Thickness distribution of actin bundles in vitro

Visualizing Actin Packing and the Effects of Actin Attachment on Lipid Membrane Viscosity Using Molecular Rotors

The actin cytoskeleton and its elaborate interplay with the plasma membrane participate in and control numerous biological processes in eukaryotic cells. Malfunction of actin networks and changes in their dynamics are related to various diseases, from actin myopathies to uncontrolled cell growth and tumorigenesis. Importantly, the biophysical and mechanical properties of actin and its assemblies are deeply intertwined with the biological functions of the cytoskeleton. Novel tools to study actin and its associated biophysical features are, therefore, of prime importance. Here we develop a new approach which exploits fluorescence lifetime imaging microscopy (FLIM) and environmentally sensitive fluorophores termed molecular rotors, acting as quantitative microviscosity sensors, to monitor dynamic viscoelastic properties of both actin structures and lipid membranes. In order to reproduce a minimal actin cortex in synthetic cell models, we encapsulated and attached actin networks to the lipid bilayer of giant unilamellar vesicles (GUVs). Using a cyanine-based molecular rotor, DiSC2(3), we show that different types of actin bundles are characterized by distinct packing, which can be spatially resolved using FLIM. Similarly, we show that a lipid bilayer-localized molecular rotor can monitor the effects of attaching cross-linked actin networks to the lipid membrane, revealing an increase in membrane viscosity upon actin attachment. Our approach bypasses constraints associated with existing methods for actin imaging, many of which lack the capability for direct visualization of biophysical properties. It can therefore contribute to a deeper understanding of the role that actin plays in fundamental biological processes and help elucidate the underlying biophysics of actin-related diseases.

Actin Bundles Dynamics and Architecture

Cells use the actin cytoskeleton for many of their functions, including their division, adhesion, mechanosensing, endo- and phagocytosis, migration, and invasion. Actin bundles are the main constituent of actin-rich structures involved in these processes. An ever-increasing number of proteins that crosslink actin into bundles or regulate their morphology is being identified in cells. With recent advances in high-resolution microscopy and imaging techniques, the complex process of bundles formation and the multiple forms of physiological bundles are beginning to be better understood. Here, we review the physiochemical and biological properties of four families of highly conserved and abundant actin-bundling proteins, namely, α-actinin, fimbrin/plastin, fascin, and espin. We describe the similarities and differences between these proteins, their role in the formation of physiological actin bundles, and their properties-both related and unrelated to their bundling abilities. We also review some aspects of the general mechanism of actin bundles formation, which are known from the available information on the activity of the key actin partners involved in this process.

Hydrodynamic and Polyelectrolyte Properties of Actin Filaments: Theory and Experiments

Actin filament’s polyelectrolyte and hydrodynamic properties, their interactions with the biological environment, and external force fields play an essential role in their biological activities in eukaryotic cellular processes. In this article, we introduce a unique approach that combines dynamics and electrophoresis light-scattering experiments, an extended semiflexible worm-like chain model, and an asymmetric polymer length distribution theory to characterize the polyelectrolyte and hydrodynamic properties of actin filaments in aqueous electrolyte solutions. A fitting approach was used to optimize the theories and filament models for hydrodynamic conditions. We used the same sample and experimental conditions and considered several g-actin and polymerization buffers to elucidate the impact of their chemical composition, reducing agents, pH values, and ionic strengths on the filament translational diffusion coefficient, electrophoretic mobility, structure factor, asymmetric length distribution, effective filament diameter, electric charge, zeta potential, and semiflexibility. Compared to those values obtained from molecular structure models, our results revealed a lower value of the effective G-actin charge and a more significant value of the effective filament diameter due to the formation of the double layer of the electrolyte surrounding the filaments. Contrary to the data usually reported from electron micrographs, the lower values of our results for the persistence length and average contour filament length agree with the significant difference in the association rates at the filament ends that shift to sub-micro lengths, which is the maximum of the length distribution.

