Design Principles of Length Control of Cytoskeletal Structures

Cluster Assembly Dynamics Drive Fidelity of Planar Cell Polarity Polarization

The planar cell polarity (PCP) signaling pathway polarizes epithelial cells in the tissue plane by segregating distinct molecular subcomplexes to opposite sides of each cell, where they interact across intercellular junctions to form asymmetric clusters. The role of clustering in this process is unknown. We hypothesized that protein cluster size distributions could be used to infer the underlying molecular dynamics and function of cluster assembly and polarization. We developed a method to count the number of monomers of core PCP proteins within individual clusters in live animals, and made measurements over time and space in wild type and in strategically chosen mutants. The data demonstrate that clustering is required for polarization, and together with mathematical modeling provide evidence that cluster assembly dynamics dictate that larger clusters are more likely to be strongly asymmetric and correctly oriented. We propose that cluster assembly dynamics thereby drive fidelity of cell- and tissue-level polarization.

Length control emerges from cytoskeletal network geometry

Many cytoskeletal networks consist of individual filaments that are organized into elaborate higher-order structures. While it is appreciated that the size and architecture of these networks are critical for their biological functions, much of the work investigating control over their assembly has focused on mechanisms that regulate the turnover of individual filaments through size-dependent feedback. Here, we propose a very different, feedback-independent mechanism to explain how yeast cells control the length of their actin cables. Our findings, supported by quantitative cell imaging and mathematical modeling, indicate that actin cable length control is an emergent property that arises from the cross-linked and bundled organization of the filaments within the cable. Using this model, we further dissect the mechanisms that allow cables to grow longer in larger cells and propose that cell length-dependent tuning of formin activity allows cells to scale cable length with cell length. This mechanism is a significant departure from prior models of cytoskeletal filament length control and presents a different paradigm to consider how cells control the size, shape, and dynamics of higher-order cytoskeletal structures.

Ultrasensitivity of microtubule severing due to damage repair

Microtubule-based cytoskeletal structures aid in cell motility, cell polarization, and intracellular transport. These functions require a coordinated effort of regulatory proteins which interact with microtubule cytoskeleton distinctively. In-vitro experiments have shown that free tubulin can repair nanoscale damages of microtubules created by severing proteins. Based on this observation, we theoretically analyze microtubule severing as a competition between the processes of damage spreading and tubulin-induced repair. We demonstrate that this model is in quantitative agreement with in-vitro experiments and predict the existence of a critical tubulin concentration above which severing becomes rare, fast, and sensitive to concentration of free tubulin. We show that this sensitivity leads to a dramatic increase in the dynamic range of steady-state microtubule lengths when the free tubulin concentration is varied, and microtubule lengths are controlled by severing. Our work demonstrates how synergy between tubulin and microtubule-associated proteins can bring about specific dynamical properties of microtubules.

Microscopic interactions control a structural transition in active mixtures of microtubules and molecular motors

Microtubules and molecular motors are essential components of the cellular cytoskeleton, driving fundamental processes in vivo, including chromosome segregation and cargo transport. When reconstituted in vitro, these cytoskeletal proteins serve as energy-consuming building blocks to study the self-organization of active matter. Cytoskeletal active gels display rich emergent dynamics, including extensile flows, locally contractile asters, and bulk contraction. However, it is unclear how the protein-protein interaction kinetics set their contractile or extensile nature. Here, we explore the origin of the transition from extensile bundles to contractile asters in a minimal reconstituted system composed of stabilized microtubules, depletant, adenosine 5'-triphosphate (ATP), and clusters of kinesin-1 motors. We show that the microtubule-binding and unbinding kinetics of highly processive motor clusters set their ability to end-accumulate, which can drive polarity sorting of the microtubules and aster formation. We further demonstrate that the microscopic time scale of end-accumulation sets the emergent time scale of aster formation. Finally, we show that biochemical regulation is insufficient to fully explain the transition as generic aligning interactions through depletion, cross-linking, or excluded volume interactions can drive bundle formation despite end-accumulating motors. The extensile-to-contractile transition is well captured by a simple self-assembly model where nematic and polar aligning interactions compete to form either bundles or asters. Starting from a five-dimensional organization phase space, we identify a single control parameter given by the ratio of the different component concentrations that dictates the material-scale organization. Overall, this work shows that the interplay of biochemical and mechanical tuning at the microscopic level controls the robust self-organization of active cytoskeletal materials.

