propose a three-dimensional mechanical model and apply it to the uniaxial compression of a multicellular aggregate in a realistic biological setting. In particular, we consider an aggregate of initially spherical shape and describe both its elastic deformations and the reorganisation of the cells forming the spheroid. The latter phenomenon, understood as remodelling, is accounted for by assuming that the aggregate undergoes plastic-like distortions. The study of the compression of the spheroid, achieved by means of two parallel, compressive plates, needs the formulation of a contact problem between the living spheroid itself and the plates, and is solved with the aid of the augmented Lagrangian method. The results of the performed numerical simulations are in qualitative agreement with the biological observations reported in the literature and can also be used to estimate quantitatively some fundamental aggregate mechanical parameters.

Effect of liquid flow by pipetting during medium change on deformation of hiPSC aggregates

Introduction

Maintaining the pluripotency and homogeneity of human induced pluripotent stem cells (hiPSCs) requires stable culture conditions with consistent medium change. In this study, we evaluated the performance of medium change by machine vs. medium change performed manually in terms of their impact on the aggregate shape of hiPSCs.

Methods

Aggregates of two hiPSC lines (1383D2 and Tic) were cultured, and the medium change was conducted either manually or with a machine. The populational homogeneity in aggregate shape was determined based on the projected aggregate area for size expansion as well as the circularity for spherical morphology.

Results

In the case of manually performed medium changes, the size of 1383D2 aggregates expanded homogeneously, maintaining its spherical morphology as culture duration increased, while spherical morphology was deformed in Tic aggregates, which had a heterogeneous population in terms of shape. In the case of medium change performed by a machine under a low flux of liquid flow, cultures of both aggregates showed homogeneous populations without deformation, although a high flux led to a heterogeneous population. The heterogeneous population observed in manually performed medium change was caused by the low stability of motion. In addition, time-lapse observation revealed that the Tic aggregates underwent tardive deformation with cellular protrusions from the aggregate surface after medium change with high flux. Histological analysis revealed a spatial heterogeneity of collagen type I inside 1383D2 aggregates, which had a shell structure with strong formation of collagen type I at the periphery of the aggregates, while Tic aggregates did not have a shell structure, suggesting that the shell structure prevented aggregate deformation.

Conclusion

Medium change by a machine led to a homogeneous population of aggregate shapes. Liquid flow caused tardive deformation of aggregates, but the shell structure of collagen type I in aggregates maintained its spherical shape.

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Mechanization of medium change leads to homogeneous shape of iPSC aggregates.

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Tardive change of aggregates was observed.

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Collagen type I distribution in aggregates induces shell structure formation.

On the morphological stability of multicellular tumour spheroids growing in porous media

Multicellular tumour spheroids (MCTSs) are extensively used as in vitro system models for investigating the avascular growth phase of solid tumours. In this work, we propose a continuous growth model of heterogeneous MCTSs within a porous material, taking into account a diffusing nutrient from the surrounding material directing both the proliferation rate and the mobility of tumour cells. At the time scale of interest, the MCTS behaves as an incompressible viscous fluid expanding inside a porous medium. The cell motion and proliferation rate are modelled using a non-convective chemotactic mass flux, driving the cell expansion in the direction of the external nutrients' source. At the early stages, the growth dynamics is derived by solving the quasi-stationary problem, obtaining an initial exponential growth followed by an almost linear regime, in accordance with experimental observations. We also perform a linear-stability analysis of the quasi-static solution in order to investigate the morphological stability of the radially symmetric growth pattern. We show that mechano-biological cues, as well as geometric effects related to the size of the MCTS subdomains with respect to the diffusion length of the nutrient, can drive a morphological transition to fingered structures, thus triggering the formation of complex shapes that might promote tumour invasiveness. The results also point out the formation of a retrograde flow in the MCTS close to the regions where protrusions form, that could describe the initial dynamics of metastasis detachment from the in vivo tumour mass. In conclusion, the results of the proposed model demonstrate that the integration of mathematical tools in biological research could be crucial for better understanding the tumour's ability to invade its host environment.

