Kinetics of binding and diffusivity of leucine-enkephalin in large unilamellar vesicle by pulsed-field-gradient ¹H NMR in situ

Abstract

The kinetics of binding, the diffusivity, and the binding amount of a neuropeptide, leucine-enkephalin (L-Enk) to lipid bilayer membranes are quantified by pulsed-field-gradient (PFG) ¹H NMR in situ. The peptide signal is analyzed by the solution of the Bloch equation with exchange terms in the presence of large unilamellar vesicles (LUVs) as confined, but fluid model cell membranes. Even in the case that the membrane-bound and the free states of L-Enk cannot be distinguished in the one-dimensional NMR spectrum, the PFG technique unveils the bound component of L-Enk after the preferential decay of the free component at the high field gradient. In 100-nm diameter LUVs consisting of egg phosphatidylcholine, the rate constants of the peptide binding and dissociation are 0.040 and 0.40 s⁻¹ at 303 K. This means that the lifetime of the peptide binding is of the order from second to ten-second. The diffusivity of the bound L-Enk is 5×10⁻¹²m²/s, almost 60 times as restricted as the movement of free L-Enk at 303K. One-tenth of 5mM L-Enk is bound to 40mM LUV. The binding free energy is calculated to be −2.9 kJ/mol, the magnitude close to the thermal fluctuation, 2.5 kJ/mol. The result demonstrates the potential of PFG ¹H NMR to quantify molecular dynamics of the peptide binding to membranes.

1. Introduction

Molecular dynamics of peptide binding to fluid lipid membranes is crucial for a better understanding of the primary stage of the bioactivities in the cell. In situ technique is powerful to gain insight into the mechanistic view of peptide functions in a natural manner. Pulsed-field-gradient (PFG) NMR spectroscopy1 is a versatile method to measure the molecular diffusion without disturbing the system. Recently we have applied high-resolution solution-state ¹⁹F NMR in combination with the PFG technique, to study the drug binding and mobility in confined but fluid membranes2–4. We have developed the strategy to quantify how much and how fast the drug is bound to the membrane and how fast the drug is moving in the membrane without the use of labeled nuclei or the aid of sample spinning to obtain well-resolved spectra of high S/N ratio. The previous studies have adopted the small-sized 5-fluorouracil (5FU, 5-fluoro-1H-pyrimidine-2,4-dione) and fluorinated bisphenol A (FBPA, (CF₃)₂C(C₆H₄OH)₂) as a drug model. Fluorine-19 NMR is advantageous to observe the drug side because the ¹⁹F nucleus is absent in natural and model cell membranes5,6. The ¹⁹F nucleus is, however, rare in the peptide. The general method is required to quantify a wide variety of peptide bindings. Proton NMR is effective for this purpose because ¹H is abundant in the natural system. In this work, the PFG ¹H NMR method is applied to explore the dynamic aspects of the peptide binding. The diffusivity, the binding amount, and the rate constants of the binding and dissociation of a neuropeptide, leucine-enkephalin (L-Enk, Tyr-Gly-Gly-Phe-Leu) are quantified in phospholipid large unilamellar vesicles (LUVs) as confined but soft membrane environments.

In the previous work, we have elucidated the exchange motion of 5FU molecules between the bound and the free states by using PFG ¹⁹F NMR3. The analysis includes (1) the decomposition of 5FU signal into the bound and free components, (2) the evaluation of the diffusion coefficients by the Stejskal-Tanner plot7, and (3) the determination of the exchange rate constants by the analytical formula of the Bloch equation with exchange terms8. In this case, the bound and the free components are not so largely overlapping and can be resolved in the one-dimensional (1D) spectrum to analyze the signal intensity by peak height. Such analysis is, however, impossible when the two components are hard to resolve, as shown in the ¹H NMR spectrum in the presence of the membrane2. Here we show that the PFG technique enables to quantify the dynamics of the peptide binding, even in the case that the bound and the free states cannot be distinguished in the 1D NMR spectrum.

Molecular study of enkephalins in model membranes has attracted great interest in relation to the analgesic effect of endogeneous neuropeptides, because the interaction of the peptide with membranes is thought to play a significant role in the subsequent receptor binding9–11. The NMR studies have focused on the conformation of enkephalins in membrane-mimicking environments involving micelles, bicelles, and vesicles9,11–18. The dynamic aspects are, however, limited to the micellar system18–20, the dynamical structure different from the bilayer membrane21. Here we elucidate how fast L-Enk binds to the membrane, dissociates from the membrane, and moves in the membrane, using bilayer vesicle as a model cell membrane.

