Structure of actin cross-linked with alpha-actinin: a network of bundles

Non-Markovian Modeling of Nonequilibrium Fluctuations and Dissipation in Active Viscoelastic Biomatter

Based on a Hamiltonian that incorporates the elastic coupling between a tracer particle and the embedding active viscoelastic biomatter, we derive a generalized non-Markovian Langevin model for the nonequilibrium mechanical tracer response. Our analytical expressions for the frequency-dependent tracer response function and the tracer positional autocorrelation function agree quantitatively with experimental data for red blood cells and actomyosin networks with and without adenosine triphosphate over the entire frequency range and in particular reproduce the low-frequency violation of the fluctuation-dissipation theorem. The viscoelastic power laws, the elastic constants and effective friction coefficients extracted from the experimental data allow straightforward physical interpretation.

Mesenchymal β-catenin signaling affects palatogenesis by regulating α-actinin-4 and F-actin

OBJECTIVE

Our previous research have found that mesenchymal β-catenin may be involved in palatal shelf (PS) elevation by regulating F-actin. Here, we further investigated the exact mechanism of β-catenin/F-actin in the PS mesenchyme to regulate palatal reorientation.

MATERIALS AND METHODS

(1) Firstly, Ctnnb1ex3f (β-catenin) mice were conditionally overexpressed in the palatal mesenchyme by crossing with the Sox9-creERT2 mice (induced by Tamoxifen injections); (2) Subsequently, histology and immunohistochemistry were used to characterize the variations of PS morphology and expression of key molecules associated with developmental process; (3) Finally, experiments in vivo and ex vivo were employed to identify the critical mechanisms in β-catenin silenced and overexpressed models.

RESULTS

We found that the Sox9CreER; Ctnnb1ex3f mice exhibited failed palatal elevation and visible cleft palate, and overexpression of β-catenin disturbed the F-actin responsible for cytoskeletal remodeling in palatal mesenchymal cells. qRT-PCR results showed mRNA levels of α-actinin4, a gene involved in F-actin cross-linking, were associated with knockdown or overexpression of β-catenin in ex vivo, respectively. Experiments in vivo revealed that mesenchymal specific inactivation or overexpression of β-catenin exhibited decreased or increased α-actinin-4 expression.

CONCLUSIONS

Mesenchymal β-catenin/F-actin plays an essential role in PS reorientation, which mediate α-actinin-4 to regulate F-actin cytoskeleton reorganization.

Identification and Characterization of α-Actinin 1 of Histomonas meleagridis and Its Potential Vaccine Candidates against Histomonosis

Histomonas meleagridis is a protozoan parasite that causes histomonosis in gallinaceous birds such as turkeys and chickens. Since the banning and restricted usage of effective drugs such as nitarsone, 80-100% morbidity and mortality occur in turkeys and 20-30% mortality in chickens. New ideas are needed to resolve the re-emergence of histomonosis in poultry. In this study, the α-actinin encoding gene from H. meleagridis was cloned. The 1839-bp gene encoding 612 amnio acids showed close phylogenetic relationships with Trichomonas vaginalis and Tritrichomonas foetus. It was then inserted into the prokaryotic expression vector pET28a(+) and induced with isopropyl-β-D-thiogalactopyranoside. A 73 kDa recombinant protein rHmα-actinin 1 was obtained and purified with a Ni-NTA chromatography column. rHmα-actinin 1 was recognized by mouse anti-rHmα-actinin 1 polyclonal antibody, mouse anti-rHmα-actinin 1 monoclonal antibody, and rehabilitation sera from H. meleagridis infected chickens. Native α-actinin 1 in the total proteins of H. meleagridis can also be detected with mouse anti-rHmα-actinin monoclonal antibody. Immunolocalization assays showed that Hmα-actinin 1 was mainly distributed in the cytoplasm of virulent histomonads JSYZ-D9 and in the peripheral regions (near the plasma membrane) of attenuated histomonads JSYZ-D195. Based on in vivo experiment, when chickens were subcutaneously immunized with rHmα-actinin 1 at 5 and 12 days old and then challenged with H. meleagridis at 19 days old, rHmα-actinin 1 reduced the lesion scores 12 days after infection (31 days old) and increased the body weight gain during the challenged period (19-31 days old). Furthermore, it also strengthened the cellular and humoral immune responses 7 days after the second immunization (19 days old). In conclusion, Hmα-actinin 1 could be used as a candidate antigen to develop vaccines against chicken histomonosis.

Actin Bundles Dynamics and Architecture

Cells use the actin cytoskeleton for many of their functions, including their division, adhesion, mechanosensing, endo- and phagocytosis, migration, and invasion. Actin bundles are the main constituent of actin-rich structures involved in these processes. An ever-increasing number of proteins that crosslink actin into bundles or regulate their morphology is being identified in cells. With recent advances in high-resolution microscopy and imaging techniques, the complex process of bundles formation and the multiple forms of physiological bundles are beginning to be better understood. Here, we review the physiochemical and biological properties of four families of highly conserved and abundant actin-bundling proteins, namely, α-actinin, fimbrin/plastin, fascin, and espin. We describe the similarities and differences between these proteins, their role in the formation of physiological actin bundles, and their properties-both related and unrelated to their bundling abilities. We also review some aspects of the general mechanism of actin bundles formation, which are known from the available information on the activity of the key actin partners involved in this process.

Ca2+ and Ag+ orient low-molecular weight amphiphile self-assembly into "nano-fishnet" fibrillar hydrogels with unusual β-sheet-like raft domains

Low-molecular weight gelators (LMWGs) are small molecules (M_w < ∼1 kDa), which form self-assembled fibrillar network (SAFiN) hydrogels in water when triggered by an external stimulus. A great majority of SAFiN gels involve an entangled network of self-assembled fibers, in analogy to a polymer in a good solvent. In some rare cases, a combination of attractive van der Waals and repulsive electrostatic forces drives the formation of bundles with a suprafibrillar hexagonal order. In this work, an unexpected micelle-to-fiber transition is triggered by Ca²⁺ or Ag⁺ ions added to a micellar solution of a novel glycolipid surfactant, whereas salt-induced fibrillation is not common for surfactants. The resulting SAFiN, which forms a hydrogel above 0.5 wt%, has a "nano-fishnet" structure, characterized by a fibrous network of both entangled fibers and β-sheet-like rafts, generally observed for silk fibroin, actin hydrogels or mineral imogolite nanotubes, but not known for SAFiNs. The β-sheet-like raft domains are characterized by a combination of cryo-TEM and SAXS and seem to contribute to the stability of glycolipid gels. Furthermore, glycolipid is obtained by fermentation from natural resources (glucose, rapeseed oil), thus showing that naturally engineered compounds can have unprecedented properties, when compared to the wide range of chemically derived amphiphiles.

