Isostaticity and controlled force transmission in the cytoskeleton: A model awaiting experimental evidence

Microtubules as a signal hub for axon growth in response to mechanical force

Microtubules are highly polar structures and are characterized by high anisotropy and stiffness. In neurons, they play a key role in the directional transport of vesicles and organelles. In the neuronal projections called axons, they form parallel bundles, mostly oriented with the plus-end towards the axonal termination. Their physico-chemical properties have recently attracted attention as a potential candidate in sensing, processing and transducing physical signals generated by mechanical forces. Here, we discuss the main evidence supporting the role of microtubules as a signal hub for axon growth in response to a traction force. Applying a tension to the axon appears to stabilize the microtubules, which, in turn, coordinate a modulation of axonal transport, local translation and their cross-talk. We speculate on the possible mechanisms modulating microtubule dynamics under tension, based on evidence collected in neuronal and non-neuronal cell types. However, the fundamental question of the causal relationship between these mechanisms is still elusive because the mechano-sensitive element in this chain has not yet been identified.

'Phase transitions' in bacteria - From structural transitions in free living bacteria to phenotypic transitions in bacteria within biofilms

Phase transitions are common in inanimate systems and have been studied extensively in natural sciences. Less explored are the rich transitions that take place at the micro- and nano-scales in biological systems. In conventional phase transitions, large-scale properties of the media change discontinuously in response to continuous changes in external conditions. Such changes play a significant role in the dynamic behaviours of organisms. In this review, we focus on some transitions in both free-living and biofilms of bacteria. Particular attention is paid to the transitions in the flagellar motors and filaments of free-living bacteria, in cellular gene expression during the biofilm growth, in the biofilm morphology transitions during biofilm expansion, and in the cell motion pattern transitions during the biofilm formation. We analyse the dynamic characteristics and biophysical mechanisms of these phase transition phenomena and point out the parallels between these transitions and conventional phase transitions. We also discuss the applications of some theoretical and numerical methods, established for conventional phase transitions in inanimate systems, in bacterial biofilms.

Review of cellular mechanotransduction on micropost substrates

As physical entities, living cells can sense and respond to various stimulations within and outside the body through cellular mechanotransduction. Any deviation in cellular mechanotransduction will not only undermine the orchestrated regulation of mechanical responses, but also lead to the breakdown of their physiological function. Therefore, a quantitative study of cellular mechanotransduction needs to be conducted both in experiments and in computational simulations to investigate the underlying mechanisms of cellular mechanotransduction. In this review, we present an overview of the current knowledge and significant progress in cellular mechanotransduction via micropost substrates. In the aspect of experimental studies, we summarize significant experimental progress and place an emphasis on the coupled relationship among cellular spreading, focal adhesion and contractility as well as the influence of substrate properties on force-involved cellular behaviors. In the other aspect of computational investigations, we outline a coupled framework including the biochemically motivated stress fiber model and thermodynamically motivated adhesion model and present their predicted biomechanical responses and then compare predicted simulation results with experimental observations to further explore the mechanisms of cellular mechanotransduction. At last, we discuss the future perspectives both in experimental technologies and in computational models, as well as facing challenges in the area of cellular mechanotransduction.

Model of cellular mechanotransduction via actin stress fibers

Mechanical stresses due to blood flow regulate vascular endothelial cell structure and function and play a key role in arterial physiology and pathology. In particular, the development of atherosclerosis has been shown to correlate with regions of disturbed blood flow where endothelial cells are round and have a randomly organized cytoskeleton. Thus, deciphering the relation between the mechanical environment, cell structure, and cell function is a key step toward understanding the early development of atherosclerosis. Recent experiments have demonstrated very rapid (∼100 ms) and long-distance (∼10 μm) cellular mechanotransduction in which prestressed actin stress fibers play a critical role. Here, we develop a model of mechanical signal transmission within a cell by describing strains in a network of prestressed viscoelastic stress fibers following the application of a force to the cell surface. We find force transmission dynamics that are consistent with experimental results. We also show that the extent of stress fiber alignment and the direction of the applied force relative to this alignment are key determinants of the efficiency of mechanical signal transmission. These results are consistent with the link observed experimentally between cytoskeletal organization, mechanical stress, and cellular responsiveness to stress. Based on these results, we suggest that mechanical strain of actin stress fibers under force constitutes a key link in the mechanotransduction chain.