Length control emerges from cytoskeletal network geometry

Many cytoskeletal networks consist of individual filaments that are organized into elaborate higher order structures. While it is appreciated that the size and architecture of these networks are critical for their biological functions, much of the work investigating control over their assembly has focused on mechanisms that regulate the turnover of individual filaments through size-dependent feedback. Here, we propose a very different, feedback-independent mechanism to explain how yeast cells control the length of their actin cables. Our findings, supported by quantitative cell imaging and mathematical modeling, indicate that actin cable length control is an emergent property that arises from the cross-linked and bundled organization of the filaments within the cable. Using this model, we further dissect the mechanisms that allow cables to grow longer in larger cells, and propose that cell length-dependent tuning of formin activity allows cells to scale cable length with cell length. This mechanism is a significant departure from prior models of cytoskeletal filament length control and presents a new paradigm to consider how cells control the size, shape, and dynamics of higher order cytoskeletal structures.

Selection for Size in Molecular Self-Assembly Drives the De Novo Evolution of a Molecular Machine

The functioning of machines typically requires a concerted action of their parts. This requirement also holds for molecular motors that drive vital cellular processes and imposes constraints on their conformational changes as well as the rates at which they occur. It remains unclear whether, during evolution, features required for functional molecular machines can emerge simultaneously or require sequential adaptation to different selection pressures. We address this question by theoretically analyzing the evolution of filament treadmilling. This process refers to the self-assembly of linear polymers that grow and shrink at equal rates at their opposite ends. It constitutes a simple biological molecular machine that is involved in bacterial cell division and requires that several conditions are met. In our simulation framework, treadmilling emerges as a consequence of selecting for a target average polymer length. We discuss why other forms of assembly dynamics, which also reach the imposed target length, do not emerge in our simulations. Our work shows that complex molecular functions can evolve de novo under selection for a single physical feature.

Vast heterogeneity in cytoplasmic diffusion rates revealed by nanorheology and Doppelgänger simulations

The cytoplasm is a complex, crowded, actively driven environment whose biophysical characteristics modulate critical cellular processes such as cytoskeletal dynamics, phase separation, and stem cell fate. Little is known about the variance in these cytoplasmic properties. Here, we employed particle-tracking nanorheology on genetically encoded multimeric 40 nm nanoparticles (GEMs) to measure diffusion within the cytoplasm of individual fission yeast (Schizosaccharomyces pombe) cellscells. We found that the apparent diffusion coefficients of individual GEM particles varied over a 400-fold range, while the differences in average particle diffusivity among individual cells spanned a 10-fold range. To determine the origin of this heterogeneity, we developed a Doppelgänger simulation approach that uses stochastic simulations of GEM diffusion that replicate the experimental statistics on a particle-by-particle basis, such that each experimental track and cell had a one-to-one correspondence with their simulated counterpart. These simulations showed that the large intra- and inter-cellular variations in diffusivity could not be explained by experimental variability but could only be reproduced with stochastic models that assume a wide intra- and inter-cellular variation in cytoplasmic viscosity. The simulation combining intra- and inter-cellular variation in viscosity also predicted weak nonergodicity in GEM diffusion, consistent with the experimental data. To probe the origin of this variation, we found that the variance in GEM diffusivity was largely independent of factors such as temperature, the actin and microtubule cytoskeletons, cell-cyle stage, and spatial locations, but was magnified by hyperosmotic shocks. Taken together, our results provide a striking demonstration that the cytoplasm is not "well-mixed" but represents a highly heterogeneous environment in which subcellular components at the 40 nm size scale experience dramatically different effective viscosities within an individual cell, as well as in different cells in a genetically identical population. These findings carry significant implications for the origins and regulation of biological noise at cellular and subcellular levels.

The effect of motor-induced shaft dynamics on microtubule stability and length

Control of microtubule abundance, stability, and length is crucial to regulate intracellular transport as well as cell polarity and division. How microtubule stability depends on tubulin addition or removal at the dynamic ends is well studied. However, microtubule rescue, the event when a microtubule switches from shrinking to growing, occurs at tubulin exchange sites along the shaft. Molecular motors have recently been shown to promote such exchanges. Using a stochastic theoretical description, we study how microtubule stability and length depend on motor-induced tubulin exchange and thus rescue. Our theoretical description matches our in vitro experiments on microtubule dynamics in the presence of kinesin-1 molecular motors. Although the overall dynamics of a population of microtubules can be captured by an effective rescue rate, by assigning rescue to exchange sites, we reveal that the dynamics of individual microtubules within the population differ dramatically. Furthermore, we study in detail a transition from bounded to unbounded microtubule growth. Our results provide novel insights into how molecular motors imprint information of microtubule stability on the microtubule network.

