Effects of Amantadine Binding on the Dynamics of Membrane-Bound Influenza A M2 Transmembrane Peptide Studied by NMR Relaxation

Abstract

The molecular motions of membrane proteins in liquid-crystalline lipid bilayers lie at the interface between motions in isotropic liquids and in solids. Specifically, membrane proteins can undergo whole-body uniaxial diffusion on the microsecond time scale. In this work, we investigate the ¹H rotating-frame spin-lattice relaxation (T_1ρ) caused by the uniaxial diffusion of the influenza A M2 transmembrane peptide (M2TMP), which forms a tetrameric proton channel in lipid bilayers. This uniaxial diffusion was proved before by ²H, ¹⁵N and ¹³C NMR lineshapes of M2TMP in DLPC bilayers. When bound to an inhibitor, amantadine, the protein exhibits significantly narrower linewidths at physiological temperature. We now investigate the origin of this line narrowing through temperature-dependent ¹H T_1ρ relaxation times in the absence and presence of amantadine. Analysis of the temperature dependence indicates that amantadine decreases the correlation time of motion from 2.8 ± 0.9 μs for the apo peptide to 0.89 ± 0.41 μs for the bound peptide at 313 K. Thus the line narrowing of the bound peptide is due to better avoidance of the NMR time scale and suppression of intermediate time scale broadening. The faster diffusion of the bound peptide is due to the higher attempt rate of motion, suggesting that amantadine creates better-packed and more cohesive helical bundles. Analysis of the temperature dependence of $\ln \left(T_{1\rho }^{-1}\right)$ indicates that the activation energy of motion increased from 14.0 ± 4.0 kJ/mol for the apo peptide to 23.3 ± 6.2 kJ/mol for the bound peptide. This higher activation energy indicates that excess amantadine outside the protein channel in the lipid bilayer increases the membrane viscosity. Thus, the protein-bound amantadine speeds up the diffusion of the helical bundles while the excess amantadine in the bilayer increases the membrane viscosity.

Introduction

Nuclear magnetic resonance has long been used as a tool for measuring molecular dynamics over a broad range of time scales, from the fast picosecond – nanosecond regime (Mandel et al., 1996), to the slow microsecond – millisecond regime (Palmer et al., 2001, Schaefer et al., 1977, Shaw et al., 2000), and to the ultra-slow supra-second regime (deAzevedo et al., 2000, Schmidt et al., 1988). Some of the most interesting applications are to biomolecules, where molecular dynamics has a particularly strong connection to function (Ishima and Torchia, 2000, Kay, 1998, Palmer et al., 1996). In solution NMR studies of biomolecular dynamics, ¹⁵N relaxation NMR has been the method of choice and the Lipari-Szabo model-free formalism (Clore et al., 1990, Lipari and Szabo, 1982) has provided a simple theoretical framework to separate the effects of internal anisotropic motions from whole-body isotropic motion and to extract the amplitudes and rates of internal motion.

In the solid state, the lack of isotropic molecular tumbling considerably simplifies studies of internal motions by NMR. Many solid-state NMR techniques directly probe the amplitudes of internal motions, most notably ²H quadrupolar NMR (Jelinski et al., 1980), which has exquisite angular resolution but no chemical resolution, and ¹H-X dipolar coupling techniques under magic-angle spinning (MAS), which have chemical site resolution (Hong et al., 2002, Munowitz et al., 1982, Schaefer et al., 1983). Nuclear spin relaxation times (T₁, T₂ and T_1ρ) have also been used to determine the correlation times and activation energies of motional processes such as methyl three-site jumps and aromatic ring flips. Combined, these amplitude and rate measurements have provided detailed information on the dynamics of structural proteins such as collagen and silk (Jelinski et al., 1980, Yang et al., 2000), enzymes (Williams and McDermott, 1995), and lipid membranes (Blume et al., 1982, Smith and Oldfield, 1984). Molecular motions of synthetic polymers (Hagemeyer et al., 1989, Schaefer et al., 1990, Schaefer et al., 1984) and small molecules (Rothwell and Waugh, 1981) have also been investigated extensively using solid-state NMR.

The dynamic environment of liquid-crystalline lipid bilayers lies at the interface between isotropic fluids and rigid solids and hence presents unique challenges to understanding membrane protein dynamics. While membrane protein sidechain motions have been studied by NMR for decades (Huster et al., 2001, Kinsey et al., 1981, Lee et al., 1993, Opella, 1986), whole-body uniaxial rotational diffusion of membrane proteins has been less examined by NMR. As the symmetry axis of the lipid bilayer, the bilayer normal is the axis around which phospholipids undergo nanosecond rotational diffusion (Bloom et al., 1991, Gennis, 1989). Membrane proteins can also undergo such rotational diffusion, because the same principle that underlies the phospholipid motion, which is Brownian diffusion in a two-dimensional fluid (Saffman and Delbruck, 1975), also applies to membrane proteins. A number of examples of this uniaxial diffusion have now been reported for membrane peptides and proteins (Hong, 2007, Hong and Doherty, 2006, Lewis et al., 1985, Macdonald and Seelig, 1988, Pauls et al., 1985, Prosser et al., 1992, Tian et al., 1998, Yamaguchi et al., 2001). Their NMR fingerprints include powder lineshapes with reduced anisotropy and an asymmetry parameter (η) of 0, vanishing intensity at the isotropic chemical shift of non-spinning cross polarization (CP) spectra, and narrow lines in macroscopically aligned samples whose alignment axis deviates from the static magnetic field (Aisenbrey and Bechinger, 2004, Glaser et al., 2004, Park et al., 2006).

