Adsorption Characteristics of P (3HB) Depolymerase as Evaluated by

Biomacromolecules 2008, 9, 3201–3207

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Adsorption Characteristics of P(3HB) Depolymerase as Evaluated by Surface Plasmon Resonance and Atomic Force Microscopy Nobuhiko Matsumoto,† Masahiro Fujita,*,‡ Tomohiro Hiraishi,‡ Hideki Abe,†,§ and Mizuo Maeda*,‡ Department of Innovative and Engineered Materials, Tokyo Institute of Technology, Nagatsuta 4259, Midori-ku, Yokohama 226-8501, Japan, Bioengeering Laboratory, RIKEN, Hirosawa 2-1, Wako-shi, Saitama 351-0198, Japan, and Chemical Analysis Team, RIKEN, Hirosawa 2-1, Wako-shi, Saitama 351-0198, Japan Received July 16, 2008; Revised Manuscript Received September 19, 2008

Molecular recognition of poly[(R)-3-hydroxybutyrate] (P(3HB)) depolymerase from Ralstonia pickettii T1 to the surfaces of biodegradable aliphatic polyesters such as P(3HB) and poly(L-lactic acid) (PLLA) was examined from the viewpoints of kinetics and dynamics. To determine the kinetic parameters on the interaction between the substrate-binding domain (SBD) of P(3HB) depolymerase and various polymer substrates with different chemical structures, surface plasmon resonance (SPR) measurements were performed. On the other hand, using an atomic force microscopic (AFM) cantilever tip functionalized with the SBD of P(3HB) depolymerase, the mechanical parameters such as unbinding force to the polymer surfaces were measured. Both the SPR and AFM measurements showed that the SBD has a high affinity to P(3HB) and PLLA. From the results of kinetics and dynamics, the energy potential landscape of SBD-polymer interaction was disclosed on the basis of a phenomenological model, and the mechanism of the interaction was discussed.

Introduction Poly[(R)-3-hydroxybutyrate] (P(3HB)) and its copolymers are made from renewable resources such as sugar, vegetable oil and organic acid by various bacteria as intracellular storage.1,2 These polymers are degraded in the environment such as soil, seawater, fresh water, and activated sludge by extracellular P(3HB) depolymerases secreted from microorganisms.3 P(3HB) and its copolymers have been thus paid much attention as ecofriendly materials. A number of the P(3HB) depolymerases have been purified and characterized.3 In particular, the domain structures and function of P(3HB) depolymerase from Ralstonia pickettii T1 (formally known as Alcaligenes faecalis T1) have been well examined.2,3 Genetic analyses revealed that the P(3HB) depolymerase consists of a catalytic domain (CD) at the N terminus, a substrate-binding domain (SBD) at the C terminus, and a linker region connecting the two domains. The SBD is responsible for binding to P(3HB) material. The truncated depolymerase without SBD does not hydrolyze the solid P(3HB) material, although the ability to hydrolyze a soluble oligomer is unaffected.2,3 It has been proposed that the enzymatic hydrolysis is a two-step reaction, which occurs at a solid-liquid interface: first, P(3HB) depolymerase adheres to a polymer surface by SBD, and then hydrolyzes the polymer chain by CD.2 It is, thus, essential to unveil the adhesion mechanism between the P(3HB) depolymerase and the polymer surface for the development of new materials with desirable biodegradability. * To whom correspondence should be addressed. Tel.: +81-48-467-9312. Fax: +81-48-462-4658. E-mail: [email protected] (M.F.); mizuo@ riken.jp (M.M.). † Tokyo Institute of Technology. ‡ Bioengeering Laboratory, RIKEN. § Chemical Analysis Team, RIKEN.

