Research Article

Filament rigidity causes F-actin depletion from nonbinding surfaces

Charles I. Fisher and Scot C. Kuo
PNAS January 6, 2009 106 (1) 133-138; https://doi.org/10.1073/pnas.0804991106

  1. Edited by John A. Cooper, Washington University, St. Louis, MO, and accepted by the Editorial Board November 11, 2008 (received for review May 22, 2008)

Abstract

Proximity to membranes is required of actin networks for many key cell functions, including mechanics and motility. However, F-actin rigidity should hinder a filament's approach to surfaces. Using confocal microscopy, we monitor the distribution of fluorescent actin near nonadherent glass surfaces. Initially uniform, monomers polymerize to create a depletion zone where F-actin is absent at the surface but increases monotonically with distance from the surface. At its largest, depletion effects can extend >35 μm, comparable with the average, mass-weighted filament length. Increasing the rigidity of actin filaments with phalloidin increases the extent of depletion, whereas shortening filaments by using capping protein reduces it proportionally. In addition, depletion kinetics are faster with higher actin concentrations, consistent with faster polymerization and faster Brownian-ratchet-driven motion. Conversely, the extent of depletion decreases with actin concentration, suggesting that entropy is the thermodynamic driving force. Quantitatively, depletion kinetics and extent match existing actin kinetics, rigidity, and lengths. However, explaining depletion profiles and concentration dependence (power-law of −1) requires modifying the rigid rod model. Within cells, surface depletion should slow membrane-associated F-actin reactions another ≈10-fold beyond hydrodynamically slowed diffusion of filaments (≈10-fold). In addition, surface depletion should cause membranes to bend spontaneously toward filaments. Such depletion principles underlie the thermodynamics of all surface-associated reactions with mechanical structures, ranging from DNA to filaments to networks. For various functions, cells must actively resist the thermodynamics of depletion.

When explaining general cell function, filamentous actin (F-actin) networks are required near membranes. For example, cortical F-actin near the plasma membrane is responsible for providing the structural integrity of the cell as well as providing the substrate for generating the forces of cellular protrusions (1, 2). Even for newly polymerized F-actin that drive lamellar or filopodial extensions, the preexisting F-actin network biochemically amplifies protrusive efficiency in a self-catalytic manner [e.g., ARP2/3-catalyzed branch growth (3)]. Although the importance of membrane-proximal actin networks is well recognized, the governing principles constraining their de novo assembly are not understood.

The mechanical properties of F-actin should hinder its association near membranes, effectively depleting filament concentration relative to bulk values. Cellular in dimensions, the persistence length of F-actin is 17 μm and 9 μm, with and without phalloidin, respectively (4, 5). Because of filament rigidity, 2 mechanisms may deplete filaments from membranes and other surfaces. In one, regardless of filament directionality, elongation moves their center of mass away from surfaces. Distal growth requires no forces, whereas proximal growth requires forces from Brownian-ratchet-like mechanisms (6, 7). In the second mechanism, entropy drives the depletion. Near surfaces, steric collisions restrict the range of orientational configurations of filaments; once filaments diffuse away from surfaces, such surface-induced steric constraints disappear. Indeed, entropic depletion should exist for all polymers, leading to macromolecular “crowding” that can accelerate associative biochemical reactions within cells (8) (reviewed in ref. 9). However, the long persistence length of F-actin should make depletion dramatic. If F-actin were uniform rigid rods, entropic calculations predict the absence of F-actin at surfaces and depletion effects that extend a filament length from the surface (10, 11), potentially affecting a significant volume of a cell.

The inhibitory effect of surfaces is well appreciated in DNA microarray technology where oligonucleotides are tethered to glass. Like F-actin, both DNA and RNA have significant molecular persistence lengths in both their single (≈2 nm; e.g., ref. 12) and double-stranded (≈50 nm; e.g., refs. 13 and 14) forms. By increasing the length of flexible polymer tethers linking oligonucleotides to glass, hybridization rates increase orders of magnitude (e.g., ref. 15). Depletion-like interactions of nucleic acids with surfaces can explain much of the suppressed kinetics near surfaces (16).

