Polymerization of ADP-actin and ATP-actin under sonication and characteristics of the ATP-actin equilibrium polymer

Polymerization under sonication has been developed as a new method to study the rapid polymerization of actin with a large number of elongating sites. The theory proposed assumes that filaments under sonication are maintained at a constant length by the constant input of energy. The data obtained for the reversible polymerization of ADP-actin under sonication have been successfully analyzed according to the proposed model and, therefore, validate the model. The results obtained for the polymerization of ATP-actin under sonication demonstrate the involvement of ATP hydrolysis in the polymerization process. At high actin concentration, polymerization was fast enough, as compared to ATP hydrolysis on the F-actin, to obtain completion of the reversible polymerization of ATP-actin before significant hydrolysis of ATP occurred. A critical concentration of 3 microM was determined as the ratio of the dissociation and association rate constants for the interaction of ATP-actin with the ATP filament ends in 1 mM MgCl2, 0.2 mM ATP. The plot of the rate of elongation of filaments versus actin monomer concentration exhibited an upward deviation at high actin concentration that is consistent with this result. The fact that F-actin at steady state is more stable than the ATP-F-actin polymer at equilibrium suggests that the interaction between ADP-actin and ATP-actin subunits at the end of the ATP-capped filament is much stronger than the interaction between two ATP-actin subunits.     

Models for the length distributions of actin filaments: II. Polymerization and fragmentation by gelsolin acting together

In a previous paper, we studied elementary models for polymerization, depolymerization, and fragmentation of actin filaments (Edelstein-Keshet and Ermentrout, 1998, Bull. Math. Biol. 60, 449–475). When these processes act together, more complicated dynamics occur. We concentrate on a particular case study, using the actin-fragmenting protein gelsolin. A set of biological parameter values (drawn from the experimental literature) is used in computer simulations of the kinetics of gelsolin-mediated actin filament fragmentation.     

Kinetic analysis of actin assembly suggests that tropomyosin inhibits spontaneous fragmentation of actin filaments

The time-course of actin assembly was measured in the absence and in the presence of tropomyosin. The polymerization was followed by the fluorescence enhancement of a 7-chloro-4-nitrobenzeno-2-oxa-1,3-diazole label attached to actin molecules or by light-scattering. The kinetic curves measured in the absence and in the presence of tropomyosin revealed characteristic differences. Tropomyosin was found to retard actin polymerization and to cause the final constant actin monomer concentration to be reached slowly. In the absence of tropomyosin, the final constant actin monomer concentration was approached considerably faster. The time-course of polymerization was interpreted quantitatively in terms of inhibition of actin filament fragmentation by tropomyosin molecules bound along the filaments. Within the limits of this model, actin monomers are consumed slowly in the presence of tropomyosin because the creation of new filament ends by spontaneous fragmentation is inhibited by tropomyosin.     

Xenopus actin-interacting protein 1 (XAip1) enhances cofilin fragmentation of filaments by capping filament ends

Xenopus actin-interacting protein 1 (XAip1) is thought to promote fragmentation of actin filaments by cofilin. To examine the mechanism of XAip1, we measured polymer lengths by fluorescence microscopy and the concentration of filament ends with an elongation assay. Cofilin creates ends by severing actin filaments. XAip1 alone does not sever actin filaments or prevent annealing/redistribution of mechanically severed filaments and has no effect on the concentration of ends available for subunit addition. In the presence of XAip1, the apparent filament fragmentation by cofilin is enhanced, but XAip1 reduces rather than increases the concentration of ends capable of adding subunits. Electron microscopy with gold-labeled antibodies showed that a low concentration of XAip1 bound preferentially to one end of the filament. A high concentration of XAip1 bound along the length of the filament. In the presence of gelsolin-actin to cap filament barbed ends, XAip1 does not enhance cofilin activity. We conclude that XAip1 caps the barbed end of filaments severed by cofilin. This capping blocks annealing and depolymerization and allows more extensive severing by cofilin.     

