J. Biol. Macromol. 8(2), 38-47 (2008)

ArticleKinetic study on the dissociation of a dimeric protein,
Streptomyces Subtilisin Inhibitor
Keiko Momma1,2, Ben’ichiro Tonomura, and Keitaro Hiromi
Department of Food Science and Technology, Faculty of Agriculture,
Kyoto University, Kyoto 606-8502

Received August 31, 2007 ; Accepted March 18, 2008
Summary: There have been few kinetic studies on the dissociation of stable dimer proteins of which monomer subunit is not detectable under normal condition. Proteinaceous proteinase inhibitor, Streptomyces subtilisin inhibitor (SSI) exists as a stable homodimer. Modified SSI (SSI*) in which the reactive site is cleaved has also inhibitory
activity and separated from SSI on native PAGE. When SSI and SSI* were mixed, aheterodimer was observed. By following the formation of the heterodimer, the dissociation rate constant of dimer into monomers was determined to be 3.2 x 10-3 s-1 at pH 7.0,
25oC. The activation energy for the dissociation was calculated to be 23.8 kcal/mol.
The dissociation of SSI dimer was also observed for subtilisin BPN’-SSI complex. The
rate constants and activation parameters for the dimer dissociation of the complex weresimilar to those of SSI dimer. These results indicated that subtilisin BPN’ bound SSI
resembled free SSI in the mechanism of dimer dissociation.

Keywords: dimer dissociation, Streptomyces subtilisin inhibitor, rate constant

There are many stable dimer proteins consisting of non-covalently bound subunits.
However, there have been rather few kinetic studies on the dissociation of those stable dimer
proteins. Koren and Hammes [1] reported the rate constants of dimer formation and dissociation of insulin, β-lactoglobulin, and α-chymotrypsin by monitoring the relaxation process of
dimer-monomer equilibrium changed by temperature jump or dilution. But it is difficult toobtain the rate constants under the condition in which monomer subunit is not detectable in an
equilibrium state.
Streptomyces subtilisin inhibitor (SSI, I, or I2) is a proteinaceous proteinase inhibitor
produced by Streptomyces albogriseolus S-3253 and strongly inhibits bacterial alkaline serine
proteinases such as subtilisin BPN’ (S-BPN’, E) [2 - 4]. SSI exists in dimeric form (MW23000) under the mild condition in the concentration range of 0.01 - 10 mg/ml (0.87______________________________________________________________________________________________________________
1

Present address: Department of Social Design Studies, Faculty of Human Studies, Kyoto
Bunkyo University, Uji, Kyoto, 611-0041, Japan
2
Corresponding author

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Kinetic study on the dissociation of a dimeric proteinμΜ − 870 μM as a monomer) [5] and β-sheets of two subunits face each other to make a coreof globular dimer SSI [6]. The monomer form of SSI has been detected only in unfolded
conditions; e.g., caused by the addition of sodium dodecyl sulfate [7], heating [8], or acidification [9].
One dimeric SSI binds and inhibits two molecules of S-BPN’ forming a tetramericcomplex, E2I2, that has been shown by X-ray crystallography [10], fluorometric titration [11],inhibition [12], and sedimentation [5]. Monomer S-BPN’-SSI complex has not been detected in any conditions.
Modified SSI (SSI*, I*, or I*2) in which the reactive site peptide bond, Met73-Val74,
was cleaved enzymatically also has strong inhibitory activity against S-BPN’. SSI* is separated from SSI on native PAGE. When I2 and I*2 were mixed, a hybrid species, II*, wasclearly detected on native PAGE. This provides us a good probe for studying the dissociation of SSI dimer. In this study, we report the dissociation rate of SSI dimer. Further we
examined the dissociation of SSI dimer bound with S-BPN’.
MATERIALS AND METHODS
Proteins - S-BPN’ (EC 3. 4. 21. 14, lot No. 730953) was purchased from Nagase Sangyo Co. Ltd. The protein concentration was determined spectrophotometrically from theabsorbance at pH 7.0 by using A278 (1 mg/ml) = 1.063 and its molecular weight 27500 [13].
The concentration of active enzyme was determined to be 75% as described previously [12].
SSI was prepared as described previously [14]. SSI* was prepared as follows [4]:S-BPN’-SSI complex was isolated by gel filtration at pH 7.0 and subjected to pH jump to pH
2.7 at 0 oC. After 2 hours incubation at 0 oC, the pH of the solution was neutralized. SSI*
was isolated by QAE-Toyopearl (Tosoh) column chromatography at pH 9.4. The protein
concentration was determined spectrophotometrically from the absorbance at pH 7.0 by using
A276 (1 mg/ml) = 0.829 and the molecular weight of 11500 (monomer) [12].
Determination of the dissociation rate constants - I2 and I*2 solutions (13 μM each as
monomer) equal in volume were mixed and incubated at pH 7.0 and at various temperatures.
After appropriate periods, the sample was put on iced water, then quickly loaded on native
PAGE [15] at pH 9.4 and 0 oC. Proteins were stained with Coomassie Brilliant Blue R-250
and the density of the bands were measured at 590 nm with a Shimadzu dual-wavelength TLC
scanner CS-900. A normalized value of [II*] (%) (= [II*] x 100/ ([I2] + [I*2] + [II*])) was
analyzed as a first-order reaction to determine the dissociation rate constant.
As for the dissociation rate constant of SSI dimer of EI complex, I2 and E2I2 solutions (7μM each as monomer) equal in volume were mixed and the time course of the amount of EI2
was analyzed as a first order reaction.
Determination of activation parameters - The free energy of activation for the dissociation of SSI dimer was calculated from the dissociation rate constantwhere kB is Boltzmann’s constant and h, Plank’s constant.

