In the electron transfer (ET) reaction from cytochrome c (Cyt c) to cytochrome c oxidase (CcO), we determined the number and sites of the hydration water released from the protein surface upon the formation of the ET complex by evaluating the osmotic pressure dependence of kinetics for the ET from Cyt c to CcO. We identified that ∼20 water molecules were dehydrated in complex formation under turnover conditions, and systematic Cyt c mutations in the interaction site for CcO revealed that nearly half of the released hydration water during the complexation were located around Ile81, one of the hydrophobic amino acid residues near the exposed heme periphery of Cyt c. Such a dehydration dominantly compensates for the entropy decrease due to the association of Cyt c with CcO, resulting in the entropy-driven ET reaction. The energetic analysis of the interprotein interactions in the ET complex predicted by the docking simulation suggested the formation of hydrophobic interaction sites surrounding the exposed heme periphery of Cyt c in the Cyt c–CcO interface (a ‘molecular breakwater'). Such sites would contribute to the formation of the hydrophobic ET pathway from Cyt c to CcO by blocking water access from the bulk water phase.

## Introduction

Electron transfer (ET) in the respiratory chain is the most essential process of energy transduction in cells [1]. Driven by ET, protons are pumped from the negative space to positive space in mitochondria, resulting in a proton concentration gradient across the inner mitochondrial membrane. The electrochemical potential induced by the process is the driving force for ATP synthesis by membrane-bound ATPase.

The final ET in the respiratory chain is mediated by a small hemoprotein, cytochrome c (Cyt c) [2], which carries one electron from the cytochrome bc1 complex (Complex III) to cytochrome c oxidase (CcO, Complex IV). Through the electron flow from Complex III, CcO can reduce molecular oxygen to water molecules to terminate the respiratory chain, where four electrons are used to reduce one molecule of dioxygen, in conjunction with proton pumping. Cyt c is a one-electron carrier, and the repetitive binding of Cyt c is required to reduce molecular oxygen. Because the efficiency of the proton pump coupled with the dioxygen reduction in CcO depends on the ET reaction from Cyt c to CcO [3], specific interactions between Cyt c and CcO are essential for energy transduction in the respiratory chain.

We have determined the interaction site for CcO on Cyt c by NMR [4] and revealed that certain hydrophobic amino acid residues are located in the interaction site, along with previously reported positively charged residues [5,6]. Our energetic analysis of the simulated Cyt c–CcO complex also indicates the primary contribution of hydrophobic interactions to the stability of the Cyt c–CcO complex [7]. A recent X-ray study of the Cyt c–CcO complex also showed that some hydrophobic amino acid residues are located in the interface, but there are no intermolecular interactions between hydrophobic amino acid residues with an interatomic distance <5 Å [8]. Although both NMR and X-ray studies suggest critical involvements of hydrophobic residues on complex formation, it has not yet been shown experimentally how these hydrophobic residues (or hydrophobic interactions) contribute to the stability of the ET complex and the ET reaction. The detailed stabilization mechanism for complex formation by hydrophobic interactions and functional significance of the formation of the hydrophobic interactions are, therefore, still key open questions in the ET reaction from Cyt c to CcO.

One line of experimental evidence shows that the hydrophobic interactions that occur in protein–protein complexes involve the dehydration of the hydrophobic amino acid residues in the interaction site [9,10]. The hydrophobic side chains of amino acid residues on the protein surface, as well as the side chains of hydrophilic amino acid residues, are hydrated. If hydrophobic amino acid residues are part of the interaction site with the partner protein, the hydrating water molecules would be expelled from the protein surface to allow the amino acid residues to form hydrophobic interactions with the amino acid residues of the partner proteins. Such dehydration is observed for both hydrophobic and hydrophilic amino acid residues [11,12], but the energetic contribution of hydrophobic interactions to the formation of the protein–protein complex is much larger than the contribution of hydrophilic interactions [13], thus suggesting that the dehydration of hydrophobic amino acid residues is a key process in the formation of the Cyt c–CcO complex that facilitates the ET reaction.

Here, we focused on the change in the partial molar volume of proteins [14], which is altered during dehydration associated with the formation of the Cyt c–CcO complex. Assuming that the molecular volume of each protein is unchanged after complex formation, the change in the partial molecular volume corresponds to the volume of the water molecules involved in dehydration (negative volume change) or hydration (positive volume change) [15,16]. The volume changes during the formation of the protein–protein complex might be estimated from a precise measurement of the difference in the volumes before and after complex formation, but the heat of the reaction and the mixing of the solution complicate interpretation of the results [17]. However, the partial molar volume change associated with complex formation is simply correlated with the osmotic pressure dependence of the dissociation constant (Eq. 1) [16]
$∂ln⁡KD∂π=ΔVRT$
1
where KD is the dissociation constant, π is the osmotic pressure, ΔV is the partial molar volume change, R is the gas constant, and T is the absolute temperature.

Although the partial volume change can be readily calculated from the osmotic pressure dependence of KD, estimating KD for the ET complex is not simple. The redox states of the two proteins change immediately after complex formation, which prevents us from estimating the KD for the ‘active' and transiently formed ES complex comprising Cyt c and CcO. Fluorescence quenching [18] or other spectroscopic techniques [19] can be used to determine the KD for the formation of the complex between oxidized Cyt c and fully oxidized CcO or between reduced Cyt c and fully reduced CcO, whereas determining KD for the ES complex between reduced Cyt c and the oxidized CcO is impossible due to the ET reaction within the complex. On the other hand, steady-state kinetic analysis for the aerobic oxidation of reduced Cyt c catalyzed by CcO can determine the stability of the ES complex as KM, Michaelis constant. KM is often treated as KD, although KM is not the dissociation constant, KD, for the ES complex. The steady-state kinetic properties of the CcO reaction have shown that oxidized Cyt c functions as a competitive inhibitor to reduced Cyt c and that the KD of the enzyme-oxidized Cyt c complex (or the enzyme-inhibitor complex) is identical with KM [20]. These kinetic properties strongly suggest that KM determined by the steady-state kinetic analysis essentially corresponds to KD of the ES complex, as described in detail in the section of Discussion.

