Counterion-induced actin ring formation

Actin filaments form rings and loops when > 20 mM divalent cations are added to very dilute solutions of phalloidin-stabilized filamentous actin (F-actin). Some rings consist of very long single actin filaments partially overlapping at their ends, and others are formed by small numbers of filaments associated laterally. In some cases, undulations of the rings are observed with amplitudes and dynamics similar to those of the thermal motions of single actin filaments. Lariat-shaped aggregates also co-exist with rings and rodlike bundles. These polyvalent cation-induced actin rings are analogous to the toroids of DNA formed by addition of polyvalent cations, but the much larger diameter of actin rings reflects the greater bending stiffness of F-actin. Actin rings can also be formed by addition of streptavidin to crosslink sparsely biotinylated F-actin at very low concentrations. The energy of bending in a ring, calculated from the persistence length of F-actin and the ring diameter, provides an estimate for the adhesion energy mediated by the multivalent counterions, or due to the streptavidin-biotin bonds, required to keep the ring closed.     

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.     

5-Fluorouracil interferes with actin organization, stress fiber formation and cell migration in corneal endothelial cells during wound repair along the natural basement membrane

Corneal endothelial cells respond to a circular freeze wound by undergoing actin cytoskeletal reorganization that is mainly characterized by the disappearance of circumferential microfilament bundles (CMBs) and the subsequent appearance of distinct stress fibers. This cytoskeletal rearrangement is associated with changes in cell shape as migrating cells lose their polyhedral appearance, spread out, and assume a stellate morphology with cell processes extending outward into the injured area. We report here that in the presence of low concentrations (0.01-0.l mM) of the anti-metabolite 5-fluorouracil (5-FU), characteristic actin organization becomes disrupted and migrating cells do not display elongated processes typical of control tissues and translocation into the injury zone is retarded, but not inhibited. Rhodamine phalloidin staining revealed no evidence of stress fiber formation. A higher concentration of 5-FU (1.0 mM) not only prevented formation of discernible stress fibers but also resulted in a more restricted cell movement during wound repair. That this was not a cytotoxic effect was demonstrated by transferring tissues back into standard medium allowing endothelia to reinitiate migration and undergo complete wound healing by 72 h post-transfer. Overnight incubation of endothelia in 4 muM phallacidin resulted in limited CMB disruption the extent of which was dependent on the 5-FU concentration. The effects of 5-FU on the actin cytoskeleton are reversible and by 24 h after placing treated endothelia into medium without 5-FU, actin begins to become re-established and by 48 h microfilament patterns in the tissue resemble those of non-treated endothelia. Similarly, when non-injured tissues are cultured in the presence of 5-FU for 24 h, subsequently injured and returned to standard medium, they exhibit no stress fibers when observed at 24 h post-wounding. However, by 48 h post-injury these cells now display stress fibers and extend processes into the wound area. Biochemical studies on isolated muscle actin demonstrated that actin polymerization is unaffected in the presence of either 0.01 or 1 mM 5-FU as determined by the F-actin sedimentation and falling ball viscosity techniques. Thus, the mechanism(s) by which 5-FU exerts its actions on the actin cytoskeleton appears to be one of an indirect nature.     

Cytoskeletal dynamics in rabbit synovial fibroblasts: I. Effects of acrylamide on intermediate filaments and microfilaments

Rabbit synovial fibroblasts respond to changes in cell shape and cytoskeletal architecture by altering specific gene expression. We have tested the ability of acrylamide, a neurotoxin that alters the distribution of intermediate filaments in cultured PtK1 cells, to induce metalloprotease expression in synovial fibroblasts. Cells treated with 2-20 mM acrylamide for 5 to 24 h underwent shape changes similar to cells treated with the tumor promoter phorbol myristate acetate. Intermediate filaments visualized with anti-vimentin antibodies did not collapse into a perinuclear cap in these rounded cells, but were still present in the extended cell processes. Unexpectedly, when actin was visualized in acrylamide-treated cells, extensive dissociation and clumping of microfilaments was observed. Concentrations of acrylamide greater than 10 mM were cytotoxic, but cells recovered completely after 24 h incubation with 5 mM acrylamide. Like other agents that alter cell shape and actin distribution in synovial fibroblasts, acrylamide also induced expression of the secreted metalloprotease collagenase. Although some recent evidence suggests that acrylamide may be able to exert its collagenase-inducing effects extracellularly, perhaps through transmembrane matrix receptors, our observation that this neurotoxin dramatically alters protein synthesis in synovial fibroblasts suggests that direct effects on cell metabolism may also play a role in acute acrylamide intoxication.     

