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Originally published In Press as doi:10.1074/jbc.M404392200 on June 7, 2004

J. Biol. Chem., Vol. 279, Issue 32, 33519-33527, August 6, 2004
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Effects of Profilin and Thymosin {beta}4 on the Critical Concentration of Actin Demonstrated in Vitro and in Cell Extracts with a Novel Direct Assay*

Elena G. Yarmola and Michael R. Bubb{ddagger}

From the Department of Medicine, University of Florida College of Medicine, Gainesville, Florida 32610 and the Research Service, Malcom Randall Department of Veterans Affairs Medical Center, Gainesville, Florida 32608

Received for publication, April 21, 2004 , and in revised form, May 28, 2004.


   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 EXPERIMENTAL PROCEDURES
 RESULTS AND DISCUSSION
 APPENDIX
 REFERENCES
 
The free actin concentration at steady state, Ac, is a variable that determines how actin regulatory proteins influence the extent of actin polymerization. We describe a novel method employing fluorescence anisotropy to directly measure Ac in any sample after the addition of a trace amount of labeled thymosin {beta}4 or thymosin {beta}4 peptide. Using this assay, we confirm earlier theoretical work on the helical polymerization of actin and confirm the effects of actin filament-stabilizing drugs and capping proteins on Ac, thereby validating the assay. We also confirm a controversial prior observation that profilin lowers the critical concentration of Mg2+-actin. A general mechanism is proposed to explain this effect, and the first quantitative dose-response curve for the effect of profilin on Ac facilitates its evaluation. This mechanism also predicts the effect of profilin on critical concentration in the presence of the limited amount of capping protein, which is the condition often found in cells, and the effect of profilin on critical concentration in cell extracts is demonstrated for the first time. Additionally, nonlinear effects of thymosin {beta}4 on the steady state amount of F-actin are explained by the observed changes in Ac. This assay has potential in vivo applications that complement those demonstrated in vitro.


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
EXPERIMENTAL PROCEDURES
 RESULTS AND DISCUSSION
 APPENDIX
 REFERENCES
 
Total cellular actin is equal to the sum of the concentration of free monomer (the critical concentration, Ac), the concentration of unpolymerized actin sequestered by various actin-binding proteins, and the concentration of actin polymer or F-actin. Changes in Ac induced by actin regulatory proteins influence actin polymer dynamics by an amplification mechanism that results in large changes in the amount of sequestered, unpolymerized actin. Quantitative evaluation of models of cytoskeletal function requires accurate knowledge of the value of Ac. Unfortunately, Ac has not yet been measured in cells and has only been estimated by very indirect methods in cell extracts (1). In vitro methods have been developed that allow for the measurement of F-actin using birefringence (2), viscosity (3), light scattering (4), centrifugation (5), binding of labeled phalloidin (6), or the fluorescence of pyrenyl-labeled actin (7). Other methods such as the DNase I binding assay yield the sum of Ac and an indeterminate fraction of sequestered actin monomer (8). Clever uses of combinations of data have in some cases allowed investigators to subtract F-actin content from total actin and then fractionate the contributions of Ac and monomer sequestration (9, 10), but the results have proven controversial (11, 12).

Based on theoretical considerations, the critical concentration is expected to be equal to the ratio of the rate constants of association and dissociation of actin subunits from actin filaments. Measurement of these rate constants using a method such as electron microscopy can be used to indirectly evaluate Ac, assuming the applicability of the theory (13, 14). However, the participation of actin bound to monomer-sequestering proteins in filament growth, such as occurs with profilin-actin (15, 16), greatly complicates this analysis, because such addition alters the observed rate constants but, in theory, can occur with (9) or without (17) a change in Ac.

The observation that actin monomer-sequestering proteins such as profilin (9) and members of the actobindin family of multirepeated thymosin {beta}4-like sequences (18) may alter Ac is controversial (11), and moreover, postulated mechanisms for this effect have been disputed (11, 12, 19). The participation of profilin (or of proteins in the actobindin family) in barbed end elongation is an independent observation that may occur with or without an effect on Ac. Two basic mechanisms were suggested during the last decade (9, 20).

The hypothesis that profilin could lower Ac by formation of a copolymer of actin monomer and actin in complex with profilin was first suggested in Ref. 20 when it was found that the cross-linked profilin-actin complex could be polymerized into filaments. According to this hypothesis, free actin and profilin-actin complex would both contribute a partial critical concentration driving polymer elongation. Although there is tantalizing crystallographic evidence that a copolymer is possible (21), experimental evidence for copolymerization is mutually exclusive with evidence of barbed end capping by profilin (12, 22, 23). Although incorporation of profilin into actin filaments would be a condition required for the copolymerization model (24), no significant incorporation of profilin into actin filaments was found experimentally when profilin was not covalently cross-linked to actin (20). Instead, there are data that suggest that covalent or other high affinity profilin-actin complexes interfere with actin polymerization (22, 23). The addition of the profilin molecule to the barbed end of the actin filament is often called "capping" because most of the literature agrees that the profilin molecule bound to the barbed end blocks further elongation, that is, profilin must dissociate from the end before the next actin subunit (free, or in complex with profilin) can be added. There is a disagreement in the literature on whether the effect of capping by profilin is significant. Some researchers assume that the affinity of profilin to the barbed end is very low and can be neglected in the modeling of actin polymerization process. Capping by profilin is very different from the capping by gelsolin or Cap Z, because unlike capping proteins that block both elongation and depolymerization, profilin blocks elongation but increases the rate of depolymerization (12, 25).