Optimization of non-equilibrium self-assembly protocols using Markov state models

The promise of self-assembly to enable the bottom-up formation of materials with prescribed architectures and functions has driven intensive efforts to uncover rational design principles for maximizing the yield of a target structure. Yet, despite many successful examples of self-assembly, ensuring kinetic accessibility of the target structure remains an unsolved problem in many systems. In particular, long-lived kinetic traps can result in assembly times that vastly exceed experimentally accessible timescales. One proposed solution is to design non-equilibrium assembly protocols in which system parameters change over time to avoid such kinetic traps. Here, we develop a framework to combine Markov state model (MSM) analysis with optimal control theory to compute a time-dependent protocol that maximizes the yield of the target structure at a finite time. We present an adjoint-based gradient descent method that, in conjunction with MSMs for a system as a function of its control parameters, enables efficiently optimizing the assembly protocol. We also describe an interpolation approach to significantly reduce the number of simulations required to construct the MSMs. We demonstrate our approach with two examples; a simple semi-analytic model for the folding of a polymer of colloidal particles, and a more complex model for capsid assembly. Our results show that optimizing time-dependent protocols can achieve significant improvements in the yields of selected structures, including equilibrium free energy minima, long-lived metastable structures, and transient states.

Quantitative Analysis of Actin Cable Length in Yeast

Polarized actin cables in S. cerevisiae are linear bundles of crosslinked actin filaments that are assembled by two formins, Bnr1 (localized to the bud neck), and Bni1 (localized to the bud tip). Actin is polymerized at these two sites, which results in cables extending along the cell cortex toward the back of the mother cell. These cables serve as polarized tracks for myosin-based transport of secretory vesicles and other cargo, from the mother cell to the growing daughter cell. Until recently, descriptions of actin cable morphology and architecture have largely been qualitative or descriptive in nature. Here, we introduce a new quantitative method that enables more precise characterization of actin cable length. This technological advance generates quantitative datasets that can be used to determine the contributions of different actin regulatory proteins to the maintenance of cable architecture, and to assess how different pharmacological agents affect cable arrays. Additionally, these datasets can be used to test theoretical models, and be compared to results from computational simulations of actin assembly. Graphical abstract: Illustration of actin cable length and morphology analysis. (A) Representative maximum intensity projection image of S. cerevisiae fixed and stained with fluorescently-conjugated phalloidin to label F-actin (displayed in color), and fluorescently-conjugated Concanavalin A to label the cell wall (displayed in grey scale). Lengths of actin cables traced from the bud neck to their ends are indicated (dashed lines). (B) Inverted grey scale image of F-actin labelled with fluorescently-conjugated phalloidin and the cell wall traced in black. The length (purple) and end-to-end distance (green) of a single actin cable is indicated. Scale bar, 2 µm. (C-E) Actin cable length (C), end-to-end distance (D), and tortuosity (E) from hypothetical datasets, where each data point represents an individual cable and larger symbols represent the mean from each hypothetical experiment. Error bars, 95% confidence intervals.

Probabilistic Inference with Polymerizing Biochemical Circuits

Probabilistic inference-the process of estimating the values of unobserved variables in probabilistic models-has been used to describe various cognitive phenomena related to learning and memory. While the study of biological realizations of inference has focused on animal nervous systems, single-celled organisms also show complex and potentially "predictive" behaviors in changing environments. Yet, it is unclear how the biochemical machinery found in cells might perform inference. Here, we show how inference in a simple Markov model can be approximately realized, in real-time, using polymerizing biochemical circuits. Our approach relies on assembling linear polymers that record the history of environmental changes, where the polymerization process produces molecular complexes that reflect posterior probabilities. We discuss the implications of realizing inference using biochemistry, and the potential of polymerization as a form of biological information-processing.

Leading edge maintenance in migrating cells is an emergent property of branched actin network growth

Animal cell migration is predominantly driven by the coordinated, yet stochastic, polymerization of thousands of nanometer-scale actin filaments across micron-scale cell leading edges. It remains unclear how such inherently noisy processes generate robust cellular behavior. We employed high-speed imaging of migrating neutrophil-like HL-60 cells to explore the fine-scale shape fluctuations that emerge and relax throughout the process of leading edge maintenance. We then developed a minimal stochastic model of the leading edge that reproduces this stable relaxation behavior. Remarkably, we find lamellipodial stability naturally emerges from the interplay between branched actin network growth and leading edge shape – with no additional feedback required – based on a synergy between membrane-proximal branching and lateral spreading of filaments. These results thus demonstrate a novel biological noise-suppression mechanism based entirely on system geometry. Furthermore, our model suggests that the Arp2/3-mediated ~70–80° branching angle optimally smooths lamellipodial shape, addressing its long-mysterious conservation from protists to mammals.