Interaction of plasma gelsolin with G-actin and F-actin in the presence and absence of calcium ions

Plasma gelsolin formed a very tight 1:2 complex with G-actin in the presence of Ca2+, but no interaction between gelsolin and G-actin was detected in the presence of excess EGTA. However, the 1:2 complex dissociated into a 1:1 gelsolin:actin complex and monomeric actin when excess EGTA was added. Plasma gelsolin bound tightly to the barbed ends of actin filaments and also severed filaments in the presence of Ca2+ and bound weakly to the filament barbed end in the presence of EGTA. The 1:2 gelsolin-actin complex bound to the barbed ends of filaments but did not sever them. By blocking the barbed end of filaments with plasma gelsolin, we determined the critical concentration at the pointed end in 1 mM MgCl2 and 0.2 mM ATP to be 4 microM. The dissociation rate constant for ADP-G-actin from the pointed end was estimated to be about 0.4 s-1 and the association rate constant to be about 5 X 10(4) M-1 s-1. Finally, we obtained evidence that plasma gelsolin accelerates but does not bypass the nucleation step and, therefore, that the concentration of gelsolin does not directly determine the concentration of filaments polymerized in its presence. Thus, gelsolin-capped filaments may not provide an absolutely reliable method for determining the rate constant for the association of ATP-G-actin at the pointed ends of filaments, but a reasonable estimate would be 1 X 10(5) M-1 s-1 in 1 mM MgCl2 and 0.2 mM ATP.     

Models of the Collective Behavior of Proteins in Cells: Tubulin, Actin and Motor Proteins

One of the most important issues of molecular biophysics is the complex and multifunctional behavior of the cell's cytoskeleton. Interiors of living cells are structurally organized by the cytoskeleton networks of filamentous protein polymers: microtubules, actin and intermediate filaments with motor proteins providing force and directionality needed for transport processes. Microtubules (MT's) take active part in material transport within the cell, constitute the most rigid elements of the cell and hence found many uses in cell motility (e.g. flagella andcilia). At present there is, however, no quantitatively predictable explanation of how these important phenomena are orchestrated at a molecular level. Moreover, microtubules have been demonstrated to self-organize leading to pattern formation. We discuss here several models which attempt to shed light on the assembly of microtubules and their interactions with motor proteins. Subsequently, an overview of actin filaments and their properties isgiven with particular emphasis on actin assembly processes. The lengths of actin filaments have been reported that were formed by spontaneous polymerization of highly purified actin monomers after labeling with rhodamine-phalloidin. The length distributions are exponential with a mean of about 7 μm. 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 mM actin over a range of CapZ concentrations. In the final part of the paper we briefly review the stochastic models used to describe the motion of motor proteins on protein filaments. The vast majority of these models are based on ratchet potentials with the presence of thermal noise and forcing due to ATP binding and a subsequent hydrolysis. Many outstanding questions remain to be quantitatively addressed on a molecular level in order to explain the structure-to-function relationship for the key elements of the cytoskeleton discussed in this review. This revised version was published online in July 2006 with corrections to the Cover Date.     

Benzamide-induced changes in the actin cytoskeleton in human skin fibroblasts.