A hypothesis for coupling ATP hydrolysis to the profilin pathway (9) has been suggested as a possible explanation of profilin effect on actin critical concentration. It implies that barbed end elongation by profilin-actin could lower Ac if the free energy change upon the addition of an actin subunit to F-actin is different when monomer is directly added to the barbed end than when addition of actin monomer occurs via a pathway that includes incorporation of profilin-actin at the barbed end (9, 12). The thermodynamic difference does not have to be large (~ 2 kcal/mol) to explain the existing data but does require direct or indirect coupling of ATP hydrolysis to addition of the profilin-actin complex. Using a novel direct assay, we have obtained the first dose-response curve for the effect of profilin on actin critical concentration. That allowed us to evaluate the hypothesis of coupled ATP hydrolysis as well as an alternative hypothesis for the effect of profilin. We formulate a general description of actin polymerization in the presence of profilin. According to this mechanism, the main effect of profilin is the acceleration of actin polymerization dynamics.


   EXPERIMENTAL PROCEDURES
TOP
 ABSTRACT
 INTRODUCTION
 EXPERIMENTAL PROCEDURES
RESULTS AND DISCUSSION
 APPENDIX
 REFERENCES
 
Proteins and Peptides—Pyrenyl-labeled and unlabeled rabbit skeletal muscle Ca2+-actin, recombinant human profilin, and recombinant rat thymosin {beta}4 (identical in sequence to human) were purified as previously described (26). For labeling with tetramethylrhodamine-5-maleimide (T-6027; Molecular Probes Inc., Eugene, OR), the thymosin {beta}4 cDNA was modified by the addition of a C-terminal cysteine. A truncated {epsilon}-amino rhodamine-labeled peptide (1-25 rhod-t{beta}4 peptide) was produced synthetically with a sequence that corresponds to the N-terminal 25 residues of thymosin {beta}4, SDKPDMAEIEKFDKSKLKKTETQEK-rhodamine. Human recombinant gelsolin was truncated to the N-terminal 406 residues (identified here as gelsolin segment 1-3) prior to expression so as to eliminate the dependence of F-actin binding on calcium (27).

Anisotropy Assay—A standard curve showing the fluorescence anisotropy of a rhodamine-labeled thymosin {beta}4 peptide (0.1 µM) as a function of Mg2+-actin concentration in F buffer (5.0 mM Tris-HCl, 40 mM KCl, 2.0 mM MgCl2, 0.2 mM ATP, 0.2 mM dithiothreitol, 0.1 mM CaCl2, 0.125 mM EGTA, and 0.01% sodium azide, pH 7.8) was generated with vertically excited polarized light at 546 nm in an L or T format steady state fluorimeter. The KCl concentration was 8.0 mM for the experiments employing unlabeled thymosin {beta}4, and in this low salt buffer the standard curve as shown in Fig. 1 yields slightly higher affinity for thymosin {beta}4 and actin with Kd = 0.12 µM relative to 0.2 µM at 40 mM KCl. The horizontal (Ih) and vertical (Iv) components of the emitted light are detected at 568 nm for 0.3-ml samples in glass cuvettes. The fluorescence anisotropy, r, is calculated using r = (Iv - GIh)/(Iv + 2GIh). The G factor is determined for the peptide in solution excited with horizontally polarized light and averaged over ~100 measurements. Bound actin does not change the total fluorescence intensity of the rhodamine-labeled thymosin {beta}4, so the observed anisotropy r is a linear function of the fraction of thymosin {beta}4 that is bound to actin: r = (rbTb + rfTf)/T0, where rf is anisotropy of free thymosin (Tf = [T]), rb is anisotropy of thymosin bound to actin (Tb = [TA]), and T0 = [T] + [TA]. Any sample containing an unknown concentration of free actin (Ac, if at steady state) is assayed using conditions identical to those of the standards. Only trace amounts of labeled peptide (0.1 µM) are required, and although the calculations correct for the differences between free and total actin, for concentrations of free actin greater than 0.1 µM, this difference is negligible, and the results can be compared directly with the standard curve to determine Ac. The following section provides a general equation for the calculation of Ac, including values of Ac for which this difference is not negligible.



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  		FIG. 1.
Anisotropy assay measures concentration of free actin. A, rhodamine-labeled thymosin {beta}4 binds to Mg2+-actin. The buffer contains 40 mM KCl and 2 mM MgCl2 with 0.1 µM labeled thymosin {beta}4. Anisotropy was measured after conversion to Mg2+-actin but before polymerization occurred. Full-length thymosin {beta}4 binds to actin (circles), with the line showing the best fit to Kd = 0.30 ± 0.04 µM. The 1-25 thymosin {beta}4 fragment (1-25 rhod-t{beta}4) binds more weakly to actin (squares) (Kd = 6.2 ± 0.5 µM). Inset, profilin displaces 1-25 rhod-t{beta}4 fragment from actin (open triangles). The actin concentration is 5.0 µM, and the line is the best fit to the data using the same Kd (6.2 µM) for the fragment, KdP = 0.2 µM for profilin and actin, and KdPT = 80 µM for the ternary complex of actin, profilin, and the fragment. B, linearization of data in A shows no systematic deviation (function {beta} is defined under "Experimental Procedures"). C, the fraction of rhodamine-labeled thymosin {beta}4 bound to F-actin is insignificant at concentrations up to 30 µM of F-actin. There is no significant variation in anisotropy of samples of varying F-actin concentration with 0.1 µM labeled thymosin {beta}4 (closed circles, left axis), consistent with binding of labeled thymosin {beta}4 only to free actin monomer. Similarly, a pelleting assay shows no dose-dependent decrease in the amount of thymosin {beta}4 found in the supernatant fraction after pelleting of F-actin with increasing actin concentration (open circles, right axis). Moreover, pelleting of F-actin in the anisotropy samples had no effect on the observed anisotropy, confirming that the measured binding activity was to G-actin (data not shown). The error bars represent 2 {sigma}.