The adhesion characteristics of P(3HB) depolymerase on various polymer surfaces have been studied. For example, the adsorption of the P(3HB) depolymerase onto thin films of P(3HB), poly[(R)-3-hydroxyoctanoate] (P(3HO)), poly(L-lactic acid) (PLLA), polystyrene (PS), and polyethylene (PE) was investigated using a quartz crystal microbalance (QCM) technique.4 It is found that the rates of adsorption of P(3HB) depolymerase for biodegradable aliphatic polyester films (P(3HB), PLLA, and P(3HO)) are higher than those for other polymer films (PS and PE). It has been suggested that the SBD might recognize the ester bonds in addition to hydrophobic interaction.4 In this decade, AFM has been widely used for measuring theintra-andintermolecularbonds5-8 suchasantigen-antibody,9-13 cell-cell,14-16 cell-protein,17 protein-polymer,18 and the denaturation of protein,19,20 DNA,21,22 and RNA,23 because of its pico-newton force sensitivity and nanometer positional accuracy. In our previous report, we evaluated the interaction between the biodegradable polyesters, such as P(3HB) and PLLA, and the P(3HB) depolymerase by AFM.24 The SBD with histidines at the N-terminus was prepared and immobilized on the AFM tip surface. Using the functionalized tip, the force-distance measurements were performed. The unbinding forces, in which single SBD molecule participates, were estimated for both P(3HB) and PLLA. It has been suggested that the SBD specifically binds to polyester surfaces. In this study, we examined the adhesion characteristics of the P(3HB) depolymerase from R. pickettii T1 to polymers such as P(3HB) and PLLA from both viewpoints of kinetics and dynamics using surface plasmon resonance (SPR) and AFM. SPR has proven to be a valuable tool for probing biomolecular interactions in real time under the continuous flow. We followed the adhesion and dissociation process of SBD and estimated the kinetic parameters of SBD-polymer interaction. By AFM, on the other hand, we measured the force-distance curves of

10.1021/bm800790q CCC: $40.75  2008 American Chemical Society Published on Web 10/22/2008

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SBD-polymer interaction and estimated the unbinding force and the binding frequency. Here, the force distance curves were obtained with various retraction velocities.25 By the combination of kinetics and dynamics, the energy potential profile of SBD-polymer interaction was deduced using a phenomenological model,25,26 and the mechanism of the interaction was discussed.

Experimental Section Preparation of Polymer Thin Films. Bacterial P(3HB) was supplied from ICI. The number-average molecular weight (Mn) and polydispersity (Mw/Mn) were 189000 and 2.6, respectively. PLLA was synthesized by ring-opening polymerization of L-lactide in the presence of a diethylzinc/water catalyst.21 The Mn and Mw/Mn of PLLA used here were 12000 and 1.9, respectively. Low-density PE (Mn ) 7700 and Mw/Mn ) 4.6; Aldrich), atactic PS (Mn ) 152000 and Mw/Mn ) 1.03; SHOWA DENKO), and amorphous polyethylene terephthalate (PET) (Goodfellow Cambridge Ltd.) were purchased commercially. As solvents, chloroform for P(3HB), PLLA, and PS, p-xylene for PE, and hexafluoroisopropanol (HFIP) for PET were used. A dilute solution of each P(3HB), PLLA, PE, PS, and PET (concn 0.5 wt %) was dropped onto a glass substrate for AFM and gold-coated SPR sensor chip (SIA Kit Au, Biacore, GE Healthcare, Sweden) for SPR measurements. To ensure that the topology of film surface does not affect the data, the amorphous thin films with well flat and isotropic surface structure were prepared.27 However, P(3HB) casting film is crystallized at room temperature. Therefore, the dried thin films of P(3HB) were once annealed at 200 °C for 1 min and crystallized rather completely at 120 °C for 24 h. For PLLA, the thin films were annealed once at 220 °C for 10-15 min, followed by quenching to room temperature to prepare a completely amorphous thin film. For PS, the thin films were annealed at 220 °C for 10-15 min. For PE, the thin films were annealed at 150 °C for 10 h. For PET, the thin films were dried under reduced pressure for 3 days to remove the solvent completely. The thickness of the resulting film was about 50 nm. His-Tagged SBD. As described in our previous paper,24 the Histagged SBD of P(3HB) depolymerase from R. pickettii T1 was constructed and purified. Construction of a recombinant plasmid for the production of an SBD with a sequence of six histidines at the N-terminus was carried out using pET15b vector (Novagen). Escherichia coli BL21(DE3) cells harboring the plasmid were grown on a Luria-Bertani medium in the presence of 50 µg · mL-1 ampicillin. Isopropyl lactopyranoside (0.1 mM at final concentration) was used to induce protein production. After the cultivation, the cells were harvested by centrifugation and stored at -80 °C. For SBD purification, the cells were resuspended in a buffer (binding buffer, His-Bind Buffer Kit, Novagen). The suspension was sonically disrupted and centrifuged. The resulting supernatant was applied to a Ni-IDA column (His, Bind Quick 900 Cartridges, Novagen), and the His-tagged SBD protein was eluted with elution buffer (His-Bind Buffer Kit, Novagen). The purity of the desired His-tagged SBD was confirmed by SDS-PAGE. Protein amount was determined by the Bradford method using BSA as standard. Surface Plasmon Resonance. The interaction between the Histagged SBD and each substrates was characterized with an SPR biosensor (BIAcore X system, Biacore, GE Healthcare, Sweden). All measurements were performed in 10 mM phosphate buffer (pH 7.0) at room temperature (∼25 °C) under continuous flow. A flow rate was set to 20 µL · min-1. The kinetic parameters such as association rate constant (ka), dissociation rate constant (kd), and affinity constant (KA ) ka/kd) for each polymer surface were evaluated by curve fitting using BIA-evaluation 3.0 software (Biacore). Atomic Force Microscopy. The His-tagged SBD molecules were immobilized on AFM cantilever tip. Triangular Si3N4 tips coated with Au (SN-AF01A and SN-AF08A, SII nanotechnology, Inc.), mounted on a 100 µm cantilever with a spring constant (ks) of 0.09 N · m-1 and 0.61 N · m-1 were used. The Au-coated cantilevers were immersed in 10 mM phosphate buffer (pH 7.0) containing 100 µΜ 3,3′-dithiobis[N-

