Self-organized optimal packing of kinesin-5-driven microtubule asters scales with cell size

Radial microtubule (MT) arrays or asters determine cell geometry in animal cells. Multiple asters interacting with motors, such as those in syncytia, form intracellular patterns, but the mechanical principles behind this are not clear. Here, we report that oocytes of the marine ascidian Phallusia mammillata treated with the drug BI-D1870 spontaneously form cytoplasmic MT asters, or cytasters. These asters form steady state segregation patterns in a shell just under the membrane. Cytaster centers tessellate the oocyte cytoplasm, that is divide it into polygonal structures, dominated by hexagons, in a kinesin-5-dependent manner, while inter-aster MTs form 'mini-spindles'. A computational model of multiple asters interacting with kinesin-5 can reproduce both tessellation patterns and mini-spindles in a manner specific to the number of MTs per aster, MT lengths and kinesin-5 density. Simulations predict that the hexagonal tessellation patterns scale with increasing cell size, when the packing fraction of asters in cells is ∼1.6. This self-organized in vivo tessellation by cytasters is comparable to the 'circle packing problem', suggesting that there is an intrinsic mechanical pattern-forming module that is potentially relevant to understanding the role of collective mechanics of cytoskeletal elements in embryogenesis. This article has an associated First Person interview with the first author of the paper.

Collective dynein transport of the nucleus by pulling on astral microtubules during Saccharomyces cerevisiae mitosis

Positioning the nucleus at the bud neck during Saccharomyces cerevisiae mitosis involves pulling forces of cytoplasmic dynein localized in the daughter cell. Although genetic analysis has revealed a complex network positioning the nucleus, quantification of the forces acting on the nucleus and the number of dyneins driving the process has remained difficult. To better understand the collective forces involved in nuclear positioning, we compare a model of dyneins-driven microtubule (MT) pulling, MT pushing, and cytoplasmic drag to experiments. During S. cerevisiae mitosis, MTs interacting with the cortex nucleated by the daughter spindle pole body (SPB) (SPB-D) are longer than the mother SPB (SPB-M), increasing further during spindle elongation in anaphase. Interphasic SPB mobility is effectively diffusive, while the mitotic mobility is directed. By optimizing a computational model of the mobility of the nucleus due to diffusion and MTs pushing at the cell membrane to experiment, we estimate the viscosity governing the drag force on nuclei during positioning. A force balance model of mitotic SPB mobility compared to experimental mobility suggests that even one or two dynein dimers are sufficient to move the nucleus in the bud neck. Using stochastic computer simulations of a budding cell, we find that punctate dynein localization can generate sufficient force to reel in the nucleus to the bud neck. Compared to uniform motor localization, puncta involve fewer motors suggesting a functional role for motor clustering. Stochastic simulations also suggest that a higher number of force generators than predicted by force balance may be required to ensure the robustness of spindle positioning.

Aster swarming by symmetry breaking of cortical dynein transport and coupling kinesins

Microtubule (MT) radial arrays or asters establish the internal topology of a cell by interacting with organelles and molecular motors. We proceed to understand the general pattern forming potential of aster-motor systems using a computational model of multiple MT asters interacting with motors in cellular confinement. In this model dynein motors are attached to the cell cortex and plus-ended motors resembling kinesin-5 diffuse in the cell interior. The introduction of 'noise' in the form of MT length fluctuations spontaneously results in the emergence of coordinated, achiral vortex-like rotation of asters. The coherence and persistence of rotation require a threshold density of both cortical dyneins and coupling kinesins, while the onset is diffusion-limited with relation to the cortical dynein mobility. The coordinated rotational motion emerges due to the resolution of a 'tug-of-war' of multiple cortical dynein motors bound to MTs of the same aster by 'noise' in the form of MT dynamic instability. This transient symmetry breaking is amplified by local coupling by kinesin-5 complexes. The lack of widespread aster rotation across cell types suggests that biophysical mechanisms that suppress such intrinsic dynamics may have evolved. This model is analogous to more general models of locally coupled self-propelled particles (SPP) that spontaneously undergo collective transport in the presence of 'noise' that have been invoked to explain swarming in birds and fish. However, the aster-motor system is distinct from SPP models with regard to the particle density and 'noise' dependence, providing a set of experimentally testable predictions for a novel sub-cellular pattern forming system.

RanGTP induces an effector gradient of XCTK2 and importin α/β for spindle microtubule cross-linking

High RanGTP around chromatin is important for governing spindle assembly during meiosis and mitosis by releasing the inhibitory effects of importin α/β. Here we examine how the Ran gradient regulates Kinesin-14 function to control spindle organization. We show that Xenopus Kinesin-14, XCTK2, and importin α/β form an effector gradient that is highest at the poles and diminishes toward the chromatin, which is opposite the RanGTP gradient. Importin α and β preferentially inhibit XCTK2 antiparallel microtubule cross-linking and sliding by decreasing the microtubule affinity of the XCTK2 tail domain. This change in microtubule affinity enables RanGTP to target endogenous XCTK2 to the spindle. We propose that these combined actions of the Ran pathway are critical to promote Kinesin-14 parallel microtubule cross-linking to help focus spindle poles for efficient bipolar spindle assembly. Furthermore, our work illustrates that RanGTP regulation in the spindle is not simply a switch, but rather generates effector gradients where importins α and β gradually tune the activities of spindle assembly factors.

Augmin accumulation on long-lived microtubules drives amplification and kinetochore-directed growth

Vertebrate cells assemble mitotic spindles through multiple pathways. It is shown that Augmin-dependent, noncentrosomal nucleation generates the vast majority of microtubules in metaphase spindles. This results in a strong directional bias of microtubule growth toward individual kinetochores.

