Effects of Confinement on the Self-Organization of Microtubules and Motors

Motor-mediated cortical versus astral microtubule organization in lipid-monolayered droplets

The correct spatial organization of microtubules is of crucial importance for determining the internal architecture of eukaryotic cells. Microtubules are arranged in space by a multitude of biochemical activities and by spatial constraints imposed by the cell boundary. The principles underlying the establishment of distinct intracellular architectures are only poorly understood. Here, we studied the effect of spatial confinement on the self-organization of purified motors and microtubules that are encapsulated in lipid-monolayered droplets in oil, varying in diameter from 5-100 μm, which covers the size range of typical cell bodies. We found that droplet size alone had a major organizing influence. The presence of a microtubule-crosslinking motor protein decreased the number of accessible types of microtubule organizations. Depending on the degree of spatial confinement, the presence of the motor caused either the formation of a cortical array of bent microtubule bundles or the generation of single microtubule asters in the droplets. These are two of the most prominent forms of microtubule arrangements in plant and metazoan cells. Our results provide insights into the combined organizing influence of spatial constraints and cross-linking motor activities determining distinct microtubule architectures in a minimal biomimetic system. In the future, this simple lipid-monolayered droplet system characterized here can be expanded readily to include further biochemical activities or used as the starting point for the investigation of motor-mediated microtubule organization inside liposomes surrounded by a deformable lipid bilayer.

Mechanical role of actin dynamics in the rheology of the Golgi complex and in Golgi-associated trafficking events

BACKGROUND

In vitro studies have shown that physical parameters, such as membrane curvature, tension, and composition, influence the budding and fission of transport intermediates. Endocytosis in living cells also appears to be regulated by the mechanical load experienced by the plasma membrane. In contrast, how these parameters affect intracellular membrane trafficking in living cells is not known. To address this question, we investigate here the impact of a mechanical stress on the organization of the Golgi complex and on the formation of transport intermediates from the Golgi complex.

RESULTS

Using confocal microscopy, we visualize the deformation of Rab6-positive Golgi membranes applied by an internalized microsphere trapped in optical tweezers and simultaneously measure the corresponding forces. Our results show that the force necessary to deform Golgi membranes drops when actin dynamics is altered and correlates with myosin II activity. We also show that the applied stress has a long-range effect on Golgi membranes, perturbs the dynamics of Golgi-associated actin, and induces a sharp decrease in the formation of Rab6-positive vesicles from the Golgi complex as well as tubulation of Golgi membranes.

CONCLUSIONS

We suggest that acto-myosin contractility strongly contributes to the local rigidity of the Golgi complex and regulates the mechanics of the Golgi complex to control intracellular membrane trafficking.

Morphogenesis of filaments growing in flexible confinements

Space-saving design is a requirement that is encountered in biological systems and the development of modern technological devices alike. Many living organisms dynamically pack their polymer chains, filaments or membranes inside deformable vesicles or soft tissue-like cell walls, chorions and buds. Surprisingly little is known about morphogenesis due to growth in flexible confinements--perhaps owing to the daunting complexity lying in the nonlinear feedback between packed material and expandable cavity. Here we show by experiments and simulations how geometric and material properties lead to a plethora of morphologies when elastic filaments are growing far beyond the equilibrium size of a flexible thin sheet they are confined in. Depending on friction, sheet flexibility and thickness, we identify four distinct morphological phases emerging from bifurcation and present the corresponding phase diagram. Four order parameters quantifying the transitions between these phases are proposed.