Figure 1. Sensorgrams of the adhesion of SBD to P(3HB), PLLA, PE, PS, and PET surfaces. SBD of concentrations of 1 µM (a) and 2 µM (b) were injected over the surfaces. Symbols and solid lines correspond to experimental and fitted data, respectively. Ion and Iend are the onset and the end of injection, respectively.

(5-amino-5-carboxypentyl)propionamide-N′,N′-diacetic acid] dihydrochloride (NTA; Dojindo) for 3 h at room temperature to form a selfassembled monolayer terminated with NTA groups on the tip surface. Subsequently, the modified cantilevers were dipped in 40 mM NiIISO4 aqueous solution for a certain period to bind nickel ions to the NTA groups. Finally, the tips were immersed in 10 mM phosphate buffer (pH 7.0) containing about 10 µg · mL-1 His-tagged SBD and washed with the same buffer.24 The force-distance curve between the substrates and the His-tagged SBD was measured using an AFM (SPA400/SPI3800N, SII Nanotechnology, Inc.). All AFM measurements were obtained at room temperature (∼25 °C) in a small vessel containing 1.2 mL of 10 mM phosphate buffer solution (pH 7.0). The force-distance (piezo-displacement) curves were measured by detecting the cantilever deflection when the sample mounted on a piezoelectric device was moved toward and withdrawn from the AFM tip, after correcting the sensitivity of photodetector for the cantilever deflection. The force-distance curves were recorded with different loading rates (r ) ksV, where V is the velocity of piezoelectric device) in the range of 1.8-610 nN · s-1. The piezo-displacement on the resulting curve was converted to the distance between the tip and film surface according to the procedure described previously.28 Statistical analysis of unbinding force was performed with Igor Pro 6.0 software (Wavemetrics, Lake Oswego, OR).