Dividing cells reorganize their microtubule cytoskeleton into a bipolar spindle, which moves one set of sister chromatids to each nascent daughter cell. Early spindle assembly models postulated that spindle pole–derived microtubules search the cytoplasmic space until they randomly encounter a kinetochore to form a stable attachment. More recent work uncovered several additional, centrosome-independent microtubule generation pathways, but the contributions of each pathway to spindle assembly have remained unclear. Here, we combined live microscopy and mathematical modeling to show that most microtubules nucleate at noncentrosomal regions in dividing human cells. Using a live-cell probe that selectively labels aged microtubule lattices, we demonstrate that the distribution of growing microtubule plus ends can be almost entirely explained by Augmin-dependent amplification of long-lived microtubule lattices. By ultrafast 3D lattice light-sheet microscopy, we observed that this mechanism results in a strong directional bias of microtubule growth toward individual kinetochores. Our systematic quantification of spindle dynamics reveals highly coordinated microtubule growth during kinetochore fiber assembly.

Stochasticity of Biological Soft Matter: Emerging Concepts in Intrinsically Disordered Proteins and Biological Phase Separation

At the turn of this century, cardinal changes took place in the perceptions of the structure and function of proteins, as well as in the organizational principles of membrane-less organelles. As a result, the model of the organization of living matter is changing to one described by highly dynamic biological soft matter positioned at the edge of chaos. Intrinsically disordered proteins (IDPs) and membrane-less organelles are key examples of this new outlook and may represent a critical foundation of life, defining its complexity and the evolution of living things.

Collective effects of yeast cytoplasmic dynein based microtubule transport

Teams of cortically anchored dyneins pulling at microtubules (MTs) are known to be essential for aster, spindle and nuclear positioning during cell division and fertilization. While the single-molecule basis of dynein processivity is now better understood, the effect of increasing numbers of motors on transport is not clear. Here, we examine the collective transport properties of a Saccharomyces cerevisiae cytoplasmic dynein fragment, widely used as a minimal model, by a combination of quantitative MT gliding assays and stochastic simulations. We find both MT lengths and motor densities qualitatively affect the degree of randomness of MT transport. However, the directionality and velocity of MTs increase above a threshold number of motors (N) interacting with a filament. To better understand this behavior, we simulate a gliding assay based on a model of uniformly distributed immobilized motors transporting semi-flexible MTs. Each dynein dimer is modeled as an effective stochastic stepper with asymmetric force dependent detachment dynamics, based on single-molecule experiments. Simulations predict increasing numbers of motors (N) result in a threshold dependent transition in directionality and transport velocity and a monotonic decrease in effective diffusivity. Thus both experiment and theory show qualitative agreement in the emergence of coordination in transport above a threshold number of motor heads. We hypothesize that the phase-transition like property of this dynein could play a role in vivo during yeast mitosis, when this dynein localizes to the cortex and pulls astral MTs of increasing length, resulting in correct positioning and orientation of the nucleus at the bud-neck.

Actin-Network Architecture Regulates Microtubule Dynamics

Coordination between actin filaments and microtubules is critical to complete important steps during cell division. For instance, cytoplasmic actin filament dynamics play an active role in the off-center positioning of the spindle during metaphase I in mouse oocytes [1-3] or in gathering the chromosomes to ensure proper spindle formation in starfish oocytes [4, 5], whereas cortical actin filaments control spindle rotation and positioning in adherent cells or in mouse oocytes [6-9]. Several molecular effectors have been found to facilitate anchoring between the meiotic spindle and the cortical actin [10-14]. In vitro reconstitutions have provided detailed insights in the biochemical and physical interactions between microtubules and actin filaments [15-20]. Yet how actin meshwork architecture affects microtubule dynamics is still unclear. Here, we reconstituted microtubule aster in the presence of a meshwork of actin filaments using confined actin-intact Xenopus egg extracts. We found that actin filament branching reduces the lengths and growth rates of microtubules and constrains the mobility of microtubule asters. By reconstituting the interaction between dynamic actin filaments and microtubules in a minimal system based on purified proteins, we found that the branching of actin filaments is sufficient to block microtubule growth and trigger microtubule disassembly. In a further exploration of Xenopus egg extracts, we found that dense and static branched actin meshwork perturbs monopolar spindle assembly by constraining the motion of the spindle pole. Interestingly, monopolar spindle assembly was not constrained in conditions supporting dynamic meshwork rearrangements. We propose that branched actin filament meshwork provides physical barriers that limit microtubule growth.

Meeting the meiotic challenge: Specializations in mammalian oocyte spindle formation

Oocytes uniquely accumulate cytoplasmic constituents to support early embryogenesis. This unique specialization is accompanied by acquisition of a large size and by execution of asymmetric meiotic divisions that preserve precious ooplasm through the expulsion of minimal size polar bodies. While often taken for granted, these basic features of oogenesis necessitate unique specializations of the meiotic apparatus. These include a chromatin-sourced RanGTP gradient that restricts spindle size by defining a spatial domain where meiotic spindles form, acentriolar centrosomes that rely on microtubule organizing centers to form spindle poles, and an actin-based mechanism for asymmetric spindle positioning. Additionally, localized protein synthesis to support spindle formation is achieved in the spindle forming region, whilst protein synthesis is reduced elsewhere in the ooplasm. This is achieved through enrichment of spindle-related mRNAs in the spindle forming region combined with local PLK1-mediated phosphorylation and inactivation of the translational repressor EIF4EBP1. This allows PLK1 to function as an important regulatory nexus through which endogenous and exogenous signals can impact spindle formation and function, and highlights the important role that PLK1 may have in maintaining oocyte quality and fertility.