2. Experimental

2.1. Sample

In this work, LUVs rather than micelles were employed as model cell membranes in view of the dynamical structure21. As the phospholipid component, egg phosphatidylcholine (EPC, MW ~770 and 98.5% pure) was purchased from NOF CORPORATION (Tokyo, Japan) and used without further purification. L-Enk (purity, 99%; MW555.62) was obtained from Peptide Institute Inc. (Osaka, Japan). The heavy water solvent (D₂O, 99.9%D) was obtained from Euriso-top (Saint Aubin, France).

LUVs were prepared by an extrusion technique22 by using Mini-Extruder (Avanti Polar Lipids, Inc., AL) with a polycarbonate membrane. The size was systematically controlled by using 100-nm pore size filter. The concentration of EPC LUV was 40mM. D₂O was used as a solvent to suppress the ¹H NMR signal of light water. The injection of L-Enk into the LUV was performed by adding the desired amount of aqueous L-Enk solution to the vesicle suspension. The final concentration of L-Enk was fixed to 5mM.

2.2. NMR Measurement

¹H NMR measurements were carried out at 399.8 MHz, by using a JEOL ECA400 NMR spectrometer equipped with a superconducting magnet of 9.4 T. Although D₂O was selected as a solvent, the DANTE presaturation pulse sequence was applied to avoid the signal overlapping of impurity light water (HDO) with the target peak. The presaturation was minimal so that the peptide resonance was not perturbed. The digital resolution was 0.5Hz (0.001 ppm). Chemical shifts of the ¹H NMR signals were obtained by referring to the absorption frequency of the solvent deuteron monitored as the lock signal. The PFG NMR measurement was performed by using a high-sensitivity multinuclear probe (JEOL, NM-40TH5AT/FG2) under a current of 30 A. The probe can exert a field gradient (FG) up to 0.91T/m, most suitable for the simultaneous observation of bound and free components of the peptide. To attenuate the spin-echo signal, the 16 different FG strengths g were applied in the range from 0.05 to 0.91T/m. The linearity of the pulsed field gradient was confirmed by the diffusion measurement of benzene in D₂O23. Bipolar Pulse Pairs (BPP)-STimulated Echo (STE)-Longitudinal Eddy current Delay (LED) pulse sequence2 was adopted to minimize the influence of eddy current. The height of the sample solution was less than 5mm to avoid the convection effect. In order to evaluate the accuracy of the results, the PFG measurements have been done at three different diffusion times (Δ_diff = 0.1, 0.5, and 1.0 s). The pulse width δ was ranging from 0.00125 to 0.004 s, except for the measurement of the peptide in water, 0.0003 to 0.002 s. The 1024 FID signals were accumulated with a recycling delay of 10 s, sufficiently longer than the longitudinal relaxation time of the peptide. For peptide solution, 32 transients were accumulated with a recycling delay of 15 s. The measurements were carried out at 303 K where lipids were in the liquid-crystalline phase. The binding of L-Enk was under equilibrium, according to the NMR observation that no variation of the bound and the free signals of L-Enk was found throughout the measurement.

To ensure that the NMR signal intensity of the peptide is not influenced by the differences in the relaxation between bound (B) and free (F) components, we have calculated and made a comparison of the damping factors of relaxation1 between these two components of the peptide signal. In BPP-STE-LED pulse sequence (Fig. 3 in Ref. 2), the period t_L to compete with the longitudinal relaxation is during the time interval T+T_e. The t_L was 0.15–1.05 s under the experimental conditions Δ_diff of 0.1–1.0 s. Since the longitudinal relaxation times T₁ observed were T_1B = 1.2 and T_1F = 2.3 s for B and F components24, the ratio of the damping factors e^−t_L/T_1B/e^−t_L/T_1F was 0.63–0.94. On the other hand, the period t_T to compete with the transverse relaxation, i.e., the twice of the interval of 90°–180°–90° RF pulse sequence, was 0.003–0.009 s. It was short enough as compared with the transverse relaxation times, T_2B = 0.078 and T_2F = 0.095 s24, to yield the ratio e^−t_T/T_2B/e^−t_T/T_2F of 0.98–0.99. Thus the influence of the relaxation was found to be within the experimental error.