In every human cell, there are tens of millions of proteins which work together to control everything from the cell’s shape to its behavior. One of the most abundant proteins is actin, which organizes itself into filaments that mechanically support the cell and help it to move.

These filaments are very dynamic, with individual actin molecules constantly being added or removed. This allows the cell to build large structures with distinct shapes and properties. Many motile cells, for example, have a structure called a lamellipodium which protrudes at their ‘leading edge’ and pushes them forward. The lamellipodium has a very robust shape that does not vary much between different cell types, or change significantly as cells migrate. But how the tens of thousands of actin molecules inside the lamellipodium organize themselves into this large, stable structure is not fully understood.

To investigate, Garner and Theriot used high-speed video microscopy to track the shape of human cells cultured in the laboratory. As the cells crawled along a glass surface, their leading edge undulated like strings being plucked on a guitar. A computer simulation showed that these ripples can be caused by filaments randomly adding and removing actin molecules.

While these random movements could destabilize the structure of the leading edge, the simulation suggests that another aspect of actin filament growth smooths out any fluctuations in the lamellipodium’s shape. Actin networks in the lamellipodium have a branched configuration, with new strands emerging off each other at an angle like branches in a tree. Garner and Theriot found that the specific angle in which new filaments are added smooths out the lamellipodium’s shape, which may explain why this geometry has persisted throughout evolution.

These findings suggest that the way in which actin filaments join together helps to maintain the shape of large cellular structures. In the future, scientists could use this design principle to build molecular machines that can self-organize into microstructures. These engineered constructs could be used to modulate the activity of living cells that have been damaged by disease.

Effects of random hydrolysis on biofilament length distributions in a shared subunit pool

The sizes of filamentous structures in a cell are often regulated for many physiological processes. A key question in cell biology is how such size control is achieved. Here, we theoretically study the length distributions of multiple filaments, growing by stochastic assembly and disassembly of subunits from a limiting subunit pool. Importantly, we consider a chemical switching of subunits (hydrolysis) prevalent in many biofilaments like microtubules (MTs). We show by simulations of different models that hydrolysis leads to a skewed unimodal length distribution for a single MT. In contrast, hydrolysis can lead to bimodal distributions of individual lengths for two MTs, where individual filaments toggle stochastically between bigger and smaller sizes. For more than two MTs, length distributions are also bimodal, although the bimodality becomes less prominent. We further show that this collective phenomenon is connected with the nonequilibrium nature of hydrolysis, and the bimodality disappears for reversible dynamics. Consistent with earlier theoretical studies, a homogeneous subunit pool, without hydrolysis, cannot control filament lengths. We thus elucidate the role of hydrolysis as a control mechanism on MT length diversity.

Tripeptides as Integrin-Linked Kinase Modulating Agents Based on a Protein-Protein Interaction with α-Parvin

Integrin-linked kinase (ILK) has emerged as a controversial pseudokinase protein that plays a crucial role in the signaling process initiated by integrin-mediated signaling. However, ILK also exhibits a scaffolding protein function inside cells, controlling cytoskeletal dynamics, and has been related to non-neoplastic diseases such as chronic kidney disease (CKD). Although this protein always acts as a heterotrimeric complex bound to PINCH and parvin adaptor proteins, the role of parvin proteins is currently not well understood. Using in silico approaches for the design, we have generated and prepared a set of new tripeptides mimicking an α-parvin segment. These derivatives exhibit activity in phenotypic assays in an ILK-dependent manner without altering kinase activity, thus allowing the generation of new chemical probes and drug candidates with interesting ILK-modulating activities.

Scaling of subcellular actin structures with cell length through decelerated growth

How cells tune the size of their subcellular parts to scale with cell size is a fundamental question in cell biology. Until now, most studies on the size control of organelles and other subcellular structures have focused on scaling relationships with cell volume, which can be explained by limiting pool mechanisms. Here, we uncover a distinct scaling relationship with cell length rather than volume, revealed by mathematical modeling and quantitative imaging of yeast actin cables. The extension rate of cables decelerates as they approach the rear of the cell, until cable length matches cell length. Further, the deceleration rate scales with cell length. These observations are quantitatively explained by a ‘balance-point’ model, which stands in contrast to limiting pool mechanisms, and describes a distinct mode of self-assembly that senses the linear dimensions of the cell.