Results and Discussion SPR Measurement. We analyzed the kinetics of the interaction between His-tagged SBD and polymer film such as P(3HB), PLLA, PE, PS, and PET using SPR. Figure 1 shows the SPR sensorgrams on injection of the His-tagged SBD solution and subsequently buffer solution over the polymer surfaces; parts (a) and (b) demonstrate the sensorgrams when the concentrations of SBD solution (C) are 1 and 2 µM, respectively. These sensorgrams show the real-time change in the resonance unit (RU), where 1 RU corresponds to the adsorption of a protein mass of 1 pg · mm-2. In this figure, Ion and Iend indicate the

Adsorption Characteristics of P(3HB) Depolymerase


onset and the end of the injection of SBD solution, respectively. At Ion, the RU showed a jump caused by the change in refractive index of solution, called bulk effect, followed by a slower increase with time, indicating that the SBD molecules adhere on the polymer surface. After the continuous flow of the solution for 180 s, the buffer solution (C ) 0) was reinjected into the flow cell at Iend. Following a rapid decrease by the change in refractive index, the RU showed a slower decrease due to the dissociation of SBD from the substrate. During the continuous flow of SBD solution, the sensorgrams for PLLA, P(3HB), and PE surfaces increased more rapidly than those for PS and PET surfaces. At the end point of SBD injection, RU was in the order of PLLA > P(3HB) ≈ PE > PET ≈ PS. It is obvious that the SBD has a high affinity to PLLA and P(3HB), identical to that evaluated previously by QCM.4 Contrary to the previous result, the affinity to PE was higher than PS. This might come from the difference between full-length depolymerase and His-tagged SBD. Although PET has ester bonds in the main chain, its SPR sensorgram showed a low affinity. The PHB depolymerase might bind to a substrate by recognizing both the hydrophobic side chains and ester bonds on the surface of a polymer.4 Next, the sensorgrams obtained here were analyzed according to a binding model, in order to evaluate the kinetic parameters. First, the simplest model, 1:1 Langmuir binding model, was tried to apply. Assuming a first order interaction kinetics, the differential rate equation of complex formation during continuous flow of SBD solution with a concentration of C (association phase) can be given by

dR ⁄ dt ) kaCRmax - (kaC + kd)R

(1)

where R is the SPR signal in RU at time t, Rmax is the maximum adsorption capacity of substrate in RU, and ka and kd are the association and dissociation rate constants, respectively. On the other hand, the rate of change in SPR signal during continuous flow of buffer after the sample injection, that is, C ) 0 (dissociation phase), is expressed by

dR ⁄ dt ) -kdR

(2)

In this study, the curve fitting was carried out simultaneously for both the association and dissociation phases up to t ) 400 s. However, the observed sensorgrams were not well fitted by this model. In particular, the RU values in association phase for PLLA and P(3HB) were lower than those of the calculated ones. This is possibly because the rate of binding is faster than that of diffusion of His-tagged SBD molecules to the polymer surfaces, implying that the SBD has a high association rate for the polyesters. Therefore, the sensorgrams were fitted by 1:1 Langmuir binding model with the effect of mass transfer.29 Its differential rate equations are described by

dCS ) kt(C - CS) - kaCS(Rmax - R) + kdR dt dR ) kaCS(Rmax - R) - kdR dt

(3) (4)

where Cs is the concentration of SBD at the sensor surface and kt is the rate constant of mass transfer.29 Using numerical integration, the sensorgrams were fitted (solid lines). Taking the effect of mass transfer into consideration, the curve fitting was improved although some discrepancy was still recognized. It was reported that the adsorbing depolymerase on the substrate is easily substituted for the depolymerase in the solution by its collision.30 In addition to the substitution effect, the rebinding effect and so on might be responsible for the discrepancy.

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Figure 2. Representative retraction curves of force-distance measurements for P(3HB) and PLLA surfaces proved by His-tagged SBD immobilized AFM cantilever tip. The minima indicate the multiple pulloff events of SBD-substrates binding. Table 1. Kinetic Parameters for the Interaction between the SBD and Polymer Surfaces, Extracted from SPR Sensorgrams

P(3HB) PLLA PE PS PET

ka (103 M-1s-1)

kd (10-3 s-1)

KA (105 M-1)