K. Momma et al.

40

RESULTS AND DISCUSSION
Assignment of II* an hybrid dimer of SSI and SSI* on native PAGE - Equal volumeof I2 and I*2 solutions (12 μM each as monomer) were mixed and incubated at pH 7.0 androom temperature for 1 h. The mixture was loaded on native PAGE at pH 9.4 and gave threebands (Fig. 1, lane 3). The top and the bottom bands are I2 and I*2, respectively, but thecentral band appeared newly by the mixing. Protein of the central band was extracted fromthe gel, and subjected to native PAGE again. That yielded similar three bands (Fig. 1, lane4). The proteins of these three bands in lane 4 were extracted separately from the gel, andthey were loaded separately to the native PAGE; the top band gave I2 (lane 5), the central
band gave three bands (lane 6), and the bottom band gave I*2 (lane 7). These results indicated that the central band was the hybrid species of SSI and SSI*, namely II*, and that respective subunits are exchanged under the ordinary conditions at pH 7.0 and room temperature within 1 h.
Dissociation rate constant of SSI dimer - We tried to determine the dissociation rate
constant of SSI dimer by following the II* formation. The equilibria between monomer anddimer are shown as follows:

Fig. 1. Native PAGE profile of I2, II*, and I*2 at pH 9.4.
lane 1, I2; lane 2, I*2; lane 3 mixture of I2 and I*2; lane 4, proteins extracted from thecentral band of lane 3; lane 5, proteins extracted from the top band of lane 4; lane 6,
proteins extracted from the central band of lane 4; lane 7, proteins extracted from thebottom band of lane 4.

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Kinetic study on the dissociation of a dimeric protein

where I2, I*2, I, and I* indicate SSI dimer, SSI* dimer, SSI monomer, and SSI* monomer, respectively; k1, k1’, and k1” are the association rate constants and k-1, k-1’, and k-1” are the dissociation rate constants at the respective steps indicated. The velocity of change of the three
species can be expressed in the linear differential equations:[I2]0 = [I2] + [I] + [II*]/2, [I*2]0 = [I*2] + [I*] + [II*]/2, where [I2]0 and [I*2]0 represent the initial concentration of those species. Since the equilibria shown in Eq. 4 are extremely in favor for the dimeric species under the conditions of present experiments, the concentrations ofmonomers, [I] and [I*], can be regarded negligibly small compared with those of dimericspecies. Accordingly, the amount of [I2] + [I*2] + [II*] ≒ [I2]0 + [I*2]0. The rate constants for I2, I*2, and II* are assumed to be same, k1 = k1’ = k1” and k-1 = k-1’ = k-1”, because
there is no significant structural change at the dimer interface between I2 and I*2 [16] and of
overall structure [4, 17] between I2 and I*2, and I*2 shows strong enzyme inhibitory activity
similar to I2 [4]. Solution of the above equations under the initial condition, [I2]0 = [I*2]0,
yields,Figure 2a shows the time dependence of the formation of II*. Figure 2b shows the timecourse of the normalized value of [II*], which was fitted to Eq. 6 by non-linear least squares
method. The value of the dissociation rate constant k-1 was determined to be 1.6 x 10-4 s-1 at

Fig. 2. Time course of II* formation with mixing of I2 and I*2.
(a) Native PAGE profile at pH 9.4. The mixture of I2 and I*2 (13 μM each) were incubated at 4.3 oC and pH 7.0. lanes 1 – 7, the incubation times were 0.5, 1.0, 1.5, 2.0, 3.0,
4.5, and 6.0 hours, respectively. 4.2 μg protein/lane was loaded. (b) Time course of ratioof the II* to total inhibitor density. The solid line is the theoretical curve drawn based on
Eq. 6 with k-1 = 1.6 x 10-4 s-1.