Actin crosslinker competition and sorting drive emergent GUV size-dependent actin network architecture

The proteins that make up the actin cytoskeleton can self-assemble into a variety of structures. In vitro experiments and coarse-grained simulations have shown that the actin crosslinking proteins α-actinin and fascin segregate into distinct domains in single actin bundles with a molecular size-dependent competition-based mechanism. Here, by encapsulating actin, α-actinin, and fascin in giant unilamellar vesicles (GUVs), we show that physical confinement can cause these proteins to form much more complex structures, including rings and asters at GUV peripheries and centers; the prevalence of different structures depends on GUV size. Strikingly, we found that α-actinin and fascin self-sort into separate domains in the aster structures with actin bundles whose apparent stiffness depends on the ratio of the relative concentrations of α-actinin and fascin. The observed boundary-imposed effect on protein sorting may be a general mechanism for creating emergent structures in biopolymer networks with multiple crosslinkers.

Actin crosslinker competition and sorting drive emergent GUV size-dependent actin network architecture

The proteins that make up the actin cytoskeleton can self-assemble into a variety of structures. In vitro experiments and coarse-grained simulations have shown that the actin crosslinking proteins α-actinin and fascin segregate into distinct domains in single actin bundles with a molecular size-dependent competition-based mechanism. Here, by encapsulating actin, α-actinin, and fascin in giant unilamellar vesicles (GUVs), we show that physical confinement can cause these proteins to form much more complex structures, including rings and asters at GUV peripheries and centers; the prevalence of different structures depends on GUV size. Strikingly, we found that α-actinin and fascin self-sort into separate domains in the aster structures with actin bundles whose apparent stiffness depends on the ratio of the relative concentrations of α-actinin and fascin. The observed boundary-imposed effect on protein sorting may be a general mechanism for creating emergent structures in biopolymer networks with multiple crosslinkers.

By encapsulating proteins in giant unilamellar vesicles, Bashirzadeh et al find that actin crosslinkers, α-actinin and fascin, can self-assemble with actin into complex structures that depend on the degree of confinement. Further analysis and modeling show that α-actinin and fascin sort to separate domains of these structures. These insights may be generalizable to other biopolymer networks containing crosslinkers.

Regulation of Actin Bundle Mechanics and Structure by Intracellular Environmental Factors

The mechanical and structural properties of actin cytoskeleton drive various cellular processes, including structural support of the plasma membrane and cellular motility. Actin monomers assemble into double-stranded helical filaments as well as higher-ordered structures such as bundles and networks. Cells incorporate macromolecular crowding, cation interactions, and actin-crosslinking proteins to regulate the organization of actin bundles. Although the roles of each of these factors in actin bundling have been well-known individually, how combined factors contribute to actin bundle assembly, organization, and mechanics is not fully understood. Here, we describe recent studies that have investigated the mechanisms of how intracellular environmental factors influence actin bundling. This review highlights the effects of macromolecular crowding, cation interactions, and actin-crosslinking proteins on actin bundle organization, structure, and mechanics. Understanding these mechanisms is important in determining in vivo actin biophysics and providing insights into cell physiology.

Measurements and characterization of the dynamics of tracer particles in an actin network

The underlying physics governing the diffusion of a tracer particle in a viscoelastic material is a topic of some dispute. The long-term memory in the mechanical response of such materials should induce diffusive motion with a memory kernel, such as fractional Brownian motion (fBM). This is the reason that microrheology is able to provide the shear modulus of polymer networks. Surprisingly, the diffusion of a tracer particle in a network of a purified protein, actin, was found to conform to the continuous time random walk type (CTRW). We set out to resolve this discrepancy by studying the tracer particle diffusion using two different tracer particle sizes, in actin networks of different mesh sizes. We find that the ratio of tracer particle size to the characteristic length scale of a bio-polymer network plays a crucial role in determining the type of diffusion it performs. We find that the diffusion of the tracer particles has features of fBm when the particle is large compared to the mesh size, of normal diffusion when the particle is much smaller than the mesh size, and of the CTRW in between these two limits. Based on our findings, we propose and verify numerically a new model for the motion of the tracer in all regimes. Our model suggests that diffusion in actin networks consists of fBm of the tracer particle coupled with caging events with power-law distributed escape times.

