Minimal vertex model explains how the amnioserosa avoids fluidization during Drosophila dorsal closure

Dorsal closure is a process that occurs during embryogenesis of Drosophila melanogaster . During dorsal closure, the amnioserosa (AS), a one-cell thick epithelial tissue that fills the dorsal opening, shrinks as the lateral epidermis sheets converge and eventually merge. During this process, the aspect ratio of amnioserosa cells increases markedly. The standard 2-dimensional vertex model, which successfully describes tissue sheet mechanics in multiple contexts, would in this case predict that the tissue should fluidize via cell neighbor changes. Surprisingly, however, the amnioserosa remains an elastic solid with no such events. We here present a minimal extension to the vertex model that explains how the amnioserosa can achieve this unexpected behavior. We show that continuous shrinkage of the preferred cell perimeter and cell perimeter polydispersity lead to the retention of the solid state of the amnioserosa. Our model accurately captures measured cell shape and orientation changes and predicts non-monotonic junction tension that we confirm with laser ablation experiments.

Significance Statement

During embryogenesis, cells in tissues can undergo significant shape changes. Many epithelial tissues fluidize, i.e. cells exchange neighbors, when the average cell aspect ratio increases above a threshold value, consistent with the standard vertex model. During dorsal closure in Drosophila melanogaster , however, the amnioserosa tissue remains solid even as the average cell aspect ratio increases well above threshold. We introduce perimeter polydispersity and allow the preferred cell perimeters, usually held fixed in vertex models, to decrease linearly with time as seen experimentally. With these extensions to the standard vertex model, we capture experimental observations quantitatively. Our results demonstrate that vertex models can describe the behavior of the amnioserosa in dorsal closure by allowing normally fixed parameters to vary with time.

Minimal vertex model explains how the amnioserosa avoids fluidization during Drosophila dorsal closure

Dorsal closure is a process that occurs during embryogenesis of Drosophila melanogaster. During dorsal closure, the amnioserosa (AS), a one-cell thick epithelial tissue that fills the dorsal opening, shrinks as the lateral epidermis sheets converge and eventually merge. During this process, the aspect ratio of amnioserosa cells increases markedly. The standard 2-dimensional vertex model, which successfully describes tissue sheet mechanics in multiple contexts, would in this case predict that the tissue should fluidize via cell neighbor changes. Surprisingly, however, the amnioserosa remains an elastic solid with no such events. We here present a minimal extension to the vertex model that explains how the amnioserosa can achieve this unexpected behavior. We show that continuous shrink-age of the preferred cell perimeter and cell perimeter polydispersity lead to the retention of the solid state of the amnioserosa. Our model accurately captures measured cell shape and orientation changes and predicts non-monotonic junction tension that we confirm with laser ablation experiments.

Nucleotide-free structures of KIF20A illuminate atypical mechanochemistry in this kinesin-6

KIF20A is a critical kinesin for cell division and a promising anti-cancer drug target. The mechanisms underlying its cellular roles remain elusive. Interestingly, unusual coupling between the nucleotide- and microtubule-binding sites of this kinesin-6 has been reported, but little is known about how its divergent sequence leads to atypical motility properties. We present here the first high-resolution structure of its motor domain that delineates the highly unusual structural features of this motor, including a long L6 insertion that integrates into the core of the motor domain and that drastically affects allostery and ATPase activity. Together with the high-resolution cryo-electron microscopy microtubule-bound KIF20A structure that reveals the microtubule-binding interface, we dissect the peculiarities of the KIF20A sequence that influence its mechanochemistry, leading to low motility compared to other kinesins. Structural and functional insights from the KIF20A pre-power stroke conformation highlight the role of extended insertions in shaping the motor's mechanochemical cycle. Essential for force production and processivity is the length of the neck linker in kinesins. We highlight here the role of the sequence preceding the neck linker in controlling its backward docking and show that a neck linker four times longer than that in kinesin-1 is required for the activity of this motor.

DeepProjection: specific and robust projection of curved 2D tissue sheets from 3D microscopy using deep learning

The efficient extraction of image data from curved tissue sheets embedded in volumetric imaging data remains a serious and unsolved problem in quantitative studies of embryogenesis. Here, we present DeepProjection (DP), a trainable projection algorithm based on deep learning. This algorithm is trained on user-generated training data to locally classify 3D stack content, and to rapidly and robustly predict binary masks containing the target content, e.g. tissue boundaries, while masking highly fluorescent out-of-plane artifacts. A projection of the masked 3D stack then yields background-free 2D images with undistorted fluorescence intensity values. The binary masks can further be applied to other fluorescent channels or to extract local tissue curvature. DP is designed as a first processing step than can be followed, for example, by segmentation to track cell fate. We apply DP to follow the dynamic movements of 2D-tissue sheets during dorsal closure in Drosophila embryos and of the periderm layer in the elongating Danio embryo. DeepProjection is available as a fully documented Python package.

Mapping Activity-Dependent Quasi-stationary States of Mitochondrial Membranes with Graphene-Induced Energy Transfer Imaging

Graphene-induced energy transfer (GIET) was recently introduced for sub-nanometric axial localization of fluorescent molecules. GIET relies on near-field energy transfer from an optically excited fluorophore to a single sheet of graphene. Recently, we demonstrated its potential by determining the distance between two leaflets of supported lipid bilayers. Here, we use GIET imaging for mapping quasi-stationary states of the inner and outer mitochondrial membranes before and during adenosine triphosphate (ATP) synthesis. We trigger the ATP synthesis state in vitro by activating mitochondria with precursor molecules. Our results demonstrate that the inner membrane approaches the outer membrane, while the outer membrane does not show any measurable change in average axial position upon activation. The inter-membrane space is reduced by ∼2 nm. This direct experimental observation of the subtle dynamics of mitochondrial membranes and the change in intermembrane distance upon activation is relevant for our understanding of mitochondrial function.