Formation of Tethers from Spreading Cellular Aggregates

Membrane tubes are commonly extruded from cells and vesicles when a point-like force is applied on the membrane. We report here the unexpected formation of membrane tubes from lymph node cancer prostate (LNCaP) cell aggregates in the absence of external applied forces. The spreading of LNCaP aggregates deposited on adhesive glass substrates coated with fibronectin is very limited because cell-cell adhesion is stronger than cell-substrate adhesion. Some cells on the aggregate periphery are very motile and try to escape from the aggregate, leading to the formation of membrane tubes. Tethered networks and exchange of cargos between cells were observed as well. Growth of the tubes is followed by either tube retraction or tube rupture. Hence, even very cohesive cells are successful in escaping aggregates, which may lead to epithelial mesenchymal transition and tumor metastasis. We interpret the dynamics of formation and retraction of tubes in the framework of membrane mechanics.

Colloquium: Mechanical formalisms for tissue dynamics

The understanding of morphogenesis in living organisms has been renewed by tremendous progress in experimental techniques that provide access to cell scale, quantitative information both on the shapes of cells within tissues and on the genes being expressed. This information suggests that our understanding of the respective contributions of gene expression and mechanics, and of their crucial entanglement, will soon leap forward. Biomechanics increasingly benefits from models, which assist the design and interpretation of experiments, point out the main ingredients and assumptions, and ultimately lead to predictions. The newly accessible local information thus calls for a reflection on how to select suitable classes of mechanical models. We review both mechanical ingredients suggested by the current knowledge of tissue behaviour, and modelling methods that can help generate a rheological diagram or a constitutive equation. We distinguish cell scale ("intra-cell") and tissue scale ("inter-cell") contributions. We recall the mathematical framework developed for continuum materials and explain how to transform a constitutive equation into a set of partial differential equations amenable to numerical resolution. We show that when plastic behaviour is relevant, the dissipation function formalism appears appropriate to generate constitutive equations; its variational nature facilitates numerical implementation, and we discuss adaptations needed in the case of large deformations. The present article gathers theoretical methods that can readily enhance the significance of the data to be extracted from recent or future high throughput biomechanical experiments.

Magnetic flattening of stem-cell spheroids indicates a size-dependent elastocapillary transition

Cellular aggregates (spheroids) are widely used in biophysics and tissue engineering as model systems for biological tissues. In this Letter we propose novel methods for molding stem-cell spheroids, deforming them, and measuring their interfacial and elastic properties with a single method based on cell tagging with magnetic nanoparticles and application of a magnetic field gradient. Magnetic molding yields spheroids of unprecedented sizes (up to a few mm in diameter) and preserves tissue integrity. On subjecting these spheroids to magnetic flattening (over 150g), we observed a size-dependent elastocapillary transition with two modes of deformation: liquid-drop-like behavior for small spheroids, and elastic-sphere-like behavior for larger spheroids, followed by relaxation to a liquidlike drop.

Assemblages: functional units formed by cellular phase separation

The partitioning of intracellular space beyond membrane-bound organelles can be achieved with collections of proteins that are multivalent or contain low-complexity, intrinsically disordered regions. These proteins can undergo a physical phase change to form functional granules or other entities within the cytoplasm or nucleoplasm that collectively we term “assemblage.” Intrinsically disordered proteins (IDPs) play an important role in forming a subset of cellular assemblages by promoting phase separation. Recent work points to an involvement of assemblages in disease states, indicating that intrinsic disorder and phase transitions should be considered in the development of therapeutics.

Microdevice arrays of high aspect ratio poly(dimethylsiloxane) pillars for the investigation of multicellular tumour spheroid mechanical properties

We report the design, fabrication and evaluation of an array of microdevices composed of high aspect ratio PDMS pillars, dedicated to the study of tumour spheroid mechanical properties. The principle of the microdevice is to confine a spheroid within a circle of micropillars acting as peripheral flexible force sensors. We present a technological process for fabricating high aspect ratio micropillars (300 μm high) with tunable feature dimensions (diameter and spacing) enabling production of flexible PDMS pillars with a height comparable to spheroid sizes. This represents an upscale of 10 along the vertical direction in comparison to more conventional PDMS pillar force sensors devoted to single cell studies, while maintaining their force sensitivity in the same order of magnitude. We present a method for keeping these very high aspect ratio PDMS pillars stable and straight in liquid solution. We demonstrate that microfabricated devices are biocompatible and adapted to long-term spheroid growth. Finally, we show that the spheroid interaction with the micropillars' surface is dependent on PDMS cellular adhesiveness. Time-lapse recordings of growth-induced micropillars' bending coupled with a software program to automatically detect and analyse micropillar displacements are presented. The use of these microdevices as force microsensors opens new prospects in the fields of tissue mechanics and pharmacological drug screening.