Assessing the flexibility of intermediate filaments by atomic force microscopy

The umbrella cell keratin network: organization as a tile-like mesh, formation of a girded layer in response to bladder filling, and dependence on the plectin cytolinker

The keratin cytoskeleton and associated desmosomes contribute to the mechanical stability of epithelial tissues, but their organization in bladder umbrella cells and their responses to bladder filling are poorly understood. Using super-resolution confocal microscopy, along with 3D image reconstruction and platinum replica electron microscopy, we observed that the apical keratin network of umbrella cells was organized as a dense tile-like mesh comprised of tesserae bordered on their edges by cortical actin filaments, filled with woven keratin filaments, and crosslinked by plectin. A band of keratin was also observed at the cell periphery that was linked to the junction-associated actin ring by plectin. During bladder filling, the junction-localized desmosomal necklace expanded, and a subjacent girded layer was formed that linked the keratin network to desmosomes, including those at the umbrella cell-intermediate cell interface. Disruption of plectin led to focal keratin network dissolution, loss of the junction-associated band of keratin, perturbation of tight junction continuity, and loss of cell-cell cohesion. Our studies reveal a novel tile-like organization of the umbrella cell keratin cytoskeleton that is dependent on plectin, that reorganizes in response to bladder filling, and that likely serves to maintain umbrella cell continuity in the face of mechanical distension.

How cytoskeletal crosstalk makes cells move: Bridging cell-free and cell studies

Cell migration is a fundamental process for life and is highly dependent on the dynamical and mechanical properties of the cytoskeleton. Intensive physical and biochemical crosstalk among actin, microtubules, and intermediate filaments ensures their coordination to facilitate and enable migration. In this review, we discuss the different mechanical aspects that govern cell migration and provide, for each mechanical aspect, a novel perspective by juxtaposing two complementary approaches to the biophysical study of cytoskeletal crosstalk: live-cell studies (often referred to as top-down studies) and cell-free studies (often referred to as bottom-up studies). We summarize the main findings from both experimental approaches, and we provide our perspective on bridging the two perspectives to address the open questions of how cytoskeletal crosstalk governs cell migration and makes cells move.

Rational Design of DNA Hydrogels Based on Molecular Dynamics of Polymers

In recent years, DNA has emerged as a fascinating building material to engineer hydrogel due to its excellent programmability, which has gained considerable attention in biomedical applications. Understanding the structure-property relationship and underlying molecular determinants of DNA hydrogel is essential to precisely tailor its macroscopic properties at molecular level. In this review, the rational design principles of DNA molecular networks based on molecular dynamics of polymers on the temporal scale, which can be engineered via the backbone rigidity and crosslinking kinetics, are highlighted. By elucidating the underlying molecular mechanisms and theories, it is aimed to provide a comprehensive overview of how the tunable DNA backbone rigidity and the crosslinking kinetics lead to desirable macroscopic properties of DNA hydrogels, including mechanical properties, diffusive permeability, swelling behaviors, and dynamic features. Furthermore, it is also discussed how the tunable macroscopic properties make DNA hydrogels promising candidates for biomedical applications, such as cell culture, tissue engineering, bio-sensing, and drug delivery.

The unique biomechanics of intermediate filaments - From single filaments to cells and tissues

Together with actin filaments and microtubules, intermediate filaments (IFs) constitute the eukaryotic cytoskeleton and each of the three filament types contributes very distinct mechanical properties to this intracellular biopolymer network. IFs assemble hierarchically, rather than polymerizing from nuclei of a small number of monomers or dimers, as is the case with actin filaments and microtubules, respectively. This pathway leads to a molecular architecture specific to IFs and intriguing mechanical and dynamic properties: they are the most flexible cytoskeletal filaments and extremely extensible. Moreover, IFs are very stable against disassembly. Thus, they contribute important properties to cell mechanics, which recently have been investigated with state-of-the-art experimental and computational methods.

Transverse Fluctuations Control the Assembly of Semiflexible Filaments

The kinetics of the assembly of semiflexible filaments through end-to-end annealing is key to the structure of the cytoskeleton, but is not understood. We analyze this problem through scaling theory and simulations, and uncover a regime where filaments' ends find each other through bending fluctuations without the need for the whole filament to diffuse. This results in a very substantial speedup of assembly in physiological regimes, and could help with understanding the dynamics of actin and intermediate filaments in biological processes such as wound healing and cell division.

Mechanotherapy in oncology: Targeting nuclear mechanics and mechanotransduction

Mechanotherapy is proposed as a new option for cancer treatment. Increasing evidence suggests that characteristic differences are present in the nuclear mechanics and mechanotransduction of cancer cells compared with those of normal cells. Recent advances in understanding nuclear mechanics and mechanotransduction provide not only further insights into the process of malignant transformation but also useful references for developing new therapeutic approaches. Herein, we present an overview of the alterations of nuclear mechanics and mechanotransduction in cancer cells and highlight their implications in cancer mechanotherapy.

Dual-wavelength stopped-flow analysis of the lateral and longitudinal assembly kinetics of vimentin

Vimentin is a highly charged intermediate filament protein that inherently forms extended dimeric coiled coils, which serve as the basic building blocks of intermediate filaments. Under low ionic strength conditions, vimentin filaments dissociate into uniform tetrameric complexes of two anti-parallel-oriented, half-staggered coiled-coil dimers. By addition of salt, vimentin tetramers spontaneously reassemble into filaments in a time-dependent process: 1) lateral assembly of tetramers into unit-length filaments, 2) longitudinal annealing of unit-length filaments, and 3) longitudinal assembly of filaments coupled with subsequent radial compaction. To independently determine the lateral and longitudinal assembly kinetics, we measure with a stopped-flow instrument the static light scattering signal at two different wavelengths (405 and 594 nm) with a temporal resolution of 3 ms and analyze the signals based on Rayleigh-Gans theory. This theory considers that the intensity of the scattered light depends not only on the molecular weight of the scattering object but also on its shape. This shape dependence is more pronounced at shorter wavelengths, allowing us to decompose the scattered light signal into its components arising from lateral and longitudinal filament assembly. We demonstrate that both the lateral and longitudinal filament assembly kinetics increase with salt concentration.