 
Calculation of Ac—The equilibrium dissociation constant of thymosin {beta}4 peptide for actin, KdT, is obtained from the titration of labeled thymosin {beta}4 with G-actin by a fit to the equation,

(Eq. 1)

where T0 is the total concentration of labeled thymosin {beta}4 peptide, and At is the total G-actin concentration for each value of r. Fitting parameters include only rb, rf, and KdT. Calculation of the free actin concentration Ac in a sample at steady state is straightforward using the measured anisotropy value and other parameters defined by calibration with a standard curve. Based on the equation [TA] = T0 [A]/(KdT + [A]) with r as defined above, [A] = {beta} KdT, where {beta} = (r - rf)/(rb - r). For measurements at steady state, Ac = [A]. Assuming that thymosin {beta}4 and G-actin are at rapid equilibrium, the equations (and the assay) are also valid for calculation of [A] prior to steady state, for example, for determination of the free actin concentration as a function of time during actin polymerization (as in Fig. 3B).



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  		FIG. 3.
Profilin lowers the critical concentration of actin. A, profilin (1 µM) lowers the steady state amount of free Mg2+-actin when the filaments are uncapped (triangles) relative to control (circles). Correction for the formation of a ternary complex with Kd of 9 ± 2 µM for the addition of thymosin {beta}4 to profilin-actin complex, as previously reported (26), has minimal effect at this concentration of profilin (closed symbols are for corrected data, and open symbols assume no ternary complex formation). When the barbed ends are capped by gelsolin segment 1-3 (squares), the addition of 1 µM profilin has no effect on Ac (diamonds), and again, the correction for ternary complex was insignificant (open diamonds). B, similar endpoints for Ac are reached when 1 µM Mg2+-G-actin is polymerized with 0.5 µM Mg2+-F-actin (triangles) or when 0.5 µM Mg2+-F-actin depolymerizes to steady state (squares). Both the initial free actin concentration and Ac at steady state are lower when the polymerization reaction is performed with the addition of 1 µM profilin (circles). The inset demonstrates that the anisotropy assay (solid symbols) and an assay of fluorescence of pyrenyl-labeled actin (open symbols) yield similar time courses of polymerization. The amount of F-actin is measured directly in the assay of pyrenyl-actin fluorescence and is calculated from the measured amount of free G-actin and the calculated amount of profilin-actin complex in the anisotropy assay.

 
Correction for Possible Ternary Complexes of Profilin, Actin, and Thymosin {beta}4 in Calculation of Ac Based on Anisotropy Data—The equation for Ac when profilin, actin, and thymosin {beta}4 form a ternary complex is,

(Eq. 2)

We assume here, as supported by our previous data (26), that any ternary complex of actin, thymosin {beta}4, and another actin-binding protein, for example profilin (PAT), has the same value of rb as rb for the actin-thymosin {beta}4 complex (AT). Then in the presence of actin and profilin Tb = [AT] + [PAT], and T0 = [T] + [AT] + [PAT]. At equilibrium or steady state conditions, [AT] and [PAT] are defined by Ac, total concentrations of thymosin {beta}4 T0 and profilin P0, and equilibrium dissociation constants KdP, KdT, and KdPT for formation profilin-actin complex PA, TA, or PAT, respectively. That means that r is completely defined by Ac, T0, P0, rb, rf, and equilibrium constants. At relatively low concentrations of thymosin {beta}4 (T0 << KdPT), which is always the case for our experiments with both profilin and thymosin {beta}4, r becomes independent of T0. So, if P0, rb, rf, and equilibrium constants are known, one can define Ac from anisotropy measurements. The values for rb, rf, and the equilibrium constants are already defined for several ionic conditions in our previous papers (and these parameters do not depend strongly on conditions), but they were independently verified by additional calibrations for each condition employed in the current manuscript.

Depolymerization Experiment—0.5 µM 10% pyrene-labeled Mg2+ F-actin polymerized from spectrin seeds was diluted immediately upon reaching the saturation level of polymerization to 0.1 µM in the same polymerization buffer (5 mM Tris-HCl, pH 7.9, 0.1 mM CaCl2, 0.125 mM EGTA, 2 mM MgCl2, 40 mM KCl; the predicted free Ca2+ concentration for this buffer is 44.5 nM) containing various concentrations of profilin. Depolymerizing actin filaments should contain predominantly ATP or ADP-Pi actin at the barbed end because the t1/2 of phosphate release from ADP-actin for muscle actin is more than 5 min (19), and the depolymerization assay was started immediately after polymerization was complete. The initial depolymerization rate was calculated from the depolymerization time course and plotted against profilin concentration (see Fig. 5C).



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  		FIG. 5.
Relative contributions of barbed and pointed ends to filament dynamics in presence and absence of profilin. A, cartoon demonstrating the effect of profilin on the relative rates of elongation and dissociation at the barbed and pointed ends at steady state. The top diagram illustrates reactions at each end in the absence of profilin, and the bottom diagram illustrates reactions in the presence of profilin (P). The width of the arrow indicates the relative rate of the reaction at steady state. Saturation by profilin accelerates the dissociation of subunits from the barbed end (12, 25) and accelerates the association of subunits in proportion to the formation of profilin-actin complex and the fraction of filaments not capped by profilin. B, contribution of barbed ends and pointed ends to the rates of subunit addition and loss (as free monomer or as profilin-actin) in the absence and presence of profilin at steady state conditions. The set of parameters used corresponds to the mixed mechanism described in the text. C, depolymerization rate of freshly polymerized actin filaments in the presence of profilin. Depolymerizing actin filaments should contain predominantly ATP or ADP-Pi actin at the barbed end. The solid line corresponds to the expected result for any of the three sets of parameters (with differing values for R) that could be used interchangeably to fit the data in Fig. 4A. D, contribution of the filament ends to the rates of subunit addition and loss in the absence and presence of profilin at conditions where net elongation occurs.