## Materials and methods

### Protein expression and purification

Wild-type (WT) and mutant Cyt c proteins were expressed and purified according to our published procedures [4,21]. The E. coli strain Rosetta 2(DE3)pLysS cells transformed with the plasmids containing the DNA of Cyt c [22] were inoculated in 5 ml of a 2xTY medium and grown overnight. This pre-cultured medium was added to 4 L of a 2xTY medium and the bacteria were further incubated at 37°C. The expression of Cyt c was initiated by adding 0.8 mM IPTG to the culture when the cell density reached an absorbance of 0.6 at 600 nm. And then 0.1 mM δ-aminolevulinic acid was added to promote heme biosynthesis. After additional incubation for 24 h, the cells were collected by centrifugation.

The cell pellet was resuspended in 50 mM Tris–HCl at pH 7.5 containing 1 g/L lysozyme, 50 mg/L DNase I, and 50 mg/L RNase A and suspended for 3 h to lyse the cell pellet completely at 4°C. The supernatant of the crude extract was obtained by centrifugation at 25 000×g for 30 min and 125 000×g for 1 h at 4°C. This supernatant was purified by HiPrep 16/10 SP HP column (GE Healthcare) with a linear salt gradient of 1–300 mM NaCl. The elution sample was concentrated by amicon ultrafiltration using 5 kDa cut-off membranes. To completely oxidize Cyt c, concentrated Cyt c was stirred for 1 hour with 10-fold potassium ferricyanide. After Cyt c was dissolved into 50 mM sodium phosphate buffer at pH 7.0, Cyt c was further purified by Mono S 10/100 GL column (GE Healthcare) with a linear salt gradient. The purified Cyt c fractions were pooled, concentrated, and applied to HiLoad 16/60 Superdex 75 gel filtration column (GE Healthcare).

Mutagenesis was conducted utilizing the PrimeSTAR mutagenesis basal kit from Takara Bio (Otsu, Japan). DNA oligonucleotides (Supplemental Table S1) were purchased from Operon Biotechnologies (Tokyo, Japan). The mutated genes were sequenced (Operon Biotechnologies, Tokyo, Japan) to ensure that the desired mutations were introduced.

CcO was purified from bovine heart as described previously [23] and dissolved into the 50 mM sodium phosphate buffer at pH 6.8 containing 0.1% n-decyl-β-d-maltoside.

### Selection of osmolytes

The osmotic pressure, π, for the solvent at different osmolyte concentration was estimated using Eq. 2
$π=−RTVH2O×ln⁡XH2O$
2
where XH2O and VH2O are the molar fraction and the molar volume of water, respectively. XH2O was calculated using tabulated values of the water content for each osmolyte/water mixtures [24]. For VH2O, a value of 18 ml mol−1 was used.

We used four kinds of osmolytes, sucrose, d-glucose, glycerol, and ethylene glycol, to increase the osmotic pressure, and previous studies have shown that these sugars and polyalcohols have no specific interactions with proteins [25,26]. By addition of one of these osmolytes, no significant spectral perturbations were induced in the absorption spectra of Cyt c (Supplemental Figure S5). However, the addition of the osmolyte increases the viscosity of the solutions, and the increased viscosity substantially perturbs the protein–protein complex formation [27]. Such perturbations induced by the viscosity was encountered for the binding of a restriction enzyme, EcoRV, to the target DNA sequence [28]. The osmotic pressure dependence of KM for the DNA cleavage reaction by EcoRV was substantially affected by the viscosity of the solution containing osmolyte. In the ET reaction from Cyt c to CcO, the combined effect of viscosity and osmotic pressure on KM in the presence of various kinds of glycerol concentrations was rather modest (Supplemental Figure S3) as previously suggested [27]. Such a modest perturbation of KM was also observed by varying the solution viscosity under the constant osmotic pressure (Supplemental Figure S4) due to the delay of the protein translational diffusion [29]. To avoid the effects of viscosity on the complex formation, we determined the concentration of osmolyte so that the viscosity of the solution is constant (summarized in Supplemental Table S2). The value of the viscosity for each osmolyte/water mixture was cited from CRC Handbook of Chemistry and Physics [24]. At the constant viscosity of the solution (1.6 mPa.s), the ET reactions were followed to estimate the KM values.

### Measurements of ET activity of Cyt c under initial steady-state conditions

The ET reaction from Cyt c to CcO was measured with a Hitachi U-3310 UV-visible spectrophotometer at 293 K in 50 mM NaPi/NaOH containing one of the osmolytes listed in Supplemental Table S2, pH 6.8, 0.1% n-decyl β-d-maltoside, as previously reported [7]. The detailed compositions of the reaction medium are also summarized in Supplemental Table S2. Ferrous Cyt c was prepared by the reduction in ferric Cyt c with dithionite and excess reductant was removed by a PD MiniTrap G-25 column [7]. The concentrations of Cyt c varied between 0.5 and 40 µM, and oxidation of Cyt c was followed by the absorbance at 550 nm after adding CcO to the reaction solution at the final concentration of 1 nM. The absorption at 550 nm was recorded with an interval of 1 s for 3 min. To determine the end point of the ET reaction from Cyt c to CcO, a small amount of potassium ferricyanide (III) was added to the reaction solution, as shown in Supplemental Figure S1A (downward arrow). The first order oxidation of reduced Cyt c was observed as shown in Supplemental Figure S1B and Eq. 3, as reported in the previous papers [30,31].
3
where $υ$ is the oxidation rate of reduced Cyt c, and $kobs$ is the apparent rate constant at the various concentrations of Cyt c. Therefore, $kobs$ can be estimated by the following equation
4
In this equation, the concentration of Cyt c2+, [Cyt c2+], can be determined by the absorbance change at 550 nm as follows
5
where ε is the difference of the extinction coefficients between reduced and oxidized Cyt c at 550 nm. By using Eq. 4 and Eq. 5, kobs can be estimated from the absorbance change at 550 nm by the following equation (Supplemental Figure S1B)
6
Consistent with previous reports [30,31], a single rectangular hyperbolic relationship between $υ$ and [Cyt c2+]0 was obtained under the present experimental conditions, as given in Eq. 7.
7
We estimated the Michaelis–Menten parameters using [Cyt c2+]0 and $kobs$, which is determined by Eq. 6. The turnover number, $kcat$, was calculated by using the following equation
$kcat=Vmax[CcO]$
8
where [CcO] denotes the total enzyme concentration.