The influenza A M2 protein forms a proton channel in the virus envelope that is important for the virus life cycle (Pinto et al., 1992, Pinto and Lamb, 2007). Acidification of the virus interior uncoats the viral RNA and releases it into the host cell. Amantadine binds the M2 proton channel and prevents its opening, thus inhibiting viral replication (Hay et al., 1985, Wang et al., 1993). The protein forms a tetrameric helical bundle in the membranes of both whole cells (Sakaguchi et al., 1997) and synthetic lipids (Luo and Hong, 2006). It undergoes uniaxial diffusion at a rate of ~10⁵ s^–1 in DLPC bilayers based on ²H NMR spectra and the 2D Brownian diffusion theory (Cady et al., 2007, Kovacs and Cross, 1997). The motional axis is the bilayer normal, which is also the helical bundle axis. Since the TM helices have tilt angles of ~38° in DLPC bilayers (Cady and Hong, 2008), the rotational diffusion has large amplitudes. Combined with the fact that the motional rate is not orders of magnitude different from the ¹H-¹³C and ¹H-¹⁵N dipolar couplings, the motion strongly impacts the NMR spectra: the ambient-temperature ¹H-decoupled ¹³C and ¹⁵N spectra of the protein in lipid bilayers are severely exchange-broadened under both MAS and static conditions (Cady et al., 2007, Li et al., 2007). Interestingly, upon amantadine binding, the resonances in both MAS and static solid-state NMR spectra of the protein sharpen considerably. This line narrowing was also observed in solution NMR spectra of M2(18-60) bound to DHPC micelles when an excess of the analogous rimantadine was added (Schnell and Chou, 2008).

Previously we have compared the ¹H-decoupled ¹³C T₂ relaxation times of the apo and bound M2TMP in DLPC bilayers to understand the amantadine-induced line narrowing. We found that the bound peptide has 30-150% longer ¹³C T₂ than the apo state at 303 K (Cady and Hong, 2008, Cady et al., 2009), indicating that the line narrowing has a significant contribution from dynamic changes of the protein. However, the nature of this amantadine-induced relaxation time increase has not been elucidated.

In this work, we have measured and analyzed temperature-dependent ¹H T_1ρ relaxation times of the apo and amantadine-bound M2TMP to better understand its motional properties. We quantify the rates and activation energies of the M2TMP microsecond motion in the absence and presence of amantadine. We find that amantadine increases the motional rates approximately three fold at 313 K by increasing the attempt rates, thus alleviating intermediate time scale broadening and narrowing the spectral lines. Further, excess amantadine in the bilayer increases the activation energy of the motion, whose physical origin will be discussed.

Material and Methods

Peptides and lipids

FMOC-protected uniformly ¹³C, ¹⁵N-labeled amino acids were either prepared in-house (Carpino and Han, 1972) or purchased from Sigma-Aldrich and Cambridge Isotope Laboratories. The M2 transmembrane domain (residues 22-46) of the Influenza A Udorn strain (Ito et al., 1991) was synthesized by PrimmBiotech (Cambridge, MA) and purified to >95% purity. The amino acid sequence is SSDPL VVAASII GILHLIL WILDRL. Three labeled peptides were used in this work, each with three to four uniformly ¹³C, ¹⁵N-labeled residues. They are LAGI (L26, A29, G34 and I35), VAIL (V27, A30, I33 and L38), and VSL (V28, S31 and L36).

Membrane sample preparation

M2TMP was reconstituted into 1,2-dilauroyl-sn-glycero-3-phosphatidylcholine (DLPC) bilayers by detergent dialysis (Luo and Hong, 2006). The lipid vesicle solution was prepared by suspending dry DLPC powder in 1 mL phosphate buffer (10 mM Na₂HPO₄/NaH₂PO₄, 1 mM EDTA, 0.1 mM NaN₃) at pH 7.5, vortexing and freeze-thawing 6 times to create uniform vesicles (Traikia et al., 2000). M2TMP was dissolved in octyl-β-D-glucopyranoside (OG) in 2 mL phosphate buffer, then mixed with an equal volume of DLPC vesicles, and dialyzed against the phosphate buffer at 4 °C for 3 days. The final peptide/lipid molar ratio was 1:15. The dialyzed peptide-DLPC solution was centrifuged at 150,000 g to give a pellet containing ~50 wt% water. For the amantadine-bound samples, 10 mM amantadine hydrochloride was added to the phosphate buffer. After pelleting, the amount of amantadine remaining in the supernatant was quantified by ¹H solution NMR, and the bound fraction indicates a peptide : amantadine molar ratio of ~1 : 8 (Cady et al., 2009). All membrane-bound M2 samples were thus studied at pH 7.5, corresponding to the closed state of the channel.

Solid-state NMR spectroscopy

NMR experiments were carried out on a Bruker AVANCE-600 (14.1 Tesla) spectrometer (Karlsruhe, Germany) using a 4 mm MAS probe. ¹H T_1ρ measurements were carried out using a Lee-Goldburg (LG) spin lock sequence shown in Figure 1 (Huster et al., 2001). The initial two 90° and 35° ¹H pulses prepare the ¹H magnetization to be alternately parallel and antiparallel to the ¹H spin lock axis, which lies at the magic angle $co{s}^{-1}(1∕\sqrt{3})$ from the static magnetic field in the yz plane. The spin-lock effective field strength, ω_e, was fixed at 2π × 61.2 kHz in all experiments, since T_1ρ depends on ω_e (equations 1-2). The samples were spun at 7000 Hz during all experiments. Six or seven spin lock time points τ_SL were measured between 0 and 8 ms to obtain the ¹H T_1ρ at each temperature, and six or seven temperatures were measured per peptide to provide a sufficient number of data points in the $\ln \left(T_{1\rho }^{-1}\right)$ versus inverse temperature plot (Figure 5) to extract the dynamic parameters. The NMR probe and samples were equilibrated for 30 minutes at each temperature before tuning and data acquisition. The ¹H LG-CP period had the same field strength as the LG spin lock period, but had a constant contact time of 300 μs. Typical radiofrequency (rf) pulse lengths were 5 μs for ¹³C and 3.5-4.0 μs for ¹H. ¹³C chemical shifts were referenced to the α-Gly ¹³C’ signal at 176.49 ppm on the TMS scale.