Crowding tunes the organization and mechanics of actin bundles formed by crosslinking proteins

Fascin and α-actinin form higher-ordered actin bundles that mediate numerous cellular processes including cell morphogenesis and movement. While it is understood crosslinked bundle formation occurs in crowded cytoplasm, how crowding affects the bundling activities of the two crosslinking proteins is not known. Here, we demonstrate how solution crowding modulates the organization and mechanical properties of fascin- and α-actinin-induced bundles, utilizing total internal reflection fluorescence and atomic force microscopy imaging. Molecular dynamics simulations support the inference that crowding reduces binding interaction between actin filaments and fascin or the calponin homology 1 domain of α-actinin evidenced by interaction energy and hydrogen bonding analysis. Based on our findings, we suggest a mechanism of crosslinked actin bundle assembly and mechanics in crowded intracellular environments.

Kinetics of actin networks formation measured by time resolved particle-tracking microrheology

Actin is one of the most studied cytoskeleton proteins showing a very rich span of structures and functions. For example, adenosine triphosphate (ATP)-assisted polymerization of actin is used to push protrusions forward in a mechanism that enables cells to crawl on a substrate. In this process, the chemical energy released from the hydrolysis of ATP is what enables force generation. We study a minimal model system comprised of actin monomers in an excess of ATP concentration. In such a system polymerization proceeds in three stages: nucleation of actin filaments, elongation, and network formation. While the kinetics of filament growth was characterized previously, not much is known about the kinetics of network formation and the evolution of networks towards a steady-state structure. In particular, it is not clear how the non-equilibrium nature of this ATP-assisted polymerization manifests itself in the kinetics of self-assembly. Here, we use time-resolved microrheology to follow the kinetics of the three stages of self-assembly as a function of initial actin monomer concentration. Surprisingly, we find that at high enough initial monomer concentrations the effective elastic modulus of the forming actin networks overshoots and then relaxes with a -2/5 power law. We attribute the overshoot to the non-equilibrium nature of the polymerization and the relaxation to rearrangements of the network into a steady-state structure.

Dynamics in steady state in vitro acto-myosin networks

It is well known that many biochemical processes in the cell such as gene regulation, growth signals and activation of ion channels, rely on mechanical stimuli. However, the mechanism by which mechanical signals propagate through cells is not as well understood. In this review we focus on stress propagation in a minimal model for cell elasticity, actomyosin networks, which are comprised of a sub-family of cytoskeleton proteins. After giving an overview of th actomyosin network components, structure and evolution we review stress propagation in these materials as measured through the correlated motion of tracer beads. We also discuss the possibility to extract structural features of these networks from the same experiments. We show that stress transmission through these networks has two pathways, a quickly dissipative one through the bulk, and a long ranged weakly dissipative one through the pre-stressed actin network.

Semiflexible Biopolymers in Bundled Arrangements

Bundles and networks of semiflexible biopolymers are key elements in cells, lending them mechanical integrity while also enabling dynamic functions. Networks have been the subject of many studies, revealing a variety of fundamental characteristics often determined via bulk measurements. Although bundles are equally important in biological systems, they have garnered much less scientific attention since they have to be probed on the mesoscopic scale. Here, we review theoretical as well as experimental approaches, which mainly employ the naturally occurring biopolymer actin, to highlight the principles behind these structures on the single bundle level.