3. Data Analysis

3.1. Exchange Rate Constant

In equilibrium, the relation

$$k_{\text{BF}}{N}_{\text{B}}=k_{\text{FB}}{N}_{\text{F}}$$ (1)

is held, where k_FB and k_BF denote the rate constants of the peptide binding and dissociation, and N_B and N_F represent the number of bound and free peptide molecules.

3.2. Analysis of the Peak Integral

As shown in the ¹H NMR spectrum (Fig. 1), it is difficult to distinguish the bound and free components of L-Enk; see the detail in section 4.1. In this case, the individual peak height analysis is impossible, and hence the peak integral

Figure 1.

1D ¹H NMR spectra of 5mM L-Enk in the presence (black) and absence (red) of EPC LUV. The aromatic region of the Tyr and Phe residues of L-Enk is expanded in the inset. Arrows show the EPC signals used for determining the diffusion coefficient of the lipid in membrane.

$$A(g)={\int }_{{\omega }_1}^{{\omega }_2}I(g,\omega )d\omega ,$$ (2)

that is in proportion to the peak height of the signal, is substituted for the signal intensity. In Eq. (2)g and ω are the FG strength and the chemical shift, respectively. ω₁ and ω₂ are the lower and upper limit of the integral. Both bound (B) and free (F) components contribute to the integral intensity.

The integral intensity A(g) of the PFG signal is analyzed by the analytical formula of the Bloch equation with exchange terms8. The intensity A(g) can be written as

$$A(g)=\left(\frac{A_0}{2}+\frac{\mathrm{\Lambda }}{2\mathrm{\Delta }}\right)\text{exp}[(-\sigma +\mathrm{\Delta })\tau ]+\left(\frac{A_0}{2}-\frac{\mathrm{\Lambda }}{2\mathrm{\Delta }}\right)\text{exp}[(-\sigma -\mathrm{\Delta })\tau ].$$ (3)

The parameters shown in Eq. (3) are defined as

$$\mathrm{\Lambda }=\lambda (A_{\text{B}0}-A_{\text{F}0})+k_{\text{FB}}{A}_{\text{F}0}+k_{\text{BF}}{A}_{\text{B}0},$$ (4)

where $\lambda =\frac{1}{2}(k_{\text{FB}}-k_{\text{BF}}+D_{\text{F}}{m}^2-D_{\text{B}}{m}^2),$,

$$\sigma =\frac{1}{2}(k_{\text{FB}}+k_{\text{BF}}+D_{\text{F}}{m}^2+D_{\text{B}}{m}^2),$$ (5)

$$\mathrm{\Delta }=\sqrt{{\lambda }^2+k_{\text{FB}}{k}_{\text{BF}}},$$ (6)

and

$$\tau =\left({\mathrm{\Delta }}_{\text{diff}}-\frac{\delta }{3}\right).$$ (7)

A_F0 and A_B0 are defined as the peak integrals A_F(g) and A_B(g) at τ = 0, and

$$A_0=A_{\text{F}0}+A_{\text{B}0}.$$ (8)

D_F and D_B are the diffusion coefficients of free and bound peptides, respectively. In this work, the FG strength g is reduced as

$$m=\delta \gamma g,$$ (9)

where γ is the gyromagnetic ratio of the ¹H nucleus (2.675×10⁸ rad/Ts).

Once Eq. (3) is successfully fitted to the experimental A(g), the intensities of the bound and free components A_B(g) and A_F(g) can be easily evaluated by

$$A_{\text{B}}(g)=\left\{\frac{A_{\text{B}0}}{2}+\frac{\lambda A_{\text{B}0}+k_{\text{FB}}{A}_{\text{F}0}}{2\mathrm{\Delta }}\right\}\text{exp}\{(-\sigma +\mathrm{\Delta })\tau \}+\left\{\frac{A_{\text{B}0}}{2}-\frac{\lambda A_{\text{B}0}+k_{\text{FB}}{A}_{\text{F}0}}{2\mathrm{\Delta }}\right\}\text{exp}\{(-\sigma -\mathrm{\Delta })\tau \},$$ (10)

and

$$A_{\text{F}}(g)=\left\{\frac{A_{\text{F}0}}{2}-\frac{\lambda A_{\text{F}0}-k_{\text{BF}}{A}_{\text{B}0}}{2\mathrm{\Delta }}\right\}\text{exp}\{(-\sigma +\mathrm{\Delta })\tau \}+\left\{\frac{A_{\text{F}0}}{2}+\frac{\lambda A_{\text{F}0}-k_{\text{BF}}{A}_{\text{B}0}}{2\mathrm{\Delta }}\right\}\text{exp}\{(-\sigma -\mathrm{\Delta })\tau \}.$$ (11)