For actin microrheology, surface depletion is believed to affect mechanical measurements, but the notion remains unproven. In such studies, Brownian motion of large particles embedded in actin networks reveals their mechanical microenvironments (17, 18). Microrheology theory initially assumed that probe particles were nonperturbing, but the particle's surface chemistry clearly affects its motions in F-actin networks (18). In addition to underestimating the network's mechanical properties, nonbinding particles do not respond to network cross-linking that shifts bulk moduli 300-fold. Although filament depletion can explain unresponsiveness, electron microscopy did not reveal any obvious differences in actin distribution (18).

To visualize actin depletion, we developed a confocal microscope assay to monitor the distribution of fluorescent F-actin polymerized in situ (Fig. 1A). Because biological membranes do not bind F-actin without binding proteins (e.g., ref. 19), we can use “blocked” surfaces to build an understanding of surface inhibition within cells. Unblocked glass binds actin [supporting information (SI) Fig. S1D] and blocking with BSA caused F-actin depletion that was indistinguishable from depletion over supported bilayers of phosphatidylcholine lipid (data not shown). Because subsequent experiments indicate that depletion is an intrinsic property of filaments, we refer to the process as “self-depletion.”

Results

Fluorescent Labeling.

Despite its long history, popular methods of fluorescently labeling F-actin proved inappropriate for this study (Fig. S1). With Alexa Fluor 488, direct labeling of actin on cys374 created filaments that were photolabile, bleaching and breaking with repeated irradiation (Fig. S1A). Even though an enzymatic O2-scavenging system improved photostability, it also caused extensive filament bundling (data not shown). Although filaments labeled indirectly with Alexa Fluor 488-phalloidin were relatively photostable, the dye's fluorescence efficiency dropped significantly upon polymerization (Fig. S1C), similar to other fluorescent derivatives of phalloidin (20). Instead, we used actin labeled on random amino groups by succinimidyl-Alexa Fluor 488 (Fig. S1). Unlike cys374 labeling, such amino labeling does not affect actin elongation kinetics (21). As a final test of our labeling strategy, we altered the mole fraction of labeled/unlabeled actin. For preparations spanning 12–48% labeled fraction, the differences in self-depletion profiles were negligible (<3%; Fig. S1B).

Actin Is Depleted from Nonbinding Surfaces.

To demonstrate that F-actin self-depletes from surfaces, we used confocal microscopy to monitor the concentration of fluorescent actin. Our strategy was to label the blocked glass surface with fluorescent TAMRA-BSA, start with monomeric fluorescent actin, and monitor polymerization-induced depletion with time (Fig. 1A). At each time point, the 2-color fluorescence of surface and actin was acquired simultaneously by confocal imaging of a 3D volume. Typically taking 2 min to complete, each time point included control images for bleed through between channels. Fig. 1B shows images from a representative time course. In the first time point, the monomeric actin signal was uniform in the aqueous phase but absent within the glass coverslip. When filaments were abundant (t = 3 h), there is much less actin near the surface, despite plentiful actin in the bulk. By averaging the fluorescence of each xy slice, the depletion effect can be analyzed quantitatively after identifying the surface (10-nm precision in curve fitting TAMRA-BSA signal; Fig. 1C). Corresponding to an averaged yz view, we refer to such plots as z-profiles. For later model testing, we use the z-profile of TAMRA-BSA as the 1D point-spread function (PSF) that quantifies the blurring of the optical system. In all experiments, the bulk fluorescence signal, effectively >35 μm from the surface, was constant during the time course.

Fig. 1.
Fig. 1.

