Leveraging single protein polymers to measure flexural rigidity

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.

From the membrane to the nucleus: mechanical signals and transcription regulation

Mechanical forces drive and modulate a wide variety of processes in eukaryotic cells including those occurring in the nucleus. Relevantly, forces are fundamental during development since they guide lineage specifications of embryonic stem cells. A sophisticated macromolecular machinery transduces mechanical stimuli received at the cell surface into a biochemical output; a key component in this mechanical communication is the cytoskeleton, a complex network of biofilaments in constant remodeling that links the cell membrane to the nuclear envelope. Recent evidence highlights that forces transmitted through the cytoskeleton directly affect the organization of chromatin and the accessibility of transcription-related molecules to their targets in the DNA. Consequently, mechanical forces can directly modulate transcription and change gene expression programs. Here, we will revise the biophysical toolbox involved in the mechanical communication with the cell nucleus and discuss how mechanical forces impact on the organization of this organelle and more specifically, on transcription. We will also discuss how live-cell fluorescence imaging is producing exquisite information to understand the mechanical response of cells and to quantify the landscape of interactions of transcription factors with chromatin in embryonic stem cells. These studies are building new biophysical insights that could be fundamental to achieve the goal of manipulating forces to guide cell differentiation in culture systems.

Constriction of Actin Rings by Passive Crosslinkers

In many organisms, cell division is driven by the constriction of a cytokinetic ring, which consists of actin filaments and crosslinking proteins. While it has long been believed that the constriction is driven by motor proteins, it has recently been discovered that passive crosslinkers that do not turn over fuel are able to generate enough force to constrict actin filament rings. To study the ring constriction dynamics, we develop a model that includes the driving force of crosslinker condensation and the opposing forces of friction and filament bending. We analyze the constriction force as a function of ring topology and crosslinker concentration, and predict forces that are sufficient to constrict an unadorned plasma membrane. Our model also predicts that actin-filament sliding arises from an interplay between filament rotation and crosslinker hopping, producing frictional forces that are low compared with those of crosslinker-mediated microtubule sliding.

Studying actin-induced cell shape changes using Giant Unilamellar Vesicles and reconstituted actin networks

Cell shape changes that are fuelled by the dynamics of the actomyosin cytoskeleton control cellular processes such as motility and division. However, the mechanisms of interplay between cell membranes and actomyosin are complicated to decipher in the complex environment of the cytoplasm. Using biomimetic systems offers an alternative approach to studying cell shape changes in assays with controlled biochemical composition. Biomimetic systems allow quantitative experiments that can help to build physical models describing the processes of cell shape changes. This article reviews works in which actin networks are reconstructed inside or outside cell-sized Giant Unilamellar Vesicles (GUVs), which are models of cell membranes. We show how various actin networks affect the shape and mechanics of GUVs and how some cell shape changes can be reproduced in vitro using these minimal systems.

Self-Sustained Regulation or Self-Perpetuating Dysregulation: ROS-dependent HIF-YAP-Notch Signaling as a Double-Edged Sword on Stem Cell Physiology and Tumorigenesis

Organ development, homeostasis, and repair often rely on bidirectional, self-organized cell-niche interactions, through which cells select cell fate, such as stem cell self-renewal and differentiation. The niche contains multiplexed chemical and mechanical factors. How cells interpret niche structural information such as the 3D topology of organs and integrate with multiplexed mechano-chemical signals is an open and active research field. Among all the niche factors, reactive oxygen species (ROS) have recently gained growing interest. Once considered harmful, ROS are now recognized as an important niche factor in the regulation of tissue mechanics and topology through, for example, the HIF-YAP-Notch signaling pathways. These pathways are not only involved in the regulation of stem cell physiology but also associated with inflammation, neurological disorder, aging, tumorigenesis, and the regulation of the immune checkpoint molecule PD-L1. Positive feedback circuits have been identified in the interplay of ROS and HIF-YAP-Notch signaling, leading to the possibility that under aberrant conditions, self-organized, ROS-dependent physiological regulations can be switched to self-perpetuating dysregulation, making ROS a double-edged sword at the interface of stem cell physiology and tumorigenesis. In this review, we discuss the recent findings on how ROS and tissue mechanics affect YAP-HIF-Notch-PD-L1 signaling, hoping that the knowledge can be used to design strategies for stem cell-based and ROS-targeting therapy and tissue engineering.

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.

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.

