INTRODUCTION

TOP ABSTRACT INTRODUCTION THEORY MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

NMR relaxation and fluorescence polarization anisotropy decay (FAD) are two important experimental methods to study the dynamics of biomolecules. The results from the two methods on protein dynamics have been compared for a number of proteins listed in Table 1. In several cases the global rotational correlation time deviates significantly between the two methods. In most cases the correlation time observed by fluorescence is shorter than the correlation time observed by NMR. The details of this table will be discussed later. A fraction of the observed discrepancies between the NMR data and the fluorescence data can be explained by the typical difference in concentration between NMR and fluorescence studies.

View this table: [in this window] [in a new window]   TABLE 1   Comparison of rotational correlation times  and corresponding hydrodynamic volumes Vh estimated from NMR and FAD data

Because FAD and NMR relaxation are about the only two experimental approaches to detailed studies of molecular dynamics, it is important to try to reconcile the results and find out where the results from the two methods deviate from each other and become less reliable.

Motilin is a gastrointestinal peptide hormone with 22 amino acids, among them the single Tyr⁷ fluorophore. In our previous study of motilin dynamics (Allard et al., 1995; Jarvet et al., 1996) we found that the overall rotational correlation time of motilin is ~5 ns at 20°C and 3 ns at 35°C in 30% hexafluoro-2-propanol (HFP), evaluated by spectral density mapping and with Leu¹⁰ -carbon as the probe for the relaxation measurements. These results were significantly different from the value (2.2 ns at 20°C in 30% HFP) measured by FAD on the single Tyr residue of the peptide.

In the present study we have continued the studies of the motilin peptide and have looked into various possible sources of systematic errors for the dynamic information from NMR and FAD. Typical peptide concentrations lie in the millimolar range for NMR and in the micromolar range for FAD. Here we have used the same sample in both experiments to eliminate this source of error. In addition, we have placed the ¹³C labels in the -positions of the tyrosine ring to probe the same region of the molecule in both the NMR and the FAD experiment. The observations show that it is possible to obtain very similar results reflecting spectral densities by fluorescence and NMR and suggest that different systematic errors may appear in the interpretation of the data when dynamic models are applied. In the course of the study we have also applied a new version of the spectral density mapping method, where only the most accurately and precisely determined relaxation rates measured at different magnetic fields are used for the determination of spectral densities.

	THEORY

TOP ABSTRACT INTRODUCTION THEORY MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

Chemical shift anisotropy and dipole-dipole mechanisms

For protonated aromatic ring carbons, both dipole-dipole (DD) and chemical shift anisotropy (CSA) mechanisms contribute to relaxation. The dipolar interaction constant is a function of distance and in the case of two half-spins I and S, it has the following value (Peng and Wagner, 1992; Allard et al., 1998):

(1)

where µ₀/4 is the conversion factor to SI system units, h is Planck's constant, and r_IS is the internuclear distance between spins I and S. The CSA interaction constant is a function of the polarizing magnetic field B₀:

(2)

where  =    is the difference between the parallel and orthogonal components of an axially symmetric CSA tensor.

A third possible relaxation mechanism is cross-correlation between the mentioned mechanisms. The interaction constant is a product of DD and CSA interaction constants and depends also on the angle between the CSA tensor and the internuclear vector. Although one of the interactions may cause a negligible auto-relaxation rate, the product of the two interaction constants may still be large. Special measures may have to be taken to suppress this interaction, as will be discussed in the Materials and Methods section dealing with the pulse sequences (Palmer et al., 1992).

The CSA mechanism interaction constant has been determined for the ¹³C-H vector on the tyrosine ring by experiments that yield the field dependence of longitudinal relaxation (Damberg et al., 1999). The CSA parameter _eff was 156 ppm, close to the value reported from solid-state NMR studies (Frydman et al., 1992). The dipolar interaction constant was calculated with a C-H distance taken from a neutron diffraction study (Frey et al., 1973). With a correction for thermal vibrations, the effective length of the C-H vector is 1.09 Å, which is the fixed value used in the present study.

