Electrostatic Repulsion during Ferritin Assembly ... - ACS Publications

Dec 30, 2015 - ABSTRACT: Escherichia coli non-heme-binding ferritin A. (EcFtnA) is a spherical cagelike protein that is composed of 24 identical subun...
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Electrostatic Repulsion during Ferritin Assembly and Its Screening by Ions Daisuke Sato, Satsuki Takebe, Atsushi Kurobe, Hideaki Ohtomo,† Kazuo Fujiwara, and Masamichi Ikeguchi* Department of Bioinformatics, Soka University, 1-236 Tangi-machi, Hachioji, Tokyo 192-8577, Japan S Supporting Information *

ABSTRACT: Escherichia coli non-heme-binding ferritin A (EcFtnA) is a spherical cagelike protein that is composed of 24 identical subunits. EcFtnA dissociates into 2-mers under acidic conditions and can reassemble into the native structure when the pH is increased. To understand how electrostatic interactions influence the assembly reaction, the dependence of the process on ionic strength and pH was investigated. The assembly reaction was initiated by stopped-flow mixing of the acid-dissociated EcFtnA solution and high-pH buffer solutions and monitored by time-resolved small-angle X-ray scattering. The rate of assembly increased with increasing ionic strength and decreased with increasing pH from 6 to 8. These dependences were thought to originate from repulsion between assembly units (2-mer in the case of EcFtnA) with the same net charge sign; therefore, to test this assumption, mutants with different net charges (net-charge mutants) were prepared. In buffers with a low ionic strength, the rate of assembly increased with a decreasing net charge. Thus, repulsion between the assembly unit net charges was demonstrated to be an important factor determining the rate of assembly. However, the difference in the assembly rate among net-charge mutants was not significant in buffers with an ionic strength of >0.1. Notably, under such high-ionic strength conditions, the assembly rate increased with an increasing ionic strength, suggesting that local electrostatic interactions are also responsible for the ionic strength dependence of the rate of assembly and are repulsive on average.

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rganisms utilize a number of protein supramolecules that are composed of many identical or similar subunits, such as microtubules,1 helical or icosahedral virus capsids,2 bacterial microcompartments,3 and ferritins.4 In homooligomers, naturally enough, all subunits have net charges of the same sign. Therefore, electrostatic interactions between the net charges on the subunits should be repulsive when the subunits come close to each other during the assembly process. The role of electrostatic interactions in macromolecular assembly was studied for various systems both theoretically5−9 and experimentally.10−14 Ferritin is a spherical, cagelike protein that consists of 24 identical or similar subunits arranged in 4/3/2 symmetry. The subunit has five helices (helices A−E) and a long loop between helices B and C. Helices A−D form a four-helix bundle structure within each subunit, and helix E forms an intersubunit four-helix bundle around a 4-fold symmetry axis.4 The protein has a large cavity within which it can store iron atoms. The assembly reaction of ferritin was investigated more than a quarter of a century ago. Gerl and Jaenicke studied the folding and assembly reaction of horse spleen ferritin (HSF) from its monomeric unfolded state by using chemical cross-linking and subsequent sodium dodecyl sulfate−polyacrylamide gel electrophoresis analysis of the oligomers.15 The authors detected 2mer, 3-mer, and 12-mer as kinetic intermediates and proposed the following scheme: © XXXX American Chemical Society

24mi → 24M1 ⇄ 8(M1 + M 2) ⇄ 8M3 ⇄ 4M 6 ⇄ 2M12 → M 24

(1)

where m1 and M1 denote the unfolded and structured monomers, respectively. The subscript indicates the number of subunits in the oligomer. Recently, we succeeded in following the assembly reaction of Escherichia coli non-heme ferritin A (EcFtnA) directly by using time-resolved small-angle X-ray scattering (TR-SAXS).16 EcFtnA dissociates into 2-mers that keep their native secondary and tertiary structures at acidic pH17 and can reassemble into the native structure when the pH increases.16 The time-dependent change in the scattering profile was consistent with a modified model:16 12M 2 ⇄ 6M4 ⇄ 4M6 ⇄ 2M12 ⇄ M 24

(2)

Direct observation of assembly reactions allows us to study the pH or ionic strength dependence of the assembly reaction. In this study, therefore, we addressed the question of how the assembly reaction of EcFtnA depends on the pH and ionic strength. The results were expected to shed light on the role of electrostatic interactions on the assembly. Furthermore, we Received: November 5, 2015 Revised: December 22, 2015