The More the Tubular: Dynamic Bundling of Actin Filaments for Membrane Tube Formation

Tubular protrusions are a common feature of living cells, arising from polymerization of stiff protein filaments against a comparably soft membrane. Although this process involves many accessory proteins in cells, in vitro experiments indicate that similar tube-like structures can emerge without them, through spontaneous bundling of filaments mediated by the membrane. Using theory and simulation of physical models, we have elaborated how nonequilibrium fluctuations in growth kinetics and membrane shape can yield such protrusions. Enabled by a new grand canonical Monte Carlo method for membrane simulation, our work reveals a cascade of dynamical transitions from individually polymerizing filaments to highly cooperatively growing bundles as a dynamical bottleneck to tube formation. Filament network organization as well as adhesion points to the membrane, which bias filament bending and constrain membrane height fluctuations, screen the effective attractive interactions between filaments, significantly delaying bundling and tube formation.

Physical model for the geometry of actin-based cellular protrusions

Actin-based cellular protrusions are a ubiquitous feature of cell morphology, e.g., filopodia and microvilli, serving a huge variety of functions. Despite this, there is still no comprehensive model for the mechanisms that determine the geometry of these protrusions. We present here a detailed computational model that addresses a combination of multiple biochemical and physical processes involved in the dynamic regulation of the shape of these protrusions. We specifically explore the role of actin polymerization in determining both the height and width of the protrusions. Furthermore, we show that our generalized model can explain multiple morphological features of these systems, and account for the effects of specific proteins and mutations.

Elasto-plastic response of reversibly crosslinked biopolymer bundles

We study the response of F-actin bundles to driving forces through a simple analytical model. We consider two filaments connected by reversibly bound crosslinks and driven by an external force. Two failure modes under load can be defined. Brittle failure is observed when crosslinks suddenly and collectively unbind, leading to catastrophic loss of bundle integrity. During ductile failure, on the other hand, bundle integrity is maintained, however at the cost of crosslink reorganization and defect formation. We present phase diagrams for the onset of failure, highlighting the importance of the crosslink stiffness for these processes. Crossing the phase boundaries, force-deflection curves display (frequency-dependent) hysteresis loops, reflecting the first-order character of the failure processes. We evidence how the introduction of defects can lead to complex elasto-plastic relaxation processes, once the force is switched off. Depending on, both the time-scale for defect motion and the crosslink stiffness, bundles can remain in a quasi-permanent plastically deformed state for a very long time.

Designing highly tunable semiflexible filament networks

Semiflexible polymers can generate a range of filamentous networks significantly different in structure from those seen in conventional polymer solutions. Our coarse-grained simulations with an implicit cross-linker potential show that networks of branching bundles, knotted morphologies, and structural chirality can be generated by a generalized approach independent of specific cross-linkers. Network structure depends primarily on filament flexibility and separation, with significant connectivity increase after percolation. Results should guide the design of engineered semiflexible polymers.

Catch-bond behaviour facilitates membrane tubulation by non-processive myosin 1b

Myosin 1b is a single-headed membrane-associated motor that binds to actin filaments with a catch-bond behaviour in response to load. In vivo, myosin 1b is required to form membrane tubules at both endosomes and the trans-Golgi network. To establish the link between these two fundamental properties, here we investigate the capacity of myosin 1b to extract membrane tubes along bundled actin filaments in a minimal reconstituted system. We show that single-headed non-processive myosin 1b can extract membrane tubes at a biologically relevant low density. In contrast to kinesins we do not observe motor accumulation at the tip, suggesting that the underlying mechanism for tube formation is different. In our theoretical model, myosin 1b catch-bond properties facilitate tube extraction under conditions of increasing membrane tension by reducing the density of myo1b required to pull tubes.