Multiscale architecture: Mechanics of composite cytoskeletal networks

Different types of biological cells respond differently to mechanical stresses, and these responses are mainly governed by the cytoskeleton. The main components of this biopolymer network are actin filaments, microtubules, and intermediate filaments, whose mechanical and dynamic properties are highly distinct, thus opening up a large mechanical parameter space. Aside from experiments on whole, living cells, "bottom-up" approaches, utilizing purified, reconstituted protein systems, tremendously help to shed light on the complex mechanics of cytoskeletal networks. Such experiments are relevant in at least three aspects: (i) from a fundamental point of view, cytoskeletal networks provide a perfect model system for polymer physics; (ii) in materials science and "synthetic cell" approaches, one goal is to fully understand properties of cellular materials and reconstitute them in synthetic systems; (iii) many diseases are associated with cell mechanics, so a thorough understanding of the underlying phenomena may help solving pressing biomedical questions. In this review, we discuss the work on networks consisting of one, two, or all three types of filaments, entangled or cross-linked, and consider active elements such as molecular motors and dynamically growing filaments. Interestingly, tuning the interactions among the different filament types results in emergent network properties. We discuss current experimental challenges, such as the comparability of different studies, and recent methodological advances concerning the quantification of attractive forces between filaments and their influence on network mechanics.

Environment-Dependent Stability and Mechanical Properties of DNA Origami Six-Helix Bundles with Different Crossover Spacings

The internal design of DNA nanostructures defines how they behave in different environmental conditions, such as endonuclease-rich or low-Mg²⁺ solutions. Notably, the inter-helical crossovers that form the core of such DNA objects have a major impact on their mechanical properties and stability. Importantly, crossover design can be used to optimize DNA nanostructures for target applications, especially when developing them for biomedical environments. To elucidate this, two otherwise identical DNA origami designs are presented that have a different number of staple crossovers between neighboring helices, spaced at 42- and 21- basepair (bp) intervals, respectively. The behavior of these structures is then compared in various buffer conditions, as well as when they are exposed to enzymatic digestion by DNase I. The results show that an increased number of crossovers significantly improves the nuclease resistance of the DNA origami by making it less accessible to digestion enzymes but simultaneously lowers its stability under Mg²⁺ -free conditions by reducing the malleability of the structures. Therefore, these results represent an important step toward rational, application-specific DNA nanostructure design.

A general mathematical model for the in vitro assembly dynamics of intermediate filament proteins

Intermediate filament (IF) proteins assemble into highly flexible filaments that organize into complex cytoplasmic networks: keratins in all types of epithelia, vimentin in endothelia, and desmin in muscle. Since IF elongation proceeds via end-to-end annealing of unit-length filaments and successively of progressively growing filaments, it is important to know how their remarkable flexibility, i.e., their persistence length l_p, influences the assembly kinetics. In fact, their l_p ranges between 0.3 μm (keratin K8/K18) and 1.0 μm (vimentin and desmin), and thus is orders of magnitude lower than that of microtubules and F-actin. Here, we present a unique mathematical model, which implements the semiflexible nature of the three IF types based on published semiflexible polymers theories and depends on a single free parameter k₀. Calibrating this model to filament mean length dynamics of the three proteins, we demonstrate that the persistence length is indeed essential to accurately describe their assembly kinetics. Furthermore, we reveal that the difference in flexibility alone does not explain the significantly faster assembly rate of keratin filaments compared with that of vimentin. Likewise, desmin assembles approximately six times faster than vimentin, even though both their filaments exhibit the same l_p value. These data strongly indicate that differences in their individual amino acid sequences significantly impact the assembly rates. Nevertheless, using a single k₀ value for each of these three key representatives of the IF protein family, our advanced model does accurately describe the length distribution and mean length dynamics and provides effective filament assembly rates. It thus provides a tool for future investigations on the impact of posttranslational modifications or amino acid changes of IF proteins on assembly kinetics. This is an important issue, as the discovery of mutations in IF genes causing severe human disease, particularly for desmin and keratins, is steadily increasing.

Molecular organization and mechanics of single vimentin filaments revealed by super-resolution imaging

Intermediate filaments (IFs) are involved in key cellular functions including polarization, migration, and protection against large deformations. These functions are related to their remarkable ability to extend without breaking, a capacity that should be determined by the molecular organization of subunits within filaments. However, this structure-mechanics relationship remains poorly understood at the molecular level. Here, using super-resolution microscopy (SRM), we show that vimentin filaments exhibit a ~49-nanometer axial repeat both in cells and in vitro. As unit-length filaments (ULFs) were measured at ~59 nanometers, this demonstrates a partial overlap of ULFs during filament assembly. Using an SRM-compatible stretching device, we also provide evidence that the extensibility of vimentin is due to the unfolding of its subunits and not to their sliding, thus establishing a direct link between the structural organization and its mechanical properties. Overall, our results pave the way for future studies of IF assembly, mechanical, and structural properties in cells.

Mechanics of Single Vimentin Intermediate Filaments Under Load

The eukaryotic cytoskeleton consists of three different types of biopolymers - microtubules, actin filaments, and intermediate filaments - and provides cells with versatile mechanical properties, combining stability and flexibility. The unique molecular structure of intermediate filaments leads to high extensibility and stability under load. With high laser power dual optical tweezers, the mechanical properties of intermediate filaments may be investigated, while monitoring the extension with fluorescence microscopy. Here, we provide detailed protocols for the preparation of single vimentin intermediate filaments and general measurement protocols for (i) stretching experiments, (ii) repeated loading and relaxation cycles, and (iii) force-clamp experiments. We describe methods for the analysis of the experimental data in combination with computational modeling approaches.

