Buckling soft tensegrities: Fickle elasticity and configurational switching in living cells

Abstract

Tensegrity structures are special architectures made by floating compressed struts kept together by a continuous system of tensioned cables. Their existence in a mechanically stable form is decided by the possibility of finding geometrical configurations such that pre-stressed tendons and bars can ensure self-equilibrium of the forces transmitted through the elastic network, the overall stiffness of which finally depends on both the rigidity of the compressed elements and the cables' pre-stress. The multiplicity of shapes that tensegrity structures can assume and their intrinsic capability to be deployable and assembled, so storing (and releasing) elastic energy, have motivated their success as paradigm -pioneeringly proposed three decades ago by the intuition of Donald E. Ingber-to explain some underlying mechanisms regulating dynamics of living cells. The interlaced structure of the cell cytoskeleton, constituted by actin microfilaments, intermediate filaments and microtubules which continuously change their spatial organization and pre-stresses through polymerization/depolymerization processes, seems in fact to steer migration, adhesion and arXiv:1904.04610v1 [physics.bio-ph] 9 Apr 2019 cell division by obeying the tensegrity construct. Even though rough calculations lead to estimate discrepancies of less than one order of magnitude when comparing axial stiffness of actin filaments (cables) and microtubules (struts) and recent works have shown bent microtubules among stretched filaments, no one has yet tried to remove the standard hypothesis of rigid struts in tensegrity structures when used to idealize the cell cytoskeleton mechanical response. With reference to the 30-element tensegrity cell paradigm, we thus introduce both compressibility and bendability of the struts and accordingly rewrite the theory to simultaneously take into account geometrical non-linearity (i.e. large deformations) and hyper-elasticity of both tendons and bars, so abandoning the classical linear stress-strain constitutive assumptions. By relaxing the hypothesis of rigidity of the struts, we demonstrate that some quantitative confirmations and many related extreme and somehow counterintuitive mechanical behaviors actually exploited by cells for storing/releasing energy, resisting to applied loads and deforming by modulating their overall elasticity and shape through pre-stress changes and instability-guided configurational switching, can be all theoretically found. It is felt that the proposed new soft-strut tensegrity model could pave the way for a wider use of engineering models in cell mechanobiology and in designing bio-inspired materials and soft robots.

Insight into Mechanobiology: How Stem Cells Feel Mechanical Forces and Orchestrate Biological Functions

“…This is a consequence of cytoskeleton tension that is transduced into an equilibrium of opposing forces that are dispersed through the network of cytoskeletal filaments. Generally, tension is generated within the actomyosin contractile microfilaments and is counteracted by microtubules, which are able to resist the compression forces [10,16,17,18]. The Ingberg model has later been confirmed and improved by many other researcher groups [8,15,19,20,21,22].…”

Lyapunov stability of competitive cells dynamics in tumor mechanobiology

“…For these reasons, the study of the effects of solid stress on soft tissue homeostasis has been investigated both theoretically and experimentally, by observing the in vitro growth of confined multicellular spheroids [11][12][13][14] as well as by means of magnetic or mechanical actuators to apply forces on in vivo systems [2,15]. The underlying mechanisms transducing a mechanical cue into a biochemical signal are explained on the basis of some conformational changes and molecular pathways that modify cancer single-cell properties, which exhibit a different cytoskeletal stiffness as well as altered adhesion and motility capabilities [11,[16][17][18][19][20]. Therefore, the understanding of the mechano-responses of cancer systems, from single-cells to entire masses, could actually lead to innovative targeting and therapeutic strategies that, by exploiting the mechanical differences between tumor and host as a selectivity principle, provide the possibility to mechanically attack cancer cells by preserving the healthy surroundings [21][22][23].…”

Stacking sequences in composite laminates through design optimization

“…Lastly, the proposed procedure is applied to optimize the mechanical performances of carbon fiber reinforced polymer (CFRP) composite cylinders under high compression regimes, used as primary structural components for advanced applications in aerospace engineering. However, the generality of these results suggests their possible extension to many other applications in which the prevention of critical load conditions is crucial to ensure the functionality of the structure [23,37,39]. Here, design optimization leads to conceive a new possible optimal microstructural arrangement of the CFRP able to avoid critical stress conditions that are associated with the instability mechanisms observed in composites with standard fiber orientation.…”