Physically-induced cytoskeleton remodeling of cells in three-dimensional culture

Characterizing how cells in three-dimensional (3D) environments or natural tissues respond to biophysical stimuli is a longstanding challenge in biology and tissue engineering. We demonstrate a strategy to monitor morphological and mechanical responses of contractile fibroblasts in a 3D environment. Cells responded to stretch through specific, cell-wide mechanisms involving staged retraction and reinforcement. Retraction responses occurred for all orientations of stress fibers and cellular protrusions relative to the stretch direction, while reinforcement responses, including extension of cellular processes and stress fiber formation, occurred predominantly in the stretch direction. A previously unreported role of F-actin clumps was observed, with clumps possibly acting as F-actin reservoirs for retraction and reinforcement responses during stretch. Responses were consistent with a model of cellular sensitivity to local physical cues. These findings suggest mechanisms for global actin cytoskeleton remodeling in non-muscle cells and provide insight into cellular responses important in pathologies such as fibrosis and hypertension.

Sarcomeric pattern formation by actin cluster coalescence

Contractile function of striated muscle cells depends crucially on the almost crystalline order of actin and myosin filaments in myofibrils, but the physical mechanisms that lead to myofibril assembly remains ill-defined. Passive diffusive sorting of actin filaments into sarcomeric order is kinetically impossible, suggesting a pivotal role of active processes in sarcomeric pattern formation. Using a one-dimensional computational model of an initially unstriated actin bundle, we show that actin filament treadmilling in the presence of processive plus-end crosslinking provides a simple and robust mechanism for the polarity sorting of actin filaments as well as for the correct localization of myosin filaments. We propose that the coalescence of crosslinked actin clusters could be key for sarcomeric pattern formation. In our simulations, sarcomere spacing is set by filament length prompting tight length control already at early stages of pattern formation. The proposed mechanism could be generic and apply both to premyofibrils and nascent myofibrils in developing muscle cells as well as possibly to striated stress-fibers in non-muscle cells.

Muscle contraction driving voluntary movements and the beating of the heart relies on the contraction of highly regular bundles of actin and myosin filaments, which share a periodic, sarcomeric pattern. We know little about the mechanisms by which these ‘biological crystals’ are assembled and it is a general question how order on a scale of 100 micrometers can emerge from the interactions of micrometer-sized building blocks, such as actin and myosin filaments. In our paper, we consider a computational model for a bundle of actin filaments and discuss physical mechanisms by which periodic order emerges spontaneously. Mutual crosslinking of actin filaments results in the formation and coalescence of growing actin clusters. Active elongation and shrinkage dynamics of actin filaments generates polymerization forces and causes local actin flow that can act like a conveyor belt to sort myosin filaments in place.

Supramolecular cellular filament systems: how and why do they form?

All cells, from simple bacteria to complex human tissues, rely on extensive networks of protein fibers to help maintain their proper form and function. These filament systems usually do not operate as single filaments, but form complex suprastructures, which are essential for specific cellular functions. Here, we describe the progress in determining the architectures of molecular filamentous suprastructures, the principles leading to their formation, and the mechanisms by which they may facilitate function. The complex eukaryotic cytoskeleton is tightly regulated by a large number of actin- or microtubule-associated proteins. In contrast, recently discovered bacterial actins and tubulins have few associated regulatory proteins. Hence, the quest to find basic principles that govern the formation of filamentous suprastructures is simplified in bacteria. Three common principles, which have been probed extensively during evolution, can be identified that lead to suprastructures formation: cationic counterion fluctuations; self-association into liquid crystals; and molecular crowding. The underlying physics of these processes will be discussed with respect to physiological circumstance.

Monodisperse domains by proteolytic control of the coarsening instability

The coarsening instability typically disrupts steady-state cluster-size distributions. We show that degradation coupled to the cluster size, such as arising from biological proteolysis, leads to a fixed-point cluster size. Stochastic evaporative and condensative fluxes determine the width of the fixed-point size distribution. At the fixed point, we show how the peak size and width depend on number, interactions, and proteolytic rate. This proteolytic size-control mechanism is consistent with the phenomenology of pseudopilus length control in the general secretion pathway of bacteria.