Nonequilibrium structure and dynamics in a microscopic model of thin-film active gels

In the presence of adenosine triphosphate, molecular motors generate active force dipoles that drive suspensions of protein filaments far from thermodynamic equilibrium, leading to exotic dynamics and pattern formation. Microscopic modeling can help to quantify the relationship between individual motors plus filaments to organization and dynamics on molecular and supramolecular length scales. Here, we present results of extensive numerical simulations of active gels where the motors and filaments are confined between two infinite parallel plates. Thermal fluctuations and excluded-volume interactions between filaments are included. A systematic variation of rates for motor motion, attachment, and detachment, including a differential detachment rate from filament ends, reveals a range of nonequilibrium behavior. Strong motor binding produces structured filament aggregates that we refer to as asters, bundles, or layers, whose stability depends on motor speed and differential end detachment. The gross features of the dependence of the observed structures on the motor rate and the filament concentration can be captured by a simple one-filament model. Loosely bound aggregates exhibit superdiffusive mass transport, where filament translocation scales with lag time with nonunique exponents that depend on motor kinetics. An empirical data collapse of filament speed as a function of motor speed and end detachment is found, suggesting a dimensional reduction of the relevant parameter space. We conclude by discussing the perspectives of microscopic modeling in the field of active gels.

Cytoplasmic volume modulates spindle size during embryogenesis

Rapid and reductive cell divisions during embryogenesis require that intracellular structures adapt to a wide range of cell sizes. The mitotic spindle presents a central example of this flexibility, scaling with the dimensions of the cell to mediate accurate chromosome segregation. To determine whether spindle size regulation is achieved through a developmental program or is intrinsically specified by cell size or shape, we developed a system to encapsulate cytoplasm from Xenopus eggs and embryos inside cell-like compartments of defined sizes. Spindle size was observed to shrink with decreasing compartment size, similar to what occurs during early embryogenesis, and this scaling trend depended on compartment volume rather than shape. Thus, the amount of cytoplasmic material provides a mechanism for regulating the size of intracellular structures.

Magnetic control of protein spatial patterning to direct microtubule self-assembly

Living systems offer attractive strategies to generate nanoscale structures because of their innate functional properties such as the dynamic assembly of ordered nanometer fibers, the generation of mechanical forces, or the directional transport mediated by molecular motors. The design of hybrid systems, capable of interfacing artificial building blocks with biomolecules, may be a key step toward the rational design of nanoscale devices and materials. Here, we have designed a bottom-up approach to organize cytoskeletal elements in space using the self-assembly properties of magnetic nanoparticles conjugated to signaling proteins involved in microtubule nucleation. We show that magnetic nanoparticles conjugated to signaling proteins involved in microtubule nucleation can control the positioning of microtubule assembly. Under a magnetic field, a self-organized pattern of biofunctionalized nanoparticles is formed and leads to the nucleation of a periodical network of microtubules in Xenopus laevis egg extract. Our method shows how bioactive nanoparticles can generate a biochemically active pattern upon magnetic actuation, which triggers the spatial organization of nonequilibrium biological structures.

Engineering spatial gradients of signaling proteins using magnetic nanoparticles

Intracellular biochemical reactions are often localized in space and time, inducing gradients of enzymatic activity that may play decisive roles in determining cell's fate and functions. However, the techniques available to examine such enzymatic gradients of activity remain limited. Here, we propose a new method to engineer a spatial gradient of signaling protein concentration within Xenopus egg extracts using superparamagnetic nanoparticles. We show that, upon the application of a magnetic field, a concentration gradient of nanoparticles with a tunable length extension is established within confined egg extracts. We then conjugate the nanoparticles to RanGTP, a small G-protein controlling microtubule assembly. We found that the generation of an artificial gradient of Ran-nanoparticles modifies the spatial positioning of microtubule assemblies. Furthermore, the spatial control of the level of Ran concentration allows us to correlate the local fold increase in Ran-nanoparticle concentration with the spatial positioning of the microtubule-asters. Our assay provides a bottom-up approach to examine the minimum ingredients generating polarization and symmetry breaking within cells. More generally, these results show how magnetic nanoparticles and magnetogenetic tools can be used to control the spatiotemporal dynamics of signaling pathways.

