Self-organization of microtubules and motors

A study on a special DNA nanotube assembled from two single-stranded tiles

Single-stranded tile (SST) strategy offers precise control over the circumferences of nanotubes while the kinetic trap in the process of the self-assembly prevents the formation of wider tubes. Here, we report a simple and efficient method to build DNA nanotubes using only 2 SSTs via one-pot annealing. The diameters of the 2-SST nanotubes were much larger than what the kinetic trap theory would predict, indicating a new mechanism was at play in the formation of these nanotubes. Further investigation suggested that the 2-SST nanotubes were assembled through a hierarchical pathway that involved an intermediate formation of 2-SST nano-lines.

Self-organized dynamics and the transition to turbulence of confined active nematics

We study how confinement transforms the chaotic dynamics of bulk microtubule-based active nematics into regular spatiotemporal patterns. For weak confinements in disks, multiple continuously nucleating and annihilating topological defects self-organize into persistent circular flows of either handedness. Increasing confinement strength leads to the emergence of distinct dynamics, in which the slow periodic nucleation of topological defects at the boundary is superimposed onto a fast procession of a pair of defects. A defect pair migrates toward the confinement core over multiple rotation cycles, while the associated nematic director field evolves from a distinct double spiral toward a nearly circularly symmetric configuration. The collapse of the defect orbits is punctuated by another boundary-localized nucleation event, that sets up long-term doubly periodic dynamics. Comparing experimental data to a theoretical model of an active nematic reveals that theory captures the fast procession of a pair of [Formula: see text] defects, but not the slow spiral transformation nor the periodic nucleation of defect pairs. Theory also fails to predict the emergence of circular flows in the weak confinement regime. The developed confinement methods are generalized to more complex geometries, providing a robust microfluidic platform for rationally engineering 2D autonomous flows.

Bio-Field Array: The Influence of Junction Mediating and Regulatory Protein Expression on Cytoskeletal Filament Behavior During Apoptosis in Triple-Negative Breast Cancer

Introduction:

The Bio-Field Array (BFA) is a device that generates a dielectrophoretic electromagnetic field (DEP-EMF) when placed in a hypotonic saline solution and a direct current (dc) of ~3 amperes is applied. Human triple-negative breast cancer (MDA-MB-231 cells) is known to have a high percentage of apoptotic (P53) deficient cells and some patients can have poor outcomes with current treatments.

Objectives:

Previously, we reported a strong upregulation of the apoptotic arm of the unfolded protein response, via reverse transcription–quantitative polymerase chain reaction (RT-qPCR), as well as positive annexin staining in this human breast carcinoma, when grown in media prepared with BFA’s dc DEP-EMF treated saline. Here we will examine and discuss cytoskeletal microtubule changes that were noted in the treated breast carcinoma that are strongly suggestive of apoptosis and the possible correlation of these microtubule changes to the upregulation of Junction Mediating and Regulatory Protein (JMY, a P53/TP53 cofactor) that is known to drive cytoskeleton microfilaments (actin) function.

Methods:

In addition to microarray and RT-qPCR analyses, we conducted 7 days of fluorescent microscopic analyses of tubulin assays in these treated versus control MDA-MB-231 cells.

Results:

These data suggest 2 possible forms of apoptosis, rounded and irregular, may be occurring and possibly facilitated by the significant upregulation (via microarray and RT-qPCR) of an important but poorly understood Nucleation-Promoting Factor (NPF), JMY.

Conclusions:

The ability of the BFA dc DEP-EMF to significantly upregulate JMY and possibly influence the regulation of unbranched (nucleation-microtubule spikes) and branched forms (autophagy) of actin in the cytoplasmic domains may facilitate a “two coffins” or round and irregular necrosis-like apoptosis for this highly aggressive and often apoptotic-deficient breast cancer cell line.

Chemical Nanomotors at the Gram Scale Form a Dense Active Optorheological Medium

The rheological properties of a colloidal suspension are a function of the concentration of the colloids and their interactions. While suspensions of passive colloids are well studied and have been shown to form crystals, gels, and glasses, examples of energy-consuming "active" colloidal suspensions are still largely unexplored. Active suspensions of biological matter, such as motile bacteria or dense mixtures of active actin-motor-protein mixtures have, respectively, reveals superfluid-like and gel-like states. Attractive inanimate systems for active matter are chemically self-propelled particles. It has so far been challenging to use these swimming particles at high enough densities to affect the bulk material properties of the suspension. Here, it is shown that light-triggered asymmetric titanium dioxide that self-propel, can be obtained in large quantities, and self-organize to make a gram-scale active medium. The suspension shows an activity-dependent tenfold reversible change in its bulk viscosity.

A dynamic preferred direction model for the self-organization dynamics of bacterial microfluidic pumping

It is known that some flagellated bacteria like Serratia marcescens, when deposited and affixed onto a surface to form a "bacterial carpet", self-organize in a collective motion of the flagella that is capable of pumping fluid through microfluidic channels. We set up a continuum model comprising two macroscopic variables that is capable of describing this self-organization mechanism as well as quantifying it to the extent that an agreement with the experimentally observed channel width dependence of the pumping is reached. The activity is introduced through a collective angular velocity of the helical flagella rotation, which is an example of a dynamic macroscopic preferred direction. Our model supports and quantifies the view that the self-coordination is due to a positive feedback loop between the bacterial flagella and the local flow generated by their rotation. Moreover, our results indicate that this biological active system is operating close to the self-organization threshold.

