Toward a generalised tensegrity model describing the mechanical behaviour of the cytoskeleton structure

Analysis of the Adherent Cell Response to the Substrate Stiffness Using Tensegrity

Cell's shape is dependent on the cytoskeleton mechanical properties. Hybrid models were developed that combine the discrete structure for the cytoskeleton and continuum parts for other cell organelles. Tensegrity-based structures that consist of tensile and compression elements are useful models to understand the cytoskeleton mechanical behavior. In this study, we are looking to examine the reaction of the cell to a variety of substrate stiffnesses and explain the relationship between cell behavior and substrate mechanical properties. However, which tensegrity structure is appropriate for modeling a living cell? Is the structure's complexity play a major role? We used two spherical tensegrities with different complexities to assess the impact of the structure on the cell's mechanical response versus substrate's stiffness. Six- and twelve-strut tensegrities together with membrane, cytoplasm, nucleoskeleton, and nucleus envelope were assembled in Abaqus package to create a hybrid cell model. A compressive load was applied to the cell model and the reaction forces versus deflection curves were analyzed for number of substrate stiffness values. By analyzing the difference due to two different tensegrities it became clear that the lower density structure is a better choice for modeling stiffer cells. It was also found that the six-strut tensegrity is sensitive to higher range of substrate stiffness.

Model-based investigation of elasticity and spectral exponent from atomic force microscopy and electrophysiology in normal versus Schizophrenia human cerebral organoids

The physiological origin of the aperiodic signal present in the electrophysiological recordings, called l/f neural noise, is unknown; nevertheless, it has been associated with health and disease. The power spectrum slope, -α in 1/f^α, has been postulated to be related to the dynamic balance between excitation (E) and inhibition (I). Our study found that human cerebral organoids grown from induced pluripotent stem cells (iPSCs) from Schizophrenia patients (SCZ) showed structural changes associated with altered elasticity compared to that of the normal cerebral organoids. Furthermore, mitochondrial drugs modulated the elasticity in SCZ that was found related to the changes in the spectral exponent. Therefore, we developed an electro-mechanical model that related the microtubular-actin tensegrity structure to the elasticity and the 1/f^α noise. Model-based analysis showed that a decrease in the number and length of the constitutive elements in the tensegrity structure decreased its elasticity and made the spectral exponent more negative while thermal white noise will make α = 0.. Based on the microtubularactin model and the cross-talk in structural (elasticity) and functional (electrophysiology) response, aberrant mitochondrial dynamics in SCZ are postulated to be related to the deficits in mitochondrial-cytoskeletal interactions for long-range transport of mitochondria to support synaptic activity for E/I balance. Clinical Relevance-Our experimental data and modeling present a structure-function relationship between mechanical elasticity and electrophysiology of human cerebral organoids that differentiated SCZ patients from normal controls.

Stem cell mechanical behaviour modelling: substrate's curvature influence during adhesion

Recent experiments hint that adherent cells are sensitive to their substrate curvature. It is already well known that cells behaviour can be regulated by the mechanical properties of their environment. However, no mechanisms have been established regarding the influence of cell-scale curvature of the substrate. Using a numerical cell model, based on tensegrity structures theory and the non-smooth contact dynamics method, we propose to investigate the mechanical state of adherent cells on concave and convex hemispheres. Our mechanical cell model features a geometrical description of intracellular components, including the cell membrane, the focal adhesions, the cytoskeleton filament networks, the stress fibres, the microtubules, the nucleus membrane and the nucleoskeleton. The cell model has enabled us to analyse the evolution of the mechanical behaviour of intracellular components with varying curvature radii and with the removal of part of these components. We have observed the influence of the convexity of the substrate on the cell shape, the cytoskeletal force networks as well as on the nucleus strains. The more convex the substrate, the more tensed the stress fibres and the cell membrane, the more compressed the cytosol and the microtubules, leading to a stiffer cell. Furthermore, the more concave the substrate, the more stable and rounder the nucleus. These findings achieved using a verified virtual testing methodology, in particular regarding the nucleus stability, might be of significant importance with respect to the division and differentiation of mesenchymal stem cells. These results can also bring some hindsights on cell migration on curved substrates.

In silico CDM model sheds light on force transmission in cell from focal adhesions to nucleus

Cell adhesion is crucial for many types of cell, conditioning differentiation, proliferation, and protein synthesis. As a mechanical process, cell adhesion involves forces exerted by the cytoskeleton and transmitted by focal adhesions to extracellular matrix. These forces constitute signals that infer specific biological responses. Therefore, analyzing mechanotransduction during cell adhesion could lead to a better understanding of the mechanobiology of adherent cells. For instance this may explain how, the shape of adherent stem cells influences their differentiation or how the stiffness of the extracellular matrix affects adhesion strength. To assess the mechanical signals involved in cell adhesion, we computed intracellular forces using the Cytoskeleton Divided Medium model in endothelial cells adherent on micropost arrays of different stiffnesses. For each cell, focal adhesion location and forces measured by micropost deflection were used as an input for the model. The cytoskeleton and the nucleoskeleton were computed as systems of multiple tensile and compressive interactions. At the end of computation, the systems respected mechanical equilibrium while exerting the exact same traction force intensities on focal adhesions as the observed cell. The results indicate that not only the level of adhesion forces, but also the shape of the cell has an influence on intracellular tension and on nucleus strain. The combination of experimental micropost technology with the present CDM model constitutes a tool able to estimate the intracellular forces.