The incubation of human skin fibroblasts in the presence of 10 mM benzamide in Joklik's modification of Eagle's Minimal Essential Medium caused an extensive reorganization of actin filaments. The disappearance of stress fibers and changes in cell morphology were observed, whereas no changes in the microtubule architecture were noticed. The observed effects appeared fully reversible within 3 hours after the removal of benzamide. The results are discussed in relation to the two known activities of benzamide as an anaesthetic and an inhibitor of ADP-ribosylation.     

Spore and crystal formation inBacillus thuringiensis var.thuringiensis during growth in cystine and cysteine

The effect of the addition of different concentratons of cystine and cysteine on sporulation and parasporal crystal formation inBacillus thuringiensis var.thuringiensis was studied. The effect was well pronounced when the cystine/cysteine additions were made after the stationary phase. Heat stable spores and crystals were formed when the culture was provided with a low concentration of cystine/cysteine (0.05 per cent w/v). At a moderate concentration of cystine or cysteine (0.15%), only heat labile spores were formed without the production of the crystal. When the cystine/cysteine concentration was high (0.25%), spore and crystal formation were completely inhibited. Partial reversal of inhibition of sporulation was brought about by sodium sulphate or Zinc sulphate and lead, copper, cadmium or cobalt acetate at 0.2 mM or at 0.2% of sodium or potassium pyruvate, citrate, cisaconitate, oxalosuccinate, ∞ -keto-glutarate, succinate, fumarate, malate, or oxalacetate. Glutamate (0.2%) overcame the inhibitory effect of cystine/cysteine completely. The structural changes observed using phase contrast microscopy were dependent upon the concentration of cystine/cysteine.     

A possible role for actin dots in the formation of the contractile ring in the ultra-micro algaCyanidium caldarium RK-1

Summary In the primitive red algaCyanidium caldarium RK-1, cytokinesis is controlled by a simple contractile ring, as in animal cells. To clarify the mechanism of formation of the contractile ring, we isolated actin genes and performed an immunocytological study.C. caldarium RK-1 has two actin genes encoding proteins with the same sequence of 377 amino acids. The primary structure indicated that the actin molecules ofC. caldarium RK-1 are typical, despite the fact that the organism is considered to be phylogenetically primitive. We prepared antiserum against aC. caldarium RK-1 actin fusion protein and indirect immunofluorescence staining was performed. In interphase cells, many actin dots were observed in the cytoplasm but none at the future cleavage plane. Prior to cytokinesis, some of these dots appeared and became aligned along the equatorial plane. At the same time, a thin immature contractile ring was observed to appear to be formed by connection of the aligned actin dots. This immature contractile ring thickened to nearly its maximum size by the time cytokinesis began. The formation of the contractile ring seemed to be a result of de novo assembly of actin monomers, rather than a result of the accumulation and bundling of pre-existing actin filaments. During the constriction of the contractile ring, no actin dots were observed in the cytoplasm. These observations suggest that actin dots are responsible for the formation of the contractile ring, but are not necessary for its disintegration. Furthermore, immunogold localization specific for actin revealed at electron microscopy level that fine filaments running just beneath the cleavage furrow are, in fact, actin filaments.Abbreviations ORF open reading frame - IPTG isopropyl--D(–)-thiogalactopyranoside - SDS-PAGE sodium dodecyl sulphate-poly-acrylamide gel electrophoresis - DAPI 4,6-diamidino-2-phenylindole     

Morphology and Physiology of Lyngbya nigra with Reference to Copper Toxicity

The effect of copper sulphate on morphology and physiology of Lyngbya nigra has been studied. The growth was inhibited in all treatments (0.4 to 80.0 μM) of copper sulphate. There were no apparent morphological changes up to 0.8 μM and during the first two days of treatment even in the higher concentrations of copper sulphate. In concentrations above 0.8 μM the first symptom of toxicity was the formation of separation discs in large numbers. The trichomes contracted longitudinally and the cells became swollen and constricted at the cross walls. The cells also became yellowish due to loss of photosynthetic pigments. Finally, in 4 μM and above, vacuoles appeared in large number indicating the moribund state of the cells. Copper sulphate increased respiration at 2 μM, and optimum effect was observed in 8 μM after 96 h. Inhibition of photosynthesis was detectable in 0.8 μM, and 100% inhibition took place in 8 μM after 96 h. In higher concentrations the effect was immediate, and a conspicuous inhibition of photosynthesis could be observed within 10 min. The copper content of the alga increased with increased concentration of copper sulphate while potassium content decreased. With rise in outside concentrations of copper, there was a comparatively great increase of absorption in 2 and 4 μM, while further increases were gradually less. The observations indicate that changes in the physiological activity of the alga under treatment are closely interlinked with marked changes in morphology.     