Spectral density function

To analyze FAD data and NMR relaxation rates in terms of dynamics parameters, a model of mobility has to be selected. The isotropic rotation model, described by a single correlation time _m, is inadequate for describing the dynamics of the tyrosine ring in the peptide. A widely used model in NMR is based on the so-called model-free approach (Lipari and Szabo, 1982). The model may be considered as a description of dynamics assuming two independent motional processes with time constants _m and _e and a generalized order parameter S².

In fluorescence a corresponding approximation is to analyze the FAD with two exponential components with time constants ₁ and ₂ and amplitudes A₁ and A₂. One can directly compare the parameters obtained by the two methods.

The expression for the spectral density obtained from the model-free approach is the sum of two Lorentzian components:

(3)

The FAD function can be expressed as follows:

(4)

In both cases, the longer time constant (_m or ₁) is assigned to the overall rotational correlation time. The correlation time for local motion in the model-free approach is _e, related to _eff as follows:  =  + . The ratio A₁/(A₁ + A₂) of the fluorescence anisotropy amplitudes corresponds to an order parameter. At the outset one would expect the same time constants to be observed in the NMR and FAD experiments, but not necessarily with the same relative amplitudes because of the different orientations of the interaction vectors relative to the tyrosine ring.

Spectral density mapping

To carry out full spectral density mapping as originally suggested by Peng and Wagner (1992), six dipolar relaxation rates have to be measured: the carbon longitudinal relaxation rate R_C(C_z), the carbon in-phase transverse relaxation rate R_C(C_x), the carbon anti-phase transverse relaxation rate R_CH(2H_zC_x), the relaxation rate of longitudinal two-spin order R_CH(2H_zC_z), the proton longitudinal relaxation rate R_H(H_z), and the heteronuclear cross-relaxation rate _CH. The proton relaxation rate _HH accounts for relaxation caused by other protons. The relation between measured relaxation rates and spectral densities is expressed by the matrix:

(5)

For simplicity, the interaction coefficients d and c are introduced, where d = [(1/6)A]² and c = [(1/)A]². The values of the constants used in the expressions are _H = 26.753 × 10¹⁰ rad s¹ T¹, _C = 6.728 × 10¹⁰ rad s¹ T¹, and h = 6.62 × 10³⁴ J s. For a C-H bond length r_CH = 1.09 Å, one obtains d = 5.37 × 10⁹ rad² s² and c = 3.22 × 10⁹ rad² s² for  = 156 ppm at the magnetic field 9.36 T.

The inverse of Eq. 5 describes how the spectral densities are calculated from the measured relaxation rates. Errors in the measured rates propagate unequally into the determined spectral densities. Fig. 1 illustrates this for the simple case of isotropic rotation with a correlation time _m = 1 ns and a 1% error in all of the measured rates. The propagated relative error is largest for J(_H) (23%). In the simplified version of spectral density mapping (SDM) to be described we will exclude this value from the spectral density map.

View larger version (12K): [in this window] [in a new window]   FIGURE 1   Error propagation for SDM. The solid line corresponds to isotropic rotation with a correlation time of 1.0 ns. Synthetic relaxation data were calculated using this spectral density function, and spectral density values were calculated using Eq. 1. Spectral density points are shown along with error bars calculated assuming a 1% error in relaxation rates. Relaxation caused by other protons, HH, was fixed to 1 s1.

Simplified SDM

When the spectral density at the proton frequency, J(_H), is not included in the SDM, one rate can also be omitted from the measurements. For reasons described below, we excluded the carbon anti-phase transverse relaxation rate from the relations. The spectral density at the proton Larmor frequency J(_H) may now be approximated by J(_H) = [J(_H  C) + J(_H + _C)]/2. The six equations described by Eq. 5 may then be simplified to five equations. The simplified spectral density matrix is obtained as follows:

(6)

By inverting the matrix of Eq. 6, the following expression is obtained for spectral densities:

(7)

Notice that there is a significant difference between this equation and those used for reduced SDM, often used when ¹⁵N relaxation rates are measured. For reduced SDM, the ¹⁵N longitudinal and transverse relaxation and the steady-state {¹H}-¹⁵N nuclear Overhauser enhancement (NOE) are measured, and from these rates J(0), J(_N), and J(0.870_H) are evaluated (Farrow et al., 1995; Ishima and Nagayama, 1995).