Multiscale Microrheology Using Fluctuating Filaments as Stealth Probes

The mechanical properties of soft materials can be probed on small length scales by microrheology. A common approach tracks fluctuations of micrometer-sized beads embedded in the medium to be characterized. This approach yields results that depend on probe size when the medium has structure on comparable length scales. Here, we introduce filament-based microrheology using high-aspect-ratio semiflexible filaments as probes. Such quasi-1D probes are much less invasive than beads due to their small cross sections. Moreover, by imaging transverse bending modes, we simultaneously determine the micromechanical response of the medium on multiple length scales corresponding to the mode wavelengths. We use semiflexible single-walled carbon nanotubes as probes that can be accurately and rapidly imaged based on their stable near-IR fluorescence. We find that the viscoelastic properties of sucrose, polyethylene oxide, and hyaluronic acid solutions measured in this way are in good agreement with those measured by conventional micro- and macrorheology.

Rapid local compression in active gels is caused by nonlinear network response

The actin cytoskeleton in living cells generates forces in conjunction with myosin motor proteins to directly and indirectly drive essential cellular processes. The semiflexible filaments of the cytoskeleton can respond nonlinearly to the collective action of motors. We here investigate mechanics and force generation in a model actin cytoskeleton, reconstituted in vitro, by observing the response and fluctuations of embedded micron-scale probe particles. Myosin mini-filaments can be modeled as force dipoles and give rise to deformations in the surrounding network of cross-linked actin. Anomalously correlated probe fluctuations indicate the presence of rapid local compression or draining of the network that emerges in addition to the ordinary linear shear elastic (incompressible) response to force dipoles. The anomalous propagation of compression can be attributed to the nonlinear response of actin filaments to the microscopic forces, and is quantitatively consistent with motor-generated large-scale stiffening of the gels.

Introduction to Active Matter

Moumita Das, Michael Murrell and Christoph Schmidt introduce the Soft Matter collection on active matter.

Length-Selective Dielectrophoretic Manipulation of Single-Walled Carbon Nanotubes

Single-walled carbon nanotubes (SWNTs) possess unique physical, optical, and electrical properties with great potential for future nanoscale device applications. Common synthesis procedures yield SWNTs with large length polydispersity and varying chirality. Electrical and optical applications of SWNTs often require specific lengths, but the preparation of SWNTs with the desired length is still challenging. Insulator-based dielectrophoresis (iDEP) integrated into a microfluidic device has the potential to separate SWNTs by length. Semiconducting SWNTs of varying length suspended with sodium deoxycholate (NaDOC) show unique dielectrophoretic properties at low frequencies (<1 kHz) that were exploited here using an iDEP-based microfluidic constriction sorter device for length-based sorting. Specific migration directions in the constriction sorter were induced for long SWNTs (≥1000 nm) with negative dielectrophoretic properties compared to short (≤300 nm) SWNTs with positive dielectrophoretic properties. We report continuous fractionation conditions for length-based iDEP migration of SWNTs, and we characterize the dynamics of migration of SWNTs in the microdevice using a finite element model. Based on the length and dielectrophoretic characteristics, sorting efficiencies for long and short SWNTs recovered from separate channels of the constriction sorter amounted to >90% and were in excellent agreement with a numerical model for the sorting process.

Analysis of Cholesterol in All Lipoprotein Classes by Single Vertical Ultracentrifugation of Fingerstick Blood and Controlled-Dispersion Flow Analysis

This new, highly sensitive analytical system, based on controlled dispersion of the flowing sample, gives a rapid, continuous, and direct analysis for cholesterol in all lipoprotein classes, separated by single vertical-spin density-gradient ultracentrifugation. In this Vertical Auto Profile-II fingerstick system, designated VAP-IIfs, a narrow-bore Teflon coil serves as the reactor with no segmentation of the analytical stream by air bubbles, in contrast to the Technicon AutoAnalyzer used in the VAP-I method. Concentrations of high-, low-, intermediate-, and very-low-density lipoprotein cholesterol and lipoprotein(a) cholesterol are determined by decomposing the spectrophotometric absorbance curve for the continuous analysis of the centrifuged sample, with use of software developed in this laboratory. Total cholesterol is determined from the total area under the absorbance curve. For assaying total cholesterol, the CV between aliquots within a rotor ranged from 1.35% to 3.15%; the CV between rotors was 2.45%. Because only 18 microL of sample is required, VAP-IIfs can be readily adapted to analysis for lipoprotein cholesterol profiles in capillary blood samples. Total cholesterol values by VAP-IIfs for fingerstick and venous samples from 23 subjects agreed well: slope = 1.01 (SD 0.03), intercept = -21 (SD 51) mg/L, Sy/x = 50 mg/L, and r = 0.992. Results by VAP-IIfs also correlated highly with results for duplicate samples analyzed at the Northwest Lipid Research Laboratories.