Ca2+ control of actin filament length. Effects of macrophage gelsolin on actin polymerization

Gelsolin complexes with calcium (gelsolin-Ca2+) binds to the ends of actin filaments to which monomers add preferentially during elongation. It forms a stable complex with actin in a low ionic strength solution which does not normally favor the polymerization of actin. Gelsolin-Ca2+ increases the rate of nucleation of actin which precedes polymerization, but decreases the rate of elongation of the filaments. The final average length of filaments formed in the presence of gelsolin-Ca2+ is shorter and the equilibrium monomer concentration increases relative to actin polymerized in the absence of gelsolin-Ca2+. Gelsolin-Ca2+ also increases the number of actin filaments because the magnitude of the increase in monomer concentration is disproportionately small compared with the reduction in polymer length. In these respects, the population of actin filaments formed during polymerization in the presence of gelsolin-Ca2+ is similar to that resulting from the action of gelsolin on previously assembled actin filaments (Yin, H. L., Zaner, K. S., and Stossel, T. P. (1980) J. Biol. Chem. 255, 9494-9500). The calcium-dependent shortening of ects, the population of actin filaments formed during polymerization in the presence of gelsolin-Ca2+ is similar to that resulting from the action of gelsolin on previously assembled actin filaments (Yin, H. L., Zaner, K. S., and Stossel, T. P. (1980) J. Biol. Chem. 255, 9494-9500). The calcium-dependent shortening of ects, the population of actin filaments formed during polymerization in the presence of gelsolin-Ca2+ is similar to that resulting from the action of gelsolin on previously assembled actin filaments (Yin, H. L., Zaner, K. S., and Stossel, T. P. (1980) J. Biol. Chem. 255, 9494-9500). The calcium-dependent shortening of actin filaments is the primary mechanism for the dissolution of an actin gel by gelsolin. Therefore, the ability of gelsolin to produce short filaments irrespective of the initial state of assembly of the actin offers flexibility for controlling the network structure of the cytoplasm in which either the monomeric or polymeric form of actin molecules might predominate at different times.     

A model for actin-filament length distribution in a lamellipod

A mathematical model is derived to describe the distributions of lengths of cytoskeletal actin filaments, along a 1 D transect of the lamellipod (or along the axis of a filopod) in an animal cell. We use the facts that actin filament barbed ends are aligned towards the cell membrane and that these ends grow rapidly in the presence of actin monomer as long as they are uncapped. Once a barbed end is capped, its filament tends to be degraded by fragmentation or depolymerization. Both the growth (by polymerization) and the fragmentation by actin-cutting agents are depicted in the model, which takes into account the dependence of cutting probability on the position along a filament. It is assumed that barbed ends are capped rapidly away from the cell membrane. The model consists of a system of discrete-integro-PDE's that describe the densities of barbed filament ends as a function of spatial position and length of their actin filament “tails”. The population of capped barbed ends and their trailing filaments is similarly represented. This formulation allows us to investigate hypotheses about the fragmentation and polymerization of filaments in a caricature of the lamellipod and compare theoretical and observed actin density profiles. Received: 19 May 2000 / Revised version: 12 March 2001 / Published online: 19 September 2001     

Stochastic simulation of actin dynamics reveals the role of annealing and fragmentation

Recent observations of F-actin dynamics call for theoretical models to interpret and understand the quantitative data. A number of existing models rely on simplifications and do not take into account F-actin fragmentation and annealing. We use Gillespie's algorithm for stochastic simulations of the F-actin dynamics including fragmentation and annealing. The simulations vividly illustrate that fragmentation and annealing have little influence on the shape of the polymerization curve and on nucleotide profiles within filaments but drastically affect the F-actin length distribution, making it exponential. We find that recent surprising measurements of high length diffusivity at the critical concentration cannot be explained by fragmentation and annealing events unless both fragmentation rates and frequency of undetected fragmentation and annealing events are greater than previously thought. The simulations compare well with experimentally measured actin polymerization data and lend additional support to a number of existing theoretical models.     

The Arp2/3 complex branches filament barbed ends: functional antagonism with capping proteins

The Arp2/3 complex is an essential regulator of actin polymerization in response to signalling and generates a dendritic array of filaments in lamellipodia. Here we show that the activated Arp2/3 complex interacts with the barbed ends of filaments to initiate barbed-end branching. Barbed-end branching by Arp2/3 quantitatively accounts for polymerization kinetics and for the length correlation of the branches of filaments observed by electron microscopy. Filament branching is visualized at the surface of Listeria in a reconstituted motility assay. The functional antagonism between the Arp2/3 complex and capping proteins is essential in the maintenance of the steady state of actin assembly and actin-based motility.     

Models for the length distributions of actin filaments: I. Simple polymerization and fragmentation

We studied mathematical models for the length distributions of actin filaments under the effects of polymerization/depolymerization, and fragmentation. In this paper, we emphasize the effects of these two processes acting alone. In this case, simple discrete and continuous models can be derived and solved explicitly (in several special cases), making the problem interesting from a modeling and pedagogical point of view. In a companion paper (Ermentrout and Edelstein-Keshet, 1998, Bull. Math. Biol. 60, 477–503) we investigate what happens when the processes act together, with particular attention to fragmentation by gelsolin, and with a greater level of biological detail.     