Figure 1.

¹³C-detected ¹H Lee-Goldburg spin lock pulse sequence used to measure ¹H T_1ρ relaxation times. The ¹H magnetization is spin-locked for a variable time τ_SL. The LG spin-lock and LG-CP have the same field strength.

Figure 5.

$\ln \left(T_{1\rho }^{-1}\right)$ versus 1000/T curves for representative Cα sites of M2TMP. (a) L26. (b A30. (c) S31. (d) G34. (e) I35. (f) L36. The apo data are shown as open squares and fit by dashed lines, and the amantadine-bound data are shown as filled squares and fit by solid lines.

The ¹H T_1ρ's were measured between 313 K and 243 K on six membrane samples with and without amantadine. The activation energy E_α, correlation time prefactor τ₀, and correlation time were extracted by least-square linear fits of the $\ln \left(T_{1\rho }^{-1}\right)$ to 1000/T curves on the high temperature side using equation 8. For the apo VAIL sample, artificially high T_1ρ values were observed at 313 K, thus the apo and amantadine-bound VAIL-M2TMP data analysis did not include the 313 K data.

C-H dipolar order parameters were measured at 313 K under 7000 Hz MAS using a dipolar-doubled DIPSHIFT experiment (Hong et al., 1997) where ¹H homonuclear decoupling was achieved by the frequency-switched Lee-Goldburg sequence (Bielecki et al., 1990). The dipolar-doubled sequence suppresses the apparent T₂ relaxation by making the total homonuclear decoupling time constant at one rotor period. The t₁ evolution time was controlled by the position of a ¹³C π pulse in the rotor period.

Theory

The membrane protein rotational diffusion of interest generally occurs on the microsecond time scale based on the 2D Brownian diffusion theory (Saffman and Delbruck, 1975). Motions on this time scale can be probed by ¹H-decoupled S-spin spin-spin relaxation times (T₂) and rotating-frame spin-lattice relaxation times (T_1ρ). The T₂ relaxation times of an S spin dipolar coupled to an I spin under conditions of random isotropic motion and I spin rf decoupling depends on the spectral density at the decoupling field strength (Rothwell and Waugh, 1981), which is typically 50-100 kHz. However, measurement of ¹³C T₂ by the Hahn-echo experiment in uniformly ¹³C-labeled residues in proteins has the shortcoming that ¹³C-¹³C scalar coupling contributes to the time-dependent intensity decay, unless a selective ¹³C π pulse is applied to remove the scalar interaction. Given the small chemical shift dispersion among the aliphatic carbons in proteins, very soft π pulses, which necessitate multiple experiments with shifted ¹³C offsets, would be required to obtain homonuclear and heteronuclear decoupled ¹³C T₂'s of all sites. A simpler alternative, then, for probing microsecond time scale motion is to measure the T_1ρ, since it is primarily sensitive to spectral densities at the frequency of the spin-lock field (Schaefer et al., 1977), which is also 50 – 100 kHz.

To obtain site-specific relaxation times, we measure the ¹H T_1ρ through the directly bonded ¹³C sites by transferring the ¹H magnetization to ¹³C, and by using spin-diffusion-free Lee-Goldburg spin lock instead of transverse spin lock (van Rossum et al., 2000). The effective spin lock field is thus tilted at the magic angle, $co{s}^{-1}(1∕\sqrt{3})$, from the static magnetic field. The ¹H magnetization, prepared along the direction of the spin-lock field (Figure 1), can only undergo spin-lattice relaxation in the rotating frame.

The ¹H T_1ρ relaxation in ¹³C-labeled molecules is driven by fluctuating ¹H-¹H and ¹H-¹³C dipolar couplings due to random molecular motions. The orientation-dependent relaxation rate depends on spectral densities, J(ω), at the spin lock field ω_e, 2ω_e, Larmor frequencies ω_H, ω_O, and the sum and difference of ω_H and ω_C (Huster et al., 2001, Mehring et al., 1983). Since the Larmor frequencies are three to four orders of magnitude larger than ω_e (ω_H = 2π × 600 MHz, ω_C = 2π × 150 MHz, and ω_e = 2π × 61.2 kHz in our experiments), for motions in the tens to hundreds of kilohertz regime, one can safely ignore the spectral density terms at the Larmor frequencies. Taking into account magic-angle spinning at a frequency ω_R, the powder averaged T_1ρ for the rotating-frame relevant part is (Fares et al., 2005):

$$\langle T_{1\rho }^{-1}\rangle =\Delta M_2(S,{\delta }_{CH},{\delta }_{HH},\beta )\cdot [J(2{\omega }_e+2{\omega }_R)+J(2{\omega }_e-2{\omega }_R)+J(2{\omega }_e+{\omega }_R)+J(2{\omega }_e-{\omega }_R)]$$ (1)

Here ΔM₂ is the product of the dynamic portion of the dipolar second moment and orientational terms that transform spin interaction tensors from their molecule-fixed principal axis frames to the rotor frame (Fares et al., 2005). The dynamic portion of the dipolar second moment is approximately (1 – S²) times the rigid-limit dipolar second moment, where the order parameter S represents the orientation-invariant part of the interaction. In solid-state NMR, the order parameter can be independently measured by various dipolar chemical-shift correlation experiments (Hong et al., 2002, Huster et al., 2001, Schmidt-Rohr et al., 1992). The dependence of ΔM₂ on the C-H (δ_CH) and H-H (δ_HH) dipolar couplings in equation (1) reflects the fact that the ¹³C-detected ¹H T_1ρ relaxation is driven by C-H and H-H dipolar couplings. β is the angle between B₀ and the spin-lock field and is $co{s}^{-1}(1∕\sqrt{3})$ in our experiments.

