Actin cable distribution and dynamics arising from cross-linking, motor pulling, and filament turnover

Discrete mechanical model of lamellipodial actin network implements molecular clutch mechanism and generates arcs and microspikes

Mechanical forces, actin filament turnover, and adhesion to the extracellular environment regulate lamellipodial protrusions. Computational and mathematical models at the continuum level have been used to investigate the molecular clutch mechanism, calculating the stress profile through the lamellipodium and around focal adhesions. However, the forces and deformations of individual actin filaments have not been considered while interactions between actin networks and actin bundles is not easily accounted with such methods. We develop a filament-level model of a lamellipodial actin network undergoing retrograde flow using 3D Brownian dynamics. Retrograde flow is promoted in simulations by pushing forces from the leading edge (due to actin polymerization), pulling forces (due to molecular motors), and opposed by viscous drag in cytoplasm and focal adhesions. Simulated networks have densities similar to measurements in prior electron micrographs. Connectivity between individual actin segments is maintained by permanent and dynamic crosslinkers. Remodeling of the network occurs via the addition of single actin filaments near the leading edge and via filament bond severing. We investigated how several parameters affect the stress distribution, network deformation and retrograde flow speed. The model captures the decrease in retrograde flow upon increase of focal adhesion strength. The stress profile changes from compression to extension across the leading edge, with regions of filament bending around focal adhesions. The model reproduces the observed reduction in retrograde flow speed upon exposure to cytochalasin D, which halts actin polymerization. Changes in crosslinker concentration and dynamics, as well as in the orientation pattern of newly added filaments demonstrate the model's ability to generate bundles of filaments perpendicular (actin arcs) or parallel (microspikes) to the protruding direction.

Formin Cdc12's specific actin assembly properties are tailored for cytokinesis in fission yeast

Formins generate unbranched actin filaments by a conserved, processive actin assembly mechanism. Most organisms express multiple formin isoforms that mediate distinct cellular processes and facilitate actin filament polymerization by significantly different rates, but how these actin assembly differences correlate to cellular activity is unclear. We used a computational model of fission yeast cytokinetic ring assembly to test the hypothesis that particular actin assembly properties help tailor formins for specific cellular roles. Simulations run in different actin filament nucleation and elongation conditions revealed that variations in formin's nucleation efficiency critically impact both the probability and timing of contractile ring formation. To probe the physiological importance of nucleation efficiency, we engineered fission yeast formin chimera strains in which the FH1-FH2 actin assembly domains of full-length cytokinesis formin Cdc12 were replaced with the FH1-FH2 domains from functionally and evolutionarily diverse formins with significantly different actin assembly properties. Although Cdc12 chimeras generally support life in fission yeast, quantitative live-cell imaging revealed a range of cytokinesis defects from mild to severe. In agreement with the computational model, chimeras whose nucleation efficiencies are least similar to Cdc12 exhibit more severe cytokinesis defects, specifically in the rate of contractile ring assembly. Together, our computational and experimental results suggest that fission yeast cytokinesis is ideally mediated by a formin with properly tailored actin assembly parameters.

Microtubule-independent movement of the fission yeast nucleus

Movement of the cell nucleus typically involves the cytoskeleton and either polymerization-based pushing forces or motor-based pulling forces. In the fission yeast Schizosaccharomyces pombe, nuclear movement and positioning are thought to depend on microtubule polymerization-based pushing forces. Here, we describe a novel, microtubule-independent, form of nuclear movement in fission yeast. Microtubule-independent nuclear movement is directed towards growing cell tips, and it is strongest when the nucleus is close to a growing cell tip, and weakest when the nucleus is far from that tip. Microtubule-independent nuclear movement requires actin cables but does not depend on actin polymerization-based pushing or myosin V-based pulling forces. The vesicle-associated membrane protein (VAMP)-associated proteins (VAPs) Scs2 and Scs22, which are critical for endoplasmic reticulum-plasma membrane contact sites in fission yeast, are also required for microtubule-independent nuclear movement. We also find that in cells in which microtubule-based pushing forces are present, disruption of actin cables leads to increased fluctuations in interphase nuclear positioning and subsequent altered septation. Our results suggest two non-exclusive mechanisms for microtubule-independent nuclear movement, which may help illuminate aspects of nuclear positioning in other cells.