Programmed Self-Assembly of a Biochemical and Magnetic Scaffold to Trigger and Manipulate Microtubule Structures

Artificial bio-based scaffolds offer broad applications in bioinspired chemistry, nanomedicine, and material science. One current challenge is to understand how the programmed self-assembly of biomolecules at the nanometre level can dictate the emergence of new functional properties at the mesoscopic scale. Here we report a general approach to design genetically encoded protein-based scaffolds with modular biochemical and magnetic functions. By combining chemically induced dimerization strategies and biomineralisation, we engineered ferritin nanocages to nucleate and manipulate microtubule structures upon magnetic actuation. Triggering the self-assembly of engineered ferritins into micrometric scaffolds mimics the function of centrosomes, the microtubule organizing centres of cells, and provides unique magnetic and self-organizing properties. We anticipate that our approach could be transposed to control various biological processes and extend to broader applications in biotechnology or material chemistry.

Myosin efflux promotes cell elongation to coordinate chromosome segregation with cell cleavage

Chromatid segregation must be coordinated with cytokinesis to preserve genomic stability. Here we report that cells clear trailing chromatids from the cleavage site by undergoing two phases of cell elongation. The first phase relies on the assembly of a wide contractile ring. The second phase requires the activity of a pool of myosin that flows from the ring and enriches the nascent daughter cell cortices. This myosin efflux is a novel feature of cytokinesis and its duration is coupled to nuclear envelope reassembly and the nuclear sequestration of the Rho-GEF Pebble. Trailing chromatids induce a delay in nuclear envelope reassembly concomitant with prolonged cortical myosin activity, thus providing forces for the second elongation. We propose that the modulation of cortical myosin dynamics is part of the cellular response triggered by a “chromatid separation checkpoint” that delays nuclear envelope reassembly and, consequently, Pebble nuclear sequestration when trailing chromatids are present at the midzone.

Chromatid segregation must be coordinated with cytokinesis to preserve genomic stability. Here the authors show that cells clear trailing chromatids from the cleavage site in a two-step cell elongation and demonstrate the role of myosin efflux in the second phase.

Molecular mechanisms facilitating the initial kinetochore encounter with spindle microtubules

The initial kinetochore (KT) encounter with a spindle microtubule (MT) is one of the rate-limiting steps in establishing proper KT–MT interaction during mitosis. This study reveals how multiple factors cooperate to facilitate the KT encounter with a spindle MT. In particular, it highlights the important roles of KT-derived MTs in this process.

The initial kinetochore (KT) encounter with a spindle microtubule (MT; KT capture) is one of the rate-limiting steps in establishing proper KT–MT interaction during mitosis. KT capture is facilitated by multiple factors, such as MT extension in various directions, KT diffusion, and MT pivoting. In addition, KTs generate short MTs, which subsequently interact with a spindle MT. KT-derived MTs may facilitate KT capture, but their contribution is elusive. In this study, we find that Stu1 recruits Stu2 to budding yeast KTs, which promotes MT generation there. By removing Stu2 specifically from KTs, we show that KT-derived MTs shorten the half-life of noncaptured KTs from 48–49 s to 28–34 s. Using computational simulation, we found that multiple factors facilitate KT capture redundantly or synergistically. In particular, KT-derived MTs play important roles both by making a significant contribution on their own and by synergistically enhancing the effects of KT diffusion and MT pivoting. Our study reveals fundamental mechanisms facilitating the initial KT encounter with spindle MTs.

Metaphase Spindle Assembly

A microtubule-based bipolar spindle is required for error-free chromosome segregation during cell division. In this review I discuss the molecular mechanisms required for the assembly of this dynamic micrometer-scale structure in animal cells.

A Motor-Gradient and Clustering Model of the Centripetal Motility of MTOCs in Meiosis I of Mouse Oocytes

Asters nucleated by Microtubule (MT) organizing centers (MTOCs) converge on chromosomes during spindle assembly in mouse oocytes undergoing meiosis I. Time-lapse imaging suggests that this centripetal motion is driven by a biased 'search-and-capture' mechanism. Here, we develop a model of a random walk in a drift field to test the nature of the bias and the spatio-temporal dynamics of the search process. The model is used to optimize the spatial field of drift in simulations, by comparison to experimental motility statistics. In a second step, this optimized gradient is used to determine the location of immobilized dynein motors and MT polymerization parameters, since these are hypothesized to generate the gradient of forces needed to move MTOCs. We compare these scenarios to self-organized mechanisms by which asters have been hypothesized to find the cell-center- MT pushing at the cell-boundary and clustering motor complexes. By minimizing the error between simulation outputs and experiments, we find a model of "pulling" by a gradient of dynein motors alone can drive the centripetal motility. Interestingly, models of passive MT based "pushing" at the cortex, clustering by cross-linking motors and MT-dynamic instability gradients alone, by themselves do not result in the observed motility. The model predicts the sensitivity of the results to motor density and stall force, but not MTs per aster. A hybrid model combining a chromatin-centered immobilized dynein gradient, diffusible minus-end directed clustering motors and pushing at the cell cortex, is required to comprehensively explain the available data. The model makes experimentally testable predictions of a spatial bias and self-organized mechanisms by which MT asters can find the center of a large cell.