Observation of the three-dimensional structure of actin bundles formed with polycations

Three-dimensional structures of actin bundles formed with polycations were observed by using transmission electron microtomography and atomic force microscopy. We found, for the first time, that the cross-sectional morphology of actin bundles depends on the polycation species and ionic strength, while it is insensitive to the degree of polymerization and concentration of polycation. Actin bundles formed with poly-N-[3-(dimethylamino)propyl] acrylamide methyl chloride quaternary show a ribbon-like cross-sectional morphology in low salt concentrations that changes to cylindrical cross-sectional morphology with hexagonal packing of the actin filaments in high salt concentrations. Contrastingly, actin bundles formed with poly-L-lysine show triangular cross-sectional morphology with hexagonal packing of the actin filaments. These variations in cross-sectional morphology are discussed in terms of anisotropy in the electrostatic energy barrier.     

Supramolecular forms of actin from amoebae of Dictyostelium discoideum.

Actin purified from amoebae of Dictyostelium discoideum polymerizes into filaments at 24 degrees upon addition of KCl, as judged by a change in optical density at 232 nm and by electron microscopy. The rate and extent of formation of this supramolecular assembly and the optimal KCl concentrations (0.1 M) for assembly are similar to those of striated muscle actin. The apparent equilibrium constant for the monomer-polymer transition is 1.3 muM for both Dictyostelium and muscle actin. Although assembly of highly purified Dictyostelium actin monomers into individual actin filaments resembles that of muscle actin, Dictyostelium actin but not muscle actin was observed to assemble into two-dimensional nets in 10 mM CaCl2. The Dictyostelium actin also forms filament bundles which are 0.1 mum in diameter and which assemble in the presence of 5 mM MgCl2. These bundles formed from partially purified Dictyostelium actin preparations but not from highly purified preparations, suggesting that their formation may depend on the presence of another component. These actin bundles reconstituted in vitro resemble the actin-containing bundles found in situ by microscopy in many non-muscle cells.     

Actin in erythrocyte ghosts and its association with spectrin. Evidence for a nonfilamentous form of these two molecules in situ

Actin was isolated from erythrocyte ghosts. It is identical to muscle actin in its molecular weight, net charge, ability to polymerize into filaments with the double helical morphology, and its decoration with heavy meromyosin (HMM). when erythrocyte ghosts are incubated in 0.1 mM EDTA, actin and spectrin are solubilized. Spectrin has a larger molecular weight than muscle myosin. When salt is added to the EDTA extract, a branching filamentous polymer is formed. However, when muscle actin and the EDTA extract are mixed together in the presence of salt, the viscosity achieved is less than the viscosity of the solution if spectrin is omitted. Thus, spectrin seems to inhibit the polymerization of actin. If the actin is already polymerized, the addition of spectrin increases the viscosity of the solution, presumably by cross-linking the actin filaments. The addition of HMM of trypsin to erythrocyte ghosts results in filament formation in situ. These agents apparently act by detaching erythrocyte actin from spectrin, thereby allowing the polmerization of one or both proteins to occur. Since filaments are not present in untreated erythrocyte ghosts, we conclude that erythrocyte actin and spectrin associate to form an anastomosing network beneath the erythrocyte membrane. This network presumably functions in restricting the lateral movement of membrane-penetrating particles.     