1.3 ( 0.13 1.6 ( 0.14 1.3 ( 0.01 0.36 ( 0.10 0.20 ( 0.04

1.5 ( 0.3 1.1 ( 0.3 1.6 ( 0.5 3.3 ( 0.3 2.1 ( 0.9

9.3 ( 2.9 19 ( 8.0 9.1 ( 3.0 1.1 ( 0.4 1.2 ( 0.7

The kinetic parameters obtained by the simple model with mass transfer are summarized in Table 1. The association rate constants, ka, for P(3HB), PLLA, and PE are obviously higher than those for PS and PET, and the dissociation rate constants, kd, for P(3HB), PLLA, and PE are relatively lower than those for PS and PET. The values for P(3HB), PLLA, and PE are comparable with those of antigen-antibody with a strong interaction,31-33 suggesting that the SBD binds strongly to P(3HB) and PLLA. In addition, as described below, the ratio of both rate constants, KA, indicates that the adsorbing SBD molecules can exist stably onto their polymer surfaces, namely, the lifetime of the bind is long. AFM Measurements. SPR provides information on the adsorption of SBD as an average of whole system. On the other hand, AFM has been employed to obtain the mechanical strength of the interaction between molecular complexes at a singlemolecular level. In this study, the force-distance measurements using AFM were carried out to estimate the SBD-polymer interaction at the molecular level as our previous study. First, the force-distance measurements for P(3HB) and PLLA of interest were performed in 10 mM phosphate buffer solution (pH 7.0) at room temperature. Figure 2 shows the retraction curves of force-distance measurements for P(3HB) and PLLA. As reported previously, there are several minima in the curves, indicative of multiple pull-off events of SBD.5-7,9,10,14 We confirmed that, for AFM tip without SBD (Au, NTA, NiII-NTA, and imidazole modified tips), only a single minimum was observed at a distance of 0 nm. This fact indicates that the first pull-off event at the distance of 0 nm is due to another nonspecific interaction rather than the interaction between SBD and polymers.24 In addition, the multiple pull-off events were reproducibly observed in the measurements of force-distance curves using one SBD modified tip, supporting that such pulloff event is not due to bond breakage of linker molecule but to unbinding of SBD from polymer surface. Accordingly, the occurrence of multiple minima in the retraction curves obtained

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Figure 3. Binding frequencies of the SBD immobilized AFM tip and polymer substrates, observed at the loading rate of 1.8 nN · s-1 (4.5 nN · s-1 for P(3HB)) in (a) 10 mM phosphate buffer solution and in (b) 10 mM phosphate buffer solution with 0.1% CHAPS.

for both P(3HB) and PLLA is considered to be attributed to the sequential ruptures of the SBD molecules from the polymer surface. The force-distance curves were measured many times (more than 200 curves for each polymer). For P(3HB) and PLLA, as a result, the frequency of the force-distance curves showing multiple pull-off events was 20-30% of all the curves measured with the SBD tip, as shown in Figure 3. Similarly, the force-distance curve measurements for PE, PS, and PET surfaces were also performed under the same conditions. The force-distance curves for PE, PS, and PET also showed the unbinding events from their surfaces, probably due to hydrophobic interaction. However, the frequencies of the events were much lower than those of P(3HB) and PLLA (Figure 3). Interestingly, the binding frequencies for these polymers were found to correspond approximately to the affinity of SBD evaluated by SPR. In force-distance measurement, first, the SBD molecules immobilized with the tip surface are brought close to the polymer surface. The possibility of binding to the polymer at that time likely depends on the affinity constant, KA. Taking the chemical structures of the polymers into account, it is deduced that the existence of an ester group in the polymer chain facilitates the association of SBD to the substrate. In addition, force-distance measurements between SBD and polymer surfaces were carried out in the presence of a surfactant, 3-[(3-cholamidopropyl) dimethylammonio]-1-propanesulfonate (CHAPS). Figure 3b shows the frequencies of the unbinding events in 10 mM phosphate buffer (pH 7.0) containing 0.1% CHAPS. Compared with the frequencies obtained without CHAPS (Figure 3a), the binding frequencies to PE, PS, and PET reduced considerably, while those to P(3HB) and PLLA did not reduce so much. It is thought that CHAPS prevents a nonspecific adhesion of SBD to the substrates. Namely, it is indicated that the SBD binds specifically to PLLA and P(3HB) surfaces. Dynamic Force Spectroscopy. Next, the mechanical properties of the SBD-polymer interaction were examined. The statistical analysis of the unbinding events collected from the force-distance curves enables us to evaluate the single unbinding force of SBD for polymer surface.5-10,22 In this study, the unbinding forces of SBD for P(3HB) and PLLA were estimated because we could collect the data enough to analyze (ca. 200 events). Figure 4 shows representative histograms of the unbinding force of SBD for P(3HB) and PLLA surfaces measured at the loading rates, r, of 610 and 240 nN · s-1, respectively. The bin size was 20 pN. The frequencies of unbinding events were approximately 20-30%. It has been previously reported that the unbinding force evaluated from the minima is integer multiples of one fundamental rupture force associated with coincident breakage of several SBD molecules