Experimental strategy and representative data. (A) Shown in the yz-slice through the sample chamber, the general strategy is to monitor monomeric Alexa Fluor 488-actin (green) as it polymerizes. Adsorbed to the glass coverslip, TAMRA-BSA (red) serves as a fiducial reference. Filament angles and distribution are from Monte Carlo simulation. (B) From the time course of polymerizing 1 μM actin, representative xy and yz slices of 3D confocal imaging (46.8 × 46.8 × 60 μm) are shown. At t = 0, actin is monomeric and uniformly distributed throughout. In 3 h, actin filaments form and show depleted concentrations near the surface. (C) Averaging fluorescence intensity of each xy-slice produces fluorescence profiles along z-axis (z-profiles). Gaussian curve fitting of the TAMRA peak (red) was used to assign z = 0 (10-nm confidence interval). The red dotted line represents the raw TAMRA signal before correcting for Alexa Fluor 488 bleed through. The actin signal is shown in green and the green circle marks Z50. Over 3 h, Z50 for 1 μM actin shifted from 0 to 2.3 μm and a significant fraction of actin (0.25 μM) remains monomeric, producing a bump at z = 0. Curve-fitting indicates depletion extends 20 μm; bulk actin fluorescence (z >20 μm) remained constant throughout the time course.

For the least assumptions, we did not perform deconvolution, leaving fluorescence profiles uncorrected for optical blurring. Instead, we quantify the extent of depletion using Z50, the depth at which the actin signal was 50% of the bulk signal. Because polymerized actin is in equilibrium with monomer (Ccrit ≈0.12 μM for ATP-actin), these raw Z50 values systematically underestimate the extent of filament depletion. Model-dependent curve fitting is required to compensate for such dynamic effects.

Time Course of Actin Depletion.

To understand the mechanisms driving actin depletion, we continuously monitored the time course of depletion while actin polymerized. As monitored by the temporal evolution of Z50, 3 distinct phases of depletion were evident (Fig. 2). The earliest phase resembled the lag in the initiation of polymerization because no filaments were seen in images, and z-profiles appeared constant. After this lag phase (t0), filaments could be detected in the images and the depletion of actin developed rapidly (time constant τ1 ≈ 20 min). Subsequently, in a slower phase, actin depletion continued to develop. In this experiment, only ≈60% of the depletion occurred quickly, with the remaining depletion developing over the next ≈20–48 h.

Fig. 2.
Fig. 2.

Kinetics of depletion. Over 48 h, the fluorescence distribution of 3 μM Alexa Fluor 488-actin was monitored with 3D confocal imaging. The evolution of Z50 with time was fit with a biexponential function. For this representative time course (statistics across all time course experiments in parentheses) fits produce lag time t0 = 7 min (8 ± 2 min, mean ± SD, n = 3), followed by 2 time constants of 17 min (19 ± 2 min) and 20 h (12–150 h), with amplitudes 60% (21–64%) and 40% (36–80%), respectively. Bulk fluorescence (z > 20 μm) remained constant throughout the time course. (Inset) Representative fluorescence z-profiles from the time course are shown.

As a working hypothesis, we attributed each kinetic phase of depletion to a molecular mechanism based on filament length and rigidity. Based on studies with pyrenyl-actin (22, 23), polymerization from G-actin starts with an early lag phase where actin nuclei are slow to form and follows with a fast elongation phase. For our experiments, the lag in depletion corresponds to slow formation of actin nuclei. The fast depletion phase corresponded to fast filament nucleation and elongation, including a Brownian ratchet-like mechanism pushing filaments away from the glass surface. After polymerization is complete, entropic considerations continue to drive depletion thermodynamically. Filaments that collide with the surface are sterically restricted and have fewer configurations than filaments far from the surface. The time to achieve equilibrium distributions depends on filament size and crowding effects. However, annealing may also contribute to the slow phase by continuing to lengthen filaments (24, 25).

To test this working hypothesis, there are 3 perturbations that we pursue below. First, filament rigidity was increased with the small molecule, phalloidin. Second, filament length was shortened with capping proteins. Finally, actin concentration was varied to control the relative thermodynamic cost of configurations as well as polymerization kinetics.

Phalloidin Increases Extent of Depletion.

To investigate the role of filament rigidity, we used saturating amounts of phalloidin, which nearly doubles F-actin's persistence length Lp (9 μm to 17 μm; 4, 5). For pyrenyl-actin, phalloidin also changes polymerization kinetics by speeding both the nucleation rate and the rate of bulk polymerization (26). For the fewest assumptions, we curve-fit all kinetics using a phenomenological lag time t0 to lump nucleation phenomena, followed by a single-exponential τ for the rate of bulk polymerization.