Complexity of the tensegrity structure for dynamic energy and force distribution of cytoskeleton during cell spreading

Cytoskeleton plays important roles in intracellular force equilibrium and extracellular force transmission from/to attaching substrate through focal adhesions (FAs). Numerical simulations of intracellular force distribution to describe dynamic cell behaviors are still limited. The tensegrity structure comprises tension-supporting cables and compression-supporting struts that represent the actin filament and microtubule respectively, and has many features consistent with living cells. To simulate the dynamics of intracellular force distribution and total stored energy during cell spreading, the present study employed different complexities of the tensegrity structures by using octahedron tensegrity (OT) and cuboctahedron tensegrity (COT). The spreading was simulated by assigning specific connection nodes for radial displacement and attachment to substrate to form FAs. The traction force on each FA was estimated by summarizing the force carried in sounding cytoskeletal elements. The OT structure consisted of 24 cables and 6 struts and had limitations soon after the beginning of spreading by declining energy stored in struts indicating the abolishment of compression in microtubules. The COT structure, double the amount of cables and struts than the OT structure, provided sufficient spreading area and expressed similar features with documented cell behaviors. The traction force pointed inward on peripheral FAs in the spread out COT structure. The complex structure in COT provided further investigation of various FA number during different spreading stages. Before the middle phase of spreading (half of maximum spreading area), cell attachment with 8 FAs obtained minimized cytoskeletal energy. The maximum number of 12 FAs in the COT structure was required to achieve further spreading. The stored energy in actin filaments increased as cells spread out, while the energy stored in microtubules increased at initial spreading, peaked in middle phase, and then declined as cells reached maximum spreading. The dynamic flows of energy in struts imply that microtubules contribute to structure stabilization.

Nature of motor control: perspectives and issues

Four perspectives on motor control provide the framework for developing a comprehensive theory of motor control in biological systems. The four perspectives, of decreasing orthodoxy, are distinguished by their sources of inspiration: neuroanatomy, robotics, self-organization, and ecological realities. Twelve major issues that commonly constrain (either explicitly or implicitly) the understanding of the control and coordination of movement are identified and evaluated within the framework of the four perspectives. The issues are as follows: (1) Is control strictly neural? (2) Is there a divide between planning and execution? (3) Does control entail a frequently involved knowledgeable executive? (4) Do analytical internal models mediate control? (5) Is anticipation necessarily model dependent? (6) Are movements preassembled? (7) Are the participating components context independent? (8) Is force transmission strictly myotendinous? (9) Is afference a matter of local linear signaling? (10) Is neural noise an impediment? (11) Do standard variables (of mechanics and physiology) suffice? (12) Is the organization of control hierarchical?

Action and perception at the level of synergies

Meeting the challenge of assembling coherent organizations of very many muscles characterizes a functional level of biological movement systems referred to as the level of muscular-articular links or synergies. The present article examines the issues confronting the forming, regulating, and ordering of synergies and the hypothesized principles, both classical and contemporary, which resolve them. A primary goal of the article is to highlight the abstractness of the concepts and tools required to understand the level's action-perception competence. Coverage is given to symmetry groups, task space, order parameters, metastability, biotensegrity, allometric scaling, and impredicative definitions.

Active mechanical stabilization of the viscoplastic intracellular space of Dictyostelia cells by microtubule-actin crosstalk

The micro-viscoelasticity of the intracellular space of Dictyostelium discoideum cells is studied by evaluating the intracellular transport of magnetic force probes and their viscoelastic responses to force pulses of 20-700 pN. The role of the actin cortex, the microtubule (MT) aster and their crosstalk is explored by comparing the behaviour of wild-type cells, myosin II null mutants, latrunculin A and benomyl treated cells. The MT coupled beads perform irregular local and long range directed motions which are characterized by measuring their velocity distributions (P(v)). The correlated motion of the MT and the centrosome are evaluated by microfluorescence of GFP-labelled MTs. P(v) can be represented by log-normal distributions with long tails and it is determined by random sweeping motions (v approximately 0.5 microm/s) of the MTs (caused by tangential forces on the filament ends coupled to the actin cortex) and by intermittent bead transports parallel to the MTs (v(max) approximately 1.5 microm/s). The tails are due to spontaneous filament deflections (with speeds up to 10 microm/s) attributed to pre-stressing of the MT by local cortical tensions, generated by dynactin motors generating plus-end directed forces in the MTs. The viscoelastic responses are strongly non-linear and are mostly directed opposite or perpendicular to the force, showing that the cytoplasm behaves as an active viscoplastic body with time and force dependent drag coefficients. Nano-Newton loads exerted on the soft MT are balanced by traction forces arising at the MT ends coupled to the actin cortex and the centrosome, respectively. The mechanical coupling between the soft microtubules and the viscoelastic actin cortex provides cells with high mechanical stability despite the softness of the cytoplasm.