Pi-stacking Enhances Stability, Scalability of Formation, Control over Flexibility and Circulation Time of Polymeric Filaments

Self-assembling filomicelles (FM) are of great interest to nanomedicine due to their structural flexibility, extensive systemic circulation time, and amenability to unique "cylinder-to-sphere" morphological transitions. However, current fabrication techniques for FM self-assembly are highly variable and difficult to scale. Here, we demonstrate that tetrablock copolymers composed of poly(ethylene glycol)-b-poly(propylene sulfide) (PEG-b-PPS) diblocks linked by a pi-stacking perylene bisimide (PBI) moiety permit rapid, scalable, and facile assembly of FM via the flash nanoprecipitation (FNP) method. Co-assembling the tetrablocks and PEG-b-PPS diblocks at different molar ratios resulted in mixed PBI-containing FM (mPBI-FM) with tunable length and flexibility. The flexibility of mPBI-FM can be optimized to decrease uptake by macrophages in vivo, leading to increased circulation time versus (-)PBI-FM without PBI tetrablocks after intravenous administration in mice. While PEG-b-PPS diblocks form FM within a narrow range of hydrophilic weight fractions, incorporation of pi-stacking PBI groups expanded this range to increase favorability of FM assembly. Furthermore, the aggregation-dependent fluorescence of PBI shifted during oxidation-induced "cylinder-to-sphere" transitions of mPBI-FM into micelles, resulting in a distinct emission wavelength for filamentous versus spherical nanostructures. Thus, incorporation of pi-stacking allows for rapid, scalable assembly of FM with tunable flexibility and stability for theranostic and nanomedicine applications.

Cytoskeleton Reorganization in EndMT-The Role in Cancer and Fibrotic Diseases

Chronic inflammation promotes endothelial plasticity, leading to the development of several diseases, including fibrosis and cancer in numerous organs. The basis of those processes is a phenomenon called the endothelial–mesenchymal transition (EndMT), which results in the delamination of tightly connected endothelial cells that acquire a mesenchymal phenotype. EndMT-derived cells, known as the myofibroblasts or cancer-associated fibroblasts (CAFs), are characterized by the loss of cell–cell junctions, loss of endothelial markers, and gain in mesenchymal ones. As a result, the endothelium ceases its primary ability to maintain patent and functional capillaries and induce new blood vessels. At the same time, it acquires the migration and invasion potential typical of mesenchymal cells. The observed modulation of cell shape, increasedcell movement, and invasion abilities are connected with cytoskeleton reorganization. This paper focuses on the review of current knowledge about the molecular pathways involved in the modulation of each cytoskeleton element (microfilaments, microtubule, and intermediate filaments) during EndMT and their role as the potential targets for cancer and fibrosis treatment.

Bend, Push, Stretch: Remarkable Structure and Mechanics of Single Intermediate Filaments and Meshworks

The cytoskeleton of the eukaryotic cell provides a structural and functional scaffold enabling biochemical and cellular functions. While actin and microtubules form the main framework of the cell, intermediate filament networks provide unique mechanical properties that increase the resilience of both the cytoplasm and the nucleus, thereby maintaining cellular function while under mechanical pressure. Intermediate filaments (IFs) are imperative to a plethora of regulatory and signaling functions in mechanotransduction. Mutations in all types of IF proteins are known to affect the architectural integrity and function of cellular processes, leading to debilitating diseases. The basic building block of all IFs are elongated α-helical coiled-coils that assemble hierarchically into complex meshworks. A remarkable mechanical feature of IFs is the capability of coiled-coils to metamorphize into β-sheets under stress, making them one of the strongest and most resilient mechanical entities in nature. Here, we discuss structural and mechanical aspects of IFs with a focus on nuclear lamins and vimentin.

Growth rate-dependent flexural rigidity of microtubules influences pattern formation in collective motion

Background

Microtubules (MTs) are highly dynamic tubular cytoskeleton filaments that are essential for cellular morphology and intracellular transport. In vivo, the flexural rigidity of MTs can be dynamically regulated depending on their intracellular function. In the in vitro reconstructed MT-motor system, flexural rigidity affects MT gliding behaviors and trajectories. Despite the importance of flexural rigidity for both biological functions and in vitro applications, there is no clear interpretation of the regulation of MT flexural rigidity, and the results of many studies are contradictory. These discrepancies impede our understanding of the regulation of MT flexural rigidity, thereby challenging its precise manipulation.

Results

Here, plausible explanations for these discrepancies are provided and a new method to evaluate the MT rigidity is developed. Moreover, a new relationship of the dynamic and mechanic of MTs is revealed that MT flexural rigidity decreases through three phases with the growth rate increases, which offers a method of designing MT flexural rigidity by regulating its growth rate. To test the validity of this method, the gliding performances of MTs with different flexural rigidities polymerized at different growth rates are examined. The growth rate-dependent flexural rigidity of MTs is experimentally found to influence the pattern formation in collective motion using gliding motility assay, which is further validated using machine learning.

Conclusion

Our study establishes a robust quantitative method for measurement and design of MT flexural rigidity to study its influences on MT gliding assays, collective motion, and other biological activities in vitro. The new relationship about the growth rate and rigidity of MTs updates current concepts on the dynamics and mechanics of MTs and provides comparable data for investigating the regulation mechanism of MT rigidity in vivo in the future.

Graphic Abstract

Supplementary Information

The online version contains supplementary material available at 10.1186/s12951-021-00960-y.

Pulling the springs of a cell by single-molecule force spectroscopy

The fundamental unit of the human body comprises of the cells which remain embedded in a fibrillar network of extracellular matrix proteins which in turn provides necessary anchorage the cells. Tissue repair, regeneration and reprogramming predominantly involve a traction force mediated signalling originating in the ECM and travelling deep into the cell including the nucleus via circuitry of spring-like filamentous proteins like microfilaments or actin, intermediate filaments and microtubules to elicit a response in the form of mechanical movement as well as biochemical changes. The 'springiness' of these proteins is highlighted in their extension-contraction behaviour which is manifested as an effect of differential traction force. Atomic force microscope (AFM) provides the magic eye to visualize and quantify such force-extension/indentation events in these filamentous proteins as well as in whole cells. In this review, we have presented a summary of the current understanding and advancement of such measurements by AFM based single-molecule force spectroscopy in the context of cytoskeletal and nucleoskeletal proteins which act in tandem to facilitate mechanotransduction.