### Molecular docking of mutant Cyt c with CcO

We predicted the ET complex between the I81S Cyt c mutant and CcO by using the molecular docking simulation we examined in a previous paper [7]. The initial geometry of the I81S mutant was constructed from the WT complex by replacing the side chain of Ile81 in the WT protein with Ser and energetically minimized the protein according to our previous procedure [7].

Based on the predicted complex structure between the I81S Cyt c mutant and CcO, we estimated the binding free energy of Cyt c with CcO (ΔGbind) and that for the dehydration from the protein surface associated with complex formation (ΔGsol). ΔGbind consists of the energy and entropy terms, and the energy term can be further divided into three terms, internal energy (ΔEint), van der Waals energy (ΔEvdW), and Coulombic energy (ΔEcoul). Among them, the contribution of the entropy term and ΔEint to ΔGbind are quite small compared with other two terms [32]. ΔEvdW and ΔEcoul are primary factors to determine ΔGbind. On the other hand, we calculated ΔGsol based on an implicit continuum solvation model using Poisson-Boltzmann equation, which is the sum of the free energy for polar interactions (ΔGpolar) and the nonpolar interactions (ΔGnonpolar). As found in most protein–protein complex formation systems [33], ΔEcoul is compensated for by ΔGpolar and there is an anti-correlation between these two energies. Consequently, the variance of the sum of electrostatic contributions (ΔGelectro = ΔEcoul + ΔGpolar) is significant as well as the variance of hydrophobic interactions, ΔEvdW and ΔGnonpolar.

## Results

### Osmotic pressure dependence of Michaelis constant for ES complex between Cyt c and CcO

To investigate the dehydration associated with the formation of Cyt c with CcO, we determined the KM values under various osmotic pressure by the steady-state kinetics for the ET from Cyt c to CcO. The initial steady-state rates determined from the time course indicate a simple Michaelis–Menten relationship (Supplemental Figures S1, S2), namely, a single Cyt c-binding model under the present pH and ionic strength conditions, consistent with a previous report [31]. The kinetics results were, therefore, analyzed using the simple Michaelis–Menten equation [34].

As described in Materials and Methods, the osmotic pressure of the protein solution was increased by the addition of sugars or polyalcohols that have no specific interactions with proteins [25,35,36]. Although recent study reported that high concentration (40%) of ethylene glycol increased the KM value for the ET reaction from Cyt c to CcO by a factor of ∼5, suggesting that ethylene glycol could directly perturb the configuration of the Cyt c–CcO complex and function as a competitive inhibitor of the steady-state reaction [37]. In this paper, however, the concentration of the osmolyte we used was less than 20%, and no significant changes in the absorption spectra of Cyt c were confirmed before the kinetic measurements in the presence of ethylene glycol (Supplemental Figure S5). In fact, the KM value in the presence of 18.6% ethylene glycol was 0.80 ± 0.11 µM (Figure 1), which was smaller than that in the presence of 7.14% ethylene glycol (0.825 ± 0.059 µM, Supplemental Figure S4) and in the absence of the osmolyte (1.2 ± 0.1 µM) [7]. Less than 20% ethylene glycol is, therefore, unlikely to induce configurational changes of the Cyt c–CcO complex to increase the KM value for the ET reaction from Cyt c to CcO. The KM values at various osmotic pressures are summarized in Table 1. As Table 1 clearly shows, the KM value decreased with increasing osmotic pressure, corresponding to the negative volume change (Eq. 1). It should be noted here that the addition of the osmolyte decreases the water activity, which suppresses the ionization of NaPi in solutions and results in the decreased ionic strength of the reaction medium (Supplemental Table S2). Such a decrease in the ionic strength by the addition of the osmolyte was, however, less than 3 mM. Perturbations in the water activity induced by the addition of the osmolyte would, therefore, not significantly affect the KM values under the conditions we followed the ET reactions.

#### Dependence of the Michaelis constants (KM) on osmotic pressure for formation of Cyt c–CcO complex.

Figure 1.
Dependence of the Michaelis constants (KM) on osmotic pressure for formation of Cyt c–CcO complex.

Each osmolyte was added to obtain a viscosity of 1.6 mPa s (sucrose: 1.3 MPa, D-glucose: 2.5 MPa, glycerol: 5.5 MPa, ethylene glycol: 8.7 MPa). Error bars represent ln (KM ± S.D.). wild-type (WT), red; I9A, black; I11A, green; K13A, yellowish brown; K79A, pink; I81A, blue; I81S, purple.

Figure 1.
Dependence of the Michaelis constants (KM) on osmotic pressure for formation of Cyt c–CcO complex.

Each osmolyte was added to obtain a viscosity of 1.6 mPa s (sucrose: 1.3 MPa, D-glucose: 2.5 MPa, glycerol: 5.5 MPa, ethylene glycol: 8.7 MPa). Error bars represent ln (KM ± S.D.). wild-type (WT), red; I9A, black; I11A, green; K13A, yellowish brown; K79A, pink; I81A, blue; I81S, purple.