Chromophore-Independent Roles of Opsin Apoproteins in Drosophila Mechanoreceptors

Rhodopsins, the major light-detecting molecules of animal visual systems [1], consist of opsin apoproteins that covalently bind a retinal chromophore with a conserved lysine residue [1, 2]. In addition to capturing photons, this chromophore contributes to rhodopsin maturation [3, 4], trafficking [3, 4], and stabilization [5], and defects in chromophore synthesis and recycling can cause dysfunction of the retina and dystrophy [6-9]. Indications that opsin apoproteins alone might have biological roles have come from archaebacteria and platyhelminths, which present opsin-like proteins that lack the chromophore binding site and are deemed to function independently of light [10, 11]. Light-independent sensory roles have been documented for Drosophila opsins [12-15], yet also these unconventional opsin functions are thought to require chromophore binding [12, 13, 15]. Unconjugated opsin apoproteins act as phospholipid scramblases in mammalian photoreceptor disks [16], yet chromophore-independent roles of opsin apoproteins outside of eyes have, to the best of our knowledge, hitherto not been described. Drosophila chordotonal mechanoreceptors require opsins [13, 15], and we find that their function remains uncompromised by nutrient carotenoid depletion. Disrupting carotenoid uptake and cleavage also left the mechanoreceptors unaffected, and manipulating the chromophore attachment site of the fly's major visual opsin Rh1 impaired photoreceptor, but not mechanoreceptor, function. Notwithstanding this chromophore independence, some proteins that process and recycle the chromophore in the retina are also required in mechanoreceptors, including visual cycle components that recycle the chromophore upon its photoisomerization. Our results thus establish biological function for unconjugated opsin apoproteins outside of eyes and, in addition, document chromophore-independent roles for chromophore pathway components.

Reply to the 'Comment on "A symmetrical method to obtain shear moduli from microrheology"' by M. Tassieri, Soft Matter, 2018, 14, DOI

The Comment on our paper introducing "a symmetric method to obtain shear moduli from microrheology" proposes an interpolation method to generate oversampled data from an original time series that are then used to approximate shear moduli at frequencies "beyond the Nyquist frequency." The author states that this can be done without the use of "preconceived fitting functions," implying that the results are unique and reliable. We disagree with these assertions. While it is possible to generate reasonable looking transforms at frequencies above the Nyquist limit by interpolation, any results obtained above the Nyquist limit will be questionable at best. Moreover, while the cubic spline interpolation the author uses may be standard, it constitutes a particular "preconceived" fit and produces oversampled data that are not unique.

Self-organized stress patterns drive state transitions in actin cortices

Biological functions rely on ordered structures and intricately controlled collective dynamics. This order in living systems is typically established and sustained by continuous dissipation of energy. The emergence of collective patterns of motion is unique to nonequilibrium systems and is a manifestation of dynamic steady states. Mechanical resilience of animal cells is largely controlled by the actomyosin cortex. The cortex provides stability but is, at the same time, highly adaptable due to rapid turnover of its components. Dynamic functions involve regulated transitions between different steady states of the cortex. We find that model actomyosin cortices, constructed to maintain turnover, self-organize into distinct nonequilibrium steady states when we vary cross-link density. The feedback between actin network structure and organization of stress-generating myosin motors defines the symmetries of the dynamic steady states. A marginally cross-linked state displays divergence-free long-range flow patterns. Higher cross-link density causes structural symmetry breaking, resulting in a stationary converging flow pattern. We track the flow patterns in the model actomyosin cortices using fluorescent single-walled carbon nanotubes as novel probes. The self-organization of stress patterns we have observed in a model system can have direct implications for biological functions.

A symmetrical method to obtain shear moduli from microrheology

Passive microrheology typically deduces shear elastic loss and storage moduli from displacement time series or mean-squared displacements (MSD) of thermally fluctuating probe particles in equilibrium materials. Common data analysis methods use either Kramers-Kronig (KK) transformation or functional fitting to calculate frequency-dependent loss and storage moduli. We propose a new analysis method for passive microrheology that avoids the limitations of both of these approaches. In this method, we determine both real and imaginary components of the complex, frequency-dependent response function χ(ω) = χ'(ω) + iχ''(ω) as direct integral transforms of the MSD of thermal particle motion. This procedure significantly improves the high-frequency fidelity of χ(ω) relative to the use of KK transformation, which has been shown to lead to artifacts in χ'(ω). We test our method on both model and experimental data. Experiments were performed on solutions of worm-like micelles and dilute collagen solutions. While the present method agrees well with established KK-based methods at low frequencies, we demonstrate significant improvement at high frequencies using our symmetric analysis method, up to almost the fundamental Nyquist limit.

Topology determines force distributions in one-dimensional random spring networks

Networks of elastic fibers are ubiquitous in biological systems and often provide mechanical stability to cells and tissues. Fiber-reinforced materials are also common in technology. An important characteristic of such materials is their resistance to failure under load. Rupture occurs when fibers break under excessive force and when that failure propagates. Therefore, it is crucial to understand force distributions. Force distributions within such networks are typically highly inhomogeneous and are not well understood. Here we construct a simple one-dimensional model system with periodic boundary conditions by randomly placing linear springs on a circle. We consider ensembles of such networks that consist of N nodes and have an average degree of connectivity z but vary in topology. Using a graph-theoretical approach that accounts for the full topology of each network in the ensemble, we show that, surprisingly, the force distributions can be fully characterized in terms of the parameters (N,z). Despite the universal properties of such (N,z) ensembles, our analysis further reveals that a classical mean-field approach fails to capture force distributions correctly. We demonstrate that network topology is a crucial determinant of force distributions in elastic spring networks.