Millimeter-sized belt-like pattern formation of actin filaments in solution by interacting with surface myosin in vitro

The movements of single actin filaments along a myosin-fixed glass surface were observed under a conventional fluorescence microscope. Although random at a low concentration, moving directions of filaments were aligned by the presence of over 1.0 mg/mL of unlabeled filaments. We found that actin filaments when at the intermediate concentrations ranging from 0.1 to 1.0 mg/mL, formed winding belt-like patterns and moved in a two-directional manner along the belts. These patterns were spread over a millimeter range and found to have bulged on the glass in a three-dimensional manner. Filaments did not get closer than about 37.5 nm to each other within each belt-pattern. The average width and the curvature radius of the pattern did not apparently change even when the range of actin concentrations was between 0.05 and 1.0 mg/mL or the sliding velocity between 1.2 and 3.2 μm/sec. However, when the length of filaments was shortened by ultrasonic treatments or the addition of gelsolin molecules, the curvature radius became small from 100 to 60 μm. These results indicate that this belt-forming nature of actin filaments may be due to some inter-filament interactions.

Minimal in vitro systems shed light on cell polarity

Cell polarity - the morphological and functional differentiation of cellular compartments in a directional manner - is required for processes such as orientation of cell division, directed cellular growth and motility. How the interplay of components within the complexity of a cell leads to cell polarity is still heavily debated. In this Review, we focus on one specific aspect of cell polarity: the non-uniform accumulation of proteins on the cell membrane. In cells, this is achieved through reaction-diffusion and/or cytoskeleton-based mechanisms. In reaction-diffusion systems, components are transformed into each other by chemical reactions and are moving through space by diffusion. In cytoskeleton-based processes, cellular components (i.e. proteins) are actively transported by microtubules (MTs) and actin filaments to specific locations in the cell. We examine how minimal systems - in vitro reconstitutions of a particular cellular function with a minimal number of components - are designed, how they contribute to our understanding of cell polarity (i.e. protein accumulation), and how they complement in vivo investigations. We start by discussing the Min protein system from Escherichia coli, which represents a reaction-diffusion system with a well-established minimal system. This is followed by a discussion of MT-based directed transport for cell polarity markers as an example of a cytoskeleton-based mechanism. To conclude, we discuss, as an example, the interplay of reaction-diffusion and cytoskeleton-based mechanisms during polarity establishment in budding yeast.

Guided by Light: Optical Control of Microtubule Gliding Assays

Force generation by molecular motors drives biological processes such as asymmetric cell division and cell migration. Microtubule gliding assays in which surface-immobilized motor proteins drive microtubule propulsion are widely used to study basic motor properties as well as the collective behavior of active self-organized systems. Additionally, these assays can be employed for nanotechnological applications such as analyte detection, biocomputation, and mechanical sensing. While such assays allow tight control over the experimental conditions, spatiotemporal control of force generation has remained underdeveloped. Here we use light-inducible protein-protein interactions to recruit molecular motors to the surface to control microtubule gliding activity in vitro. We show that using these light-inducible interactions, proteins can be recruited to the surface in patterns, reaching a ∼5-fold enrichment within 6 s upon illumination. Subsequently, proteins are released with a half-life of 13 s when the illumination is stopped. We furthermore demonstrate that light-controlled kinesin recruitment results in reversible activation of microtubule gliding along the surface, enabling efficient control over local microtubule motility. Our approach to locally control force generation offers a way to study the effects of nonuniform pulling forces on different microtubule arrays and also provides novel strategies for local control in nanotechnological applications.

Thin-film models for an active gel

In this study, we present a free-boundary problem for an active liquid crystal starting with the Beris-Edwards theory that uses a tensorial order parameter and includes active contributions to the stress tensor and then derive from it the Eriksen model for an active polar gel and scalar order parameter to analyse the rich defect structure observed in applications such as the adenosinetriphosphate-driven motion of a thin film of an actin filament network. The small aspect ratio of the film geometry allows for an asymptotic approximation of the free-boundary problem in the limit of weak elasticity of the network and strong active terms. The new thin-film model captures the defect dynamics in the bulk as well as wall defects and thus presents a significant extension of previous models based on the Leslie-Erickson-Parodi theory. As an example we derive the explicit solution for an active gel confined to a channel, which has discontinuous director profile leading to a bidirectional flow structure generated by the active terms.

From cytoskeletal assemblies to living materials

Many subcellular structures contain large numbers of cytoskeletal filaments. Such assemblies underlie much of cell division, motility, signaling, metabolism, and growth. Thus, understanding cell biology requires understanding the properties of networks of cytoskeletal filaments. While there are well established disciplines in biology dedicated to studying isolated proteins - their structure (Structural Biology) and behaviors (Biochemistry) - it is much less clear how to investigate, or even just describe, the structure and behaviors of collections of cytoskeletal filaments. One approach is to use methodologies from Mechanics and Soft Condensed Matter Physics, which have been phenomenally successful in the domains where they have been traditionally applied. From this perspective, collections of cytoskeletal filaments are viewed as materials, albeit very complex, 'active' materials, composed of molecules which use chemical energy to perform mechanical work. A major challenge is to relate these material level properties to the behaviors of the molecular constituents. Here we discuss this materials perspective and review recent work bridging molecular and network scale properties of the cytoskeleton, focusing on the organization of microtubules by dynein as an illustrative example.