MyD88 oligomer size functions as a physical threshold to trigger IL1R Myddosome signaling

A recurring feature of innate immune receptor signaling is the self-assembly of signaling proteins into oligomeric complexes. The Myddosome is an oligomeric complex that is required to transmit inflammatory signals from TLR/IL1Rs and consists of MyD88 and IRAK family kinases. However, the molecular basis for how Myddosome proteins self-assemble and regulate intracellular signaling remains poorly understood. Here, we developed a novel assay to analyze the spatiotemporal dynamics of IL1R and Myddosome signaling in live cells. We found that MyD88 oligomerization is inducible and initially reversible. Moreover, the formation of larger, stable oligomers consisting of more than four MyD88s triggers the sequential recruitment of IRAK4 and IRAK1. Notably, genetic knockout of IRAK4 enhanced MyD88 oligomerization, indicating that IRAK4 controls MyD88 oligomer size and growth. MyD88 oligomer size thus functions as a physical threshold to trigger downstream signaling. These results provide a mechanistic basis for how protein oligomerization might function in cell signaling pathways.

Stochastic combinations of actin regulatory proteins are sufficient to drive filopodia formation

Assemblies of actin and its regulators underlie the dynamic morphology of all eukaryotic cells. To understand how actin regulatory proteins work together to generate actin-rich structures such as filopodia, we analyzed the localization of diverse actin regulators within filopodia in Drosophila embryos and in a complementary in vitro system of filopodia-like structures (FLSs). We found that the composition of the regulatory protein complex where actin is incorporated (the filopodial tip complex) is remarkably heterogeneous both in vivo and in vitro. Our data reveal that different pairs of proteins correlate with each other and with actin bundle length, suggesting the presence of functional subcomplexes. This is consistent with a theoretical framework where three or more redundant subcomplexes join the tip complex stochastically, with any two being sufficient to drive filopodia formation. We provide an explanation for the observed heterogeneity and suggest that a mechanism based on multiple components allows stereotypical filopodial dynamics to arise from diverse upstream signaling pathways.

Equilibrium mechanisms of self-limiting assembly

Self-assembly is a ubiquitous process in synthetic and biological systems, broadly defined as the spontaneous organization of multiple subunits (e.g. macromolecules, particles) into ordered multi-unit structures. The vast majority of equilibrium assembly processes give rise to two states: one consisting of dispersed disassociated subunits, and the other, a bulk-condensed state of unlimited size. This review focuses on the more specialized class of self-limiting assembly, which describes equilibrium assembly processes resulting in finite-size structures. These systems pose a generic and basic question, how do thermodynamic processes involving non-covalent interactions between identical subunits "measure" and select the size of assembled structures? In this review, we begin with an introduction to the basic statistical mechanical framework for assembly thermodynamics, and use this to highlight the key physical ingredients that ensure equilibrium assembly will terminate at finite dimensions. Then, we introduce examples of self-limiting assembly systems, and classify them within this framework based on two broad categories: self-closing assemblies and open-boundary assemblies. These include well-known cases in biology and synthetic soft matter - micellization of amphiphiles and shell/tubule formation of tapered subunits - as well as less widely known classes of assemblies, such as short-range attractive/long-range repulsive systems and geometrically-frustrated assemblies. For each of these self-limiting mechanisms, we describe the physical mechanisms that select equilibrium assembly size, as well as potential limitations of finite-size selection. Finally, we discuss alternative mechanisms for finite-size assemblies, and draw contrasts with the size-control that these can achieve relative to self-limitation in equilibrium, single-species assemblies.

Gold nanoclusters elicit homeostatic perturbations in glioblastoma cells and adaptive changes of lysosomes

Unique physicochemical features place gold nanoclusters at the forefront of nanotechnology for biological and biomedical applications. To date, information on the interactions of gold nanoclusters with biological macromolecules is limited and restricts their use in living cells. Methods: Our multidisciplinary study begins to fill the current knowledge gap by focusing on lysosomes and associated biological pathways in U251N human glioblastoma cells. We concentrated on lysosomes, because they are the intracellular destination for many nanoparticles, regulate cellular homeostasis and control cell survival. Results: Quantitative data presented here show that gold nanoclusters (with 15 and 25 gold atoms), surface-modified with glutathione or PEG, did not diminish cell viability at concentrations ≤1 µM. However, even at sublethal concentrations, gold nanoclusters modulated the abundance, positioning, pH and enzymatic activities of lysosomes. Gold nanoclusters also affected other aspects of cellular homeostasis. Specifically, they stimulated the transient nuclear accumulation of TFEB and Nrf2, transcription factors that promote lysosome biogenesis and stress responses. Moreover, gold nanoclusters also altered the formation of protein aggregates in the cytoplasm. The cellular responses elicited by gold nanoclusters were largely reversible within a 24-hour period. Conclusions: Taken together, this study explores the subcellular and molecular effects induced by gold nanoclusters and shows their effectiveness to regulate lysosome biology. Our results indicate that gold nanoclusters cause homeostatic perturbations without marked cell loss. Notably, cells adapt to the challenge inflicted by gold nanoclusters. These new insights provide a framework for the further development of gold nanocluster-based applications in biological sciences.