Topology Counts: Force Distributions in Circular Spring Networks

Filamentous polymer networks govern the mechanical properties of many biological materials. Force distributions within these networks are typically highly inhomogeneous, and, although the importance of force distributions for structural properties is well recognized, they are far from being understood quantitatively. Using a combination of probabilistic and graph-theoretical techniques, we derive force distributions in a model system consisting of ensembles of random linear spring networks on a circle. We show that characteristic quantities, such as the mean and variance of the force supported by individual springs, can be derived explicitly in terms of only two parameters: (i) average connectivity and (ii) number of nodes. Our analysis shows that a classical mean-field approach fails to capture these characteristic quantities correctly. In contrast, we demonstrate that network topology is a crucial determinant of force distributions in an elastic spring network. Our results for 1D linear spring networks readily generalize to arbitrary dimensions.

Mechanical Properties of a Drosophila Larval Chordotonal Organ

Proprioception is an integral part of the feedback circuit that is essential for locomotion control in all animals. Chordotonal organs perform proprioceptive and other mechanosensory functions in insects and crustaceans. The mechanical properties of these organs are believed to be adapted to the sensory functions, but had not been probed directly. We measured mechanical properties of a particular chordotonal organ-the lateral pentascolopidial (lch5) organ of Drosophila larvae-which plays a key role in proprioceptive locomotion control. We applied tension to the whole organ in situ by transverse deflection. Upon release of force, the organ displayed overdamped relaxation with two widely separated time constants, tens of milliseconds and seconds, respectively. When the muscles covering the lch5 organ were excised, the slow relaxation was absent, and the fast relaxation became faster. Interestingly, most of the strain in the stretched organ is localized in the cap cells, which account for two-thirds of the length of the entire organ, and could be stretched by ∼10% without apparent damage. In laser ablation experiments we found that cap cells retracted by ∼100 μm after being severed from the neurons, indicating considerable steady-state stress and strain in these cells. Given the fact that actin as well as myosin motors are abundant in cap cells, the results point to a mechanical regulatory role of the cap cells in the lch5 organ.

Single-Walled Carbon Nanotubes Probed with Insulator-Based Dielectrophoresis

Single-walled carbon nanotubes (SWNTs) offer unique electrical and optical properties. Common synthesis processes yield SWNTs with large length polydispersity (several tens of nanometers up to centimeters) and heterogeneous electrical and optical properties. Applications often require suitable selection and purification. Dielectrophoresis is one manipulation method for separating SWNTs based on dielectric properties and geometry. Here, we present a study of surfactant and single-stranded DNA-wrapped SWNTs suspended in aqueous solutions manipulated by insulator-based dielectrophoresis (iDEP). This method allows us to manipulate SWNTs with the help of arrays of insulating posts in a microfluidic device around which electric field gradients are created by the application of an electric potential to the extremities of the device. Semiconducting SWNTs were imaged during dielectrophoretic manipulation with fluorescence microscopy making use of their fluorescence emission in the near IR. We demonstrate SWNT trapping at low-frequency alternating current (AC) electric fields with applied potentials not exceeding 1000 V. Interestingly, suspended SWNTs showed both positive and negative dielectrophoresis, which we attribute to their ζ potential and the suspension properties. Such behavior agrees with common theoretical models for nanoparticle dielectrophoresis. We further show that the measured ζ potentials and suspension properties are in excellent agreement with a numerical model predicting the trapping locations in the iDEP device. This study is fundamental for the future application of low-frequency AC iDEP for technological applications of SWNTs.

Feedback-tracking microrheology in living cells

Living cells are composed of active materials, in which forces are generated by the energy derived from metabolism. Forces and structures self-organize to shape the cell and drive its dynamic functions. Understanding the out-of-equilibrium mechanics is challenging because constituent materials, the cytoskeleton and the cytosol, are extraordinarily heterogeneous, and their physical properties are strongly affected by the internally generated forces. We have analyzed dynamics inside two types of eukaryotic cells, fibroblasts and epithelial-like HeLa cells, with simultaneous active and passive microrheology using laser interferometry and optical trapping technology. We developed a method to track microscopic probes stably in cells in the presence of vigorous cytoplasmic fluctuations, by using smooth three-dimensional (3D) feedback of a piezo-actuated sample stage. To interpret the data, we present a theory that adapts the fluctuation-dissipation theorem (FDT) to out-of-equilibrium systems that are subjected to positional feedback, which introduces an additional nonequilibrium effect. We discuss the interplay between material properties and nonthermal force fluctuations in the living cells that we quantify through the violations of the FDT. In adherent fibroblasts, we observed a well-known polymer network viscoelastic response where the complex shear modulus scales as G* ∝ (-iω)3/4. In the more 3D confluent epithelial cells, we found glassy mechanics with G* ∝ (-iω)1/2 that we attribute to glassy dynamics in the cytosol. The glassy state in living cells shows characteristics that appear distinct from classical glasses and unique to nonequilibrium materials that are activated by molecular motors.

Nonequilibrium dynamics of probe filaments in actin-myosin networks

Active dynamic processes of cells are largely driven by the cytoskeleton, a complex and adaptable semiflexible polymer network, motorized by mechanoenzymes. Small dimensions, confined geometries, and hierarchical structures make it challenging to probe dynamics and mechanical response of such networks. Embedded semiflexible probe polymers can serve as nonperturbing multiscale probes to detect force distributions in active polymer networks. We show here that motor-induced forces transmitted to the probe polymers are reflected in nonequilibrium bending dynamics, which we analyze in terms of spatial eigenmodes of an elastic beam under steady-state conditions. We demonstrate how these active forces induce correlations among the mode amplitudes, which furthermore break time-reversal symmetry. This leads to a breaking of detailed balance in this mode space. We derive analytical predictions for the magnitude of resulting probability currents in mode space in the white-noise limit of motor activity. We relate the structure of these currents to the spatial profile of motor-induced forces along the probe polymers and provide a general relation for observable currents on two-dimensional hyperplanes.