Globulelike Conformation and Enhanced Diffusion of Active Polymers

We study the dynamics and conformation of polymers composed by active monomers. By means of Brownian dynamics simulations we show that, when the direction of the self-propulsion of each monomer is aligned with the backbone, the polymer undergoes a coil-to-globulelike transition, highlighted by a marked change of the scaling exponent of the gyration radius. Concurrently, the diffusion coefficient of the center of mass of the polymer becomes essentially independent of the polymer size for sufficiently long polymers or large magnitudes of the self-propulsion. These effects are reduced when the self-propulsion of the monomers is not bound to be tangent to the backbone of the polymer. Our results, rationalized by a minimal stochastic model, open new routes for activity-controlled polymers and, possibly, for a new generation of polymer-based drug carriers.

Biological Tissues as Active Nematic Liquid Crystals

Live tissues can self-organize and be described as active materials composed of cells that generate active stresses through continuous injection of energy. In vitro reconstituted molecular networks, as well as single-cell cytoskeletons show that their filamentous structures can portray nematic liquid crystalline properties and can promote nonequilibrium processes induced by active processes at the microscale. The appearance of collective patterns, the formation of topological singularities, and spontaneous phase transition within the cell cytoskeleton are emergent properties that drive cellular functions. More integrated systems such as tissues have cells that can be seen as coarse-grained active nematic particles and their interaction can dictate many important tissue processes such as epithelial cell extrusion and migration as observed in vitro and in vivo. Here, a brief introduction to the concept of active nematics is provided, and the main focus is on the use of this framework in the systematic study of predominantly 2D tissue architectures and dynamics in vitro. In addition how the nematic state is important in tissue behavior, such as epithelial expansion, tissue homeostasis, and the atherosclerosis disease state, is discussed. Finally, how the nematic organization of cells can be controlled in vitro for tissue engineering purposes is briefly discussed.

Determinants of Polar versus Nematic Organization in Networks of Dynamic Microtubules and Mitotic Motors

During cell division, mitotic motors organize microtubules in the bipolar spindle into either polar arrays at the spindle poles or a "nematic" network of aligned microtubules at the spindle center. The reasons for the distinct self-organizing capacities of dynamic microtubules and different motors are not understood. Using in vitro reconstitution experiments and computer simulations, we show that the human mitotic motors kinesin-5 KIF11 and kinesin-14 HSET, despite opposite directionalities, can both organize dynamic microtubules into either polar or nematic networks. We show that in addition to the motor properties the natural asymmetry between microtubule plus- and minus-end growth critically contributes to the organizational potential of the motors. We identify two control parameters that capture system composition and kinetic properties and predict the outcome of microtubule network organization. These results elucidate a fundamental design principle of spindle bipolarity and establish general rules for active filament network organization.

Microtubule Dynamics, Kinesin-1 Sliding, and Dynein Action Drive Growth of Cell Processes

Recent experimental studies of the role of microtubule sliding in neurite outgrowth suggested a qualitative model, according to which kinesin-1 motors push the minus-end-out microtubules against the cell membrane and generate the early cell processes. At the later stage, dynein takes over the sliding, expels the minus-end-out microtubules from the neurites, and pulls in the plus-end-out microtubules that continue to elongate the nascent axon. This model leaves unanswered a number of questions: why is dynein unable to generate the processes alone, whereas kinesin-1 can? What is the role of microtubule dynamics in process initiation and growth? Can the model correctly predict the rates of process growth in control and dynein-inhibited cases? What triggers the transition from kinesin-driven to dynein-driven sliding? To answer these questions, we combine computational modeling of a network of elastic dynamic microtubules and kinesin-1 and dynein motors with measurements of the process growth kinetics and pharmacological perturbations in Drosophila S2 cells. The results verify quantitatively the qualitative model of the microtubule polarity sorting and suggest that dynein-powered elongation is effective only when the processes are longer than a threshold length, which explains why kinesin-1 alone, but not dynein, is sufficient for the process growth. Furthermore, we show that the mechanism of process elongation depends critically on microtubule dynamic instability. Both modeling and experimental measurements show, surprisingly, that dynein inhibition accelerates the process extension. We discuss implications of the model for the general problems of cell polarization, cytoskeletal polarity emergence, and cell process protrusion.

Kinetic theory of pattern formation in mixtures of microtubules and molecular motors

In this study we formulate a theoretical approach, based on a Boltzmann-like kinetic equation, to describe pattern formation in two-dimensional mixtures of microtubular filaments and molecular motors. Following the previous work by Aranson and Tsimring [Phys. Rev. E 74, 031915 (2006)PLEEE81539-375510.1103/PhysRevE.74.031915] we model the motor-induced reorientation of microtubules as collision rules, and devise a semianalytical method to calculate the corresponding interaction integrals. This procedure yields an infinite hierarchy of kinetic equations that we terminate by employing a well-established closure strategy, developed in the pattern-formation community and based on a power-counting argument. We thus arrive at a closed set of coupled equations for slowly varying local density and orientation of the microtubules, and study its behavior by performing a linear stability analysis and direct numerical simulations. By comparing our method with the work of Aranson and Tsimring, we assess the validity of the assumptions required to derive their and our theories. We demonstrate that our approximation-free evaluation of the interaction integrals and our choice of a systematic closure strategy result in a rather different dynamical behavior than was previously reported. Based on our theory, we discuss the ensuing phase diagram and the patterns observed.