Resistance to alveolar shape change limits range of force propagation in lung parenchyma

We have recently shown that if the lung parenchyma is modeled in 2 dimensions as a network of springs arranged in a pattern of repeating hexagonal cells, the distortional forces around a contracting airway propagate much further from the airway wall than classic continuum theory predicts. In the present study we tested the hypothesis that this occurs because of the negligible shear modulus of a hexagonal spring network. We simulated the narrowing of an airway embedded in a hexagonal network of elastic alveolar walls when the hexagonal cells of the network offered some resistance to a change in shape. We found that as the forces resisting shape change approach about 10% of the forces resisting length change of an individual spring the range of distortional force propagation in the spring network fell of rapidly as in an elastic continuum. We repeated these investigations in a 3-dimensional spring network composed of space-filling polyhedral cells and found similar results. This suggests that force propagation away from a point of local parenchymal distortion also falls off rapidly in real lung tissue.

Tensegrity, cellular biophysics, and the mechanics of living systems

The recent convergence between physics and biology has led many physicists to enter the fields of cell and developmental biology. One of the most exciting areas of interest has been the emerging field of mechanobiology that centers on how cells control their mechanical properties, and how physical forces regulate cellular biochemical responses, a process that is known as mechanotransduction. In this article, we review the central role that tensegrity (tensional integrity) architecture, which depends on tensile prestress for its mechanical stability, plays in biology. We describe how tensional prestress is a critical governor of cell mechanics and function, and how use of tensegrity by cells contributes to mechanotransduction. Theoretical tensegrity models are also described that predict both quantitative and qualitative behaviors of living cells, and these theoretical descriptions are placed in context of other physical models of the cell. In addition, we describe how tensegrity is used at multiple size scales in the hierarchy of life—from individual molecules to whole living organisms—to both stabilize three-dimensional form and to channel forces from the macroscale to the nanoscale, thereby facilitating mechanochemical conversion at the molecular level.

Mechanics of biological networks: from the cell cytoskeleton to connective tissue

From the cell cytoskeleton to connective tissues, fibrous networks are ubiquitous in metazoan life as the key promoters of mechanical strength, support and integrity. In recent decades, the application of physics to biological systems has made substantial strides in elucidating the striking mechanical phenomena observed in such networks, explaining strain stiffening, power law rheology and cytoskeletal fluidisation - all key to the biological function of individual cells and tissues. In this review we focus on the current progress in the field, with a primer into the basic physics of individual filaments and the networks they form. This is followed by a discussion of biological networks in the context of a broad spread of recent in vitro and in vivo experiments.

Influence of parenchymal heterogeneity on airway-parenchymal interdependence

To estimate the influence of parenchymal heterogeneities on airway-parenchymal interdependence, we considered a circular airway embedded within elastic parenchyma modeled as (1) a hexagonal spring network, (2) a triangular spring network, or (3) a continuum. The deformation in the parenchyma due to active airway contraction was simulated using the finite element method. Random perturbations of elastic moduli in the parenchyma did not significantly affect the overall pattern of force transmission. By contrast, when elastic moduli were increased along a path projecting radially outward from the airway, the hexagonal spring network model predicted significantly increased force along this line as the airway contracted, but this was not observed in other two models. These results indicate that tissue heterogeneities generally have minimal effect on the global nature of airway-parenchymal interdependence. However, in the exceptional circumstance of scar tissue aligned radially from the airway wall, parenchymal distortion forces may propagate much farther from the airway wall than was previously thought.