Divided medium-based model for analyzing the dynamic reorganization of the cytoskeleton during cell deformation

Cell deformability and mechanical responses of living cells depend closely on the dynamic changes in the structural architecture of the cytoskeleton (CSK). To describe the dynamic reorganization and the heterogeneity of the prestressed multi-modular CSK, we developed a two-dimensional model for the CSK which was taken to be a system of tension and compression interactions between the nodes in a divided medium. The model gives the dynamic reorganization of the CSK consisting of fast changes in connectivity between nodes during medium deformation and the resulting mechanical behavior is consistent with the strain-hardening and prestress-induced stiffening observed in cells in vitro. In addition, the interaction force networks which occur and balance to each other in the model can serve to identify the main CSK substructures: cortex, stress fibers, intermediate filaments, microfilaments, microtubules and focal adhesions. Removing any of these substructures results in a loss of integrity in the model and a decrease in the prestress and stiffness, and suggests that the CSK substructures are highly interdependent. The present model may therefore provide a useful tool for understanding the cellular processes involving CSK reorganization, such as mechanotransduction, migration and adhesion processes.

Cellular mechanotransduction: putting all the pieces together again

Analysis of cellular mechanotransduction, the mechanism by which cells convert mechanical signals into biochemical responses, has focused on identification of critical mechanosensitive molecules and cellular components. Stretch-activated ion channels, caveolae, integrins, cadherins, growth factor receptors, myosin motors, cytoskeletal filaments, nuclei, extracellular matrix, and numerous other structures and signaling molecules have all been shown to contribute to the mechanotransduction response. However, little is known about how these different molecules function within the structural context of living cells, tissues, and organs to produce the orchestrated cellular behaviors required for mechanosensation, embryogenesis, and physiological control. Recent work from a wide range of fields reveals that organ, tissue, and cell anatomy are as important for mechanotransduction as individual mechanosensitive proteins and that our bodies use structural hierarchies (systems within systems) composed of interconnected networks that span from the macroscale to the nanoscale in order to focus stresses on specific mechanotransducer molecules. The presence of isometric tension (prestress) at all levels of these multiscale networks ensures that various molecular scale mechanochemical transduction mechanisms proceed simultaneously and produce a concerted response. Future research in this area will therefore require analysis, understanding, and modeling of tensionally integrated (tensegrity) systems of mechanochemical control.

Topographically induced direct cell mechanotransduction

This review is designed to introduce the cytoskeleton and then discuss how mechanical forces may be transduced to the cell nucleus. In addition to this, it also tries to explain current thinking as to how the nucleus turns these mechanical cues into gene changes and is especially interested in mechanotransduction arising from topographically induced morphological changes, specifically nanotopography. Thus, this review also describes cell responses to topography.

The Aqueous Outflow System as a Mechanical Pump

PURPOSE

To describe a new aqueous outflow model involving a mechanical pump.

MATERIALS AND METHODS

Laboratory materials include human and monkey eyes; methods include the dissecting microscope, light microscopy, scanning electron microscopy, transmission electron microscopy, and tracer studies. Clinical methods involve human subject slit lamp, gonioscopy, and operating microscope examination.

RESULTS

Laboratory evidence demonstrates that aqueous outflow tissues are responsive to intraocular pressure induced deformation. Deformation occurs in response to small pressure gradients. Laboratory evidence also demonstrates the presence of valves discharging aqueous to Schlemm's canal. The laboratory model predicts pulsatile aqueous discharge in vivo. Clinical in vivo evidence demonstrates pulsatile aqueous flow from the anterior chamber into Schlemm's canal, from Schlemm's canal into collector channels, and from Schlemm's canal into aqueous and episcleral veins, all synchronous with the ocular pulse.

CONCLUSIONS

Aqueous outflow tissue deformation caused by normal intraocular pressure transients induces pulsatile one-way discharge of aqueous to the vascular system. The model identifies biomechanical coupling of intraocular pressure with aqueous outflow tissue deformation and also sites of high flow capable of inducing shear stress. These mechanotransduction mechanisms, well characterized as a means of controlling pressure and flow in the vascular system, also provide a means of regulatory feedback to control intraocular pressure and aqueous flow.