Table 1
Osmotic pressure dependence of the dissociation constants for formation of Cyt c–CcO complex
Osmotic pressure (π) (MPa)KM (µM)Osmolyte and concentrationWater activity
1.3 2.05 ± 0.14 15.2% Sucrose 0.991
2.5 1.94 ± 0.27 15.6% D-Glucose 0.982
5.5 1.38 ± 0.13 17.5% Glycerol 0.960
8.7 0.80 ± 0.11 18.6% Ethylene glycol 0.938
Osmotic pressure (π) (MPa)KM (µM)Osmolyte and concentrationWater activity
1.3 2.05 ± 0.14 15.2% Sucrose 0.991
2.5 1.94 ± 0.27 15.6% D-Glucose 0.982
5.5 1.38 ± 0.13 17.5% Glycerol 0.960
8.7 0.80 ± 0.11 18.6% Ethylene glycol 0.938

To calculate the volume change associated with the formation of the Cyt c–CcO complex, the KM value was plotted against the osmotic pressure, as shown in Figure 1. Based on the slope of the fitting line for wild-type Cyt c (WT: red) in Figure 1, the partial volume change was negative and estimated to be −314 ± 50 ml mol−1 (Table 2), implying that dehydration was induced during complex formation. Given the assumption that the volume change for dehydration from hydrophobic amino acid residues is −17.5 ml mol−1 [38], the volume change we obtained here corresponds to dehydration involving 17 ± 3 water molecules. On the other hand, assuming that the number of the released hydration water molecules simply depends on the area of the interaction site [39,40], the interaction area estimated by our NMR experiments [4] (∼1800 Å2) suggests that nearly 100 water molecules can be expelled from the interaction site. A much smaller number of released hydration water molecules estimated by the osmotic pressure experiments (<20 water molecules) suggests that the number of direct interactions of amino acid residues that induce dehydration is much less than that we expected from the NMR measurement. The smaller number of released hydration water molecules associated with complex formation is also supported by the crystal structure of the complex between Cyt c and CcO [8]. The interface between the two proteins is loosely packed and three water layers with a long-molecular span are formed in the interface [8], which is sufficient for many hydrating water molecules to remain around the amino acid residues in the interaction site at the Cyt c–CcO protein–protein interface and consistent with our recent results from the docking simulation [7].

Table 2
Volume changes and numbers of the dehydrated water molecule associated with formation of the Cyt c–CcO complex
Cyt cΔV (ml mol−1)Number of dehydrated water molecule
Wild-type 314 ± 50 17 ± 3
I9A 317 ± 48 18 ± 3
I11A 246 ± 72 14 ± 4
I81A 139 ± 38 8 ± 2
I81S 197 ± 38 11 ± 3
K13A 241 ± 20 13 ± 1
K79A 278 ± 44 15 ± 2
Cyt cΔV (ml mol−1)Number of dehydrated water molecule
Wild-type 314 ± 50 17 ± 3
I9A 317 ± 48 18 ± 3
I11A 246 ± 72 14 ± 4
I81A 139 ± 38 8 ± 2
I81S 197 ± 38 11 ± 3
K13A 241 ± 20 13 ± 1
K79A 278 ± 44 15 ± 2

The comparison of the crystal structure of the Cyt c–CcO complex (PDB: 5IY5) [8] with those of unbound Cyt c (PDB: 3ZCF) [41] and CcO (PDB: 2DYR) [42] also suggests that the dehydration is associated with complex formation. Analysis of the electron density map of these crystal structures at different sigma levels [43] revealed that the number of hydration water molecules located within 3.5 Å from the nearest atom of the interacting residues of Cyt c with CcO [4] was estimated to be 21 (1.5 σ) or 16 (2.0 σ), respectively, and that of CcO with Cyt c [7] was 38 (1.5 σ) or 32 (2.0 σ), respectively. By the complex formation between Cyt c and CcO, the number of the hydration water molecules in the Cyt c surface of the complex is decreased to 15 (1.5 σ) or 7 (2.0 σ), respectively, showing that 6–9 hydration molecules are released from the surface of Cyt c. Such release of hydration water molecules is also encountered for the surface of CcO. The complexation with Cyt c expels 2–7 hydration water molecules from the surface of CcO. Based on the comparison of these crystal structures, 8–16 hydration water molecules at the Cyt c and CcO surfaces in the interaction site would be dehydrated by the complexation, which is consistent with our estimation of the decrease in the hydration water molecules based on the osmotic pressure experiments.

### Dehydration sites for Cyt c–CcO complexation

To identify the dehydration sites in the interface between CcO and Cyt c, we focused on hydrophobic amino acid residues in the CcO interaction site on Cyt c and mutated one of the hydrophobic amino acid residues to examine the osmotic pressure effects on KM for complex formation. As we previously reported [4], three isoleucine residues, Ile9, Ile11, and Ile81, are located in the interaction site (Supplemental Figure S6). The exposed surface areas of the side chains [44] (Supplemental Table S3) indicate hydration by 1, 4, and 7 water molecules around the side chains of Ile9, Ile11, and Ile81, respectively. We replaced each Ile with Ala, which has a smaller hydrophobic side chain and fewer hydrating water molecules around the side chain, and measured the Cyt c oxidation reaction at various osmotic pressures. As we recently reported [7], these mutations at the interaction site induce only localized structural changes and the structures of mutant Cyt c are quite similar to that of the WT protein, confirming that the mutations affect only the hydration of water molecules at the mutation site. Supplemental Tables S4, S5 summarize the obtained Michaelis–Menten kinetic parameters of the WT and mutant proteins.