A finite element model of an osteoblast to quantify the transduction of exogenous forces to cellular components

Encouraged by recent advances of biophysical and biochemical assays we introduce a 3D finite element model of an osteoblast, seeking an analogue between exogenous forces and intracellularly activated sensory mechanisms. The cell was reverse engineered and the dimensions of the internal cellular structures were based on literature data. The model was verified and validated against atomic force microscopy experiments and four loading scenarios were considered. The stress distributions developing on the main cellular components were calculated along with their corresponding strain values. The nucleus and mitochondria exhibited similar loading trends, with the mitochondria being stressed by an order of magnitude higher than the nucleus (e.g. 1.4 vs. 0.16 MPa). Equivalent stiffness was determined to increase by almost 50%, from the apex to the cell's periphery, as was the cell's elasticity, which was lowest when the load was exerted directly above the nucleus. The assessment of how extrinsic loads are propagated to a cell's internal structures is inherently a problem of high complexity. The findings presented in this study can provide important insight into biophysical and biochemical responses elicited in cells through mechanical stimulus. This was evident in both the nuclear and mitochondrial loading and would stipulate the important contribution of even more accurate models in the interpretation of cellular events. One Sentence Summary: The results of this numerical biomechanical study demonstrated that even minor extrinsic loads irrespective of the application site, are transduced by a fraction of the cytoskeleton to its internal structure (primarily to its mitochondria and secondary to the cell's nucleus), indicating mechanical stimulus as the dominant pathway to cell expression.

FtsZ induces membrane deformations via torsional stress upon GTP hydrolysis

FtsZ is a key component in bacterial cell division, being the primary protein of the presumably contractile Z ring. In vivo and in vitro, it shows two distinctive features that could so far, however, not be mechanistically linked: self-organization into directionally treadmilling vortices on solid supported membranes, and shape deformation of flexible liposomes. In cells, circumferential treadmilling of FtsZ was shown to recruit septum-building enzymes, but an active force production remains elusive. To gain mechanistic understanding of FtsZ dependent membrane deformations and constriction, we design an in vitro assay based on soft lipid tubes pulled from FtsZ decorated giant lipid vesicles (GUVs) by optical tweezers. FtsZ filaments actively transform these tubes into spring-like structures, where GTPase activity promotes spring compression. Operating the optical tweezers in lateral vibration mode and assigning spring constants to FtsZ coated tubes, the directional forces that FtsZ-YFP-mts rings exert upon GTP hydrolysis can be estimated to be in the pN range. They are sufficient to induce membrane budding with constricting necks on both, giant vesicles and E.coli cells devoid of their cell walls. We hypothesize that these forces result from torsional stress in a GTPase activity dependent manner.

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.

Optical Tweezers Approaches for Probing Multiscale Protein Mechanics and Assembly

Multi-step assembly of individual protein building blocks is key to the formation of essential higher-order structures inside and outside of cells. Optical tweezers is a technique well suited to investigate the mechanics and dynamics of these structures at a variety of size scales. In this mini-review, we highlight experiments that have used optical tweezers to investigate protein assembly and mechanics, with a focus on the extracellular matrix protein collagen. These examples demonstrate how optical tweezers can be used to study mechanics across length scales, ranging from the single-molecule level to fibrils to protein networks. We discuss challenges in experimental design and interpretation, opportunities for integration with other experimental modalities, and applications of optical tweezers to current questions in protein mechanics and assembly.

A Weak Link with Actin Organizes Tight Junctions to Control Epithelial Permeability

In vertebrates, epithelial permeability is regulated by the tight junction (TJ) formed by specialized adhesive membrane proteins, adaptor proteins, and the actin cytoskeleton. Despite the TJ's critical physiological role, a molecular-level understanding of how TJ assembly sets the permeability of epithelial tissue is lacking. Here, we identify a 28-amino-acid sequence in the TJ adaptor protein ZO-1, which is responsible for actin binding, and show that this interaction is essential for TJ permeability. In contrast to the strong interactions at the adherens junction, we find that the affinity between ZO-1 and actin is surprisingly weak, and we propose a model based on kinetic trapping to explain how affinity could affect TJ assembly. Finally, by tuning the affinity of ZO-1 to actin, we demonstrate that epithelial monolayers can be engineered with a spectrum of permeabilities, which points to a promising target for treating transport disorders and improving drug delivery.

Insights into the Structure, Function, and Dynamics of the Bacterial Cytokinetic FtsZ-Ring

The FtsZ protein is a highly conserved bacterial tubulin homolog. In vivo, the functional form of FtsZ is the polymeric, ring-like structure (Z-ring) assembled at the future division site during cell division. While it is clear that the Z-ring plays an essential role in orchestrating cytokinesis, precisely what its functions are and how these functions are achieved remain elusive. In this article, we review what we have learned during the past decade about the Z-ring's structure, function, and dynamics, with a particular focus on insights generated by recent high-resolution imaging and single-molecule analyses. We suggest that the major function of the Z-ring is to govern nascent cell pole morphogenesis by directing the spatiotemporal distribution of septal cell wall remodeling enzymes through the Z-ring's GTP hydrolysis-dependent treadmilling dynamics. In this role, FtsZ functions in cell division as the counterpart of the cell shape-determining actin homolog MreB in cell elongation.

