Article pubs.acs.org/JPCB
Strong Dependence of Hydration State of F‑Actin on the Bound Mg2+/Ca2+ Ions Makoto Suzuki,*,†,‡ Asato Imao,† George Mogami,†,‡ Ryotaro Chishima,† Takahiro Watanabe,† Takaya Yamaguchi,† Nobuyuki Morimoto,† and Tetsuichi Wazawa§ †
Department of Materials Processing, Graduate School of Engineering, Tohoku University, 6-6-02 Aoba, Aramaki-aza, Aoba-ku, Sendai, Miyagi 980-8579, Japan ‡ Frontier Research Institute for Interdisciplinary Sciences, Tohoku University, Sendai, Miyagi 980-8578, Japan § Department of Biomolecular Science and Engineering, The Institute of Scientific and Industrial Research, Osaka University, Mihogaoka 8-1, Ibaraki, Osaka 567-0047, Japan S Supporting Information *
ABSTRACT: Understanding of the hydration state is an important issue in the chemomechanical energetics of versatile biological functions of polymerized actin (F-actin). In this study, hydration-state differences of F-actin by the bound divalent cations are revealed through precision microwave dielectric relaxation (DR) spectroscopy. G- and F-actin in Caand Mg-containing buffer solutions exhibit dual hydration components comprising restrained water with DR frequency f 2 (f w). The hydration state of F-actin is strongly dependent on the ionic composition. In every buffer tested, the HMW signal Dhyme (≡ ( f1 − f w)δ1/( f wδw)) of F-actin is stronger than that of G-actin, where δw is DR-amplitude of bulk solvent and δ1 is that of HMW in a fixed-volume ellipsoid containing an F-actin and surrounding water in solution. Dhyme value of F-actin in Ca2.0-buffer (containing 2 mM Ca2+) is markedly higher than in Mg2.0-buffer (containing 2 mM Mg2+). Moreover, in the presence of 2 mM Mg2+, the hydration state of F-actin is changed by adding a small fraction of Ca2+ (∼0.1 mM) and becomes closer to that of the Ca-bound form in Ca2.0-buffer. This is consistent with the results of the partial specific volume and the Cotton effect around 290 nm in the CD spectra, indicating a change in the tertiary structure and less apparent change in the secondary structure of actin. The number of restrained water molecules per actin (N2) is estimated to be 1600−2100 for Ca2.0- and F-buffer and ∼2500 for Mg2.0-buffer at 10−15 °C. These numbers are comparable to those estimated from the available F-actin atomic structures as in the first water layer. The number of HMW molecules is roughly explained by the volume between the equipotential surface of − kT/2e and the first water layer of the actin surface by solving the Poisson−Boltzmann equation using UCSF Chimera.
1. INTRODUCTION
Hydration processes in the energetics of structural changes in protein molecules induced by protein−ligand interactions, protein-divalent ion interactions, or other stimuli have been extensively studied.4,5 To investigate the energy transduction mechanism of actomyosin, experimental and theoretical advancements in the understanding of hydration processes are required. Matubayasi et al.6 demonstrated with a small protein that the hydration energy due to solvent−protein surface interaction was nearly balanced with the internal energy change of the protein molecule. Kinoshita et al.7 showed that large structural changes of proteins such as protein folding and protein−ligand binding were strongly correlated with the
Actin is a protein that plays key roles in living cells, for example, as cytoskeletal proteins and molecular motors of muscles. An actin filament (F-actin) is a polymerized form of globular actin (G-actin) and known to exhibit structural polymorphism (PM) induced by divalent metal ions or actin-binding proteins.1,2 Actin has many versatile functions in cells, which must be closely related to the PM. Fuller and Rand3 showed that Ca-actin polymerization was affected by osmolytes, where a dozen of water molecules per actin were found to be released on polymerization, while Mg-actin polymerization did not depend on osmolytes. Their result indicated that action of water molecules on polymerization was different between Mg-actin and Ca-actin. In the physiological condition, actins work in the presence of both Mg2+ and Ca2+ ions. Thus, it is an interesting problem to find the hydration-state change of F-actin at different combinations of Mg2+ and Ca2+ ion concentrations. © XXXX American Chemical Society
Received: March 11, 2016 Revised: June 22, 2016
A
DOI: 10.1021/acs.jpcb.6b02584 J. Phys. Chem. B XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry B Table 1. Buffer Conditions
a
reagent
KCl
MgCl2
CaCl2
HEPES
ATP
DTT
EGTA
buffer solution name
(mM)
(mM)
(mM)
(pH 7.8) (mM)
(mM)
(mM)
(mM)
GF- (Mg2/Ca0.1-) Mg2/Ca0.03Mg2/Ca0.01Mg2.0Ca0.1Ca2.0-
0 50 50 50 50 50 50
0 (0.1)a 2 2 2 2 0 0
0.1 (0)a 0.1 0.1 (0.03)b 0.1 (0.01)b 0 0.1 2
2 10 10 10 10 10 10
0.1 0.1 0.1 0.1 0.1 0.1 0.1
0.6 0.6 0.6 0.6 0.6 0.6 0.6
0 0 0.07 0.09 0.10 0 0
For Mg-G-actin, values in the parentheses are used. bValues in the parentheses are the actual free Ca2+ concentrations.