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DOI: 10.1021/acs.biochem.5b01197 Biochemistry XXXX, XXX, XXX−XXX

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Biochemistry

located just above the mixer. The temperature was maintained at 25 °C by circulating water from a thermostat bath. Dissociation of EcFtnA was achieved by mixing the protein stock solution and 500 mM phosphoric acid at a ratio of 15:1, which resulted in 50 mM sodium phosphate (pH 2.5). The reassembly of EcFtnA was initiated by mixing this protein solution at a ratio of 1:1 with a solution containing 50 mM Tris, 2 mM EDTA, and appropriate amounts of HCl, NaOH, and NaCl, which gave reassembly conditions of various ionic strengths and pH values. The scattering data obtained during 10 ms of exposure were corrected as time point data. For each stopped-flow mixing, 10−30 points were acquired by setting various intervals; these data points were combined to obtain a time course for the assembly reaction. When the interval was longer than 50 ms, the shutter was closed immediately after each data acquisition period and then reopened before the next data acquisition. The delay time between the shutter trigger and data acquisition was set to 10 ms. In some cases, a delay was introduced between the mixing trigger and the shutter trigger time points to obtain data at a late reaction time without causing radiation damage to the sample. For static data acquisition, the same solution was placed in the two reservoirs of a stopped-flow apparatus and mixed. In this case, data obtained during an exposure of 10 ms were corrected sequentially, without intervals. After the absence of X-ray damage in each data set had been confirmed, the results were averaged. Data Processing. Two-dimensional images were circularly integrated using FIT2D,21 to obtain one-dimensional scattering profiles. After subtraction of the scattering profile of the buffer solution, the apparent radius of gyration, Rapp, and the forward scattering intensity, I(0), were calculated by using the Guinier approximation:

investigated the rate of assembly of mutants with different net charges to delineate the effect of repulsion between the net charges of the assembly units (AUs), 2-mer in the present case.



EXPERIMENTAL PROCEDURES Construction of Mutant Expression Plasmids. The wild-type EcFtnA gene was inserted into expression vector pET-3c, and mutant genes were constructed by introducing mutations into the wild-type EcFtnA gene by using either a Quikchange Kit (Agilent Technologies) or the overlap extension method.18 The DNA sequences were confirmed by analysis with an ABI PRISM 3100-Avant sequencer. Plasmids carrying the mutant genes were used to transform E. coli BL21(DE3) cells. Expression and Purification of Wild-Type (WT) and Mutant EcFtnA. WT and mutant proteins were expressed and purified as described previously.17 Briefly, E. coli harboring the expression plasmid was grown in Luria-Bertani medium, and the expression of proteins was induced by the addition of isopropyl β-D-thiogalactopyranoside. After being expressed for 24 h, cells were collected and lysed by sonication. The soluble fraction of cell lysates was heated to 75 °C for 10 min and then cooled rapidly in iced water. The precipitate formed was removed by centrifugation. This heating process was repeated twice. After polyethylenimine treatment, the protein was precipitated with ammonium sulfate (60% saturation). The pellet was resuspended in 50 mM Tris-HCl (pH 8.0) and then dialyzed against the same buffer at 4 °C. The protein was further purified by Sephacryl S-300 and Q-Sepharose chromatography. To remove iron, the sample was treated with 5 mM sodium dithionite and 10 mM EDTA. Finally, the buffer was exchanged to 20 mM sodium phosphate (pH 7.0) by using a Sephadex G-25 column. CD Measurements. CD spectra were measured with a Chirascan CD spectrometer (Applied Photophysics) at 25 °C. Near- and far-UV CD spectra were recorded in cuvettes with optical path lengths of 10 and 1 mm, respectively. Typical protein concentrations were 0.1 and 0.3 mg/mL for far- and near-UV regions, respectively. The protein concentration was determined as described previously.17 Analytical Gel Filtration Chromatography. Analytical gel filtration chromatography was performed using a Superose 6 column (1 cm × 30 cm, GE Healthcare) or a Superdex 75 column (1 cm × 30 cm, GE Healthcare) at room temperature. The former column was used for native conditions [50 mM Tris-HCl and 200 mM NaCl (pH 8.0)] at a flow rate of 0.4 mL/min, and the latter column was used for acidic conditions [50 mM sodium phosphate (pH 2.5)] at a flow rate of 1 mL/ min. The concentration of applied sample was 1.0 mg/mL. The elution was monitored by following the change in UV absorbance at 280 nm. SAXS Measurements. All SAXS measurements were performed at SPring-8 beamline 45XU.19 The wavelength of the X-ray and the sample-to-detector distance were 1.0 Å and 1.5 m, respectively. The accurate sample-to-detector distance and the beam center were determined by measuring the scattering of silver behenate.20 Two-dimensional scattering images were measured with a photon-counting detector [PILATUS300k-w or PILATUS3X 2M (Dectris)] with a readout time of 2.3 or 0.95 ms, respectively. The sample was mixed with a stopped-flow apparatus (Unisoku Co. Ltd., Osaka, Japan) that had a quartz capillary cell with a diameter of 2 mm