Nonequilibrium phase diagrams for actomyosin networks

Living cells dynamically modulate the local morphologies of their actin networks to perform biological functions, including force transduction, intracellular transport, and cell division. A major challenge is to understand how diverse structures of the actin cytoskeleton are assembled from a limited set of molecular building blocks. Here we study the spontaneous self-assembly of a minimal model of cytoskeletal materials, consisting of semiflexible actin filaments, crosslinkers, and molecular motors. Using coarse-grained simulations, we demonstrate that by changing concentrations and kinetics of crosslinkers and motors, as well as filament lengths, we can generate three distinct structural phases of actomyosin assemblies: bundled, polarity-sorted, and contracted. We introduce new metrics to distinguish these structural phases and demonstrate their functional roles. We find that the binding kinetics of motors and crosslinkers can be tuned to optimize contractile force generation, motor transport, and mechanical response. By quantitatively characterizing the relationships between the modes of cytoskeletal self-assembly, the resulting structures, and their functional consequences, our work suggests new principles for the design of active materials.

Active nematics

Active matter extracts energy from its surroundings at the single particle level and transforms it into mechanical work. Examples include cytoskeleton biopolymers and bacterial suspensions. Here, we review experimental, theoretical and numerical studies of active nematics - a type of active system that is characterised by self-driven units with elongated shape. We focus primarily on microtubule-kinesin mixtures and the hydrodynamic theories that describe their properties. An important theme is active turbulence and the associated motile topological defects. We discuss ways in which active turbulence may be controlled, a pre-requisite to harvesting energy from active materials, and we consider the appearance, and possible implications, of active nematics and topological defects to cellular systems and biological processes.

Active Brownian Filamentous Polymers under Shear Flow

The conformational and rheological properties of active filaments/polymers exposed to shear flow are studied analytically. Using the continuous Gaussian semiflexible polymer model extended by the activity, we derive analytical expressions for the dependence of the deformation, orientation, relaxation times, and viscosity on the persistence length, shear rate, and activity. The model yields a Weissenberg-number dependent shear-induced deformation, alignment, and shear thinning behavior, similarly to the passive counterpart. Thereby, the model shows an intimate coupling between activity and shear flow. As a consequence, activity enhances the shear-induced polymer deformation for flexible polymers. For semiflexible polymers/filaments, a nonmonotonic deformation is obtained because of the activity-induced shrinkage at moderate and swelling at large activities. Independent of stiffness, activity-induced swelling facilitates and enhances alignment and shear thinning compared to a passive polymer. In the asymptotic limit of large activities, a polymer length- and stiffness-independent behavior is obtained, with universal shear-rate dependencies for the conformations, dynamics, and rheology.

Microtubule minus-end aster organization is driven by processive HSET-tubulin clusters

Higher-order structures of the microtubule (MT) cytoskeleton are comprised of two architectures: bundles and asters. Although both architectures are critical for cellular function, the molecular pathways that drive aster formation are poorly understood. Here, we study aster formation by human minus-end-directed kinesin-14 (HSET/KIFC1). We show that HSET is incapable of forming asters from preformed, nongrowing MTs, but rapidly forms MT asters in the presence of soluble (non-MT) tubulin. HSET binds soluble (non-MT) tubulin via its N-terminal tail domain to form heterogeneous HSET-tubulin clusters containing multiple motors. Cluster formation induces motor processivity and rescues the formation of asters from nongrowing MTs. We then show that excess soluble (non-MT) tubulin stimulates aster formation in HeLa cells overexpressing HSET during mitosis. We propose a model where HSET can toggle between MT bundle and aster formation in a manner governed by the availability of soluble (non-MT) tubulin.

Dissipative assemblies that inhibit their deactivation

Dissipative self-assembly is a process in which energy-consuming chemical reaction networks drive the assembly of molecules. Prominent examples from biology include the GTP-fueled microtubule and ATP-driven actin assembly. Pattern formation and oscillatory behavior are some of the unique properties of the emerging assemblies. While artificial counterparts exist, researchers have not observed such complex responses. One reason for the missing complexity is the lack of feedback mechanisms of the assemblies on their chemical reaction network. In this work, we describe the dissipative self-assembly of colloids that protect the hydrolysis of their building blocks. The mechanism of inhibition is generalized and explored for other building blocks. We show that we can tune the level of inhibition by the assemblies. Finally, we show that the robustness of the assemblies towards starvation is affected by the degree of inhibition.

Internal dynamics of semiflexible polymers with active noise

The intramolecular dynamics of flexible and semiflexible polymers in response to active noise is studied theoretically. The active noise may either originate from interactions of a passive polymer with a bath of active Brownian particles or the polymer itself is comprised of active Brownian particles. We describe the polymer by the continuous Gaussian semiflexible-polymer model, taking into account the finite polymer extensibility. Our analytical calculations predict a strong dependence of the polymer dynamics on the activity. In particular, active semiflexible polymers exhibit a crossover from a bending elasticity-dominated dynamics at weak activity to that of flexible polymers at strong activity. The end-to-end vector correlation function decays exponentially for times longer than the longest polymer relaxation time. Thereby, the polymer relaxation determines the decay of the correlation function for long and flexible polymers. For shorter and stiffer polymers, the relaxation behavior of individual active Brownian particles dominates the decay above a certain activity. The diffusive dynamics of a polymer is substantially enhanced by the activity. Three regimes can be identified in the mean square displacement for sufficiently strong activities: an activity-induced ballistic regime at short times, followed by a Rouse-type polymer-specific regime for any polymer stiffness, and free diffusion at long times, again determined by the activity.