adjusted to pH 7.8 with KOH) containing 0.1 mM ATP, 0.6 mM DTT and 0.1 mM CaCl2, here referred to as G-buffer. Gactin was polymerized into F-actin (FA) by adding KCl and MgCl2 (or CaCl2 for Ca−F-actin (Ca-FA)) to a final concentration of 50 and 2 mM, respectively. After ultracentrifugation, F-actin pellets were dissolved in G-buffer and dialyzed against G-buffer overnight. For the preparation of MgG-actin, 0.1 mM MgCl2 was used instead of 0.1 mM CaCl2 in Gbuffer, and for Mg-FA 0.1 mM ethylene glycol tetraacetic acid (EGTA) was added to chelate Ca2+ ions in Mg2.0-buffer (2 mM MgCl2, 0.1 mM EGTA, 0.1 mM ATP, 1 mM DTT, 10 mM HEPES-KOH, pH 7.8). The buffer conditions are summarized in Table 1. The purity of G-actin was examined by SDS-PAGE analysis, which confirmed a purity of 99% using ImageJ (ver. 1.45).15 (see Figure S1 in the Supporting Information) 2.2. Preparation of Pyrenyl-Actin. To estimate the polymerization degree of actin in G-buffer solution with a low salt concentration, pyrene-labeled actin (PA) was prepared as follows. First, G-actin solutions were prepared by dialysis against DTT-free G-buffer. The G-actin concentration was determined using an extinction coefficient of 0.63 mL·mg−1·cm−1 at 290 nm. The actin was then polymerized in 0.1 M KCl and 10 mM HEPES-KOH (pH 7.8) for 30 min at room temperature. This Factin solution was mixed with N-(1-pyrene)iodoacetamide (PIA) and incubated for 1 h in the dark, according to a previous report.16 The PA solution was mixed with 1 mM DTT and ultracentrifuged at 520 000g and 4 °C for 10 min. The PA pellets were dissolved in G-buffer and the solution was dialyzed against G-buffer for 1 day to remove free PIA. After ultracentrifugation, the supernatant was used as the pyrenyl G-actin (PGA, a mixture of labeled and nonlabeled actins) solution. The lowest fluorescence spectrum of a 1 mg/mL PGA solution indicated the residue of free PIA in the PGA solution in Figure 1. The PIA solution displayed absorption peaks at 275 and 340 nm, whereas the ATP-bound G-actin solution only displayed the absorption
entropy change of water molecules including those beyond the first water layer. We previously reported a dual hydration structure of F-actin containing restrained and hypermobile water (HMW) layers.8 HMW was detected as a water component having a smaller dielectric relaxation (DR) time than that of bulk water through precision microwave DR spectroscopy. In this Article, “DR frequency” (in other words, DR loss peak frequency) is used instead of DR time, τD, as defined by 1/(2πτD). An increase in the DR amplitude of HMW was also observed upon binding of the myosin head (S1) to F-actin, where S1 alone did not have HMW, indicating PM of F-actin.9 The importance of the change in translational water entropy upon structural change of myosin S1 on F-actin as a driving force was demonstrated using a statistical mechanical theory.10 Kinoshita and Suzuki11 also showed that HMW was closely correlated to the high rotational entropy of water molecules surrounding a charged particle and a charged protein such as a large ion and an actin, respectively. Large scale molecular dynamics calculations verified that the DR process of water molecules around an ion was faster than that of bulk water.12 In addition, an ab initio molecular dynamics study13 successfully reproduced the far-infrared-to-terahertz region absorption spectra of Raman, optical Kerr effect, and terahertz experiments. The result explained the response-time range faster than ∼1 ps for the hydrogen-bond networks of water surrounding ions. HMW treated here is distinguished from those terahertz modes because the dielectric response of HMWmode is still one order slower than those modes. Although we have no direct method to measure the local entropy of water around the protein at this moment, we should be able to acquire responses including many-body interactions of water molecules around F-actin using our high-resolution DR spectroscopy (DRS) technique. The relation between the dielectric property and the thermodynamic quantities of water is an ongoing subject of the statistical physics6,10−12 and will be resolved in the near future. Thus, the elucidation of hydrationstate change of proteins is a critical issue for building the energetics of protein machineries. In this study, the authors experimentally examined the coupling between the hydration property of F-actin and the structure of F-actin by exchange of divalent ions between Mg2+ and Ca2+.
