J. Phys. Chem. B 2006, 110, 2881-2887
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Intermolecular Interaction of Actin Revealed by a Dynamic Light Scattering Technique Noriko Kanzaki,*,† Taro Q. P. Uyeda,‡ and Kazuo Onuma† Institute for Human Science and Biomedical Engineering, National Institute of AdVanced Industrial Science and Technology, Higashi 1-1-1, Central 6, Tsukuba 305-8566, Japan, and Gene Function Research Center, National Institute of AdVanced Industrial Science and Technology, Higashi 1-1-1, Central 4, Tsukuba 305-8562, Japan ReceiVed: August 28, 2005; In Final Form: NoVember 28, 2005
The intermolecular interaction force of actin was studied by a dynamic light scattering technique. The mutual diffusion coefficients (D) of monomeric actin were accurately determined in a G-buffer with a low concentration of KCl from 0 to 10 mM. The translational diffusion coefficient was obtained as D0 ) (87 ( 3) × 10-12 m2‚s-1 at 25 °C and pH 7.4, which gives a hydrodynamic radius of monomeric actin of rH ) 2.8 ( 0.1 nm. The Derjaguin-Landau-Verwey-Overbeek (DLVO) theory, assuming electrostatic and van der Waals potentials, failed to describe the change in interaction parameter (λ) with KCl concentration, but the extended DLVO theory succeeded if an additional repulsive potential was assumed. The Hamaker constant of actin in the Ca2+-ATP bound state was determined for the first time as AH ) 10.4 ( 0.6 kBT.
1. Introduction Actin is one of the most abundant proteins in eukaryotic cells. Its distinct feature is to polymerize into two-stranded helical filaments under physiological salt conditions and to disperse into monomeric forms in low salt buffers such as the G-buffer. The polymerization process has been established by many kinetic studies.1-8 Oligomers are formed as nuclei above a critical monomer concentration and elongate from both ends at each rate constant of polymerization. The elongation process reaches a steady state where filaments keep the average length by addition of actin to one end balanced by dissociation from the other end. The elongation and steady-state processes have been elucidated by directly observing the filament lengths by fluorescence microscopy.8-10 However, the nucleation process is still poorly understood, although oligomers such as dimers, trimers, or tetramers have been predicted to serve as a nucleus.5-7 The intermolecular interaction force operating between actin molecules is a very important issue in clarifying the nucleation process. The force operating between particles often follows the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory.11 This theory describes the force by the combination of repulsive electrostatic and attractive van der Waals potentials. For several proteins, it has also been reported that the DLVO theory well explained the force,12-14 although an additional potential such as depletion,12 salt bridging,15,16 or hydration force17,18 should be assumed in the presence of a polymer, specific cation, or high salt concentration, respectively. In the case of actin, a specific hydrophobic attractive potential tends to be assumed as the additional potential between specific binding sites providing the actin’s polymerization behavior.19,20 * To whom correspondence should be addressed. Phone: +81-29-8614832. Fax: +81-29-861-6149. E-mail:
[email protected]. † Institute for Human Science and Biomedical Engineering. ‡ Gene Function Research Center.
To analyze intermolecular forces using the DLVO theory, we should accurately determine the actin concentration dependence of mutual diffusion coefficients (D) of monomeric actin at various salt concentrations. Because salts induce the nucleation of actin, it is interesting how the intermolecular interaction force changes depending on the salt concentrations. Therefore, we measured D of monomeric actin by a dynamic light scattering (DLS) technique both in a G-buffer where actin was stable as a monomeric form and in G-buffers with several concentrations of KCl below 10 mM where actin was subcritical or in the very early stages of polymerization during the measurements. Then, we analyzed the data using the DLVO theory and tried to understand the kind of potentials operating between monomeric actin and their energy balance. We also attempted to determine the Hamaker constant of monomeric actin, which is an important physical parameter in the polymerization process. 2. Experimental Section 2.1. Purification of Actin. Actin was prepared from acetone powder of rabbit back muscle according to the method of Supdich and Watt21 with the following two modifications. We repeated the step of removing tropmyosin once more by homogenizing and ultracentrifuging actin in a G-buffer with 0.8 M KCl, 2 mM MgCl2, and 1 mM ATP. We performed a gel filtration as a final purification step according to Fletcher and Pollard.22 We used a Sephacryl S300HR column (Amarsham Bioscience, U.S.A.) for gel filtration, and the appropriate fractions were collected and concentrated to 4-5 mg‚mL-1. Purified actin was dialyzed for 48 h at 4 °C against a G-buffer (2 mM Tris-HCl, 0.2 mM CaCl2, 0.2 mM ATP, 0.5 mM dithiothreitol, and 0.005% NaN3, pH 7.4 ( 0.2 at 25 °C). It was ultracentrifuged at 150 000g for 30 min at 4 °C, and the concentration of supernatant was determined by adsorption at a wavelength of 290 nm using an extinction coefficient of 0.62 mg-1‚mL‚cm-1.23 We stored it on ice and used it up within 3 days.