Internuclear distance

The interaction constants determine the area under the spectral density function. The dipolar interaction depends on the inverse of the sixth power of the internuclear distance of the CH bond in the tyrosine ring. Therefore it is important that an accurate distance value is used when relaxation rates are analyzed. The value obtained from neutron diffraction studies (1.08 Å (Frey et al., 1973)) has to be corrected for rapid thermal motions (internal motions much faster than the Larmor frequency in NMR). The resulting value of 1.09 Å is generally used, also in the present study.

The C-H bond lengths for the two distinct ions in calcium formate were determined to be 1.130 and 1.126 Å by dipolar switching-angle sample spinning NMR in the solid state without considering vibrations (Terao et al., 1986). Anisotropic out-of-plane vibrations (librations) with an amplitude of 12-15° could account for this increase of the effective bond length (Nakai et al., 1989). For the C-H bond in proteins it was observed already in the pioneering relaxation experiments on alumichrome (Llinas et al., 1977) and on lysozyme (Dill and Allerhand, 1979) that longer effective distances of 1.11 Å and 1.15 Å, respectively, will improve the fit to the experimentally measured ¹³C relaxation rates. The average bond length of C-H was recently determined with high accuracy for ubiquitin in a dilute liquid-crystalline phase (Ottiger and Bax, 1998) and found to be 1.117 ± 0.007 Å. This is considerably longer than the equilibrium or average internuclear distances derived from ab initio calculations, neutron diffraction, or microwave spectroscopy. This longer distance value is in excellent agreement with the effective internuclear distance determined by treating the internuclear distance as an adjustable parameter when fitting the model-free model to spectral density data points, obtained by SDM for the C-H bond of Leu¹⁰ in motilin (Jarvet et al., 1996). The longer effective bond length has also been reproduced by quantum chemical methods by taking vibrations into account (Case, 1999).

The effective bond lengths in L-tyrosine-HCl were recently determined by solid-state NMR (De Paul et al., 2000). The effective bond lengths of the two nonequivalent carbon-proton pairs in ortho position were found to be 1.12 ± 0.02 Å and 1.15 ± 0.05 Å, respectively. Those distances are considerably longer than the distances estimated by neutron diffraction (Frey et al., 1973). An increase of the effective internuclear distance from 1.09 to 1.12 Å corresponds to an 18% decrease of the evaluated spectral densities. How the internuclear distance parameter affects the evaluated dynamic parameters will be discussed later. It is important to note that bending vibrations (librations) lead to an increase of the effective internuclear distance. Stretching vibrations in the harmonic approximation result in a decrease in the effective internuclear distance (Lipari and Szabo, 1982).

	MATERIALS AND METHODS

TOP ABSTRACT INTRODUCTION THEORY MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

Sample

The motilin sample is described in detail in Damberg et al. (1999). The peptide contained two specific ¹³C labels in the -positions of the single tyrosine residue (Fig. 2). The peptide was 5 mM in 30% hexafluoroisopropanol-d/10% D₂O/60% H₂O. All experiments were performed at 35°C ± 0.1°C. The temperature was measured with a thermocouple thermometer directly inserted into the NMR sample tube.

View larger version (14K): [in this window] [in a new window]   FIGURE 2   The tyrosine residue with atom definitions according to IUPAC recommendations (Markley et al., 1998). The fluorescence transition moment for the 1Lb transition makes an ~30° angle with the NMR dipolar C-H vector, 13C-labeled (*) in 1, 2 for the present study.