2. MATERIALS AND METHODS 2.1. Preparation of Actin Solutions. A G-actin solution was prepared from acetone powder in Tris-HCl buffer (0.1 mM ATP, 0.6 mM dithiothreitol (DTT), 2 mM Tris(hydroxymethyl) aminomethane, 0.2 mM CaCl2, pH 8.0) made from chicken pectoral and leg muscles using the Spudich and Watt method.14 Then, the G-actin solution was dialyzed against 2 mM HEPESKOH (4-(2-hydroxyethyl)-1-piperazine ethanesulfonic acid,
Figure 1. Fluorescence spectra of PA in G-buffer compared with that in F-buffer at 20 °C. B
DOI: 10.1021/acs.jpcb.6b02584 J. Phys. Chem. B XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry B peak at 279 nm and the ATP solution had quite small absorption at 290 nm (data not shown). As such, the labeling ratio (R) of actin, which is the concentration ratio of pyrenylated actin to total actin, was determined as follows PIA Abs PGA 290nm − Abs 290nm
[Actin] = [PA] =
(
PGA Abs340nm PIA Abs340nm
0.63 × 42300 PGA Abs340nm
26000
,
R=
[PA] [Actin]
concentration of the actin solution was controlled with EGTA by using Maxchelator software20 and the dissociation constants of Mg2+ and Ca2+ from EGTA4− to be 10−5.21 and 10−11 M, respectively. Using the proton dissociation constant of EGTA (pK1 = 1.9, pK2 = 2.7, pK3 = 8.71, and pK4 = 9.32), it was found that EGTA was in a divalent form with an apparent binding constant of 10−6.91 M with Ca2+ under the present conditions with pH = 7.8. Further examination confirmed the results using Maxchelator by calculating the equilibrium concentrations based on the dissociation constants given by NIST21 as follows
), (1)
L·Ca → L + Ca pKd = 10.86
PIA where AbsPGA x nm and Absx nm are the measured absorbances of PGA
solution and PIA solution at wavelength of x nanometers at equal PIA concentration, respectively (see Figure S2 in Supporting Information). [PA] was calculated with absorption coefficient 2.6 × 104 M−1·cm−1 (P-29 by Invitrogen).33 The R of actin was determined to be ∼30%. 2.3. Determination of F-Actin Fraction. Fluorescence spectra of 1, 2, 4, 6, and 8 mg·mL−1 PGA solutions were measured using a Fluorolog-2 spectrofluorometer (SPEX; Edison, NJ, U.S.A.) with λexc = 365 nm in a temperature range from 5 to 40 °C. For calibration, copolymerized actin with PA in F-buffer (50 mM KCl, 2 mM MgCl2, 0.1 mM CaCl2, 0.1 mM ATP, 0.6 mM DTT, 10 mM HEPES pH 7.8) was used as 100% Factin, where a fluorescence peak (FF−actin) was present at 385 nm. A 1 mg·mL−1 G-actin solution in G-buffer was used as 0% F-actin (the lowest curve in Figure 1), considering that the critical polymerization concentrations of actin are ∼0.05 mg·mL−1 in Fbuffer and ∼6 mg·mL−1 in G-buffer.17 Here, PA concentration was adjusted to A350 nm = 0.03 in every case. The apparent fluorescence intensity at 385 nm (Fapp) can be expressed with the following equation using F-actin fraction x, that is, degree of polymerization of actin. Fapp = xFF − actin + (1 − x)FG − actin
LH·Ca → LCa + H pKd = 3.81 L·Mg → L + Mg pKd = 5.28 LH·Mg → LMg + H pKd = 7.59 A·Ca → A + Ca pKd = 3.76
(3)
AH· Ca → ACa + H pKd = 2.16 A·Mg → A + Mg pKd = 4.1 AH· Mg → AMg + H pKd = 2.32 A·Mg 2 → AMg + Mg pKd = 1.7
where L = EGTA and A = ATP. Proton dissociation constants of ATP are pK1 ∼ 0, pK2 = 2.0, pK3 = 4.3, and pK4 = 6.95. Using the dissociation constants of Ca2+ and Mg2+ from actin (pKd,Ca = 8.22 and pKd,Mg = 7.68 at pH 7.8),22,23 the ratio of Cabound F-actin (Ca-FA) to Mg-bound F-actin (Mg-FA) was estimated to be 24:76 in F-buffer. The occupation ratio of Mg2+ to the high-affinity site of F-actin was ∼100% in Mg2.0-buffer (containing 2 mM Mg2+) and that of Ca2+ was ∼100% in Ca0.1buffer (containing 0.1 mM Ca2+) and Ca2.0-buffer (containing 2 mM Ca2+), as shown in Table 2. 2.5. Partial Specific Volume of Actin. Partial specific volume (vB) of G-actin or F-actin (1−7 mg/mL) in each solution was measured from the solution densities of the protein solution and its dialyzing buffer solution using an Anton-Paar DMA-5000 M density meter (Graz, Austria). 2.6. Circular Dichroism Measurements. Circular dichroism (CD) spectra of F-actin solutions with Ca2.0-, F-, and Mg2.0buffers were measured with a spectropolarimeter (J-720, Jasco, Tokyo, Japan) under nitrogen gas flow with a 10 mm light path length cell thermocontrolled at 10.0 °C. The actin concentrations were 1 mg/mL for the short-wavelength range of 200− 250 nm and 2 mg/mL for the long-wavelength range of 280−320 nm. The results are expressed as mean residue molar ellipticity (θ, deg·cm2·dmol−1), which is defined as [θ] = 1000θobs/lc, where θobs, l, and c are the observed ellipticity in degrees, the length of the light path in millimeters, and the concentration in mol·L−1, respectively. 2.7. Electric Field Calculations. The electrostatic equipotential surfaces around F-actin were calculated using the PDB files 2y83 of Ca-FA24 and 3mfp of Mg-FA.25 The atomic structures of actin-pentamers and actin-trimers from the pointed ends of 2y83 and 3mfp were reproduced by removing the uncommon residues and protonating the lacked hydrogen sites using UCSF Chimera software.26 2.8. Dielectric Relaxation Spectroscopy. All measurements were performed in a conical glass cell (total volume = 3.2 mL) facilitated with the open-ended probe connected to a
(2)