As clearly illustrated in Figure 1, the slope of the osmotic pressure dependence of the KM for the Ile mutants is less steep than that for the WT protein except for the Ile9 mutant (Supplemental Table S4). The estimated volume changes for complex formation are −246 ± 72, −197 ± 38, −139 ± 38 ml mol−1 for the Ile11 → Ala, Ile81 → Ser and Ile81 → Ala mutants, respectively. The decreased volume changes in the Ile mutants imply that the number of water molecules released during dehydration was reduced to 14 ± 4, 11 ± 3 and 8 ± 2 due to the mutations of Ile11 → Ala, Ile81 → Ser and Ile81 → Ala, respectively. Although the decreased number of dehydrated water molecules for the Ile11 mutant is within the experimental error, the reduced numbers of water molecules involved in dehydration in the Ile81 mutants are significant. This result indicates that the hydrating water molecules around Ile81 are expelled to the solvent during formation of the ET complex between Cyt c and CcO. In particular, ∼10 water molecules are released during the dehydration of Ile81, which allows us to conclude that Ile81 is the primary dehydration site for complex formation between Cyt c and CcO under the turnover conditions.

In sharp contrast with the mutations at Ile81, the mutations at lysine residues in the interaction sites were less effective for decreasing the number of dehydrated water molecules (Figure 1, Table 2 and Supplemental Table S4). We have revealed that Lys13 is involved in the key interaction with CcO [4] and it has many hydrophobic methylene groups in the long side chain, but the number of dehydrated water molecules decreased by less than 5 upon the substitution of Ala for Lys13. The mutation of Lys79, which is located adjacent to Ile81, also induced a minor perturbation to dehydration. The comparable number of dehydrated water molecules in the Lys mutant relative to that in the WT protein also supports the preferential and specific dehydration from Ile81 in formation of the transient ET complex between Cyt c and CcO.

### Thermodynamic analysis of association of Cyt c with CcO

To examine functional significance of the release of 10 water molecules during the dehydration of hydrophobic amino acid residues, we focused on the thermodynamic contribution of dehydration to ET complex formation and determined the enthalpy (ΔH) and entropy (ΔS) for the complex formation between Cyt c and CcO. Based on the temperature dependence of KM for the steady-state kinetics of the ET reaction from Cyt c to CcO (van't Hoff plot analysis) (Figure 2 and Supplemental Figure S7, Michaelis–Menten kinetic parameters are listed in Supplemental Tables S6, S7), ΔH and ΔS for complex formation in WT Cyt c were determined to be 13.0 ± 1.6 kJ mol−1 and 161 ± 6 JK−1 mol−1, respectively (Figure 2, closed circle and Table 3). These obtained values indicate that complex formation between Cyt c and CcO is an energetically unfavorable and entropy-driven reaction. After mutation of Ile81 to Ala, the plots of ln KM versus 1/T (Figure 2, closed square) are completely different from those of the WT protein, which presents a negative ΔH (−3.53 ± 3.01 kJ mol−1) and reduced ΔS (103 ± 10 JK−1 mol−1). The introduction of a more hydrophilic residue—Ser—into the Ile81 position resulted in a more negative ΔH (−14.9 ± 1.4 kJ mol−1) and smaller ΔS (72 ± 5 JK−1 mol−1) (summarized in Table 3). The complex formation between Ile81-mutated Cyt c and CcO is an energetically favorable reaction and the contribution of entropy to the thermal stability of the complex was reduced in the Cyt c mutant. Such reduced contribution of entropy to complex formation in the I81A mutant (ΔΔSI81A-WT = ΔSI81A − ΔSWT = −58 JK−1 mol−1) can be contributed to the decreased number of hydration water molecules released from the protein surface around position 81, assuming that the mutation at Ile81 does not affect the entropy changes for the overall rotational and translational degrees of freedom and the conformational changes of the proteins associated with the Cyt c–CcO complex formation.

#### Temperature dependence of the Michaelis constant (KM) for Cyt c–CcO complex formation.

Figure 2.
Temperature dependence of the Michaelis constant (KM) for Cyt c–CcO complex formation.

Experimental conditions: 50 mM sodium phosphate buffer at pH 6.8 containing 0.1% n-decyl-β-d-maltoside. Error bars represent ln (KM ± S.D.). wild-type (closed circle); I81A (closed square), I81S (closed triangle).

Figure 2.
Temperature dependence of the Michaelis constant (KM) for Cyt c–CcO complex formation.

Experimental conditions: 50 mM sodium phosphate buffer at pH 6.8 containing 0.1% n-decyl-β-d-maltoside. Error bars represent ln (KM ± S.D.). wild-type (closed circle); I81A (closed square), I81S (closed triangle).

Table 3
Thermodynamic parameters for formation of the ES complex between Cyt c and CcO at 293 K.
Cyt cΔH (kJ mol−1)ΔS (JK−1 mol−1)
Wild-type 13.0 ± 1.6 161 ± 6
I81A −3.53 ± 3.01 103 ± 10
I81S −14.9 ± 1.4  72 ± 5
Cyt cΔH (kJ mol−1)ΔS (JK−1 mol−1)
Wild-type 13.0 ± 1.6 161 ± 6
I81A −3.53 ± 3.01 103 ± 10
I81S −14.9 ± 1.4  72 ± 5