Toll-like receptor activation and mechanical force stimulation promote the secretion of matrix metalloproteinases 1, 3 and 10 of human periodontal fibroblasts via p38, JNK and NF-kB

Matrix metalloproteinases (MMPs) are known to play a key role during orthodontic treatment leading to periodontal remodelling and tooth movement. MMPs may be induced by mechanical forces. However, the role played by toll-like receptors (TLRs) in modulating the effects of the mechanical force on periodontal fibroblasts is not known. To investigate the interaction between mechanical force and TLR stimulation, primary cultures of human periodontal fibroblasts were submitted to centrifugation in the presence of LPS and Pam3Cys, which are known TLR-4 and TLR-2 ligands, respectively. The expression of MMP-1, -2, -3, -8, -9, -10 and -13; TIMP (Tissue Inhibitor of Metalloproteinases) -1, -2 and -4; TNF-α (Tumour Necrosis Factor alpha); IL-1β (Interleukin 1 beta); ERK 1/2 (Extracellular Signal-Regulated Kinase 1/2); p38; JNK (c-jun N-terminal Kinase); IRAK1 (Interleukin-1 Receptor-Associated Kinase); and NF-κB (Nuclear Factor kappa B) were measured by antibody array, ELISA and immunoblotting methods. The activation of TLRs associated with centrifugation induced an increase in the secretion of MMPs 1, 3 and 10, with no increase in TNF-α or IL-1β. An increase in the phosphorylation of the MAP kinases p38 and JNK and the transcription factor NF-κB, without an increase in TIMPs was also observed. These findings suggest that the secretion of MMPs by cultured periodontal fibroblasts that is induced by combined TLR activation and mechanical force stimulation is regulated via the p38, JNK and NF-κB pathways. The increased secretion of MMPs by TLR activation may be an important factor that should be considered during orthodontic treatment.

Quantification of intracellular mitochondrial displacements in response to nanomechanical forces

Mechanical stress affects various aspects of cell behavior, including cell growth, morphology, differentiation, and genetic expression. Here, we describe a method to quantify the intracellular mechanical response to an extracellular mechanical perturbation, specifically the displacement of mitochondria. A combined fluorescent-atomic force microscope (AFM) was used to simultaneously produce well-defined nanomechanical stimulation to a living cell while optically recording the real-time displacement of fluorescently labeled mitochondria. A single-particle tracking (SPT) approach was then applied in order to quantify the two-dimensional displacement of mitochondria in response to local forces.

Continuum vs. spring network models of airway-parenchymal interdependence

The outward tethering forces exerted by the lung parenchyma on the airways embedded within it are potent modulators of the ability of the airway smooth muscle to shorten. Much of our understanding of these tethering forces is based on treating the parenchyma as an elastic continuum; yet, on a small enough scale, the lung parenchyma in two dimensions would seem to be more appropriately described as a discrete spring network. We therefore compared how the forces and displacements in the parenchyma surrounding a contracting airway are predicted to differ depending on whether the parenchyma is modeled as an elastic continuum or as a spring network. When the springs were arranged hexagonally to represent alveolar walls, the predicted parenchymal stresses and displacements propagated substantially farther away from the airway than when the springs were arranged in a triangular pattern or when the parenchyma was modeled as a continuum. Thus, to the extent that the parenchyma in vivo behaves as a hexagonal spring network, our results suggest that the range of interdependence forces due to airway contraction may have a greater influence than was previously thought.