Collective dynamics of self-propelled semiflexible filaments

The collective behavior of active semiflexible filaments is studied with a model of tangentially driven self-propelled worm-like chains. The combination of excluded-volume interactions and self-propulsion leads to several distinct dynamic phases as a function of bending rigidity, activity, and aspect ratio of individual filaments. We consider first the case of intermediate filament density. For high-aspect-ratio filaments, we identify a transition with increasing propulsion from a state of free-swimming filaments to a state of spiraled filaments with nearly frozen translational motion. For lower aspect ratios, this gas-of-spirals phase is suppressed with growing density due to filament collisions; instead, filaments form clusters similar to self-propelled rods. As activity increases, finite bending rigidity strongly effects the dynamics and phase behavior. Flexible filaments form small and transient clusters, while stiffer filaments organize into giant clusters, similarly to self-propelled rods, but with a reentrant phase behavior from giant to smaller clusters as activity becomes large enough to bend the filaments. For high filament densities, we identify a nearly frozen jamming state at low activities, a nematic laning state at intermediate activities, and an active-turbulence state at high activities. The latter state is characterized by a power-law decay of the energy spectrum as a function of wave number. The resulting phase diagrams encapsulate tunable non-equilibrium steady states that can be used in the organization of living matter.

Cooperative Accumulation of Dynein-Dynactin at Microtubule Minus-Ends Drives Microtubule Network Reorganization

Cytoplasmic dynein-1 is a minus-end-directed motor protein that transports cargo over long distances and organizes the intracellular microtubule (MT) network. How dynein motor activity is harnessed for these diverse functions remains unknown. Here, we have uncovered a mechanism for how processive dynein-dynactin complexes drive MT-MT sliding, reorganization, and focusing, activities required for mitotic spindle assembly. We find that motors cooperatively accumulate, in limited numbers, at MT minus-ends. Minus-end accumulations drive MT-MT sliding, independent of MT orientation, resulting in the clustering of MT minus-ends. At a mesoscale level, activated dynein-dynactin drives the formation and coalescence of MT asters. Macroscopically, dynein-dynactin activity leads to bulk contraction of millimeter-scale MT networks, suggesting that minus-end accumulations of motors produce network-scale contractile stresses. Our data provide a model for how localized dynein activity is harnessed by cells to produce contractile stresses within the cytoskeleton, for example, during mitotic spindle assembly.

The Effects of the Interplay between Motor and Brownian Forces on the Rheology of Active Gels

Active gels perform key mechanical roles inside the cell, such as cell division, motion, and force sensing. The unique mechanical properties required to perform such functions arise from the interactions between molecular motors and semiflexible polymeric filaments. Molecular motors can convert the energy released in the hydrolysis of ATP into forces of up to piconewton magnitudes. Moreover, the polymeric filaments that form active gels are flexible enough to respond to Brownian forces but also stiff enough to support the large tensions induced by the motor-generated forces. Brownian forces are expected to have a significant effect especially at motor activities at which stable noncontractile in vitro active gels are prepared for rheological measurements. Here, a microscopic mean-field theory of active gels originally formulated in the limit of motor-dominated dynamics is extended to include Brownian forces. In the model presented here, Brownian forces are included accurately, at real room temperature, even in systems with high motor activity. It is shown that a subtle interplay, or competition, between motor-generated forces and Brownian forces has an important impact on the mass transport and rheological properties of active gels. The model predictions show that at low frequencies the dynamic modulus of active gels is determined mostly by motor protein dynamics. However, Brownian forces significantly increase the breadth of the relaxation spectrum and can affect the shape of the dynamic modulus over a wide frequency range even for ratios of motor to Brownian forces of more than a hundred. Since the ratio between motor and Brownian forces is sensitive to ATP concentration, the results presented here shed some light on how the transient mechanical response of active gels changes with varying ATP concentration.

Gold nanocrystal-mediated sliding of doublet DNA origami filaments

Sliding is one of the fundamental mechanical movements in machinery. In macroscopic systems, double-rack pinion machines employ gears to slide two linear tracks along opposite directions. In microscopic systems, kinesin-5 proteins crosslink and slide apart antiparallel microtubules, promoting spindle bipolarity and elongation during mitosis. Here we demonstrate an artificial nanoscopic analog, in which gold nanocrystals can mediate coordinated sliding of two antiparallel DNA origami filaments powered by DNA fuels. Stepwise and reversible sliding along opposite directions is in situ monitored and confirmed using fluorescence spectroscopy. A theoretical model including different energy transfer mechanisms is developed to understand the observed fluorescence dynamics. We further show that such sliding can also take place in the presence of multiple DNA sidelocks that are introduced to inhibit the relative movements. Our work enriches the toolbox of DNA-based nanomachinery, taking one step further toward the vision of molecular nanofactories.

Kinesin, a motor protein, moves along filaments in a walk-like fashion to transport cargo to specific places in the cell. Here, the authors developed an analogous, artificial system consisting of nanoparticles moving along DNA filaments.