3.3. Fitting Procedure

There are 6 parameters, k_BF, k_FB, D_B, D_F, A_B0, and A_F0 in Eq. (3). A_B0 and A_F0 are in proportion to the number of bound and free molecules, respectively. From Eq. (1), we can write the similar relation as

$$k_{\text{FB}}{A}_{\text{F}0}=k_{\text{BF}}{A}_{\text{B}0}.$$ (12)

When we obtain the experimental A₀, the two parameters A_B0 and A_F0 can be removed from Eq. (3) by using Eqs. (8) and (12).

At large g, the Stejskal-Tanner plot clearly shows that the intensity is a linear function of g², so that it is possible to obtain D_B by fitting the equation

$$\text{ln}\frac{A(g)}{A_0}=-D_{\text{B}}{m}^2\tau$$ (13)

to the experimental A(g); the detail will be described in section 4.2. Thus, the fitting parameters can be reduced to k_FB, k_BF, and D_F. Finally, we have only to fit Eq. (3) to the experimental A(g) in the whole range of g and evaluate k_FB, k_BF, and D_F simultaneously.

4. Results and Discussion

4.1. 1D and PFG ¹H NMR Spectra of L-Enk in the Presence of Vesicle

First we examine how the NMR spectrum of L-Enk is modified by the presence of the vesicle. Figure 1 shows the 1D ¹H NMR spectra of L-Enk in the presence and absence of EPC LUV with 100-nm diameters. The aromatic proton region at 7.4–6.7 ppm is expanded in the inset. The region is useful to analyze the peptide side because no lipid signal is overlapping2. The peaks at 7.35–7.20 and 7.15–6.80 ppm are assigned to the aromatic protons of Phe and Tyr, respectively 9,12. It is found that the line broadening of the peptide signals is induced by the presence of the vesicle; see the black line. The Phe peaks at 7.25 ppm are shifted to downfield, while the signals around 7.3 ppm slightly move to a high field. These are analogous to the change in the chemical shift when the peptide is added to the micelle of lysophosphatidylcholine 9. For the Tyr peaks, in contrast, the chemical shifts are almost unaltered even in the presence of the vesicle. The result indicates that L-Enk is oriented with its Phe residue toward to the membrane inside.

The line broadening and the peak shift in Figure 1 imply that L-Enk is bound to the membrane. The bound component of L-Enk is, however, hardly separated from free L-Enk in the 1D NMR spectrum. To separate the bound component from the peptide signal, we apply the PFG technique. The criterion is that the signal assignable to the free peptide preferentially decays with increasing the field gradient (FG) strength to unveil the bound component at the high FG2. In Figure 2 is demonstrated how the signal of L-Enk is attenuated by applying the magnetic field gradient. It is evident that all signals decay in intensity with increasing the FG strength (from top to bottom). Instead, the broad components are uncovered. The intensities of the broad components are less attenuated up to the FG strength of 0.91T/m (the bottom). From these results, the broad components are considered to be bound L-Enk with its motion slowed down in the viscous membrane environment21,25. The situation is quite similar to the 5FU binding reported previously2.

Figure 2.

PFG ¹H NMR spectra of the aromatic region of L-Enk in the presence of LUV at 303K. Here, the 16 FG strengths g = 0.05, 0.15, 0.225, 0.30, 0.35, 0.40, 0.45, 0.50, 0.55, 0.60, 0.65, 0.70, 0.75, 0.80, 0.85, 0.91T/m are applied (from top to bottom) with the pulse width of 0.004 s at the diffusion time, 0.1 s.