Shear recovery and temperature stability of Ca2+ and Ag+ glycolipid fibrillar metallogels with unusual β-sheet-like domains

Low-molecular weight gelators (LMWGs) are small molecules (M_w < ∼1 kDa), which form self-assembled fibrillar network (SAFiN) hydrogels in water. A great majority of SAFiN gels are described by an entangled network of self-assembled fibers, in analogy to a polymer in a good solvent. Here, fibrillation of a biobased glycolipid bolaamphiphile is triggered by Ca²⁺ or Ag⁺ ions which are added to its diluted micellar phase. The resulting SAFiN, which forms a hydrogel above 0.5 wt%, has a "nano-fishnet" structure, characterized by a fibrous network of both entangled fibers and β-sheet-like rafts, generally observed for silk fibroin, actin hydrogels or mineral imogolite nanotubes, but generally not known for SAFiN. This work focuses on the strength of the SAFIN gels, their fast recovery after applying a mechanical stimulus (strain) and their unusual resistance to temperature, studied by coupling rheology to small angle X-ray scattering (rheo-SAXS) using synchrotron radiation. The Ca²⁺-based hydrogel maintains its properties up to 55 °C, while the Ag⁺-based gel shows a constant elastic modulus up to 70 °C, without the appearance of any gel-to-sol transition temperature. Furthermore, the glycolipid is obtained by fermentation from natural resources (glucose and rapeseed oil), thus showing that naturally engineered compounds can have unprecedented properties, when compared to the wide range of chemically derived amphiphiles.

Versicotide G suppresses osteoclastogenesis and prevents osteolysis

Excessive formation and function of osteoclasts cause various osteolytic bone diseases. Natural products are a potential source for the discovery of new therapeutic candidates to treat bone destruction diseases. In this study, chemical informatics and bioassay guided examination of the marine-derived Aspergillus versicolor F77 fungus chemically resulted in the isolation of seven cyclopeptides, of which versicotides G-J (1-4) are new cyclohexapeptides. Their structures were identified by spectroscopic data in association with Marfey method and single crystal X-ray diffraction data for configurational assignments. Bioassay revealed that versicotide G (1, VG) is the most active among the analogs to suppress the receptor activator of nuclear factor-KB ligand (RANKL)-induced osteoclastogenesis in bone marrow derived monocytes (BMMs) without affecting BMMs viability. VG also suppressed RANKL-induced actin-ring formation and resorbing function of osteoclast dose-dependently. Mechanistically, VG attenuated RANKL-induced intracellular calcium elevation by inhibiting PLCγ1 phosphorylation and blocking the activation of downstream phosphatase calcineurin. In addition, VG abrogated the expression and translocation of nuclear factor of activated T cells cytoplasmic-1 (NFATc1), leading to the downregulation of the expression of osteoclast-specific genes and the abolishment of the osteoclast formation. In the in vivo test, VG suppressed osteoclast formation and bone loss in Ti-induced calvarial osteolytic mouse model.These findings imply that VG is a promising candidate for the remedy of bone destruction-related diseases.

Actin crosslinker competition and sorting drive emergent GUV size-dependent actin network architecture

The proteins that make up the actin cytoskeleton can self-assemble into a variety of structures. In vitro experiments and coarse-grained simulations have shown that the actin crosslinking proteins α-actinin and fascin segregate into distinct domains in single actin bundles with a molecular size-dependent competition-based mechanism. Here, by encapsulating actin, α-actinin, and fascin in giant unilamellar vesicles (GUVs), we show that physical confinement can cause these proteins to form much more complex structures, including rings and asters at GUV peripheries and centers; the prevalence of different structures depends on GUV size. Strikingly, we found that α-actinin and fascin self-sort into separate domains in the aster structures with actin bundles whose apparent stiffness depends on the ratio of the relative concentrations of α-actinin and fascin. The observed boundary-imposed effect on protein sorting may be a general mechanism for creating emergent structures in biopolymer networks with multiple crosslinkers.

Actin crosslinker competition and sorting drive emergent GUV size-dependent actin network architecture

The proteins that make up the actin cytoskeleton can self-assemble into a variety of structures. In vitro experiments and coarse-grained simulations have shown that the actin crosslinking proteins α-actinin and fascin segregate into distinct domains in single actin bundles with a molecular size-dependent competition-based mechanism. Here, by encapsulating actin, α-actinin, and fascin in giant unilamellar vesicles (GUVs), we show that physical confinement can cause these proteins to form much more complex structures, including rings and asters at GUV peripheries and centers; the prevalence of different structures depends on GUV size. Strikingly, we found that α-actinin and fascin self-sort into separate domains in the aster structures with actin bundles whose apparent stiffness depends on the ratio of the relative concentrations of α-actinin and fascin. The observed boundary-imposed effect on protein sorting may be a general mechanism for creating emergent structures in biopolymer networks with multiple crosslinkers.

By encapsulating proteins in giant unilamellar vesicles, Bashirzadeh et al find that actin crosslinkers, α-actinin and fascin, can self-assemble with actin into complex structures that depend on the degree of confinement. Further analysis and modeling show that α-actinin and fascin sort to separate domains of these structures. These insights may be generalizable to other biopolymer networks containing crosslinkers.

Quantification of the mesh structure of bundled actin filaments

Biopolymer networks are essential for a wide variety of cellular functions. The biopolymer actin is known to self-assemble into a variety of spatial structures in response to physiological and physical mechanisms. So far, the mechanics of networks of single actin filaments and bundles has previously been described. However, the spatial structure of actin bundles remains poorly understood. Here, we investigate this question by bundling actin filaments with systematically varied concentrations of known physical bundling agents (MgCl2 and PEG) and physiological bundling agents (α-actinin and fascin). We image bundled actin networks with confocal microscopy and perform analysis to describe their mesh size and the nearest-distance distribution, which we call "mesh structure". We find that the mesh size ξ scales universally with actin concentration as ξ ∼ [actin]-1/2. However, the dependence of ξ on the concentration of the bundling agent depends on the agent used. Finally, we find that nearest-distance distributions are best fit by Weibull and Gamma distributions. A complete understanding of the mesh structure of biopolymer networks leads to a more mechanistic understanding of the structure of the cytoskeleton, and can be exploited to design filters with variable porosity for microfluidic devices.