Game of Zones: how actin-binding proteins organize muscle contraction

Locomotion of C. elegans requires coordinated, efficient transmission of forces generated on the molecular scale by myosin and actin filaments in myocytes to dense bodies and the hypodermis and cuticle enveloping body wall muscles. The complex organization of the acto-myosin scaffold with its accessory proteins provides a fine-tuned machinery regulated by effectors that guarantees that sarcomere units undergo controlled, reversible cycles of contraction and relaxation. Actin filaments in sarcomeres dynamically undergo polymerization and depolymerization. In a recent study, the actin-binding protein DBN-1, the C. elegans ortholog of human drebrin and drebrin-like proteins, was discovered to stabilize actin in muscle cells. DBN-1 reversibly changes location between actin filaments and myosin-rich regions during muscle contraction. Mutations in DBN-1 result in mislocalization of other actin-binding proteins. Here we discuss implications of this finding for the regulation of sarcomere actin stability and the organization of other actin-binding proteins.

Broken Detailed Balance of Filament Dynamics in Active Networks

Myosin motor proteins drive vigorous steady-state fluctuations in the actin cytoskeleton of cells. Endogenous embedded semiflexible filaments such as microtubules, or added filaments such as single-walled carbon nanotubes are used as novel tools to noninvasively track equilibrium and nonequilibrium fluctuations in such biopolymer networks. Here, we analytically calculate shape fluctuations of semiflexible probe filaments in a viscoelastic environment, driven out of equilibrium by motor activity. Transverse bending fluctuations of the probe filaments can be decomposed into dynamic normal modes. We find that these modes no longer evolve independently under nonequilibrium driving. This effective mode coupling results in nonzero circulatory currents in a conformational phase space, reflecting a violation of detailed balance. We present predictions for the characteristic frequencies associated with these currents and investigate how the temporal signatures of motor activity determine mode correlations, which we find to be consistent with recent experiments on microtubules embedded in cytoskeletal networks.

Broken detailed balance at mesoscopic scales in active biological systems

Systems in thermodynamic equilibrium are not only characterized by time-independent macroscopic properties, but also satisfy the principle of detailed balance in the transitions between microscopic configurations. Living systems function out of equilibrium and are characterized by directed fluxes through chemical states, which violate detailed balance at the molecular scale. Here we introduce a method to probe for broken detailed balance and demonstrate how such nonequilibrium dynamics are manifest at the mesosopic scale. The periodic beating of an isolated flagellum from Chlamydomonas reinhardtii exhibits probability flux in the phase space of shapes. With a model, we show how the breaking of detailed balance can also be quantified in stationary, nonequilibrium stochastic systems in the absence of periodic motion. We further demonstrate such broken detailed balance in the nonperiodic fluctuations of primary cilia of epithelial cells. Our analysis provides a general tool to identify nonequilibrium dynamics in cells and tissues.

Swelling and softening of the cowpea chlorotic mottle virus in response to pH shifts

Cowpea chlorotic mottle virus (CCMV) forms highly elastic icosahedral protein capsids that undergo a characteristic swelling transition when the pH is raised from 5 to 7. Here, we performed nano-indentation experiments using an atomic force microscope to track capsid swelling and measure the shells' Young's modulus at the same time. When we chelated Ca(2+) ions and raised the pH, we observed a gradual swelling of the RNA-filled capsids accompanied by a softening of the shell. Control experiments with empty wild-type virus and a salt-stable mutant revealed that the softening was not strictly coupled to the swelling of the protein shells. Our data suggest that a pH increase and Ca(2+) chelation lead primarily to a loosening of contacts within the protein shell, resulting in a softening of the capsid. This appears to render the shell metastable and make swelling possible when repulsive forces among the capsid proteins become large enough, which is known to be followed by capsid disassembly at even higher pH. Thus, softening and swelling are likely to play a role during inoculation.

Super-Resolution Optical Fluctuation Bio-Imaging with Dual-Color Carbon Nanodots

Success in super-resolution imaging relies on a proper choice of fluorescent probes. Here, we suggest novel easily produced and biocompatible nanoparticles-carbon nanodots-for super-resolution optical fluctuation bioimaging (SOFI). The particles revealed an intrinsic dual-color fluorescence, which corresponds to two subpopulations of particles of different electric charges. The neutral nanoparticles localize to cellular nuclei suggesting their potential use as an inexpensive, easily produced nucleus-specific label. The single particle study revealed that the carbon nanodots possess a unique hybrid combination of fluorescence properties exhibiting characteristics of both dye molecules and semiconductor nanocrystals. The results suggest that charge trapping and redistribution on the surface of the particles triggers their transitions between emissive and dark states. These findings open up new possibilities for the utilization of carbon nanodots in the various super-resolution microscopy methods based on stochastic optical switching.

