Session D26: Mechanics of cells and tissues across scales III

Controlled neighbor exchanges drive intermittency and cell streaming in epithelial tissues

Cell neighbor exchanges are integral to tissue rearrangements in biology, including development and repair. Often these processes occur via topological T1 transitions analogous to those in foams, grains and colloids. However, in contrast to non-living materials the T1 transitions in tissues are rate-limited and cannot occur instantaneously due to finite time required to remodel complex structure at cell-cell junctions. Here we introduce this important biological constraint in a vertex-based model as an intrinsic single-cell property and study how this rate-limiting process affects the mechanics and collective behavior of cells in a tissue. We report in the absence of this time constraint, the tissue undergoes a motility-driven glass transition characterized by a sharp increase in the intermittency of cell-cell rearrangements. Remarkably, this glass transition disappears as T1 transitions are temporally limited. As a unique consequence of limited rearrangements, we also find that the tissue develops dynamically heterogeneous pockets of fast and slow cells, in which the fast cells organize into long streams with leader-follower interactions, maintaining optimally stable cell-cell contacts. We compare our predictions with existing in-vivo experiments on Drosophila pupal development.   

Mechanical Instabilities in Growing Biological Systems: Wrinkling and Branching

Morphological shape transformations in biological systems often arise from patterned biochemical processes, which can produce mechanical forces either directly via molecular motors or indirectly via differential growth of connected tissues. The growth mismatch produces internal stresses, which can be released via shape transformations and mechanical instabilities. In this talk I will focus on mechanical instabilities that cause the wrinkling of Vibrio cholerae bacterial biofilms and branching in developing lungs. Biofilms grown on agar substrates form wrinkled patterns, which are radial in the outer region and zig-zag herringbone in the inner region. We demonstrate that the wavelength of wrinkles as well as their spatiotemporal pattern can be predicted by a chemo-mechanical model that takes into account the diffusion of nutrients and their uptake by bacteria, growth of the biofilm, mechanical deformation of the biofilm and the agar substrate, and the friction between them. In the second part I will discuss the branching morphogenesis of lungs. We investigate how patterned differential growth between the inner epithelium and the outer mesenchyme tissue as well as the spatial pattern of smooth muscles lead to formation of new branches and their subsequent development. Experiments and mathematical model suggest that the patterned formation of stiff smooth muscles is very important for the proper development of new branches. In the absence of smooth muscles, the wrinkling instability of growing epithelium on the soft mesenchyme produces several ectopic branches. However, when stiff smooth muscles are formed, they suppress the wrinkling instability and new branches are formed only between the gaps of smooth muscles.   

Quasi-realistic modelling of expanding epithelial cell monolayer

An expanding epithelial cell monolayer on a 2-dimensional substrate exhibits intriguing mechanical patterns. The distribution of mechanical quantities over space and time thereby hints a picture integrating cell-cell and cell-substrate interactions. We propose a quasi-realistic model for this phenomenon. Specifically, we model cells as active constituents that would maintain force-equilibrium at the end of each motile step. The model cells contract with a tension-dependent speed, and protrude after reaching the maximum allowed contraction. Cell-substrate and cell-cell elastic adhesion bonds form, break and relocate stochastically, so as to capture contact inhibition as well as other effects. We bring forward this bottom-up approach to reveal the essential mechanisms leading to the macroscopic patterns.   

Symmetry breaking and axis formation in Hydra

During animal development, a near-uniform collection of genetically identical cells self-organizes to form an organism with a well-defined anterior-posterior body axis. Axial patterning is the earliest and most fundamental event that gives rise to the complexities of a full animal. The freshwater polyp Hydra is an excellent model system to study axial patterning due to its simple anatomy and incredible regenerative abilities. Hydra can regenerate from small tissue pieces or from cell aggregates. The physicists Alfred Gierer and Hans Meinhardt recognized Hydra’s self-organizing properties > 40 years ago. However, the physical mechanisms underlying cell sorting, symmetry breaking, and axis specification in Hydra remained elusive as existing studies failed to distinguish between different driving mechanisms. In my talk, I will present our recent work that answers some of these questions. Our results challenge key assumptions in existing mathematical models of Hydra regeneration and require that we re-examine the mechanisms driving axis specification and pattern formation.   

Configurations and dynamics of membrane-bound elastic filaments

Changes in the curvature and topology of cell membranes are responsible for numerous biological processes. Many of these changes are driven by interactions with thin filament-like protein structures which form on the membrane surface. While there are a number of proposed mechanisms, how exactly the filament-membrane interactions produce changes in curvature remains an open question. The feasibility of proposed mechanisms can be be investigated by modeling the filament as a thin elastic rod which is confined to the membrane surface. The interplay between the geometries of the the surface and the filament give rise to complex distributions of force and torque which are believed to play a crucial role in reshaping the membrane. We discuss the mechanics of surface-bound filaments and present a collection of analytical and numerical results.   