Actin bundle architecture and mechanics regulate myosin II force generation

The actin cytoskeleton is a soft, structural material that underlies biological processes such as cell division, motility, and cargo transport. The cross-linked actin filaments self-organize into a myriad of architectures, from disordered meshworks to ordered bundles, which are hypothesized to control the actomyosin force generation that regulates cell migration, shape, and adhesion. Here, we use fluorescence microscopy and simulations to investigate how actin bundle architectures with varying polarity, spacing, and rigidity impact myosin II dynamics and force generation. Microscopy reveals that mixed-polarity bundles formed by rigid cross-linkers support slow, bidirectional myosin II filament motion, punctuated by periods of stalled motion. Simulations reveal that these locations of stalled myosin motion correspond to sustained, high forces in regions of balanced actin filament polarity. By contrast, mixed-polarity bundles formed by compliant, large cross-linkers support fast, bidirectional motion with no traps. Simulations indicate that trap duration is directly related to force magnitude and that the observed increased velocity corresponds to lower forces resulting from both the increased bundle compliance and filament spacing. Our results indicate that the microstructures of actin assemblies regulate the dynamics and magnitude of myosin II forces, highlighting the importance of architecture and mechanics in regulating forces in biological materials.

Predictive assembling model reveals the self-adaptive elastic properties of lamellipodial actin networks for cell migration

Branched actin network supports cell migration through extracellular microenvironments. However, it is unknown how intracellular proteins adapt the elastic properties of the network to the highly varying extracellular resistance. Here we develop a three-dimensional assembling model to simulate the realistic self-assembling process of the network by encompassing intracellular proteins and their dynamic interactions. Combining this multiscale model with finite element method, we reveal that the network can not only sense the variation of extracellular resistance but also self-adapt its elastic properties through remodeling with intracellular proteins. Such resistance-adaptive elastic behaviours are versatile and essential in supporting cell migration through varying extracellular microenvironments. The bending deformation mechanism and anisotropic Poisson's ratios determine why lamellipodia persistently evolve into sheet-like structures. Our predictions are confirmed by published experiments. The revealed self-adaptive elastic properties of the networks are also applicable to the endocytosis, phagocytosis, vesicle trafficking, intracellular pathogen transport and dendritic spine formation.

Crowding tunes the organization and mechanics of actin bundles formed by crosslinking proteins

Fascin and α-actinin form higher-ordered actin bundles that mediate numerous cellular processes including cell morphogenesis and movement. While it is understood crosslinked bundle formation occurs in crowded cytoplasm, how crowding affects the bundling activities of the two crosslinking proteins is not known. Here, we demonstrate how solution crowding modulates the organization and mechanical properties of fascin- and α-actinin-induced bundles, utilizing total internal reflection fluorescence and atomic force microscopy imaging. Molecular dynamics simulations support the inference that crowding reduces binding interaction between actin filaments and fascin or the calponin homology 1 domain of α-actinin evidenced by interaction energy and hydrogen bonding analysis. Based on our findings, we suggest a mechanism of crosslinked actin bundle assembly and mechanics in crowded intracellular environments.

Competitive Supramolecular Associations Mediate the Viscoelasticity of Binary Hydrogels

Supramolecular polymers are known to form strong and resilient hydrogels which can take up large amounts of water while exhibiting ease of processing and self-healing. They also possess similarities with networks of biological macromolecules. The combination of these features makes supramolecular polymers ideal candidates for studying mechanisms and consequences of self-assembly, which are relevant to biological materials. At the same time, this renders investigations of mixed hydrogels based on different supramolecular compounds necessary, since this substantially widens their applicability. Here, we address unusual viscoelastic properties of a class of binary hydrogels made by mixing fibrillar supramolecular polymers that are formed from two compounds: 1,3,5-benzene-tricarboxamide decorated with aliphatic chains terminated by tetra(ethylene glycol) (BTA) and a 20 kg/mol telechelic poly(ethylene glycol) decorated with the same hydrogen bonding BTA motif on both ends (BTA-PEG-BTA). Using a suite of experimental and simulation techniques, we find that the respective single-compound-based supramolecular systems form very different networks which exhibit drastically different rheology. More strikingly, mixing the compounds results in a non-monotonic dependence of modulus and viscosity on composition, suggesting a competition between interactions of the two compounds, which can then be used to fine-tune the mechanical properties. Simulations offer insight into the nature of this competition and their remarkable qualitative agreement with the experimental results is promising for the design of mixed hydrogels with desired and tunable properties. Their combination with a sensitive dynamic probe (here rheology) offer a powerful toolbox to explore the unique properties of binary hydrogel mixtures.

Tuning molecular motor transport through cytoskeletal filament network organization

Within cells, crosslinking proteins organize cytoskeletal filaments both temporally and spatially to create dynamic and structurally diverse networks. Molecular motors move on these networks for both force generation and transport processes. How the transport statistics depend on the network architecture remains poorly characterized. Using cross-linking proteins (α-actinin, fimbrin, fascin, or filamin) and purified actin, we create cytoskeletal networks with diverse microscopic architectures. We track the motion of myosin II motor proteins moving on these networks and calculate transport statistics. We observe that motor dynamics change predictably based on the bundling of filaments within the underlying networks and discuss implications for network function.

Polyamine-induced, chiral expression from liquid crystalline peptide nanofilaments to long-range ordered nanohelices

We reported the condensation and transformation of peptide micelles into well-defined nanohelices through the incorporation of natural polyamines. The liquid-crystalline peptide micelles are assembled by a short dipeptide amphiphile driven by strong electrostatic repulsions and aromatic stacking attractions. By incorporating polyamines into the peptide solutions, like-charge attractions were achieved to induce the condensation of the like-charged nanofilaments into giant bundles. Intriguingly, by increasing the temperature or electrostatic screening effects, the nanofilaments within the bundles fuse with each other into well-defined flat ribbons which then spontaneously twisted into macroscopically aligned nanohelices. Moreover, the chiral interactions between the aromatic groups of adjacent peptides are inverted from right-handedness to left-handedness during the formation of nanohelices. The results provide new insights into the chiral evolution during peptide self-assembly and offer opportunities for the design of peptide materials with new properties, such as anisotropic hydrogels and long-range ordered chiral nanostructures.