10.1021/jp054865g CCC: $33.50 © 2006 American Chemical Society Published on Web 01/24/2006
2882 J. Phys. Chem. B, Vol. 110, No. 6, 2006
Kanzaki et al.
2.2. Sample Preparation for DLS Measurement. We prepared a G-buffer with the same composition as the dialysis buffer and G-buffers containing 10, 30, 50, and 100 mM KCl. These five kinds of buffers were filtered with a 0.1-µm poresized filter and stored on ice. Actin solution was diluted with the KCl-free G-buffer to the desired actin concentration and filtered with a 0.22-µm poresized filter just before DLS measurement. A 150-µL sample was put into a precleaned glass tube with a diameter of 5 mm and placed in a light scattering system kept at 25 ( 0.1 °C by an external water bath. Measurement was started after a waiting time of 5 min, which was intended to suppress convection in the solution and settle temperature fluctuations. For the KClcontaining condition, a G-buffer containing 10, 30, 50, or 100 mM KCl was added to the filtered actin solution so that the final KCl concentration was 1, 3, 5, or 10 mM. The sample was quickly mixed and put into a glass tube and placed in a light scattering system as fast as possible. No filtration was carried out after the KCl-containing buffer was added to avoid changing the actin concentration by removing aggregates that could appear in the solution. 2.3. DLS Measurement. DLS measurement was performed with a DLS-7000 optical system (Otsuka Electronics Co., Ltd., Osaka, Japan) with an Ar+ laser (Spectra-Physics Lasers, Mountain View, CA) at a wavelength (λW) of 488 nm. The second autocorrelation functions (g(2)(q,t)) were measured at scattering angles (θ) from 20 to 90° with a step of 10° to check the angular dependence. The accumulation time for g(2)(q,t) was 60 s for the KCl-free conditions where actin was stable as a monomeric form and was 30 s for the KCl conditions where actin might change its particle size distribution during the measurement. Thus, DLS measurement for each sample took approximately 15 min for KCl-free conditions and 10 min for KCl-containing conditions including a waiting time of 5 min. The laser power was changed from 10 to 950 mW to keep the average scattering intensity above 30 000 cps. The g(2)(q,t) was analyzed using an ALV-5000/E correlation system (ALV-Laser Vetriebsgesellschaft). Several fitting models, such as a normal exponential function fitting and CONTIN analysis,24,25 were applied to analyze the autocorrelation function data. 2.4. Capillary Electrophoresis Measurement. The surface potential (ψ0) of an actin molecule was estimated using a capillary electrophoresis measuring system called CAPI-3300 (Otsuka Electronics Co., Ltd., Osaka, Japan). We measured the electrophoretic mobility of actin in the G-buffer at 25 °C and pH 7.4 under an applied voltage of 20 kV. We used a silica capillary with a total length of 50 cm (38 cm effective length) and an inside diameter of 75 µm. The temperature was kept at 25 °C by air circulation in the capillary chamber. Actin solution was prepared by dialyzing against the G-buffer at 4 °C at a concentration of 5.0 mg‚mL-1. It was diluted with the G-buffer to the desired actin concentration and filtered with a 0.22-µm pore-sized filter just before measurement. The sample solution was introduced into the capillary by gravity and detected by the absorbance at a wavelength of 200 nm. ψ0 relates to the electrophoretic mobility of particles (µ) according to Henry’s equation as26,27
µ) f(κa) )
[ (
0ζ f(κa) η
1 2.5 2 1+ 1+ 3 2 κa{1 + 2 exp(-κa)}
(1)
)] -3
(2)
where ζ is the zeta potential, which is assumed to be equal to
ψ0 in the present study, η denotes the viscosity of the medium, is the dielectric constant of the medium, 0 is the permittivity of free space, a is the particle radius, and κ is the screening parameter given by
e2
κ ) 2
0kBT
∑j njzj2
(3)
where e is the elemental charge, kΒ is the Boltzmann constant, T is the absolute temperature, nj is the number density (m-3), and zj is the ion valence of the jth ion. 3. Theory 3.1. Analysis of the Autocorrelation Function. g(2)(q,t) is expressed as
g(2)(q,t) )
〈I(q,t)‚I(q,0)〉 〈I(q,0)〉2
(4)
where I(q,0) and I(q,t) denote scattered intensities at time zero and time difference t between photon-counting measurements and the angle brackets denote the time average. The scattering vector (q) is related to the refractive index of the solution (n), the wavelength of the laser light (λW), and the scattering angle (θ) by
q ) 4πn sin(θ/2)/λW
(5)
For example, g(2)(q,t) can be fitted by an exponential function as follows:
g(2)(q,t) - 1 )
{
(( ) )}
∑i Ki exp
-t
β
2
τi
(i ) 1, 2, 3, ...)