Spatiotemporal control of microtubule nucleation and assembly using magnetic nanoparticles

Decisions on the fate of cells and their functions are dictated by the spatiotemporal dynamics of molecular signalling networks. However, techniques to examine the dynamics of these intracellular processes remain limited. Here, we show that magnetic nanoparticles conjugated with key regulatory proteins can artificially control, in time and space, the Ran/RCC1 signalling pathway that regulates the cell cytoskeleton. In the presence of a magnetic field, RanGTP proteins conjugated to superparamagnetic nanoparticles can induce microtubule fibres to assemble into asymmetric arrays of polarized fibres in Xenopus laevis egg extracts. The orientation of the fibres is dictated by the direction of the magnetic force. When we locally concentrated nanoparticles conjugated with the upstream guanine nucleotide exchange factor RCC1, the assembly of microtubule fibres could be induced over a greater range of distances than RanGTP particles. The method shows how bioactive nanoparticles can be used to engineer signalling networks and spatial self-organization inside a cell environment.

Microtubule organization in vitro

Microtubules organize into a set of distinct patterns with the help of associated molecules that control nucleation, polymerization, crosslinking, and transport. These patterns, alone or in combination with each other, define the functional architecture of the microtubule cytoskeleton in living cells. In vitro experiments of increasing complexity help understand, in combination with theoretical models, the basic mechanisms by which elementary microtubule patterns arise, how they are maintained, and how they position themselves with respect to the confining geometry of living cells.

Spontaneous motion in hierarchically assembled active matter

With exquisite precision and reproducibility, cells orchestrate the cooperative action of thousands of nanometer-sized molecular motors to carry out mechanical tasks at much larger length scales, such as cell motility, division and replication¹. Besides their biological importance, such inherently non-equilibrium processes are an inspiration for developing biomimetic active materials from microscopic components that consume energy to generate continuous motion^2–4. Being actively driven, these materials are not constrained by the laws of equilibrium statistical mechanics and can thus exhibit highly sought-after properties such as autonomous motility, internally generated flows and self-organized beating^5–7. Starting from extensile microtubule bundles, we hierarchically assemble active analogs of conventional polymer gels, liquid crystals and emulsions. At high enough concentration, microtubules form a percolating active network characterized by internally driven chaotic flows, hydrodynamic instabilities, enhanced transport and fluid mixing. When confined to emulsion droplets, 3D networks spontaneously adsorb onto the droplet surfaces to produce highly active 2D nematic liquid crystals whose streaming flows are controlled by internally generated fractures and self-healing, as well as unbinding and annihilation of oppositely charged disclination defects. The resulting active emulsions exhibit unexpected properties, such as autonomous motility, which are not observed in their passive analogues. Taken together, these observations exemplify how assemblages of animate microscopic objects exhibit collective biomimetic properties that are starkly different from those found in materials assembled from inanimate building blocks, challenging us to develop a theoretical framework that would allow for a systematic engineering of their far-from-equilibrium material properties.

End-on microtubule-dynein interactions and pulling-based positioning of microtubule organizing centers

During important cellular processes such as centrosome and spindle positioning, dynein at the cortex interacts with dynamic microtubules in an apparent "end-on" fashion. It is well-established that dynein can generate forces by moving laterally along the microtubule lattice, but much less is known about dynein's interaction with dynamic microtubule ends. In this paper, we review recent in vitro experiments that show that dynein, attached to an artificial cortex, is able to capture microtubule ends, regulate microtubule dynamics and mediate the generation of pulling forces on shrinking microtubules. We further review existing ideas on the involvement of dynein-mediated cortical pulling forces in the positioning of microtubule organizing centers such as centrosomes. Recent in vitro experiments have demonstrated that cortical pulling forces in combination with pushing forces can lead to reliable centering of microtubule asters in quasi two-dimensional microfabricated chambers. In these experiments, pushing leads to slipping of microtubule ends along the chamber boundaries, resulting in an anisotropic distribution of cortical microtubule contacts that favors centering, once pulling force generators become engaged. This effect is predicted to be strongly geometry-dependent, and we therefore finally discuss ongoing efforts to repeat these experiments in three-dimensional, spherical and deformable geometries.