Under physiological conditions actin disassembles slowly from the nonpreferred end of an actin filament

Incubation of the isolated acrosomal bundles of Limulus sperm with skeletal muscle actin results in assembly of actin onto both ends of the bundles. Because of the taper of these cross-linked bundles of actin filaments, one can distinguish directly the preferred end for assembly from the nonpreferred end. Loss of growth with time from the nonpreferred end was directly assessed by electron microscopy and found to be dependent upon salt concentration. Under physiological conditions (100 mM KCl, 1 mM MgCl2) and excess ATP (0.5 mM), depolymerization of the newly assembled actin filaments at the nonpreferred end over an 8-h period was 0.024 micron/h. Thus, even after 8 h, 63% of the bundles retained significant growth on their nonpreferred ends, the average length being 0.21 micron +/- 0.04. However, in the presence of 1.2 mM CaCl2, disassembly of actin monomers from the nonpreferred end increased substantially. By 8 h, only 7% of the bundles retained any actin growth on the nonpreferred ends, and the depolymerization rate off the nonpreferred end was 0.087 micron/h. From these results we conclude that, in the absence of other cellular factors, disassembly of actin subunits from actin filaments (subunit exchange) is too slow to influence most of the motile events that occur in cells. We discuss how this relates to treadmilling.     

Actin-polyamines interaction: Relationship between physicochemical properties and cytokinesis induction

Turbidimetric experiments show that both biological polyamines, spermidine and spermine, can associate already formed actin filaments. This association takes place within 30 seconds and this result is in agreement with the rate of formation of the contractile ring actin filaments observed in vivo. This highly polymerized state of actin is also induced from monomeric actin by spermidine or spermine. ATP can disorganize this actin association induced from monomeric action or from actin filaments by the action of spermidine or spermine.     

Calcium regulation of cell-cell contact and differentiation of epidermal cells in culture. An ultrastructural study

Calcium modulation of keratinocyte growth in culture was studied by both transmission (TEM) and scanning electron microscopy (SEM). Under standard culture conditions (1.2-1.8 mM calcium), cells were connected by desmosomes and stratified to 4-6 cell layers. Many aspects of in vitro epidermal maturation were analogous to the in vivo process, with formation of keratohyalin granules, loss of nuclei, formation of cornified envelopes and shedding of cornified cells containing keratin filaments. When the medium calcium concentration was lowered to 0.02-0.1 mM, the pattern of keratinocyte growth was strikingly changed. Cells grew as a monolayer with no desmosomal connections and proliferated rapidly, shedding largely non-cornified cells into the medium. Large bundles of keratin filaments were concentrated in the perinuclear cytoplasm. The elevation of extracellular calcium to 1.2 mM induced low calcium keratinocytes to stratify, keratinize and cornify in a manner analogous to that seen when plated in standard calcium medium. The earliest calcium-induced ultrastructural change was the asymmetric formation of desmosomes between adjacent cells. Desmosomal plaques with associated tonofilaments were observed 5 min after calcium addition; symmetric desmosomes were formed within 1-2 h. This system is presented as a useful model for the study of the regulation of desmosome assembly and disassembly.     

Preparation of membrane-bound and of solubilized (Na+ + K+)-ATPase from rectal glands of Squalus acanthias. The effect of preparative procedures on purity, specific and molar activity.

The effect of spectrin on the polymerization of muscle actin has been investigated by hydrodynamic methods and electron microscopy. Spectrin markedly accelerated polymerization of actin. The effect was more easily observed in lower concentrations of KCl (e.g. 24 mM) where spontaneous polymerization was negligibly small. Similarly large acceleration was observed for polymerization in MgCl2 or CaCl2. The rate of polymerization of actin was proportionally increased with the concentration of spectrin added to a fixed concentration of action. The stationary level of specific viscosity also increased with the spectrin concentration, but at larger concentrations it became smaller. The flow birefringence and electron microscope measurements indicated that actin polymers formed under the influence of spectrin were shorter than those of control F-actin filaments. The structural viscosity and electron microscope observations suggested that the interaction between F-actin fibers was not increased by spectrin. These data strongly suggest a seeding role of spectrin in the polymerization of actin. Spectrin accelerates formation of the nuclei for polymerization. The more the nuclei are formed, the larger the number of the grown polymers are and this leads to rapid formation of shorter polymers since the amount of actin is limited. The acceleration activity was found only in freshly prepared spectrin from fresh ghosts taken from freshly drawn blood.     