To get further insights into the energetic contribution of each amino acid residue to the complex formation between Cyt c and CcO, the structure of the ET complex between the I81S Cyt c mutant and CcO was predicted by using molecular docking simulation as previously reported [7]. Based on the predicted complex structure, we estimated the free energy change for the formation of hydrophobic interaction (ΔEvdW) for the binding of Cyt c with CcO and those for the dehydrations from hydrophobic (ΔGnonpolar) and charged (ΔGelectro) protein surface associated with the complex formation (Figure 3). The validity of the energy calculation was confirmed by the total free energy change (ΔGtot = ΔGbind + ΔGsol) for the complexation; the calculated ΔGtot for the I81S mutant was −8.51 kcal mol−1, which is in good agreement with the experimental value (−8.60 kcal mol−1) calculated for the thermodynamic parameter in Table 3. One of the significant perturbations induced by this mutation is enhancement of the favorable electrostatic interactions (ΔGelectro) in Lys72 (−6.86 and −5.17 kcal mol−1 for I81S and WT Cyt c, respectively) and Lys79 (−6.91 and −5.64 kcal mol−1 for I81S and WT Cyt c, respectively). These enhanced electrostatic interactions suggest that there are more polar environments around Lys72 and Lys79 in the I81S mutant, compared with those in the WT protein. Another significant change in the energy profile of the I81S mutant is the increased unfavorable electrostatic interaction of Val83 and Glu90. Val83 is one of the hydrophobic amino acid residues near the exposed heme periphery and the free energy for the dehydration (ΔGelectro) was positively shifted from 0.68 kcal mol−1 [7] to 2.16 kcal mol−1 (Figure 3) by the mutation of Ile to Ser at position 81. Although Glu90 is far from the exposed heme periphery and the energetic contribution to the complex formation between WT Cyt c and CcO was rather small (less than 3 kcal mol−1) [7], the significant unfavorable electrostatic energy at Glu90 (3.90 kcal mol−1) was detected in the I81S mutant. These findings suggest that the mutation at position 81 induced significant perturbation of the binding orientation of Cyt c to CcO, which is supported by the predicted complex structure between the I81S Cyt c mutant and CcO (Supplemental Figure S8(a)). As illustrated in Figure 4, the distribution of amino acid residues forming hydrophobic interactions to stabilize the ET complex between Cyt c and CcO is significantly perturbed in the I81S Cyt c mutant.

#### Free energy decomposition of ΔGtot(=ΔGbind + ΔGsol) on a per residue basis into the contributions from ΔEvdW, ΔGelectro, and ΔGnonpolar in I81S Cyt c mutant.

Figure 3.
Free energy decomposition of ΔGtot(=ΔGbind + ΔGsol) on a per residue basis into the contributions from ΔEvdW, ΔGelectro, and ΔGnonpolar in I81S Cyt c mutant.

Residues with a |ΔGtot| value rounded off to the nearest integer ≥3.0 kcal mol−1 are shown.

Figure 3.
Free energy decomposition of ΔGtot(=ΔGbind + ΔGsol) on a per residue basis into the contributions from ΔEvdW, ΔGelectro, and ΔGnonpolar in I81S Cyt c mutant.

Residues with a |ΔGtot| value rounded off to the nearest integer ≥3.0 kcal mol−1 are shown.

#### Amino acid residues of Cyt c forming hydrophobic interaction with CcO (|ΔEvdW + ΔGnonpolar| ≥ 2.5 kcal mol−1) based on the energy analysis shown in Figure 3.

Figure 4.
Amino acid residues of Cyt c forming hydrophobic interaction with CcO (|ΔEvdW + ΔGnonpolar| ≥ 2.5 kcal mol−1) based on the energy analysis shown in Figure 3.

The total interaction energy of Glu89 and Glu90 in the I81 mutant and that of Glu89 in wild-type Cyt c are positive due to the large electrostatic repulsion energy. I81S (A); wild-type (B).

Figure 4.
Amino acid residues of Cyt c forming hydrophobic interaction with CcO (|ΔEvdW + ΔGnonpolar| ≥ 2.5 kcal mol−1) based on the energy analysis shown in Figure 3.

The total interaction energy of Glu89 and Glu90 in the I81 mutant and that of Glu89 in wild-type Cyt c are positive due to the large electrostatic repulsion energy. I81S (A); wild-type (B).

## Discussion

### Significance of Michaelis constant, KM, determined by steady-state kinetic analysis

It has been well established that a rectangular hyperbolic relationship between the enzyme activity and [Cyt c2+] as given in Eq. 7 is detectable under the present experimental conditions (Cyt c2+ oxidation by a catalytic amount of CcO under the initial steady-state conditions) and that this steady-state kinetic system shows the first order oxidation of Cyt c2+ and the competitive inhibition of Cyt c3+ against the binding of Cyt c2+ to CcO [20,45,46]. The above rectangular hyperbolic relationship as given by Eq. 7 indicates, at least apparently, that a single electron equivalent from Cyt c2+ reduces one equivalent of molecular oxygen to produce two water molecules. Discussion on this apparent discrepancy, which has not been done in detail thus far, would be helpful to understand the significance of the experimentally determinable parameters (Vmax and KM).

The rectangular hyperbolic relationship indicates a steady-state kinetic model as given in Figure 5, which implies four discrete ET events to provide four different intermediate species of CcO, designated as E, F, G and H in Figure 5. The kinetic model given in Figure 5 provides the following initial steady-state equation
$υ[CcO]=[S]{KM1+[S]+(KM1/Ki1)[P]k3+KM2+[S]+(KM2/Ki2)[P]k8+KM3+[S]+(KM3/Ki3)[P]k13+KM4+[S]+(KM4/Ki4)[P]k18}$
9
where S and P denote Cyt c2+ and Cyt c3+, respectively, and $KM1=k2+k3k1$, $KM2=k7+k8k6$, $KM3=k12+k13k11$, $KM4=k17+k18k16$, $Ki1=k5k4$, $Ki2=k10k9$, $Ki3=k15k14$, and $Ki4=k20k19$. The numbers of the rate constants are as given in Figure 5. The rate constants, k3, k8, k13 and k18 are those of the release of Cyt c3+. This equation shows a rectangular hyperbolic relationship between the activity and [Cyt c2+]0, as given in Eq. 7 and the competitive inhibitor function of Cyt c3+ against Cyt c2+. Furthermore, when KM1 = Ki1, KM2 = Ki2, KM3 = Ki3, and KM4 = Ki4, Eq. 9 becomes Eq. 10, as follows
$υ[CcO]=[S]KM1+[S]+[P]k3+KM2+[S]+[P]k8+KM3+[S]+[P]k13+KM4+[S]+[P]k18$
10