 
Measurements of Critical Concentration in Cell Extracts—Calf brain cell extracts prepared from 200 grams of frozen bovine brain cut into very thin slices and placed in 100 ml of ice-cold extraction buffer (20 mM HEPES, 0.2 mM CaCl2, 0.5 mM ATP, 1 mM dithiothreitol, 100 mM potassium acetate, 1 mM MgCl2, 1 mM EGTA, 1 mM phenylmethylsulfonyl fluoride, pH 7.5). A Dounce homogenizer (Pestle B) was used to open the cells, and 0.6 mM diisopropyl fluorophosphate was added to the extract. The whole cell lysate was centrifuged at 35,000 x g for 1 h, and supernatant was frozen in liquid nitrogen. Fluorescence anisotropy was recorded as described above, except special attention was paid for control and correction of the effects of absorption and light scattering by the samples. To suppress the effect of light scattering, emission fluorescence was recorded at the wavelength of 575 nm rather than 568 nm. To control for light scattering, the base-line fluorescence of each sample was recorded before the addition of labeled thymosin {beta}4, and the initial reading was subtracted from the level of fluorescence in presence of thymosin {beta}4. Base-line fluorescence corresponded to 1-3% of the final sample reading. Fluorescence anisotropy was calculated for corrected and uncorrected fluorescence levels, and the results showed no significant difference. To control for the effect of light absorption in the samples, the G factor was separately recorded for each sample. Profilin was depleted from the extract by the addition of concentrated polyproline beads equilibrated with the same extraction buffer used to prepare cell extracts. After incubation for 10 min, the beads were removed by low spin centrifugation. The dilution of the sample because of bead addition was calculated based on initial and final volumes, and the control sample was diluted by the same factor. Nonmuscle (platelet) actin was used for calibration of anisotropy measurements in cell extracts. The affinity of platelet actin to labeled thymosin {beta}4 in cell extract buffer was two or three times higher than that of muscle actin.

Nonmuscle Actin—Lyophilized platelet actin was purchased from Cytoskeleton (APHL99). 100 µl of H2O and 500 µl of G buffer were added to 1 mg of lyophilized actin. After 30 min of incubation at room temperature 200 µl more of G buffer was added. Actin was centrifuged for 1 h at 4 °C and 65,000 rpm. 650 µl of supernatant was withdrawn, and the concentration was defined through optical density measurements at 290 nm with an extinction coefficient of 26 mM-1 cm-1.


   RESULTS AND DISCUSSION
TOP
 ABSTRACT
 INTRODUCTION
 EXPERIMENTAL PROCEDURES
 RESULTS AND DISCUSSION
APPENDIX
 REFERENCES
 
Validation of the Anisotropy Assay for Measurement of the Free Actin Concentration—We and others have made frequent use of steady state fluorescence anisotropy measurements to determine the equilibrium binding kinetics of various fluorescently labeled actin-binding proteins to actin. Specifically, we have previously used this technique to assess binding of thymosin {beta}4 to actin (26). The binding isotherm for this interaction, when plotted as anisotropy versus total actin for trace levels of rhodamine-labeled thymosin {beta}4 (or synthetic 1-25 rhod-t{beta}4 peptide), provides a standard curve for determination of the free actin concentration in any sample in which the anisotropy is determined under the same standard conditions (Fig. 1, A and B). Full-length, recombinant thymosin {beta}4 peptide interacts with actin with a Kd of 0.30 ± 0.04 µM, and the synthetic peptide 1-25 rhod-t{beta}4 binds with a Kd of 6.2 ± 0.5 µM. Because the assay is most accurate when the binding constant of the labeled thymosin {beta}4 peptide is similar to the free actin concentration (or for Ac, when measuring at steady state), the use of 1-25 rhod-t{beta}4 peptide provides a standard curve with utility at higher free actin concentrations than does intact thymosin {beta}4. We previously showed that thymosin {beta}4 competes with rhodamine-labeled thymosin {beta}4 in this anisotropy assay; with a dose response as expected if both have similar affinities for actin (26). Moreover, because labeled thymosin {beta}4 also inhibits binding by profilin, either competitively (9) or noncompetitively (26), the use of thymosin {beta}4 uniquely determines the free actin concentration in the presence of either or both of these actin monomer-sequestering proteins. Binding of 1-25 rhod-t{beta}4 peptide to actin is inhibited by profilin in a manner consistent with either competitive or noncompetitive inhibition, with the equilibrium dissociation constant for the ternary complex formation KdPT ≥ 80 µM (Fig. 1A, inset). If noncompetitive, then the binding of peptide to profilin-actin is so weak as to make a correction for ternary complex formation unnecessary for the data reported here. We confirm that the fraction of thymosin {beta}4 bound to F-actin is insignificant at concentrations up to 30 µM (Fig. 1C), in agreement with prior data that implied that if such binding occurred, the Kd was several millimolar (10). This observation simplifies the analysis of the anisotropy data, because the anisotropy of labeled thymosin {beta}4 will therefore only reflect binding to monomeric actin.

As expected based on polymer theory, (28), the critical concentration of rabbit muscle skeletal actin of 0.16 ± 0.03 µM is shown to be independent of total actin concentration (Fig. 2). Capping the barbed end of actin filaments with gelsolin increases the Ac value to 0.8 ± 0.2 µM, a value consistent with previous reports (29). Calcium actin in 100 mM KCl is shown to have Ac of 0.7 ± 0.2 µM, as previously reported (30). The actin-filament stabilizing drug jasplakinolide decreases Ac to 0.08 ± 0.02 µM as speculated by us based on indirect evidence (31). The monomer sequestering drug latrunculin A does not lower Ac, either in the presence (1.0 ± 0.3 µM) or in the absence (0.22 ± 0.04 µM) of gelsolin, as expected for an agent that only sequesters monomeric actin (32).