NMR measurements

NMR relaxation rates were measured with Varian Inova spectrometers equipped with inverse detection probe heads, and sensitivity-enhanced pulse sequences were used. Delay lists for relaxation experiments consisted of 10 linearly spaced delays starting from zero and covered up to two time constants. Good solvent suppression was achieved, and no baseline corrections were needed.

Translational diffusion coefficients were measured by the longitudinal eddy-current delay pulsed field gradient pulse sequence (Gibbs and Johnson, 1991). The gradient strength was calibrated and the attenuation curves were evaluated as suggested in Damberg et al. (2001). The gradient pulses had a duration of 5 ms, and the strength of the gradient pulses was varied between 0 and 0.3 T/m in 30 steps. The spacing between the diffusion encoding gradient pulses was 0.2 s. The solvent signal was suppressed by 2 s of presaturation during the 5-s recycling delay.

The NMR longitudinal relaxation rates R_C(C_z) and R_CH(2H_zC_z), and the steady-state {¹H}-¹³C NOE were measured as described previously (Dayie and Wagner, 1994).

Transverse inphase relaxation rate R_C(C_x) and anti-phase rate R_CH(2H_zC_x)

The ¹³C transverse relaxation rate R_C(C_x) was measured using an on-resonance spin lock. Proton inversion pulses every 500 µs during the relaxation delay were used to suppress the CSA-DD cross-correlation. The anti-phase rate R_CH(2H_zC_x) was first measured by the previously described pulse sequence (Dayie and Wagner, 1994). A decay curve that was clearly not a single-exponential decay was obtained. An initial approximation of the apparent decay rate was found to be 19 s¹, which is twice as fast as the expected rate. The method of Loria et al. (1999), i.e. an ordinary spin echo with a long delay between refocusing pulses, is supposed to yield a single-exponential decay curve. Its rate should be the average of the anti-phase and in-phase relaxation rates. This method indeed yielded a single-exponential decay curve, but the back-calculated anti-phase rate was still too fast by a factor of two. Others have also reported serious problems in measuring the anti-phase relaxation rates accurately (Markus et al., 1996). In the present case, the high rate may be related to the fact that both -carbons, separated by only one carbon atom in the tyrosine ring, are labeled by ¹³C. Because of the problems with the anti-phase rate, we decided to exclude it from the SDM and used the simplified version based on Eqs. 6 and 7.

Proton longitudinal relaxation rate R_H(H_z)

An important experimental development for SDM is the pulse sequence for measuring proton auto-relaxation rate without interference from other protons. The pulse sequence is previously illustrated by Fig. 2 in the study by Damberg et al. (1999). In this experiment, cross-relaxation from other protons (spin diffusion) is eliminated by performing selective pulses in accordance with the suggestions by Norwood (1996, 1997). The experiments are performed in an add/subtract manner, with selective proton inversion in the middle of the of the relaxation delay. With this technique one observes a single-exponential decay with a time constant of ¹H T₁.

Fluorescence measurements

Time-resolved fluorescence experiments were performed using the time-correlated single-photon counting method. A laser system, consisting of a mode-locked argon ion laser pumping a cavity-dumped rhodamine 6G dye laser, including frequency doubling, was used for excitation at 286 nm. Such a long wavelength was chosen to have a sufficiently low absorbance of the tyrosine fluorophore, because, to measure under identical conditions with the NMR sample, a high concentration (5 mM) of motilin was used. The sample temperature was controlled with a thermostated water bath. The temperature was measured with a thermocouple thermometer, directly inserted into the sample, and was adjusted to 35°C ± 0.1°C in all experiments.