4.2. Kinetics of Binding, Diffusivity, and Binding Amount of L-Enk

It is found that the bound component of L-Enk is uncovered by ¹H NMR in combination with the PFG technique. Therefore, the diffusivity, the kinetics of binding, and the binding amount of L-Enk can be quantified by using the signal intensity decay of the PFG ¹H NMR spectrum. We analyze the signal attenuation in accordance with the procedure in section 3.3, by using the peak integral of the aromatic region in Figure 2.

The result is summarized in Figure 3 at various diffusion times, Δ_diff. The circles, triangles, and squares designate the experimental values at Δ_diff of 0.1, 0.5, and 1.0 s, respectively. The red lines are obtained by fitting Eq. (3) to the experimental values. Each line well reproduces the observed decay of the signal intensities. The dashed black lines are the fitting results of Eq. (13) to the signal intensity at the large g limit (g→∞). Thus we can evaluate the diffusivity and the rate of the binding and dissociation of L-Enk from Eqs. (3) and (13). It is found that the signal intensity decay is a biexponential function with respect to the FG strength, in contrast to the single exponential decay of L-Enk in water (not shown). The intensities rapidly attenuate at τm² < 2×10¹⁰m⁻² s, while slowly at τm² > 2×10¹⁰m⁻² s. The non-linear behavior of the signal attenuation is due to the exchange of the peptide molecule between free and bound states that is similar to the 5FU binding to the membrane3.

Figure 3.

Intensity decay of the L-Enk signal as a function of the FG strength at the diffusion time Δ_diff of 0.1 (filled circle), 0.5 (filled triangle), and 1.0 s (filled square). Here the signal intensity is evaluated as the peak integral of the aromatic region in Figure 2. Symbols represent the experimental values. The red lines are obtained by fitting Eq. (3) to the experimental values of peak integrals at the respective Δ_diff. The blue and the green lines demonstrate the decay curves evaluated by Eqs. (10) and (11), respectively. The dashed black lines are the fitting result of the Stejskal-Tanner plot at the large g limit (g→∞), from which the diffusion coefficients of bound L-Enk, D_B are calculated. The results of Δ_diff =0.5 and 1.0 s are shifted to negative value by −1.0 and −2.0, respectively.

The PFG signal of the bound component not only comes from L-Enk bound throughout the time Δ_diff but also from that transferring from the free to bound states within the time Δ_diff. The transferring peptides are considered to have a large displacement and a large effective diffusion coefficient, because they have undergone a free state during the time Δ_diff. The influence of the transferring peptides leads to the rapid attenuation at τm² < 2×10¹⁰m⁻² s. On the other hand, the peptide keeping on binding throughout the time Δ_diff has a small diffusion coefficient, so that the decay of the signal intensity is small. Slow attenuation at τm² > 2×10¹⁰m⁻² s in Figure 3 is due to the contribution of these binding molecules. The decay of the signal intensities has thus two different gradients and becomes non-linear.

The diffusivity of the free and the bound peptide is evaluated by fitting Eqs. (3) and (13) to the experimental A(g) in Figure 3. The fitting of Eq. (3) to the experimental value in the whole range of g gives the diffusion coefficient of the free peptide, D_F, together with the rate constants k_FB and k_BF. Next, we calculate the diffusion coefficient of the bound peptide, D_B, by using the linear relation of the decay plot (Stejskal-Tanner plot) at g→∞³; see the dashed black lines. The results are summarized in Figure 4a as a function of the time Δ_diff. It is found that D_F and D_B give the values of (2.9±0.1)×10⁻¹⁰ and (5.0±1.4)×10⁻¹²m²/s, respectively, at 303K26. The diffusivity of bound L-Enk is almost 60 times as restricted as free L-Enk. Both values are independent of the time, Δ_diff, indicating the accuracy of the experiment. D_F is in good agreement with the diffusion coefficient of L-Enk in water (D_W = (3.3±0.1)×10⁻¹⁰m²/s), and D_B corresponds to that of the lipid membrane (D_M = (7.3±0.7)×10⁻¹²m²/s) obtained simultaneously by the EPC signal27. All results demonstrate that D_F and D_B are the diffusion coefficients of free and bound L-Enk in the presence of the vesicle.

Figure 4.

The Δ_diff dependence of (a) the diffusion coefficients, (b) the rate constants of the binding and dissociation, and (c) the binding amount of L-Enk at 303K.