Construction of artificial cilia from microtubules and kinesins through a well-designed bottom-up approach

Self-organized structures of biomolecular motor systems, such as cilia and flagella, play key roles in the dynamic processes of living organisms, like locomotion or the transportation of materials. Although fabrication of such self-organized structures from reconstructed biomolecular motor systems has attracted much attention in recent years, a systematic construction methodology is still lacking. In this work, through a bottom-up approach, we fabricated artificial cilia from a reconstructed biomolecular motor system, microtubule/kinesin. The artificial cilia exhibited a beating motion upon the consumption, by the kinesins, of the chemical energy obtained from the hydrolysis of adenosine triphosphate (ATP). Several design parameters, such as the length of the microtubules, the density of the kinesins along the microtubules, the depletion force among the microtubules, etc., have been identified, which permit tuning of the beating frequency of the artificial cilia. The beating frequency of the artificial cilia increases upon increasing the length of the microtubules, but declines for the much longer microtubules. A high density of the kinesins along the microtubules is favorable for the beating motion of the cilia. The depletion force induced bundling of the microtubules accelerated the beating motion of the artificial cilia and increased the beating frequency. This work helps understand the role of self-assembled structures of the biomolecular motor systems in the dynamics of living organisms and is expected to expedite the development of artificial nanomachines, in which the biomolecular motors may serve as actuators.

Spatial Cytoskeleton Organization Supports Targeted Intracellular Transport

The efficiency of intracellular cargo transport from specific sources to target locations is strongly dependent upon molecular motor-assisted motion along the cytoskeleton. Radial transport along microtubules and lateral transport along the filaments of the actin cortex underneath the cell membrane are characteristic for cells with a centrosome. The interplay between the specific cytoskeleton organization and the motor performance results in a spatially inhomogeneous intermittent search strategy. To analyze the efficiency of such intracellular search strategies, we formulate a random velocity model with intermittent arrest states. We evaluate efficiency in terms of mean first passage times for three different, frequently encountered intracellular transport tasks: 1) the narrow escape problem, which emerges during cargo transport to a synapse or other specific region of the cell membrane; 2) the reaction problem, which considers the binding time of two particles within the cell; and 3) the reaction-escape problem, which arises when cargo must be released at a synapse only after pairing with another particle. Our results indicate that cells are able to realize efficient search strategies for various intracellular transport tasks economically through a spatial cytoskeleton organization that involves only a narrow actin cortex rather than a cell body filled with randomly oriented actin filaments.

Dissipative out-of-equilibrium assembly of man-made supramolecular materials

The use of dissipative self-assembly driven by chemical reaction networks for the creation of unique structures is gaining in popularity. In dissipative self-assembly, precursors are converted into self-assembling building blocks by the conversion of a source of energy, typically a photon or a fuel molecule. The self-assembling building block is intrinsically unstable and spontaneously reverts to its original precursor, thus giving the building block a limited lifetime. As a result, its presence is kinetically controlled, which gives the associated supramolecular material unique properties. For instance, formation and properties of these materials can be controlled over space and time by the kinetics of the coupled reaction network, they are autonomously self-healing and they are highly adaptive to small changes in their environment. By means of an example of a biological dissipative self-assembled material, the unique concepts at the basis of these supramolecular materials will be discussed. We then review recent efforts towards man-made dissipative assembly of structures and how their unique material properties have been characterized. In order to help further the field, we close with loosely defined design rules that are at the basis of the discussed examples.

Spherical network contraction forms microtubule asters in confinement

Microtubules and motor proteins form active filament networks that are critical for a variety of functions in living cells. Network topology and dynamics are the result of a self-organisation process that takes place within the boundaries of the cell. Previous biochemical in vitro studies with biomimetic systems consisting of purified motors and microtubules have demonstrated that confinement has an important effect on the outcome of the self-organisation process. However, the pathway of motor/microtubule self-organisation under confinement and its effects on network morphology are still poorly understood. Here, we have investigated how minus-end directed microtubule cross-linking kinesins organise microtubules inside polymer-stabilised microfluidic droplets of well-controlled size. We find that confinement can impose a novel pathway of microtubule aster formation proceeding via the constriction of an initially spherical motor/microtubule network. This mechanism illustrates the close relationship between confinement, network contraction, and aster formation. The spherical constriction pathway robustly produces single, well-centred asters with remarkable reproducibility across thousands of droplets. These results show that the additional constraint of well-defined confinement can improve the robustness of active network self-organisation, providing insight into the design principles of self-organising active networks in micro-scale confinement.

Dynamically generated patterns in dense suspensions of active filaments

We use Langevin dynamics simulations to study dynamical behavior of a dense planar layer of active semiflexible filaments. Using the strength of active force and the thermal persistence length as parameters, we map a detailed phase diagram and identify several nonequilibrium phases in this system. In addition to a slowly flowing melt phase, we observe that, for sufficiently high activity, collective flow accompanied by signatures of local polar and nematic order appears in the system. This state is also characterized by strong density fluctuations. Furthermore, we identify an activity-driven crossover from this state of coherently flowing bundles of filaments to a phase with no global flow, formed by individual filaments coiled into rotating spirals. This suggests a mechanism where the system responds to activity by changing the shape of active agents, an effect with no analog in systems of active particles without internal degrees of freedom.

