Distribution and propagation of mechanical stress in simulated structurally heterogeneous tissue spheroids

Effective mechanical potential of cell-cell interaction explains three-dimensional morphologies during early embryogenesis

Mechanical forces are critical for the emergence of diverse three-dimensional morphologies of multicellular systems. However, it remains unclear what kind of mechanical parameters at cellular level substantially contribute to tissue morphologies. This is largely due to technical limitations of live measurements of cellular forces. Here we developed a framework for inferring and modeling mechanical forces of cell-cell interactions. First, by analogy to coarse-grained models in molecular and colloidal sciences, we approximated cells as particles, where mean forces (i.e. effective forces) of pairwise cell-cell interactions are considered. Then, the forces were statistically inferred by fitting the mathematical model to cell tracking data. This method was validated by using synthetic cell tracking data resembling various in vivo situations. Application of our method to the cells in the early embryos of mice and the nematode Caenorhabditis elegans revealed that cell-cell interaction forces can be written as a pairwise potential energy in a manner dependent on cell-cell distances. Importantly, the profiles of the pairwise potentials were quantitatively different among species and embryonic stages, and the quantitative differences correctly described the differences of their morphological features such as spherical vs. distorted cell aggregates, and tightly vs. non-tightly assembled aggregates. We conclude that the effective pairwise potential of cell-cell interactions is a live measurable parameter whose quantitative differences can be a parameter describing three-dimensional tissue morphologies.

Stability of asymmetric cell division: A deformable cell model of cytokinesis applied to C. elegans

Cell division during early embryogenesis is linked to key morphogenic events such as embryo symmetry breaking and tissue patterning. It is thought that the physical surrounding of cells together with cell intrinsic cues act as a mechanical "mold," guiding cell division to ensure these events are robust. To quantify how cell division is affected by the mechanical and geometrical environment, we present a novel computational mechanical model of cytokinesis, the final phase of cell division. Simulations with the model reproduced experimentally observed furrow dynamics and describe the volume ratio of daughter cells in asymmetric cell divisions, based on the position and orientation of the mitotic spindle. For dividing cells in geometrically confined environments, we show how the orientation of confinement relative to the division axis modulates the volume ratio in asymmetric cell division. Further, we quantified how cortex viscosity and surface tension determine the shape of a dividing cell and govern bubble-instabilities in asymmetric cell division. Finally, we simulated the formation of the three body axes via sequential (a)symmetric divisions up until the six-cell stage of early C. elegans development, which proceeds within the confines of an eggshell. We demonstrate how model input parameters spindle position and orientation provide sufficient information to reliably predict the volume ratio of daughter cells during the cleavage phase of development. However, for egg geometries perturbed by compression, the model predicts that a change in confinement alone is insufficient to explain experimentally observed differences in cell volume. This points to an effect of the compression on the spindle positioning mechanism. Additionally, the model predicts that confinement stabilizes asymmetric cell divisions against bubble-instabilities.

Interacting active surfaces: A model for three-dimensional cell aggregates

We introduce a modelling and simulation framework for cell aggregates in three dimensions based on interacting active surfaces. Cell mechanics is captured by a physical description of the acto-myosin cortex that includes cortical flows, viscous forces, active tensions, and bending moments. Cells interact with each other via short-range forces capturing the effect of adhesion molecules. We discretise the model equations using a finite element method, and provide a parallel implementation in C++. We discuss examples of application of this framework to small and medium-sized aggregates: we consider the shape and dynamics of a cell doublet, a planar cell sheet, and a growing cell aggregate. This framework opens the door to the systematic exploration of the cell to tissue-scale mechanics of cell aggregates, which plays a key role in the morphogenesis of embryos and organoids.

Correlation of the regenerative potential of dermal fibroblasts in 2D culture with the biological properties of fibroblast-derived tissue spheroids

In situ 3D bioprinting is a new emerging therapeutic modality for treating human skin diseases. The tissue spheroids have been previously suggested as a powerful tool in rapidly expanding bioprinting technology. It has been demonstrated that the regenerative potential of human dermal fibroblasts could be quantitatively evaluated in 2D cell culture and confirmed after implantation in vivo. However, the development of unbiassed quantitative criteria of the regenerative potential of 3D tissue spheroids in vitro before their in situ bioprinting remains to be investigated. Here it has been demonstrated for the first time that specific correlations exist between the regenerative potential of human dermal fibroblasts cultured in vitro as 2D cell monolayer with biological properties of 3D tissue spheroids fabricated from these fibroblasts. In vitro assessment of biological properties included diameter, spreading and fusion kinetics, and biomechanical properties of 3D tissue spheroids. This comprehensive characterization could be used to predict tissue spheroids' regenerative potential in vivo.

Microsphere sensors for characterizing stress fields within three-dimensional extracellular matrix

Stress in the three-dimensional extracellular matrix is one of the key cues in regulating multiscale biological processes. Thus far, noticeable progress in methods and techniques (e.g., micropipette aspiration, AFM, and molecule probes) has been made to quantify stress in cell microenvironment at different length scales. Among them, the microsphere sensor-based method (MSS-based method) has emerged as an advantageous approach over conventional techniques in quantifying stress in situ and in vivo at cellular and supra-cellular scales. This method is implemented by seven sequential steps, including fabrication, modification, characterization, cell adhesion, imaging, displacement field extraction and stress calculation. Precise control of each step and inter-tunning between steps can provide quantitative characterization of stress field. However, detailed procedural information associated with each step and process has been scattered. This review aims to provide a comprehensive overview of MSS-based method, systematically summarizing the principles and research progresses. Firstly, the basic principles are introduced, and the specific experiment and calculation processes of MSS-based method are presented in detail. Then, recent advances and applications of this method are summarized. Finally, perspectives of the limitations and development trends of MSS-based method are discussed. This specific and comprehensive review would provide a guideline for the widespread application of MSS-based method as an advantageous method for in situ and in vivo stress characterization at cellular and supra-cellular scale within three-dimensional extracellular matrix. STATEMENT OF SIGNIFICANCE: In this review, a method based on a microsphere sensor (MSS-based method) as an advantageous approach over conventional techniques in quantifying stress in situ and in vivo at cellular and supra-cellular scales is introduced and discussed. This technique is implemented by seven sequential steps, including fabrication, modification, characterization, cell junction, imaging, displacement field extraction, and stress calculation. Precise control of each step and inter-tunning between steps can provide quantitative stress field. However, detailed procedural information associated with each step has been scattered. Thus, a comprehensive review collating recent advances and perspective discussions is a necessity to introduce a better option for quantifying the stress field in biological processes at the cellular and supra-cellular scales.