Two- and Three-Dimensional Tracking of MFA2 mRNA Molecules in Mating Yeast

Intracellular mRNA transport contributes to the spatio-temporal regulation of mRNA function and localized translation. In the budding yeast, Saccharomyces cerevisiae, asymmetric mRNA transport localizes ~30 specific mRNAs including those encoding polarity and secretion factors, to the bud tip. The underlying process involves RNA-binding proteins (RBPs), molecular motors, processing bodies (PBs), and the actin cytoskeleton. Recently, pheromone a-factor expression in mating yeast was discovered to depend on proper localization of its mRNA, MFA2 mRNAs in conjunction with PBs cluster at the shmoo tip to form "mating bodies", from which a-factor is locally expressed. The mechanism ensuring the correct targeting of mRNA to the shmoo tip is poorly understood. Here we analyzed the kinetics and trajectories of MFA2 mRNA transport in living, alpha-factor treated yeast. Two- (2D) and three-dimensional (3D) analyses allowed us to reconstruct the granule tracks and estimate granule velocities. Tracking analysis of single MFA2 mRNA granules, labeled using a fluorescent aptamer system, demonstrated three types movement: vibrational, oscillatory and translocational. The mRNA granule transport was complex; a granule could change its movement behavior and composition during its journey to the shmoo. Processing body assembly and the actin-based motor, Myo4p, were involved in movement of MFA2 mRNA to the shmoo, but neither was required, indicating that multiple mechanisms for translocation were at play. Our visualization studies present a dynamic view of the localization mechanism in shmoo-bearing cells.

Mutations in a Single Signaling Pathway Allow Cell Growth in Heavy Water

Life is completely dependent on water. To analyze the role of water as a solvent in biology, we replaced water with heavy water (D₂O) and investigated the biological effects by a wide range of techniques, using Schizosaccharomyces pombe as model organism. We show that high concentrations of D₂O lead to altered glucose metabolism and growth retardation. After prolonged incubation in D₂O, cells displayed gross morphological changes, thickened cell walls, and aberrant cytoskeletal organization. By transcriptomics and genetic screens, we show that the solvent replacement activates two signaling pathways: (1) the heat-shock response pathway and (2) the cell integrity pathway. Although the heat-shock response system upregulates various chaperones and other stress-relieving enzymes, we find that the activation of this pathway does not offer any fitness advantage to the cells under the solvent-replaced conditions. However, limiting the D₂O-triggered activation of the cell integrity pathway allows cell growth when H₂O is completely replaced with D₂O. The isolated D₂O-tolerant strains may aid biological production of deuterated biomolecules.

Organization of associating or crosslinked actin filaments in confinement

A key factor of actin cytoskeleton organization in cells is the interplay between the dynamical properties of actin filaments and cell geometry, which restricts, confines and directs their orientation. Crosslinking interactions among actin filaments, together with geometrical cues and regulatory proteins can give rise to contractile rings in dividing cells and actin rings in neurons. Motivated by recent in vitro experiments, in this work we performed computer simulations to study basic aspects of the interplay between confinement and attractive interactions between actin filaments. We used a spring-bead model and Brownian dynamics to simulate semiflexible actin filaments that polymerize in a confining sphere with a rate proportional to the monomer concentration. We model crosslinking, or attraction through the depletion interaction, implicitly as an attractive short-range potential between filament beads. In confining geometries smaller than the persistence length of actin filaments, we show rings can form by curving of filaments of length comparable to, or longer than the confinement diameter. Rings form for optimal ranges of attractive interactions that exist in between open bundles, irregular loops, aggregated, and unbundled morphologies. The probability of ring formation is promoted by attraction to the confining sphere boundary and decreases for large radii and initial monomer concentrations, in agreement with prior experimental data. The model reproduces ring formation along the flat plane of oblate ellipsoids.