Isomorphic coalescence of aster cores formed in vitro from microtubules and kinesin motors

We report fluorescence microscopy studies of the formation of aster-like structures emerging from a cellular element-based active system and a novel analysis of the aster condensation. The system consists of rhodamine labeled microtubules which are dynamically coupled by functionalized kinesin motor proteins cross-linked via streptavidin-coated quantum dots (QDs). The aster-shaped objects contain core structures. The cores are aggregates of the QD-motor protein complexes, and result from the dynamic condensation of sub-clusters that are connected to each other randomly. The structural specificity of the aster core reflects a configuration of the initial connectivity between sub-clusters. Detailed image analysis allows us to extract a novel correlation between the condensation speed and the sub-cluster separation. The size of the core is scaled down during the condensation process, following a power law dependence on the distance between sub-clusters. The exponent of the power law is close to two, as expected from a geometric model. This single exponent common to all the contractile lines implies that there exists a time regime during which an isomorphic contraction of the aster core continues during the condensation process. We analyze the observed contraction by using a model system with potential applicability in a wide range of emergent phenomena in randomly coupled active networks, which are prevalent in the cellular environment.

Spatial organization of the Ran pathway by microtubules in mitosis

Concentration gradients of soluble proteins are believed to be responsible for control of morphogenesis of subcellular systems, but the mechanisms that generate the spatial organization of these subcellular gradients remain poorly understood. Here, we use a newly developed multipoint fluorescence fluctuation spectroscopy technique to study the ras-related nuclear protein (Ran) pathway, which forms soluble gradients around chromosomes in mitosis and is thought to spatially regulate microtubule behaviors during spindle assembly. We found that the distribution of components of the Ran pathway that influence microtubule behaviors is determined by their interactions with microtubules, resulting in microtubule nucleators being localized by the microtubules whose formation they stimulate. Modeling and perturbation experiments show that this feedback makes the length of the spindle insensitive to the length scale of the Ran gradient, allows the spindle to assemble outside the peak of the Ran gradient, and explains the scaling of the spindle with cell size. Such feedback between soluble signaling pathways and the mechanics of the cytoskeleton may be a general feature of subcellular organization.

Feedback mechanism for microtubule length regulation by stathmin gradients

We formulate and analyze a theoretical model for the regulation of microtubule (MT) polymerization dynamics by the signaling proteins Rac1 and stathmin. In cells, the MT growth rate is inhibited by cytosolic stathmin, which, in turn, is inactivated by Rac1. Growing MTs activate Rac1 at the cell edge, which closes a positive feedback loop. We investigate both tubulin sequestering and catastrophe promotion as mechanisms for MT growth inhibition by stathmin. For a homogeneous stathmin concentration in the absence of Rac1, we find a switchlike regulation of the MT mean length by stathmin. For constitutively active Rac1 at the cell edge, stathmin is deactivated locally, which establishes a spatial gradient of active stathmin. In this gradient, we find a stationary bimodal MT-length distribution for both mechanisms of MT growth inhibition by stathmin. One subpopulation of the bimodal length distribution can be identified with fast-growing and long pioneering MTs in the region near the cell edge, which have been observed experimentally. The feedback loop is closed through Rac1 activation by MTs. For tubulin sequestering by stathmin, this establishes a bistable switch with two stable states: one stable state corresponds to upregulated MT mean length and bimodal MT length distributions, i.e., pioneering MTs; the other stable state corresponds to an interrupted feedback with short MTs. Stochastic effects as well as external perturbations can trigger switching events. For catastrophe-promoting stathmin, we do not find bistability.

Role of Cdc42 dynamics in the control of fission yeast cell polarization

Cell polarization is fundamental to many cellular processes, including cell differentiation, cell motility and cell fate determination. A key regulatory enzyme in the control of cell morphogenesis is the conserved Rho GTPase Cdc42, which breaks symmetry via self-amplifying positive-feedback mechanisms. Additional mechanisms of control, including competition between different sites of polarized cell growth and time-delayed negative feedback, define a cellular-level system that promotes Cdc42 oscillatory dynamics and modulates activated Cdc42 intracellular distribution.

Spindle assembly on immobilized chromatin micropatterns

We describe a method to assemble meiotic spindles on immobilized micropatterns of chromatin built on a first layer of biotinylated BSA deposited by microcontact printing. Such chromatin patterns routinely produce bipolar spindles with a yield of 60%, and offer the possibility to follow spindle assembly dynamics, from the onset of nucleation to the establishment of a quasi steady state. Hundreds of spindles can be recorded in parallel for different experimental conditions. We also describe the semi-automated image analysis pipeline, which is used to analyze the assembly kinetics of spindle arrays, or the final morphological diversity of the spindles.

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.

Single cell pattern formation and transient cytoskeletal arrays

A major goal of developmental biology is to explain the emergence of pattern in cell layers, tissues and organs. Developmental biologists now accept that reaction diffusion-based mechanisms are broadly employed in developing organisms to direct pattern formation. Here we briefly consider these mechanisms and then apply some of the concepts derived from them to several processes that occur in single cells: wound repair, yeast budding, and cytokinesis. Two conclusions emerge from this analysis: first, there is considerable overlap at the level of general mechanisms between developmental and single cell pattern formation; second, dynamic structures based on the actin cytoskeleton may be far more ordered than is generally recognized.