Directed cytoskeleton self-organization

The cytoskeleton architecture supports many cellular functions. Cytoskeleton networks form complex intracellular structures that vary during the cell cycle and between different cell types according to their physiological role. These structures do not emerge spontaneously. They result from the interplay between intrinsic self-organization properties and the conditions imposed by spatial boundaries. Along these boundaries, cytoskeleton filaments are anchored, repulsed, aligned, or reoriented. Such local effects can propagate alterations throughout the network and guide cytoskeleton assembly over relatively large distances. The experimental manipulation of spatial boundaries using microfabrication methods has revealed the underlying physical processes directing cytoskeleton self-organization. Here we review, step-by-step, from molecules to tissues, how the rules that govern assembly have been identified. We describe how complementary approaches, all based on controlling geometric conditions, from in vitro reconstruction to in vivo observation, shed new light on these fundamental organizing principles.

Hierarchical self-assembly of actin in micro-confinements using microfluidics

We present a straightforward microfluidics system to achieve step-by-step reaction sequences in a diffusion-controlled manner in quasi two-dimensional micro-confinements. We demonstrate the hierarchical self-organization of actin (actin monomers-entangled networks of filaments-networks of bundles) in a reversible fashion by tuning the [Formula: see text] ion concentration in the system. We show that actin can form networks of bundles in the presence of [Formula: see text] without any cross-linking proteins. The properties of these networks are influenced by the confinement geometry. In square microchambers we predominantly find rectangular networks, whereas triangular meshes are predominantly found in circular chambers.

The effect of ultrasound stimulation on the cytoskeletal organization of chondrocytes seeded in three-dimensional matrices

The impact of low-intensity diffuse ultrasound (LIDUS) stimulation on the cytoskeletal organization of chondrocytes seeded in three-dimensional (3D) scaffolds was evaluated. Chondrocytes seeded on 3D chitosan matrices were exposed to LIDUS at 5.0 MHz (approx. 15 kPa, 51 s, 4 applications/day) in order to study the organization of actin, tubulin and vimentin. The results showed that actin presented a punctate cytosolic distribution and tubulin presented a quasiparallel organization of microtubules, whereas vimentin distribution was unaffected. Chondrocytes seeded on 3D scaffolds responded to US stimulation by the disruption of actin stress fibers and were sensitive to the presence of Rho-activated kinase (ROCK) inhibitor (Y27632). The gene expression of ROCK-I, a key element in the formation of stress fibers and mDia1, was significantly upregulated under the application of US. We conclude that the results of both the cytoskeletal analyses and gene expression support the argument that the presence of punctate actin upon US stimulation was accompanied by the upregulation of the RhoA/ROCK pathway.

Confinement induces actin flow in a meiotic cytoplasm

In vivo, F-actin flows are observed at different cell life stages and participate in various developmental processes during asymmetric divisions in vertebrate oocytes, cell migration, or wound healing. Here, we show that confinement has a dramatic effect on F-actin spatiotemporal organization. We reconstitute in vitro the spontaneous generation of F-actin flow using Xenopus meiotic extracts artificially confined within a geometry mimicking the cell boundary. Perturbations of actin polymerization kinetics or F-actin nucleation sites strongly modify the network flow dynamics. A combination of quantitative image analysis and biochemical perturbations shows that both spatial localization of F-actin nucleators and actin turnover play a decisive role in generating flow. Interestingly, our in vitro assay recapitulates several symmetry-breaking processes observed in oocytes and early embryonic cells.

Topological singularities and symmetry breaking in development

The review presents a topological interpretation of some morphogenetic events through the use of well-known mathematical concepts and theorems. Spatial organization of the biological fields is analyzable in topological terms. Topological singularities inevitably emerging in biological morphogenesis are retained and transformed during pattern formation. It is the topological language that can provide strict and adequate description of various phenomena in developmental and evolutionary transformations. The relationship between local and global orders in metazoan development, i.e., between local morphogenetic processes and integral developmental patterns, is established. A topological inevitability of some developmental events through the use of classical topological concepts is discussed. This methodology reveals a topological imperative as a certain set of topological rules that constrains and directs embryogenesis. A breaking of spatial symmetry of preexisting pattern plays a critical role in biological morphogenesis in development and evolution.