Remarkable structural transformations of actin bundles are driven by their initial polarity, motor activity, crosslinking, and filament treadmilling

Bundled actin structures play a key role in maintaining cellular shape, in aiding force transmission to and from extracellular substrates, and in affecting cellular motility. Recent studies have also brought to light new details on stress generation, force transmission and contractility of actin bundles. In this work, we are primarily interested in the question of what determines the stability of actin bundles and what network geometries do unstable bundles eventually transition to. To address this problem, we used the MEDYAN mechano-chemical force field, modeling several micron-long actin bundles in 3D, while accounting for a comprehensive set of chemical, mechanical and transport processes. We developed a hierarchical clustering algorithm for classification of the different long time scale morphologies in our study. Our main finding is that initially unipolar bundles are significantly more stable compared with an apolar initial configuration. Filaments within the latter bundles slide easily with respect to each other due to myosin activity, producing a loose network that can be subsequently severely distorted. At high myosin concentrations, a morphological transition to aster-like geometries was observed. We also investigated how actin treadmilling rates influence bundle dynamics, and found that enhanced treadmilling leads to network fragmentation and disintegration, while this process is opposed by myosin and crosslinking activities. Interestingly, treadmilling bundles with an initial apolar geometry eventually evolve to a whole gamut of network morphologies based on relative positions of filament ends, such as sarcomere-like organization. We found that apolar bundles show a remarkable sensitivity to environmental conditions, which may be important in enabling rapid cytoskeletal structural reorganization and adaptation in response to intracellular and extracellular cues.

Multiscale model of integrin adhesion assembly

The ability of adherent cells to form adhesions is critical to numerous phases of their physiology. The assembly of adhesions is mediated by several types of integrins. These integrins differ in physical properties, including rate of diffusion on the plasma membrane, rapidity of changing conformation from bent to extended, affinity for extracellular matrix ligands, and lifetimes of their ligand-bound states. However, the way in which nanoscale physical properties of integrins ensure proper adhesion assembly remains elusive. We observe experimentally that both β-1 and β-3 integrins localize in nascent adhesions at the cell leading edge. In order to understand how different nanoscale parameters of β-1 and β-3 integrins mediate proper adhesion assembly, we therefore develop a coarse-grained computational model. Results from the model demonstrate that morphology and distribution of nascent adhesions depend on ligand binding affinity and strength of pairwise interactions. Organization of nascent adhesions depends on the relative amounts of integrins with different bond kinetics. Moreover, the model shows that the architecture of an actin filament network does not perturb the total amount of integrin clustering and ligand binding; however, only bundled actin architectures favor adhesion stability and ultimately maturation. Together, our results support the view that cells can finely tune the expression of different integrin types to determine both structural and dynamic properties of adhesions.

Automated Tracking of Biopolymer Growth and Network Deformation with TSOAX

Studies of how individual semi-flexible biopolymers and their network assemblies change over time reveal dynamical and mechanical properties important to the understanding of their function in tissues and living cells. Automatic tracking of biopolymer networks from fluorescence microscopy time-lapse sequences facilitates such quantitative studies. We present an open source software tool that combines a global and local correspondence algorithm to track biopolymer networks in 2D and 3D, using stretching open active contours. We demonstrate its application in fully automated tracking of elongating and intersecting actin filaments, detection of loop formation and constriction of tilted contractile rings in live cells, and tracking of network deformation under shear deformation.