⎛ R 2Q 2 ⎞ app ⎟ I(Q ) = I(0) exp⎜⎜ − 3 ⎟⎠ ⎝

(3)

where the scattering vector Q = (4π/λ) sin θ (where λ is the wavelength and 2θ is the scattering angle) and I(Q) is the scattering intensity at a given Q value. The I(0) and Rapp values were calculated from the intercept and slope of the Guinier plot in the Q range satisfying QRapp ≤ 1.3. For analysis of the kinetic data, we used a wider Q range satisfying QRapp ≤ 1.8 because the narrow Q range produced a large error in estimated I(0) and Rapp values. This analysis was performed automatically by using procedures that were developed using Igor Pro (WaveMetrics, Inc.). Isoelectric Focusing. The isoelectric points (pI values) of WT and mutants were determined by isoelectric focusing using a PhastGel IEF 5-8 instrument (GE Healthcare) and a Phast system (GE Healthcare). The buffer was exchanged with distilled water by using a PD-10 desalting column (GE Healthcare) before applying samples. Ionic Strength Calculation. Ionic strength was calculated by assuming that molarity (moles per kilogram) is approximately equal to volume molarity (moles per liter). The concentrations of ionized buffer species (phosphate anions and protonated Tris) were calculated from known dissociation constants (pKa) and pH values. The ionic strength dependence of pKa was not considered. B

DOI: 10.1021/acs.biochem.5b01197 Biochemistry XXXX, XXX, XXX−XXX

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Biochemistry



RESULTS Dependence of the Rate of Assembly of EcFtnA on Ionic Strength and pH. The assembly reaction of EcFtnA was monitored by TR-SAXS. The Rapp and I(0) were calculated from the scattering curves by using the Guinier approximation. In systems in which a single particle is present in solution, Rapp is the radius of gyration (Rg) of that particle, and I(0) is proportional to the mass concentration and molecular weight of the particle.22 In systems in which two or more particles are present in solution, I(0) is an arithmetic average of the values obtained for the particles present in solution. The Rapp is a weight average of the Rg values of the particles and is biased toward the values of the larger particles. Although both I(0) and Rapp increase as the assembly reaction proceeds (Figure 1

1B). The isoelectric point pI of EcFtnA is 5.43 (see below), which means that the net charge of AU is expected to be negative and to become more negative at higher pH values. Therefore, the pH dependence of the assembly rate may be explained by an increased level of electrostatic repulsion because of increased AU net charges at higher pH values. To verify this expectation, we designed several mutant proteins that exhibit a range of net charges. Construction and Characterization of Net-Charge Mutants. To construct mutants with different net charges (net-charge mutants), we selected charged residues that (1) held side chains that were exposed to solvent, (2) did not participate in a salt bridge, and (3) were located far from subunit interfaces. Selected residues were Glu5, Glu8, Glu12, Glu85, and Glu89 of the outer surface and Arg56, located at the inner surface (Figure 2). We replaced one to five Glu residues with Gln or Lys and also substituted Arg56 with Glu (Table 1).

Figure 1. Assembly reactions of EcFtnA monitored by following changes in I(0) under various pH and ionic strength conditions. (A) The ionic strength dependence was examined at a constant pH 8.0. (B) The pH dependence was examined at a constant ionic strength μ of 0.08. The protein concentration was 2.5 mg/mL.