Role of mechanical flow for actin network organization

The major cytoskeletal protein actin forms complex networks to provide structural support and perform vital functions in cells. In vitro studies have revealed that the structure of the higher-order actin network is determined primarily by the type of actin binding protein (ABP). By comparison, there are far fewer studies about the role of the mechanical environment for the organization of the actin network. In particular, the duration over which cells reorganize their shape in response to functional demands is relatively short compared to the in vitro protein polymerization time, suggesting that such changes can influence the actin network formation. We hypothesize that mechanical flows in the cytoplasm generated by exogenous and endogenous stimulation play a key role in the spatiotemporal regulation of the actin architecture. To mimic cytoplasmic streaming, we generated a circulating flow using surface acoustic wave in a microfluidic channel and investigated its effect on the formation of networks by actin and ABPs. We found that the mechanical flow affected the orientation and thickness of actin bundles, depending on the type and concentration of ABPs. Our computational model shows that the extent of alignment and thickness of actin bundle are determined by the balance between flow-induced drag forces and the tendency of ABPs to crosslink actin filaments at given angles. These results suggest that local intracellular flows can affect the assembly dynamics and morphology of the actin cytoskeleton. STATEMENT OF SIGNIFICANCE: Spatiotemporal regulation of actin cytoskeleton structure is essential in many cellular functions. It has been shown that mechanical cues including an applied force and geometric boundary can alter the structural characteristics of actin network. However, even though the cytoplasm accounts for a large portion of the cell volume, the effect of the cytoplasmic streaming flow produced during cell dynamics on actin network organization has not been reported. In this study, we demonstrated that the mechanical flow exerted during actin network organization play an important role in determining the orientation and dimension of actin bundle network. Our result will be beneficial in understanding the mechanism of the actin network reorganization occurred during physiological and pathological processes.

Architectural Dynamics of CaMKII-Actin Networks

Calcium-calmodulin-dependent kinase II (CaMKII) has an important role in dendritic spine remodeling upon synaptic stimulation. Using fluorescence video microscopy and image analysis, we investigated the architectural dynamics of rhodamine-phalloidin stabilized filamentous actin (F-actin) networks cross-linked by CaMKII. We used automated image analysis to identify F-actin bundles and crossover junctions and developed a dimensionless metric to characterize network architecture. Similar networks were formed by three different CaMKII species with a 10-fold length difference in the linker region between the kinase domain and holoenzyme hub, implying linker length is not a primary determinant of F-actin cross-linking. Electron micrographs showed that at physiological molar ratios, single CaMKII holoenzymes cross-linked multiple F-actin filaments at random, whereas at higher CaMKII/F-actin ratios, filaments bundled. Light microscopy established that the random network architecture resisted macromolecular crowding with polyethylene glycol and blocked ATP-powered compaction by myosin-II miniature filaments. Importantly, the networks disassembled after the addition of calcium-calmodulin and were then spaced within 3 min into compacted foci by myosin motors or more slowly (30 min) aggregated by crowding. Single-molecule total internal reflection fluorescence microscopy showed CaMKII dissociation from surface-immobilized globular actin exhibited a monoexponential dwell-time distribution, whereas CaMKII bound to F-actin networks had a long-lived fraction, trapped at crossover junctions. Release of CaMKII from F-actin, triggered by calcium-calmodulin, was too rapid to measure with flow-cell exchange (<20 s). The residual bound fraction was reduced substantially upon addition of an N-methyl-D-aspartate receptor peptide analog but not ATP. These results provide mechanistic insights to CaMKII-actin interactions at the collective network and single-molecule level. Our findings argue that CaMKII-actin networks in dendritic spines maintain spine size against physical stress. Upon synaptic stimulation, CaMKII is disengaged by calcium-calmodulin, triggering network disassembly, expansion, and subsequent compaction by myosin motors with kinetics compatible with the times recorded for the poststimulus changes in spine volume.

Cysteine-rich protein 2 accelerates actin filament cluster formation

Filamentous actin (F-actin) forms many types of structures and dynamically regulates cell morphology and movement, and plays a mechanosensory role for extracellular stimuli. In this study, we determined that the smooth muscle-related transcription factor, cysteine-rich protein 2 (CRP2), regulates the supramolecular networks of F-actin. The structures of CRP2 and F-actin in solution were analyzed by small-angle X-ray solution scattering (SAXS). The general shape of CRP2 was partially unfolded and relatively ellipsoidal in structure, and the apparent cross sectional radius of gyration (R_c) was about 15.8 Å. The predicted shape, derived by ab initio modeling, consisted of roughly four tandem clusters: LIM domains were likely at both ends with the middle clusters being an unfolded linker region. From the SAXS analysis, the R_c of F-actin was about 26.7 Å, and it was independent of CRP2 addition. On the other hand, in the low angle region of the CRP2-bound F-actin scattering, the intensities showed upward curvature with the addition of CRP2, which indicates increasing branching of F-actin following CRP2 binding. From biochemical analysis, the actin filaments were augmented and clustered by the addition of CRP2. This F-actin clustering activity of CRP2 was cooperative with α-actinin. Thus, binding of CRP2 to F-actin accelerates actin polymerization and F-actin cluster formation.

The dynamics of filament assembly define cytoskeletal network morphology

The actin cytoskeleton is a key component in the machinery of eukaryotic cells, and it self-assembles out of equilibrium into a wide variety of biologically crucial structures. Although the molecular mechanisms involved are well characterized, the physical principles governing the spatial arrangement of actin filaments are not understood. Here we propose that the dynamics of actin network assembly from growing filaments results from a competition between diffusion, bundling and steric hindrance, and is responsible for the range of observed morphologies. Our model and simulations thus predict an abrupt dynamical transition between homogeneous and strongly bundled networks as a function of the actin polymerization rate. This suggests that cells may effect dramatic changes to their internal architecture through minute modifications of their nonequilibrium dynamics. Our results are consistent with available experimental data.

The dynamics of actin cytoskeleton is essential to the function of living cells. Here, Foffano et al. describe a nonequilibrium filament model to mimic the formation of cytoskeleton and pinpoint the key role played by the actin entanglement during the transition from homogeneous to bundled networks.

Discontinuous bundling transition in semiflexible polymer networks induced by Casimir interactions

Fluctuation-induced interactions are an important organizing principle in a variety of soft matter systems. We investigate the role of fluctuation-based or thermal Casimir interactions between cross linkers in a semiflexible network. One finds that, by integrating out the polymer degrees of freedom, there is an attractive logarithmic potential between nearest-neighbor cross linkers in a bundle, with a significantly weaker next-nearest-neighbor interaction. Here we show that a one-dimensional gas of these strongly interacting linkers in equilibrium with a source of unbound ones admits a discontinuous phase transition between a sparsely and a densely bound bundle. This discontinuous transition induced by the long-ranged nature of the Casimir interaction allows for a similarly abrupt structural transition in semiflexible filament networks between a low cross linker density isotropic phase and a higher cross link density bundle network. We support these calculations with the results of finite element Brownian dynamics simulations of semiflexible filaments and transient cross linkers.