For motions with a single correlation time τ, the spectral density is given by (Lipari and Szabo, 1982):

$$J\left({\omega }_i\right)=\frac{\tau }{1+{\omega }_i^2{\tau }^2},$$ (2)

Explicitly writing the spectral density terms in equation (1), we obtain

$$\langle T_{1\rho }^{-1}\rangle =\Delta M_2(S,{\delta }_{CH},{\Delta }_{HH},\beta )\cdot \left[\frac{\tau }{1+{(2{\omega }_e+2{\omega }_R)}^2{\tau }^2}+\frac{\tau }{1+{(2{\omega }_e-2{\omega }_R)}^2{\tau }^2}+\frac{\tau }{1+{(2{\omega }_e+{\omega }_R)}^2{\tau }^2}+\frac{\tau }{1+{(2{\omega }_e-{\omega }_R)}^2{\tau }^2}\right]$$ (3)

The dependence of T_1ρ on correlation time τ can be considered in three regimes. In the long correlation time or strong collision limit where 2ω_eτ >> 1, equation 3 is approximated as:

$$\langle T_{1\rho }^{-1}\rangle \approx \Delta M_2(S,{\delta }_{CH},{\delta }_{HH},\beta )\cdot \left[\frac{1}{{(2{\omega }_e+2{\omega }_R)}^2}+\frac{1}{{(2{\omega }_e-2{\omega }_R)}^2}+\frac{1}{{(2{\omega }_e+{\omega }_R)}^2}+\frac{1}{{(2{\omega }_e-{\omega }_R)}^2}\right]\cdot \frac{1}{\tau },2{\omega }_e\tau >>1,$$ (4)

In the short correlation time or weak collision regime, equation (3) is simplified to:

$$\langle T_{1\rho }^{-1}\rangle \approx 4\Delta M_2(S,{\delta }_{CH},{\delta }_{HH},\beta )\cdot \tau ,2{\omega }_e\tau <<1$$ (5)

In the intermediate motional regime where 2ω_eτ = 1, for ω_e >> ω_R, the relaxation rate is the fastest, corresponding to a T_1ρ minimum.:

$$\langle T_{1\rho }^{-1}\rangle \approx 2\Delta M_2(S,{\delta }_{CH},{\delta }_{HH},\beta )\cdot \tau ,2{\omega }_e\tau =1$$ (6)

For an activated motional process, the correlation time is given by the Arrhenius law:

$$\tau ={\tau }_0{e}^{E_a∕RT},$$ (7)

where E_a is the activation energy and τ₀ is the prefactor describing the attempt rate of motion. The larger the attempt rate, the smaller the τ₀, and the shorter the correlation time τ. Substituting τ into equation (5), we find that E_a can be extracted from a plot of $\ln \left(T_{1\rho }^{-1}\right)$ versus 1000/T in the short τ limit:

$$\ln \langle T_{1\rho }^{-1}\rangle =\ln \left(4\Delta M_2{\tau }_0\right)+\frac{E_a}{1000R}\cdot \frac{1000}{T},2{\omega }_e\tau <<1$$ (8)

Equation (8) indicates that the natural logarithm of relaxation rates is linear with 1000/T with a slope of E_a/1000R in the short correlation time regime. Moreover, the pre-exponential factor τ₀ can be extracted from the intercept of the linear fit. For this purpose, we use the second moment expression from Mehring, which takes into account both C-H and H-H dipolar relaxation as well as the LG spin lock factor (Huster et al., 2001, Mehring et al., 1983):

$$4\Delta M_2{\tau }_0=\left(1-S^2\right)\left(\frac{3}{10}{\delta }_{HH}^2+\frac{1}{15}{\delta }_{CH}^2\right){\tau }_0,2{\omega }_e\tau <<1$$ (9)

The motional correlation time is fully determined once the activation energy E_a and the pre-exponential factor τ₀ are obtained from the slope and the intercept, respectively.

In principle, an alternative method to determine the pre-exponential factor τ₀ is to exploit the T_1ρ minimum temperature, where 2ω_eτ = 1. However, as we show below, the T_1ρ minima observed for membrane-bound M2TMP result from the lipid phase transition, and are thus not the true minima of a single motional process. On the other hand, the lipid-induced T_1ρ minima should not affect the high-temperature slopes or intercepts, thus the activation energy E_a and τ₀ can still be extracted reliably from these features.

The T_1ρ in the long correlation time limit can in principle also be used to extract E_a and τ. Equations (4) and (5) indicate that the slope of the $\ln \left(T_{1\rho }^{-1}\right)$ plot with 1/T on the low temperature side has the same magnitude but the opposite sign from that of the high temperature side. But this scenario is true only if a single motional process with the same E_a persists throughout the temperature range. Thus, the lipid phase transition makes this assumption invalid. Since our purpose is to understand the physiological temperature dynamics of M2TMP, below we will analyze only the high temperature regime of the T_1ρ data to extract M2TMP motional parameters.

Results

Site-specific ¹H T_1ρ relaxation times were measured on six membrane samples with three sets of labeled residues (LAGI, VAIL, and VSL) without and with amantadine. The eleven labeled residues are distributed from position 26 to 38 in the transmembrane domain, with I32 and H37 being the only residues not measured in this range.