Figure 2. Crystal structure of EcFtnA (Protein Data Bank entry 1EUM26) viewed along the 2-fold symmetry axis from (A) outside and (B) inside the cage. Mutated Glu and Arg residues are colored red and blue, respectively. The structure of a subunit is shown as a ribbon model and depicted in blue to red from the N- to C-terminus, respectively (C and D). The side chain atoms of mutated residues and Trp122 are shown as white spheres.

and Figure S1, respectively), monitoring I(0) is a more convenient way to follow the progress of the reaction. The assembly reaction was measured either at various ionic strengths at constant pH 8.0 (Figure 1A) or at various pH values and a constant ionic strength μ of 0.08 (Figure 1B). Given that the assembly reaction is a complex reaction involving many rate constants, the effect of ionic strength or pH on the individual rate constant was not clear from these data. However, the reaction curve would be expected to shift horizontally in the plot of the logarithmic time axis if the effect is the same for all rate constants. The data shown in Figure 1 are in line with this hypothesis. The reaction curve shifts to the left with an increasing ionic strength; that is, the assembly rate increases with an increasing ionic strength at pH 8.0 (Figure 1A). Given that the electrostatic interactions between the AU net charges are repulsive, the ions may screen the electrostatic repulsion and accelerate the assembly. On the other hand, within the pH range examined, the reaction curve shifts to the right with an increasing pH (Figure

Mutants KKKKK and KKKEE were expressed as inclusion bodies and were not purified. Although QQQQQ, QQQEQ, and EEEKK could be purified, their solubilities were poor. The CD spectrum of QQQEQ was nativelike, but the CD intensity of EEEKK was reduced, indicating some conformational change (Figure S2). Gel filtration experiments indicated that QQQEQ and EEEKK mutants both formed a 24-mer (Figure S3). The solubility of QQQQQ was too poor to perform CD or gel filtration experiments. R56E showed a CD spectrum that differed significantly from that of WT (Figure S2) and eluted as two peaks corresponding to a 24-mer and a 2-mer (Figure S3). The latter result indicates that R56E partially dissociated under the experimental conditions. Far- and near-UV CD spectra of EEEEQ, EQQEE, EQQEQ, and EQQQQ were also similar to those of WT, indicating that the secondary structure and the packing around the aromatic residues are similar to those of C

DOI: 10.1021/acs.biochem.5b01197 Biochemistry XXXX, XXX, XXX−XXX

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Biochemistry Table 1. Mutants Designed in This Study

a

mutant name

substitutions

expression in E. coli

solubility at pH 7

assembly at pH 8a

CD spectrum at pH 8

pI

EEEEQ EQQEE EQQEQ EQQQQ QQQEQ QQQQQ EEEKK KKKEE KKKKK R56E

E89Q E8Q, E12Q E8Q, E12Q, E89Q E8Q, E12Q, E85Q, E89Q E5Q, E8Q, E12Q, E89Q E5Q, E8Q, E12Q, E85Q, E89Q E85K, E89K E5K, E8K, E12K E5K, E8K, E12K, E85K, E89K R56E

soluble soluble soluble soluble soluble soluble soluble inclusion body inclusion body soluble

good good good good poor poor poor NEb NEb good

24-mer 24-mer 24-mer 24-mer 24-mer 24-mer 24-mer NEb NEb 24-mer 2-mer

nativelike nativelike nativelike nativelike nativelike NEb deformed NEb NEb deformed

5.47 5.73 6.27 7.31 NEb NEb NEb NEb NEb NEb

From gel filtration (Figure S3). bNot examined.

WT in the native and acid-dissociated states (Figures S2 and S4). Gel filtration experiments indicated that the four mutants formed 24-mer and 2-mer in buffers at neutral and acidic pH, respectively (Figure S3). These four mutants showed sufficient solubility to allow TR-SAXS analysis; therefore, SAXS measurements were performed to characterize the four mutants under native and acid-dissociated conditions. The scattering curves of mutants were indistinguishable from those of WT under both conditions (Figure 3). The isoelectric points of the mutants were determined by isoelectric focusing. As expected, the pI value became larger with increasing numbers of Glu to Gln mutations (Table 1). Assembly Reactions of Net-Charge Mutants. The assembly reactions of net-charge mutants were investigated at pH 8.0 and at three different ionic strengths (0.08, 0.11, and 0.17). It was expected that WT and mutants would be negatively charged at pH 8.0 and that the absolute value of the