Polymorphism of highly cross-linked F-actin networks: probing multiple length scales

The assembly properties of F-actin filaments in the presence of different biological cross-linker concentrations and types have been investigated using a combined approach of fluorescence confocal microscopy and coarse-grained molecular dynamics simulation. In particular for highly cross-linked regimes, new network morphologies are observed. Complex network formation and the details of the resulting structure are strongly dependent on the ratio of cross-linkers to actin monomers and cross-linker shape but only weakly dependent on overall actin concentration and filament length. The work presented here may help to provide some fundamental understanding of how excessive cross-linkers interact with the actin filament solution, creating different structures in the cell under high cross-linker concentrations. F-actin is not only of biological importance but also, as an example of a semiflexible polymer, has attracted significant interest in its physical behavior. In combination with different cross-linkers semiflexible filaments may provide new routes to bio-materials development and act as the inspiration for new hierarchical network-based materials.

Actin cross-linkers and the shape of stereocilia

Stereocilia are actin-based cellular protrusions essential for hearing. We propose that they are shaped by the detachment dynamics of actin cross-linkers, in particular espin. We account for experimentally observed stereocilium shapes, treadmilling velocity to length relationship, espin 1 localization profile, and microvillus length to espin level relationship. If the cross-linkers are allowed to reattach, our model yields a dynamical phase transition toward unbounded growth. Considering the simplified case of a noninteracting, one-filament system, we calculate the length probability distribution in the growing phase and its stationary form in a continuum approximation of the finite-length phase. Numerical simulations of interacting filaments suggest an anomalous power-law divergence of the protrusion length at the growth transition, which could be a universal feature of cross-linked depolymerizing systems.

Structural reorganization of parallel actin bundles by crosslinking proteins: incommensurate states of twist

We construct a coarse-grained model of parallel actin bundles crosslinked by compact globular bundling proteins, such as fascin and espin, necessary components of filopodial and mechanosensory bundles. Consistent with structural observations of bundles, we find that the optimal geometry for crosslinking is overtwisted, requiring a coherent structural change of the helical geometry of the filaments. We study the linker-dependent thermodynamic transition of bundled actin filaments from their native state to the overtwisted state and map out the "twist-state" phase diagram in terms of the availability as well as the flexibility of crosslinker proteins. We predict that the transition from the uncrosslinked to fully crosslinked state is highly sensitive to linker flexibility: flexible crosslinking smoothly distorts the twist state of bundled filaments, while rigidly crosslinked bundles undergo a phase transition, rapidly overtwisting filaments over a narrow range of free crosslinker concentrations. Additionally, we predict a rich spectrum of intermediate structures, composed of alternating domains of sparsely bound (untwisted) and strongly bound (overtwisted) filaments. This model reveals that subtle differences in crosslinking agents themselves modify not only the detailed structure of parallel actin bundles, but also the thermodynamic pathway by which they form.

Modeling the formation of in vitro filopodia

Filopodia are bundles of actin filaments that extend out ahead of the leading edge of a crawling cell to probe its upcoming environment. In vitro experiments (Vignjevic et al. in J Cell Biol 160:951-962, 2003) have determined the minimal ingredients required for the formation of filopodia from the dendritic-like morphology of the leading edge. We model these experiments using kinetic aggregation equations for the density of growing bundle tips. In mean field, we determine the bundle size distribution to be broad for bundle sizes smaller than a characteristic bundle size above which the distribution decays exponentially. Two-dimensional simulations incorporating both bundling and cross-linking measure a bundle size distribution that agrees qualitatively with mean field. The simulations also demonstrate a nonmonotonicity in the radial extent of the dendritic region as a function of capping protein concentration, as was observed in experiments, due to the interplay between percolation and the ratcheting of growing filaments off a spherical obstacle.