Demonstrating the kinetic effects of phalloidin, Fig. 3A shows matched time courses with kinetic fits. Across all matched experiments with 3 μM actin, kinetics shifted from t0 = 9.5 ± 1.3 to 2.3 ± 0.5 min and τ = 17.7 ± 3.8 to 12.5 ± 0.8 min (n = 8) with the addition of phalloidin. These values derived from depletion kinetics are comparable with those reported for pyrenyl-actin (26), quantitatively linking depletion kinetics with polymerization.

Fig. 3.
Fig. 3.

Effect of varying rigidity and length. (A) Representative time courses of 3 μM Alexa Fluor 488-actin with or without phalloidin. To ensure maximum rigidity effects, phalloidin was used in excess over actin (2:1 molar ratio). The curve-fits are lags (t0) followed by single exponentials (τ). Delays from preparing and mounting slides (≈2 min) are not included. (B) From overnight data (15–18 h), the effect of saturating phalloidin on Z50 at different actin concentrations is summarized. Data are mean ± SD from n ≥ 8 z-profiles from ≥2 independent slides. (C) From representative overnight data (15–18 h), capping protein shifts the fluorescence z-profile of 3 μM actin. A fluorescence z-profile of monomeric G-actin is included for comparison. (D) Statistics from multiple experiments with 3 μM actin show Z50 decreases with increasing capping protein concentration. For each bar, mean ± SD are calculated from ≥10 z-profiles from ≥2 independent slides. (Inset) By using the Carlsson model (27) to predict capped filament lengths, measured Z50 (mean ± SD) is proportional to predicted length (slope 0.43 ± 0.03).

To demonstrate the thermodynamic effects of phalloidin, we measured the extent of depletion after overnight incubation (Fig. 3B). For higher concentrations of actin, depletions are harder to quantify, thus obscuring the effects of phalloidin. For the lowest concentrations (≤2 μM), phalloidin enhanced actin depletion 1.6- to 1.9-fold, remarkably similar to phalloidin's effect on persistence length. Hence, the extent of actin depletion appears to scale with rigidity.

Shortening Filaments Decreases Depletion.

Because steric depletion cannot extend further than filament lengths, shortening filaments should reduce the extent of depletion. To understand the effects of filament length on depletion, we used 2 different proteins, capping protein and gelsolin, to limit elongation and shorten filaments. After overnight copolymerization with actin (15–18 h), both capping protein and gelsolin affected actin self-depletion similarly. For 3 μM actin, more capping protein causes Z50 to decrease (Fig. 3 C and D). To calculate filament lengths, we used the kinetic model developed by Carlsson (27) even though it lacks annealing reactions (25). Overnight Z50 values are a proportional fraction of average capped filament lengths (Inset, Fig. 3D). As discussed later, model testing requires mass-weighted length statistics rather than average length used here.

Effect of Concentration on Depletion.

Because there are 2 concurrent mechanisms, we expect that altering actin concentration will have 2 differing effects on depletion: speeding its formation while reducing its extent. At early times, depletion should reflect the accelerated kinetics of filament formation with actin concentration. For long-term thermodynamics, concentrated actin solutions are more crowded, hindering filament motions throughout. Such crowding should reduce the relative entropic cost of proximity to the surface, thus reducing the extent of depletion.

For early kinetics, we monitored the first hour of self-depletion while varying actin over a 2–8 μM range (Fig. S2). As predicted, increasing actin concentration both shortens the lag time t0 and speeds the formation of depletion by shortening τ. In particular, the depletion kinetics matches the published values for the kinetics of pyrenyl-actin polymerization at the same actin concentrations (22, 23, 28). Clearly, self-depletion and filament formation are tightly correlated.

To understand the role of actin concentration on the thermodynamics of self-depletion, we measured depletions after overnight incubation (15–18 h). Compared with kinetic studies, these measurements are more robust and allow the exploration of a wider range of concentrations. As shown in Fig. 4A, increasing actin concentration suppressed the extent of depletion. At concentrations >16 μM, depletions become too small for easy detection by our strategy, whereas depletions at the lowest actin concentrations are skewed by the large fraction of free monomer.