The denominator of Eq. 10 depends on the total concentration of Cyt c irrespective of the ratio of [Cyt c2+] to [Cyt c3+]. Thus, in each enzyme assay measuring oxidation of Cyt c2+, the constant denominator provides the first order oxidation of Cyt c2+, as described by Eq. 3. Thus, the first order oxidation of Cyt c2+ indicates that the KM value of each intermediate species is identical with its Ki value. In fact, Yonetani and Ray reported that significant deviation from the first order oxidation process was detectable when KM was not identical with Ki under significantly alkaline conditions [45].

#### Schematic representation of four-electron reduction in CcO by Cyt c.

Figure 5.
Schematic representation of four-electron reduction in CcO by Cyt c.

The four intermediate CcO species are designated as E, F, G and H. S and P represent Cyt c2+ and Cyt c3+, respectively.

Figure 5.
Schematic representation of four-electron reduction in CcO by Cyt c.

The four intermediate CcO species are designated as E, F, G and H. S and P represent Cyt c2+ and Cyt c3+, respectively.

The experimentally obtainable parameters, KM and kcat, can, therefore, be written as follows
$KM=KM1/k3+KM2/k8+KM3/k13+KM4/k181/k3+1/k8+1/k13+1/k18$
11

$kcat=11/k3+1/k8+1/k13+1/k18$
12
It should be noted that KM1, KM2, KM3, and KM4 are equal to Ki1, Ki2, Ki3, and Ki4, respectively. Eq. 11 indicates that the experimentally obtainable parameter KM is the average of the microscopic KM values for the four intermediate species, weighted by the relative rates of the product (or Cyt c3+) release.
In general, KM is not KD for ES complex in the Michaelis–Menten system, namely, KM is not a thermodynamic parameter. However, in the present steady-state kinetic system of CcO, KM of each ET step is identical with Ki of the ET step. For example, in the initial step in Figure 5, two binding reactions proceed:

where E is the first intermediate, S is reduced Cyt c, P is oxidized Cyt c, and F is the second intermediate. While the steady-state kinetic results indicate Ki1 = KM1, the NMR analysis for interactions between Cyt c and CcO revealed that the interaction site for CcO in oxidized Cyt c was almost overlapped with that in reduced Cyt c [4], supporting the assumption that the overall affinity of oxidized Cyt c for CcO is equal to that of reduced Cyt c, namely k5/k4 = k2/k1. These observations suggest that KM1 can be considered as the dissociation constant, KD1 (=k2/k1) for the ES complex in Figure 5. In other words, the KM of each step can be treated as the KD of the ES complex in the step. The experimentally obtainable parameter, KM, is the weighted average of the microscopic KD values for the four intermediate species. Thus, the KM, obtained under the present conditions can be treated as a thermodynamic parameter. Although stable CcO forms including various inhibitor-bound forms [46], the fully reduced form and the fully oxidized form as isolated [47] have been often used as models of the unstable catalytic intermediate species under the turnover conditions [46], they are not directly involved in the catalytic cycle. It is, therefore, noteworthy that the present and previous [7] works have introduced a new approach for characterization of enzyme species under turnover conditions using the initial steady-state kinetics.

### Energetic contribution of dehydration to complex formation between Cyt c and CcO

As clearly shown in Figure 1 and Table 2, the osmotic pressure dependence of KM for the ET reaction from Cyt c to CcO revealed that ∼20 hydration water molecules were expelled to the bulk upon the complex formation between Cyt c and CcO. By mutation of Ile81 to Ala, the number of hydration water molecules released upon the complex formation is decreased from 17 ± 3 to 8 ± 2, implying that ∼10 water molecules would still be hydrated in the complex between I81A Cyt c mutant and CcO. Because the entropy change for dehydration involving one water molecule and a hydrophobic amino acid residue was estimated to be 5.5 JK1 mol1 [48], the entropy change due to dehydration involving 10 water molecules corresponds to ∼60 JK1 mol1, which is comparable to ΔΔSI81A-WT from Table 3. Considering that the entropy change due to the reductions in the overall rotational and translational degrees of freedom associated with the formation of a protein–protein complex, which is one of the major entropy change in protein–protein complex formation, is −33.5 JK1 mol1 [49], thermodynamic contribution from dehydration around Ile81 (∼60 JK1 mol1) is significant. This contribution compensates for the reduced entropy due to complex formation and the dehydration is one of the major factors that increases the entropy during complex formation.

### Functional significance of dehydration to ET from Cyt c to CcO

The most remarkable finding of this work is that the primary dehydration site during the formation of the Cyt c–CcO complex is located near a hydrophobic area including a hydrophobic thioether group (Supplemental Figure S6) in Cyt c. The electron entry site for CcO, the CuA site, is also in the hydrophobic region constructed by several aromatic amino acid residues on the protein surface of CcO [23]; thus, the dehydration results in induction of interactions involving the hydrophobic area around the exposed heme periphery of Cyt c and the hydrophobic region of CcO. Our previous energetic analysis revealed the distribution of amino acid residues mediating hydrophobic interactions between Cyt c and CcO [7]. As shown in Figure 4A, amino acid residues showing relatively large free energy for hydrophobic interactions, ΔEvdW and ΔGnonpolar, surround the exposed heme periphery, acting as a ‘molecular breakwater’ to inhibit the invasion of the bulk water molecules to the hydrophobic interaction site around the exposed heme periphery of Cyt c and the hydrophobic region of CcO. The hydrophobic methylene groups (–CH2–) of the side chain of charged or hydrophilic amino acid residues including Lys13, Gln16, Lys27, and Thr28 also contribute to the formation of the hydrophobic interactions. These amino acid residues surrounding the redox centers supports the function of nearby solvent-exposed hydrophobic residues such as Ile81 by dehydrating water molecules around the redox centers for formation of the ‘molecular breakwater', which inhibits the exchange of water molecules between the sterically constrained ET region and the more turbulent surrounding bulk water molecules [50]. Such hydrophobic interactions surrounding the redox center are also encountered for other ET complexes [50–52], suggesting that the ‘molecular breakwater' inhibits the invasion of bulk water molecules to form nonspecific hydrogen bonds around the protein–protein interaction sites, which is likely to form alternative ET pathways and reduce the specificity of the ET reaction.