Polarity sorting drives remodeling of actin-myosin networks

Cytoskeletal networks of actin filaments and myosin motors drive many dynamic cell processes. A key characteristic of these networks is their contractility. Despite intense experimental and theoretical efforts, it is not clear what mechanism favors network contraction over expansion. Recent work points to a dominant role for the nonlinear mechanical response of actin filaments, which can withstand stretching but buckle upon compression. Here we present an alternative mechanism. We study how interactions between actin and myosin-2 at the single filament level translate into contraction at the network scale by performing time-lapse imaging on reconstituted quasi-2D-networks mimicking the cell cortex. We observe myosin end-dwelling after it runs processively along actin filaments. This leads to transport and clustering of actin filament ends and the formation of transiently stable bipolar structures. Further we show that myosin-driven polarity sorting produces polar actin asters, which act as contractile nodes that drive contraction in crosslinked networks. Computer simulations comparing the roles of the end-dwelling mechanism and a buckling-dependent mechanism show that the relative contribution of end-dwelling contraction increases as the network mesh-size decreases.

Filament turnover tunes both force generation and dissipation to control long-range flows in a model actomyosin cortex

Actomyosin-based cortical flow is a fundamental engine for cellular morphogenesis. Cortical flows are generated by cross-linked networks of actin filaments and myosin motors, in which active stress produced by motor activity is opposed by passive resistance to network deformation. Continuous flow requires local remodeling through crosslink unbinding and and/or filament disassembly. But how local remodeling tunes stress production and dissipation, and how this in turn shapes long range flow, remains poorly understood. Here, we study a computational model for a cross-linked network with active motors based on minimal requirements for production and dissipation of contractile stress: Asymmetric filament compliance, spatial heterogeneity of motor activity, reversible cross-links and filament turnover. We characterize how the production and dissipation of network stress depend, individually, on cross-link dynamics and filament turnover, and how these dependencies combine to determine overall rates of cortical flow. Our analysis predicts that filament turnover is required to maintain active stress against external resistance and steady state flow in response to external stress. Steady state stress increases with filament lifetime up to a characteristic time τm, then decreases with lifetime above τm. Effective viscosity increases with filament lifetime up to a characteristic time τc, and then becomes independent of filament lifetime and sharply dependent on crosslink dynamics. These individual dependencies of active stress and effective viscosity define multiple regimes of steady state flow. In particular our model predicts that when filament lifetimes are shorter than both τc and τm, the dependencies of effective viscosity and steady state stress on filament turnover cancel one another, such that flow speed is insensitive to filament turnover, and shows a simple dependence on motor activity and crosslink dynamics. These results provide a framework for understanding how animal cells tune cortical flow through local control of network remodeling.

Enhanced Dynamics of Confined Cytoskeletal Filaments Driven by Asymmetric Motors

Cytoskeletal filaments and molecular motors facilitate the micron-scale force generation necessary for the distribution of organelles and the restructuring of the cytoskeleton within eukaryotic cells. Although the mesoscopic structure and the dynamics of such filaments have been studied in vitro and in vivo, their connection with filament polarity-dependent motor-mediated force generation is not well understood. Using 2D Brownian dynamics simulations, we study a dense, confined mixture of rigid microtubules (MTs) and active springs that have arms that cross-link neighboring MT pairs and move unidirectionally on the attached MT. We simulate depletion interactions between MTs using an attractive potential. We show that dimeric motors, with a motile arm on only one of the two MTs, produce large polarity-sorted MT clusters, whereas tetrameric motors, with motile arms on both microtubules, produce bundles. Furthermore, dimeric motors induce, on average, higher velocities between antialigned MTs than tetrameric motors. Our results, where MTs move faster near the confining wall, are consistent with experimental observations in Drosophila oocytes where enhanced microtubule activity is found close to the confining plasma membrane.

Spontaneous symmetry breaking induced unidirectional rotation of a chain-grafted colloidal particle in the active bath

Exploiting the energy of randomly moving active agents such as bacteria is a fascinating way to power a microdevice. Here we show, by simulations, that a chain-grafted disk-like colloidal particle can rotate unidirectionally and hence output work when immersed in a thin film of active particle suspension. The collective spontaneous symmetry breaking of chain configurations is the origin of the unidirectional rotation. Long persistence time, large propelling force and/or small rotating friction are keys to sustaining the collective broken symmetry and realizing the rotation. In the rotating state, we find very simple linear relations, e.g. between the mean angular speed and the propelling force. The time-evolving asymmetry of chain configurations reveals that there are two types of non-rotating state. The basic phenomena are also observed in the macroscopic granular experiments, implying the generic nature of these phenomena. Our findings provide new insights into the collective spontaneous symmetry breaking in active systems with flexible objects and also open the way to conceive new soft/deformable microdevices.

Filament rigidity and connectivity tune the deformation modes of active biopolymer networks

Molecular motors embedded within collections of actin and microtubule filaments underlie the dynamics of cytoskeletal assemblies. Understanding the physics of such motor-filament materials is critical to developing a physical model of the cytoskeleton and designing biomimetic active materials. Here, we demonstrate through experiments and simulations that the rigidity and connectivity of filaments in active biopolymer networks regulates the anisotropy and the length scale of the underlying deformations, yielding materials with variable contractility. We find that semiflexible filaments can be compressed and bent by motor stresses, yielding materials that undergo predominantly biaxial deformations. By contrast, rigid filament bundles slide without bending under motor stress, yielding materials that undergo predominantly uniaxial deformations. Networks dominated by biaxial deformations are robustly contractile over a wide range of connectivities, while networks dominated by uniaxial deformations can be tuned from extensile to contractile through cross-linking. These results identify physical parameters that control the forces generated within motor-filament arrays and provide insight into the self-organization and mechanics of cytoskeletal assemblies.