AU net charge would decrease as the number of mutations from Glu to Gln increases. The time courses of changes in I(0) and Rapp during the assembly reactions under three different ionic strengths are shown in Figure 4 and Figure S5, respectively. It can be seen clearly that at μ = 0.08 the assembly rate increases with increasing numbers of mutations

Figure 3. SAXS profiles of (A) EEEEQ, (B) EQQEE, (C) EQQEQ, and (D) EQQQQ under native (pH 8.0) and acid-dissociated conditions (pH 2.5), shown as black and green dots, respectively. The number of data points has been reduced for the sake of clarity. For comparison, SAXS profiles of WT under the same conditions are included (orange and purple lines).

Figure 4. Assembly reactions of WT and net-charge mutants monitored by following changes in I(0) at pH 8.0 and (A) μ = 0.08, (B) μ = 0.11, and (C) μ = 0.17. The protein concentration was 2.5 mg/mL. D

DOI: 10.1021/acs.biochem.5b01197 Biochemistry XXXX, XXX, XXX−XXX

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Biochemistry

Dependence of the Assembly Rate on pH. As described above, the pH dependence of the assembly rate may, at least partly, also be explained by electrostatic repulsion between AU net charges. Given that the pI values of the net-charge mutants increase with the number of mutations (Table 1), the net charge at pH 8.0 is expected to decrease correspondingly. In this context, it is noticeable that the pI of EEEEQ (5.47) is not significantly different from that of WT (5.43), although the former is assembled much faster (Figure 4A). The acceleration of the rate of assembly of EEEEQ suggests that its net charge is reduced at pH 8.0, as expected. If the pKa values of all ionizable groups except for Glu89 are not influenced by the E89Q mutation, the pI of EEEEQ should increase. However, it is likely that the E89Q mutation affects the pKa of the surrounding ionizable groups. If this effect is taken into account, it is not surprising that the pI of EEEEQ is not significantly changed from that of WT. In fact, the same E89Q mutation induced a significant shift of pI from EQQEE (5.67) to EQQEQ (6.27). Thus, interpretation of pH dependence is complex, and we could not conclude that repulsion between AU net charges is the only factor in operation. Furthermore, there are local interactions between ionizable groups located at AU interfaces such as a salt bridge between H128 and D63.26 Given that H128 is likely to be deprotonated in the pH range investigated, the attractive interaction between the positive charge of H128 and the negative charge on D63 may be lost with an increase in pH from 6.0 to 8.0, resulting in a decrease in the rate of assembly. Dependence of the Rate of Assembly on Ionic Strength. We showed that the rate of assembly of EcFtnA increased with an increasing ionic strength at pH 8.0. We interpreted this phenomenon as an indication that the screening effect of ions suppresses the electrostatic repulsion between AUs. Given that the rate of assembly of net-charge mutants increased with decreasing net charge at low ionic strength, this interpretation is, at least partly, correct. At higher ionic strengths, the difference in the rates of assembly of netcharge mutants was not significant; however, the assembly rate still increased with increasing ionic strength. This was interpreted as an indication that the screening effect of ions suppressed “local electrostatic repulsions”. This means that the local electrostatic interaction is less sensitive to ionic strength than the repulsion between the net charges of AUs. This is consistent with theoretical calculations of the electrostatic energy required to transfer a unit in the oligomeric state (EET).5 Takahashi calculated the EET of horse L ferritin as a function of ionic strength and found that the total EET decreased with an increasing ionic strength; that is, the assembly became more favorable at higher ionic strengths. Takahashi also calculated the 5 Å-limit EET, which is the EET due to atoms within 5 Å of the subunit interface, and showed that it was less sensitive to ionic strength. In strict terms, the ionic strength would affect the rate constants of individual steps of the assembly reaction differently. Therefore, the apparent assembly mechanism may depend on the ionic strength. The shape of the reaction curve tends to be slightly more abrupt at high ionic strengths (Figure 1A). This suggests that later-stage reactions are more effectively accelerated by ions than the earlier reactions. This may reflect the fact that the electrostatic repulsion is stronger in the docking of larger parts (for example, docking of two 12-mers) than in the docking of smaller parts such as docking of two 2-mers.