Nuclear filaments: role in chromosomal positioning and gene expression

Nuclear lamins form an elastic meshwork underlying the inner nuclear membrane and provide mechanical rigidity to the nucleus and maintain shape. Lamins also maintain chromosome positioning and play important roles in several nuclear processes like replication, DNA damage repair, transcription, and epigenetic modifications. LMNA mutations affect cardiac tissue, muscle tissues, adipose tissues to precipitate several diseases collectively termed as laminopathies. However, the rationale behind LMNA mutations and laminopathies continues to elude scientists. During interphase, several chromosomes form inter/intrachromosomal contacts inside nucleoplasm and several chromosomal loops also stretch out to make a ‘loop-cluster’ which are key players to regulate gene expressions. In this perspective, we have proposed that the lamin network in tandem with nuclear actin and myosin provide mechanical rigidity to the chromosomal contacts and facilitate loop-clusters movements. LMNA mutations thus might perturb the landscape of chromosomal contacts or loop-clusters positioning which can impair gene expression profile.

Drops and fibers - how biomolecular condensates and cytoskeletal filaments influence each other

The cellular cytoskeleton self-organizes by specific monomer-monomer interactions resulting in the polymerization of filaments. While we have long thought about the role of polymerization in cytoskeleton formation, we have only begun to consider the role of condensation in cytoskeletal organization. In this review, we highlight how the interplay between polymerization and condensation leads to the formation of the cytoskeleton.

The vimentin cytoskeleton: when polymer physics meets cell biology

The proper functions of tissues depend on the ability of cells to withstand stress and maintain shape. Central to this process is the cytoskeleton, comprised of three polymeric networks: F-actin, microtubules, and intermediate filaments (IFs). IF proteins are among the most abundant cytoskeletal proteins in cells; yet they remain some of the least understood. Their structure and function deviate from those of their cytoskeletal partners, F-actin and microtubules. IF networks show a unique combination of extensibility, flexibility and toughness that confers mechanical resilience to the cell. Vimentin is an IF protein expressed in mesenchymal cells. This review highlights exciting new results on the physical biology of vimentin intermediate filaments and their role in allowing whole cells and tissues to cope with stress.

Vimentin S-glutathionylation at Cys328 inhibits filament elongation and induces severing of mature filaments in vitro

Vimentin intermediate filaments are a significant component of the cytoskeleton in cells of mesenchymal origin. In vivo, filaments assemble and disassemble and thus participate in the dynamic processes of the cell. Post-translational modifications (PTMs) such as protein phosphorylation regulate the multiphasic association of vimentin from soluble complexes to insoluble filaments and the reverse processes. The thiol side chain of the single vimentin cysteine at position 328 (Cys328) is a direct target of oxidative modifications inside cells. Here, we used atomic force microscopy, electron microscopy and a novel hydrogen-deuterium exchange mass spectrometry (HDex-MS) procedure to investigate the structural consequences of S-nitrosylation and S-glutathionylation of Cys328 for in vitro oligomerisation of human vimentin. Neither modification affects the lateral association of tetramers to unit-length filaments (ULF). However, S-glutathionylation of Cys328 blocks the longitudinal assembly of ULF into extended filaments. S-nitrosylation of Cys328 does not hinder but slows down the elongation. Likewise, S-glutathionylation of preformed vimentin filaments causes their extensive fragmentation to smaller oligomeric species. Chemical reduction of the S-glutathionylated Cys328 thiols induces reassembly of the small fragments into extended filaments. In conclusion, our in vitro results suggest S-glutathionylation as a candidate PTM for an efficient molecular switch in the dynamic rearrangements of vimentin intermediate filaments, observed in vivo, in response to changes in cellular redox status. Finally, we demonstrate that HDex-MS is a powerful method for probing the kinetics of vimentin filament formation and filament disassembly induced by PTMs.

Tuning intermediate filament mechanics by variation of pH and ion charges

The cytoskeleton is formed by three types of filamentous proteins - microtubules, actin filaments, and intermediate filaments (IFs) - and enables cells to withstand external and internal forces. Vimentin is the most abundant IF protein in humans and assembles into 10 nm diameter filaments with remarkable mechanical properties, such as high extensibility and stability. It is, however, unclear to which extent these properties are influenced by the electrostatic environment. Here, we study the mechanical properties of single vimentin filaments by employing optical trapping combined with microfluidics. Force-strain curves, recorded at varying ion concentrations and pH values, reveal that the mechanical properties of single vimentin IFs are influenced by pH and ion concentration. By combination with Monte Carlo simulations, we relate these altered mechanics to electrostatic interactions of subunits within the filaments. We thus suggest possible mechanisms that allow cells to locally tune their stiffness without remodeling the entire cytoskeleton.

Cryoelectron Tomography Reveals Nanoscale Organization of the Cytoskeleton and Its Relation to Microtubule Curvature Inside Cells

Microtubules (MTs) are the most rigid elements of the cytoskeleton with in vitro persistence lengths (L_p) in the range of 1-6 mm. In cellular environments, however, MTs often appear strongly curved. This has been attributed to the forces acting upon them in situ where they are embedded in composite networks of different cytoskeletal elements. Hitherto, the nanoscale organization of these networks has remained largely uncharacterized. Cryo-electron tomography (cryo-ET) allowed to visualize and analyze the in situ structure of cytoskeletal networks in pristinely preserved cellular environments and at high resolution. Here, we studied the molecular organization of MTs and their interactions with the composite cytoskeleton in frozen-hydrated HeLa and P19 cells at different cell-cycle stages. We describe modulation of MT curvature correlated with the surrounding molecular architecture, and show that nanoscale defects occur in curved MTs. The data presented here contribute to constructing realistic models of cytoskeletal biomechanics.

