Structural transition of actin filament in a cell-sized water droplet with a phospholipid membrane

Actin filament, F-actin, is a semiflexible polymer with a negative charge, and is one of the main constituents of cell membranes. To clarify the effect of cross talk between a phospholipid membrane and actin filaments in cells, we conducted microscopic observations on the structural changes in actin filaments in a cell-sized (several tens of micrometers in diameter) water droplet coated with a phospholipid membrane such as phosphatidylserine (PS; negatively charged head group) or phosphatidylethanolamine (PE; neutral head group) as a simple model of a living cell membrane. With PS, actin filaments are distributed uniformly in the water phase without adsorption onto the membrane surface between 2 and 6 mM Mg2+, while between 6 and 12 mM Mg2+, actin filaments are adsorbed onto the inner membrane surface. With PE, the actin filaments are uniformly adsorbed onto the inner membrane surface between 2 and 12 mM Mg2+. With both PS and PE membranes, at Mg2+ concentrations higher than 12 mM, thick bundles are formed in the bulk water droplet accompanied by the dissolution of actin filaments from the membrane surface. The attraction between actin filaments and membrane is attributable to an increase in the translational entropy of counterions accompanied by the adsorption of actin filaments onto the membrane surface. These results suggest that a microscopic water droplet coated with phospholipid can serve as an easy-to-handle model of cell membranes.     

Diffusion and segmental dynamics of rodlike molecules by fluorescence correlation spectroscopy

The dynamics of weakly bending polymers is analyzed on the basis of a Gaussian semiflexible chain model and the fluorescence correlation spectroscopy (FCS) correlation function is determined. Particular attention is paid to the influence of the rotational motion on the decay of the FCS correlation function. An analytical expression for the correlation function is derived, from which the averaged segmental mean square displacement can be determined independent of any specific model for the polymer dynamics. The theoretical analysis exhibits a strong dependence of the correlation function on the rotational motion for semiflexible polymers with typical lengths and persistence lengths of actin filaments or fd viruses. Hence, FCS allows for a measurement of the rotational motion of such semiflexible polymers. The theoretical results agree well with experimental measurements on actin filaments and confirm the importance of large relaxation times.     

Guidance of actin filament elongation on filament-binding tracks

Biomolecular motors, which convert chemical energy into mechanical work in intracellular processes, have high potential in bionanotechnology in vitro as molecular shuttles or nanoscale actuators. In this context, guided elongation of actin filaments in vitro could be used to lay tracks for myosin motor-based shuttles or to direct nanoscale actuators based on actin filament end-tracking motors. To guide the direction of filament polymerization on surfaces, microcontact printing was used to create tracks of chemically modified myosin, which binds to, but cannot exert force on, filaments. These filament-binding tracks captured nascent filaments from solution and guided the direction of their subsequent elongation. The effect of track width and protein surface density on filament alignment and elongation rate was quantified. These results indicate that microcontact printing is a useful method for guiding actin filament polymerization in vitro for biomolecular motor-based applications.     

Fluorescence correlation spectroscopy analysis of segmental dynamics in actin filaments

We adapt fluorescence correlation spectroscopy (FCS) formalism to the studies of the dynamics of semiflexible polymers and derive expressions relating FCS correlation function to the longitudinal and transverse mean-square displacements of polymer segments. The obtained relations do not depend on any specific model of polymer dynamics. We use the derived expressions to measure the dynamics of actin filaments in two experimental situations: filaments labeled at distinct positions and homogeneously labeled filaments. Both approaches give consistent results and allow to measure the temporal dependence of the segmental mean-square displacement over almost five decades in time, from approximately 40 micros to approximately 2 s. These noninvasive measurements allow for a detailed quantitative comparison of the experimental data to the current theories of semiflexible polymer dynamics. Good quantitative agreement is found between the experimental results and theories explicitly accounting for the hydrodynamic interactions between polymer segments.     

Diffusion dynamics of motor-driven transport: gradient production and self-organization of surfaces

The interaction between cytoskeletal filaments (e.g., actin filaments) and molecular motors (e.g., myosin) is the basis for many aspects of cell motility and organization of the cell interior. In the in vitro motility assay (IVMA), cytoskeletal filaments are observed while being propelled by molecular motors adsorbed to artificial surfaces (e.g., in studies of motor function). Here we integrate ideas that cytoskeletal filaments may be used as nanoscale templates in nanopatterning with a novel approach for the production of surface gradients of biomolecules and nanoscale topographical features. The production of such gradients is challenging but of increasing interest (e.g., in cell biology). First, we show that myosin-induced actin filament sliding in the IVMA can be approximately described as persistent random motion with a diffusion coefficient (D) given by a relationship analogous to the Einstein equation (D = kT/gamma). In this relationship, the thermal energy (kT) and the drag coefficient (gamma) are substituted by a parameter related to the free-energy transduction by actomyosin and the actomyosin dissociation rate constant, respectively. We then demonstrate how the persistent random motion of actin filaments can be exploited in conceptually novel methods for the production of actin filament density gradients of predictable shapes. Because of regularly spaced binding sites (e.g., lysines and cysteines) the actin filaments act as suitable nanoscale scaffolds for other biomolecules (tested for fibronectin) or nanoparticles. This forms the basis for secondary chemical and topographical gradients with implications for cell biological studies and biosensing.     