Chromatin-bound Xenopus Dppa2 shapes the nucleus by locally inhibiting microtubule assembly

Nuclear shape and size vary between species, during development, and in many tissue pathologies, but the causes and effects of these differences remain poorly understood. During fertilization, sperm nuclei undergo a dramatic conversion from a heavily compacted form into decondensed, spherical pronuclei, accompanied by rapid nucleation of microtubules from centrosomes. Here we report that the assembly of the spherical nucleus depends on a critical balance of microtubule dynamics, which is regulated by the chromatin-binding protein Developmental pluripotency-associated 2 (Dppa2). Whereas microtubules normally promote sperm pronuclear expansion, in Dppa2-depleted Xenopus egg extracts excess microtubules cause pronuclear assembly defects, leading to abnormal morphology and disorganized DNA replication. Dppa2 inhibits microtubule polymerization in vitro, and Dppa2 activity is needed at a precise time and location during nascent pronuclear formation. This demonstrates a strict spatiotemporal requirement for local suppression of microtubules during nuclear formation, fulfilled by chromatin-bound microtubule regulators.

Branching microtubule nucleation in Xenopus egg extracts mediated by augmin and TPX2

The microtubules that comprise mitotic spindles in animal cells are nucleated at centrosomes and by spindle assembly factors that are activated in the vicinity of chromatin. Indirect evidence has suggested that microtubules also might be nucleated from pre-existing microtubules throughout the spindle, but this process has not been observed directly. Here, we demonstrate microtubule nucleation from the sides of existing microtubules in meiotic Xenopus egg extracts. Daughter microtubules grow at a low branch angle and with the same polarity as mother filaments. Branching microtubule nucleation requires γ-tubulin and augmin and is stimulated by factors previously implicated in chromatin-stimulated nucleation, guanosine triphosphate(GTP)-bound Ran and its effector, TPX2. Because of the rapid amplification of microtubule numbers and the preservation of microtubule polarity, microtubule-dependent microtubule nucleation is well suited for spindle assembly and maintenance.

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.

Unusual biophysics of intrinsically disordered proteins

Research of a past decade and a half leaves no doubt that complete understanding of protein functionality requires close consideration of the fact that many functional proteins do not have well-folded structures. These intrinsically disordered proteins (IDPs) and proteins with intrinsically disordered protein regions (IDPRs) are highly abundant in nature and play a number of crucial roles in a living cell. Their functions, which are typically associated with a wide range of intermolecular interactions where IDPs possess remarkable binding promiscuity, complement functional repertoire of ordered proteins. All this requires a close attention to the peculiarities of biophysics of these proteins. In this review, some key biophysical features of IDPs are covered. In addition to the peculiar sequence characteristics of IDPs these biophysical features include sequential, structural, and spatiotemporal heterogeneity of IDPs; their rough and relatively flat energy landscapes; their ability to undergo both induced folding and induced unfolding; the ability to interact specifically with structurally unrelated partners; the ability to gain different structures at binding to different partners; and the ability to keep essential amount of disorder even in the bound form. IDPs are also characterized by the "turned-out" response to the changes in their environment, where they gain some structure under conditions resulting in denaturation or even unfolding of ordered proteins. It is proposed that the heterogeneous spatiotemporal structure of IDPs/IDPRs can be described as a set of foldons, inducible foldons, semi-foldons, non-foldons, and unfoldons. They may lose their function when folded, and activation of some IDPs is associated with the awaking of the dormant disorder. It is possible that IDPs represent the "edge of chaos" systems which operate in a region between order and complete randomness or chaos, where the complexity is maximal. This article is part of a Special Issue entitled: The emerging dynamic view of proteins: Protein plasticity in allostery, evolution and self-assembly.

Spatial and temporal sensing limits of microtubule polarization in neuronal growth cones by intracellular gradients and forces

Neuronal growth cones are the most sensitive among eukaryotic cells in responding to directional chemical cues. Although a dynamic microtubule cytoskeleton has been shown to be essential for growth-cone turning, the precise nature of coupling of the spatial cue with microtubule polarization is less understood. Here we present a computational model of microtubule polarization in a turning neuronal growth cone. We explore the limits of directional cues in modifying the spatial polarization of microtubules by testing the role of microtubule dynamics, gradients of regulators, and retrograde forces along filopodia. We analyze the steady state and transition behavior of microtubules on being presented with a directional stimulus. Our model makes novel, to our knowledge, predictions about the minimal angular spread of the chemical signal at the growth cone and the fastest polarization times. A regulatory reaction-diffusion network based on the cyclic phosphorylation-dephosphorylation of a regulator predicts that the receptor-signal magnitude can generate the maximal polarization of microtubules and not feedback loops or amplifications in the network. Using both the phenomenological and network models, we have demonstrated some of the physical limits within which the microtubule polarization system works in turning the neuron.