Fig. 4.
Fig. 4.

Effects of actin concentration and model testing. (A) At each concentration across a range 0.25–16 μM actin, statistics of Z50 (mean ± SD) were calculated from ≥12 z-profiles of overnight data from ≥3 independent slides. Filled circles are the uncorrected data where [Actin] = [Total Actin], and open circles are data where [Actin] = [F-actin] after correcting for unpolymerized actin by using curve fitting with the rigid rod plus monomer model. The solid line is a power law of γ = −0.94 ± 0.05 fitted to corrected data. For comparison, data measuring mesh size of F-actin (34) are included as a dashed line. (B) Fluorescence data from all overnight 0.5 μM actin experiments (n = 24) were scaled, averaged (open circles), and curve fitted (dashed line). Curve-fitting iterations included numerical convolution of theoretical curves with a 1D PSF estimated from the TAMRA-BSA signal. Offset below for clarity, the fitted theoretical function is shown without convolution. The residuals of curve fitting include representative error bars showing standard deviation of measurements. Fit values are L = 34 ± 0.6 μm, 18 ± 0.5% monomer (0.09 μM) and maximal residual of 1.9%. Fitting of additional models are shown in Fig. S3. (Inset) Distribution of filament lengths (bars) for 0.5 μM actin polymerized under comparable conditions and subsequently stabilized with phalloidin for dilution.

Model Testing.

Two types of models from polymer physics have been used to analyze self-depletion from surfaces (reviewed by ref. 29). In one type, filaments are approximated as rigid rods. For various rod lengths and surface curvatures, geometric arguments allow calculating entropic cost and depletion profiles (10, 11). However, these calculations are only appropriate for dilute solutions because they ignore interactions between filaments. The other type of model addresses very flexible polymers (29, 30), approximated as tangled balls with a statistical radius of gyration determined by contour length and persistence length. At low polymer concentration, radius of gyration determines the extent of depletion. At higher concentrations, flexible filaments form an entangled network with a characteristic mesh size. Once filaments are long enough to entangle, mesh size is only a function of polymer concentration and not filament length. Entangling reduces the entropic cost of surface proximity such that depletion is proportional to mesh size. Both types of models assume unchanging filament length and cannot explain the early depletion kinetics in our experiments.

First, we compared the predicted shapes of the depletion profiles with empirically measured z-profiles (15–18 h). Because numerical deconvolution is not deterministic and can create artifacts, we avoid it by fitting fluorescence data directly by blurring computed concentration profiles with the empirically determined point-spread function of our confocal microscope (TAMRA-BSA surface signal). Furthermore, models required introducing an extra parameter to account for the free monomeric actin signal (Fig. S3). Of all of the models considered, the rigid rod model with unpolymerized actin was the best description of overnight 0.5 μM actin (Fig. 4B). Simultaneously compensating for free actin monomers (90 ± 3 nM), model fitting yielded Z50 = 6.3 ± 0.1 μm, requiring rods of length 34 ± 0.6 μm. Direct visualization of diluted filaments show lengths of 18 ± 16 μm (SD, n = 293; Inset, Fig. 4B), consistent with published lengths (20 ± 13 μm, e.g., ref. 31). Because longer filaments have more fluorescent actin, they contribute proportionally more to the depletion profile. After accounting for actin mass (weighting factor L/〈L〉), length statistics shift to 32 ± 3.4 μm (SEM), which matches curve-fitted values. At all concentrations, the rigid rod model best described the data, including an excellent match with measured free actin concentrations (Fig. S4) (32). At the highest concentrations, small systematic deviations (<6.5%) appear, probably because of slow filament diffusion that did not reach equilibrium, even after overnight incubation.

Second, we compared the predictions of depletion depth with actin concentration. F-actin could behave like xanthan gum: Individual depletion profiles behave like rigid rods, but concentration dependence of depletion behaves like flexible polymers (33). As described above, flexible polymer theory predicts that the extent of depletion should vary proportionally with mesh size, which is solely determined by concentration once filaments are long enough to entangle. After compensating for free actin by curve-fitting z-profiles with the rigid rod model, the effective Z50 values follow a unity power law at concentrations >0.5 μM (Fig. 4A). Shown in Fig. 4A for comparison, actin's mesh size has been measured, and it varies with a power law of 0.5 (34). F-actin self-depletion does not follow predictions for a flexible polymer.