Hybrid molecular dynamics simulations of living filaments

We propose a hybrid molecular dynamics/multi-particle collision dynamics model to simulate a set of self-assembled semiflexible filaments and free monomers. Further, we introduce a Monte Carlo scheme to deal with single monomer addition (polymerization) or removal (depolymerization), satisfying the detailed balance condition within a proper statistical mechanical framework. This model of filaments, based on the wormlike chain, aims to represent equilibrium polymers with distinct reaction rates at both ends, such as self-assembled adenosine diphosphate-actin filaments in the absence of adenosine triphosphate (ATP) hydrolysis and other proteins. We report the distribution of filament lengths and the corresponding dynamical fluctuations on an equilibrium trajectory. Potential generalizations of this method to include irreversible steps like ATP-actin hydrolysis are discussed.     

Droplets wetting on filament rails: Surface energy and morphology transition

The morphology of liquid droplets wetting on filaments depends on the filament configuration, droplet volume, and contact angle. A stable morphology is the one that minimizes the potential energy of the droplet–filament system, while morphology transition may happen when an intermediate state exists which corresponds to a higher potential energy. This paper aims to explore such morphology transition of droplet wetting on filament rails made of two parallel identical microfilaments. Detailed numerical simulations were performed to extract the surface energy of the droplet–filament system at varying filament spacings, droplet volumes, and contact angles. Critical conditions of the morphology transition between two symmetrical wetting morphologies (i.e., liquid droplet bridge and barrel-shaped droplet) were determined. A family of characteristic curves in terms of the dimensionless droplet volume vs the filament spacing at varying contact angles was obtained, which can be used as a universal law to govern the morphology transition for such droplet–filament rail systems. The results and concepts presented in this work can be extended to broad wetting systems and utilized for the analysis and design of microfluidic devices and testers based on droplet–filament systems.     

A simple model for the disintegration of highly charged solvent droplets during electrospray ionization

This work uses a minimalist model for deciphering the opposing effects of Coulomb repulsion and surface tension on the stability of electrosprayed droplets. Guided by previous observations, it is assumed that progeny droplets are ejected from the tip of liquid filaments that are formed as protrusions of an initially spherical parent. Nonspherical shapes are approximated as assemblies of multiple closely spaced beads. This strategy greatly facilitates the calculation of electrostatic and surface energies. For a droplet at the Rayleigh limit the model predicts that growth of a very thin filament is a spontaneous process with a negligible activation barrier. In contrast, significant barriers are encountered for the formation of larger diameter filaments. These different barrier heights favor highly asymmetric droplet fission because the dimensions of the filament determine those of the ejected droplet(s). Substantial charge accumulation occurs at the filament termini. This allows each progeny droplet to carry a significant fraction of charge, despite its very small volume. In the absence of a long connecting filament, relieving electrostatic stress through progeny droplet emission would be ineffective. The model predicts the prevalence of fission events leading to the formation of several progeny droplets, instead of just a single one. Ejection bursts are followed by collapse back to a spherical shape. The resulting charge depleted system is incapable of producing additional progeny droplets until solvent evaporation returns it to the Rayleigh limit. Despite the very simple nature of the model used here, all of these predictions agree with experimental data.     

Structure and dynamics of actin filament solutions in the presence of latrunculin A

We study the polymerization kinetics and linear rheology of actin filaments in the absence and in the presence of latrunculin A. Filamentous actin is a semiflexible polymer, and latrunculin A is an organic, actin-binding molecule. Using diffusing wave spectroscopy (DWS), we monitor the thermally excited motion of monodisperse polystyrene microspheres in semidilute solutions of actin filaments. From these measurements, we extract the microspheres mean-square displacement, which is related to the viscoelastic nature of the actin solutions. These optical measurements, along with mechanical measurements, suggest that despite its depolymerizing effect, latrunculin A promotes the strengthening of actin networks. DWS shows that while the scaling nature of the viscoelastic properties of actin filaments is essentially unmodified in the presence of latrunculin A at small time scales, the elasticity of actin solutions becomes enhanced for increasing latrunculin concentrations at large time scales. Complementary electron-microscopy measurements help uncover the structural origin of this enhanced elasticity at small time scales. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 3007–3015, 1998     