Fascin- and α-Actinin-Bundled Networks Contain Intrinsic Structural Features that Drive Protein Sorting

Cells assemble and maintain functionally distinct actin cytoskeleton networks with various actin filament organizations and dynamics through the coordinated action of different sets of actin-binding proteins. The biochemical and functional properties of diverse actin-binding proteins, both alone and in combination, have been increasingly well studied. Conversely, how different sets of actin-binding proteins properly sort to distinct actin filament networks in the first place is not nearly as well understood. Actin-binding protein sorting is critical for the self-organization of diverse dynamic actin cytoskeleton networks within a common cytoplasm. Using in vitro reconstitution techniques including biomimetic assays and single-molecule multi-color total internal reflection fluorescence microscopy, we discovered that sorting of the prominent actin-bundling proteins fascin and α-actinin to distinct networks is an intrinsic behavior, free of complicated cellular signaling cascades. When mixed, fascin and α-actinin mutually exclude each other by promoting their own recruitment and inhibiting recruitment of the other, resulting in the formation of distinct fascin- or α-actinin-bundled domains. Subdiffraction-resolution light microscopy and negative-staining electron microscopy revealed that fascin domains are densely packed, whereas α-actinin domains consist of widely spaced parallel actin filaments. Importantly, other actin-binding proteins such as fimbrin and espin show high specificity between these two bundle types within the same reaction. Here we directly observe that fascin and α-actinin intrinsically segregate to discrete bundled domains that are specifically recognized by other actin-binding proteins.

Flexibility and rigidity of cross-linked Straight Fibrils under axial motion constraints

The Straight Fibrils are stiff rod-like filaments and play a significant role in cellular processes as structural stability and intracellular transport. Introducing a 3D mechanical model for the motion of braced cylindrical fibrils under axial motion constraint; we provide some mechanism and a graph theoretical model for fibril structures and give the characterization of the flexibility and the rigidity of this bar-and-joint spatial framework. The connectedness and the circuit of the bracing graph characterize the flexibility of these structures. In this paper, we focus on the kinematical properties of hierarchical levels of fibrils and evaluate the number of the bracing elements for the rigidity and its computational complexity. The presented model is a good characterization of the frameworks of bio-fibrils such as microtubules, cellulose, which inspired this work.

Actin bundles cross-linked with α-actinin studied by nanobeam X-ray diffraction

We have performed scanning nano-beam small-angle X-ray scattering (nano-SAXS) experiments on in vitro-formed actin filaments cross-linked with [Formula: see text]-actinin. The experimental method combines a high resolution in reciprocal space with a real space resolution as given by the spot-size of the nano-focused X-ray beam, and opens up new opportunities to study local super-molecular structures of actin filaments. In this first proof-of-concept, we show that the local orientation of actin bundles formed by the cross-linking can be visualized by the X-ray darkfield maps. The filament bundles give rise to highly anisotropic diffraction patterns showing distinct streaks perpendicular to the bundle axes. Interestingly, some diffraction patterns exhibit a fine structure in the form of intensity modulations allowing for a more detailed analysis of the order within the bundles. A first empirical quantification of these modulations is included in the present work.

Revealing the structure of stereociliary actin by X-ray nanoimaging

Hair cell stereocilia are crucial for hearing and the sense of balance. They include an array of accurately packed, parallel actin filaments and act as levers, which transform mechanical deformation into neuronal signals. The length of vestibular stereocilia reaches several micrometers, whereas, for individual microfilaments, the diameter and therefore the characteristic length scale in the lateral direction is on the order of a few nanometers. These orders of magnitude render X-rays an ideal tool for investigating actin packing, and numerous studies on reconstituted in vitro systems have revealed important information. Here we report on the characterization of intact stereocilia using two nanoscale X-ray techniques. We use X-ray ptychography to image stereocilia with quantitative phase contrast and high dose efficiency, showing stereocilia with diameters and lengths in the expected range. We further employ X-ray nanodiffraction using a nanofocused X-ray beam on the same order of magnitude as the width of a stereocilium. Despite the small probe volume we can clearly visualize the stereocilia bundles. From the individual diffraction patterns we determine the local orientation of the actin structures and can clearly correlate them with the corresponding visible-light fluorescence images. Furthermore, azimuthal integration of individual diffraction patterns reveals distinct intensity curves, showing modulations of the signal, which reflect the relevant length scales and pronounced order in the biological system. The applied techniques are not limited to the studies on stereocilia but have the potential of being applied to many biological and soft-matter systems, in particular if a pronounced degree of order is present.

Scanning x-ray nanodiffraction on Dictyostelium discoideum

We have performed scanning x-ray nanobeam diffraction experiments on single cells of the amoeba Dictyostelium discoideum. Cells have been investigated in 1), freeze-dried, 2), frozen-hydrated (vitrified), and 3), initially alive states. The spatially resolved small-angle x-ray scattering signal shows characteristic streaklike patterns in reciprocal space, which we attribute to fiber bundles of the actomyosin network. From the intensity distributions, an anisotropy parameter can be derived that indicates pronounced local variations within the cell. In addition to nanobeam small-angle x-ray scattering, we have evaluated the x-ray differential phase contrast in view of the projected electron density. Different experimental aspects of the x-ray experiment, sample preparation, and data analysis are discussed. Finally, the x-ray results are correlated with optical microscopy (differential phase contrast and confocal microscopy of mutant strains with fluorescently labeled actin and myosin II), which have been carried out in live and fixed states, including optical microscopy under cryogenic conditions.

Sacs knockout mice present pathophysiological defects underlying autosomal recessive spastic ataxia of Charlevoix-Saguenay

Autosomal recessive spastic ataxia of Charlevoix-Saguenay (ARSACS [MIM 270550]) is an early-onset neurodegenerative disorder caused by mutations in the SACS gene. Over 170 SACS mutations have been reported worldwide and are thought to cause loss of function of sacsin, a poorly characterized and massive 520 kDa protein. To establish an animal model and to examine the pathophysiological basis of ARSACS, we generated Sacs knockout (Sacs(-/-)) mice. Null animals displayed an abnormal gait with progressive motor, cerebellar and peripheral nerve dysfunctions highly reminiscent of ARSACS. These clinical features were accompanied by an early onset, progressive loss of cerebellar Purkinje cells followed by spinal motor neuron loss and peripheral neuropathy. Importantly, loss of sacsin function resulted in abnormal accumulation of non-phosphorylated neurofilament (NF) bundles in the somatodendritic regions of vulnerable neuronal populations, a phenotype also observed in an ARSACS brain. Moreover, motor neurons cultured from Sacs(-/-) embryos exhibited a similar NF rearrangement with significant reduction in mitochondrial motility and elongated mitochondria. The data points to alterations in the NF cytoskeleton and defects in mitochondrial dynamics as the underlying pathophysiological basis of ARSACS.