Harmonic Generation Microscopy 2.0: New Tricks Empowering Intravital Imaging for Neuroscience

Optical harmonic generation, e.g., second- (SHG) and third-harmonic generation (THG), provides intrinsic contrasts for three-dimensional intravital microscopy. Contrary to two-photon excited fluorescence (TPEF), however, they have found relatively specialized applications, such as imaging collagenous and non-specific tissues, respectively. Here we review recent advances that broaden the capacity of SHG and THG for imaging the central nervous system in particular. The fundamental contrast mechanisms are reviewed as they encode novel information including molecular origin, spectroscopy, functional probes, and image analysis, which lay foundations for promising future applications in neuroscience.

Distinct Binding Modes of Vinculin Isoforms Underlie Their Functional Differences

Vinculin and its splice isoform metavinculin play key roles in regulating cellular morphology, motility, and force transduction. Vinculin is distinct from metavinculin in its ability to bundle filamentous actin (F-actin). To elucidate the molecular basis for these differences, we employed computational and experimental approaches. Results from these analyses suggest that the C terminus of both vinculin and metavinculin form stable interactions with the F-actin surface. However, the metavinculin tail (MVt) domain contains a 68 amino acid insert, with helix 1 (H1) sequestered into a globular subdomain, which protrudes from the F-actin surface and prevents actin bundling by sterically occluding actin filaments. Consistent with our model, deletion and selective point mutations within the MVt H1 disrupt this protruding structure, and facilitate actin bundling similar to vinculin tail (Vt) domain.

From isolated structures to continuous networks: A categorization of cytoskeleton-based motile engineered biological microstructures

As technology at the small scale is advancing, motile engineered microstructures are becoming useful in drug delivery, biomedicine, and lab-on-a-chip devices. However, traditional engineering methods and materials can be inefficient or functionally inadequate for small-scale applications. Increasingly, researchers are turning to the biology of the cytoskeleton, including microtubules, actin filaments, kinesins, dyneins, myosins, and associated proteins, for both inspiration and solutions. They are engineering structures with components that range from being entirely biological to being entirely synthetic mimics of biology and on scales that range from isotropic continuous networks to single isolated structures. Motile biological microstructures trace their origins from the development of assays used to study the cytoskeleton to the array of structures currently available today. We define 12 types of motile biological microstructures, based on four categories: entirely biological, modular, hybrid, and synthetic, and three scales: networks, clusters, and isolated structures. We highlight some key examples, the unique functionalities, and the potential applications of each microstructure type, and we summarize the quantitative models that enable engineering them. By categorizing the diversity of motile biological microstructures in this way, we aim to establish a framework to classify these structures, define the gaps in current research, and spur ideas to fill those gaps. This article is categorized under: Nanotechnology Approaches to Biology > Nanoscale Systems in Biology Nanotechnology Approaches to Biology > Cells at the Nanoscale Biology-Inspired Nanomaterials > Protein and Virus-Based Structures Therapeutic Approaches and Drug Discovery > Emerging Technologies.

Effect of Nucleotide State on the Protofilament Conformation of Tubulin Octamers

At the molecular level, the dynamic instability (random growth and shrinkage) of the microtubule (MT) is driven by the nucleotide state (GTP vs GDP) in the β subunit of the tubulin dimers at the MT cap. Here, we use large-scale molecular dynamics (MD) simulations and normal-mode analysis (NMA) to characterize the effect of a single GTP cap layer on tubulin octamers composed of two neighboring protofilaments (PFs). We utilize recently reported high-resolution structures of dynamic MTs to simulate a GDP octamer both with and without a single GTP cap layer. We perform multiple replicas of long-time atomistic MD simulations (3 replicas, 0.3 μs for each replica, 0.9 μs for each octamer system, and 1.8 μs total) of both octamers. We observe that a single GTP cap layer induces structural differences in neighboring PFs, finding that one PF possesses a gradual curvature, compared to the second PF which possesses a kinked conformation. This results in either curling or splaying between these PFs. We suggest that this is due to asymmetric strengths of longitudinal contacts between the two PFs. Furthermore, using NMA, we calculate mechanical properties of these octamer systems and find that octamer system with a single GTP cap layer possesses a lower flexural rigidity.

Microtubules soften due to cross-sectional flattening

We use optical trapping to continuously bend an isolated microtubule while simultaneously measuring the applied force and the resulting filament strain, thus allowing us to determine its elastic properties over a wide range of applied strains. We find that, while in the low-strain regime, microtubules may be quantitatively described in terms of the classical Euler-Bernoulli elastic filament, above a critical strain they deviate from this simple elastic model, showing a softening response with increasingdeformations. A three-dimensional thin-shell model, in which the increased mechanical compliance is caused by flattening and eventual buckling of the filament cross-section, captures this softening effect in the high strain regime and yields quantitative values of the effective mechanical properties of microtubules. Our results demonstrate that properties of microtubules are highly dependent on the magnitude of the applied strain and offer a new interpretation for the large variety in microtubule mechanical data measured by different methods.