Fluorescence emission data were collected in four different ways, alternating for 20 s each: laser light (for the response function), dark current, and perpendicular and parallel polarized fluorescence components, as previously described (Rigler et al., 1985; MacKerell et al., 1987). This cycle was repeated 10 times, resulting in 200 s of data collection for each signal. The data were analyzed in two steps as described previously (Kawato et al., 1977; Kouyama et al., 1989). First the isotropic fluorescence decay S(t) = I + 2I was fitted, using deconvolution with the measured response function. In the second step the fluorescence decay parameters were fixed, and the difference D(t) = I  I of the parallel and perpendicular fluorescence components was fitted, again using deconvolution. The deconvoluted theoretical fit function for this difference is d(t) = r(t)s(t), where r(t) is FAD and s(t) is isotropic fluorescence decay, both corresponding to delta function excitation. For visual display of the fitting results, the fluorescence polarization anisotropy decay curves were calculated also directly from the experimental data as (I  I)/(I + 2I). The rotational correlation times were evaluated under the assumption that each rotational component is associated with all fluorescence decay components.

	RESULTS

TOP ABSTRACT INTRODUCTION THEORY MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

NMR relaxation rate measurements

NMR relaxation rates of the selectively isotope labeled ¹³C¹-H and ¹³C²-H vectors in the aromatic ring of tyrosine in the motilin peptide were measured at four magnetic field strengths of 9.36, 11.74, 14.09, and 18.79 T, corresponding to proton frequencies of 400, 500, 600, and 800 MHz, respectively. The relaxation rates needed for full SDM are the carbon longitudinal relaxation rate R_C(C_z), the carbon in-phase transverse relaxation rate R_C(C_x), the relaxation rate of longitudinal two-spin order R_CH(2H_zC_z), the relaxation rate of carbon anti-phase coherence R_CH(H_zC_x), and the proton longitudinal relaxation rate R_H(H_z). The cross-relaxation rate _CH between proton and carbon was calculated from R_C(C_z) and the steady-state {¹H}-¹³C NOE using the relation:

(8)

The pulse sequences were based on those originally described in Dayie and Wagner (1994), except for the proton longitudinal relaxation rate. The accuracy of the measurement of ¹H T₁ is significantly increased by minimizing the interference from other protons (Damberg et al., 1999). This was achieved by a pulse sequence described in Materials and Methods.

The measured relaxation curves for the motilin peptide, 5 mM in concentration and in 30% HFP at 35°C were found to be single exponentials, except for the carbon anti-phase rate. This relaxation curve had the appearance of a double exponential, when it was measured using the original pulse sequence (Dayie and Wagner, 1994). When using the recently proposed improved pulse sequence (Loria et al., 1999), the curve became monoexponential in character, but still the rate was too fast to be consistent with the other rates in the full SDM. Despite various experimental efforts, including selective saturation of the protons in the -position, we were never confident that the anti-phase rate could be measured with any certainty. For this reason we decided to omit it from the SDM and instead use the simplified version (Eq. 7). Table 2 shows the six measured relaxation rates at the four magnetic fields.

View this table: [in this window] [in a new window]   TABLE 2   Relaxation rates of -carbon C-H vector of Tyr7 in the peptide hormone motilin in 30% HFP at 35°C measured at four magnetic fields

The experimental errors in the relaxation rates (with the exception of the anti-phase rate that was omitted from the SDM) were estimated from the field dependences (Fig. 3). As the variation in the field strength is relatively small, a factor of only two, second-order polynomials were used to approximate the field dependences. The residuals were then used to estimate the measurement precision of the individual rates as the square root of the sum of squared residuals divided by the number of degrees of freedom. The results are included in Table 2. This approach is reasonable when the measurement precision is approximately equal at all fields. In practice, it has the advantage of including temperature miscalibration errors in the estimates of the imprecision.

View larger version (13K): [in this window] [in a new window]   FIGURE 3   The relaxation rates as functions of magnetic field for the 13C-labeled carbon-proton vector in -position of Tyr7 in motilin in 30% (v/v) HFP at 35°C. The rates were measured at 9.39, 11.74, 14.09, and 18.79 T. The rates used for SDM are the carbon longitudinal relaxation rate RC(Cz) (), the carbon in-phase transverse relaxation rate RC(Cx) (), the relaxation rate of longitudinal two-spin order RCH(2HzCz) (), the proton longitudinal relaxation rate RH(Hz) (), and the heteronuclear cross-relaxation rate CH (). Curves connecting the points represent the best fit of relaxation rates using second-order polynomials.