Figure 2 shows representative ¹³C spectra of LAGI-M2TMP in the apo- and amantadine-bound states at 313 K, 273 K and 243 K. At 313 K, the amantadine-bound peptide has narrower linewidths than the apo peptide, whereas at 243 K the peptide signals of the two samples have similar intensities and linewidths, indicating immobilization of both states of the peptide. At 273 K, both the apo and bound peptide spectra exhibit significant exchange broadening with very low ¹³C intensities. This broadening coincides with the gel to liquid-crystalline phase transition temperature (271 K) of the DLPC membrane, indicating that the M2TMP motion responsible for the exchange broadening is intimately associated with the phase property of the lipid bilayer. The VAIL and VSL spectra exhibit similar temperature dependences and are given in the Supporting Information (Figures S1, S2). The fact that the amantadine-bound samples show narrower and higher backbone Cα signals than the apo samples at high temperature (Cady and Hong, 2008) indicates dynamic differences induced by amantadine, the nature of which are analyzed below.

Figure 2.

1D ¹³C CP-MAS spectra of LAGI M2TMP in DLPC bilayers at 313 K, 273 K, and 243 K. (a) With amantadine. (b) Without amantadine.

¹H T_1ρ were measured at six to seven temperatures between 313 and 243 K. Figure 3 displays representative T_1ρ decay curves at 313 K, 273 K, and 243 K as a function of spin-lock time. The decay curves are well fit by single exponential functions, where the decay constants correspond to T_1ρ. At 313 K, the T_1ρ decays are slower for the amantadine-bound peptide than for the apo peptide for all residues, indicating the bound peptide has longer T_1ρ's. At 273 K, the ¹H T_1ρ's are significantly shorter than the high-temperature values for both the apo and bound peptides, and the bound peptide has marginally longer T_1ρ's than the apo peptide. At 243 K, the T_1ρ values increase significantly over the high temperature values, and there is no longer a consistent difference between the apo and bound peptide. Supporting information Table S1-S3 lists all T_1ρ values for backbone Hα, sidechain Hβ, and sidechain methyl protons in the apo and bound M2TMP at all temperatures.

Figure 3.

Representative ¹H T_1ρ relaxation decays of M2TMP in DLPC bilayers at 313 K, 273 K, and 243 K. (a) L26 Cα, (b) I33 Cδ, (c) I35 Cα, and (d) I35 Cβ. The apo data are shown as open squares and fit by dashed lines. The amantadine-bound data are shown as filled squares and fit by solid lines. The decay constants are indicated for all sites.

Figure 4 shows the ¹H T_1ρ's as a function of 1000/T (K⁻¹) for representative backbone and sidechain sites. All curves have a V shape, indicative of passage through the fastest relaxing intermediate motional regime. Between the apo and bound peptides, the minimum T_1ρ positions match well, with relatively similar T_1ρ values as well as the transition temperature T₀. On the high temperature side of the minimum, the bound peptide has progressively longer T_1ρ's than the apo peptide with increasing temperature, indicating that M2TMP has shorter correlation times in the presence of amantadine (equation 5). On the low temperature side, the apo and bound peptides have smaller T_1ρ differences for the small number of temperatures measured.

Figure 4.

¹H T_1ρ versus 1000/T for representative M2TMP Cα sites in the apo (open squares and dashed line) and amantadine-bound (closed squares and solid line) states in DLPC bilayers. (a) L26 Cα, (b) S31 Cα, (c) G34 Cα, (d) L36, (e) V27 Cγ2, (f) I35 Cδ.

To quantify the amantadine-induced dynamic differences of M2TMP, we convert the T_1ρ plots to $\ln \left(T_{1\rho }^{-1}\right)$ and extract the activation energy and correlation time prefactor τ₀ using equations (8-9). Figure 5 shows $\ln \left(T_{1\rho }^{-1}\right)$ as a function of 1000/T for a number of Hα sites. As expected, the shapes of the plots are roughly inverted from those of Figure 4, with the amantadine-bound peptide showing smaller relaxation rates than the apo peptide at physiological temperature. On the high temperature side of the T_1ρ minimum, $\ln \left(T_{1\rho }^{-1}\right)$ is roughly linear with inverse temperature for most sites, thus supporting the assumption that the rotational diffusion can be regarded as an activated process (vide infra). Moreover, the amantadine-bound peptide has more positive slopes than the apo peptide, indicating larger E_a. Least-square linear fits of the high-temperature side of the $\ln \left(T_{1\rho }^{-1}\right)$ curves yielded the activation energies, listed in Table 1.

Table 1.

E_a, τ₀, and τ_313K of M2TMP in DLPC bilayers in the absence and presence of amantadine extracted from Hα T_1ρ's. The 313 K T_1ρ and S_CH are also listed along with their uncertainties (superscript).