Designing highly tunable semiflexible filament networks

Semiflexible polymers can generate a range of filamentous networks significantly different in structure from those seen in conventional polymer solutions. Our coarse-grained simulations with an implicit cross-linker potential show that networks of branching bundles, knotted morphologies, and structural chirality can be generated by a generalized approach independent of specific cross-linkers. Network structure depends primarily on filament flexibility and separation, with significant connectivity increase after percolation. Results should guide the design of engineered semiflexible polymers.

Ubiquitin C-terminal hydrolase L1 deletion ameliorates glomerular injury in mice with ACTN4-associated focal segmental glomerulosclerosis

Renal ubiquitin C-terminal hydrolase L1 (UCHL1) is upregulated in a subset of human glomerulopathies, including focal segmental glomerulosclerosis (FSGS), where it may serve to promote ubiquitin pools for degradation of cytotoxic proteins. In the present study, we tested whether UCHL1 is expressed in podocytes of a mouse model of ACTN4-associated FSGS. Podocyte UCHL1 protein was detected in glomeruli of K256E-ACTN4(pod+)/UCHL1+/+ mice. UCHL1+/- mice were intercrossed with K256E-ACTN4(pod+) mice and monitored for features of glomerular disease. 10-week-old K256E-ACTN4(pod+)/UCHL1-/- mice exhibited significantly ameliorated albuminuria, glomerulosclerosis, tubular pathology and blood pressure. Interestingly, while UCHL1 deletion diminished both tubular and glomerular apoptosis, WT1-positive nuclei were unchanged. Finally, UCHL1 levels correlated positively with poly-ubiquitinated proteins but negatively with K256E-α-actinin-4 levels, implying reduced K256E-α-actinin-4 proteolysis in the absence of UCHL1. Our data suggest that UCHL1 upregulation in ACTN4-associated FSGS fuels the proteasome and that UCHL1 deletion may impair proteolysis and thereby preserve K256E/wt-α-actinin-4 heterodimers, maintaining podocyte cytoskeletal integrity and protecting the glomerular filtration barrier.

Protein conformation as a regulator of cell–matrix adhesion

Conformational changes within proteins play key roles in the regulation of cell–matrix adhesion. We discuss the mechanisms involved in conformational regulation, including mechanical signals, posttranslational modifications and intrinsically disordered proteins.

Using cell structures to develop functional nanomaterials and nanostructures – case studies of actin filaments and microtubules

Actin filaments and microtubules are utilized as building blocks to create functional nanomaterials and nanostructures for nature-inspired small-scale devices and systems.

3D actin network centerline extraction with multiple active contours

Fluorescence microscopy is frequently used to study two and three dimensional network structures formed by cytoskeletal polymer fibers such as actin filaments and actin cables. While these cytoskeletal structures are often dilute enough to allow imaging of individual filaments or bundles of them, quantitative analysis of these images is challenging. To facilitate quantitative, reproducible and objective analysis of the image data, we propose a semi-automated method to extract actin networks and retrieve their topology in 3D. Our method uses multiple Stretching Open Active Contours (SOACs) that are automatically initialized at image intensity ridges and then evolve along the centerlines of filaments in the network. SOACs can merge, stop at junctions, and reconfigure with others to allow smooth crossing at junctions of filaments. The proposed approach is generally applicable to images of curvilinear networks with low SNR. We demonstrate its potential by extracting the centerlines of synthetic meshwork images, actin networks in 2D Total Internal Reflection Fluorescence Microscopy images, and 3D actin cable meshworks of live fission yeast cells imaged by spinning disk confocal microscopy. Quantitative evaluation of the method using synthetic images shows that for images with SNR above 5.0, the average vertex error measured by the distance between our result and ground truth is 1 voxel, and the average Hausdorff distance is below 10 voxels.

Podosomes in adhesion, migration, mechanosensing and matrix remodeling

Cells use various actin-based motile structures to allow them to move across and through matrix of varying density and composition. Podosomes are actin cytoskeletal structures that form in motile cells and that mediate adhesion to substrate, migration, and other specialized functions such as transmigration through cell and matrix barriers. The podosome is a unique and interesting entity, which appears in the light microscope as an individual punctum, but is linked to other podosomes like a node on a network of the underlying cytoskeleton. Here, we discuss the signals that control podosome assembly and dynamics in different cell types and the actin organising proteins that regulate both the inner actin core and integrin-rich surrounding ring structures. We review the structure and composition of podosomes and also their functions in various cell types of both myeloid and endothelial lineage. We also discuss the emerging idea that podosomes can sense matrix stiffness and enable cells to respond to their environment.

Spatiotemporal dynamics of actomyosin networks

Rhodamine-phalloidin-labeled actin filaments were visualized gliding over a skeletal heavy meromyosin (HMM)-coated surface. Experiments at low filament densities showed that when two filaments collided, their paths were affected in a manner that depended on collision angle. Some collisions resulted in complete alignment of the filament paths; in others, the filaments crossed over one another. Filament crossover or alignment was equally probable at ∼40° contact angle. Filaments often underwent significant bending during collision and analysis of filament shape indicated an energy requirement of ∼13 kBT. Experiments were performed over a wide range of HMM surface density and actin filament bulk concentration. Actin filament gliding speed and path persistence plateaued above a critical HMM surface density, and at high (micromolar) actin filament concentrations, filament motion became dramatically aligned in a common direction. Spatiotemporal features of alignment behavior were determined by correlation analysis, supported by simulations. The thermal drift of individual filament tracks was suppressed as the population became more oriented. Spatial correlation analysis revealed that long-range alignment was due to incremental recruitment rather than fusion of locally ordered seed domains. The global alignment of filament movement, described by an "order parameter," peaked at optimal actin concentrations and myosin surface densities, in contrast to previous predictions of a critical phase transition. Either hydrodynamic coupling or exchange of filaments between the surface bound and adjacent bulk phase layers might degrade order at high actin filament concentration, and high HMM surface densities might decrease alignment probability during collisions. Our results are compatible with generation of long-range order from mechanical interaction between individual actin filaments. Furthermore, we show that randomly oriented myosin motors align relatively short, submicrometer actin filaments into motile surface domains that extend over many tens of micrometers and these patterns persist for several minutes.