Assembly of MreB filaments on liposome membranes: a synthetic biology approach

The physical interaction between the cytoskeleton and the cell membrane is essential in defining the morphology of living organisms. In this study, we use a synthetic approach to polymerize bacterial MreB filaments inside phospholipid vesicles. When the proteins MreB and MreC are expressed inside the liposomes, the MreB cytoskeleton structure develops at the inner membrane. Furthermore, when purified MreB is used inside the liposomes, MreB filaments form a 4-10 μm rigid bundle structure and deform the lipid vesicles in physical contact with the vesicle inner membrane. These results indicate that the fibrillation of MreB filaments can take place either in close proximity of deformable lipid membrane or in the presence of associated protein. Our finding might be relevant for the self-assembly of cytoskeleton filaments toward the construction of artificial cell systems.

Spindles and active vortices in a model of confined filament-motor mixtures

Background

Robust self-organization of subcellular structures is a key principle governing the dynamics and evolution of cellular life. In fission yeast cells undergoing division, the mitotic spindle spontaneously emerges from the interaction of microtubules, motor proteins and the confining cell walls, and asters and vortices have been observed to self-assemble in quasi-two dimensional microtubule-kinesin assays. There is no clear microscopic picture of the role of the active motors driving this pattern formation, and the relevance of continuum modeling to filament-scale structures remains uncertain.

Results

Here we present results of numerical simulations of a discrete filament-motor protein model confined to a pressurised cylindrical box. Stable spindles, nematic configurations, asters and high-density semi-asters spontaneously emerge, the latter pair having also been observed in cytosol confined within emulsion droplets. State diagrams are presented delineating each stationary state as the pressure, motor speed and motor density are varied. We further highlight a parameter regime where vortices form exhibiting collective rotation of all filaments, but have a finite life-time before contracting to a semi-aster. Quantifying the distribution of life-times suggests this contraction is a Poisson process. Equivalent systems with fixed volume exhibit persistent vortices with stochastic switching in the direction of rotation, with switching times obeying similar statistics to contraction times in pressurised systems. Furthermore, we show that increasing the detachment rate of motors from filament plus-ends can both destroy vortices and turn some asters into vortices.

Conclusions

We have shown that discrete filament-motor protein models provide new insights into the stationary and dynamical behavior of active gels and subcellular structures, because many phenomena occur on the length-scale of single filaments. Based on our findings, we argue the need for a deeper understanding of the microscopic activities underpinning macroscopic self-organization in active gels and urge further experiments to help bridge these lengths.

Effects of dynein on microtubule mechanics and centrosome positioning

When microtubules are severed by laser ablation, newly created minus ends increase in curvature, but they straighten when dynein is inhibited. It is found that cytoplasmic dynein generates tension and friction along microtubule lengths and that these forces govern the dynamics of centrosome centering.

To determine forces on intracellular microtubules, we measured shape changes of individual microtubules following laser severing in bovine capillary endothelial cells. Surprisingly, regions near newly created minus ends increased in curvature following severing, whereas regions near new microtubule plus ends depolymerized without any observable change in shape. With dynein inhibited, regions near severed minus ends straightened rapidly following severing. These observations suggest that dynein exerts a pulling force on the microtubule that buckles the newly created minus end. Moreover, the lack of any observable straightening suggests that dynein prevents lateral motion of microtubules. To explain these results, we developed a model for intracellular microtubule mechanics that predicts the enhanced buckling at the minus end of a severed microtubule. Our results show that microtubule shapes reflect a dynamic force balance in which dynein motor and friction forces dominate elastic forces arising from bending moments. A centrosomal array of microtubules subjected to dynein pulling forces and resisted by dynein friction is predicted to center on the experimentally observed time scale, with or without the pushing forces derived from microtubule buckling at the cell periphery.