Residue	Amantadine-bound peptide					Apo peptide
	Ea (kJ/mol)	τ0 (ns)	τ313K (μs)	$T_{1\rho }^{313K}$ (ms)	S CH	Ea (kJ/mol)	τ0 (ns)	τ313K (μs)	$T_{1\rho }^{313K}$ (ms)	S CH
L26	20.91.3	0.25	0.76	3.10.1	0.420.02	13.51.3	10.3	1.9	1.30.1	0.440.02
V27	25.17.8	0.03	0.40	4.00.3	0.330.04	17.1–	3.8	2.8	1.40.1	0.310.02
V28	32.45.4	0.004	1.07	2.60.3	0.460.04	18.36.2	2.1	2.4	1.20.1	0.460.04
A29	21.71.3	0.18	0.76	3.50.1	0.440.02	17.51.3	1.7	1.4	1.70.1	0.460.02
A30	15.94.7	2.32	4.3	1.90.2	0.600.02	11.0–	62.9	1.1	1.20.1	0.600.07
S31	30.77.8	0.0086	1.1	2.30.3	0.500.02	13.67.2	15.0	2.8	0.90.1	0.400.02
I33	25.11.8	0.027	0.40	4.00.3	0.460.02	17.1–	4.4	3.2	1.40.1	0.310.02
G34	12.10.4	17.5	1.8	1.70.1	0.600.02	5.40.9	514	4.1	0.90.1	0.690.09
I35	22.21.3	0.16	0.79	3.10.1	0.420.02	12.01.3	18.0	1.9	1.30.1	0.420.02
L36	30.22.1	0.010	1.1	2.20.2	0.480.04	18.68.1	1.8	2.3	1.20.1	0.440.02
L38	20.69.9	0.18	0.48	2.90.2	0.350.02	9.6–	96.6	3.8	1.30.1	0.330.07
Mean	23.3±6.2		0.89±0.41	2.8±0.8		14.0±4.2		2.8±0.9	1.3±0.2

The amantadine-bound peptide has an average E_a of 23.3 kJ/mol, which is 66% larger than the average E_a of 14.0 kJ/mol for the apo peptide. The average experimental uncertainty of the E_a is 17%. The standard deviation of the E_a distributions is 6.2 kJ/mol for the bound peptide and 4.2 kJ/mol for the apo peptide. Figure 6 compares the E_a values of the apo and bound peptides for each Hα site. With the exception of G34, the E_a's are relatively uniform across all residues, given the experimental uncertainty. The small E_a distribution is consistent with the approximation that the main motional process driving T_1ρ relaxation is whole-body uniaxial diffusion rather than segmental motion. In addition, the E_a ratio between the bound and apo peptides for each site is relatively uniform, with an average ratio of 1.73 and a standard deviation of 0.35.

Figure 6.

Activation energy E_a (kJ/mol) extracted from the high-temperature slopes of the Hα $\ln \left(T_{1\rho }^{-1}\right)$ versus 1000/T curves. The amantadine-bound M2TMP (filled bars) has larger activation energies than the apo peptide (open bars).

To obtain the motional correlation times, we need the C-H order parameters and E_a (equations 7 and 9). The Cα-Hα order parameters (Table 1) are found to be similar between the apo and bound peptides, indicating that the amantadine-induced spectral line narrowing is not due to amplitude changes but due to rate changes. Using the high-temperature intercepts and S_CH, we calculated τ₀ and τ_313K for the apo and amantadine-bound M2TMP (Table 1). The bound peptide exhibits smaller τ₀ values, indicating higher attempt rates. As a result, the average τ_{313 K} is shorter for the bound peptide (0.89 ± 0.41 μs) than the apo peptide (2.8 ± 0.9 μs). The three-fold reduction of τ_{313 K} in the presence of amantadine is qualitatively consistent with the two-fold longer T_1ρ, since $T_{1\rho }^{-1}$ is linear with τ in the short τ regime (equation 5). The magnitude of τ_{313 K} is also reasonable, as it is similar to or shorter than the inverse of the spin lock field of 2.7 μs. In other words, the amantadine-bound M2TMP has a shorter correlation time than the characteristic time scale of the spin-lock field, thus alleviating exchange broadening, while the apo peptide correlation time is closer to the NMR time scale, thus giving rise to broader lines. Decreasing the temperature to 273 K increased the τ to 6.0 μs and 3.4 μs for the apo and bound peptides, respectively.

It is also interesting to examine the sidechain ¹H T_1ρ trends. Table S3 shows that the methyl proton T_1ρ's are much longer than the backbone Hα T_1ρ's and are relatively similar between the apo and bound peptides at high temperatures. Figure 7 shows representative $\ln \left(T_{1\rho }^{-1}\right)$ plots of two methyl groups and one methine Cβ site. The methyl protons have more similar high-temperature slopes between the apo and bound peptides, with an apparent activation energy difference of only 20% between the two states. The similarities can be attributed to three-site jumps of the methyl groups that are additional to the uniaxial diffusion, which reduce the dynamic difference between the apo and bound peptide. In comparison, the Cβ sites show more distinct activation energies between the apo and bound states, consistent with the Hα T_1ρ behavior.

Figure 7.

(a-c) $\ln \left(T_{1\rho }^{-1}\right)$ versus 1000/T curves for several M2TMP sidechains. (a) L26 methyl Cδ1/ Cδ2. (b) A30 Cβ and I33 Cγ2 methyl groups. (c) L36 Cβ. Apo data: open squares and dashed lines. Amantadine-bound data: filled squares and solid lines. (d) Activation energy (kJ/mol) of the methyl protons. The average E_a difference between the apo and bound peptides is ~20%.

Discussion

M2TMP uniaxial diffusion is the main motion driving T_1ρ relaxation

The motivation for this work is to quantify the motion of M2TMP that is responsible for exchange broadening of its NMR spectra in phosphocholine bilayers at physiological temperatures, and to understand the origin of amantadine-induced line narrowing.

The exchange broadening is due to microsecond motion of the peptide that interferes with ¹³C-¹H and ¹⁵N-¹H dipolar decoupling and cross polarization. We assign the motion to whole-body uniaxial rotational diffusion of the M2 helical bundle. The presence of this uniaxial diffusion has been previously shown based on the lineshapes of ²H quadrupolar spectra, ¹⁵N static powder spectra, and ¹⁵N-¹H and ¹³C-¹H dipolar couplings (Cady et al., 2007). Two lines of evidence support the assignment of the T_1ρ relaxation mechanism to this uniaxial diffusion. First, all eleven measured residues exhibit rapid T_1ρ relaxation at high temperatures, and all T_1ρ values are increased by amantadine. Such across-the-board effects can only result from a whole-body motion. Second, the two-dimensional Brownian diffusion theory of Saffman and Delbrück predicts a rate of 10⁵ s^–1 for the uniaxial diffusion of the M2 helical bundle, which agrees well with the time scale probed by the T_1ρ experiments.