Matsumoto et al.

that exert on the polyester surface, so that the histogram are often distributed. Therefore, a multiple-peak curve fitting was applied to the histograms.6,10,19,22 In Figure 4, the red and blue lines indicate the individual Gaussian function and their summation, respectively. The resulting multiple Gaussian functions lay at an almost equal interval of the first peak value. Therefore, a one-paired unbinding forces and their standard deviations were estimated from the peak position and the width of the first Gaussian, respectively. For P(3HB) at r ) 610 nN · s-1 and PLLA at r ) 244 nN · s-1, the first peak values were 147 ( 12 and 139 ( 13 pN, respectively. These values correspond to the single unbinding force of SBD at the loading rates. When force-curve measurements are carried out at a wide range of loading rate, the unbinding force is observed to depend on the loading rate,25 unless the dissociation rate is not so fast, that is, the lifetime of the binding is not shorter than the time scale of the measurements.34,35 The dependence of unbinding force on loading rates provides information on unbinding pathway of bound molecules.25 The same fitting was thus applied to the histograms obtained at other loading rates, and the first peak values were assigned as a one-paired unbinding force. The first peak values were determined to be 111 ( 9 pN (r ) 4.5 nN · s-1), 110 ( 18 pN (r ) 9 nN · s-1), 115 ( 10 pN (r ) 31 nN · s-1), and 132 ( 12 pN (r ) 120 nN · s-1) for P(3HB), and to be 125 ( 13 pN (r ) 1.8 nN · s-1), 121 ( 14 pN (r ) 3.6 nN · s-1), 116 ( 10 pN (r ) 12 nN · s-1), and 128 ( 9 pN (r ) 49 nN · s-1) for PLLA. The dependence of loading rates on unbinding force of bound molecules can be explained using Bell-Evans model,25,26 assuming that single activation barrier is reduced by external force. According to this model, the unbinding force, F, is related to the loading rate, r, as follows:

( )

F ) fβ ln

r fβkd

(5)

Here, fβ is given by

fβ )

kBT xβ

(6)

where kB is the Boltzmann constant, T is the temperature, and xβ is the width of the potential barrier. As given by eq 5, it is predicted that the (most probable) unbinding force, F, increases linearly with the logarithm of loading rate, r. By the linear regression on the basis of eqs 5 and 6, therefore, the parameters xβ and kd can be derived from the experimental data. Figure 5 shows the plots of the unbinding force against the logarithm of loading rate, called dynamic force spectrum (DFS), for P(3HB) and PLLA. These spectra demonstrate that the unbinding force depends on the loading rate but is not linearly proportional to the logarithm of the loading rate. Besides the lifetime of the binding, some possibilities on the deviation from the theoretical prediction have been pointed out so far. One is that the real activation potential barrier is not single but multiple, so that the unbinding forces show more than one linear regime.25 Others are associated with the softness of the polymer substrate25,35 and nonspecific interactions.36 As can be seen in Figure 5, the unbinding force at a limited range of loading rates from 10 to 1000 nN · s-1 increased linearly. The linear regression in this range, indicated with the solid line in this figure, yielded xβ ) 0.44 ( 0.04 nm and kd ) (9.3 ( 0.8) × 10-3 s-1 for P(3HB), and xβ ) 0.62 ( 0.09 nm and kd ) (4.2 ( 0.6) × 10-5 s-1 for PLLA (Table 2). The square of correlation coefficient was 0.98 for both cases. These values are comparable with those in other biomolecular systems reported so far8,11,15,16

Adsorption Characteristics of P(3HB) Depolymerase


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Figure 4. Histograms of pull-off forces between SBD functionalized tip and P(3HB) (a) and PLLA (b) surfaces, measured at the loading rates of 610 nN · s-1 and 244 nN · s-1 for P(3HB) and PLLA surfaces, respectively. The solid line indicates Gaussian fit to the experimental data.