The results presented in Fig. 3 show that the precision is generally very high in the measured rates. The least precise rate appears to be the proton longitudinal rate, which shows some very small deviations from a smooth second-order polynomial. The relaxation rates presented in Table 2 were used to calculate spectral densities according to Eq. 7, describing the simplified SDM method. The transverse anti-phase rates were not included in the calculation, for reasons stated above. The results in terms of spectral densities J(0), J(_C), J(_H  C), and J(_H + _C), measured at the four magnetic fields, are shown in Table 3. The values calculated for J(_H  C) are not included in Fig. 4. Apart from J(_H), this spectral density has the highest propagated error of the spectral densities (Fig. 1). The values of J(0) evaluated from the results at the different magnetic fields showed some variations (Table 3), which will be further treated below. The other spectral densities seem to fall on a relatively smooth curve. Error bars show the propagated spread of the calculated errors in the spectral densities from the estimated errors in the measured relaxation rates. These calculations were done assuming a fixed internuclear distance of 1.09 Å and an effective CSA of 156 ppm (Damberg et al., 1999).

View larger version (10K): [in this window] [in a new window]   FIGURE 4   Spectral density values for the 13C-labeled carbon-proton vector in -position of Tyr7 in motilin at 35°C in 30% (v/v) HFP at different frequencies. The spectral density values were calculated from experimental relaxation rates measured at four magnetic fields using rCH = 1.09 Å. The sampling frequencies are at zero frequency; at 100, 125, 150, and 200 MHz for J(C); and at 500, 625, 750, and 1000 MHz for J(H + C). The zero frequency spectral density is represented by the average of the four values estimated for each field, with the uncertainty estimated from the standard deviation of the four values. (A) The solid curve represents the best fit to a model-free spectral density function with m = 1.7 ns, S2 = 0.5, and e = 60 ps. The dashed curve represents the fluorescence best fit to a two-component anisotropy decay function with corresponding model-free approach spectral density function parameters m = 1.7 ns, S2 = 0.47, and e = 54 ps. (B) The two three-component models of molecular dynamics are shown together with the experimental spectral densities derived from NMR. The solid curve shows the spectraldensity function corresponding to the best-fitting three-component model (Eq. 10) to the NMR data with the following parameters: A1 = 0.36, 1 = 2.1 ns, A2 = 0.22, 2 = 0.59 ns, A3 = (1  A1  A2) = 0.42, and 3 = 0.037 ns. The dashed curve represents the three-component model obtained from fluorescence (Eq. 9) by fitting to the FAD data with the following parameters: A1 = 0.33, 1 = 2.2 ns, A2 = 0.17, 2 = 0.42 ns, A3 = (1  A1  A2) = 0.50, and 3 = 0.029 ns.

The spectral densities are truly model-free parameters of the dynamics of a system. However, to obtain a more physical picture of the dynamics, a dynamic model has to be applied to the data. A simple three-parameter model, based on the assumption of two uncorrelated time constants, is provided by the model-free approach (Lipari and Szabo, 1982), as described in Eq. 3. The model was fitted to the spectral densities obtained by simplified SDM (SSDM), where the penalty function included weights according to the propagated error. The result is shown as the full curve in Fig. 4 A. The corresponding parameters (an order parameter and two correlation times) are shown in Table 4. In a dynamic interpretation, the longer rotational correlation time should correspond to the overall rotational motion of the molecule.

Exchange contributions to transverse relaxation

To search for possible evidence of the presence of a slow exchange process, the spin-lock field dependence of the carbon transverse auto-relaxation rate R_C(C_x), i.e., R₁, was studied. The R₁ rate was measured at varying spin-lock power at 11.7 T. No systematic decrease in the rate with increasing spin-lock power was detectable (data not shown) in the range studied (20 Hz to 4.5 kHz). This is an indication of the absence of slow exchange in the kilohertz domain. At the highest spin-lock power it proved essential to use a long, i.e., 15 s, recovery time between transients to maintain the temperature at 35°C. With shorter recovery times, a false decrease in the relaxation rate was observed, concomitant with small phase and chemical shift changes probably caused by heating of both the sample and the RF-coil and/or amplifier power drop.