Mitotic membrane helps to focus and stabilize the mitotic spindle

During mitosis, microtubules (MTs), aided by motors and associated proteins, assemble into a mitotic spindle. Recent evidence supports the notion that a membranous spindle matrix aids spindle formation; however, the mechanisms by which the matrix may contribute to spindle assembly are unknown. To search for a mechanism by which the presence of a mitotic membrane might help spindle morphology, we built a computational model that explores the interactions between these components. We show that an elastic membrane around the mitotic apparatus helps to focus MT minus ends and provides a resistive force that acts antagonistically to plus-end-directed MT motors such as Eg5.

Towards high throughput production of artificial egg oocytes using microfluidics

The production of micron-size droplets using microfluidic tools offers new opportunities to carry out biological assays in a controlled environment. We apply these strategies by using a flow-focusing microfluidic device to encapsulate Xenopus egg extracts, a biological system recapitulating key events of eukaryotic cell functions in vitro. We present a method to generate monodisperse egg extract-in-oil droplets and use high-speed imaging to characterize the droplet pinch-off dynamics leading to the production of trains of droplets. We use fluorescence microscopy to show that our method does not affect the biological activity of the encapsulated egg extract by observing the self-organization of microtubules and actin filaments, two main biopolymers of the cell cytoskeleton, encapsulated in the produced droplets. We anticipate that this assay might be useful for quantitative studies of biological systems in a confined environment as well as high throughput screenings for drug discovery.

Symmetry, stability, and reversibility properties of idealized confined microtubule cytoskeletons

Many cell cytoskeletons include an aster of microtubules, with the centrosome serving as the focal point. The position of the centrosome within the cell is important in such directional activities as wound closure and interactions of immune cells. Here we analyzed the centrosome positioning as it is dictated by microtubule elasticity alone in a mechanical model of an intrinsically fully symmetric microtubule aster. We demonstrate that the symmetry and the central position of the centrosome are unstable. The equilibrium deviation of the centrosome from the center is approximately proportional to the difference of the microtubule length and cell radius. The proportionality coefficient is 1 in flat cells and 2 in three-dimensional cells. The loss of symmetry is irreversible, and in general, the equilibrium form of the aster exhibits memory of past perturbations. The equilibrium position of the centrosome as a function of the microtubule length exhibits hysteresis, and the history of the length variation is reflected in the aster form. These properties of the simple aster of elastic microtubules must be taken into account in the analysis of more comprehensive theoretical models, and in the design and interpretation of experiments addressing the complex process of cytoskeleton morphogenesis.

Mechanisms of self-organization of cortical microtubules in plants revealed by computational simulations

Microtubules confined to the two-dimensional cortex of elongating plant cells must form a parallel yet dispersed array transverse to the elongation axis for proper cell wall expansion. Some of these microtubules exhibit free minus-ends, leading to migration at the cortex by hybrid treadmilling. Collisions between microtubules can result in plus-end entrainment ("zippering") or rapid depolymerization. Here, we present a computational model of cortical microtubule organization. We find that plus-end entrainment leads to self-organization of microtubules into parallel arrays, whereas catastrophe-inducing collisions do not. Catastrophe-inducing boundaries (e.g., upper and lower cross-walls) can tune the orientation of an ordered array to a direction transverse to elongation. We also find that changes in dynamic instability parameters, such as in mor1-1 mutants, can impede self-organization, in agreement with experimental data. Increased entrainment, as seen in clasp-1 mutants, conserves self-organization, but delays its onset and fails to demonstrate increased ordering. We find that branched nucleation at acute angles off existing microtubules results in distinctive sparse arrays and infer either that microtubule-independent or coparallel nucleation must dominate. Our simulations lead to several testable predictions, including the effects of reduced microtubule severing in katanin mutants.

Origin and function of fluctuations in cell behaviour and the emergence of patterns

Morphogenesis is the process whereby cells assemble into tissues and organs. Recent studies of this process have revealed heterogeneity of individual cell behaviours that contrasts with the deterministic activity of tissues as a whole. Here we review these observations and suggest that fluctuations and heterogeneities are a central substrate for morphogenesis and that there might exist mechanisms dedicated to the averaging of these fluctuations to ensure robust and reproducible behaviours at the tissue level.