Effect of Divalent Cations on the Structure and Mechanics of Vimentin Intermediate Filaments

Divalent cations behave as effective cross-linkers of intermediate filaments (IFs) such as vimentin IF (VIF). These interactions have been mostly attributed to their multivalency. However, ion-protein interactions often depend on the ion species, and these effects have not been widely studied in IFs. Here, we investigate the effects of two biologically important divalent cations, Zn²⁺ and Ca²⁺, on VIF network structure and mechanics in vitro. We find that the network structure is unperturbed at micromolar Zn²⁺ concentrations, but strong bundle formation is observed at a concentration of 100 μM. Microrheological measurements show that network stiffness increases with cation concentration. However, bundling of filaments softens the network. This trend also holds for VIF networks formed in the presence of Ca²⁺, but remarkably, a concentration of Ca²⁺ that is two orders higher is needed to achieve the same effect as with Zn²⁺, which suggests the importance of salt-protein interactions as described by the Hofmeister effect. Furthermore, we find evidence of competitive binding between the two divalent ion species. Hence, specific interactions between VIFs and divalent cations are likely to be an important mechanism by which cells can control their cytoplasmic mechanics.

Loops versus lines and the compression stiffening of cells

Both animal and plant tissue exhibit a nonlinear rheological phenomenon known as compression stiffening, or an increase in moduli with increasing uniaxial compressive strain. Does such a phenomenon exist in single cells, which are the building blocks of tissues? One expects an individual cell to compression soften since the semiflexible biopolymer-based cytoskeletal network maintains the mechanical integrity of the cell and in vitro semiflexible biopolymer networks typically compression soften. To the contrary, we find that mouse embryonic fibroblasts (mEFs) compression stiffen under uniaxial compression via atomic force microscopy studies. To understand this finding, we uncover several potential mechanisms for compression stiffening. First, we study a single semiflexible polymer loop modeling the actomyosin cortex enclosing a viscous medium modeled as an incompressible fluid. Second, we study a two-dimensional semiflexible polymer/fiber network interspersed with area-conserving loops, which are a proxy for vesicles and fluid-based organelles. Third, we study two-dimensional fiber networks with angular-constraining crosslinks, i.e. semiflexible loops on the mesh scale. In the latter two cases, the loops act as geometric constraints on the fiber network to help stiffen it via increased angular interactions. We find that the single semiflexible polymer loop model agrees well with the experimental cell compression stiffening finding until approximately 35% compressive strain after which bulk fiber network effects may contribute. We also find for the fiber network with area-conserving loops model that the stress-strain curves are sensitive to the packing fraction and size distribution of the area-conserving loops, thereby creating a mechanical fingerprint across different cell types. Finally, we make comparisons between this model and experiments on fibrin networks interlaced with beads as well as discuss implications for single cell compression stiffening at the tissue scale.

Apparent stiffness of vimentin intermediate filaments in living cells and its relation with other cytoskeletal polymers

The cytoskeleton is a complex network of interconnected biopolymers intimately involved in the generation and transmission of forces. Several mechanical properties of microtubules and actin filaments have been extensively explored in cells. In contrast, intermediate filaments (IFs) received comparatively less attention despite their central role in defining cell shape, motility and adhesion during physiological processes as well as in tumor progression. Here, we explored relevant biophysical properties of vimentin IFs in living cells combining confocal microscopy and a filament tracking routine that allows localizing filaments with ~20 nm precision. A Fourier-based analysis showed that IFs curvatures followed a thermal-like behavior characterized by an apparent persistence length (lp*) similar to that measured in aqueous solution. Additionally, we determined that certain perturbations of the cytoskeleton affect lp* and the lateral mobility of IFs as assessed in cells in which either the microtubule dynamic instability was reduced or actin filaments were partially depolymerized. Our results provide relevant clues on how vimentin IFs mechanically couple with microtubules and actin filaments in cells and support a role of this network in the response to mechanical stress.

Qualitative analysis of contribution of intracellular skeletal changes to cellular elasticity

Cells are dynamic structures that continually generate and sustain mechanical forces within their environments. Cells respond to mechanical forces by changing their shape, moving, and differentiating. These reactions are caused by intracellular skeletal changes, which induce changes in cellular mechanical properties such as stiffness, elasticity, viscoelasticity, and adhesiveness. Interdisciplinary research combining molecular biology with physics and mechanical engineering has been conducted to characterize cellular mechanical properties and understand the fundamental mechanisms of mechanotransduction. In this review, we focus on the role of cytoskeletal proteins in cellular mechanics. The specific role of each cytoskeletal protein, including actin, intermediate filaments, and microtubules, on cellular elasticity is summarized along with the effects of interactions between the fibers.

Lateral Subunit Coupling Determines Intermediate Filament Mechanics

The cytoskeleton is a composite network of three types of protein filaments, among which intermediate filaments (IFs) are the most extensible ones. Two very important IFs are keratin and vimentin, which have similar molecular architectures but different mechanical behaviors. Here we compare the mechanical response of single keratin and vimentin filaments using optical tweezers. We show that the mechanics of vimentin strongly depends on the ionic strength of the buffer and that its force-strain curve suggests a high degree of cooperativity between subunits. Indeed, a computational model indicates that in contrast to keratin, vimentin is characterized by strong lateral subunit coupling of its charged monomers during unfolding of α helices. We conclude that cells can tune their mechanics by differential use of keratin versus vimentin.

Vimentin Intermediate Filaments Undergo Irreversible Conformational Changes during Cyclic Loading

Intermediate filaments (IFs) are part of the cytoskeleton of eukaryotic cells and, therefore, are largely responsible for the cell's mechanical properties. IFs are characterized by a pronounced extensibility and remarkable resilience that enable them to support cells in extreme situations. Previous experiments showed that, under strain, α-helices in vimentin IFs might unfold to β-sheets. Upon repeated stretching, the filaments soften; however, the remaining plastic strain is negligible. Here, we observe that vimentin IFs do not recover their original stiffness on reasonable time scales, and we explain these seemingly contradicting results by introducing a third, less well-defined conformational state. Reversibility on the nanoscale can be fully rescued by introducing cross-linkers that prevent transition to the β-sheet. Our results classify IFs as a nanomaterial with intriguing mechanical properties, which is likely to play a major role for the cell's local adaption to external stimuli.