Transition from turbulent to coherent flows in confined three-dimensional active fluids

Transport of fluid through a pipe is essential for the operation of macroscale machines and microfluidic devices. Conventional fluids only flow in response to external pressure. We demonstrate that an active isotropic fluid, composed of microtubules and molecular motors, autonomously flows through meter-long three-dimensional channels. We establish control over the magnitude, velocity profile, and direction of the self-organized flows and correlate these to the structure of the extensile microtubule bundles. The inherently three-dimensional transition from bulk-turbulent to confined-coherent flows occurs concomitantly with a transition in the bundle orientational order near the surface and is controlled by a scale-invariant criterion related to the channel profile. The nonequilibrium transition of confined isotropic active fluids can be used to engineer self-organized soft machines.

DNA Nanotubes as a Versatile Tool to Study Semiflexible Polymers

Mechanical properties of complex, polymer-based soft matter, such as cells or biopolymer networks, can be understood in neither the classical frame of flexible polymers nor of rigid rods. Underlying filaments remain outstretched due to their non-vanishing backbone stiffness, which is quantified via the persistence length (lp), but they are also subject to strong thermal fluctuations. Their finite bending stiffness leads to unique, non-trivial collective mechanics of bulk networks, enabling the formation of stable scaffolds at low volume fractions while providing large mesh sizes. This underlying principle is prevalent in nature (e.g., in cells or tissues), minimizing the high molecular content and thereby facilitating diffusive or active transport. Due to their biological implications and potential technological applications in biocompatible hydrogels, semiflexible polymers have been subject to considerable study. However, comprehensible investigations remained challenging since they relied on natural polymers, such as actin filaments, which are not freely tunable. Despite these limitations and due to the lack of synthetic, mechanically tunable, and semiflexible polymers, actin filaments were established as the common model system. A major limitation is that the central quantity lp cannot be freely tuned to study its impact on macroscopic bulk structures. This limitation was resolved by employing structurally programmable DNA nanotubes, enabling controlled alteration of the filament stiffness. They are formed through tile-based designs, where a discrete set of partially complementary strands hybridize in a ring structure with a discrete circumference. These rings feature sticky ends, enabling the effective polymerization into filaments several microns in length, and display similar polymerization kinetics as natural biopolymers. Due to their programmable mechanics, these tubes are versatile, novel tools to study the impact of lp on the single-molecule as well as the bulk scale. In contrast to actin filaments, they remain stable over weeks, without notable degeneration, and their handling is comparably straightforward.

A theory that predicts behaviors of disordered cytoskeletal networks

Morphogenesis in animal tissues is largely driven by actomyosin networks, through tensions generated by an active contractile process. Although the network components and their properties are known, and networks can be reconstituted in vitro, the requirements for contractility are still poorly understood. Here, we describe a theory that predicts whether an isotropic network will contract, expand, or conserve its dimensions. This analytical theory correctly predicts the behavior of simulated networks, consisting of filaments with varying combinations of connectors, and reveals conditions under which networks of rigid filaments are either contractile or expansile. Our results suggest that pulsatility is an intrinsic behavior of contractile networks if the filaments are not stable but turn over. The theory offers a unifying framework to think about mechanisms of contractions or expansion. It provides the foundation for studying a broad range of processes involving cytoskeletal networks and a basis for designing synthetic networks.

Non-equilibrium assembly of microtubules: from molecules to autonomous chemical robots

Biological systems have evolved to harness non-equilibrium processes from the molecular to the macro scale. It is currently a grand challenge of chemistry, materials science, and engineering to understand and mimic biological systems that have the ability to autonomously sense stimuli, process these inputs, and respond by performing mechanical work. New chemical systems are responding to the challenge and form the basis for future responsive, adaptive, and active materials. In this article, we describe a particular biochemical-biomechanical network based on the microtubule cytoskeletal filament - itself a non-equilibrium chemical system. We trace the non-equilibrium aspects of the system from molecules to networks and describe how the cell uses this system to perform active work in essential processes. Finally, we discuss how microtubule-based engineered systems can serve as testbeds for autonomous chemical robots composed of biological and synthetic components.

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.

Existence and uniqueness for a coupled PDE model for motor-induced microtubule organization

Microtubules (MTs) are protein filaments that provide structure to the cytoskeleton of cells and a platform for the movement of intracellular substances. The spatial organization of MTs is crucial for a cell's form and function. MTs interact with a class of proteins called motor proteins that can transport and position individual filaments, thus contributing to overall organization. In this paper, we study the mathematical properties of a coupled partial differential equation (PDE) model, introduced by White et al. in 2015, that describes the motor-induced organization of MTs. The model consists of a nonlinear coupling of a hyperbolic PDE for bound motor proteins, a parabolic PDE for unbound motor proteins, and a transport equation for MT dynamics. We locally smooth the motor drift velocity in the equation for bound motor proteins. The mollification is not only critical for the analysis of the model, but also adds biological realism. We then use a Banach Fixed Point argument to show local existence and uniqueness of mild solutions. We highlight the applicability of the model by showing numerical simulations that are consistent with in vitro experiments.