In G-buffer, when the actin concentration was higher than 4 mg·mL−1, x exhibited an increase with temperature. While for an actin concentration of 2 mg·mL−1, x stayed near zero (G-actin) up to 40 °C, as shown in Figure 2. For actin concentrations higher than 4 mg·mL−1, slight decreases were observed above 35 °C, which was consistent with the denaturing temperature of actin of 51 °C.18 2.4. Estimation of Binding Ratios of Ca2+/Mg2+ with FActin in the Presence of ATP. Actin has high- and low-affinity binding sites for divalent cations, and the stability of actin is known to be reduced when a divalent ion was released from the high-affinity binding site.19 In the present study, the Ca2+
Figure 2. Change in degree of polymerization of actin in G-buffer with increasing temperature. C
DOI: 10.1021/acs.jpcb.6b02584 J. Phys. Chem. B XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry B Table 2. Occupation Ratios of Cations at High/Low-Affinity Binding Sites of Actin cation (mM)
occupation ratio of high-affinity site (%)
buffer solution name
Ca2+
Mg2+
K+
F- (FB) Mg2/Ca0.03Mg2/Ca0.01Mg2.0Ca0.1Ca2.0-
0.1 0.03 0.01
2.0 2.0 2.0 2.0
50 50 50 50 50 50
0.1 2.0
free
Δε*(f ) = εap,raw *(f ) − εw *(f ) + = Δε′(f ) − iΔε″(f )
Mg2+
free
Ca2+
Mg2+
K+
24 9 3
76 91 97 ∼100
5 5 5 5 15 5
3.3 1 1
66.7 72 72 70 0 0
25 26 26 25 75 25
∼100 ∼100
microwave network analyzer with a solution-temperature accuracy of ±0.01 °C (8364C-85070E, Agilent, Palo Alto, CA; NESLAB RTE-17, Thermo Fisher Scientific, Waltham, MA). Microwaves in the frequency range of 0.2−26 GHz were applied to the cell through the open-end probe. The calibration was done by a procedure consisting of an open circuit in air and a short circuit with mercury and in pure water at each temperature within 0.01 °C. The reflected waves were sampled by the network analyzer and converted into a complex dielectric spectrum consisting of real and imaginary parts, ε*(f) = ε′( f) − iε″(f) with 85070E software. Noise inherent to the measuring system due to small impedance mismatch of the probe, cables, and connectors as well as those from thermal drift of the network analyzer and systematic interference were superimposed on the dielectric spectra. Thus, to reduce this noise, the actual measurement and data processing were performed using the procedures as described in the previous papers.8,27,29,30 Briefly, the spectra of the reference solution (εw*(f) with a relaxation frequency (f w)) and protein solution (εap,raw*( f)) were measured in pairs repeatedly at a given protein concentration with ∼15 min interval. The difference was then taken for each pair (difference spectrum = protein solution spectrum−reference solution spectrum)
occupation ratio of low-affinity site (%)
Ca2+
10 70
Figure 3. Partial specific volume of actin under various ionic conditions.
bound nucleotide. In fact, some partly unfolded protein structures exhibited smaller vB than the native structures,27,28 and the α-helix content (from the 222 nm peak of CD spectrum) of Mg-FA was found to be slightly lower than those of F-actin in the Ca-containing buffers as shown in Figure 4a. 3.2. Circular Dichroism Measurements. All spectra of actin solutions at 1 mg/mL were analyzed by subtracting the solvent baseline from the recorded spectra. In Figure 4a, ellipticities at 222 nm of F-actin in F- and Ca2.0-buffers exhibited equivalent minima, and that in Mg2.0-buffer was ∼94% of the amplitude in Ca2.0-buffer, showing that the proteins in Ca2.0buffers were in their folded state and actins in Mg2.0-buffer had slightly less α-helices than in Ca2.0- or F-buffer. Figure 4b shows the CD spectra of F-actin solutions in the wavelength range of 280−320 nm to examine the difference in the tertiary structure of F-actin in three different buffers. A clear difference in the spectral curves around 290 nm indicated a steric arrangement of tryptophans in F-actin.31 From the ellipticity at 290 nm, the tertiary structure of F-actin in F-buffer was suggested to be looser than in Mg2.0-buffer and tighter than in Ca2.0-buffer. 3.3. Dielectric Spectroscopy and Data Analysis. The spectra of the reference solution (εw*( f) with a relaxation frequency ( f w)) and protein solution (εap,raw*( f)) are shown in Figure 5a,d. The difference spectra obtained by eq 4 as in Figure 5b,e with standard errors in Figure 5c,f were then averaged and subjected to mathematical “‘smoothing’” using third to fifth order polynomial functions of log10 f in three ranges, 0.2−2, 1−10, and 8−26 GHz.(for more details, see refs 29 and 30) This gave a smoothed difference dielectric spectrum (Δεsm*( f)) (Figure 5b,e in orange lines; a−c at 10 °C, d−f at 20 °C). Finally, the spectrum of the sample protein solution (εap*(f)) was calculated by adding the smoothed difference spectrum (Δεsm*( f)) to the reference-solution spectrum (εw*(f)). Note that the inherent noises of the reference-solution spectrum are mostly canceled out when εq*(f) is calculated by using mixture theories as
iΔσ (2πε0f ) (4)
Here, a small inevitable conductivity difference Δσ between protein and reference solutions due to the restraining of ions around proteins was determined through fitting, as described in a previous paper.29 Some difference spectra are shown in Figure S3 of Supporting Information, where the spectra were normalized at protein concentration of 10 mg/mL. Details of the noise reduction process are given in the Supporting Information (Figures S4−S7), including the characteristics of noises of the measured spectrum.