Control of molecular shuttles by designing electrical and mechanical properties of microtubules

Kinesin-driven microtubules have been focused on to serve as molecular transporters, called "molecular shuttles," to replace micro/nanoscale molecular manipulations necessitated in micro total analysis systems. Although transport, concentration, and detection of target molecules have been demonstrated, controllability of the transport directions is still a major challenge. Toward broad applications of molecular shuttles by defining multiple moving directions for selective molecular transport, we integrated a bottom-up molecular design of microtubules and a top-down design of a microfluidic device. The surface charge density and stiffness of microtubules were controlled, allowing us to create three different types of microtubules, each with different gliding directions corresponding to their electrical and mechanical properties. The measured curvature of the gliding microtubules enabled us to optimize the size and design of the device for molecular sorting in a top-down approach. The integrated bottom-up and top-down design achieved separation of stiff microtubules from negatively charged, soft microtubules under an electric field. Our method guides multiple microtubules by integrating molecular control and microfluidic device design; it is not only limited to molecular sorters but is also applicable to various molecular shuttles with the high controllability in their movement directions.

Force percolation of contractile active gels

Living systems provide a paradigmatic example of active soft matter. Cells and tissues comprise viscoelastic materials that exert forces and can actively change shape. This strikingly autonomous behavior is powered by the cytoskeleton, an active gel of semiflexible filaments, crosslinks, and molecular motors inside cells. Although individual motors are only a few nm in size and exert minute forces of a few pN, cells spatially integrate the activity of an ensemble of motors to produce larger contractile forces (∼nN and greater) on cellular, tissue, and organismal length scales. Here we review experimental and theoretical studies on contractile active gels composed of actin filaments and myosin motors. Unlike other active soft matter systems, which tend to form ordered patterns, actin-myosin systems exhibit a generic tendency to contract. Experimental studies of reconstituted actin-myosin model systems have long suggested that a mechanical interplay between motor activity and the network's connectivity governs this contractile behavior. Recent theoretical models indicate that this interplay can be understood in terms of percolation models, extended to include effects of motor activity on the network connectivity. Based on concepts from percolation theory, we propose a state diagram that unites a large body of experimental observations. This framework provides valuable insights into the mechanisms that drive cellular shape changes and also provides design principles for synthetic active materials.

Single microtubules and small networks become significantly stiffer on short time-scales upon mechanical stimulation

The transfer of mechanical signals through cells is a complex phenomenon. To uncover a new mechanotransduction pathway, we study the frequency-dependent transport of mechanical stimuli by single microtubules and small networks in a bottom-up approach using optically trapped beads as anchor points. We interconnected microtubules to linear and triangular geometries to perform micro-rheology by defined oscillations of the beads relative to each other. We found a substantial stiffening of single filaments above a characteristic transition frequency of 1–30 Hz depending on the filament’s molecular composition. Below this frequency, filament elasticity only depends on its contour and persistence length. Interestingly, this elastic behavior is transferable to small networks, where we found the surprising effect that linear two filament connections act as transistor-like, angle dependent momentum filters, whereas triangular networks act as stabilizing elements. These observations implicate that cells can tune mechanical signals by temporal and spatial filtering stronger and more flexibly than expected.

Introduction to Optical Tweezers

Thirty years after their invention by Arthur Ashkin and colleagues at Bell Labs in 1986 [1], optical tweezers (or traps) have become a versatile tool to address numerous biological problems. Put simply, an optical trap is a highly focused laser beam that is capable of holding and applying forces to micron-sized dielectric objects. However, their development over the last few decades has converted these tools from boutique instruments into highly versatile instruments of molecular biophysics. This introductory chapter intends to give a brief overview of the field, highlight some important scientific achievements, and demonstrate why optical traps have become a powerful tool in the biological sciences. We introduce a typical optical setup, describe the basic theoretical concepts of how trapping forces arise, and present the quantitative position and force measurement techniques that are most widely used today.

DeFiNe: an optimisation-based method for robust disentangling of filamentous networks

Thread-like structures are pervasive across scales, from polymeric proteins to root systems to galaxy filaments, and their characteristics can be readily investigated in the network formalism. Yet, network links usually represent only parts of filaments, which, when neglected, may lead to erroneous conclusions from network-based analyses. The existing alternatives to detect filaments in network representations require tuning of parameters over a large range of values and treat all filaments equally, thus, precluding automated analysis of diverse filamentous systems. Here, we propose a fully automated and robust optimisation-based approach to detect filaments of consistent intensities and angles in a given network. We test and demonstrate the accuracy of our solution with contrived, biological, and cosmic filamentous structures. In particular, we show that the proposed approach provides powerful automated means to study properties of individual actin filaments in their network context. Our solution is made publicly available as an open-source tool, "DeFiNe", facilitating decomposition of any given network into individual filaments.