K. Momma et al.

42

4.3 oC, pH 7.0, accordingly, the half-life time of this reaction was 71 min (Table 1).
The maximum ratio of [II*] to the total inhibitor concentration obtained in this experiments were 35 to 40% against the theoretical value of 50%, but the reason was not clear.
The ratio of II* would be lower than 50% if one monomer protein (for example I) prefers tobind with same protein (I) than the other (I*), however it has no effects on dissociation. The
experiment using SSID68N, a mutant SSI without nick, instead of I* gave the similar dissociation rate constant and the final hybrid species ratio (data not shown). So the final ratio
would not be the results of the system using of SSI*.
Akasaka et al. reported that the dissociation rate constant of I2 was 1.6 x 10–6 s-1 (halflife time c.a. 120 h) at pH 8.7, 4 oC by using chemically modified SSI (nitorotyrosyl -SSI)with HPLC (ion exchange column) [18]. The reason of the large difference between the report and this study is not specified. The differences of pH, protein (chemically modified or
enzymatically modified), and the method for detection might be the cause.
The association rate constant of SSI monomer to SSI dimer (2I → I2) has not been obtained experimentally. It may be estimated by assuming a diffusion-controlled association.
The encounter rate constant for this size of proteins can be assumed as 6 x 109 M-1s-1 [19].
The steric factor which determines the probability of occurrence of specific association
among random encounter of two subunits is assumed to be 10-2, based on the considerationthat about 10% of whole the surface of the monomer is covered by the dimer formation [20].
Thus, the rate constant for the diffusion-controlled association of SSI monomer would be 6 x
107 M-1s-1. Accordingly, the dissociation equilibrium constant of the dimeric SSI, Kd = k-1/k1,
is calculated to be 5 x 10-11 M at 25oC.
The dissociation rate constants were determined at 1 – 25 oC (Table 1). The activationenergy, EA, for the dissociation process of I2 to 2I was obtained to be 23.8 kcal/mol from the
Arrhenius plot (Fig. 6). ΔG‡ was 20.9 kcal/mol, ΔH‡was 23.2 kcal/mol, and ΔS‡ was 7.7
kcal/(mol･K).
Assignment of enzyme-inhibitor complexes, EI2 and EII* - S-BPN’ and an excess
amount of I2 were mixed at pH 7.0, 25 oC, and applied to native PAGE. Three bands, E2I2, X,
and I2 from the top were observed (Fig. 3, lanes 1 - 5). E2I2 indicates the enzyme inhibitor
complex of SSI dimer and two molecules of S-BPN’. Protein of X extracted from the gel
was loaded to native PAGE and gave the bands corresponding to E2I2, X, and I2 again (datanot shown). So the band X was presumed to be EI2 in which one enzyme molecule binds

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Kinetic study on the dissociation of a dimeric protein

Fig. 3. Native PAGE profile of E2I2, EI2, EII*, I2, and I*2 at pH 9.4.
S-BPN’ (7.5 μM) was mixed with I2 or I*2 at various molar ratio and incubated for 10
min at room temperature; lanes 1 – 5 for I2, lanes 6 –10 for I*2. The molar ratio ([I]/[E]or [I*]/[E]) is 0.5 (lanes 1 and 6), 1.0 (lanes 2 and 7), 2.0 (lanes 3 and 8), 3.0 (lanes 4
and 9), 4.0 (lanes 5 and 10). The sub-bands of I2 in lanes 3 – 5 were observed becauseof the heterogeneity of the N-terminal. The N-terminus amino acid of I*2 and the top
band of I2 is Tyr7.
with one SSI dimer. When S-BPN’ and an excess amount of I*2 were mixed, three bands,
E2I2, Y, and I*2 were observed (Fig. 3, lanes 6 - 10). The band Y migrated a little further
than EI2, which was assumed to be EII*. The interaction between S-BPN’ and SSI isthought to follow the standard mechanism of serine proteinase and proteinaseous inhibitor[21] proposed as follows: .