Equilibrium polyelectrolyte bundles with different multivalent counterion concentrations

We present the results of molecular-dynamics simulations on the salt concentration dependence of the formation of polyelectrolyte bundles in thermodynamic equilibrium. Extending our results on salt-free systems we investigate here deficiency or excess of trivalent counterions in solution. Our results reveal that the trivalent counterion concentration significantly alters the bundle size and size distribution. The onset of bundle formation takes place at earlier Bjerrum length values with increasing trivalent counterion concentration. For the cases of 80%, 95%, and 100% charge compensation via trivalent counterions, the net charge of the bundles decreases with increasing size. We suggest that competition among two different mechanisms, counterion condensation and merger of bundles, leads to a nonmonotonic change in line-charge density with increasing Bjerrum length. The investigated case of having an abundance of trivalent counterions by 200% prohibits such a behavior. In this case, we find that the difference in effective line-charge density of different size bundles diminishes. In fact, the system displays an isoelectric point, where all bundles become charge neutral.

Molecular mechanism of bundle formation by the bacterial actin ParM

The actin homolog ParM plays a microtubule-like role in segregating DNA prior to bacterial cell division. Fluorescence and cryo-electron microscopy have shown that ParM forms filament bundles between separating DNA plasmids in vivo. Given the lack of ParM bundling proteins it remains unknown how ParM bundles form at the molecular level. Here we show using time-lapse TIRF microscopy, under in vitro molecular crowding conditions, that ParM-bundle formation consists of two distinct phases. At the onset of polymerization bundle thickness and shape are determined in the form of nuclei of short helically disordered filaments arranged in a liquid-like lattice. These nuclei then undergo an elongation phase whereby they rapidly increase in length. At steady state, ParM bundles fuse into one single large aggregate. This behavior had been predicted by theory but has not been observed for any other cytomotive biopolymer, including F-actin. We employed electron micrographs of ParM rafts, which are 2-D analogs of 3-D bundles, to identify the main molecular interfilament contacts within these suprastructures. The interface between filaments is similar for both parallel and anti-parallel orientations and the distribution of filament polarity is random within a bundle. We suggest that the interfilament interactions are not due to the interactions of specific residues but rather to long-range, counter ion mediated, electrostatic attractive forces. A randomly oriented bundle ensures that the assembly is rigid and that DNA may be captured with equal efficiency at both ends of the bundle via the ParR binding protein.

Cooperativity and frustration in protein-mediated parallel actin bundles

We examine the mechanism of bundling of cytoskeletal actin filaments by two representative bundling proteins, fascin and espin. Small-angle x-ray studies show that increased binding from linkers drives a systematic overtwist of actin filaments from their native state, which occurs in a linker-dependent fashion. Fascin bundles actin into a continuous spectrum of intermediate twist states, while espin only allows for untwisted actin filaments and fully overtwisted bundles. Based on a coarse-grained, statistical model of protein binding, we show that the interplay between binding geometry and the intrinsic flexibility of linkers mediates cooperative binding in the bundle. We attribute the respective continuous (discontinuous) bundling mechanisms of fascin (espin) to difference in the stiffness of linker bonds themselves.

Traction forces during collective cell motion

Collective motion of cell cultures is a process of great interest, as it occurs during morphogenesis, wound healing, and tumor metastasis. During these processes cell cultures move due to the traction forces induced by the individual cells on the surrounding matrix. A recent study [Trepat, et al. (2009). Nat. Phys. 5, 426-430] measured for the first time the traction forces driving collective cell migration and found that they arise throughout the cell culture. The leading 5-10 rows of cell do play a major role in directing the motion of the rest of the culture by having a distinct outwards traction. Fluctuations in the traction forces are an order of magnitude larger than the resultant directional traction at the culture edge and, furthermore, have an exponential distribution. Such exponential distributions are observed for the sizes of adhesion domains within cells, the traction forces produced by single cells, and even in nonbiological nonequilibrium systems, such as sheared granular materials. We discuss these observations and their implications for our understanding of cellular flows within a continuous culture.