From atomistic simulation to the dynamics, structure and helical network formation of dendronized polymers: the Janus chain model

It is the purpose of this paper to establish a bottom-up multiscale approach for dendronized polymers. Based on our understanding of the phenomenology of an atomistic model for this class of polymers, we introduce a "Janus chain" (JC) model which adds a vectorial degree of freedom (Janus vector)--related to the sectorial amphiphilicity--to each segment of the linear backbone of a (classical) uncharged, semiflexible, and multibead chain representation of a polymer. The JC features induced polymeric curvature and ultimately triggers complexation. JC parameters related to the topology and chemical details are obtained from the atomistic level. Available experimental observations including the formation of superstructures and double helical conformations are well reproduced by the JC model. JC is efficiently solved via Brownian dynamics simulation and can be seen as a member of a universality class which is one (two) level(s) above the magnetic (semiflexible) chain model. It therefore should allow to model not only dendronized polymers but also structures belonging to the same class-exhibiting induced (or spontaneous) curvature--such as single stranded DNA and actin filaments.     

Brownian dynamics algorithm for entangled wormlike threads

The authors present a hybrid Brownian dynamics/Monte Carlo algorithm for simulating solutions of highly entangled semiflexible polymers or filaments. The algorithm combines a Brownian dynamics time-stepping approach with an efficient scheme for rejecting moves that cause chains to cross or that lead to excluded volume overlaps. The algorithm allows simulation of the limit of infinitely thin but uncrossable threads, and is suitable for simulating the conditions obtained in experiments on solutions of long actin protein filaments.     

B7 Liquid Crystal Filament Growth in Presence of Carbon Nanotubes

Liquid crystal phases formed from bent-core mesogens have attracted much interest of the liquid crystal research community, due to the manifestation of chirality effects from achiral molecules. One of the most elusive of the bent-core phases is the B7 phase, which at its early stage often forms in a helical filament fashion. We investigate the growth of such filaments in the presence of single-walled nanotubes to elucidate possible effects on the growth dynamics and helicity of B7 helical filaments. It is found that the filament width slightly decreases in comparison to the neat B7 material, suggesting a more tightly bound structure around the nanotubes, with the nanotubes likely acting as the core of the helical filament. No effects on pitch or periodicity of the helical superstructure is observed. The filament growth velocity quickly decreases as nanotubes are added to the B7 phase, indicating that a more tightly bound structure needs a longer time of formation. An observed buckling instability is of interest as a microscopic example for the study of nonlinear dynamics theories of filaments. The present investigation is thus of general importance for nanoparticle directed growth of filaments, which has applications in biomolecular growth and high tensile strength fibres.     

Cross-linked biopolymer bundles: cross-link reversibility leads to cooperative binding/unbinding phenomena

We consider a biopolymer bundle consisting of filaments that are cross-linked together. The cross-links are reversible: they can dynamically bind and unbind adjacent filament pairs as controlled by a binding enthalpy. The bundle is subjected to a bending deformation and the corresponding distribution of cross-links is measured. For a bundle consisting of two filaments, upon increasing the bending amplitude, a first-order transition is observed. The transition is from a state where the filaments are tightly coupled by many bound cross-links, to a state of nearly independent filaments with only a few bound cross-links. For a bundle consisting of more than two filaments, a series of first-order transitions is observed. The transitions are connected with the formation of an interface between regions of low and high cross-link densities. Combining umbrella sampling Monte Carlo simulations with analytical calculations, we present a detailed picture of how the competition between cross-link shearing and filament stretching drives the transitions. We also find that, when the cross-links become soft, collective behavior is not observed: the cross-links then unbind one after the other leading to a smooth decrease of the average cross-link density.     

Elasticity and flow properties of actin gels

Actin gels formed by polymerizing monomeric actin have been studied by use of small amplitude oscillatory deformations and steady shear flow. The length of actin filaments within the gel was varied by copolymerization in the presence of the filament-capping protein gelsolin. The results for short filaments are in qualitative agreement with a model for semi-dilute solutions of inter-penetrating rods. Long filaments give rise to additional motions, believed to be flexing of rods. Steady shear viscosities, at high shear rates, are independent of initial filament length. Results are explained as due to breaking of filaments in shear flows.     