Dynamics and length distribution of microtubules under force and confinement

We investigate the microtubule polymerization dynamics with catastrophe and rescue events for three different confinement scenarios, which mimic typical cellular environments: (i) The microtubule is confined by rigid and fixed walls, (ii) it grows under constant force, and (iii) it grows against an elastic obstacle with a linearly increasing force. We use realistic catastrophe models and analyze the microtubule dynamics, the resulting microtubule length distributions, and force generation by stochastic and mean field calculations; in addition, we perform stochastic simulations. Freely growing microtubules exhibit a phase of bounded growth with finite microtubule length and a phase of unbounded growth. The main results for the three confinement scenarios are as follows: (i) In confinement by fixed rigid walls, we find exponentially decreasing or increasing stationary microtubule length distributions instead of bounded or unbounded phases, respectively. We introduce a realistic model for wall-induced catastrophes and investigate the behavior of the average length as a function of microtubule growth parameters. (ii) Under a constant force, the boundary between bounded and unbounded growth is shifted to higher tubulin concentrations and rescue rates. The critical force f(c) for the transition from unbounded to bounded growth increases logarithmically with tubulin concentration and the rescue rate, and it is smaller than the stall force. (iii) For microtubule growth against an elastic obstacle, the microtubule length and polymerization force can be regulated by microtubule growth parameters. For zero rescue rate, we find that the average polymerization force depends logarithmically on the tubulin concentration and is always smaller than the stall force in the absence of catastrophes and rescues. For a nonzero rescue rate, we find a sharply peaked steady-state length distribution, which is tightly controlled by microtubule growth parameters. The corresponding average microtubule length self-organizes such that the average polymerization force equals the critical force f(c) for the transition from unbounded to bounded growth. We also investigate the force dynamics if growth parameters are perturbed in dilution experiments. Finally, we show the robustness of our results against changes of catastrophe models and load distribution factors.

Geometry sensing by self-organized protein patterns

In the living cell, proteins are able to organize space much larger than their dimensions. In return, changes of intracellular space can influence biochemical reactions, allowing cells to sense their size and shape. Despite the possibility to reconstitute protein self-organization with only a few purified components, we still lack knowledge of how geometrical boundaries affect spatiotemporal protein patterns. Following a minimal systems approach, we used purified proteins and photolithographically patterned membranes to study the influence of spatial confinement on the self-organization of the Min system, a spatial regulator of bacterial cytokinesis, in vitro. We found that the emerging protein pattern responds even to the lateral, two-dimensional geometry of the membrane such that, as in the three-dimensional cell, Min protein waves travel along the longest axis of the membrane patch. This shows that for spatial sensing the Min system does not need to be enclosed in a three-dimensional compartment. Using a computational model we quantitatively analyzed our experimental findings and identified persistent binding of MinE to the membrane as requirement for the Min system to sense geometry. Our results give insight into the interplay between geometrical confinement and biochemical patterns emerging from a nonlinear reaction-diffusion system.

Speed, dissipation, and error in kinetic proofreading

Proofreading mechanisms increase specificity in biochemical reactions by allowing for the dissociation of intermediate complexes. These mechanisms disrupt and reset the reaction to undo errors at the cost of increased time of reaction and free energy expenditure. Here, we draw an analogy between proofreading and microtubule growth which share some of the features described above. Our analogy relates the statistics of growth and shrinkage of microtubules in physical space to the cycling of intermediate complexes in the space of chemical states in proofreading mechanisms. Using this analogy, we find a new kinetic regime of proofreading in which an exponential speed-up of the process can be achieved at the cost of a somewhat larger error rate. This regime is analogous to the transition region between two known growth regimes of microtubules (bounded and unbounded) and is sharply defined in the limit of large proofreading networks. We find that this advantageous regime of speed-error tradeoff might be present in proofreading schemes studied earlier in the charging of tRNA by tRNA synthetases, in RecA filament assembly on ssDNA, and in protein synthesis by ribosomes.

A journey from reductionist to systemic cell biology aboard the schooner Tara

In this essay I describe my personal journey from reductionist to systems cell biology and describe how this in turn led to a 3-year sea voyage to explore complex ocean communities. In describing this journey, I hope to convey some important principles that I gleaned along the way. I realized that cellular functions emerge from multiple molecular interactions and that new approaches borrowed from statistical physics are required to understand the emergence of such complex systems. Then I wondered how such interaction networks developed during evolution. Because life first evolved in the oceans, it became a natural thing to start looking at the small organisms that compose the plankton in the world's oceans, of which 98% are … individual cells—hence the Tara Oceans voyage, which finished on 31 March 2012 in Lorient, France, after a 60,000-mile around-the-world journey that collected more than 30,000 samples from 153 sampling stations.

Nucleation and transport organize microtubules in metaphase spindles

Spindles are arrays of microtubules that segregate chromosomes during cell division. It has been difficult to validate models of spindle assembly due to a lack of information on the organization of microtubules in these structures. Here we present a method, based on femtosecond laser ablation, capable of measuring the detailed architecture of spindles. We used this method to study the metaphase spindle in Xenopus laevis egg extracts and found that microtubules are shortest near poles and become progressively longer toward the center of the spindle. These data, in combination with mathematical modeling, imaging, and biochemical perturbations, are sufficient to reject previously proposed mechanisms of spindle assembly. Our results support a model of spindle assembly in which microtubule polymerization dynamics are not spatially regulated, and the proper organization of microtubules in the spindle is determined by nonuniform microtubule nucleation and the local sorting of microtubules by transport.

How to build a robust intracellular concentration gradient

Concentration gradients of morphogens are critical regulators of patterning in developmental biology. Increasingly, intracellular concentration gradients have also been found to orchestrate spatial organization, but inside single cells, where they regulate processes such as cell division, polarity and mitotic spindle dynamics. Here, we discuss recent progress in understanding how such intracellular gradients can be built robustly. We focus particularly on the Pom1p gradient in fission yeast, elucidating how various buffering mechanisms operate to ensure precise gradient formation. In this case, a systems-level understanding of the entire mechanism of precise gradient construction is now within reach, with important implications for gradients in both intracellular and developmental contexts.

Biophysics of mitosis

Mitosis is the process by which eukaryotic cells organize and segregate their chromosomes in preparation for cell division. It is accomplished by a cellular machine composed largely of microtubules (MTs) and their associated proteins. This article reviews literature on mitosis from a biophysical point of view, drawing attention to the assembly and motility processes required to do this complex job with precision. Work from both the recent and the older literature is integrated into a description of relevant biological events and the experiments that probe their mechanisms. Theoretical work on specific subprocesses is also reviewed. Our goal is to provide a document that will expose biophysicists to the fascination of this quite amazing process and provide them with a good background from which they can pursue their own research interests in the subject.