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  		FIG. 2.
Modulation of Ac by actin-binding proteins and drugs. Fluorescence anisotropy was measured for samples with varying concentrations of actin, and the free actin concentration, Ac, was determined at steady state at the same ionic conditions (or as noted) as in Fig. 1. There is no dependence of Ac on actin in any of the samples, which include controls (open circles), 1.5 µM latrunculin A (open triangles), jasplakinolide at a fixed ratio of 1:3, jasplakinolide to actin (open squares), gelsolin segments 1-3 at a fixed ratio of 1:100, gelsolin segments 1-3 to actin (closed circles), and gelsolin as before with 1.5 µM latrunculin A (closed triangles). For calcium actin, Ac was measured in 0.1 mM CaCl2 and 100 mM KCl (open diamonds).

 
Effects of Profilin on the Critical Concentration—Using the anisotropy assay, profilin is seen to lower Ac when the barbed ends of Mg2+-F-actin are free, but not when they are capped by gelsolin (Fig. 3A). The free actin concentration, followed as a function of time, demonstrates a unique end point when steady state is approached from either G- or F-actin (Fig. 3B). Although both assays adequately track F-actin concentration (Fig. 3B, inset), relative to the measurement of F-actin by pyrenyl fluorescence, the anisotropy assay does not require labeled actin, yields data for Ac and not the sum of Ac and sequestered actin, and when F-actin concentration is large relative to Ac, does so more precisely. Only small amounts of profilin are necessary to alter Ac, and Ac varies continuously as a function of profilin concentration (Fig. 4A). When barbed ends are capped by gelsolin, the assay does not reveal any change of Ac at profilin concentrations up to 6 µM (Fig. 4B).



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  		FIG. 4.
Increased dynamics at the barbed end relative to the pointed end of Mg2+-F-actin can explain the dose dependence of Ac on profilin. A, the dependence of Ac on profilin (1 µM total actin) reveals that only low concentrations of profilin are required to lower Ac. At greater than 1 µM profilin, a more obvious difference results from the correction for ternary complex formation than seen in Fig. 3 (closed symbols are for corrected data, and open symbols assume no ternary complex formation). The change in weighting of dynamics at the barbed end relative to the pointed end caused by profilin can account for the decrease in Ac, and this is shown by the solid lines. The fit using R = 1 (balanced energy square) to the uncorrected data requires Ac = 0.042 µM at the barbed end or to the corrected data, Ac = 0.021 µM. The solid line demonstrating the fit to the corrected data is obtained using any of the three sets of parameters defined in the text for profilin-actin interactions that reflect energy balance, imbalance, or mixed thermodynamic effects. Inset, dependence of the relative weighting of the barbed end critical concentration, w = wR, on profilin when parameters are fit to the data corrected for ternary complex formation and the balanced energy square. B, the critical concentration is independent of profilin in the presence of gelsolin segments 1-3 (6 µM total actin and 60 nM total gelsolin). The data for the dose response of profilin in the presence of gelsolin are less noisy for the 1-25 rhod-t{beta}4 peptide (open squares) than for full-length labeled thymosin {beta}4 (closed squares).

 
The Mechanism of the Effect of Profilin on Actin Critical Concentration—The data shown in Fig. 4A provide a basis for a quantitative test of theories regarding the mechanism by which profilin decreases Ac. A derivation of the equations for the effect of profilin on Ac is provided in the "Appendix," and the results are as follows. The rate of change in the concentration of F-actin subunits, Af, is,

(Eq. 3)

where

(Eq. 4)

(Eq. 5)

(Eq. 6)

At steady state dAf/dt = 0, and

(Eq. 7)

In these equations, f0 is the concentration of actin polymer (i.e. the concentration of filaments). The constants kp+, kb+, kp-, and kb- are the respective elongation and dissociation rate constants from the pointed and barbed ends of F-actin, respectively. The primed rate constants are for the addition of profilin-actin and the loss of profilin-actin occurring at the barbed end. The constants KdP and Kdb are equilibrium dissociation constants for profilin for monomers and barbed ends, respectively, and [A] and [P] are the concentrations of free actin and free profilin. Parameters wR and w provide relative weighting factors for the barbed end off and on rates, respectively. Parameter R, characterizing the misbalance of the apparent energy square, is defined in the "Appendix," and R = 1 when the energy square is balanced; in this case wR = w. At saturation with profilin, w = wsat = ((k'b+/kb+) Kdb/KdP) and equals ~100 according to published values for the rate and equilibrium constants. The value of wR varies from 1 to wRsat = wsat/R. Fig. 4A (inset) demonstrates the dependence of w on profilin concentration when the energy square is assumed to be balanced and when the rate constants are equal to those used in Fig. 4A in the fit to the data corrected for formation of ternary complex.

As can be seen from Equation 4, the measured values of Ac yield a weighted average of the critical concentration at each end of an actin filament. Profilin, by accelerating the addition and removal of actin subunits from the barbed end, would be predicted to increase the effective weight of the barbed end, lowering Ac (Fig. 5, A-C). Acceleration of removal is because of a difference in off rates for profilin-actin and actin (Refs. 12 and 25 and Fig. 5C), whereas the acceleration of addition is because of the increased abundance of profilin-actin relative to free actin, with similar on rates for both species (Ref. 16 and Fig. 5B). The data from the two independent experiments shown on Figs. 4A and 5C are fit with the same sets of parameters.