In Figure 4b, the rate constants of the binding (k_FB) and dissociation (k_BF) of L-Enk are plotted as a function of Δ_diff. The values of k_FB and k_BF are estimated to be 0.040±0.004 and 0.40±0.01 s⁻¹, respectively, and almost independent of Δ_diff. The obtained rate constants correspond to the half-value periods, t_FB and t_BF, of the peptide binding and dissociation,

$${\tau }_{\alpha }=\frac{\text{ln}\hspace{0.17em}2}{k_{\alpha }},\mathrm{\hspace{0.17em} }\alpha =\{\text{FB},\text{BF}\}$$ (14)

as 11.0±1.0 and 1.2±0.1 s. This means that the lifetime of the binding and dissociation of L-Enk is of the order of ten second and a second timescale. Finally, the dissociation constant K_d of the peptide is estimated to be 10.1±0.8 from the relation K_d = k_BF/k_FB.

To make sure that the obtained rate constants are reasonable, we compare the values of k_FB and k_BF with those of small-sized solutes quantified recently by ¹⁹F NMR3,4. The rate constants of membrane binding and dissociation are 0.2 and 4.1 s⁻¹ for 5FU molecules3. For FBPA, k_FB and k_BF are enhanced to 22–280 and 68–107 s⁻¹ at 303K4. The time span of the binding and dissociation of 5FU is 10⁻¹–10⁰ s timescale3, while that of FBPA is decreased to 10⁻³–10⁻² s4. This means that the membrane binding of rather hydrophilic 5FU is 2–3 orders of magnitude slower than that of hydrophobic FBPA. In case of L-Enk, the rate constants k_FB and k_BF are 0.040 and 0.40 s⁻¹. It means that the time span of the binding and dissociation is 10⁰ to 10¹ s timescale, almost 10 times as slow as 5FU. The larger size and the hydrophilic nature of L-Enk slow down the exchange motion between the bound and free states. It is in marked contrast to the rapid exchange motion of small-sized hydrophobic FBPA on millisecond timescale, the exchange rate of which more than 3 orders of magnitude as large as the peptide.

The bound fraction of L-Enk can also be evaluated by using K_d. In Figure 4c is demonstrated how much of L-Enk is bound to the vesicle. It is found that the bound fraction is 0.09±0.01 and almost unaltered throughout the measurement. The result indicates that 0.45mM of L-Enk is bound to the 40mM LUV that corresponds to the peptide/lipid molar ratio of 0.011. Finally, the binding free energy ΔG of L-Enk from water to LUV is calculated to be −2.9 kJ/mol, the magnitude close to the thermal fluctuation, 2.5 kJ/mol. The value is reasonable in terms of rather hydrophilic nature of L-Enk, that is in sharp contrast to ΔG of hydrophobic FPBA, −20 kJ/mol4.

5. Conclusions

In this work, we show how to quantify the dynamics of peptide binding to fluid lipid membranes in situ. The PFG ¹H NMR technique is applied for this purpose, using a neuropeptide L-Enk in the presence of LUV with 100-nm diameters. Even in the case that the bound and free states of L-Enk cannot be distinguished in the 1D NMR spectrum, the PFG technique has unveiled the bound component of L-Enk after the preferential decay of the free component at the high field gradient. The success is notable because the ¹H nucleus is not rare and the method can be a general standard to quantify the dynamics of a variety of peptide bindings. By analyzing the peak integral of the peptide signal as a function of the gradient strength, we have quantified the diffusivity, the kinetics of the binding, and the bound amount of L-Enk by the analytical formula of the Bloch equation with exchange terms.

As compared with the diffusion coefficient of the free L-Enk, 2.9×10⁻¹⁰m²/s, the mobility of the bound L-Enk is slowed down in LUV where the diffusion coefficient of the peptide is 5.0×10⁻¹²m²/s at 303 K. The rate constants of the binding and dissociation of L-Enk are 0.040 and 0.40 s⁻¹, respectively. This means that the exchange motion of L-Enk between the bound and free states is more than 1–3 orders of magnitude slower than the small-sized 5FU and FBPA. About one tenth of the total L-Enk is bound to the LUV with the peptide/lipid molar ratio of 0.011. The free energy of the peptide binding is −2.9 kJ/mol, the magnitude close to the thermal fluctuation, 2.5 kJ/mol. This is due to rather hydrophilic nature of L-Enk that is in sharp contrast to the hydrophobic FBPA molecule with the binding free energy of −20 kJ/mol.