Figure 5. Loading rate dependence of the most probable pull-off forces between P(3HB) (a), PLLA (b), and SBD molecules, resulting from a Gaussian fit to the histogram distribution. Force statistical errors are given by SD. The solid-curve is a numerical fit of experimental data to the Bell-Evans model. Table 2. Energy Landscape Parameters for the Interactions of the SBD with P(3HB) and PLLA Surfaces, Estimated from DFS and SPR Results ∆G‡ (kBT) -1

xβ (nm)

kd (s

DFS SPR ∆Gbu (kBT)

) -3

P(3HB) 0.44 ( 0.04 (9.3 ( 0.8) × 10 PLLA 0.62 ( 0.09 (4.2 ( 0.6) × 10-5

35 38

36 36

14 14

and, thus, seem reasonable. Furthermore, the values of kd estimated by DFS almost fit with those by SPR (see Table 1), taking into account kd being obtained as its logarithm value by linear regression. This agreement between two independent methods means that the rupture force measured by AFM is not due to the bond cleavage of spacer molecule but the dissociation of SBD from substrate.5 On the basis of these parameters, one can explore a plausible energy landscape of the unbinding of SBD from the data range. We tried to deduce a dissociation pathway of SBD on the basis of these parameters, assuming the single potential barrier.25 As reported in ref 37, the height of the activation potential barrier, ∆G‡, is related to the dissociation rate constant, kd, as follows

kd )

( )

kBT ∆G‡ exp h kBT

(7)

where h is the Planck constant. In addition, the energy difference between the bound state and the unbound state, ∆Gbu, are given by

∆Gbu ) -kBT ln KD

(8)

where KD (1/KA) is the dissociation equilibrium constant. The values of ∆G‡ and ∆Gbu are summarized in Table 2.

Figure 6. Conceptual energy landscape of the unbinding process of the interactions of the SBD with P(3HB) and PLLA surface. The energy landscape parameters, xβ, ∆G‡, ∆Gbu, are the width of the potential barrier, the height of activation potential barrier, and the energy difference between the bound state and the unbound state. The values for P(3HB) and PLLA are given in Table 2.

Figure 6 schematically illustrates the energy potential landscape of the dissociation process of SBD from biodegradable polyester with the parameters of the position of activation energy, xβ, which corresponds to the distance from equilibrium state to rupture of bond, the activation free energy, ∆G‡, and the binding free energy, ∆Gbu. There is no significant difference

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in the shape of the landscape between P(3HB) and PLLA. It is, however, interesting that the bound state of PLLA is more stable than that of P(3HB) and that the xβ of PLLA is larger, implying that the attractive force acts farther, depending on the number density of the ester and methyl groups in the polymer chain. These parameters, such as xβ, ∆G‡, and ∆Gbu, shown here, are comparable with those of various interactions in biomolecular system disclosed so far.8,11,13,15,16 Compared with the biomolecular interactions, however, the widths of potential barrier, xβ of P(3HB) and PLLA seem to be slightly larger. This might be due to elasticity of substrate.12,17,23 On the other hand, the activation potential energy, ∆G‡, was higher, associated with slower dissociation.17 The binding strength, intermolecular potential (∆Gbu ∼ 14 kBT), estimated here, is much less than that of the covalent bond, which is mostly in the range of 100 to 300 kBT (200 ∼ 800 kJ mol-1), and other chemical bonds.38 The value plainly proves that the binding of SBD is caused by noncovalent bond such as Van der Waals force and hydrogen bond (

Adsorption Characteristics of P (3HB) Depolymerase as Evaluated by

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