Myosin filament polymerization and depolymerization in a model of partial length adaptation in airway smooth muscle

Length adaptation in airway smooth muscle (ASM) is attributed to reorganization of the cytoskeleton, and in particular the contractile elements. However, a constantly changing lung volume with tidal breathing (hence changing ASM length) is likely to restrict full adaptation of ASM for force generation. There is likely to be continuous length adaptation of ASM between states of incomplete or partial length adaption. We propose a new model that assimilates findings on myosin filament polymerization/depolymerization, partial length adaptation, isometric force, and shortening velocity to describe this continuous length adaptation process. In this model, the ASM adapts to an optimal force-generating capacity in a repeating cycle of events. Initially the myosin filament, shortened by prior length changes, associates with two longer actin filaments. The actin filaments are located adjacent to the myosin filaments, such that all myosin heads overlap with actin to permit maximal cross-bridge cycling. Since in this model the actin filaments are usually longer than myosin filaments, the excess length of the actin filament is located randomly with respect to the myosin filament. Once activated, the myosin filament elongates by polymerization along the actin filaments, with the growth limited by the overlap of the actin filaments. During relaxation, the myosin filaments dissociate from the actin filaments, and then the cycle repeats. This process causes a gradual adaptation of force and instantaneous adaptation of shortening velocity. Good agreement is found between model simulations and the experimental data depicting the relationship between force development, myosin filament density, or shortening velocity and length.     

Impact of profilin on actin-bound nucleotide exchange and actin polymerization dynamics

We have investigated the effects of profilin on nucleotide binding to actin and on steady state actin polymerization. The rate constants for the dissociation of ATP and ADP from monomeric Mg-actin at physiological conditions are 0.003 and 0.009 s-1, respectively. Profilin increases these dissociation rate constants to 0.08 s-1 for MgATP-actin and 1.4 s-1 for MgADP-actin. Thus, profilin can increase the rate of exchange of actin-bound ADP for ATP by 140-fold. The affinity of profilin for monomeric actin is found to be similar for MgATP-actin and MgADP-actin. Continuous sonication was used to allow study of solutions having sustained high filament end concentrations. During sonication at steady state, F-actin depolymerizes toward the critical concentration of ADP-actin [Pantaloni, D., et al. (1984)J. Biol. Chem. 259, 6274-6283], our analysis indicates that under these conditions a significant number of filaments contain terminal ADP-actin subunits. Addition of profilin to this system increases the polymer concentration and increases the steady state ATPase activity during sonication. These data are explained by the fast exchange of ATP for ADP on the profilin-ADP-actin complex, resulting in rapid ATP-actin regeneration. An important function of profilin may be to provide the growing ends of filaments with ATP-actin during periods when the monomer cycling rate exceeds the intrinsic nucleotide exchange rate of monomeric actin.     

Kinetic analysis of F-actin depolymerization in polymorphonuclear leukocyte lysates indicates that chemoattractant stimulation increases actin filament number without altering the filament length distribution

The rate of filamentous actin (F-actin) depolymerization is proportional to the number of filaments depolarizing and changes in the rate are proportional to changes in filament number. To determine the number and length of actin filaments in polymorphonuclear leukocytes and the change in filament number and length that occurs during the increase in F-actin upon chemoattractant stimulation, the time course of cellular F-actin depolymerization in lysates of control and peptide-stimulated cells was examined. F-actin was quantified by the TRITC-labeled phalloidin staining of pelletable actin. Lysis in 1.2 M KCl and 10 microM DNase I minimized the effects of F-actin binding proteins and G-actin, respectively, on the kinetics of depolymerization. To determine filament number and length from a depolymerization time course, depolymerization kinetics must be limited by the actin monomer dissociation rate. Comparison of time courses of depolymerization in the presence (pointed ends free) or absence (barbed and pointed ends free) of cytochalasin suggested depolymerization occurred from both ends of the filament and that monomer dissociation was rate limiting. Control cells had 1.7 +/- 0.4 x 10(5) filaments with an average length of 0.29 +/- 0.09 microns. Chemo-attractant stimulation for 90 s at room temperature with 0.02 microM N-formylnorleucylleucylphenylalanine caused a twofold increase in F-actin and about a two-fold increase in the total number of actin filaments to 4.0 +/- 0.5 x 10(5) filaments with an average length of 0.27 +/- 0.07 microns. In both cases, most (approximately 80%) of the filaments were quite short (less than or equal to 0.18 micron). The length distributions of actin filaments in stimulated and control cells were similar.     