The introduction of a hydrophilic residue into the ‘molecular breakwater' by mutation of Ile81 to Ser was found to affect the energetic contributions of the amino acid residues to the complex formation between Cyt c and CcO as shown in Figure 3. The amino acid residues in Cyt c interacting with CcO were significantly perturbed in the mutant, but the interaction site of the mutant was also located near the exposed hydrophobic periphery, as observed for WT Cyt c. Although the interface between Cyt c and CcO in the X-ray structure has more space than that of the simulated complex structure, the X-ray structure also indicates that the hydrophobic heme periphery is involved in the interaction site of Cyt c to CcO, supporting the simulated complex structure. As described in the section of RESULTS, introduction of a hydrophilic amino acid residue, Ser, into the position of Ile81 resulted in more polar environments around Lys72 and Lys79. The decreased hydrophobicity around Lys79, located adjacent to residue 81 and the exposed hydrophobic heme periphery (Supplemental Figure S6), would weaken the effects of the ‘molecular breakwater' to protect the hydrophobic interaction site from bulk water molecules. The enhanced unfavorable electrostatic interaction for the complex formation was detected at Val83, one of the surrounding amino acid residues constructing the ‘molecular breakwater' around the exposed hydrophobic heme periphery, in the I81S mutant. The decreased stabilization energy at Val83 would also result in a weakened ‘molecular breakwater'. As illustrated in Figure 4, the distribution of amino acid residues forming hydrophobic interactions to stabilize the ET complex between Cyt c and CcO is significantly perturbed in the I81S Cyt c mutant, and the distribution of the ‘molecular breakwater' in the mutant has a gap around position 81.

Although the hydrophobic interactions were weakened in the complex between the I81S Cyt c mutant and CcO, a new hydrogen bond between Ser81 of the I81S Cyt c mutant and Glu157 in Subunit II of CcO was formed (Supplemental Supplemental Figure S8(b)), which also contributes to the reduced hydrophobicity of the interaction site of the mutant. The formation of the hydrogen bond reduced the repulsive electrostatic interaction by Glu157 in Subunit II of CcO (+6.2 and <+3 kcal mol−1 in WT Cyt c and the I81S mutant, respectively) [7], thus supporting the enthalpy-driven complex formation between the I81S Cyt c mutant and CcO and not the entropy-driven formation observed for WT Cyt c (Table 3). While hydrogen bonds are efficient ET mediators in proteins [53], the kcat value of the I81S mutant at 293 K was 96.0 ± 1.7 s−1 (Supplemental Figure S7C), which is significantly slower than that of the WT protein under the same conditions (119 ± 4 s−1) (Supplemental Table S7). Thus, the newly formed hydrogen bond between Ser81 in Cyt c and Glu157 in subunit II of CcO would not contribute to formation of a more effective ET pathway and the reduced hydrophobicity in the interface between Cyt c and CcO as discussed above would decrease the efficiency of the ET process.

Therefore, the simulation analysis for the Ile81 mutation revealed decreased hydrophobic interactions and increased electrostatic interactions in the interface between Cyt c and CcO due to the introduction of the hydrophilic amino acid residue Ser into position of 81. The decreased dehydration around Ser81 was also confirmed by the reduced entropy required for the I81S mutant to form the ET complex with CcO (Figure 2 and Table 3). These observations strongly support the primary contribution of the dehydration from Ile81 to the formation of the ‘molecular breakwater' upon Cyt c–CcO complex formation during catalytic turnover. The present analyses also suggest that once the breakwater is broken by the mutation, water molecules around the redox centers are not effectively expelled and bulk solvent molecules penetrating into the redox centers perturb the interaction site of Cyt c for CcO which forms the ET pathway from Cyt c to CcO.

In conclusion, by measuring the steady-state kinetics at various osmotic pressures, we successfully determined the number of water molecules released during the dehydration of hydrophobic amino acid residues in the CcO–Cyt c interaction site. The present extensive mutational analysis has identified the hydrophobic region near the exposed heme periphery region as the major dehydration site in Cyt c. The present results suggest that such dehydration is a primary factor to increase the entropy for the formation of the Cyt c–CcO complex, which contributes to the formation of the hydrophobic ET pathway and suppress the formation of hydrogen bond-mediated nonspecific ET pathways, thus promoting effective and specific ET from Cyt c to CcO.

## Competing Interests

The authors declare that there are no competing interests associated with the manuscript.

## Funding

This work was supported by Grants-in-aid 25288072, 25109501 and 19K22193 (to K. I.), 26234567 (to S. Y.), and 24109014 and 15K13710 (to K. Y.) from the Japan Society for the Promotion of Science.

## Author Contribution

W.S. and K.I. designed research. W.S. and K.S-I. performed experiments. W.S., T.U., and K.I. analyzed data. S.H. and K.Y conducted the simulations and analyzes. W.S., S.Y., and K.I. wrote the article.

## Abbreviations

• ET

electron transfer

•
• WT

wild-type

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