Constructing 3D microtubule networks using holographic optical trapping

Developing abilities to assemble nanoscale structures is a major scientific and engineering challenge. We report a technique which allows precise positioning and manipulation of individual rigid filaments, enabling construction of custom-designed 3D filament networks. This approach uses holographic optical trapping (HOT) for nano-positioning and microtubules (MTs) as network building blocks. MTs are desirable engineering components due to their high aspect ratio, rigidity, and their ability to serve as substrate for directed nano-transport, reflecting their roles in the eukaryotic cytoskeleton. The 3D architecture of MT cytoskeleton is a significant component of its function, however experimental tools to study the roles of this geometric complexity in a controlled environment have been lacking. We demonstrate the broad capabilities of our system by building a self-supporting 3D MT-based nanostructure and by conducting a MT-based transport experiment on a dynamically adjustable 3D MT intersection. Our methodology not only will advance studies of cytoskeletal networks (and associated processes such as MT-based transport) but will also likely find use in engineering nanostructures and devices.

Cortical microtubule nucleation can organise the cytoskeleton of Drosophila oocytes to define the anteroposterior axis

Many cells contain non-centrosomal arrays of microtubules (MTs), but the assembly, organisation and function of these arrays are poorly understood. We present the first theoretical model for the non-centrosomal MT cytoskeleton in Drosophila oocytes, in which bicoid and oskar mRNAs become localised to establish the anterior-posterior body axis. Constrained by experimental measurements, the model shows that a simple gradient of cortical MT nucleation is sufficient to reproduce the observed MT distribution, cytoplasmic flow patterns and localisation of oskar and naive bicoid mRNAs. Our simulations exclude a major role for cytoplasmic flows in localisation and reveal an organisation of the MT cytoskeleton that is more ordered than previously thought. Furthermore, modulating cortical MT nucleation induces a bifurcation in cytoskeletal organisation that accounts for the phenotypes of polarity mutants. Thus, our three-dimensional model explains many features of the MT network and highlights the importance of differential cortical MT nucleation for axis formation.

DOI:http://dx.doi.org/10.7554/eLife.06088.001

Cells contain a network of filaments known as microtubules that serve as tracks along which proteins and other materials can be moved from one location to another. For example, molecules called messenger ribonucleic acids (or mRNAs for short) are made in the nucleus and are then moved to various locations around the cell. Each mRNA molecule encodes the instructions needed to make a particular protein and the network of microtubules allows these molecules to be directed to wherever these proteins are needed.

In female fruit flies, an mRNA called bicoid is moved to one end (called the anterior end) of a developing egg cell, while another mRNA called oskar is moved to the opposite (posterior) end. These mRNAs determine which ends of the cell will give rise to the head and the abdomen if the egg is fertilized. The microtubules start to form at sites near the inner face of the membrane that surrounds the cell, known as the cortex. From there, the microtubules grow towards the interior of the egg cell. However, it is not clear how this allows bicoid, oskar and other mRNAs to be moved to the correct locations.

Khuc Trong et al. used a combination of computational and experimental techniques to develop a model of how microtubules form in the egg cells of fruit flies. The model produces a very similar arrangement of microtubules as observed in living cells and can reproduce the patterns of bicoid and oskar RNA movements.

This study suggests that microtubules are more highly organised than previously thought. Furthermore, Khuc Trong et al.'s findings indicate that the anchoring of microtubules in the cortex is sufficient to direct bicoid and oskar RNAs to the opposite ends of the cell. The next challenge will be to find out how the microtubules are linked to the cortex and how this is regulated.

DOI:http://dx.doi.org/10.7554/eLife.06088.002

Intracellular and extracellular forces drive primary cilia movement

Primary cilia are ubiquitous, microtubule-based organelles that play diverse roles in sensory transduction in many eukaryotic cells. They interrogate the cellular environment through chemosensing, osmosensing, and mechanosensing using receptors and ion channels in the ciliary membrane. Little is known about the mechanical and structural properties of the cilium and how these properties contribute to ciliary perception. We probed the mechanical responses of primary cilia from kidney epithelial cells [Madin-Darby canine kidney-II (MDCK-II)], which sense fluid flow in renal ducts. We found that, on manipulation with an optical trap, cilia deflect by bending along their length and pivoting around an effective hinge located below the basal body. The calculated bending rigidity indicates weak microtubule doublet coupling. Primary cilia of MDCK cells lack interdoublet dynein motors. Nevertheless, we found that the organelles display active motility. 3D tracking showed correlated fluctuations of the cilium and basal body. These angular movements seemed random but were dependent on ATP and cytoplasmic myosin-II in the cell cortex. We conclude that force generation by the actin cytoskeleton surrounding the basal body results in active ciliary movement. We speculate that actin-driven ciliary movement might tune and calibrate ciliary sensory functions.