Critical Concentration Changes Induced by Profilin with a Balanced Energy Square—According to the published values of rates constants (33), the effect of pointed ends cannot be neglected in the absence of profilin, and either kp- ~ kb- or kp+ ~ kb+. Then in the absence of profilin Ac = (kp- + kb-)/(kp+ + kb+), the value intermediate between the pointed end critical concentration, Acp = kp-/kp+, and the barbed end critical concentration, Acb = kb-/kb+. When the energy square is balanced, wR = w, and the change of critical concentration with increasing profilin concentration occurs through the change of relative contributions of the barbed and pointed ends in polymerization and depolymerization events. In the absence of profilin w = 1 and Ac > Acb. At saturating profilin concentration, w reaches ~100, and kp- << w·kb-, kp+ << w·kb+, and Ac decreases to Acb. The data in Fig. 4A are fit with parameters: R = 1, Acp = 0.8 µM, k'b+ = kb+ = 10 µM-1 s-1, Kdb = 13.8 µM, kp+ =2.24 µM-1 s-1, Acb = 0.02 µM, and KdP = 0.15 µM for the data corrected for the formation of a ternary complex of actin, profilin, and thymosin {beta}4 (closed symbols), and kp+ = 2.0 µM-1 s-1, Acb = 0.04 µM, and KdP = 0.07 µM for the uncorrected data (open symbols). The range of predicted values for the critical concentration of the barbed end (0.02-0.04 µM) is very low, but previously reported experimental values have been in this range (9, 34).

Contribution of an Energy Imbalance to the Effect of Profilin on Critical Concentration—If the effect of pointed end dynamics on critical concentration is negligible, i.e. kp- << kb-, kp+ << kb+, then Ac = kb-/kb+ = Acb, then at saturating profilin concentrations Ac = (wR kb-)/(w kb+) = Acb/R. In this case profilin affects critical concentration only through the use of ATP hydrolysis coupled with the profilin pathway. A physical interpretation of this result is that profilin lowers Ac to that of a barbed end with terminal subunits containing ATP, and there is evidence that the nucleotide content of terminal subunits influences Ac (35). With a balanced energy square and insignificant contribution from pointed ends, Ac = Acb. Importantly, this means that the fact that the profilin-actin complex can add to the barbed end, by itself, cannot explain the effect of profilin on critical concentration. The data in Fig. 4A can be fit indistinguishably from the pictured theoretical curve, assuming only energy imbalance with parameters, kp+ = kp- = 0, k'b+ = kb+ = 10 µM-1 s-1, Acb = 0.16 µM, KdP = 0.20 µM, and Kdb = 15.4 µM, R = 7.5. The fit to the data in Fig. 4A is very sensitive to increasing R and becomes poor when R exceeds 7.5.

A "mixed mechanism" resulting from the combination of increased barbed end weighting and energy imbalance could explain the effect of profilin on critical concentration. When the contributions of the pointed ends are non-negligible and R > 1, then profilin may not only lower Ac to that of the barbed end but also further lower Ac to that of a barbed end with terminal subunits containing ATP. The data in Fig. 4A can also be well fit with these assumptions, with the best fit obtained with parameters of kp+ = 1 µM-1 s-1, Acp = 0.8 µM, k'b+ = kb+ = 10 µM-1 s-1, Acb = 0.1 µM, KdP = 0.18 µM, and Kdb = 14.7 µM, R = 4.7.

Increased Dynamics at the Barbed End—The steady state subunit flux on the barbed end increases with concentration of profilin (Fig. 5B). The on flux (Equation 8) and off flux (Equation 9) are as follows (see "Appendix").

(Eq. 8)

(Eq. 9)

The increase of the on flux occurs because both actin and profilin-actin complex add to the barbed end, and even if [A] decreases with profilin concentration, the total sum of unpolymerized actin [A] + [PA] still exceeds the critical concentration in the absence of profilin. The increase of the off flux is demonstrated in the experimental data shown in Fig. 5C. Note that the same sets of parameters used to fit the data on Fig. 4A also fit these depolymerization data. Fig. 5B shows the relative contributions from different terms at steady state conditions corresponding to that of Fig. 4A. The set of parameters corresponding to a mixed mechanism is demonstrated here, although any of the sets of parameters show that the barbed end dynamics at 10 µM profilin is greatly enhanced compared with the dynamics in the absence of profilin.

Importance of Depolymerization Term for Actin Polymerization Dynamics—Fig. 5D shows relative contributions from different terms at elongation conditions when the total actin concentration is 3 µM and the profilin concentration is 0 or 10 µM. It is clearly seen that the total depolymerization rate is about 35% of the total polymerization rate, and the term corresponding to profilin pathway contributes to about 80% of the net depolymerization. Although it is commonly assumed that this term is negligible and therefore ignored, this result shows that term should not be neglected in models describing actin polymerization.

Effect of Profilin on Critical Concentration in Cell Extracts—Fig. 6 shows the effect of profilin on critical concentration in cell extracts. The cell extracts were treated with polyproline beads to deplete free profilin and profilin-actin complex from the extract, and the critical concentration of the treated extracts was compared with the Ac in the untreated extracts. In polyproline-treated extracts, Ac is three times higher than the Ac in untreated extracts, and both are relatively low.



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  		FIG. 6.
Critical concentration in cell extracts. The cell extracts were treated with polyproline beads to deplete free profilin and profilinactin complex, and the critical concentration of the treated and untreated extracts was measured. Inset, predicted values of critical concentration in presence of profilin when 95% of the total barbed ends are capped. The lines correspond to the parameter sets with R = 1 (dotted line), 4.7 (dashed line), and 7.5 (solid line) used to fit the data on Figs. 4A and 5C. At these conditions the predicted dependences of critical concentration on profilin differ significantly for different values of R. This is in contrast to the data in Figs. 4A and 5C, for which three sets of parameters were defined that fit all of those data equally well. Two data points (circles) correspond to the average values received in the two experiments shown on the main panel for the treated and untreated extracts and to our best estimate for the profilin concentration in these extracts.

