Many types of animal cells exert active, contractile forces and mechanically deform their elastic substrate, to accomplish biological functions such as migration. These substrate deformations provide a mechanism in principle by which cells may sense other cells, leading to long-range mechanical inter–cell interactions and possible self-organization. Here, inspired by cell mechanobiology, we propose an active matter model comprising self-propelling particles that interact at a distance through their mutual deformations of an elastic substrate. By combining a minimal model for the motility of individual particles with a linear elastic model that accounts for substrate-mediated, inter–particle interactions, we examine emergent collective states that result from the interplay of motility and long-range elastic dipolar interactions. In particular, we show that particles self-assemble into flexible, motile chains which can cluster to form diverse larger-scale compact structures with polar order. By computing key structural and dynamical metrics, we distinguish between the collective states at weak and strong elastic interaction strength, as well as at low and high motility. We also show how these states are affected by confinement within a channel geometry–an important characteristic of the complex mechanical micro-environment inhabited by cells. Our model predictions may be generally applicable to active matter with dipolar interactions ranging from biological cells to synthetic colloids endowed with electric or magnetic dipole moments.
more »
« less
Optimal mechanical interactions direct multicellular network formation on elastic substrates
Cells self-organize into functional, ordered structures during tissue morphogenesis, a process that is evocative of colloidal self-assembly into engineered soft materials. Understanding how intercellular mechanical interactions may drive the formation of ordered and functional multicellular structures is important in developmental biology and tissue engineering. Here, by combining an agent-based model for contractile cells on elastic substrates with endothelial cell culture experiments, we show that substrate deformation–mediated mechanical interactions between cells can cluster and align them into branched networks. Motivated by the structure and function of vasculogenic networks, we predict how measures of network connectivity like percolation probability and fractal dimension as well as local morphological features including junctions, branches, and rings depend on cell contractility and density and on substrate elastic properties including stiffness and compressibility. We predict and confirm with experiments that cell network formation is substrate stiffness dependent, being optimal at intermediate stiffness. We also show the agreement between experimental data and predicted cell cluster types by mapping a combined phase diagram in cell density substrate stiffness. Overall, we show that long-range, mechanical interactions provide an optimal and general strategy for multicellular self-organization, leading to more robust and efficient realizations of space-spanning networks than through just local intercellular interactions.
more » « less- PAR ID:
- 10527306
- Publisher / Repository:
- National Academy of Sciences
- Date Published:
- Journal Name:
- Proceedings of the National Academy of Sciences
- Volume:
- 120
- Issue:
- 45
- ISSN:
- 0027-8424
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
null (Ed.)Cells in vivo generate mechanical traction on the surrounding 3D extracellular matrix (ECM) and neighboring cells. Such traction and biochemical cues may remodel the matrix, e.g., increase stiffness, which, in turn, influences cell functions and forces. This dynamic reciprocity mediates development and tumorigenesis. Currently, there is no method available to directly quantify single-cell forces and matrix remodeling in 3D. Here, we introduce a method to fulfill this long-standing need. We developed a high-resolution microfabricated sensor that hosts a 3D cell-ECM tissue formed by self-assembly. This sensor measures cell forces and tissue stiffness and can apply mechanical stimulation to the tissue. We measured single and multicellular force dynamics of fibroblasts (3T3), human colon (FET) and lung (A549) cancer cells, and cancer-associated fibroblasts (CAF05) with 1-nN resolution. Single cells show notable force fluctuations in 3D. FET/CAF coculture system, mimicking cancer tumor microenvironment, increased tissue stiffness by three times within 24 hours.more » « less
-
Local substrate stiffness is one of the major mechanical inputs for tissue organization during its development and remodeling. It is widely recognized that adherent cells use transmembrane proteins (integrins) at focal adhesions to translate ECM mechanical cues into intracellular bioprocess. Here we show that epithelial cells respond to substrate stiffening primarily via actin cytoskeleton organization, that requires activation of mechanosensitive Piezo1 channels. Piezo1 Knockdown cells eliminated the actin stress fibers that formed on stiff substrates, while it had minimal effect on cell morphology and spreading area. Inhibition of Piezo1 channels with GsMTx4 also significantly reduced stiffness-induced F-actin reorganization, suggesting Piezo1 mediated cation current plays a role. Activation of Piezo1 channels with specific agonist (Yoda1) resulted in thickening of F-actin fibers and enlargement of FAs on stiffer substrates, whereas it did not affect the formation of nascent FAs that facilitate spreading on the soft substrates. These results demonstrate that Piezo1 functions as a force sensor that couples with actin cytoskeleton to distinguish the substrate stiffness and facilitate epithelial adaptive remodeling.more » « less
-
We introduce an amorphous mechanical metamaterial inspired by how cells pack in biological tissues. The spatial heterogeneity in the local stiffness of these materials has been recently shown to impact the mechanics of confluent biological tissues and cancer tumor invasion. Here we use this bio-inspired structure as a design template to construct mechanical metamaterials and show that this heterogeneity can give rise to amorphous cellular solids with large, tunable acoustic bandgaps. Unlike acoustic crystals with periodic structures, the bandgaps here are directionally isotropic and robust to defects due to their complete lack of positional order. Possible ways to manipulate bandgaps are explored with a combination of the tissue-level elastic modulus and local stiffness heterogeneity of cells. To further demonstrate the existence of bandgaps, we dynamically perturb the system with an external sinusoidal wave in the perpendicular and horizontal directions. The transmission coefficients are calculated and show valleys that coincide with the location of bandgaps. Experimentally this design should lead to the engineering of self- assembled rigid acoustic structures with full bandgaps that can be controlled via mechanical tuning and promote applications in a broad area from vibration isolations to mechanical waveguides.more » « less
-
more » « less
The spongy mesophyll is a complex, porous tissue found in plant leaves that enables carbon capture and provides mechanical stability. Unlike many other biological tissues, which remain confluent throughout development, the spongy mesophyll must develop from an initially confluent tissue into a tortuous network of cells with a large proportion of intercellular airspace. How the airspace in the spongy mesophyll develops while the tissue remains mechanically stable is unknown. Here, we use computer simulations of deformable polygons to develop a purely mechanical model for the development of the spongy mesophyll tissue. By stipulating that cell wall growth and remodelling occurs only near void space, our computational model is able to recapitulate spongy mesophyll development observed in
Arabidopsis thaliana leaves. We find that robust generation of pore space in the spongy mesophyll requires a balance of cell growth, adhesion, stiffness and tissue pressure to ensure cell networks become porous yet maintain mechanical stability. The success of this mechanical model of morphogenesis suggests that simple physical principles can coordinate and drive the development of complex plant tissues like the spongy mesophyll.
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1073/pnas.2301555120