Purification and characterization of actophorin, a new 15,000-dalton actin-binding protein from Acanthamoeba castellanii

Actophorin is a new actin-binding protein from Acanthamoeba castellanii that consists of a single polypeptide with a molecular weight of 15,000. The isoelectric point is 6.1, and amino acid analysis shows an excess of acidic residues over basic residues. The phosphate content is less than 0.2 mol/mol. There is 0.4 +/- 0.1 mg of actophorin/g of cells, so that the molar ratio of actin to actophorin is about 10:1 in the cell. Unique two-dimensional maps of tryptic and chymotryptic peptides and complete absence of antibody cross-reactivity show that Acanthamoeba actophorin, profilin, capping protein, and actin are separate gene products with minimal homology. Actophorin has features of both an actin monomer-binding protein and an actin filament-severing protein. Actophorin reduces the extent of actin polymerization at steady state in a concentration-dependent fashion and forms a complex with pyrene-labeled actin that has spectral properties of unpolymerized actin. During ultracentrifugation a complex of actophorin and actin sediments more rapidly than either actin monomers or actophorin. Although actophorin inhibits elongation at both ends of actin filaments, it accelerates the late stage of spontaneous polymerization like mechanical shearing and theoretical predictions of polymer fragmentation. Low concentrations of actophorin decrease the length and the low shear viscosity of actin filaments. High concentrations cause preformed filaments to shorten rapidly. Ca2+ is not required for any of these effects. Muscle and amoeba actin are equally sensitive to actophorin.     

Interaction of microtubule-associated proteins with actin filaments. Studies using the fluorescence-photobleaching recovery technique

The interaction of microtubule-associated proteins with actin filaments has been investigated by measuring the diffusion coefficient of either the filament or the microtubule-associated proteins. Experiments were performed using the technique of fluorescence photobleaching recovery with actin labeled with iodoacetamidotetramethyl rhodamine or microtubule-associated proteins labeled with iodoacetamidofluorescein. Actin filaments composed of pure rhodamine-labeled actin are not immobilized under a variety of conditions (Tait, J. F., and Frieden, C. (1982c) Biochemistry 21, 6046-6053). We find that addition of microtubule-associated proteins to rhodamine-labeled actin in a ratio as low as 1:1000 can cause immobilization, presumably cross-linking actin into a network of nondiffusible filaments. Immobilization occurs after polymerization is complete, suggesting either a length redistribution of actin filaments, a redistribution of the cross-links between filaments, or the slow addition of actin filaments to other filaments via the microtubule-associated protein. Experiments using fluorescein-labeled microtubule-associated proteins show that these proteins are bound to actin filaments as they are formed and that binding depended on actin concentration, indicating that there are a number of binding sites on the actin filaments. However, while the actin filaments become completely immobilized, the microtubule-associated proteins become only partially immobilized suggesting at least two different classes of binding affinities. The large peptide obtained from trypsin-treated fluorescein-labeled microtubule-associated proteins is not able to immobilize actin filaments since it does not bind to the filaments.     

Study of a protein complex from the brain which reduces actin viscosity. II. The complex inhibits elongation of actin filaments at the end preferable for polymerization and fragments the filaments

Functional properties of the protein complex from bovine brain that shortens actin filaments are described. In the presence of Ca2+ complex shortens actin filaments and increases the initial rate of actin polymerization. In the absence of free calcium ions the complex loses its accelerating effect on actin polymerization, but still possesses actin filament shortening activity. Neither phalloidin nor tropomyosin prevent the shortening of actin filaments induced by the protein complex. Therefore the protein complex causes the fragmentation of actin filament. The data on actin polymerization in the presence of F-actin nuclei have indicated that the protein complex inhibits the elongation step of actin polymerization. The analysis of elongation in the presence of both the protein complex and cytochalasin D has demonstrated that the inhibition occurs on the fast-growing end of actin filaments.     