Intrinsically disordered tubulin tails: complex tuners of microtubule functions?

Microtubules are essential cellular polymers assembled from tubulin heterodimers. The tubulin dimer consists of a compact folded globular core and intrinsically disordered C-terminal tails. The tubulin tails form a lawn of densely grafted, negatively charged, flexible peptides on the exterior of the microtubule, potentially akin to brush polymers in the field of synthetic materials. These tails are hotspots for conserved, chemically complex posttranslational modifications that have the potential to act in a combinatorial fashion to regulate microtubule polymer dynamics and interactions with microtubule effectors, giving rise to a "tubulin code". In this review, I summarize our current knowledge of the enzymes that generate the astonishing tubulin chemical diversity observed in cells and describe recent advances in deciphering the roles of tubulin C-terminal tails and their posttranslational modifications in regulating the activity of molecular motors and microtubule associated proteins. Lastly, I outline the promises, challenges and potential pitfalls of deciphering the tubulin code.

Direct visualization of flow-induced conformational transitions of single actin filaments in entangled solutions

While semi-flexible polymers and fibres are an important class of material due to their rich mechanical properties, it remains unclear how these properties relate to the microscopic conformation of the polymers. Actin filaments constitute an ideal model polymer system due to their micron-sized length and relatively high stiffness that allow imaging at the single filament level. Here we study the effect of entanglements on the conformational dynamics of actin filaments in shear flow. We directly measure the full three-dimensional conformation of single actin filaments, using confocal microscopy in combination with a counter-rotating cone-plate shear cell. We show that initially entangled filaments form disentangled orientationally ordered hairpins, confined in the flow-vorticity plane. In addition, shear flow causes stretching and shear alignment of the hairpin tails, while the filament length distribution remains unchanged. These observations explain the strain-softening and shear-thinning behaviour of entangled F-actin solutions, which aids the understanding of the flow behaviour of complex fluids containing semi-flexible polymers.

Force spectroscopy of complex biopolymers with heterogeneous elasticity

Cellular biopolymers can exhibit significant compositional heterogeneities as a result of the non-uniform binding of associated proteins, the formation of microstructural defects during filament assembly, or the imperfect bundling of filaments into composite structures of variable diameter. These can lead to significant variations in the local mechanical properties of biopolymers along their length. Existing spectral analysis methods assume filament homogeneity and therefore report only a single average stiffness for the entire filament. However, understanding how local effects modulate biopolymer mechanics in a spatially resolved manner is essential to understanding how binding and bundling proteins regulate biopolymer stiffness and function in cellular contexts. Here, we present a new method to determine the spatially varying material properties of individual complex biopolymers from the observation of passive thermal fluctuations of the filament conformation. We develop new statistical mechanics-based approaches for heterogeneous filaments that estimate local bending elasticities as a function of the filament arc-length. We validate this methodology using simulated polymers with known stiffness distributions, and find excellent agreement between derived and expected values. We then determine the bending elasticity of microtubule filaments of variable composition generated by repeated rounds of tubulin polymerization using either GTP or GMPCPP, a nonhydrolyzable GTP analog. Again, we find excellent agreement between mechanical and compositional heterogeneities.

Measuring microtubule persistence length using a microtubule gliding assay

The mechanical properties of microtubules have been an area of active research for the past two decades, in part because understanding the mechanics of individual microtubules contributes to modeling whole-cell rigidity and structure and hence to better understanding the processes underlying motility and transport. Moreover, the role of microtubule structure and microtubule-associated proteins (MAPs) in microtubule stiffness remains unclear. In this chapter, we present a kinesin-driven microtubule gliding assay analysis of persistence length that is amenable to simultaneous variation of microtubule parameters such as length, structure, or MAP coverage and determination of persistence length. By combining sparse fluorescent labeling of individual microtubules with single particle tracking of individual fluorophores, microtubule gliding trajectories are tracked with nanometer-level precision. The fluctuations in these trajectories, due to thermal fluctuations in the microtubules themselves, are analyzed to extract the microtubule persistence length. In the following, we describe this gliding assay and analysis and discuss two example microtubule variables, length and diameter, in anticipation that the method may be of wide use for in vitro study of microtubule mechanical properties.