Force fluctuations in three-dimensional suspended fibroblasts

Cells are sensitive to mechanical cues from their environment and at the same time generate and transmit forces to their surroundings. To test quantitatively forces generated by cells not attached to a substrate, we used a dual optical trap to suspend 3T3 fibroblasts between two fibronectin-coated beads. In this simple geometry, we measured both the cells' elastic properties and the force fluctuations they generate with high bandwidth. Cell stiffness decreased substantially with both myosin inhibition by blebbistatin and serum-starvation, but not with microtubule depolymerization by nocodazole. We show that cortical forces generated by non-muscle myosin II deform the cell from its rounded shape in the frequency regime from 0.1 to 10 Hz. The amplitudes of these forces were strongly reduced by blebbistatin and serum starvation, but were unaffected by depolymerization of microtubules. Force fluctuations show a spectrum that is characteristic for an elastic network activated by random sustained stresses with abrupt transitions.

Deletion of the Tail Domain of the Kinesin-5 Cin8 Affects Its Directionality

The bipolar kinesin-5 motors are one of the major players that govern mitotic spindle dynamics. Their bipolar structure enables them to cross-link and slide apart antiparallel microtubules (MTs) emanating from the opposing spindle poles. The budding yeast kinesin-5 Cin8 was shown to switch from fast minus-end- to slow plus-end-directed motility upon binding between antiparallel MTs. This unexpected finding revealed a new dimension of cellular control of transport, the mechanism of which is unknown. Here we have examined the role of the C-terminal tail domain of Cin8 in regulating directionality. We first constructed a stable dimeric Cin8/kinesin-1 chimera (Cin8Kin), consisting of head and neck linker of Cin8 fused to the stalk of kinesin-1. As a single dimeric motor, Cin8Kin switched frequently between plus and minus directionality along single MTs, demonstrating that the Cin8 head domains are inherently bidirectional, but control over directionality was lost. We next examined the activity of a tetrameric Cin8 lacking only the tail domains (Cin8Δtail). In contrast to wild-type Cin8, the motility of single molecules of Cin8Δtail in high ionic strength was slow and bidirectional, with almost no directionality switches. Cin8Δtail showed only a weak ability to cross-link MTs in vitro. In vivo, Cin8Δtail exhibited bias toward the plus-end of the MTs and was unable to support viability of cells as the sole kinesin-5 motor. We conclude that the tail of Cin8 is not necessary for bidirectional processive motion, but is controlling the switch between plus- and minus-end-directed motility.

The mechanical properties of early Drosophila embryos measured by high-speed video microrheology

In early development, Drosophila melanogaster embryos form a syncytium, i.e., multiplying nuclei are not yet separated by cell membranes, but are interconnected by cytoskeletal polymer networks consisting of actin and microtubules. Between division cycles 9 and 13, nuclei and cytoskeleton form a two-dimensional cortical layer. To probe the mechanical properties and dynamics of this self-organizing pre-tissue, we measured shear moduli in the embryo by high-speed video microrheology. We recorded position fluctuations of injected micron-sized fluorescent beads with kHz sampling frequencies and characterized the viscoelasticity of the embryo in different locations. Thermal fluctuations dominated over nonequilibrium activity for frequencies between 0.3 and 1000 Hz. Between the nuclear layer and the yolk, the cytoplasm was homogeneous and viscously dominated, with a viscosity three orders of magnitude higher than that of water. Within the nuclear layer we found an increase of the elastic and viscous moduli consistent with an increased microtubule density. Drug-interference experiments showed that microtubules contribute to the measured viscoelasticity inside the embryo whereas actin only plays a minor role in the regions outside of the actin caps that are closely associated with the nuclei. Measurements at different stages of the nuclear division cycle showed little variation.

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.

Elasticity of 3D networks with rigid filaments and compliant crosslinks

Disordered filamentous networks with compliant crosslinks exhibit a low linear elastic shear modulus at small strains, but stiffen dramatically at high strains. Experiments have shown that the elastic modulus can increase by up to three orders of magnitude while the networks withstand relatively large stresses without rupturing. Here, we perform an analytical and numerical study on model networks in three dimensions. Our model consists of a collection of randomly oriented rigid filaments connected by flexible crosslinks that are modeled as wormlike chains. Due to zero probability of filament intersection in three dimensions, our model networks are by construction prestressed in terms of initial tension in the crosslinks. We demonstrate how the linear elastic modulus can be related to the prestress in these networks. Under the assumption of affine deformations in the limit of infinite crosslink density, we show analytically that the nonlinear elastic regime in 1- and 2-dimensional networks is characterized by power-law scaling of the elastic modulus with the stress. In contrast, 3-dimensional networks show an exponential dependence of the modulus on stress. Independent of dimensionality, if the crosslink density is finite, we show that the only persistent scaling exponent is that of the single wormlike chain. We further show that there is no qualitative change in the stiffening behavior of filamentous networks even if the filaments are bending-compliant. Consequently, unlike suggested in prior work, the model system studied here cannot provide an explanation for the experimentally observed linear scaling of the modulus with the stress in filamentous networks.

Regulation of bi-directional movement of single kinesin-5 Cin8 molecules

Kinesin-5 mechanoenzymes drive mitotic spindle dynamics as slow, processive microtubule (MT)-plus-end directed motors. Surprisingly, the Saccharomyces cerevisiae kinesin-5 Cin8 was recently found to be bi-directional: it can move processively in both directions on MTs. Two hypotheses have been suggested for the mechanism of the directionality switch: (1) single molecules of Cin8 are intrinsically minus-end directed, but mechanical coupling between two or more motors triggers the switch; (2) a single motor can switch direction, and "cargo binding" i.e., binding between two MTs triggers the switch to plus-end motility. Single-molecule fluorescence data we published recently, and augment here, favor hypothesis (2). In low-ionic-strength conditions, single molecules of Cin8 move in both minus- and plus-end directions. Fluorescence photo bleaching data rule out aggregation of Cin8 while they move in the plus and in the minus direction. The evidence thus points toward cargo regulation of directionality, which is likely to be related to cargo regulation in other kinesins. The molecular mechanisms of this regulation, however, remain to be elucidated.