Stiffening and inelastic fluidization in vimentin intermediate filament networks

Intermediate filaments are cytoskeletal proteins that are key regulators of cell mechanics, a role which is intrinsically tied to their hierarchical structure and their unique ability to accommodate large axial strains. However, how the single-filament response to applied strains translates to networks remains unclear, particularly with regards to the crosslinking role played by the filaments' disordered "tail" domains. Here we test the role of these noncovalent crosslinks in the nonlinear rheology of reconstituted networks of the intermediate filament protein vimentin, probing their stress- and rate-dependent mechanics. Similarly to previous studies we observe elastic stress-stiffening but unlike previous work we identify a characteristic yield stress σ*, above which the networks exhibit rate-dependent softening of the network, referred to as inelastic fluidization. By investigating networks formed from tail-truncated vimentin, in which noncovalent crosslinking is suppressed, and glutaraldehyde-treated vimentin, in which crosslinking is made permanent, we show that rate-dependent inelastic fluidization is a direct consequence of vimentin's transient crosslinking. Surprisingly, although the tail-tail crosslinks are individually weak, the effective timescale for stress relaxation of the network exceeds 1000 s at σ*. Vimentin networks can therefore maintain their integrity over a large range of strains (up to ∼1000%) and loading rates (10-3 to 10-1 s-1). Our results provide insight into how the hierarchical structure of vimentin networks contributes to the cell's ability to be deformable yet strong.

Deciphering the transport of elastic filaments by antagonistic motor proteins

Intermediate filaments are long elastic fibers that are transported by the microtubule-associated motor proteins kinesin and dynein inside the cell. How elastic filaments are efficiently transported by antagonistic motors is not well understood and is difficult to measure with current experimental techniques. Adapting the tug-of-war paradigm for vesiclelike cargos, we develop a mathematical model to describe the motion of an elastic filament punctually bound to antagonistic motors. As observed in cells, up to three modes of transport are obtained; dynein-driven retrograde, kinesin-driven anterograde fast motions, and a slow motion. Motor properties and initial conditions that depend on intracellular context regulate the transport of filaments. Filament elasticity is found to affect both the mode and the efficiency of transport. We further show that the coordination of motors along the filament emerges from the interplay between intracellular context and elastic properties of filaments.

Helical Superstructure of Intermediate Filaments

Intermediate filaments are the least explored among the large cytoskeletal elements. We show here that they display conformational anomalies in narrow microfluidic channels. Their unusual behavior can be understood as the consequence of a previously undetected, large-scale helically curved superstructure. Confinement in a channel orders the otherwise soft, strongly fluctuating helical filaments and enhances their structural correlations, giving rise to experimentally detectable, strongly oscillating tangent correlation functions. We propose an explanation for the detected intrinsic curving phenomenon-an elastic shape instability that we call autocoiling. The mechanism involves self-induced filament buckling via a surface stress located at the outside of the cross section. The results agree with ultrastructural findings and rationalize for the commonly observed looped intermediate filament shapes. Beyond curvature, explaining the molecular origin of the detected helical torsion remains an interesting challenge.

Mutation-induced alterations of intra-filament subunit organization in vimentin filaments revealed by SAXS

Vimentin intermediate filaments constitute a distinct filament system in mesenchymal cells that is instrumental for cellular mechanics and migration. In vitro, the rod-like monomers assemble in a multi-step, salt-dependent manner into micrometer long biopolymers. To disclose the underlying mechanisms further, we employed small angle X-ray scattering on two recombinant vimentin variants, whose assembly departs at strategic points from the normal assembly route: (i) vimentin with a tyrosine to leucine change at position 117; (ii) vimentin missing the non-α-helical carboxyl-terminal domain. Y117L vimentin assembles into unit-length filaments (ULFs) only, whereas ΔT vimentin assembles into filaments containing a higher number of tetramers per cross section than normal vimentin filaments. We show that the shape and inner structure of these mutant filaments is significantly altered. ULFs assembled from Y117L vimentin contain more, less tightly bundled vimentin tetramers, and ΔT vimentin filaments preserve the number density despite the higher number of tetramers per filament cross-section.

Mechanical loading of desmosomes depends on the magnitude and orientation of external stress

Desmosomes are intercellular adhesion complexes that connect the intermediate filament cytoskeletons of neighboring cells, and are essential for the mechanical integrity of mammalian tissues. Mutations in desmosomal proteins cause severe human pathologies including epithelial blistering and heart muscle dysfunction. However, direct evidence for their load-bearing nature is lacking. Here we develop Förster resonance energy transfer (FRET)-based tension sensors to measure the forces experienced by desmoplakin, an obligate desmosomal protein that links the desmosomal plaque to intermediate filaments. Our experiments reveal that desmoplakin does not experience significant tension under most conditions, but instead becomes mechanically loaded when cells are exposed to external mechanical stresses. Stress-induced loading of desmoplakin is transient and sensitive to the magnitude and orientation of the applied tissue deformation, consistent with a stress absorbing function for desmosomes that is distinct from previously analyzed cell adhesion complexes.

Desmosomes are intercellular adhesion complexes that connect the intermediate filament cytoskeletons of neighboring cells but direct evidence for their load-bearing nature is lacking. Here the authors develop FRET-based tension sensors to measure the forces experienced by desmoplakin and infer that desmosomes become mechanically loaded when cells are exposed to external mechanical stresses.

Structure and Nanomechanics of Dry and Hydrated Intermediate Filament Films and Fibers Produced from Hagfish Slime Fibers

Intermediate filaments (IFs) are known for their extensibility, flexibility, toughness, and their ability to hydrate. Using keratin-like IFs obtained from slime fibers from the invertebrate Atlantic hagfish ( Myxine glutinosa), films were produced by drop-casting and coagulation on the surface of a MgCl₂ buffer. Drop-casting produced self-supporting, smooth, and dense films rich in β-sheets (61%), whereas coagulation formed thin, porous films with a nanorough surface and a lower β-sheet content (51%). The films hydrated and swelled immediately when immersed in water and did not dissolve. X-ray diffraction showed that the β-crystallites remained stable upon hydration, that swelling presumably happens in the amorphous C-terminal tail-domains of the IFs, and that high salt conditions caused a denser network mesh size, suggesting polyelectrolyte behavior. Hydration resulted in a roughly 1000-fold decrease in apparent Young's modulus from 10⁹ to 10⁶ Pa as revealed by atomic force microscopy nanoindentation. Nanoindentation-based power-law rheology and stress-relaxation measurements indicated viscoelasticity and a soft-solid hydrogel character for hydrated films, where roughly 80% of energy is elastically stored and 20% is dissipated. By pulling coagulation films from the buffer interface, macroscopic fibers with highly aligned IF β-crystals similar to natural hagfish fibers were produced. We propose that viscoelasticity and strong hydrogen bonding interactions with the buffer interface are crucial for the production of such long biomimetic fibers with aligned β-sheets. This study demonstrates that hagfish fiber IFs can be reconstituted into functional biomimetic materials that are stiff when dry and retain the ability to hydrate to become soft and viscoelastic when in water.