Length-dependent disassembly maintains four different flagellar lengths in Giardia

With eight flagella of four different lengths, the parasitic protist Giardia is an ideal model to evaluate flagellar assembly and length regulation. To determine how four different flagellar lengths are maintained, we used live-cell quantitative imaging and mathematical modeling of conserved components of intraflagellar transport (IFT)-mediated assembly and kinesin-13-mediated disassembly in different flagellar pairs. Each axoneme has a long cytoplasmic region extending from the basal body, and transitions to a canonical membrane-bound flagellum at the 'flagellar pore'. We determined that each flagellar pore is the site of IFT accumulation and injection, defining a diffusion barrier functionally analogous to the transition zone. IFT-mediated assembly is length-independent, as train size, speed, and injection frequencies are similar for all flagella. We demonstrate that kinesin-13 localization to the flagellar tips is inversely correlated to flagellar length. Therefore, we propose a model where a length-dependent disassembly mechanism controls multiple flagellar lengths within the same cell.

Predicted Effects of Severing Enzymes on the Length Distribution and Total Mass of Microtubules

Microtubules are dynamic cytoskeletal polymers whose growth and shrinkage are highly regulated as eukaryotic cells change shape, move, and divide. One family of microtubule regulators includes the ATP-hydrolyzing enzymes spastin, katanin, and fidgetin, which sever microtubule polymers into shorter fragments. Paradoxically, severases can increase microtubule number and mass in cells. Recent work with purified spastin and katanin accounts for this phenotype by showing that, in addition to severing, these enzymes modulate microtubule dynamics by accelerating the conversion of microtubules from their shrinking to their growing states and thereby promoting their regrowth. This leads to the observed exponential increase in microtubule mass. Spastin also influences the steady-state distribution of microtubule lengths, changing it from an exponential, as predicted by models of microtubule dynamic instability, to a peaked distribution. This effect of severing and regrowth by spastin on the microtubule length distribution has not been explained theoretically. To solve this problem, we formulated and solved a master equation for the time evolution of microtubule lengths in the presence of severing and microtubule dynamic instability. We then obtained numerical solutions to the steady-state length distribution and showed that the rate of severing and the speed of microtubule growth are the dominant parameters determining the steady-state length distribution. Furthermore, we found that the amplification rate is predicted to increase with severing, which is, to our knowledge, a new result. Our results establish a theoretical basis for how severing and dynamics together can serve to nucleate new microtubules, constituting a versatile mechanism to regulate microtubule length and mass.

Stress relaxation in F-actin solutions by severing

Networks of filamentous actin (F-actin) are important for the mechanics of most animal cells. These cytoskeletal networks are highly dynamic, with a variety of actin-associated proteins that control cross-linking, polymerization and force generation in the cytoskeleton. Inspired by recent rheological experiments on reconstituted solutions of dynamic actin filaments, we report a theoretical model that describes stress relaxation behavior of these solutions in the presence of severing proteins. We show that depending on the kinetic rates of assembly, disassembly, and severing, one can observe both length-dependent and length-independent relaxation behavior.

The Limiting-Pool Mechanism Fails to Control the Size of Multiple Organelles

How the size of micrometer-scale cellular structures such as the mitotic spindle, cytoskeletal filaments, the nucleus, the nucleolus, and other non-membrane bound organelles is controlled despite a constant turnover of their constituent parts is a central problem in biology. Experiments have implicated the limiting-pool mechanism: structures grow by stochastic addition of molecular subunits from a finite pool until the rates of subunit addition and removal are balanced, producing a structure of well-defined size. Here, we consider these dynamics when multiple filamentous structures are assembled stochastically from a shared pool of subunits. Using analytical calculations and computer simulations, we show that robust size control can be achieved only when a single filament is assembled. When multiple filaments compete for monomers, filament lengths exhibit large fluctuations. These results extend to three-dimensional structures and reveal the physical limitations of the limiting-pool mechanism of size control when multiple organelles are assembled from a shared pool of subunits.