The presence of whole-body motion does not exclude additional internal motions. Sidechain motions are certainly present, although they do not interfere with the extraction of the rates and activation energy of uniaxial diffusion from the backbone Hα T_1ρ data. The clearest manifestation of sidechain motions is the fact that the methyl protons have longer T_1ρ's than the backbone protons, and the methyl ¹H T_1ρ's are similar between the apo and bound peptides at high temperatures (Table S3). These observations are not surprising, since the fast methyl rotation on the nanosecond time scale pre-averages the dipolar second moment, and thus reduce the relaxation rates (equation 1). The local nature of the methyl rotation also makes the motion less sensitive to amantadine binding. The full T_1ρ dependence includes spectral densities at the ¹H and ¹³C Larmor frequencies, which are more relevant time scales for the methyl rotation. Thus, equation 1 does not apply fully to methyl groups. Since the main purpose of this study is to understand the motion that causes exchange broadening of the NMR spectra, but sidechain methyl ¹³C signals do not suffer from exchange broadening, we do not consider the combined motion of three-site jumps and uniaxial diffusion experienced by the methyl groups further. Another manifestation of possible segmental motions is the distribution of E_a. Specifically, the G34 E_a is two standard deviations lower than the average, suggesting the local motion at this residue (vide infra).

Correlation time of M2TMP diffusion and origin of spectral line narrowing by amantadine

The three-fold shorter correlation time of the amantadine-bound M2TMP (Table 1) explains the amantadine-induced line narrowing of the peptide spectra. The faster motional rates better avoid the intermediate time scale condition, thus alleviating line broadening. The faster diffusion rates result from the one to two orders of magnitude reduction of the prefactor τ₀, as obtained from the high-temperature intercepts of the $\ln \left(T_{1\rho }^{-1}\right)$ curves. The intercept depends both on τ₀ and the dipolar second moment (equation 9), whose exact magnitude differs somewhat between different theories, depending on how many spin interactions are included and whether the MAS or the static condition is operative (Fares et al., 2005, Huster et al., 2001, Mehring et al., 1983). However, the ratio of the intercepts between the apo and bound peptide depends only on τ₀. Thus, the relative size of τ₀ between the apo peptide (long τ₀) and the bound peptide (short τ₀) is unambiguous.

The shorter τ₀ of the amantadine-bound M2TMP indicates higher attempt rates of motion, which suggest that the M2 helices form better-packed tetramers in the presence of amantadine. Amantadine may interact with all four helices of the tetramer, thus serving as a non-covalent linker that brings the four helices together to form a more cohesive tetrameric bundle. A more cohesive helical bundle can diffuse faster, and would also have structurally and dynamically more homogeneous individual helices. This interpretation is consistent with the relative lack of correlation time distribution for the bound peptide (vide infra), as manifested by the sharpness of the T_1ρ minima, and is also consistent with disulfide cross linking data that indicate increased tetramer association in the presence of amantadine (Cristian et al., 2003). Thus, the reduced τ₀ of the bound M2TMP suggests that amantadine is centrally located in the pore of the channel, shared by all four helices, consistent with the binding site seen in a recent crystal structure (Stouffer et al., 2008). In comparison, a solution NMR study (Schnell and Chou, 2008) found four rimantadine molecules at the lipid-facing surface of each channel. It is difficult to imagine how this surface binding motif would homogenize the peptide conformation and speed up its motion.

A question that is beyond the scope of the current study is the correlation time distribution of apo M2TMP, which is manifested by the broad T_1ρ minima of the apo peptide. The τ distribution suggests that without amantadine, the M2 helical bundles are floppier, with more internal degrees of freedom, and may exhibit dynamic heterogeneities between different tetramers. Such dynamic heterogeneity may be functionally relevant, as it may allow the apo peptide to adopt appropriate conformations to achieve its many functions, including channel activation, gating, and inhibition.

The activation energy of M2TMP uniaxial diffusion is related to membrane viscosity

A basic assumption in our dynamic analysis is that the rotational diffusion of a membrane protein in lipid bilayers can be considered an activated process that follows an Arrhenius law (equation 7). The linearity of the observed $\ln \left(T_{1\rho }^{-1}\right)$ with respect to 1000/T at high temperatures (Figure 5) validates this assumption, but it is of interest to consider the physical basis for the activated diffusion. Membrane protein diffusion in lipid bilayers requires the availability of free volume in the vicinity of the protein, which is achieved by discrete hopping of the lipid molecules. Thus, activated lateral and rotational diffusion of membrane proteins has its molecular origin in the free volume theory of liquids (Cohen and Turbill, 1959, Galla et al., 1979). Considered in this light, the activation energy essentially reflects the macroscopic viscosity of the membrane. Higher activation energies indicate higher viscosities. Thus, the higher E_a of the amantadine-bound peptide indicates that excess amantadine increases the membrane viscosity. If this is true, then the lipid ¹H T_1ρ values should be affected by the excess amantadine outside the channel in the bilayer, in the same manner as the protein.