Effect of ionic strength on the structure and elongational kinetics of vimentin filaments

Intermediate filaments are a major structural element in the cytoskeleton of animal cells that mechanically integrate other cytoskeletal components and absorb externally applied stress. Their role is likely to be linked to their complex molecular architecture which is the product of a multi-step assembly pathway. Intermediate filaments form tetrameric subunits which assemble in the presence of monovalent salts to form unit length filaments that subsequently elongate by end-to-end annealing. The present work characterizes this complex assembly process using reconstituted vimentin intermediate filaments with monovalent salts as an assembly trigger. A multi-scale approach is used, comprising static light scattering, dynamic light scattering and quantitative scanning transmission electron microscopy (STEM) mass measurements. Light scattering reveals the radius of gyration (Rg), molecular weight (Mw) and diffusion coefficient (D) of the assembling filaments as a function of time and salt concentration (cS) for the given protein concentration of 0.07 g L-1. At low cS (10 mM KCl) no lateral or elongational growth is observed, whereas at cS = 50-200 mM, the hydrodynamic cross-sectional radius and the elongation rate increases with cS. Rgversus Mw plots suggest that the mass per unit length increases with increasing salt content, which is confirmed by STEM mass measurements. A kinetic model based on rate equations for a two step process is able to accurately describe the variation of mass, length and diffusion coefficient of the filaments with time and provides a consistent description of the elongation accelerated by increasing cS.

Glassy dynamics in composite biopolymer networks

The cytoskeleton is a highly interconnected meshwork of strongly coupled subsystems providing mechanical stability as well as dynamic functions to cells. To elucidate the underlying biophysical principles, it is central to investigate not only one distinct functional subsystem but rather their interplay as composite biopolymeric structures. Two of the key cytoskeletal elements are actin and vimentin filaments. Here, we show that composite networks reconstituted from actin and vimentin can be described by a superposition of two non-interacting scaffolds. Arising effects are demonstrated in a scale-spanning frame connecting single filament dynamics to macro-rheological network properties. The acquired results of the linear and non-linear bulk mechanics can be captured within an inelastic glassy wormlike chain model. In contrast to previous studies, we find no emergent effects in these composite networks. Thus, our study paves the way to predict the mechanics of the cytoskeleton based on the properties of its single structural components.

Viscoelastic properties of vimentin originate from nonequilibrium conformational changes

Structure and dynamics of living matter rely on design principles fundamentally different from concepts of traditional material science. Specialized intracellular filaments in the cytoskeleton permit living systems to divide, migrate, and grow with a high degree of variability and durability. Among the three filament systems, microfilaments, microtubules, and intermediate filaments (IFs), the physical properties of IFs and their role in cellular mechanics are the least well understood. We use optical trapping of individual vimentin filaments to investigate energy dissipation, strain history dependence, and creep behavior of stretched filaments. By stochastic and numerical modeling, we link our experimental observations to the peculiar molecular architecture of IFs. We find that individual vimentin filaments display tensile memory and are able to dissipate more than 70% of the input energy. We attribute these phenomena to distinct nonequilibrium folding and unfolding of α helices in the vimentin monomers constituting the filaments.

Assembly Kinetics of Vimentin Tetramers to Unit-Length Filaments: A Stopped-Flow Study

Intermediate filaments (IFs) are principal components of the cytoskeleton, a dynamic integrated system of structural proteins that provides the functional architecture of metazoan cells. They are major contributors to the elasticity of cells and tissues due to their high mechanical stability and intrinsic flexibility. The basic building block for the assembly of IFs is a rod-like, 60-nm-long tetrameric complex made from two antiparallel, half-staggered coiled coils. In low ionic strength, tetramers form stable complexes that rapidly assemble into filaments upon raising the ionic strength. The first assembly products, "frozen" by instantaneous chemical fixation and viewed by electron microscopy, are 60-nm-long "unit-length" filaments (ULFs) that apparently form by lateral in-register association of tetramers. ULFs are the active elements of IF growth, undergoing longitudinal end-to-end annealing with one another and with growing filaments. Originally, we have employed quantitative time-lapse atomic force and electron microscopy to analyze the kinetics of vimentin-filament assembly starting from a few seconds to several hours. To obtain detailed quantitative insight into the productive reactions that drive ULF formation, we now introduce a "stopped-flow" approach in combination with static light-scattering measurements. Thereby, we determine the basic rate constants for lateral assembly of tetramers to ULFs. Processing of the recorded data by a global fitting procedure enables us to describe the hierarchical steps of IF formation. Specifically, we propose that tetramers are consumed within milliseconds to yield octamers that are obligatory intermediates toward ULF formation. Although the interaction of tetramers is diffusion controlled, it is strongly driven by their geometry to mediate effective subunit targeting. Importantly, our model conclusively reflects the previously described occurrence of polymorphic ULF and mature filaments in terms of their number of tetramers per cross section.

Intermediate Filaments at the Junction of Mechanotransduction, Migration, and Development

Mechanically induced signal transduction has an essential role in development. Cells actively transduce and respond to mechanical signals and their internal architecture must manage the associated forces while also being dynamically responsive. With unique assembly-disassembly dynamics and physical properties, cytoplasmic intermediate filaments play an important role in regulating cell shape and mechanical integrity. While this function has been recognized and appreciated for more than 30 years, continually emerging data also demonstrate important roles of intermediate filaments in cell signal transduction. In this review, with a particular focus on keratins and vimentin, the relationship between the physical state of intermediate filaments and their role in mechanotransduction signaling is illustrated through a survey of current literature. Association with adhesion receptors such as cadherins and integrins provides a critical interface through which intermediate filaments are exposed to forces from a cell's environment. As a consequence, these cytoskeletal networks are posttranslationally modified, remodeled and reorganized with direct impacts on local signal transduction events and cell migratory behaviors important to development. We propose that intermediate filaments provide an opportune platform for cells to both cope with mechanical forces and modulate signal transduction.