(6)
where Ki is a constant and τi is the decay time. The parameter β varies from 0 to 1: β ) 1 indicates a normal exponential decay, and β < 1 indicates a stretched exponential decay, which has been frequently reported in a gel-transition process. The obtained decay time is related to q and the mutual diffusion coefficient of scattered particles (D) as
1/τ ) q2D
(7)
D is affected by the interaction between scattered particles as28
D ) D0(1 + λφ)
(8)
where D0 is the translational diffusion coefficient extrapolated to zero concentration of particles, φ is the volume fraction, and λ is the particle interaction parameter. The rH value of a particle is associated with D0 via the Einstein-Stokes relationship as
D0 )
kB T 6πηrH
(9)
3.2. Analysis of Intermolecular Interaction Forces. Intermolecular interaction forces between actin molecules were analyzed using the DLVO theory.11 The radial distribution function (g(r)) of scattered particles expresses the intermolecular interaction potential of mean force (U(r)) as28
g(r) ) exp
( ) -U(r) kBT
(10)
The particle interaction parameter (λ) is related to g(r) by the
Intermolecular Interaction of Actin
J. Phys. Chem. B, Vol. 110, No. 6, 2006 2883
following equations in the DLVO theory.28
λ ) λV + λO + λA + λS + λD
(11)
∫0∞[g(r) - 1]r2 dr
(12)
λV ) λO ) λA )
3 a3
∫0∞[g(r) - 1]r dr
3 a2
∫0∞[89(ar)
3 a3
6
λS )
-
∫0∞
75 4 a 4
(13)
5a4 g(r)r2 dr 4r
(14)
[ ]
(15)
( )]
g(r) r5
dr
λD ) 1
(16)
where r is the distance between the particles and a is the particle radius (r > 2a). For the DLVO theory, U(r) is defined using only the repulsive electrostatic potential (Ues)29 and the attractive van der Waals potential (Uvdw)30 as follows:
U(r) ) Ues + Uvdw Ues ) Uvdw ) -
(
(17)
2π0aψ02 exp(-2κax) x+1
(
(18)
))
AH 1 1 x2 + 2x + + 2 ln 12 (x + 1)2 x2 + 2x (x + 1)2
(19)
where x ) (r - 2a)/2a, AH is the Hamaker constant, and ψ0 is expressed using the net surface charge of a particle (Z) as
ψ0 )
Ze 4π0a(1 + κa)
(20)
4. Results and Discussion 4.1. Diffusion Coefficient and Hydrodynamic Radius of Actin Molecules under KCl-Free Conditions. We measured the D values of actin in the G-buffer at various actin concentrations. Figure 1a shows autocorrelation functions (g(2)(q,t)) at θ ) 20 and 90° at an actin concentration of 4.2 mg‚mL-1. Those g(2)(q,t) values could be fitted by a normal two-exponential function (i ) 2 and β ) 1 in eq 6) with the appropriate parameters Ki and τi, although a normal single-exponential function (i ) 1 and β ) 1 in eq 6) failed to fit them. The twoexponential function fitting, which assumes two relaxation processes (fast and slow) in the solution, was successful at any θ and any actin concentration in the G-buffer. Figure 1b shows the decay time distribution obtained by CONTIN analysis for the data shown in Figure 1a. Two well-separated peaks were found, indicating that CONTIN analysis also supported the existence of two relaxation modes as well as the two-exponential function fitting. As we will show later, the fast mode corresponds to monomeric actin, while, in the slow mode, actin aggregates with an apparent hydrodynamic radius (rA) of 6580 nm. Despite the gel filtration and extensive dialysis, actin aggregates (slow mode) always coexisted with monomeric actin. The amount of aggregates depended on the actin concentration during the dialysis. For instance, actin completely dispersed as a monomeric form after dialyzing for 48 h at an actin
concentration of 2.6 mg‚mL-1 (data not shown). The monomeric actin was dominant with >99.9% of the mass weight even at the highest actin concentration of 4.2 mg‚mL-1, estimated from the relative peak height in CONTIN analysis. Actin aggregates might be very short filaments whose formation is unavoidable due to actin’s polymerization behavior at 4-5 mg‚mL-1, although this is lower than the critical monomer concentration (approximately 6 mg‚mL-1) in a G-buffer.31 We could not find any conclusive evidence of such short filaments using depolarized light scattering (VH scattering), which detects light scattered by anisotropy in the shape or internal bonds of particles. This is probably because they were present in a small amount (