3. RESULTS AND DISCUSSION 3.1. Partial Specific Volume of Actin. vB of actin in each solution exhibited an increase with temperature, as shown in Figure 3 and Table S1 in Supporting Information. The difference in vB between Ca-G-actin and actin in F-buffer was not obvious. Conversely, the vB of Ca-FA (actin in Ca0.1- and Ca2.0-buffers, Figure 3) was much higher than that of Mg-FA (actin in Mg2.0buffer, Figure 3). The vB of F-actin in F-buffer was found to be higher than in Mg2.0-buffer and lower than in Ca0.1-buffer. The large vB of Ca-FA can be explained if the protein has a cavity-rich tertiary structure. On the other hand, the small vB of Mg-FA can be explained if the side chains of the protein became more exposed due to the stress caused by smaller Mg2+ than Ca2+ at the binding site of, probably, the phosphate group of the proteinD
DOI: 10.1021/acs.jpcb.6b02584 J. Phys. Chem. B XXXX, XXX, XXX−XXX
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Figure 4. CD spectra of F-actin solutions in Ca2.0-, F-, and Mg2.0-buffers (a) in the short wavelength range of 200−250 nm and (b) in the long wavelength range of 280−320 nm.
Figure 5. Measured spectra of F-actin in F-buffer. (a−c) at 10 °C, (d−f) at 20 °C. (a,d) Four sets of raw DR spectra overlaid of sample and reference solutions, showing excellent reproducibility. (b,e) In gray and pink thin lines: difference spectra given by eq 4 corresponding to (a,d), respectively. (b,e) In black and red thick lines: smoothed difference dielectric spectra. (c,f) Standard errors of (b,e) over n = 4, respectively.
described in refs 27, 29, 32, and 33, because the mixture theories of dispersed particles (spheres32 or ellipsoids33) in a homogeneous solvent can reproduce the dielectric permittivity of the particle if the solvent permittivity and the particle volume are known.32,33 Also, it is well-known that the methods fitting on the measured DR spectrum using linearly coupled-Debye functions overestimate the volume of the dispersed particles if the particle permittivity is given.32 Therefore, in this study, we adopted the mixture theories for spheres and ellipsoids. 3.4. Dielectric Spectra of Actin Solutions. Dielectric spectra of the actin solutions with G-, F-, Ca0.1-, Ca2.0-, and Mg2.0-buffers were measured. (e.g., Figure 5a,d for F-actin in Fbuffer; for other actin solution spectra with G-, Ca2.0-, and Mg2.0-buffers, see Figure S3 in Supporting Information) A small but systematic difference between the dielectric spectra of the protein solution and each reference (buffer) solution were seen over the frequency range investigated, as clearly shown in the
difference spectra (Figure 5b,e). The standard errors of both Δε′(f) and Δε″( f) were between 0.020 and 0.027 in this case in the frequency range of 1−26 GHz (Figure 5c,f). The linear dependence of Δε′( f) and Δε″(f) on protein concentration for F-actin at 20 °C is shown in Figure 6, indicating that the tested solutions were well-dissolved and in the monodisperse state. 3.5. Relaxation Component Analysis of the Hydration Shell of Actin. The DR spectrum εap*(f) was analyzed as previously described8,29 to derive the dielectric spectrum εq*( f) of an ellipsoid containing an F-actin filament and surrounding water by using eqs 3−5 of ref 8, where the total volume fraction of ellipsoids in solution was ϕ. εq*(f) was approximated with a linear combination of two Debye components and the bulk component as follows E
DOI: 10.1021/acs.jpcb.6b02584 J. Phys. Chem. B XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry B
where an approximation value around 200 GHz was adopted according to ref 34, and α is the fraction of bulk solvent component. With decreasing ϕ from a value sufficiently larger than the volume fraction of F-actin with a hydration shell, fitting was repeated until α became zero or changed from positive to negative; ϕ was then denoted as ϕB. The DR spectrum of hydrated F-actin was analyzed with the shelled ellipsoid model using a dielectric constant of 2.5 for the protein core, as described in detail previously.8 The numbers of HMW and restrained water molecules per actin-monomer, N1 and N2, were estimated by eq 6 by simply assuming equivalent DR amplitudes for restrained water, HMW, and bulk water.