Persistence length of collagen molecules based on nonlocal viscoelastic model

Persistence length is one of the most interesting properties of a molecular chain, which is used to describe the stiffness of a molecule. The experimentally measured values of the persistence length of the collagen molecule are widely scattered from 14 to 180 nm. Therefore, an alternative approach is highly desirable to predict the persistence length of a molecule and also to explain the experimental results. In this paper, a nonlocal viscoelastic model is developed to obtain the persistence length of the collagen molecules in solvent. A new explicit formula is proposed for the persistence length of the molecule with the consideration of the small-scale effect, viscoelastic properties of the molecule, loading frequency, and viscosity of the solvent. The presented model indicates that there exists a range of molecule lengths in which the persistence length strongly depends on the frequency and spatial mode of applied loads, small-scale effect, and viscoelastic properties of the collagen.

Phosphorylation-Induced Mechanical Regulation of Intrinsically Disordered Neurofilament Proteins

The biological function of protein assemblies has been conventionally equated with a unique three-dimensional protein structure and protein-specific interactions. However, in the past 20 years it has been found that some assemblies contain long flexible regions that adopt multiple structural conformations. These include neurofilament proteins that constitute the stress-responsive supportive network of neurons. Herein, we show that the macroscopic properties of neurofilament networks are tuned by enzymatic regulation of the charge found on the flexible protein regions. The results reveal an enzymatic (phosphorylation) regulation of macroscopic properties such as orientation, stress response, and expansion in flexible protein assemblies. Using a model that explains the attractive electrostatic interactions induced by enzymatically added charges, we demonstrate that phosphorylation regulation is far richer and versatile than previously considered.

Wrinkles in Polytetrafluoroethylene on Polystyrene: Persistence Lengths and the Effect of Nanoinclusions

We characterize wrinkling on the surfaces of prestrained polystyrene sheets coated with thin polytetrafluoroethylene skins using a combination of mechanical strain measurements and 3D finite element simulations. The simulations show that wrinkle wavelength increases with skin thickness, in agreement with a well-known continuum model and recent experiments. The wrinkle amplitudes also increase with strain. Nanoinclusions, such as holes and patterned lines, influence wrinkle patterns over limited distances, and these distances are shown to scale with the wrinkle wavelengths. Good agreement between experimental and simulated influence distances is observed. The inclusions provide strain relief, and they behave as if they are attracting adjacent material when the sheets are under strain. The wrinkles have stiffnesses in much the same way as do polymers (but at different length scales), a property that is quantified for polymers using persistence lengths. We show that the concept of persistence length can be useful in characterizing the wrinkle properties that we have observed. However, the calculated persistence lengths do not vary systematically with thickness and strain, as interactions between neighboring wrinkles produce confinement that is analogous to the kinetic confinement of polymers.

Theory of Semiflexible Filaments and Networks

We briefly review the recent developments in the theory of individual semiflexible filaments, and of a crosslinked network of such filaments, both permanent and transient. Starting from the free energy of an individual semiflexible chain, models on its force-extension relation and other mechanical properties such as Euler buckling are discussed. For a permanently crosslinked network of filaments, theories on how the network responds to deformation are provided, with a focus on continuum approaches. Characteristic features of filament networks, such as nonlinear stress-strain relation, negative normal stress, tensegrity, and marginal stability are discussed. In the new area of transient filament network, where the crosslinks can be dynamically broken and re-formed, we show some recent attempts for understanding the dynamics of the crosslinks, and the related rheological properties, such as stress relaxation, yield stress and plasticity.

Nonlinear Loading-Rate-Dependent Force Response of Individual Vimentin Intermediate Filaments to Applied Strain

The mechanical properties of eukaryotic cells are to a great extent determined by the cytoskeleton, a composite network of different filamentous proteins. Among these, intermediate filaments (IFs) are exceptional in their molecular architecture and mechanical properties. Here we directly record stress-strain curves of individual vimentin IFs using optical traps and atomic force microscopy. We find a strong loading rate dependence of the mechanical response, supporting the hypothesis that IFs could serve to protect eukaryotic cells from fast, large deformations. Our experimental results show different unfolding regimes, which we can quantitatively reproduce by an elastically coupled system of multiple two-state elements.

Structural Dynamics of the Vimentin Coiled-coil Contact Regions Involved in Filament Assembly as Revealed by Hydrogen-Deuterium Exchange

Intermediate filaments (IF) are major constituents of the cytoskeleton of metazoan cells. They are not only responsible for the mechanical properties but also for various physiological activities in different cells and tissues. The building blocks of IFs are extended coiled-coil-forming proteins exhibiting a characteristic central α-helical domain ("rod"). The fundamental principles of the filament assembly mechanism and the network formation have been widely elucidated for the cytoplasmic IF protein vimentin. Also, a comprehensive structural model for the tetrameric complex of vimentin has been obtained by X-ray crystallography in combination with various biochemical and biophysical techniques. To extend these static data and to investigate the dynamic properties of the full-length proteins in solution during the various assembly steps, we analyzed the patterns of hydrogen-deuterium exchange in vimentin and in four variants carrying point mutations in the IF consensus motifs present at either end of the α-helical rod that cause an assembly arrest at the unit-length filament (ULF) stage. The results yielded unique insights into the structural properties of subdomains within the full-length vimentin, in particular in regions of contact in α-helical and linker segments that stabilize different oligomeric forms such as tetramers, ULFs, and mature filaments. Moreover, hydrogen-deuterium exchange analysis of the point-mutated variants directly demonstrated the active role of the IF consensus motifs in the oligomerization mechanism of tetramers during ULF formation. Ultimately, using molecular dynamics simulation procedures, we provide a structural model for the subdomain-mediated tetramer/tetramer interaction via "cross-coiling" as the first step of the assembly process.