Sound of an axon's growth

Axons are linear structures of nerve cells that can range from a few tens of micrometers up to meters in length. In addition to external cues, the length of an axon is also regulated by unknown internal mechanisms. Molecular motors have been suggested to generate oscillations with an axon-length-dependent frequency that could be used to measure an axon's extension. Here, we present a mechanism for determining the axon length that couples the mechanical properties of an axon to the spectral decomposition of the oscillatory signal.

Theory of Cytoskeletal Reorganization during Cross-Linker-Mediated Mitotic Spindle Assembly

Cells grow, move, and respond to outside stimuli by large-scale cytoskeletal reorganization. A prototypical example of cytoskeletal remodeling is mitotic spindle assembly, during which microtubules nucleate, undergo dynamic instability, bundle, and organize into a bipolar spindle. Key mechanisms of this process include regulated filament polymerization, cross-linking, and motor-protein activity. Remarkably, using passive cross-linkers, fission yeast can assemble a bipolar spindle in the absence of motor proteins. We develop a torque-balance model that describes this reorganization because of dynamic microtubule bundles, spindle-pole bodies, the nuclear envelope, and passive cross-linkers to predict spindle-assembly dynamics. We compare these results to those obtained with kinetic Monte Carlo-Brownian dynamics simulations, which include cross-linker-binding kinetics and other stochastic effects. Our results show that rapid cross-linker reorganization to microtubule overlaps facilitates cross-linker-driven spindle assembly, a testable prediction for future experiments. Combining these two modeling techniques, we illustrate a general method for studying cytoskeletal network reorganization.

Active regeneration unites high- and low-temperature features in cooperative self-assembly

Cytoskeletal filaments are capable of self-assembly in the absence of externally supplied chemical energy, but the rapid turnover rates essential for their biological function require a constant flux of adenosine triphosphate (ATP) or guanosine triphosphate (GTP) hydrolysis. The same is true for two-dimensional protein assemblies employed in the formation of vesicles from cellular membranes, which rely on ATP-hydrolyzing enzymes to rapidly disassemble upon completion of the process. Recent observations suggest that the nucleolus, p granules, and other three-dimensional membraneless organelles may also demand dissipation of chemical energy to maintain their fluidity. Cooperative binding plays a crucial role in the dynamics of these higher-dimensional structures, but is absent from classic models of one-dimensional cytoskeletal assembly. In this paper, we present a thermodynamically consistent model of active regeneration with cooperative assembly, and compute the maximum turnover rate and minimum disassembly time as a function of the chemical driving force and the binding energy. We find that these driven structures resemble different equilibrium states above and below the nucleation barrier. In particular, we show that the maximal acceleration under large binding energies unites infinite-temperature local fluctuations with low-temperature nucleation kinetics.

Triggered disassembly and reassembly of actin networks induces rigidity phase transitions

Non-equilibrium soft materials, such as networks of actin proteins, have been intensely investigated over the past decade due to their promise for designing smart materials and understanding cell mechanics. However, current methods are unable to measure the time-dependent mechanics of such systems or map mechanics to the corresponding dynamic macromolecular properties. Here, we present an experimental approach that combines time-resolved optical tweezers microrheology with diffusion-controlled microfluidics to measure the time-evolution of microscale mechanical properties of dynamic systems during triggered activity. We use these methods to measure the viscoelastic moduli of entangled and crosslinked actin networks during chemically-triggered depolymerization and repolymerization of actin filaments. During disassembly, we find that the moduli exhibit two distinct exponential decays, with experimental time constants of ∼169 min and ∼47 min. Conversely, during reassembly, measured moduli initially exhibit power-law increase with time, after which steady-state values are achieved. We develop toy mathematical models that couple the time-evolution of filament lengths with rigidity percolation theory to shed light onto the molecular mechanisms underlying the observed mechanical transitions. The models suggest that these two distinct behaviors both arise from phase transitions between a rigidly percolated network and a non-rigid regime. Our approach and collective results can inform the general principles underlying the mechanics of a large class of dynamic, non-equilibrium systems and materials of current interest.

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.

Self-organized system-size oscillation of a stochastic lattice-gas model

The totally asymmetric simple exclusion process (TASEP) is a paradigmatic stochastic model for nonequilibrium physics, and has been successfully applied to describe active transport of molecular motors along cytoskeletal filaments. Building on this simple model, we consider a two-lane lattice-gas model that couples directed transport (TASEP) to diffusive motion in a semiclosed geometry, and simultaneously accounts for spontaneous growth and particle-induced shrinkage of the system's size. This particular extension of the TASEP is motivated by the question of how active transport and diffusion might influence length regulation in confined systems. Surprisingly, we find that the size of our intrinsically stochastic system exhibits robust temporal patterns over a broad range of growth rates. More specifically, when particle diffusion is slow relative to the shrinkage dynamics, we observe quasiperiodic changes in length. We provide an intuitive explanation for the occurrence of these self-organized temporal patterns, which is based on the imbalance between the diffusion and shrinkage speed in the confined geometry. Finally, we formulate an effective theory for the oscillatory regime, which explains the origin of the oscillations and correctly predicts the dependence of key quantities, such as the oscillation frequency, on the growth rate.