Effect of short-range forces on the length distribution of fibrous cytoskeletal proteins

The length distribution of cytoskeletal filaments is an important physical parameter, which can modulate physiological cell functions. In both eukaryotic and prokaryotic cells various biological cytoskeletal polymers form supramolecular structures due to short-range forces induced mainly by molecular crowding or cross linking proteins, but their in vivo length distribution remains difficult to measure. In general, based on experimental evidence and mathematical modeling of actin filaments in aqueous solutions, the steady state length distribution of fibrous proteins is believed to be exponential. We performed in vitro TIRF- and electron-microscopy to demonstrate that in the presence of short-range forces, which are an integral part of any living cell, the steady state length distributions of the eukaryotic cytoskeletal biopolymer actin, its prokaryotic homolog ParM and microtubule homolog FtsZ deviate from the classical exponential and are either double-exponential or Gaussian, as recent theoretical modeling predicts. Double exponential or Gaussian distributions opposed to exponential can change for example the visco-elastic properties of actin networks within the cell, influence cell motility by decreasing the amount of free ends at the leading edge of the cell or effect the assembly of FtsZ into the bacterial Z-ring thus modulating membrane constriction.     

Direct demonstration of actin filament annealing in vitro

Direct electron microscopic examination confirms that short actin filaments rapidly anneal end-to-end in vitro, leading over time to an increase in filament length at steady state. During annealing of mixtures of native unlabeled filaments and glutaraldehyde-fixed filaments labeled with myosin subfragment-1, the structural polarity within heteropolymers is conserved absolutely. Annealing does not appear to require either ATP hydrolysis or the presence of exogenous actin monomers, suggesting that joining occurs through the direct association of filament ends. During recovery from sonication the initial rate of annealing is consistent with a second-order reaction involving the collision of two filament ends with an apparent annealing rate constant of 10(7) M-1s-1. This rapid phase lasts less than 10 s and is followed by a slow phase lasting minutes to hours. Annealing is calculated to contribute minimally to filament elongation during the initial stages of self-assembly. However, the rapid rate of annealing of sonicated fixed filaments observed in vitro suggests that it may be an efficient mechanism for repairing breaks in filaments and that annealing together with polymer-severing mechanisms may contribute significantly to the dynamics and function of actin filaments in vivo.     

Mechanism of action of cytochalasin B on actin

Substoichiometric cytochalasin B (CB) inhibits both the rate of actin polymerization and the interaction of actin filaments in solution. The polymerization rate is reduced by inhibition of actin monomer addition to the "barbed" end of the filaments where monomers normally add more rapidly. 2 microM CB reduces the polymerization rate by up to 90%, but has little effect on the rate of monomer addition at the slow ("pointed") end of the filaments and no effect on the rate of filament annealing. Under most ionic conditions tested, 2 microM CB reduces the steady state high shear viscosity by 10-20% and increases the steady state monomer concentration by a factor of 2.5 or less. In addition to the effects on the polymerization process, 2 microM CB strongly reduces the low shear viscosity of actin filaments alone and actin filaments cross-linked by a variety of macromolecules. This may be due to inhibition of actin filament-filament interactions which normally contribute to network formation. Since the inhibition of monomer addition and of actin filament network formation have approximately the same CB concentration dependence, a common CB binding site, probably the barbed end of the filament, may be responsible for both effects.     

Annealing accounts for the length of actin filaments formed by spontaneous polymerization

We measured the lengths of actin filaments formed by spontaneous polymerization of highly purified actin monomers by fluorescence microscopy after labeling with rhodamine-phalloidin. The length distributions are exponential with a mean of approximately 7 microm (2600 subunits). This length is independent of the initial concentration of actin monomer, an observation inconsistent with a simple nucleation-elongation mechanism. However, with the addition of physically reasonable rates of filament annealing and fragmenting, a nucleation-elongation mechanism can reproduce the observed average length of filaments in two types of experiments: 1) filaments formed from a wide range of highly purified actin monomer concentrations, and 2) filaments formed from 24 microM actin over a range of CapZ concentrations.     

Kinetic mechanism of end-to-end annealing of actin filaments

We investigated the effect of actin filament length and capping protein on the rate of end-to-end annealing of actin filaments. Long filaments were fragmented by shearing and allowed to recover. Stabilizing filaments with phalloidin in most experiments eliminated any contribution of subunit dissociation and association to the redistribution of lengths but did not affect the results. Two different assays, fluorescence microscopy to measure filament lengths and polymerization to measure concentration of barbed filament ends, gave the same time-course of annealing. The rate of annealing declines with time as the average filament length increases. Longer filaments also anneal slower than short filaments. The second-order annealing rate constant is inversely proportional to mean polymer length with a value of 1.1 mM(-1) s(-1)/length in subunits. Capping protein slows but does not prevent annealing. Annealing is a highly favorable reaction with a strong influence on the length of polymers produced by spontaneous polymerization and should be considered in thinking about polymer dynamics in cells.