The site of RanGTP generation can act as an organizational cue for mitotic microtubules

BACKGROUND INFORMATION

RanGTP, which is generated on chromosomes during mitosis, is required for microtubule spindle assembly. Due to its restricted spatial generation within the cell it has been suggested that RanGTP acts as a spatial cue to organize site-specific spindle assembly within the cell. However, the absence of a detectable sharp gradient of RanGTP in somatic cells has led to suggestions that it may only act as a spatial cue in large cells and that it may operate as a general activator of the mitotic cytosol in somatic cells.

RESULTS

We report that ectopic generation of RanGTP at the plasma membrane stimulates the formation of organized arrays of microtubules at the plasma membrane.

CONCLUSIONS

These results suggest that the site of RanGTP generation in a mitotic somatic cell can generate critical spatial information that specifies where microtubules grow towards and where microtubules are organized. As RanGTP is normally generated on chromosomes, these results suggest that RanGTP may play an important role in specifying that spindle assembly occurs around chromosomes.

Localized Aurora B activity spatially controls non-kinetochore microtubules during spindle assembly

Efficient spindle assembly involves the generation of spatial cues around chromosomes that locally stabilize microtubule (MT) plus-ends. In addition to the small GTPase Ran, there is evidence that Aurora B kinase might also generate a spatial cue around chromosomes but direct proof for this is still lacking. Here, we find that the Aurora B substrate MCAK localizes to MT plus-ends throughout the mitotic spindle, but its accumulation is strongly reduced on MT plus-ends near chromatin, suggesting that a signal emanating from chromosomes negatively regulates MCAK plus-end binding. Indeed, we show that Aurora B is the kinase responsible for producing this chromosome-derived signal. These results are the first to visualize spatially restricted Aurora B kinase activity around chromosomes on an endogenous substrate and explain how Aurora B could spatially control the dynamics of non-kinetochore MTs during spindle assembly.

Phenotypic analysis of misato function reveals roles of noncentrosomal microtubules in Drosophila spindle formation

Mitotic spindle assembly in centrosome-containing cells relies on two main microtubule (MT) nucleation pathways, one based on centrosomes and the other on chromosomes. However, the relative role of these pathways is not well defined. In Drosophila, mutants without centrosomes can form functional anastral spindles and survive to adulthood. Here we show that mutations in the Drosophila misato (mst) gene inhibit kinetochore-driven MT growth, lead to the formation of monopolar spindles and cause larval lethality. In most prophase cells of mst mutant brains, asters are well separated, but collapse with progression of mitosis, suggesting that k-fibers are essential for maintenance of aster separation and spindle bipolarity. Analysis of mst; Sas-4 double mutants showed that mitotic cells lacking both the centrosomes and the mst function form polarized MT arrays that resemble monopolar spindles. MT regrowth experiments after cold exposure revealed that in mst; Sas-4 metaphase cells MTs regrow from several sites, which eventually coalesce to form a single polarized MT array. By contrast, in Sas-4 single mutants, chromosome-driven MT regrowth mostly produced robust bipolar spindles. Collectively, these results indicate that kinetochore-driven MT formation is an essential process for proper spindle assembly in Drosophila somatic cells.

Towards a quantitative understanding of mitotic spindle assembly and mechanics

The 'simple' view of the mitotic spindle is that it self-assembles as a result of microtubules (MTs) randomly searching for chromosomes, after which the spindle length is maintained by a balance of outward tension exerted by molecular motors on the MTs connecting centrosomes and chromosomes, and compression generated by other motors on the MTs connecting the spindle poles. This picture is being challenged now by mounting evidence indicating that spindle assembly and maintenance rely on much more complex interconnected networks of microtubules, molecular motors, chromosomes and regulatory proteins. From an engineering point of view, three design principles of this molecular machine are especially important: the spindle assembles quickly, it assembles accurately, and it is mechanically robust--yet malleable. How is this design achieved with randomly interacting and impermanent molecular parts? Here, we review recent interdisciplinary studies that have started to shed light on this question. We discuss cooperative mechanisms of spindle self-assembly, error correction and maintenance of its mechanical properties, speculate on analogy between spindle and lamellipodial dynamics, and highlight the role of quantitative approaches in understanding the mitotic spindle design.

The role of RanGTP gradient in vertebrate oocyte maturation

The maturation of vertebrate oocyte into haploid gamete, the egg, consists of two specialized asymmetric cell divisions with no intervening S-phase. Ran GTPase has an essential role in relaying the active role of chromosomes in their own segregation by the meiotic process. In addition to its conserved role as a key regulator of macromolecular transport between nucleus and cytoplasm, Ran has important functions during cell division, including in mitotic spindle assembly and in the assembly of nuclear envelope at the exit from mitosis. The cellular functions of Ran are mediated by RanGTP interactions with nuclear transport receptors (NTRs) related to importin β and depend on the existence of chromosome-centered RanGTP gradient. Live imaging with FRET biosensors indeed revealed the existence of RanGTP gradient throughout mouse oocyte maturation. NTR-dependent transport of cell cycle regulators including cyclin B1, Wee2, and Cdc25B between the oocyte cytoplasm and germinal vesicle (GV) is required for normal resumption of meiosis. After GVBD in mouse oocytes, RanGTP gradient is required for timely meiosis I (MI) spindle assembly and provides long-range signal directing egg cortex differentiation. However, RanGTP gradient is not required for MI spindle migration and may be dispensable for MI spindle function in chromosome segregation. In contrast, MII spindle assembly and function in maturing mouse and Xenopus laevis eggs depend on RanGTP gradient, similar to X. laevis MII-derived egg extracts.