Stem cell differentiation indicated by noninvasive photonic characterization and fractal analysis of subcellular architecture

We hypothesised that global structural changes in stem cells would manifest with differentiation, and that these changes would be observable with light scattering microscopy. Analysed with a fractal dimension formalism, we observed significant structural changes in differentiating human mesenchymal stem cells within one day after induction, earlier than could be detected by gene expression profiling. Moreover, light scattering microscopy is entirely non-perturbative, so the same sample could be monitored throughout the differentiation process. We explored one possible mechanism, chromatin remodelling, to account for the changes we observed. Correlating with the staining of HP1α, a heterochromatin protein, we applied novel microscopy methods and fractal analysis to monitor the plastic dynamics of chromatin within stem cell nuclei. We showed that the level of chromatin condensation changed during differentiation, and provide one possible explanation for the changes seen with the light scattering method. These results lend physical insight into stem cell differentiation while providing physics-based methods for non-invasive detection of the differentiation process.

Stress transmission within the cell

An outstanding problem in cell biology is how cells sense mechanical forces and how those forces affect cellular functions. During past decades, it has become evident that the deformable cytoskeleton (CSK), an intracellular network of various filamentous biopolymers, provides a physical basis for transducing mechanical signals into biochemical responses. To understand how mechanical forces regulate cellular functions, it is necessary to first understand how the CSK develops mechanical stresses in response to applied forces, and how those stresses are propagated through the CSK where various signaling molecules are immobilized. New experimental techniques have been developed to quantify cytoskeletal mechanics, which together with new computational approaches have given rise to new theories and models for describing mechanics of living cells. In this article, we discuss current understanding of cell biomechanics by focusing on the biophysical mechanisms that are responsible for the development and transmission of mechanical stresses in the cell and their effect on cellular functions. We compare and contrast various theories and models of cytoskeletal mechanics, emphasizing common mechanisms that those theories are built upon, while not ignoring irreconcilable differences. We highlight most recent advances in the understanding of mechanotransduction in the cytoplasm of living cells and the central role of the cytoskeletal prestress in propagating mechanical forces along the cytoskeletal filaments to activate cytoplasmic enzymes. It is anticipated that advances in cell mechanics will help developing novel therapeutics to treat pulmonary diseases like asthma, pulmonary fibrosis, and chronic obstructive pulmonary disease.

Simulating the formation of keratin filament networks by a piecewise-deterministic Markov process

Keratin intermediate filament networks are part of the cytoskeleton in epithelial cells. They were found to regulate viscoelastic properties and motility of cancer cells. Due to unique biochemical properties of keratin polymers, the knowledge of the mechanisms controlling keratin network formation is incomplete. A combination of deterministic and stochastic modeling techniques can be a valuable source of information since they can describe known mechanisms of network evolution while reflecting the uncertainty with respect to a variety of molecular events. We applied the concept of piecewise-deterministic Markov processes to the modeling of keratin network formation with high spatiotemporal resolution. The deterministic component describes the diffusion-driven evolution of a pool of soluble keratin filament precursors fueling various network formation processes. Instants of network formation events are determined by a stochastic point process on the time axis. A probability distribution controlled by model parameters exercises control over the frequency of different mechanisms of network formation to be triggered. Locations of the network formation events are assigned dependent on the spatial distribution of the soluble pool of filament precursors. Based on this modeling approach, simulation studies revealed that the architecture of keratin networks mostly depends on the balance between filament elongation and branching processes. The spatial distribution of network mesh size, which strongly influences the mechanical characteristics of filament networks, is modulated by lateral annealing processes. This mechanism which is a specific feature of intermediate filament networks appears to be a major and fast regulator of cell mechanics.