Mechanisms of formin-mediated actin assembly and dynamics

Cellular viability requires tight regulation of actin cytoskeletal dynamics. Distinct families of nucleation-promoting factors enable the rapid assembly of filament nuclei that elongate and are incorporated into diverse and specialized actin-based structures. In addition to promoting filament nucleation, the formin family of proteins directs the elongation of unbranched actin filaments. Processive association of formins with growing filament ends is achieved through continuous barbed end binding of the highly conserved, dimeric formin homology (FH) 2 domain. In cooperation with the FH1 domain and C-terminal tail region, FH2 dimers mediate actin subunit addition at speeds that can dramatically exceed the rate of spontaneous assembly. Here, I review recent biophysical, structural, and computational studies that have provided insight into the mechanisms of formin-mediated actin assembly and dynamics.

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

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

Structural organization and energy storage in crosslinked actin assemblies

During clathrin-mediated endocytosis in yeast cells, short actin filaments (< 200nm) and crosslinking protein fimbrin assemble to drive the internalization of the plasma membrane. However, the organization of the actin meshwork during endocytosis remains largely unknown. In addition, only a small fraction of the force necessary to elongate and pinch off vesicles can be accounted for by actin polymerization alone. In this paper, we used mathematical modeling to study the self-organization of rigid actin filaments in the presence of elastic crosslinkers in conditions relevant to endocytosis. We found that actin filaments condense into either a disordered meshwork or an ordered bundle depending on filament length and the mechanical and kinetic properties of the crosslinkers. Our simulations also demonstrated that these nanometer-scale actin structures can store a large amount of elastic energy within the crosslinkers (up to 10kBT per crosslinker). This conversion of binding energy into elastic energy is the consequence of geometric constraints created by the helical pitch of the actin filaments, which results in frustrated configurations of crosslinkers attached to filaments. We propose that this stored elastic energy can be used at a later time in the endocytic process. As a proof of principle, we presented a simple mechanism for sustained torque production by ordered detachment of crosslinkers from a pair of parallel filaments.

Cell-wall remodeling drives engulfment during Bacillus subtilis sporulation

When starved, the Gram-positive bacterium Bacillus subtilis forms durable spores for survival. Sporulation initiates with an asymmetric cell division, creating a large mother cell and a small forespore. Subsequently, the mother cell membrane engulfs the forespore in a phagocytosis-like process. However, the force generation mechanism for forward membrane movement remains unknown. Here, we show that membrane migration is driven by cell wall remodeling at the leading edge of the engulfing membrane, with peptidoglycan synthesis and degradation mediated by penicillin binding proteins in the forespore and a cell wall degradation protein complex in the mother cell. We propose a simple model for engulfment in which the junction between the septum and the lateral cell wall moves around the forespore by a mechanism resembling the ‘template model’. Hence, we establish a biophysical mechanism for the creation of a force for engulfment based on the coordination between cell wall synthesis and degradation.

DOI:http://dx.doi.org/10.7554/eLife.18657.001

Some bacteria, such as Bacillus subtilis, form spores when starved of food, which enables them to lie dormant for years and wait for conditions to improve. To make a spore, the bacterial cell divides to make a larger mother cell and a smaller forespore cell. Then the membrane that surrounds the mother cell moves to surround the forespore and engulf it. For this process to take place, a rigid mesh-like layer called the cell wall, which lies outside the cell membrane, needs to be remodelled. This happens once a partition in the cell wall, called a septum, has formed, separating mother and daughter cells. However, it is not clear how the mother cell can generate the physical force required to engulf the forespore under the cramped conditions imposed by the cell wall.

To address this question, Ojkic, López-Garrido et al. used microscopy to investigate how B. subtilis makes spores. The experiments show that, in order to engulf the forespore, the mother cell must produce new cell wall and destroy cell wall that is no longer needed. Running a simple biophysical model on a computer showed that coordinating these two processes could generate enough force for a mother cell to engulf a forespore.

Ojkic, López-Garrido et al. propose that the junction between the septum and the cell wall moves around the forespore to make room for the mother cell’s membrane for expansion. Other spore-forming bacteria that threaten human health – such as Clostridium difficile, which causes bowel infections, and Bacillus anthracis, which causes anthrax – might form their spores in the same way, but this remains to be tested. More work will also be needed to understand exactly how bacterial cells coordinate the cell wall synthesis and cell wall degradation.