The requirements for bicarbonate and metabolism of the inducer during germ tube formation by Candida albicans

Factors affecting germ tube formation in Candida albicans at suboptimal temperatures were investigated. Candida albicans formed germ tubes between 22 and 30 degrees C in solution when incubated without shaking, in the presence of bicarbonate (2 mg mL-1). Other conditions depended on the inducer used. Proline could induce germ tube formation optimally only when its concentration was between 200 and 400 mM. A concentration of 0.05 mM N-acetylglucosamine was sufficient to induce germ tube formation. N-Acetylglucosamine could induce germ tube formation at 30 but not at 25 degrees C. N-Acetylglucosamine induced germ tube formation was most reproducible when the cells were first starved by incubation in water for 16-24 h at 20 degrees C. Germ tubes induced by proline could be formed at pH values between 3.8 and 9.0 at 30 degrees C, but only between 7.0 and 7.5 at 25 degrees C. The addition of 0.05 to 5 mM glucose to a 5 mM proline induction solution allowed germ tube formation at 30 but not at 25 degrees C. Glucose (400 mM) did not suppress germ tube formation at 30 degrees C but only 5 mM was sufficient to cause a 65% suppression at 25 degrees C. The results show the importance of CO2 and (or) bicarbonate to the induction of germ tube formation and are consistent with the metabolism of the inducer.     

Mechanism of the formation of contractile ring in dividing cultured animal cells. I. Recruitment of preexisting actin filaments into the cleavage furrow

Cytokinesis of animal cells involves the formation of the circumferential actin filament bundle (contractile ring) along the equatorial plane. To analyze the assembly mechanism of the contractile ring, we microinjected a small amount of rhodamine-labeled phalloidin (rh-pha) or rhodamine-labeled actin (rh-actin) into dividing normal rat kidney cells. rh-pha was microinjected during prometaphase or metaphase to label actin filaments that were present at that stage. As mitosis proceeded into anaphase, the labeled filaments became associated with the cortex of the cell. During cytokinesis, rh-pha was depleted from polar regions and became highly concentrated into the equatorial region. The distribution of total actin filaments, as revealed by staining the whole cell with fluorescein phalloidin, showed a much less pronounced difference between the polar and the equatorial regions. The sites of de novo assembly of actin filaments during the formation of the contractile ring were determined by microinjecting rh-actin shortly before cytokinesis, and then extracting and fixing the cell during mid-cytokinesis. Injected rhodamine actin was only slightly concentrated in the contractile ring, as compared to the distribution of total actin filaments. Our results indicate that preexisting actin filaments, probably through movement and reorganization, are used preferentially for the formation of the contractile ring. De novo assembly of filaments, on the other hand, appears to take place preferentially outside the cleavage furrow.     

Polymerization of actin induced by a molar excess of ATP in a low salt buffer.

The polymerization of actin induced by dilution has previously been reported, where a 1000-fold molar excess of ATP over actin resulted when actin was diluted to 4.0 micrograms/ml in low salt buffer A (0.1 mM ATP, 0.1 mM CaCl2, 2 mM Tris-HCl, pH 8.0, 5 mM 2-mercaptoethanol, 1 mM NaN3). Filaments formed by the addition of ATP to a 1000-fold molar excess over actin in buffer B (0.1 mM CaCl2, 2 mM Tris-HCl, pH 8.0, 1 mM NaN3) were then separated by gel-filtration. When ATP was removed from these filaments using Dowex-1, depolymerization occurred. Thus, the reversible polymerization induced by the dilution of actin or by addition of ATP can be ascribed to the binding of ATP at the low affinity site of actin.