Figure 6. Proportionality between Δε′, Δε″, and concentration of Factin in F-buffer at 20 °C. Notations of x GHz-i and x GHz-r represent the imaginary and real parts of Δε* at x GHz, respectively. 2
εq*(f ) = εq ∞ +
∑ i=1
δi
⎛f⎞ 1 + j⎜ f ⎟ ⎝ i⎠
N1 =
δ1 φ − v Mactin ρH2O δ1 + δ2 + δw c MH2O
N2 =
δ2 φ − v Mactin ρH2O δ1 + δ2 + δw c MH2O
v = cvB
+ α{εw*(f ) − εw*∞}
(6)
where c is actin concentration in g·mL−1, ρH2O is water density in g·mL−1, and Mactin and MH2O are the molecular masses of actinmonomer and water, respectively. ϕ was fixed at 0.07, which was selected to be two to three times larger than ϕB for an actin concentration of 10 mg·mL−1 in the present analysis. Here, when f1 (>f w) is close to f w HMW has a DR property close to that of bulk water, meaning that even if δ1 is large the whole solution property is close to that of bulk water. Therefore,
(5)
where δi is DR amplitude of the ith component, f1 and f 2 (3kT/e,penta (Å3) VkT/e,penta (Å3) VkT/2e,penta (Å3) V1 × 1010 >1 × 1010 >1 × 1010 2.1 × 109 4.1 × 108
3.3 × 108 9.9 × 107 4.4 × 107 1.7 × 107 6.9 × 106 >1 × 1010 2.77 × 109 9.3 × 108 2.7 × 108 1.0 × 108
Figure 10. Equipotential surfaces of Ca-FA and Mg-FA at I = 0.07 M. Positive and negative equipotential surfaces are shown in dark blue and light red, respectively, using UCSF Chimera.26
close to the protein surface and are located below the SSES and partially below the SES. In Table 5, the numbers of water molecules and the electric field strength between two equipotential surfaces of the F-actin models are tabulated, where the water number of each layer was calculated simply from the layer volume divided by 30 Å3. In addition, the numbers of water molecules in the first water layer of Ca-FA and Mg-FA are also noted. The electric field strength was estimated from the potential difference divided by the average thickness of each water layer of negative or positive potential region separately. By comparing the results of the present experiment and the atomic structural analysis, the following points were deduced. (1) Restrained water. The average of the experimental restrained water numbers (N2) of F-actin in Table 3 over the three temperatures in Mg2.0-buffer containing 2 mM Mg2+ was ∼2270 per actin, approximately 28% larger than that (∼1770) in Ca2.0-buffer (containing 2 mM Ca2+), whereas SASA,penta and SASA*mono = (SASA,penta − SASA,tri)/2 of Mg-FA were 28% and 46% larger than those of Ca-FA, respectively as in Table 4. There is good consistency between the restrained water number (N2) and SASA. As SASA*mono of the actin-monomer unit in Mg-FA can hold ∼1540 water molecules (15405/10, 10 Å2: the occupation area of a water molecule at SAS), the restrained water molecules of both
monomer, actin-trimer, and actin-pentamer, respectively. Note that actin units were different in the 2y83 model but the same in the 3mfp model; therefore, Ymono for 2y83 represents the average of Y over five monomers, where Y is a quantity such as SASA or VSES. To exclude the terminal contribution of each F-actinpentamer, we calculated Y*mono = (Ypenta − Ytri)/2 as a monomerunit value of Y in F-actin. Additionally, we introduced SSES as the second-solvent-excluded surface, which was made with the extended radii (rvdw + 2.8 Å) of the surface atoms of the protein to include most water molecules in the first water layer. SASA,mono of Mg-FA was approximately 20% larger, more surface-exposed, than that of Ca-FA; however, VSES of Mg-FA was almost the same or slightly smaller than that of Ca-FA. Moreover, SASA,penta of MgFA was 28% larger than that of Ca-FA, due to the wider interstice between the two protofilaments of Mg-FA than of Ca-FA. After reproducing the atomic charges with CHIMERA-PDB 2PQR,36,37 the Poisson−Boltzman equation was solved at an ionic strength of 0.07 M with CHIMERA-APBS.38 The equipotential surfaces are shown in Figure 9c,f, where light red represents −3kT/e (∼−77 mV) and dark blue represents +3kT/e (∼+77 mV). V2 × 107 V/m, agreeing with the experimental order of N1. However, these numbers of N1 cal are four to five folds smaller than the experimental values. Possible reasons of this difference are that (1) the present electric field calculations were roughly
made, (2) the real structures, particularly the side-chain structures, of F-actin in solutions are not necessarily same to the pdb atomic models of F-actin used in this study, and (3) the theoretical understanding of HMW is still in progress, which would be resolved in future. In this study, a remarkable change of the hydration state of Factin has been observed when a small fraction of Ca2+ ions were added to the F-actin solution in Mg2.0-buffer (containing 2 mM Mg2+). Ca regulation often appears in many of cell functions including muscle cells. As mentioned in Introduction, the theoretical research on the relation between the dielectric properties and the thermodynamic quantities of hydration water is being in progress.6,11,12,35 In the context of the hydration thermodynamics, control of the hydration water of protein complexes should become an energetic basis of the molecular driving mechanism.
4. CONCLUSION The present DR study revealed the change of multihydration state of F-actin, which had strong dependence on the divalent ions Mg2+/Ca2+. Multihydration shells of G- and F-actin were composed of restrained water and HMW layers. In every buffer tested, the HMW signal (Dhyme) of F-actin was higher than that of G-actin. With increasing temperature, both DR frequency and DR amplitude of HMW of F-actin in F-buffer containing 0.1 mM Ca2+ and 2 mM Mg2+ increased; however, Dhyme was less temperature dependent in F-buffer and Ca2.0-buffer containing 2 mM Ca2+. Dhyme of F-actin in Ca2.0- and F-buffers were markedly higher than in Mg2.0-buffer containing 2 mM Mg2+. In Mg2.0-buffer, the hydration state of F-actin changed when a small fraction of Ca2+ (∼0.1 mM) was introduced and became closer to that of the Ca-bound form in Ca2.0-buffer. The number of restrained water molecules per actin was explained as the number of water molecules located mostly in the first water layer of the protein atomic structures of PDB 2y83 and 3mfp. The number of HMW molecules was estimated in good approximation from the volume between the equipotential surface of − kT/2e and the second solvent excluded surface of F-actin by solving the Poisson−Boltzmann equation, although the difference of HMW numbers for Ca-FA and Mg-FA was not clearly explained with the pdb models used in this study. Thus, consideration of electric-field distribution based on the atomic structure of F-actin could successfully explain the main feature of the multihydration-state change of F-actin by Mg2+/Ca2+ ionexchange; however, higher precision of the experiments and calculations is required for further details. In the present study, we have indicated that the state change of water surrounding F-actin was coupled with the structure change of F-actin by Mg2+/Ca2+ ion-exchange. Thus, we emphasize a new aspect to understanding the mechanism of enzyme-protein machinery and exploiting a novel technology such as designing and construction of artificial protein machinery involving the surrounding water molecules as another key player.