Discussion

Although the role of membrane-anchored actin-binding proteins to coordinate diverse actin functions is well accepted, the inhibitory role of surface proximity is largely ignored. To understand how the cytoskeleton interacts with biological surfaces, we used confocal microscopy to monitor fluorescent actin distribution near nonadherent surfaces. Requiring only the inherent physical properties of F-actin, actin depletes itself from surfaces. In vitro, such self-depletion can extend as much as 35–45 μm (Fig. S4).

Despite decades of visualizing F-actin, a number of technical issues have conspired to obscure its self-depletion near surfaces. Based on our study, visualizing depletion only requires filaments of moderate length (>5 μm), thoroughly blocked surfaces, and moderate actin concentrations. In general, actin experiments are not attempted with all of these conditions. The notable exceptions are single-filament studies of myosin motility or of actin dynamics. For myosin-motility experiments (35), the phalloidin-stabilized filaments are so sparse (≈20 nM), that the acquisition of reliable statistics of actin distribution is challenging, particularly for control experiments lacking myosin. Visualization by using electron microscopy also suffers from a paucity of filaments for reliable statistics (18). For actin dynamics experiments (36), actin concentrations are sufficient for statistics (≈1 μM), but filament imaging often requires total internal reflectance microscopy (TIRF). TIRF, like other high-resolution techniques, relies on oil-immersion lenses to achieve sufficiently high numerical aperture. Despite their excellent fluorescence performance at surfaces, oil-immersion lenses introduce increasing spherical aberration with depth into aqueous specimens, thus reducing resolution and fluorescence efficiency with depth (Fig. S5). Hence, popular optics for high-resolution imaging directly counteract efforts to visualize self-depletion.

The concept that polymers self-deplete from surfaces has very little precedence among cytoskeleton studies, but it is more common for synthetic polymers. Early actin pioneers recognized that all polymers necessarily self-deplete near surfaces (8). In the intervening half century, there were no reported attempts other than our own (18) to visualize the self-depletion by F-actin, despite several microrheology studies suggesting the existence of F-actin self-depletion zones (18, 37–39). In addition, microrheology studies indicated that interfilament cross-linking does not prevent actin depletion from surfaces (18). In contrast, understanding of synthetic flexible polymers, such as polystyrene or DNA, is more mature. For such polymers, theories of surface self-depletion have a long history (30) and are better accepted for their effects on surface-bound reactions (e.g., DNA and microarrays) (15, 16). For some synthetic polymers, surface depletion has been measured directly and compared with polymer theories (33, 40–42).

Because the extent and speed of depletion is contingent on the formation, length, and rigidity of F-actin, we propose 2 concurrent mechanisms to explain actin depletion. Starting from monomeric actin, self-nucleated filaments grow rapidly, often from both ends. For filaments near the glass surface, their growing tips push the rest of the filament in a Brownian-ratchet manner, thus depleting this subpopulation from the surface. Empirically, the quantitative match is striking for depletion properties (kinetics and extent) with pyrenyl-actin polymerization properties (kinetics and length). At later times when polymerization should be steady-state, thermodynamic considerations will dominate. For a diffusing filament, proximity to a surface sterically reduces its rotational freedom, thus imposing an entropic cost. Limited by their slow diffusion due to size and shape, filaments will redistribute themselves to minimize this entropic cost. These 2 mechanisms only require proximity to an impenetrable surface and would occur to varying degrees at all biological membranes.

Quantitative Models.

Qualitatively, both rigid rod and flexible polymer models are consistent with our data. These models take the extreme approximations that filaments are entirely rigid or mostly flexible for their lengths. Quantitatively, the rigid rod model best describes actin's self-depletion profiles in dilute solutions (Fig. 4B). However, at higher concentrations, the model's length parameter L becomes an estimate of depletion extent rather than filament length as crowding dominates (Fig. S4, Table S1). Only flexible polymer theory has attempted to explain concentration-dependent data. With xanthan gum, there is precedence of mixed behaviors: rod-like depletion profiles, but flexible polymer concentration dependence (33). From flexible polymer theory, concentration-dependent depletion should exhibit an inverse power law of 0.75 (33). Empirically, all prior measurements of depletion match this theory (33, 41).