Mitochondrial displacements in response to nanomechanical forces

Mechanical stress affects and regulates many aspects of the cell, including morphology, growth, differentiation, gene expression and apoptosis. In this study we show how mechanical stress perturbs the intracellular structures of the cell and induces mechanical responses. In order to correlate mechanical perturbations to cellular responses, we used a combined fluorescence-atomic force microscope (AFM) to produce well defined nanomechanical perturbations of 10 nN while simultaneously tracking the real-time motion of fluorescently labelled mitochondria in live cells. The spatial displacement of the organelles in response to applied loads demonstrates the highly dynamic mechanical response of mitochondria in fibroblast cells. The average displacement of all mitochondrial structures analysed showed an increase of approximately 40%, post-perturbation ( approximately 160 nm in comparison to basal displacements of approximately 110 nm). These results show that local forces can produce organelle displacements at locations far from the initial point of contact (up to approximately 40 microm). In order to examine the role of the cytoskeleton in force transmission and its effect on mitochondrial displacements, both the actin and microtubule cytoskeleton were disrupted using Cytochalasin D and Nocodazole, respectively. Our results show that there is no significant change in mitochondrial displacement following indentation after such treatments. These results demonstrate the role of the cytoskeleton in force transmission through the cell and on mitochondrial displacements. In addition, it is suggested that care must be taken when performing mechanical experiments on living cells with the AFM, as these local mechanical perturbations may have significant structural and even biochemical effects on the cell.

Magnetic microposts for mechanical stimulation of biological cells: fabrication, characterization, and analysis

Cells use force as a mechanical signal to sense and respond to their microenvironment. Understanding how mechanical forces affect living cells requires the development of tool sets that can apply nanoscale forces and also measure cellular traction forces. However, there has been a lack of techniques that integrate actuation and sensing components to study force as a mechanical signal. Here, we describe a system that uses an array of elastomeric microposts to apply external forces to cells through cobalt nanowires embedded inside the microposts. We first biochemically treat the posts' surfaces to restrict cell adhesion to the posts' tips. Then by applying a uniform magnetic field (B<0.3 T), we induce magnetic torque on the nanowires that is transmitted to a cell's adhesion site as an external force. We have achieved external forces of up to 45 nN, which is in the upper range of current nanoscale force-probing techniques. Nonmagnetic microposts, similarly prepared but without nanowires, surround the magnetic microposts and are used to measure the traction forces and changes in cell mechanics. We record the magnitude and direction of the external force and the traction forces by optically measuring the deflection of the microposts, which linearly deflect as cantilever springs. With this approach, we can measure traction forces before and after force stimulation in order to monitor cellular response to forces. We present the fabrication methods, magnetic force characterization, and image analysis techniques used to achieve the measurements.

Cell and biomolecular mechanics in silico

Recent developments in computational cell and biomolecular mechanics have provided valuable insights into the mechanical properties of cells, subcellular components and biomolecules, while simultaneously complementing new experimental techniques used for deciphering the structure-function paradigm in living cells. These computational approaches have direct implications in understanding the state of human health and the progress of disease and can therefore aid immensely in the diagnosis and treatment of diseases. We provide an overview of the computational approaches that are currently used in understanding various aspects of cell and bimolecular mechanics. Our emphasis is on state-of-the-art techniques and the progress made in addressing key challenges in biomechanics.

Magnetic microposts as an approach to apply forces to living cells

Cells respond to mechanical forces whether applied externally or generated internally via the cytoskeleton. To study the cellular response to forces separately, we applied external forces to cells via microfabricated magnetic posts containing cobalt nanowires interspersed among an array of elastomeric posts, which acted as independent sensors to cellular traction forces. A magnetic field induced torque in the nanowires, which deflected the magnetic posts and imparted force to individual adhesions of cells attached to the array. Using this system, we examined the cellular reaction to applied forces and found that applying a step force led to an increase in local focal adhesion size at the site of application but not at nearby nonmagnetic posts. Focal adhesion recruitment was enhanced further when cells were subjected to multiple force actuations within the same time interval. Recording the traction forces in response to such force stimulation revealed two responses: a sudden loss in contractility that occurred within the first minute of stimulation or a gradual decay in contractility over several minutes. For both types of responses, the subcellular distribution of loss in traction forces was not confined to locations near the actuated micropost, nor uniformly across the whole cell, but instead occurred at discrete locations along the cell periphery. Together, these data reveal an important dynamic biological relationship between external and internal forces and demonstrate the utility of this microfabricated system to explore this interaction.