 
The effect of profilin on Ac is consistent with predictions based on the assumption that cell extracts have limited amounts of capping protein. The inset to Fig. 6 shows the predicted dependence of critical concentration on profilin when 95% of the barbed ends are capped. The three different sets of parameters used to fit the data in Fig. 4A (with R = 1, 4.7, or 7.5) were used to generate the theoretical curves. Numerical computer simulation done in Ref. 36 with the set of parameters corresponding to R = 14 gives similar results. The two data points on the inset of Fig. 6 correspond to the average values received in polyproline-treated and untreated extracts and to our best estimate of the profilin concentration in these extracts. First, note that in these conditions of subtotal capping, profilin now is expected to have a marked effect on Ac. Note that in contrast to the data in Fig. 4A, which do not distinguish between energy balance and imbalance because those data can be fit by a range of values for R, the dependence of Ac on profilin with partial capping should be highly sensitive to the value of R. Thus, the data obtained in cell extracts are most consistent with the kinetic parameters used to fit the data in Fig. 4A, in which R is 4.7. Because profilin alters the filament number by sequestration of actin monomer, the fraction of capped filaments will be different in samples that differ only in their profilin concentration, and the conditions of Fig. 6 (inset) are difficult to precisely reproduce in vitro. Because it is unlikely that filament length is distributed exponentially in cells (as in vitro) (37), the error resulting from the assumption of a constant fraction of capped filaments is likely small in cells or in cell extracts.

Effects of Thymosin {beta}4 on the Critical Concentration—At high concentrations, thymosin {beta}4 has been observed to cause nonlinear effects on the steady state amount of F-actin (Ref. 10 and Fig. 7A). Proposed explanations have included the possible formation of copolymers of actin and thymosin {beta}4-actin complex or an effect on Ac (10). Here we demonstrate that thymosin {beta}4 decreases the Ac value of capped actin filaments (Fig. 7B). Thymosin {beta}4 has a very similar effect on Ac when filaments are uncapped (data not shown). The effect of dose response on Ac is much different for profilin and for thymosin {beta}4, and no detectable change in Ac is induced at low concentrations such as that used for rhodamine-labeled thymosin {beta}4 in the anisotropy assay. Steady state data for the fluorescence of pyrenyl-labeled actin cannot be fit by a single Kd, assuming constant Ac (Fig. 7A). However, using values for Ac as a function of thymosin {beta}4 as determined by a fit to the fluorescence anisotropy data in Fig. 7B, the single Kd of 0.12 µM (determined as in Fig. 1) is shown to fit all of the data reasonably well. Similarly, assuming a single Kd of 0.12 µM, the critical concentrations required to explain the data in Fig. 7A are shown to correspond to the experimental values determined by anisotropy in Fig. 7B. Although the data are empirically consistent, we know of no satisfactory explanation that accurately predicts the dependence of Ac on thymosin {beta}4 concentration. An effect of thymosin {beta}4 caused by an interaction with F-actin is ruled out by the data in Fig. 1C. Thymosin {beta}4 may bind to the complex of gelsolin with actin dimers or small oligomers, thereby sequestering the gelsolin from solution. If thymosin {beta}4 binds to gelsolin-actin complexes with affinity of ~5-10 µM and does not allow these complexes to polymerize, then thymosin {beta}4 may deplete gelsolin available for capping and lower Ac. But this hypothesis does not explain why thymosin {beta}4 also decreases critical concentration for uncapped filaments. Also, nucleotide exchange on G-actin seems to be irrelevant to the effect of thymosin {beta}4 on Ac because the presence of profilin in the experiment with thymosin {beta}4 and completely capped filaments does not change the Ac when compared with that determined for thymosin {beta}4 alone (data not shown).



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  		FIG. 7.
Steady state effects of thymosin {beta}4 on gelsolin-capped Mg2+-F-actin are explained by alteration of Ac. A, pyrenyl-actin assay for monomer sequestration by thymosin {beta}4 has a nonlinear dependence on thymosin {beta}4 so that the data cannot be explained with any single Kd (dashed lines). However, the data are well fit assuming a single Kd and a variable Ac determined by fluorescence anisotropy (solid lines). Samples from the left have 0 (squares), 1 (circles), 2 (triangles), 4 (inverted triangles), 8 (diamonds), 16 (leftward triangles), and 24 µM (rightward triangles) thymosin {beta}4. B, fluorescence anisotropy confirms that thymosin {beta}4 causes a dose-dependent decrease in Ac (closed circles). The line provides values for critical concentration as a function of thymosin {beta}4 that are used in A. Assuming a Kd of 0.12 µM, the best fit to the data in A for Ac for each concentration of thymosin {beta}4 (shown as open triangles) corresponds well to the experimental data in B.

 
Implications for Actin Dynamics—Rapid growth of actin filaments in local regions of a cell with dynamic filament assembly is assumed to occur through the addition of the profilinactin complex to the barbed end (38). Profilin has relatively high affinity for globular actin (G-actin), and at moderate concentrations of profilin a large amount of unpolymerized actin is present in a form of profilin-actin complex. The concentration of free actin, Ac, defines the concentration of profilin-actin complex in any given intracellular region in which other factors, such as VASP, may bind profilin so as to increase local profilin concentration (39). Thus, the ability to determine the effect of actin regulatory proteins on Ac is absolutely essential to predicting how these proteins work in cells. Toward this end, our preliminary data show that the anisotropy technique described here works well in cell extracts, yielding results within the limits of those previously reported (1) and consistent with theoretical predictions. Most promisingly, fluorescence anisotropy methods are suitable for microscopic applications in live cells, with measurements of both local and whole cell anisotropy being feasible (40).