Controlled arrays of self-assembled peptide nanostructures in solution and at interface

Controlling the formation of large and homogeneous arrays of bionanostructures through the self-assembly approach is still a great challenge. Here, we report the spontaneous formation of highly ordered arrays based on aligned peptide nanostructures in a solution as well as at an interface by self-assembly. By controlling the time and temperature of self-assembly in the solution, parallel fibrous alignments and more sophisticated two-dimensional "knitted" fibrous arrays could be formed from aligned rod-like fibers. During the formation of such arrays, the "disorder-to-order" transitions are controlled by the temperature-responsible motile short hydrophobic tails of the gemini-like amphiphilic peptides (GAPs) with asymmetric molecular conformation. In addition, the resulting long-range-ordered "knitted" fibrous arrays are able to direct mineralization of calcium phosphate to form organic-inorganic composite materials. In this study, the self-assembly behavior of these peptide building blocks at an interface was also studied. Highly ordered spatial arrays with vertically or horizontally aligned nanostructures such as nanofibers, microfibers, and microtubes could be formed through interfacial assembly. The regular structures and their alignments on the interface are controlled by the alkyl chain length of building blocks and the hydrophilicity/hydrophobicity property of the interface.

Ion specific effects in bundling and depolymerization of taxol-stabilized microtubules

Microtubules (MTs) are nanometer scale hollow cylindrical biological polyelectrolytes. They are assembled from alpha/beta-tubulin dimers, which stack to form protofilaments (PFs) with lateral interactions between PFs resulting in the curved MT. In cells, MTs and their assemblies are critical components in a range of functions from providing tracks for the transport of cargo to forming the spindle structure during mitosis. Previous studies have, shown that while cations with valence equal to or larger than 3+ tend to assemble tight 3D bundles of taxol-stabilized MTs, certain divalent cations induce relatively loose 2D bundles of different symmetry (D. J. Needleman et al., Proc. Natl. Acad. Sci. U. S. A., 2004, 101, 16099). Similarly, divalent cations form 2D bundles of DNA adsorbed on cationic membranes (I. Koltover et al., Proc. Natl. Acad. Sci. U. S. A., 2000, 97, 14046). The bundling behavior for these biological polyelectrolyte systems is qualitatively in agreement with current theory. Here, we present results which show that, unlike the case for DNA adsorbed on cationic membranes, bundling of taxol-stabilized MTs occurs only for certain divalent cations above a critical ion concentration (e.g. Ca2+, Sr2+, Ba2+). Instead, many divalent cations pre-empt the bundling transition and depolymerize taxol-stabilized MTs at a lower counterion concentration. Although previous cryogenic TEM has shown that, in the absence of taxol, Ca2+ depolymerizes MTs assembling in buffers containing GTP (guanosine triphosphate), our finding is surprising given the know stabilizing effects of taxol on GDP (guanosine diphosphate)-MTs. The ion concentration required for MT depolymerization decreases with increasing atomic number for the divalents Mg2+, Mn2+, Co2+, and Zn2+. GdCl3 (3+) is found to be extremely efficient at MT depolymerization requiring ion concentrations of about 1 mM, while oligolysine(2+), is observed not to depolymerize MTs at concentrations as high as 144 mM. The surprising MT depolymerization results are discussed in the context of divalents either disrupting lateral interactions between PFs (which are strengthened for taxol containing beta-tubulin) or interfering with taxol's ability to induce flexibility at the interface between two tubulin dimers in the same PF (which has been recently suggested as a mechanism by which taxol stabilizes MTs post-hydrolysis with the induced flexibility counteracting the kink between GDP-tublin dimers in a PF).

Liquid crystal assemblies in biologically inspired systems

In this paper, which is part of a collection in honor of Noel Clark's remarkable career on liquid crystal and soft matter research, we present examples of biologically inspired systems, which form liquid crystal (LC) phases with their LC nature impacting biological function in cells or being important in biomedical applications. One area focuses on understanding network and bundle formation of cytoskeletal polyampholytes (filamentous-actin, microtubules, and neurofilaments). Here, we describe studies on neurofilaments (NFs), the intermediate filaments of neurons, which form open network nematic liquid crystal hydrogels in axons. Synchrotron small-angle-x-ray scattering studies of NF-protein dilution experiments and NF hydrogels subjected to osmotic stress show that neurofilament networks are stabilized by competing long-range repulsion and attractions mediated by the neurofilament's polyampholytic sidearms. The attractions are present both at very large interfilament spacings, in the weak sidearm-interpenetrating regime, and at smaller interfilament spacings, in the strong sidearm-interpenetrating regime. A second series of experiments will describe the structure and properties of cationic liposomes (CLs) complexed with nucleic acids (NAs). CL-NA complexes form liquid crystalline phases, which interact in a structure-dependent manner with cellular membranes enabling the design of complexes for efficient delivery of nucleic acid (DNA, RNA) in therapeutic applications.

The major transitions of life from a network perspective

Many attempts have been made to understand the origin of life and biological complexity both at the experimental and theoretical levels but neither is fully explained. In an influential work, Maynard Smith and Szathmáry (1995) argued that the majority of the increase in complexity is not gradual, but it is associated with a few so-called major transitions along the way of the evolution of life. For each major transition, they identified specific mechanisms that could account for the change in complexity related to information transmission across generations. In this work, I propose that the sudden and unexpected improvement in the functionality of an organism that followed a major transition was enabled by a phase transition in the network structure associated with that function. The increase in complexity following a major transition is therefore directly linked to the emergence of a novel structure-function relation which altered the course of evolution. As a consequence, emergent phenomena arising from these network phase transitions can serve as a common organizing principle for understanding the major transitions. As specific examples, I analyze the emergence of life, the emergence of the genetic apparatus, the rise of the eukaryotic cells, the evolution of movement and mechanosensitivity, and the emergence of consciousness. Finally, I discuss the implications of network associated phase transitions to issues that bear relevance to the history, the immediate present and perhaps the future, of life.

Active membrane viscoelasticity by the bacterial FtsZ-division protein

At the early stages of the division process in Escherichia coli, the protein FtsZ forms a septal ring at the midcell. This Z-ring causes membrane constriction during bacterial division. The Z-ring associates to the lipid membrane through several membrane proteins, ZipA among them. Here, a simplified FtsZ-ZipA model was reconstituted onto Langmuir monolayers based in E. coli polar lipid extract. Brewster angle and atomic force microscopy have revealed membrane FtsZ-polymerization upon GTP hydrolysis. The compression viscoelasticity of these monolayers has been also investigated. The presence of protein induced softening and fluidization with respect to the bare lipid membrane. An active mechanism, based on the internal forces stressed by FtsZ filaments and transduced to the lipid membrane by ZipA, was suggested to underlie the observed behavior.