High-resolution mapping of intracellular fluctuations using carbon nanotubes

Cells are active systems with molecular force generation that drives complex dynamics at the supramolecular scale. We present a quantitative study of molecular motions in cells over times from milliseconds to hours. Noninvasive tracking was accomplished by imaging highly stable near-infrared luminescence of single-walled carbon nanotubes targeted to kinesin-1 motor proteins in COS-7 cells. We observed a regime of active random "stirring" that constitutes an intermediate mode of transport, different from both thermal diffusion and directed motor activity. High-frequency motion was found to be thermally driven. At times greater than 100 milliseconds, nonequilibrium dynamics dominated. In addition to directed transport along microtubules, we observed strong random dynamics driven by myosins that result in enhanced nonspecific transport. We present a quantitative model connecting molecular mechanisms to mesoscopic fluctuations.

A surprising twist

X-ray crystallography has revealed an unusual structural element in kinesin-5 motor proteins.

Kinesin-5 Kip1 is a bi-directional motor that stabilizes microtubules and tracks their plus-ends in vivo

In this study, we examined the anaphase functions of the S. cerevisiae kinesin-5 homolog Kip1. We show that Kip1 is attached to the mitotic spindle midzone during late anaphase. This attachment is essential to stabilize interpolar microtubule (iMTs) plus-ends. By detailed examination of iMT dynamics we show that at the end of anaphase, iMTs depolymerize in two stages: during the first stage, one pair of anti-parallel iMTs depolymerizes at a velocity of 7.7 µm/minute; during the second stage, ∼90 seconds later, the remaining pair of iMTs depolymerizes at a slower velocity of 5.4 µm/minute. We show that upon the second depolymerization stage, which coincides with spindle breakdown, Kip1 follows the plus-ends of depolymerizing iMTs and translocates toward the spindle poles. This movement is independent of mitotic microtubule motor proteins or the major plus-end binding or tracking proteins. In addition, we show that Kip1 processively tracks the plus-ends of growing and shrinking MTs, both inside and outside the nucleus. The plus-end tracking activity of Kip1 requires its catalytic motor function, because a rigor mutant of Kip1 does not exhibit this activity. Finally, we show that Kip1 is a bi-directional motor: in vitro, at high ionic strength conditions, single Kip1 molecules move processively in the minus-end direction of the MTs, whereas in a multi-motor gliding assay, Kip1 is plus-end directed. The bi-directionality and plus-end tracking activity of Kip1, properties revealed here for the first time, allow Kip1 to perform its multiple functions in mitotic spindle dynamics and to partition the 2-micron plasmid.

Differential interference contrast microscopy using light-emitting diode illumination in conjunction with dual optical traps

Differential interference contrast (DIC) microscopy is a common mode of biological light microscopy used to achieve maximal resolution and contrast with label-free, weakly absorbing specimens such as cells. Maintaining the polarization state of the illuminating light is essential for the technique, and this requirement can conflict with optical trapping. We describe how to optimize DIC imaging using a light-emitting diode illumination source in a microscope while integrating a dual optical trap into the set up. Every time a polarized light beam reflects off or transmits through a dichroic mirror in the beam path, its polarization state will change if it is not polarized exactly parallel (p) or perpendicular (s) to the plane of incidence. We observe wavelength-dependent optical rotation and depolarization effects in our illumination light upon reflection from/transmission through dichroic mirrors in the beam path, resulting in significant degradation of image quality. We describe a method to compensate for these effects by introducing quarter-waveplates and a laser clean-up filter into the imaging pathway. We show that this approach achieves a full recovery of image quality.

Endoplasmic reticulum sorting and kinesin-1 command the targeting of axonal GABAB receptors

In neuronal cells the intracellular trafficking machinery controls the availability of neurotransmitter receptors at the plasma membrane, which is a critical determinant of synaptic strength. Metabotropic γ amino-butyric acid (GABA) type B receptors (GABA_BRs) are neurotransmitter receptors that modulate synaptic transmission by mediating the slow and prolonged responses to GABA. GABA_BRs are obligatory heteromers constituted by two subunits, GABA_BR1 and GABA_BR2. GABA_BR1a and GABA_BR1b are the most abundant subunit variants. GABA_BR1b is located in the somatodendritic domain whereas GABA_BR1a is additionally targeted to the axon. Sushi domains located at the N-terminus of GABA_BR1a constitute the only difference between both variants and are necessary and sufficient for axonal targeting. The precise targeting machinery and the organelles involved in sorting and transport have not been described. Here we demonstrate that GABA_BRs require the Golgi apparatus for plasma membrane delivery but that axonal sorting and targeting of GABA_BR1a operate in a pre-Golgi compartment. In the axon GABA_BR1a subunits are enriched in the endoplasmic reticulum (ER), and their dynamic behavior and colocalization with other secretory organelles like the ER-to-Golgi intermediate compartment (ERGIC) suggest that they employ a local secretory route. The transport of axonal GABA_BR1a is microtubule-dependent and kinesin-1, a molecular motor of the kinesin family, determines axonal localization. Considering that progression of GABA_BRs through the secretory pathway is regulated by an ER retention motif our data contribute to understand the role of the axonal ER in non-canonical sorting and targeting of neurotransmitter receptors.