Unlike all prior depletion measurements, F-actin does not crowd like flexible polymers (Fig. 4A). For flexible polymers, pore or mesh size is the largest relevant dimension of entangled networks. For F-actin, where its persistence length can span multiple pores, we propose that network pores near the ends of the filament are most important for limiting its orientational diffusion. Indeed, this is the essence of reptation models of filaments entangled within F-actin networks (43). The power-scaling argument is straightforward. The mesh size of F-actin scales as − 12 with concentration (34), but the area of the pores scales as the square of the mesh size, or −1 with concentration. Because rods near a surface lose orientational configurations proportionally with proximity to the surface (10), the distance where surface constraints balance crowding constraints should scale as −1 with concentration. In SI Appendix is a more formal derivation where the actin depletion zone should follow a 1/[Actin] (−1 power law) concentration dependence.

Implications for Cell Biology.

The general success of the rigid rod model allows us to extrapolate to cellular conditions. For membrane-anchored actin-binding proteins, we will estimate the inhibitory effects of surface proximity for capturing free actin filaments. For Dictyostelium, physiological F-actin is ≈70 μM with an average 0.1–0.2 μm in length (44, 45). At these concentrations, the network mesh size would have been >0.2 μm (34), but this is comparable with or larger than the filaments, so crowding effects should be minor. By the rigid rod model, 0.2 μm F-actin should self-deplete with an equivalent Z50 ≈40 nm. Assuming that an actin-binding protein reaches 5 nm from a flat membrane surface (diameter of ≈60-kDa globular domain), F-actin concentration would be <12% of the bulk concentration. Alternatively stated, the 70 μM bulk F-actin is only 8 μM near the tips of membrane-anchored actin-binding proteins, thus slowing reactions by reduced concentration. In addition, filament size should slow reactions by slowing diffusion (≈10-fold over monomer, ≈L−0.8). Although subcellular variations in actin concentration complicate the situation, the convex curvature of the plasma membrane would further enhance depletion (11). Hence, for plausible physiological conditions, membrane reactions are slowed ≈100-fold, scaling ≈L−1.8 with filament length.

Although our study is of free F-actin, the same physical and thermodynamic principles apply to any subcellular structure with some rigidity. By using the confocal assay, addition of α-actinin or VCA and ARP2/3 during actin polymerization still generated actin depletion comparable with or larger than pure actin (data not shown). Despite complicated kinetics and larger network structure, thermodynamics of depletion still persists. Bipolar myosin rods and microtubules should also deplete from surfaces. To combat the continual thermodynamic tendency to deplete, active biological processes are required to maintain cortical association.

Physiologically, cells have a rich cortical actin structure poised for fast kinetic responses to environmental cues. Because of the kinetic and thermodynamic costs of membrane proximity, evolutionary pressures should favor strategies that avoid capturing preexisting filaments. Instead, cortical actin probably forms from filaments nucleated at the membrane (e.g., 46). With additional autocatalytic properties, ARP2/3 and formins are plausible molecular candidates to help form cortical actin (3, 47).

For flexible surfaces such as plasma membranes, filament depletion should still occur, but necessarily affects membrane bending stiffness and equilibrium curvature. Depending on lipid composition, bending moduli can increase manyfold because of rod depletion (11). When rods are on only one side of the membrane, depletion also favors spontaneous bending toward the rods (11). Reminiscent of membrane shapes initiating phagocytosis and protruding lamellae, spherical invaginations and sheet-like cylindrical protrusions, respectively, disfavor and favor accumulation of rods (11).

Self-depletion by F-actin is a large-scale example of entropic depletion that should exist for all polymers (8). Also called molecular crowding, generalized depletion forces favor intermolecule associations within cells, thus accelerating biochemical reactions (9). Often used to promote cell–cell fusion (48, 49), depletion forces should also favor organelle fusion within cells. Because rod-like shapes accentuate depletion effects (11), F-actin should facilitate such crowding processes, potentially influencing membrane-bound reactions and membrane mechanics in multiple ways.