Nanoscale assembly in biological systems: from neuronal cytoskeletal proteins to curvature stabilizing lipids

The review will describe experiments inspired by the rich variety of bundles and networks of interacting microtubules (MT), neurofilaments, and filamentous-actin in neurons where the nature of the interactions, structures, and structure-function correlations remain poorly understood. We describe how three-dimensional (3D) MT bundles and 2D MT bundles may assemble, in cell free systems in the presence of counter-ions, revealing structures not predicted by polyelectrolyte theories. Interestingly, experiments reveal that the neuronal protein tau, an abundant MT-associated-protein in axons, modulates the MT diameter providing insight for the control of geometric parameters in bio- nanotechnology. In another set of experiments we describe lipid-protein-nanotubes, and lipid nano-tubes and rods, resulting from membrane shape evolution processes involving protein templates and curvature stabilizing lipids. Similar membrane shape changes, occurring in cells for the purpose of specific functions, are induced by interactions between membranes and proteins. The biological materials systems described have applications in bio-nanotechnology.

Cooperative crosslink (un)binding in slowly driven bundles of semiflexible filaments

Combining simulations and theory I study the interplay between bundle elastic degrees of freedom and crosslink binding propensity. By slowly driving bundles into a deformed configuration, and depending on the mechanical stiffness of the crosslinking agent, the binding affinity is shown to display a sudden and discontinuous drop. This indicates a cooperative unbinding process that involves the crossing of a free-energy barrier. Choosing the proper crosslinker therefore not only allows us to change the composite elastic properties of the bundle but also the relevant time scales which can be tuned from the single crosslink binding rate to the much longer escape time over the free-energy barrier.

Statistical model with two order parameters for ductile and soft fiber bundles in nanoscience and biomaterials

Traditional fiber bundles models (FBMs) have been an effective tool to understand brittle heterogeneous systems. However, fiber bundles in modern nano- and bioapplications demand a new generation of FBM capturing more complex deformation processes in addition to damage. In the context of loose bundle systems and with reference to time-independent plasticity and soft biomaterials, we formulate a generalized statistical model for ductile fracture and nonlinear elastic problems capable of handling more simultaneous deformation mechanisms by means of two order parameters (as opposed to one). As the first rational FBM for coupled damage problems, it may be the cornerstone for advanced statistical models of heterogeneous systems in nanoscience and materials design, especially to explore hierarchical and bio-inspired concepts in the arena of nanobiotechnology. Applicative examples are provided for illustrative purposes at last, discussing issues in inverse analysis (i.e., nonlinear elastic polymer fiber and ductile Cu submicron bars arrays) and direct design (i.e., strength prediction).

Polymorphism of highly cross-linked F-actin networks: probing multiple length scales

The assembly properties of F-actin filaments in the presence of different biological cross-linker concentrations and types have been investigated using a combined approach of fluorescence confocal microscopy and coarse-grained molecular dynamics simulation. In particular for highly cross-linked regimes, new network morphologies are observed. Complex network formation and the details of the resulting structure are strongly dependent on the ratio of cross-linkers to actin monomers and cross-linker shape but only weakly dependent on overall actin concentration and filament length. The work presented here may help to provide some fundamental understanding of how excessive cross-linkers interact with the actin filament solution, creating different structures in the cell under high cross-linker concentrations. F-actin is not only of biological importance but also, as an example of a semiflexible polymer, has attracted significant interest in its physical behavior. In combination with different cross-linkers semiflexible filaments may provide new routes to bio-materials development and act as the inspiration for new hierarchical network-based materials.

Actin cross-link assembly and disassembly mechanics for alpha-Actinin and fascin

Self-assembly of complex structures is commonplace in biology but often poorly understood. In the case of the actin cytoskeleton, a great deal is known about the components that include higher order structures, such as lamellar meshes, filopodial bundles, and stress fibers. Each of these cytoskeletal structures contains actin filaments and cross-linking proteins, but the role of cross-linking proteins in the initial steps of structure formation has not been clearly elucidated. We employ an optical trapping assay to investigate the behaviors of two actin cross-linking proteins, fascin and alpha-actinin, during the first steps of structure assembly. Here, we show that these proteins have distinct binding characteristics that cause them to recognize and cross-link filaments that are arranged with specific geometries. alpha-Actinin is a promiscuous cross-linker, linking filaments over all angles. It retains this flexibility after cross-links are formed, maintaining a connection even when the link is rotated. Conversely, fascin is extremely selective, only cross-linking filaments in a parallel orientation. Surprisingly, bundles formed by either protein are extremely stable, persisting for over 0.5 h in a continuous wash. However, using fluorescence recovery after photobleaching and fluorescence decay experiments, we find that the stable fascin population can be rapidly competed away by free fascin. We present a simple avidity model for this cross-link dissociation behavior. Together, these results place constraints on how cytoskeletal structures assemble, organize, and disassemble in vivo.

Statics and dynamics of the wormlike bundle model

Bundles of filamentous polymers are primary structural components of a broad range of cytoskeletal structures, and their mechanical properties play key roles in cellular functions ranging from locomotion to mechanotransduction and fertilization. We give a detailed derivation of a wormlike bundle model as a generic description for the statics and dynamics of polymer bundles consisting of semiflexible polymers interconnected by crosslinking agents. The elastic degrees of freedom include bending as well as twist deformations of the filaments and shear deformation of the crosslinks. We show that a competition between the elastic properties of the filaments and those of the crosslinks leads to renormalized effective bend and twist rigidities that become mode-number dependent. The strength and character of this dependence is found to vary with bundle architecture, such as the arrangement of filaments in the cross section and pretwist. We discuss two paradigmatic cases of bundle architecture, a uniform arrangement of filaments as found in F -actin bundles and a shell-like architecture as characteristic for microtubules. Each architecture is found to have its own universal ratio of maximal to minimal bending rigidity, independent of the specific type of crosslink-induced filament coupling; our predictions are in reasonable agreement with available experimental data for microtubules. Moreover, we analyze the predictions of the wormlike bundle model for experimental observables such as the tangent-tangent correlation function and dynamic response and correlation functions. Finally, we analyze the effect of pretwist (helicity) on the mechanical properties of bundles. We predict that microtubules with different number of protofilaments should have distinct variations in their effective bending rigidity.