Neck-linker length dependence of processive Kinesin-5 motility

Processive motility of individual molecules is essential for the function of many kinesin motors. Processivity for kinesins relies on communication between the two heads of a dimeric molecule, such that binding strictly alternates. The main communicating elements are believed to be the two neck linkers connecting the motors' stalks and heads. A proposed mechanism for coordination is the transmission of stress through the neck linkers. It is believed that the efficiency of gating depends on the length of the neck linker. Recent studies have presented support for a simple model in which the length of the neck linker directly controls the degree of processivity. Based on a previously published Kinesin-1/Kinesin-5 chimera, Eg5Kin, we have analyzed the motility of 12 motor constructs: we have varied the length of the neck linker in the range between 9 and 21 amino acids using the corresponding native Kinesin-5 sequence (Xenopus laevis Eg5). We found, surprisingly, that neither velocity nor force generation depended on neck-linker length. We also found that constructs with short neck linkers, down to 12 amino acids, were still highly processive, while processivity was lost at a length of 9 amino acids. Run lengths were maximal with neck linkers close to the native Kinesin-5 length and decreased beyond that length. This finding generally confirms the coordinating role of the neck linker for kinesin motility but challenges the simplest model postulating a motor-type-independent optimal length. Instead, our results suggest that different kinesins might be optimized for different neck-linker lengths.

High-resolution microrheology in the pericellular matrix of prostate cancer cells

Many cells express a membrane-coupled external mechanical layer, the pericellular matrix (PCM), which often contains long-chain polymers. Its role and properties are not entirely known, but its functions are believed to include physical protection, mechanosensing, chemical signalling or lubrication. The viscoelastic response of the PCM, with polysaccharides as the main structural components, is therefore crucial for the understanding of its function. We have here applied microrheology, based on optically trapped micrometre-sized colloids, to the PCM of cultured PC3 prostate cancer cells. This technology allowed us to measure the extremely soft response of the PCM, with approximately 1 µm height resolution. Exogenously added aggrecan, a hyaluronan-binding proteoglycan, caused a remarkable increase in thickness of the viscoelastic layer and also triggered filopodia-like protrusions. The viscoelastic response of the PCM, however, did not change significantly.

Directionality of individual kinesin-5 Cin8 motors is modulated by loop 8, ionic strength and microtubule geometry

Kinesin-5 motors fulfil essential roles in mitotic spindle morphogenesis and dynamics as slow, processive microtubule (MT) plus-end directed motors. The Saccharomyces cerevisiae kinesin-5 Cin8 was found, surprisingly, to switch directionality. Here, we have examined directionality using single-molecule fluorescence motility assays and live-cell microscopy. On spindles, Cin8 motors mostly moved slowly (∼25 nm/s) towards the midzone, but occasionally also faster (∼55 nm/s) towards the spindle poles. In vitro, individual Cin8 motors could be switched by ionic conditions from rapid (380 nm/s) and processive minus-end to slow plus-end motion on single MTs. At high ionic strength, Cin8 motors rapidly alternated directionalities between antiparallel MTs, while driving steady plus-end relative sliding. Between parallel MTs, plus-end motion was only occasionally observed. Deletion of the uniquely large insert in loop 8 of Cin8 induced bias towards minus-end motility and affected the ionic strength-dependent directional switching of Cin8 in vitro. The deletion mutant cells exhibited reduced midzone-directed motility and efficiency to support spindle elongation, indicating the importance of directionality control for the anaphase function of Cin8.

Kinesin walks the line: single motors observed by atomic force microscopy

Motor proteins of the kinesin family move actively along microtubules to transport cargo within cells. How exactly a single motor proceeds on the 13 narrow lanes or protofilaments of a microtubule has not been visualized directly, and there persists controversy on the relative position of the two kinesin heads in different nucleotide states. We have succeeded in imaging Kinesin-1 dimers immobilized on microtubules with single-head resolution by atomic force microscopy. Moreover, we could catch glimpses of single Kinesin-1 dimers in their motion along microtubules with nanometer resolution. We find in our experiments that frequently both heads of one dimer are microtubule-bound at submicromolar ATP concentrations. Furthermore, we could unambiguously resolve that both heads bind to the same protofilament, instead of straddling two, and remain on this track during processive movement.

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.

THE ACTION OF DRUGS ON RESPIRATION : I. THE MORPHINE SERIES

1. A method is described for recording intrathoracic pressure in cats without opening the pleural cavity; active expiratory movements were elicited by inhalation of a constant CO₂-air mixture for a given time and a study was made of the action of drugs on inspiration and expiration. 2. Morphine and heroine were found to exert a selective depressant action on the central expiratory mechanism, and the slower rate, with relatively unaltered depth, seemed to be due at least partly to the slower rate of emptying the lungs. Codeine had no depressant action on the respiration of decerebrated cats. 3. Larger doses of morphine or heroine had no further depressant effect on rate or depth of breathing after expiration was made passive, unless circulatory depression appeared, and failure of circulation seemed to be the cause of respiratory depression, rather than the reverse relation. In decerebrated animals large doses of morphine and moderate doses of codeine stimulated the spinal cord, and expiration became active, with a faster rate of breathing. The characteristic action of morphine and heroine on the respiration of the cat is apparently limited to a depression of active expiration.