Limited Resources Induce Bistability in Microtubule Length Regulation

The availability of protein is an important factor for the determination of the size of the mitotic spindle. Involved in spindle-size regulation is kinesin-8, a molecular motor and microtubule (MT) depolymerase, which is known to tightly control MT length. Here, we propose and analyze a theoretical model in which kinesin-induced MT depolymerization competes with spontaneous polymerization while supplies of both tubulin and kinesin are limited. In contrast to previous studies where resources were unconstrained, we find that, for a wide range of concentrations, MT length regulation is bistable. We test our predictions by conducting in vitro experiments and find that the bistable behavior manifests in a bimodal MT length distribution.

PAWS1 controls cytoskeletal dynamics and cell migration through association with the SH3 adaptor CD2AP

Our previous studies of PAWS1 (protein associated with SMAD1; also known as FAM83G) have suggested that this molecule has roles beyond BMP signalling. To investigate these roles, we have used CRISPR/Cas9 to generate PAWS1-knockout U2OS osteosarcoma cells. Here, we show that PAWS1 plays a role in the regulation of the cytoskeletal machinery, including actin and focal adhesion dynamics, and cell migration. Confocal microscopy and live cell imaging of actin in U2OS cells indicate that PAWS1 is also involved in cytoskeletal dynamics and organization. Loss of PAWS1 causes severe defects in F-actin organization and distribution as well as in lamellipodial organization, resulting in impaired cell migration. PAWS1 interacts in a dynamic fashion with the actin/cytoskeletal regulator CD2AP at lamellae, suggesting that its association with CD2AP controls actin organization and cellular migration. Genetic ablation of CD2AP from U2OS cells instigates actin and cell migration defects reminiscent of those seen in PAWS1-knockout cells.

This article has an associated First Person interview with the first authors of the paper.

Summary: PAWS1 (also known as FAM83G) controls cell migration by influencing the organization of F-actin and focal adhesions and the distribution of the actin stress fibre network through its association with CD2AP.

Centriole Biogenesis: From Identifying the Characters to Understanding the Plot

The centriole is a beautiful microtubule-based organelle that is critical for the proper execution of many fundamental cellular processes, including polarity, motility, and division. Centriole biogenesis, the making of this miniature architectural wonder, has emerged as an exemplary model to dissect the mechanisms governing the assembly of a eukaryotic organelle. Centriole biogenesis relies on a set of core proteins whose contributions to the assembly process have begun to be elucidated. Here, we review current knowledge regarding the mechanisms by which these core characters function in an orderly fashion to assemble the centriole. In particular, we discuss how having the correct proteins at the right place and at the right time is critical to first scaffold, then initiate, and finally execute the centriole assembly process, thus underscoring fundamental principles governing organelle biogenesis.

Exact Length Distribution of Filamentous Structures Assembled from a Finite Pool of Subunits

Self-assembling filamentous structures made of protein subunits are ubiquitous in cell biology. These structures are often highly dynamic, with subunits in a continuous state of flux, binding to and falling off of filaments. In spite of this constant turnover of their molecular parts, many cellular structures seem to maintain a well-defined size over time, which is often required for their proper functioning. One widely discussed mechanism of size regulation involves the cell maintaining a finite pool of protein subunits available for assembly. This finite pool mechanism can control the length of a single filament by having assembly proceed until the pool of free subunits is depleted to the point when assembly and disassembly are balanced. Still, this leaves open the question of whether the same mechanism can provide size control for multiple filamentous structures that are assembled from a common pool of protein subunits, as is often the case in cells. We address this question by solving the steady-state master equation governing the stochastic assembly and disassembly of multifilament structures made from a shared finite pool of subunits. We find that, while the total number of subunits within a multifilament structure is well-defined, individual filaments within the structure have a wide, power-law distribution of lengths. We also compute the phase diagram for two multifilament structures competing for the same pool of subunits and identify conditions for coexistence when both have a well-defined size. These predictions can be tested in cell experiments in which the size of the subunit pool or the number of filament nucleators is tuned.