Physical model for the width distribution of axons

The distribution of widths of axons was recently investigated, and was found to have a distinct peak at an optimized value. The optimized axon width at the peak may arise from the conflicting demands of minimizing energy consumption and assuring signal transmission reliability. The distribution around this optimized value is found to have a distinct non-Gaussian shape, with an exponential "tail". We propose here a mechanical model whereby this distribution arises from the interplay between the elastic energy of the membrane surrounding the axon core, the osmotic pressure induced by the neurofilaments inside the axon bulk, and active processes that remodel the microtubules and neurofilaments inside the axon. The axon's radius of curvature can be determined by the cell's control of the osmotic pressure difference across the membrane, the membrane tension or by changing the composition of the different components of the membrane. We find that the osmotic pressure, determined by the neurofilaments, seems to be the dominant control parameter.

Mechanism on polarity sorting of actin bundles formed with polycations

In this paper we explored factors that determine the polarity of an Actin bundle formed with polycation through electrostatic interaction. We found that the polarity decreases with an increase in the polycation concentration while it hardly depends on the KCl salt concentration. Additionally, the polarity of the Actin bundle increases with an increase in the degree of polymerization of the polycation at a constant polymer concentration. From these results we proposed that the kinetics of nuclei formation determines the polarity of the Actin bundle.

Morphogenesis of liposomes caused by polycation-induced actin assembly formation

We investigated the effects of polycation-mediated actin assembly on the morphological transformation of the lipid vesicle membrane by spatiotemporally controlling actin assembly. By triggering the radical polymerization of the cationic monomer using UV irradiation, we achieved a varied photoinduced assembly of actin in bulk solution. Furthermore, we designed liposomes containing actin and cationic monomers. In these actin-encapsulated liposomes, various actin assemblies were formed by UV irradiation similar to that observed in bulk solution. Moreover, morphogenesis of actin-encapsulated liposomes was observed in liposomes encapsulated with G-actin but not with F-actin. This result indicates that a dynamic polymerization of G-actin is important for vesicle protrusion.

Packing defects and the width of biopolymer bundles

The formation of bundles composed of actin filaments and cross-linking proteins is an essential process in the maintenance of the cells' cytoskeleton. It has also been recreated by in-vitro experiments, where actin networks are routinely produced to mimic and study the cellular structures. It has been observed that these bundles seem to have a well-defined width distribution, which has not been adequately described theoretically. We propose here that packing defects of the filaments, quenched and random, contribute an effective repulsion that counters the cross-linking adhesion energy and leads to a well-defined bundle width. This is a two-dimensional strain-field version of the classic Rayleigh instability of charged droplets.

Helical twist controls the thickness of F-actin bundles

In the presence of condensing agents such as nonadsorbing polymer, multivalent counter ions, and specific bundling proteins, chiral biopolymers typically form bundles with a finite thickness, rather than phase-separating into a polymer-rich phase. Although short-range repulsive interactions or geometrical frustrations are thought to force the equilibrium bundle size to be limited, the precise mechanism is yet to be resolved. The importance of the tight control of biopolymer bundle size is illustrated by the ubiquitous cytoskeletal actin filament bundles that are crucial for the proper functioning of cells. Using an in vitro model system, we show that size control relies on a mismatch between the helical structure of individual actin filaments and the geometric packing constraints within bundles. Small rigid actin-binding proteins change the twist of filamentous actin (F-actin) in a concentration-dependent manner, resulting in small, well defined bundle thickness up to approximately 20 filaments, comparable to those found in filopodia. Other F-actin cross-linking proteins can subsequently link these small, well organized bundles into larger structures of several hundred filaments, comparable to those found in, for example, Drosophila bristles. The energetic tradeoff between filament twisting and cross-linker binding within a bundle is suggested as a fundamental mechanism by which cells can precisely adjust bundle size and strength.