(Figure 4A). This can be explained by weakened electrostatic repulsion between AU net charges, which decreases with an increasing number of mutations. However, the difference in the assembly rate between WT and mutants was not remarkable at μ = 0.11 and 0.17 (Figure 4B,C). Therefore, the electrostatic repulsion between AU net charges is not significant under the conditions in which μ > 0.1 and is not a serious problem for assembly under physiological conditions (intracellular solutions contain 140 mM potassium ion23). Rather, local electrostatic repulsions between charges located near the AU interface seem to be important. The assembly rates at μ = 0.17 were much faster than those at μ = 0.11, although the difference between WT and net-charge mutants was not significant under either condition (Figure 4B,C). This can be interpreted as follows. If two AUs are far apart, their net charges can be regarded as point charges. In such cases, the probability that two AUs are separated by a certain distance is lower at a shorter distance because of the repulsion between net charges. This tendency is remarkable when the ionic strength is low. At high ionic strengths, however, the distribution becomes relatively uniform except for very close distances, so that the assembly rate becomes independent of the net charges of AUs. In a situation in which two oligomers are in the proximity of each other, we must consider electrostatic interactions between specific charges at the interface. In this case, the electrostatic interaction may be either attractive or repulsive depending on the charge pair considered. We call this “local electrostatic interaction”. The fact that the assembly rates at μ = 0.17 were much faster than those at μ = 0.11 suggests that the local electrostatic interactions are repulsive on average and that they are screened by ions.



DISCUSSION Effect of Mutation on the Structure and Stability of EcFtnA. Of the 10 mutants constructed in this study, only R56E had a net charge that became more negative. The fact that R56E was present as an equilibrium mixture of 24-mer and 2-mer (Figure S3) indicates the importance of R56 in the stabilization of the cagelike structure. This may be due to the increased magnitude of the AU net charge, that is, due to enhanced electrostatic repulsion. Although the near-UV CD spectrum of R56E differed significantly from that of WT (Figure S2), this spectral change may result from the elimination of a cation−π interaction24 between the guanido group of the R56 side chain and the Trp122 side chain (Figure 2D). Indeed, the fact that R56E can form a 24-mer suggests that the mutant retains its tertiary structure. The other nine mutants have either single or multiple mutations of the residues at the N-terminus of helix A (E5, E8, and E12) or at the Nterminus of helix C (E85 and E89). These residues may interact with the helix macrodipole. It is known that the α-helix resembles a macrodipole with a positive pole near the Nterminus and a negative pole near the C-terminus, and that negatively charged side chains near the N-terminus and positively charged side chains near the C-terminus stabilize the α-helix.25 The reason that KKKKK and KKKEE expressed as inclusion bodies may be the destabilization of the subunit structure because of unfavorable electrostatic interactions between the helix macrodipole and positively charged side chains near the N-terminus. The conformational change of EEEKK, which was suggested from the reduced near-UV CD intensity (Figure S2), may also arise for the same reason. E

DOI: 10.1021/acs.biochem.5b01197 Biochemistry XXXX, XXX, XXX−XXX

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Implication for Assembly Design. Electrostatic interactions have been utilized in the design of lattice arrangements of nanoparticles.27,28 In such studies, positively and negatively charged particles were arranged in a three-dimensional binary superlattice. Another way to construct well-designed threedimensional architectures is to introduce asymmetry into the ferritin nanocage. Zheng et al.29 generated a covalently linked ferritin dimer (dimer of 24-mer) by constructing a mutant ferritin in which Ser86 located at the outer surface was replaced with cysteine. The wild-type and mutant ferritins were dissociated into subunit dimers (2-mers) at pH 2, which were then mixed in a 11:1 ratio and reassembled under neutral pH. Through the use of a cross-linking agent that was reactive to cysteine, Zheng et al. then succeeded in constructing a hybrid ferritin dimer. However, the number of mutant 2-mer subunits incorporated into the 24-meric nanocage was not completely controlled; thus, the cross-linked trimer and other oligomers were also formed in addition to the cross-linked dimer. If it were possible to control the number and relative positions of incorporated mutant 2-mer subunits in the nanocage, it would be feasible to design three-dimensional arrays of nanocages. The control of electrostatic interactions is a promising way to approach this goal. This study has shown that the repulsion between AU net charges is effective only at an ionic strength of