The concentration of free actin is a critical parameter not only at steady state conditions but also during polymerization. As seen from Equation 3, the polymerization rate is proportional to the value of ([A] - Ac), and this value may become very small under conditions when almost all unpolymerized actin is present in the form of complex with actin-binding proteins. With increasing concentration of profilin, the term (kp+ + wkb+) may become large, but the value of ([A] - Ac) would decrease faster and at some conditions may even become negative, which would lead to fast depolymerization of actin. Acceleration of actin polymerization dynamics by profilin may play an important regulatory role in cells when rearrangements of the cytoskeleton occur within a short periods of time. Also, in conditions in which temporal or spatial concentration of capping protein becomes insufficient to cap all of the barbed ends, changes in profilin concentration may switch actin filaments from depolymerization to fast polymerization, and fine regulation of actin polymerization by profilin in ensemble with capping proteins is possible.

The value of R depends on a combination of various factors that include, but are not limited to, the energy of ATP hydrolysis, the energy of the phosphate release, and the rate of the phosphate release. Also, in general, R may be a function of profilin concentration. The importance of phosphate release is supported by the fact that the critical concentration is very low in the presence of inorganic phosphate (35). Of interest, the observed difference in the values of R for muscle and nonmuscle actin correlates with the difference in the phosphate release rates. For muscle actin R varies between 1 and 14 (9, 11) and is as high as 33 for nonmuscle actin (12). Published data confirm that the rate of phosphate release for yeast actin is much faster than for muscle actin (41). The faster rate of release may lead to less energy dissipation and therefore to a larger potential difference in free energy between the pathways for addition of profilin-actin and actin alone. These differences may reflect differences in the physiological function of actin derived from various sources.


   APPENDIX
TOP
 ABSTRACT
 INTRODUCTION
 EXPERIMENTAL PROCEDURES
 RESULTS AND DISCUSSION
 APPENDIX
REFERENCES
 
Thermodynamic Constraints—The thermodynamic energy square (9, 12) describes the interdependence of the binding and/or rate constants for two different pathways for filament elongation (Fig. 8). Without ATP hydrolysis involved, when all reactions are reversible, as for example, in the case for ADP actin, the two pathways are energetically identical and the ratio R = ((kb-/kb+) Kdb)/((k'b-/k'b+) KdP) = 1, where kb+ and kb- are the respective elongation and dissociation rate constants from the barded end of F-actin, KdP and Kdb are the equilibrium dissociation constants of profilin for monomers and the barbed end, respectively, and the primed rate constants are for the addition of profilin-actin and the loss of profilin-actin occurring at the barbed end. R is the factor of misbalance that is equal to 1 if the energy square is satisfied.



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  		FIG. 8.
Actin filament elongation in the presence of profilin. A, thermodynamic energy square for filament elongation. B, equations and rates of reaction for elongation and depolymerization from each end of F-actin in the absence or presence of profilin.

 
In the case when ATP hydrolysis is involved, R may no longer be equal to 1, and is, in general, a function of profilin concentration. According to data by different authors (9, 11, 12), R varies between 1 and 33. There is also evidence that hydrolysis of actin is not fast enough to be coupled with profilin dissociation (19), and that implies that hydrolysis of ATP is not directly involved in the profilin pathway. A factor of 33 for R would correspond to free energy input of about 2 kcal/mol, corresponding approximately to the energy of ATP hydrolysis without dissociation of inorganic phosphate. At conditions existing in cells, the complete energy of ATP hydrolysis with the inorganic phosphate dissociation corresponds to 11.5 kcal/mol. That would correspond to R = 1.6 x 108 if the total energy of ATP hydrolysis were utilized for polymerization. However, there is an agreement in the literature that the whole energy of ATP is not used for actin polymerization and that only a small part of it, if any, might be involved in the profilin pathway.

Equations for the Interaction of Actin and Profilin-Actin—In the absence of profilin, the rate of change in the concentration of F-actin subunits, Af, is

(Eq. 10)

with

(Eq. 11)

where f0 is the concentration of actin polymer (i.e. the concentration of filaments) and kp+ and kp- are the elongation and dissociation rate constants from the pointed end of F-actin. When profilin is present,

(Eq. 12)

where f = f0/(1 + [P]/Kdb) is the concentration of uncapped filaments, and [PA] = [P][A]/KdP is the amount of the profilinactin complex. Assumptions that equilibrium between free profilin and both G-actin and barbed ends establishes much faster than the net rate of polymerization were used here. These assumption are consistent with the agreement in literature that the dissociation rate of profilin from the barbed end (which is the measure of the establishment of equilibrium) is very fast. Then

(Eq. 13)

or

(Eq. 14)

where

(Eq. 15)

(Eq. 16)

(Eq. 17)

and

(Eq. 18)

because

(Eq. 19)

according to the apparent energy square relation. At steady state,

(Eq. 20)

and

(Eq. 21)


   FOOTNOTES
 
* This work was supported by the Medical Research Service of the Department of Veterans Affairs, National Science Foundation Grant NSF-0316015 (to M. R. B.), and NIAMS, National Institutes of Health Grant 5K25AR048918 (to E. G. Y.). The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact. Back

{ddagger} To whom correspondence should be addressed: Box 100221, Dept. of Medicine, University of Florida, Gainesville, FL 32610. Tel.: 352-392-4681; Fax: 352-374-6170; E-mail: bubbmr{at}medicine.ufl.edu.


   ACKNOWLEDGMENTS
 
We thank Iman M. Al-Naggar and Bruce G. Gibson for help in the preparation of cell extracts.



   REFERENCES
TOP
 ABSTRACT
 INTRODUCTION
 EXPERIMENTAL PROCEDURES
 RESULTS AND DISCUSSION
 APPENDIX
 REFERENCES
 

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