Flexural rigidity measurements of biopolymers using gliding assays

Microtubules are cytoskeletal polymers which play a role in cell division, cell mechanics, and intracellular transport. Each of these functions requires microtubules that are stiff and straight enough to span a significant fraction of the cell diameter. As a result, the microtubule persistence length, a measure of stiffness, has been actively studied for the past two decades(1). Nonetheless, open questions remain: short microtubules are 10-50 times less stiff than long microtubules(2-4), and even long microtubules have measured persistence lengths which vary by an order of magnitude(5-9). Here, we present a method to measure microtubule persistence length. The method is based on a kinesin-driven microtubule gliding assay(10). By combining sparse fluorescent labeling of individual microtubules with single particle tracking of individual fluorophores attached to the microtubule, the gliding trajectories of single microtubules are tracked with nanometer-level precision. The persistence length of the trajectories is the same as the persistence length of the microtubule under the conditions used(11). An automated tracking routine is used to create microtubule trajectories from fluorophores attached to individual microtubules, and the persistence length of this trajectory is calculated using routines written in IDL. This technique is rapidly implementable, and capable of measuring the persistence length of 100 microtubules in one day of experimentation. The method can be extended to measure persistence length under a variety of conditions, including persistence length as a function of length along microtubules. Moreover, the analysis routines used can be extended to myosin-based acting gliding assays, to measure the persistence length of actin filaments as well.

Force transduction and strain dynamics in actin stress fibres in response to nanonewton forces

It is becoming clear that mechanical stimuli are crucial factors in regulating the biology of the cell, but the short-term structural response of a cell to mechanical forces remains relatively poorly understood. We mechanically stimulated cells transiently expressing actin-EGFP with controlled forces (0-20 nN) in order to investigate the structural response of the cell. Two clear force-dependent responses were observed: a short-term (seconds) local deformation of actin stress fibres and a long-term (minutes) force-induced remodelling of stress fibres at cell edges, far from the point of contact. By photobleaching markers along stress fibres we were also able to quantify strain dynamics occurring along the fibres throughout the cell. The results reveal that the cell exhibits complex heterogeneous negative and positive strain fluctuations along stress fibres in resting cells that indicate localized contraction and stretch dynamics. The application of mechanical force results in the activation of myosin contractile activity reflected in an ~50% increase in strain fluctuations. This approach has allowed us to directly observe the activation of myosin in response to mechanical force and the effects of cytoskeletal crosslinking on local deformation and strain dynamics. The results demonstrate that force application does not result in simplistic isotropic deformation of the cytoarchitecture, but rather a complex and localized response that is highly dependent on an intact microtubule network. Direct visualization of force-propagation and stress fibre strain dynamics have revealed several crucial phenomena that take place and ultimately govern the downstream response of a cell to a mechanical stimulus.

Spectral analysis methods for the robust measurement of the flexural rigidity of biopolymers

The mechanical properties of biopolymers can be determined from a statistical analysis of the ensemble of shapes they exhibit when subjected to thermal forces. In practice, extracting information from fluorescence microscopy images can be challenging due to low signal/noise ratios and other artifacts. To address these issues, we develop a suite of tools for image processing and spectral data analysis that is based on a biopolymer contour representation expressed in a spectral basis of orthogonal polynomials. We determine biopolymer shape and stiffness using global fitting routines that optimize a utility function measuring the amount of fluorescence intensity overlapped by such contours. This approach allows for filtering of high-frequency noise and interpolation over sporadic gaps in fluorescence. We use benchmarking to demonstrate the validity of our methods, by analyzing an ensemble of simulated images generated using a simulated biopolymer with known stiffness and subjected to various types of image noise. We then use these methods to determine the persistence lengths of taxol-stabilized microtubules. We find that single microtubules are well described by the wormlike chain polymer model, and that ensembles of chemically identical microtubules show significant heterogeneity in bending stiffness, which cannot be attributed to sampling or fitting errors. We expect these approaches to be useful in the study of biopolymer mechanics and the effects of associated regulatory molecules.

Remodeling of actin filaments by ADF/cofilin proteins

Cofilin/ADF proteins play key roles in the dynamics of actin, one of the most abundant and highly conserved eukaryotic proteins. We used cryoelectron microscopy to generate a 9-Å resolution three-dimensional reconstruction of cofilin-decorated actin filaments, the highest resolution achieved for a complex of F-actin with an actin-binding protein. We show that the cofilin-induced change in the filament twist is due to a unique conformation of the actin molecule unrelated to any previously observed state. The changes between the actin protomer in naked F-actin and in the actin-cofilin filament are greater than the conformational changes between G- and F-actin. Our results show the structural plasticity of actin, suggest that other actin-binding proteins may also induce large but different conformational changes, and show that F-actin cannot be described by a single molecular model.