A computational model predicts Xenopus meiotic spindle organization

Spatially dispersed nucleation and minus end–directed transport of microtubule end disassembly activity can lead to bipolar spindle assembly.

The metaphase spindle is a dynamic bipolar structure crucial for proper chromosome segregation, but how microtubules (MTs) are organized within the bipolar architecture remains controversial. To explore MT organization along the pole-to-pole axis, we simulated meiotic spindle assembly in two dimensions using dynamic MTs, a MT cross-linking force, and a kinesin-5–like motor. The bipolar structures that form consist of antiparallel fluxing MTs, but spindle pole formation requires the addition of a NuMA-like minus-end cross-linker and directed transport of MT depolymerization activity toward minus ends. Dynamic instability and minus-end depolymerization generate realistic MT lifetimes and a truncated exponential MT length distribution. Keeping the number of MTs in the simulation constant, we explored the influence of two different MT nucleation pathways on spindle organization. When nucleation occurs throughout the spindle, the simulation quantitatively reproduces features of meiotic spindles assembled in Xenopus egg extracts.

Kinetochore-microtubule interactions: steps towards bi-orientation

Eukaryotic cells segregate their chromosomes accurately to opposite poles during mitosis, which is necessary for maintenance of their genetic integrity. This process mainly relies on the forces generated by kinetochore-microtubule (KT-MT) attachment. During prometaphase, the KT initially interacts with a single MT extending from a spindle pole and then moves towards a spindle pole. Subsequently, MTs from the other spindle pole also interact with the KT. Eventually, one sister KT becomes attached to MTs from one pole while the other sister to those from the other pole (sister KT bi-orientation). If sister KTs interact with MTs with aberrant orientation, this must be corrected to attain proper bi-orientation (error correction) before the anaphase is initiated. Here, I discuss how KTs initially interact with MTs and how this interaction develops into bi-orientation; both processes are fundamentally crucial for proper chromosome segregation in the subsequent anaphase.

Control of mitotic spindle length

The mitotic spindle accurately segregates genetic instructions by moving chromosomes to spindle poles (anaphase A) and separating the poles (anaphase B) so that, in general, the chromosomes and poles are positioned near the centers of the nascent daughter cell products of each cell division. Because the size of different types of dividing cells, and thus the spacing of their daughter cell centers, can vary significantly, the length of the metaphase or postanaphase B spindle often scales with cell size. However, significant exceptions to this scaling rule occur, revealing the existence of cell size–independent, spindle-associated mechanisms of spindle length control. The control of spindle length reflects the action of mitotic force-generating mechanisms, and its study may illuminate general principles by which cells regulate the size of internal structures. Here we review molecules and mechanisms that control spindle length, how these mechanisms are deployed in different systems, and some quantitative models that describe the control of spindle length.

Signalling over a distance: gradient patterns and phosphorylation waves within single cells

Recent discoveries of phosphorylation gradients and microdomains with different protein activities have revolutionized our perception of information transfer within single cells. The different spatial localization of opposing reactions in protein-modification cycles has been shown to bring about heterogeneous stationary patterns and travelling waves of protein activities. We review spatial patterns and modes of signal transfer through phosphorylation/dephosphorylation and GDP/GTP exchange cycles and cascades. We show how switches between low-activity and high-activity states in a bistable activation–deactivation cycle can initiate the propagation of travelling protein-modification waves in the cytoplasm. Typically, an activation wave is initiated at the plasma membrane and propagates through the cytoplasm until it reaches the nucleus. An increase in deactivator activity is followed by the initiation of an inactivation wave that moves in the reverse direction from the nucleus. We show that the ratio of opposing enzyme rates is a key parameter that controls both the spread of activation through cascades and travelling waves.

Reaction-diffusion systems in intracellular molecular transport and control

Chemical reactions make cells work only if the participating chemicals are delivered to desired locations in a timely and precise fashion. Most research to date has focused on active-transport mechanisms, although passive diffusion is often equally rapid and energetically less costly. Capitalizing on these advantages, cells have developed sophisticated reaction-diffusion (RD) systems that control a wide range of cellular functions-from chemotaxis and cell division, through signaling cascades and oscillations, to cell motility. These apparently diverse systems share many common features and are "wired" according to "generic" motifs such as nonlinear kinetics, autocatalysis, and feedback loops. Understanding the operation of these complex (bio)chemical systems requires the analysis of pertinent transport-kinetic equations or, at least on a qualitative level, of the characteristic times of the constituent subprocesses. Therefore, in reviewing the manifestations of cellular RD, we also describe basic theory of reaction-diffusion phenomena.

Signalling ballet in space and time

Although we have amassed extensive catalogues of signalling network components, our understanding of the spatiotemporal control of emergent network structures has lagged behind. Dynamic behaviour is starting to be explored throughout the genome, but analysis of spatial behaviours is still confined to individual proteins. The challenge is to reveal how cells integrate temporal and spatial information to determine specific biological functions. Key findings are the discovery of molecular signalling machines such as Ras nanoclusters, spatial activity gradients and flexible network circuitries that involve transcriptional feedback. They reveal design principles of spatiotemporal organization that are crucial for network function and cell fate decisions.