Experimental Procedures

Details of reagents, protein purification, fluorescent labeling of proteins, microscope flow chamber assembly, and confocal microscopy can be found in SI Materials and Methods.

Microscopy.

Three technical issues deserve highlighting. First, bare acid-washed glass adsorbs enough actin to exceed 0.5 μM equivalent, exceeding the bulk concentration in some experiments (Fig. S1). Supported lipid bilayers and ovalbumin each produced F-actin depletions equivalent to BSA-blocking (data not shown). Second, a water-immersion lens (60×/1.2 UPlanSApo) was used for confocal microscopy to avoid the spherical aberration inherent in using oil-immersion lenses deep in aqueous specimens (Fig. S5). Third, the coverslips of the microscopy chambers required extra support (solved by allowing VALAP infiltration, see SI Materials and Methods) to resist transient compression forces from the viscosity of optical immersion fluids, both oil and water. Sample compression causes fluid flow that aligns actin filaments; for long actin filaments in networks, alignments can persist for days.

Data Processing and Analysis.

All confocal data were processed by using custom code developed in MATLAB (MathWorks). After correcting for the dark signal and bleed through, Gaussian fitting of the TAMRA signal was used to assign position of surface as z = 0 μm. For some curve-fitting, multiple experiments spanning different fluorescence sensitivities needed averaging. Before such averaging, fluorescence z-profile data were normalized by the average “bulk” fluorescence (average across z = 30–50 μm). Phenomenological kinetic parameters were extracted by fitting plots of Z50 against time, either with a single exponential, Z50(t) = A*[1 − exp(−(t − t0)/τ)] + C, or a sum of 2 exponentials, Z50(t) = A*[1 − exp(−(t − t0)/τ1)] + B*[1 − exp(−(t − t0)/τ2)] + C.

To fit model profiles, we normalized with 3 considerations: (i) fluorescence F(z) is proportional to subunit concentration, (ii) F(z) = 0 when z < 0, and (iii) F(z) increases monotonically with z to a limit of F(∞) = Fbulk. When appropriate, a fraction of the actin, fMono, was allowed to remain monomeric and not polymerize. The 4 theoretical functions used were:

  • Rigid rod (10); L = rod length: Embedded Image

  • Rigid rod + Monomer: Embedded Image Embedded Image

  • Flexible polymer (29, 30); ξ = mesh size (or radius of gyration when very dilute): Embedded Image

  • Flexible polymer + Monomer: Embedded Image

In our fitting algorithm, we mimicked the blurring of the microscope by convolving theoretical predictions with a constant 1D PSF, as estimated with the TAMRA-BSA signal. Because the TAMRA-BSA signal was measured at every time point, no additional free parameters were introduced when using this scheme. The statistics of all fitted parameters express the 68% confidence interval. See Tables S1 and S2 for additional information.

Acknowledgments

We thank Douglas Robinson and Susan Craig for critically reading this manuscript, David Yue and Michael Tadross for training and conversations about confocal microscopy, and Steven Merrill for critical comments and technical assistance preparing reagents and archiving datasets. We also thank Dorothy Schafer for the gift of capping protein. This work was supported by National Institutes of Health Grant R01GM59285.

Footnotes

  • 1To whom correspondence should be addressed. E-mail: skuo{at}jhu.edu

  • Author contributions: C.I.F. and S.C.K. designed research, performed research, contributed new reagents/analytic tools, analyzed data, and wrote the paper.

  • The authors declare no conflict of interest.

  • This article is a PNAS Direct Submission. J.A.C. is a guest editor invited by the Editorial Board.

  • This article contains supporting information online at www.pnas.org/cgi/content/full/0804991106/DCSupplemental.

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Filament rigidity causes F-actin depletion from nonbinding surfaces
Charles I. Fisher, Scot C. Kuo
Proceedings of the National Academy of Sciences Jan 2009, 106 (1) 133-138; DOI: 10.1073/pnas.0804991106
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