Treadmilling of actin filaments via Brownian dynamics simulations

Actin polymerization is coupled to the hydrolysis of adenosine triphosphate (ATP) into adenosine diphosphate (ADP) and inorganic phosphate (P(i)). Therefore, each protomer within an actin filament can attain three different nucleotide states corresponding to bound ATP, ADP/P(i), and ADP. These protomer states form spatial patterns on the growing (or shrinking) filaments. Using Brownian dynamics simulations, the growth behavior of long filaments is studied, together with the associated protomer patterns, as a function of ATP-actin monomer concentration, C(T), within the surrounding solution. For concentrations close to the critical concentration C(T)=C(T,cr), the filaments undergo treadmilling, i.e., they grow at the barbed and shrink at the pointed end, which leads to directed translational motion of the whole filament. The corresponding nonequilibrium states are characterized by several global fluxes and by spatial density and flux profiles along the filaments. We focus on a certain set of transition rates as deduced from in vitro experiments and find that the associated treadmilling (or turnover) rate is about 0.08 monomers per second.     

Mechanism of actin polymerization by myosin subfragment-1 probed by dynamic light scattering

Monomeric actin (G-actin) polymerizes spontaneously into helical filaments in the presence of inorganic salts. The slowest, rate-limiting step of the polymerization process is formation of actin trimers, the smallest oligomers that serve as nuclei for fast filament growth (filament elongation) by monomer addition at the filament ends. In low ionic-strength solutions, actin can be polymerized by myosin subfragment-1 (S1). In early works it has been suggested that G-actin-S1 1:1 complexes (GS) assemble into filaments according to the nucleation-filament elongation scheme. Subsequent studies indicated that one S1 molecule can bind two actin monomers, and that oligomerization of the initial complexes is a fast reaction. This has led to suggest an alternative mechanism, with a ternary G(2)S complex and its oligomers being predominant intermediates of S1-induced assembly of G-actin into filaments. We used dynamic light scattering to analyze the initial steps of S1-induced polymerization of actin. Our results suggest formation of GS complexes and their oligomers in the presence of S1 equimolar to or in excess over actin. We confirm formation of G(2)S complexes as intermediates of S1-induced polymerization in the presence of actin in excess over S1.     

p41-Arc, a regulatory subunit of Arp2/3 complex, can induce premature senescence in the absence of p53 and Rb

Cellular senescence is a tumor-suppressive process instigated by proliferation in the absence of telomere replication, by cellular stresses such as oncogene activation, or by activation of the tumor suppressor proteins, such as Rb or p53. This process is characterized by an irreversible cell cycle exit, a unique morphology, and expression of senescence-associated-β-galactosidase (SA-β-gal). Despite the potential biological importance of cellular senescence, little is known of the mechanisms leading to the senescent phenotype. p41-Arc has been known to be a putative regulatory component of the mammalian Arp2/3 complex, which is required for the formation of branched networks of actin filaments at the cell cortex. In this study, we demonstrate that p41-Arc can induce senescent phenotypes when it is overexpressed in human tumor cell line, SaOs-2, which is deficient in p53 and Rb tumor suppressor genes, implying that p41 can induce senescence in a p53-independent way. p41-Arc overexpression causes a change in actin filaments, accumulating actin filaments in nuclei. Therefore, these results imply that a change in actin filament can trigger an intrinsic senescence program in the absence of p53 and Rb tumor suppressor genes.     

Thermal characterisation of actin filaments prepared from adp-actin monomers

The thermodynamic properties of the ADP- and ATP-actin filaments were compared by the method of differential scanning calorimetry. The lower melting point for the ADP-F-actin filament (58.4 vs. 64.5°C for ATP-F-actin) indicated that compared to the ATP-actin filaments its structure was less resistant to heat denaturation. The detailed thermodynamic characterisation of the proteins was carried out by the analysis of the calorimetric enthalpy, the entropy and the free enthalpy changes. All of the determined parameters gave lower values to the ADP-actin filaments than to the ATP-actin filaments. The calculated values of the activation energy also demonstrated that compared to the ADP-F-actin the ATP-F-actin was thermodynamically more resistant to the denaturing effect of heat. Based on all of this information we have concluded that the actin filament prepared from ADP containing magnesium saturated actin monomers at pH 8.0 is thermodynamically less stable than the ones obtained from ATP-actin monomers.     

Polymerization of actin filaments coupled with adenosine triphosphate hydrolysis: Brownian dynamics and theoretical analysis

Polymerization dynamics of single actin filaments coupled with adenosine triphosphate (ATP) hydrolysis is investigated via both theoretical analysis and Brownian dynamics simulations. Brownian dynamics simulations have been applied recently to study the growth behaviors of long filaments as a function of the free actin monomer concentrations, C(T), which is found to be in agreement with the associated experiments. In the present study, both ATP cap length and length diffusivity are studied as a function of the free ATP-actin monomer concentrations, C(T). The exact analytical expressions are found to be in perfect consistency with Brownian dynamics simulations. Likewise, we find that the length diffusion coefficient is peaked near the critical concentration, C(T,cr). It is, therefore, expected that the dependence of length diffusivity on ATP-actin monomer concentrations is utilized to analyze the surprising experiments on the length fluctuations of individual actin filaments.