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.6b02584. Nine additional figures and two additional tables.(PDF) J
DOI: 10.1021/acs.jpcb.6b02584 J. Phys. Chem. B XXXX, XXX, XXX−XXX
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(15) Rasband, W. S. Image J; U.S. NIH: Bethesda, MD; http://imagej. nih.gov/ij/docs/index.html, accessed July 5, 2013. (16) Kouyama, T.; Mihashi, K. Fluorimetry Study of N-(1-pyreny1)iodoacetamide-Labelled F-actin. Eur. J. Biochem. 1981, 114, 33−38. (17) Sheterline, P.; Clayton, J.; Sparrow, J. C. Protein Profile: Actin, 4th ed.; Oxford University Press: New York, 1998. (18) Orbán, J.; Pozsonyi, K.; Szarka, K.; Barkó, S.; Bódis, E.; Lő rinczy, D. Thermal Characterization of Actin Filaments Prepared from ADPActin Monomers. J. Therm. Anal. Calorim. 2006, 84, 619−623. (19) Gershman, L. C.; Newman, J.; Selden, L. A.; Estes, J. E. BoundCation Exchange Affects the Lag Phase in Actin Polymerization. Biochemistry 1984, 23, 2199−2203. (20) MAXCHELATOR; http://maxchelator.stanford.edu/index.html, accessed December 10, 2013. (21) NIST Standard Reference Data; http://www.nist.gov/srd/nist46. cfm, accessed December 10, 2013. (22) Estes, J. E.; Selden, L. A.; Kinosian, H. J.; Gershman, L. C. TightlyBound Divalent Cation of Actin. J. Muscle Res. Cell Motil. 1992, 13, 272− 284. (23) Estes, J. E.; Selden, L. A.; Gershman, L. C. Tight Binding of Divalent Cations to Monomeric Actin. J. Biol. Chem. 1987, 262, 4952− 4957. (24) Narita, A.; Oda, T.; Maéda, Y. Structural Basis for the Slow Dynamics of the Actin Filament Pointed End. EMBO J. 2011, 30, 1230− 1237. (25) Fujii, T.; Iwane, A. H.; Yanagida, T.; Namba, K. Direct Visualization of Secondary Structures of F-actin by Electron Cryomicroscopy. Nature 2010, 467, 724−728. (26) UCSF Chimera; http://www.cgl.ucsf.edu/chimera/, accessed May 20, 2014. (27) Miyashita, Y.; Wazawa, T.; Mogami, G.; Takahashi, S.; Sambongi, Y.; Suzuki, M. Hydration-State Change of Horse Heart Cytochrome c Corresponding to Trifluoroacetic-Acid-Induced Unfolding. Biophys. J. 2013, 104, 163−172. (28) Murphy, L. R.; Matubayasi, N.; Payne, V. A.; Levy, R. M. Protein Hydration and Unfolding − Insights from Experimental Partial Specific Volumes and Unfolded Protein Models. Folding Des. 1998, 3, 105−118. (29) Wazawa, T.; Miyazaki, T.; Sambongi, Y.; Suzuki, M. Hydration Analysis of Pseudomonas Aeruginosa Cytochrome c551 upon Acid Unfolding by Dielectric Relaxation Spectroscopy. Biophys. Chem. 2010, 151, 160−169. (30) Mogami, G.; Wazawa, T.; Morimoto, N.; Kodama, T.; Suzuki, M. Hydration Properties of Adenosine Phosphate Series as Studied by Microwave Dielectric Spectroscopy. Biophys. Chem. 2011, 154, 1−7. (31) Strickland, E. H.; Beychok, S. Aromatic Contributions to Circular Dichroism Spectra of Protein. Critical Reviews in Biochemistry 1974, 2, 113−175. (32) Wagner, K. W. Erklärung der Dielektrischen nach Wirkungsvorgänge auf Grund Maxwellscher Vorstellungen. Arch. Elektrotech. 1914, 2, 371−387. (33) Asami, K.; Hanai, T.; Koizumi, N. Dielectric Analysis of Escherichia Coli Suspensions in the Light of the Theory of Interfacial Polarization. Biophys. J. 1980, 31, 215−228. (34) Buchner, R.; Barthel, J.; Stauber, J. The Dielectric Relaxation of Water between 0°C and 35°C. Chem. Phys. Lett. 1999, 306 (1999), 57− 63. (35) Mogami, G.; Suzuki, M.; Matubayasi, N. Spatial-Decomposition Analysis of Energetics of Ionic Hydration. J. Phys. Chem. B 2016, 120, 1813−1821. (36) Dolinsky, T. J.; Nielsen, J. E.; McCammon, J. A.; Baker, N. A. PDB2PQR: An Automated Pipeline for the Setup, Execution, and Analysis of Poisson-Boltzmann Electrostatics Calculations. Nucleic Acids Res. 2004, 32, W665−W667. (37) Dolinsky, T. J.; Czodrowski, P.; Li, H.; Nielsen, J. E.; Jensen, J. H.; Klebe, G.; Baker, N. A. PDB2PQR: Expanding and Upgrading Automated Preparation of Biomolecular Structures for Molecular Simulations. Nucleic Acids Res. 2007, 35, W522−W525.