Examination of several resolved lipid ¹³C signals confirms that there is indeed an amantadine-induced increase of the lipid E_a. Figure 8 shows the $\ln \left(T_{1\rho }^{-1}\right)$ curves of the lipid glycerol G3 and the acyl chain C2 signals. The excess-amantadine-containing membrane clearly has larger slopes than the amantadine-free membrane, similar to the peptide T_1ρ behavior. The amantadine-bound samples in our experiments contain 8-fold molar excess of amantadine to the peptide, or 32-fold excess amantadine to the channel. The excess amantadine partitions into the bilayer (Subczynski et al., 1998, Wang et al., 2004). Paramagnetic relaxation enhancement NMR data indicate that amantadine is located at the interfacial region of the DMPC bilayer with the amine group pointing to the surface (Li et al., 2008). This depth and orientation are consistent with the amphipathic nature of amantadine, with its hydrophobic adamantane cage close the hydrocarbon core and its polar ammonium moiety pointing to the polar region of the bilayer.

Figure 8.

$\ln \left(T_{1\rho }^{-1}\right)$ versus 1000/T curves for several lipid ¹³C signals in M2TMP-containing DLPC bilayers. (a) Glycerol backbone G3. (b) Acyl chain C2. Apo data: open squares and dashed lines; Amantadine-bound data: filled squares and solid lines.

Our recently measured lipid ¹³C T₂ relaxation times at 313 K in peptide-free DLPC bilayers showed no discernible difference between amantadine-containing and amantadine-free bilayers (Cady et al., 2009), in contrast to the current lipid ¹H T_1ρ data. This discrepancy is likely due to the presence of the peptide in the current measurements but the lack of the peptide in the previous T₂ experiments. Membrane viscosity is a function of molecular crowding: peptide-containing bilayers have much smaller free volumes for amantadine than pure lipid bilayers, thus amantadine may cause detectable fluidity changes only in M2-containing bilayers.

The viscosity origin of the activation energy of M2TMP diffusion also explains the asymmetric slope of the $\ln \left(T_{1\rho }^{-1}\right)$ curves on the two sides of the T_1ρ minimum. Both the apo and bound peptides have steeper slopes or larger apparent activation energies on the low temperature side. Since this T_1ρ minimum is associated with phase transition of the DLPC bilayer, the slope increase at low temperature is caused by the significant viscosity increase of the gel-phase membrane compared to the liquid-crystalline phase. Thus, the M2TMP rotational diffusion is not a single motional process above and below the lipid phase transition temperature, in contrast to most other motions that have been characterized by NMR (Douglass and Jones, 1966, Rothwell and Waugh, 1981).

The viscosity origin of the activation energy may also partly explain the E_a distribution among the residues. Since a perfectly rigid-body motion should have a single E_a, the observed E_a distribution beyond the experimental uncertainty must reflect additional motions, which may result from varying membrane viscosity across the bilayer thickness. The abnormally low E_a of G34 may then be partly due to the location of G34 at the center of the TM helix and thus at the center of the bilayer, which has the lowest viscosity due to large-amplitude motions of the lipid chain ends. While the exact nature of the local G34 motion is unknown, the conclusion of increased conformational flexibility is consistent with a large number of NMR parameters for this site: its ¹⁵N anisotropic chemical shifts, N-H dipolar coupling (Hu et al., 2007), and ¹⁵N isotropic chemical shifts were all found to change with drug binding (Cady et al., 2009, Wang et al., 2009) and membrane composition (Luo et al., 2009).

The lipid-mediated influences of excess amantadine on the diffusion dynamics of M2TMP do not change the previous conclusion that the protein-bound amantadine causes site-specific conformational changes through direct amantadine-protein interactions. The structural changes are manifested as chemical shift perturbations that are highly site specific, with residues S31, G34, and V28 exhibiting large chemical shift perturbations while other residues showing little changes (Cady and Hong, 2008, Cady et al., 2009).

Conclusion

The temperature-dependent ¹H T_1ρ relaxation times shown here indicate that the uniaxial diffusion of the M2TMP in liquid-crystalline DLPC bilayers causes efficient ¹H T_1ρ relaxation, and the diffusion rates are increased by amantadine through an increase in the attempt frequencies. The average motional correlation time at 313 K is 0.89 μs for the bound peptide and 2.8 μs for the apo peptide. The faster diffusion of the bound peptide suggests that amantadine induces more homogeneous and better-packed M2TMP tetramers by coordinating with all four helices. Thus, the well documented amantadine-induced NMR line narrowing is due to suppression of the intermediate time scale broadening.

From the linear relation of $\ln \left(T_{1\rho }^{-1}\right)$ with 1/T at high temperature, we extracted the activation energy of the M2 uniaxial diffusion. The average E_a is 23.3 kJ/mol for the bound peptide and 14.0 kJ/mol for the apo peptide. The higher E_a of the bound peptide is attributed to larger membrane viscosity by excess amantadine, which is confirmed by the lipid T_1ρ data.

Similar exchange broadening of the apo protein and line narrowing of the bound protein have also been reported for solution NMR spectra of M2(18-60) in DHPC micelles (Schnell and Chou, 2008). There, the exchange broadening of the apo protein spectra was alleviated by the addition of 40 mM rimantadine. At 53-fold molar excess to the protein (0.75 mM), the excess rimantadine is expected to significantly increase the viscosity of the micelle interior, which may affect the dynamics of the micelle-bound rimantadine in a way that facilitates the observation of its NOEs with the protein.

The present study illustrates the rich information that can be obtained from temperature-dependent relaxation studies of membrane proteins. Compared to most relaxation NMR studies so far, which were targeted to either small molecules with a single motion (Rothwell and Waugh, 1981) or macromolecules with a well-defined local motion (Batchelder et al., 1982), the present study examines the rates and energetics of the global motion of a membrane protein (Reuther et al., 2006). It gives a glimpse into the energetic driving force behind membrane protein uniaxial diffusion, which is not easily obtained by other biophysical techniques (Gennis, 1989).