The stable complex is generally in the form of Michaelis complex, EI. S-BPN’-SSI complex
was also revealed in the form of Michaelis complex by X-ray crystallography [10]. NMR
study revealed that the reactive site peptide bond of SSI* was resynthesized within a measuring time (about 3 hours) [16], and we have observed that the resynthesis occurs within 15 s atroom temperature (Momma et al., unpublished result). Thus, E2I2 and EII* would be observed instead of E2I*2 and EI*2, respectively.
When E2I2 complex was mixed with I*2, EII* was observed (Fig. 4a, lane 2). Let us
consider the case of mixing E2I2 and I*2. If the dissociation occurs at the enzyme-inhibitor
interface, EI2 and EII* should be observed (Fig. 4b). However, only EII* was observed, thatmeans dissociation occurred at the SSI dimer interface (Fig. 4c) in this time scale.
Dissociation rate constant of SSI dimer in enzyme-inhibitor complex - Then we
tried to determine the dissociation rate constant of SSI dimer in the enzyme-inhibitor complex
by analyzing the EI2 formation with mixing of E2I2 complex and I2. The equilibria are shownas follows:K. Momma et al.

44

Fig. 4. The EII* formation by mixing of E2I2 and I*2.
(a) Equal volume of S-BPN'-SSI complex was mixed with I2 or I*2 (7.5 μM each as
monomer) and incubated for 10 min at room temperature. lane 1, E2I2 + I2; lane 2,
E2I2 + I*2, The sub-bands of I2 were observed because of the heterogeneity of the
N-terminal. (b) Model of the case if the dissociation occurs at the enzyme-inhibitor
interface. When S-BPN’ binds to I*, EII* is observed instead of EI*2 because of thereverse reaction of S-BPN’. (c) Model of the case if dissociation occurs at the SSI
dimer interface.
By the similar calculation to the equilibria for I2 and I*2, Eq. 9 was obtained under the initialcondition, [I2]0 = [E2I2]0,

Figure 5a shows the time course of the formation of EI2 by mixing of equal volume ofE2I2 and I2 solutions (7 μM each as monomer) and the density of spots on native PAGE wasmonitored. The rate constant of the dissociation was determined to be 3.0 x 10-3 s-1 at 26 oC,
pH 7.0 (Fig. 5b). The rate constants for other temperatures and for the system of E2I2 + I*2,

Fig. 5. Time course of EI2 formation after mixing of E2I2 and I2.
(a) Native PAGE at pH 9.4. The mixture of E2I2 and I2 (7 μM each) were incubated at 26o
C and pH 7.0. lanes 1 – 7, the incubation times were 1.5, 3, 4.5, 6, 9, 14, and 20 min, respectively. 9.5 μg protein/lane was loaded. (b) Time course of ratio of the EI2. The solidline is the theoretical curve drawn based on Eq. 9 with k-1 = 3.0 x 10-3 s-1.

45

Kinetic study on the dissociation of a dimeric protein

detection of the formation of EII*, are listed on Table 2. Arrhenius plots of all the data areshown in Fig. 6. The dissociation rate constants were equal each other for the system of I2 +I*2, E2I2 + I2 and E2I2+I*2. It was reported that the β-sheets structure at dimeric interface of
SSI has little change between I2 and E2I2 by X-ray crystallographic study [10]. The boundenzymes would have no influence on the SSI dimer dissociation. After 6 h of incubation of
the mixture of S-BPN’ and SSI*, not only EII* but also EI2 was detected (data not shown).
The results indicated that the dissociation at the interface between SSI and S-BPN’ also took
place. The dissociation rate constant of SSI and S-BPN’ was determined to be 0.9 x 10-4 s-1,
at pH 7.0, 25oC [14]. So we neglected the dissociation of SSI and S-BPN’ in this study.
The subunit-subunit interaction of SSI dimer is dominantly hydrophobic and the entire
SSI molecule as a dimer forms a single egg-shaped structure [6]. SSI monomer has been
detected only in the denatured form, so it has been thought that the dimerization is necessary
to exist as a stable protein. The actual structure of the free monomer SSI under physiological conditions has not been known. And the structure of monomer S-BPN’-SSI complex has
not been observed. However the formation of EII* with mixing of E2I2 and I*2 supports theexistence of monomer S-BPN’-SSI complex in a short time.

Fig. 6. Arrhenius plots of the dissociation rate constant of SSI dimer at pH 7.0.
○, I2 + I*2; □,E2I2 + I2; ■E2I2 + I*2.

K. Momma et al.

46

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Kinetic study on the dissociation of a dimeric protein

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Communicated by Ohnishi Masatake