DOI:http://dx.doi.org/10.7554/eLife.18657.002

A Combination of Actin Treadmilling and Cross-Linking Drives Contraction of Random Actomyosin Arrays

We investigate computationally the self-organization and contraction of an initially random actomyosin ring. In the framework of a detailed physical model for a ring of cross-linked actin filaments and myosin-II clusters, we derive the force balance equations and solve them numerically. We find that to contract, actin filaments have to treadmill and to be sufficiently cross linked, and myosin has to be processive. The simulations reveal how contraction scales with mechanochemical parameters. For example, they show that the ring made of longer filaments generates greater force but contracts slower. The model predicts that the ring contracts with a constant rate proportional to the initial ring radius if either myosin is released from the ring during contraction and actin filaments shorten, or if myosin is retained in the ring, while the actin filament number decreases. We demonstrate that a balance of actin nucleation and compression-dependent disassembly can also sustain contraction. Finally, the model demonstrates that with time pattern formation takes place in the ring, worsening the contractile process. The more random the actin dynamics are, the higher the contractility will be.

MEDYAN: Mechanochemical Simulations of Contraction and Polarity Alignment in Actomyosin Networks

Active matter systems, and in particular the cell cytoskeleton, exhibit complex mechanochemical dynamics that are still not well understood. While prior computational models of cytoskeletal dynamics have lead to many conceptual insights, an important niche still needs to be filled with a high-resolution structural modeling framework, which includes a minimally-complete set of cytoskeletal chemistries, stochastically treats reaction and diffusion processes in three spatial dimensions, accurately and efficiently describes mechanical deformations of the filamentous network under stresses generated by molecular motors, and deeply couples mechanics and chemistry at high spatial resolution. To address this need, we propose a novel reactive coarse-grained force field, as well as a publicly available software package, named the Mechanochemical Dynamics of Active Networks (MEDYAN), for simulating active network evolution and dynamics (available at www.medyan.org). This model can be used to study the non-linear, far from equilibrium processes in active matter systems, in particular, comprised of interacting semi-flexible polymers embedded in a solution with complex reaction-diffusion processes. In this work, we applied MEDYAN to investigate a contractile actomyosin network consisting of actin filaments, alpha-actinin cross-linking proteins, and non-muscle myosin IIA mini-filaments. We found that these systems undergo a switch-like transition in simulations from a random network to ordered, bundled structures when cross-linker concentration is increased above a threshold value, inducing contraction driven by myosin II mini-filaments. Our simulations also show how myosin II mini-filaments, in tandem with cross-linkers, can produce a range of actin filament polarity distributions and alignment, which is crucially dependent on the rate of actin filament turnover and the actin filament’s resulting super-diffusive behavior in the actomyosin-cross-linker system. We discuss the biological implications of these findings for the arc formation in lamellipodium-to-lamellum architectural remodeling. Lastly, our simulations produce force-dependent accumulation of myosin II, which is thought to be responsible for their mechanosensation ability, also spontaneously generating myosin II concentration gradients in the solution phase of the simulation volume.

Active matter systems have the distinct ability to convert energy from their surroundings into mechanical work, which gives rise to them having highly dynamic properties. Modeling active matter systems and capturing their complex behavior has been a great challenge in past years due to the many coupled interactions between their constituent parts, including not only distinct chemical and mechanical properties, but also feedback between them. One of the most intriguing biological active matter systems is the cell cytoskeleton, which can dynamically respond to chemical and mechanical cues to control cell structure and shape, playing a central role in many higher-order cellular processes. To model these systems and reproduce their behavior, we present a new modeling approach which combines the chemical, mechanical, and molecular transport aspects of active matter systems, all represented with equivalent complexity, while also allowing for various forms of mechanochemical feedback. This modeling approach, named MEDYAN, and software implementation is flexible so that a wide range of active matter systems can be simulated with a high level of detail, and ultimately can help to describe active matter phenomena, and in particular, the dynamics of the cell cytoskeleton. In this work, we have used MEDYAN to simulate a cytoskeletal network consisting of actin filaments, cross-linking proteins, and myosin II molecular motors. We found that these systems show rich dynamical behaviors, undergoing alignment and bundling transitions, with an emergent contractility, as the concentrations of myosin II and cross-linking proteins, as well as actin filament turnover rates, are varied.