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We thank Professor Takao Kodama for giving his kind comments on the manuscript and also thank Dr. Kiyoto Kamagata and Professor Satoshi Takahashi for their support. This work was carried out as a FRIS Supported Research Program of Frontier Research Institute for Interdisciplinary Sciences of Tohoku University and supported partly by grants from the Ministry of Education, Culture, Sports, Science, and Technology of Japan (Grant-in-Aid for Scientific Research on Innovative Areas: 20118001, 20118008, and 23310071). Molecular graphics and analyses were performed with the UCSF Chimera package. Chimera is developed by the Resource for Biocomputing, Visualization, and Informatics at the University of California, San Francisco (supported by NIGMS P41-GM103311).
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REFERENCES
(1) Galkin, V. E.; Orlova, A.; Schröder, G. F.; Egelman, E. H. Structural Polymorphism in F-Actin. Nat. Struct. Mol. Biol. 2010, 17, 1318−1323. (2) Orlova, A.; Prochniewicz, E.; Egelman, E. H. Structural Dynamics of F-Actin: II. Cooperativity in Structural Transitions. J. Mol. Biol. 1995, 245, 598−607. (3) Fuller, N.; Rand, R. P. Water in Actin Polymerization. Biophys. J. 1999, 76, 3261−3266. (4) Gregory, R. B. Protein-Solvent Interactions; Marcel Dekker: New York, 1995. (5) Bryant, R. G. The Dynamics of Water-Protein Interactions. Annu. Rev. Biophys. Biomol. Struct. 1996, 25, 29−53. (6) Karino, Y.; Matubayasi, N. Free-Energy Analysis of Hydration Effect on Protein with Explicit Solvent: Equilibrium Fluctuation of Cytochrome c. J. Chem. Phys. 2011, 134, 041105−1−041105−4. (7) Yasuda, S.; Yoshidome, T.; Harano, Y.; Roth, R.; Oshima, H.; Oda, K.; Sugita, Y.; Ikeguchi, M.; Kinoshita, M. Free-Energy Function for Discriminating the Native Fold of a Protein from Misfolded Decoys. Proteins: Struct., Funct., Genet. 2011, 79, 2161−2171. (8) Kabir, S. R.; Yokoyama, K.; Mihashi, K.; Kodama, T.; Suzuki, M. Hyper-Mobile Water is Induced around Actin Filaments. Biophys. J. 2003, 85, 3154−3161. (9) Suzuki, M.; Kabir, S. R.; Siddique, M. S. P.; Nazia, U. S.; Miyazaki, T.; Kodama, T. Myosin-Induced Volume Increase of the Hyper-Mobile Water surrounding Actin Filaments. Biochem. Biophys. Res. Commun. 2004, 322, 340−346. (10) Amano, K.; Yoshidome, T.; Iwaki, M.; Suzuki, M.; Kinoshita, M. 2010. Entropic Potential Field Formed for a Linear-Motor Protein near a Filament: Statistical-Mechanical Analyses using Simple Models. J. Chem. Phys. 2010, 133, 045103−1−045103−11. (11) Kinoshita, M.; Suzuki, M. A Statistical-Mechanical Analysis on the Hypermobile Water around a Large Solute with High Surface Charge Density. J. Chem. Phys. 2009, 130, 014707−1−014707−11. (12) Kubota, Y.; Yoshimori, A.; Matubayasi, N.; Suzuki, M.; Akiyama, R. Molecular Dynamics Study of Fast Dielectric Relaxation of Water around a Molecular-Sized Ion. J. Chem. Phys. 2012, 137, 224502. ́ (13) Smiechowski, M.; Sun, J.; Forbert, H.; Marx, D. Solvation Shell Resolved THz Spectra of Simple Aqua Ions − Distinct Distance- and Frequency-Dependent Contributions of Solvation Shells. Phys. Chem. Chem. Phys. 2015, 17, 8323−8329. (14) Spudich, J. A.; Watt, S. The Regulation of Rabbit Skeletal Muscle Contraction. 1. Biochemical Studies of the Interaction of the Tropomyosin-Troponin Complex with Actin and the Proteolytic Fragments of Myosin. J. Biol. Chem. 1971, 246, 4866−4871. K
DOI: 10.1021/acs.jpcb.6b02584 J. Phys. Chem. B XXXX, XXX, XXX−XXX
Article
The Journal of Physical Chemistry B (38) Baker, N. A.; Sept, D.; Joseph, S.; Holst, M. J.; McCammon, J. A. 2001. Electrostatics of Nanosystems: Application to Microtubules and the Ribosome. Proc. Natl. Acad. Sci. U. S. A. 2001, 98, 10037−10041. (39) Miyazaki, T.; Mogami, G.; Wazawa, T.; Kodama, T.; Suzuki, M. Measurement of the Dielectric Relaxation Property of Water-Ion Loose Complex in Aqueous Solutions of Salt at Low Concentrations. J. Phys. Chem. A 2008, 112, 10801−10806. (40) Mogami, G.; Miyazaki, T.; Wazawa, T.; Matubayasi, N.; Suzuki, M. Anion-Dependence of Fast Relaxation Component in Na-, K-Halide Solutions at Low Concentrations Measured by High-Resolution Microwave Dielectric Spectroscopy. J. Phys. Chem. A 2013, 117, 4851−4862. (41) Kabsch, W.; Mannherz, H. G.; Suck, D.; Pai, E. F.; Holmes, K. C. Atomic Structure of the Actin: DNase I Complex. Nature 1990, 347, 37−44.
L
DOI: 10.1021/acs.jpcb.6b02584 J. Phys. Chem. B XXXX, XXX, XXX−XXX