Physical properties of polymorphic yeast prion amyloid fibers

Amyloid fibers play important roles in many human diseases and natural biological processes and have immense potential as novel nanomaterials. We explore the physical properties of polymorphic amyloid fibers formed by yeast prion protein Sup35. Amyloid fibers that conferred distinct prion phenotypes ([PSI(+)]), strong (S) versus weak (W) nonsense suppression, displayed different physical properties. Both S[PSI(+)] and W[PSI(+)] fibers contained structural inhomogeneities, specifically local regions of static curvature in S[PSI(+)] fibers and kinks and self-cross-linking in W[PSI(+)] fibers. Force-extension experiments with optical tweezers revealed persistence lengths of 1.5 μm and 3.3 μm and axial stiffness of 5600 pN and 9100 pN for S[PSI(+)] and W[PSI(+)] fibers, respectively. Thermal fluctuation analysis confirmed the twofold difference in persistence length between S[PSI(+)] and W[PSI(+)] fibers and revealed a torsional stiffness of kinks and cross-links of ~100-200 pN·nm/rad.

Wave propagation in protein microtubules modeled as orthotropic elastic shells including transverse shear deformations

Wave propagation along the microtubules is one of the issues of major concern in various microtubule cellular functions. In this study, the general wave propagation behavior in protein microtubules is investigated based on a first-order shear deformation shell theory for orthotropic materials, with particular emphasis on the role of strongly anisotropic elastic properties of microtubules. According to experimental observation, the first-order shear deformation theory is used for the modeling of microtubule walls. A general displacement representation is introduced and a type of coupled polynomial eigenvalue problem is developed. Numerical examples describe the effects of shear deformation and rotary inertia on wave velocities in orthotropic microtubules. Finally, the influences of the microtubule shear modulus, axial external force, effective thickness and material temperature dependency on wave velocities along the microtubule protofilaments, helical pathway and radial directions are elucidated. Most results presented in the present investigation have been absent from the literature for the wave propagation in microtubules.

Bidirectional power stroke by ncd kinesin

Optical trapping experiments reveal details of molecular motor dynamics. In noisy data, temporal structure within the power stroke of motors can be analyzed by ensemble averaging, but this obscures infrequent subcategories of events. We have here developed an analysis method that uses Kalman filtering of measurements, model-based estimation of the power strokes produced by the motor head, and automatic event classification to discriminate between different types of motor events. This method was applied to optical trap measurements of power strokes of the Drosophila kinesin-14 ncd in a three-bead geometry. We found the majority of events to be consistent with the previously discovered minus-end directed power stroke of ncd, occurring with ATP binding. Unexpectedly, 30% of apparent power strokes were plus-directed and 6% of binding events did not terminate in a discernible stroke. Ensemble averaging for each event category revealed that plus- and minus-directed strokes have different size and occur at different instants within the ncd-MT attachment sequence.

Moving into the cell: single-molecule studies of molecular motors in complex environments

Much has been learned in the past decades about molecular force generation. Single-molecule techniques, such as atomic force microscopy, single-molecule fluorescence microscopy and optical tweezers, have been key in resolving the mechanisms behind the power strokes, 'processive' steps and forces of cytoskeletal motors. However, it remains unclear how single force generators are integrated into composite mechanical machines in cells to generate complex functions such as mitosis, locomotion, intracellular transport or mechanical sensory transduction. Using dynamic single-molecule techniques to track, manipulate and probe cytoskeletal motor proteins will be crucial in providing new insights.

Direct observation of the myosin-Va power stroke and its reversal

Complex forms of cellular motility, including cell division, organelle trafficking or signal amplification in the auditory system, require strong coordination of the myosin motors involved. The most basic mechanism of coordination is via direct mechanical interactions of individual motor heads leading to modification of their mechano-chemical cycles. Here we used an optical trap-based assay to investigate the reversibility of the force- generating conformational change (power stroke) of single myosin-V motor heads. By applying load to the head shortly after binding to actin, we found that at a certain load the power stroke could be reversed and the head fluctuated between an actin-bound pre- and a post-power stroke conformation. This load-dependent mechanical instability might be critical to coordinate the heads of processive, dimeric myosin-V. Non-linear response to load leading to coordination or oscillations amongst motors might be relevant for many cellular functions.

Mechanics of microtubules

Microtubules are rigid cytoskeletal filaments, and their mechanics affect cell morphology and cellular processes. For instance, microtubules for the support structures for extended morphologies, such as axons and cilia. Further, microtubules act as tension rods to pull apart chromosomes during cellular division. Unlike other cytoskeletal filaments (e.g., actin) that work as large networks, microtubules work individually or in small groups, so their individual mechanical properties are quite important to their cellular function. In this review, we explore the past work on the mechanics of individual microtubules, which have been studied for over a quarter of a century. We also present some prospective on future endeavors to determine the molecular mechanisms that control microtubule rigidity.