Computational model of polarized actin cables and cytokinetic actin ring formation in budding yeast

The budding yeast actin cables and contractile ring are important for polarized growth and division, revealing basic aspects of cytoskeletal function. To study these formin-nucleated structures, we built a three-dimensional (3D) computational model with actin filaments represented as beads connected by springs. Polymerization by formins at the bud tip and bud neck, crosslinking, severing, and myosin pulling, are included. Parameter values were estimated from prior experiments. The model generates actin cable structures and dynamics similar to those of wild type and formin deletion mutant cells. Simulations with increased polymerization rate result in long, wavy cables. Simulated pulling by type V myosin stretches actin cables. Increasing the affinity of actin filaments for the bud neck together with reduced myosin V pulling promotes the formation of a bundle of antiparallel filaments at the bud neck, which we suggest as a model for the assembly of actin filaments to the contractile ring.

Geometrical and mechanical properties control actin filament organization

The different actin structures governing eukaryotic cell shape and movement are not only determined by the properties of the actin filaments and associated proteins, but also by geometrical constraints. We recently demonstrated that limiting nucleation to specific regions was sufficient to obtain actin networks with different organization. To further investigate how spatially constrained actin nucleation determines the emergent actin organization, we performed detailed simulations of the actin filament system using Cytosim. We first calibrated the steric interaction between filaments, by matching, in simulations and experiments, the bundled actin organization observed with a rectangular bar of nucleating factor. We then studied the overall organization of actin filaments generated by more complex pattern geometries used experimentally. We found that the fraction of parallel versus antiparallel bundles is determined by the mechanical properties of actin filament or bundles and the efficiency of nucleation. Thus nucleation geometry, actin filaments local interactions, bundle rigidity, and nucleation efficiency are the key parameters controlling the emergent actin architecture. We finally simulated more complex nucleation patterns and performed the corresponding experiments to confirm the predictive capabilities of the model.

Dynamic network morphology and tension buildup in a 3D model of cytokinetic ring assembly

During fission yeast cytokinesis, actin filaments nucleated by cortical formin Cdc12 are captured by myosin motors bound to a band of cortical nodes and bundled by cross-linking proteins. The myosin motors exert forces on the actin filaments, resulting in a net pulling of the nodes into a contractile ring, while cross-linking interactions help align actin filaments and nodes into a single bundle. We used these mechanisms in a three-dimensional computational model of contractile ring assembly, with semiflexible actin filaments growing from formins at cortical nodes, capturing of filaments by neighboring nodes, and cross-linking among filaments through attractive interactions. The model was used to predict profiles of actin filament density at the cell cortex, morphologies of condensing node-filament networks, and regimes of cortical tension by varying the node pulling force and strength of cross-linking among actin filaments. Results show that cross-linking interactions can lead to confinement of actin filaments at the simulated cortical boundary. We show that the ring-formation region in parameter space lies close to regions leading to clumps, meshworks or double rings, and stars/cables. Since boundaries between regions are not sharp, transient structures that resemble clumps, stars, and meshworks can appear in the process of ring assembly. These results are consistent with prior experiments with mutations in actin-filament turnover regulators, myosin motor activity, and changes in the concentration of cross-linkers that alter the morphology of the condensing network. Transient star shapes appear in some simulations, and these morphologies offer an explanation for star structures observed in prior experimental images. Finally, we quantify tension along actin filaments and forces on nodes during ring assembly and show that the mechanisms describing ring assembly can also drive ring constriction once the ring is formed.