Bacteria sense and respond to the mechanics of the surface to which they attach

The attachment of bacteria to a surface is often a key initial step in the development of biofilms, communities of bacteria that are significant contributors to disease, fouling, and damage to the built environment. Understanding how bacteria sense surface attachment and, in response, begin the process of biofilm initiation, should give rise to new avenues to biofilm prevention as well as advance basic science. Here, we examine the relationship between substrate stiffness, mechanical deformation of the bacterial cell, accumulation of bacteria on the surface, and dynamics of an intracellular signal that control biofilms development. Pseudomonas aeruginosa, a widely-used model organism for biofilm development and a common hospital-acquired pathogen. We find that when the chemistry of a gel substrate is held constant but the effective elasticity is increased, more bacteria accumulate and signaling activates earlier. The response to the substrate mechanics at times greater than one hour after attachment depends on different cellular structures than at earlier times. Thus, the bacterial mechanosensing leading to biofilm development is likely a multi-step process involving more than one sensory element.   

Mechanical impacts of complex topology on epithelial cells

Although complex curvatures are general features of in-vivo tissues where the fundamental biological functions are performed in our bodies, no in-depth study on the impact of complex curvature has been provided yet. In the current study, we found that strong mechanical impacts of complex topology on the epithelial system. With a great advantage of a torus having positive, zero, negative Gaussian curvature in a single structure, we demonstrated that the cells on tori showed polarized architecture than that of a flat surface. In addition, the cells manipulate the cellular mechanical elements to gain physically stable conditions. The current study sheds light on the mechanical adaption of cells on complex topology by which the relevance can be expanded in the in-vivo biological processes such as tumorigenicity and morphogenesis, also can provide insights on the design of biomaterials, tissue engineering and organoid/organ-on-a-chips.   

Three-dimensional Packing of Curved Epithelia: Biology and Topology meet Physics

Building and shaping tissues and organs relies on the ability of epithelial cells to efficiently pack together. In this context, we recently produced a major breakthrough by showing that epithelial cells display a previously undescribed geometrical shape when tissues are subjected to bending (curvature): the scutoid [1]. This discovery has opened the door to a deeper understanding of morphogenesis. Yet, the consequences of this new paradigm in terms of the 3D cellular organization remains largely uncharacterized. Here we address this problem using a combination of experiments, mathematical analyses, computer simulations, and biophysical approaches. In that context we derive the "Flintstones' Law" [2]: the thickness and curvature of epithelial tubes are linked to the cellular connectivity of the tissue via energetic cues. This principle explains how the topological and physical constraints inherent to living matter contribute to build functional complex shapes and lead to the self-organization of tissues.

[1] P. Gómez-Gálvez et al., Scutoids are a geometrical solution to three- dimensional packing of epithelia, Nature Comm. 9, 2960 (2018)
[2] P. Gómez-Gálvez et al., A quantitative principle to understand 3D self-organization in epithelial tubes, EMBO J (under review)   

Topological analysis of multicellular structures

Recent advances in microscopy techniques make it possible to study the growth, dynamics and response of complex biological systems at single-cell resolution, from bacterial biofilms to tissues. When seeking to understand the formation and mechanical properties of these multicellular materials, the local spatial arrangement of their discrete cellular building blocks is of principal importance. To compare the similarity of crystals, we can compare lattice vectors or motifs, but when there is no crystal structure it is less obvious how one can reliably distinguish two amorphous yet structurally different materials. In this talk we introduce a topological distance between materials that needs only the coordinates of the centroid of each discrete object, and is based on the local graph structure around each centroid. Using this distance we will differentiate and classify structures formed from various ellipsoid and sphere packings, as well as biological cell data.   

Tissue-Tissue Interactions at Boundaries of Colliding Monolayers

Classic ‘wound healing’ studies in epithelial monolayers use a wound or barrier removal to induce and study collective migration, focusing on the migration rather than the ultimate collision and tissue healing. Here, we address this by comprehensively studying epithelial tissue-tissue interactions in homotypic tissues from the initial outgrowth of multiple tissues through collision until a single, mature tissue is formed. We show the boundary between two non-mixing tissues is directly modulated by their size, shape, and density, and the boundary varies over time until the newly fused tissue stabilizes. In addition to characterizing interactions and boundary dynamics between colliding tissues, we predict the resulting fused tissue forms using a simple computational model assuming isotropic growth, which is used to systematically design the final resulting “mosaic” from many growing tissues. Finally, we show that unexpected boundary dynamics occur at the confluence of three or more tissues coming together that can lead to surprising planar extrusions where one tissue pushes out between converging neighboring tissues resulting in long, stretched regions of tissues.   

Patterning Potential of Cell-cell signalling Molecules in Flowing Tissue

Cell motility and cell-cell signalling are expected to play important roles in determining the mechanics behind deformation and patterning in tissues. Modelling efforts have, thus far, treated these two processes separately. Experiments in recent years, however, suggest that both these processes could be tightly coupled.

Cell deformation depends on membrane and cytoskeletal elasticity, cell-cell adhesion and active forces. Cell-cell signalling occurs through signalling molecules. A large number of complex tissue behaviours are controlled by contact signalling. Such interactions can occur only between cells that are in physical contact, either directly at the junctions of adjacent cells or through cellular protrusions. It is as yet unclear how the spatial distribution these molecules or the kinetics of their interactions are influenced by the collective migration in tissues driven by cell motility.

We present a model which accounts for contact signalling between adjacent cells and between non-adjacent neighbours through long protrusions that occur along the direction of cell polarization. The spatial patterns that develop are observed to qualitatively depend on polarization of protrusions, cell motility and the relative strengths of adjacent and non-adjacent signalling interactions.