Contributions to the transverse auto-relaxation from conformational exchange faster than what can be observed in the spin-lock experiments can be detected as an increase of the apparent spectral density at zero frequency, J(0), as a function of the static magnetic field B₀ (Peng and Wagner, 1995). They derive the following relation: J(0)^apparent = J(0)^true + 3R_ex/(2c + 6d) in the fast exchange limit. Here c and d have the same meaning as above and the conformational exchange rate R_ex = (_CB₀)² for fast exchange and on-resonance spin-lock, where  is a proportionality constant.

If an exchange term is included in the spectral density model we obtain a slightly better fit of the spectral density function, but an F-test using the reduced ² revealed that the improvement is not significant in the statistical sense. Fig. 5 shows the fitted spectral density functions with and without an assumed exchange term. Table 4 also includes the parameters obtained with the model-free approach when the exchange term is included in the fitting. In terms of parameters evaluated from the model-free approach for the two cases we found that the order parameter remained unchanged, whereas the rotational correlation time _m decreased from 1.7 to 1.5 ns (Table 4). The question of exchange contribution to R₂ illustrates a remaining systematic error in the measurements, which leaves the spectral density at zero frequency with a significant uncertainty and mainly affects the estimated _m. This is despite the fact that extreme care was taken to ensure precision. It should be pointed out that these deliberations are not even possible to make, unless the relaxation is measured at several different fields. We would probably have needed measurements using at least one or two even lower fields to be able to conclude with any certainty about the absence or presence of conformational exchange contributions to the dephasing of transverse magnetization.

View larger version (17K): [in this window] [in a new window]   FIGURE 5   Probing the existence of conformational exchange contributions to the transverse auto-relaxation and, consequently, J(0)apparent. Two graphs on planes at an angle with one another are shown together to indicate that they have a common intercept. The J(0)apparent as a function of B is shown in the plane directed inwards and the J() as a function of /2 in the plane directed outwards. The solid curves represent the model-free approach when the conformational exchange is assumed to be negligible; i.e.,  = 0. The dashed curves represent the model-free approach when contributions from fast conformational exchange is treated as an adjustable parameter.

Fluorescence polarization anisotropy decay

The intrinsic fluorophore, the single tyrosine of the motilin peptide, was used to probe the rotational motion. The sample was identical in terms of concentration and other conditions to that of the NMR studies. The temperature was carefully calibrated and measured to coincide with the temperature used in the NMR studies. The isotropic fluorescence decay, which is a measure of the fluorescence lifetime, was fitted with a sum of three exponential components with amplitudes F_i and lifetimes _i. The best-fitting parameters were F₁ = 0.00292, ₁ = 4.03 ns; F₂ = 0.0123, ₂ = 1.33 ns; and F₃ = 0.00439, ₃ = 0.28 ns.

The fluorescence anisotropy was evaluated by fitting a model with two exponential components (Eq. 4) to the data. The result is shown in Fig. 6, where also the residuals are included. The best-fitting values are A₁ = 0.13, ₁ = 1.7 ns, A₂ = 0.14, and ₂ = 0.054 ns. The sum of the amplitudes, A₁ and A₂, deviates from the theoretical value of 2/5, which is expected for parallel excitation and emission dipole moments. The amplitudes were rescaled so that their sum becomes unity for easier comparison with the NMR results and are included in Table 4. The result agrees reasonably well with the result of a previous fluorescence study of motilin at a lower concentration (0.1 mM in 30% HFP and at 35°C by linear interpolation between 20°C and 40°C), where the longer rotational correlation time was 1.2 ns (Backlund et al., 1995). The new fluorescence anisotropy parameters were used to calculate a spectral density function according to Eq. 3, assuming that the order parameter S² can be taken as A₁/(A₁ + A₂). The spectral density function obtained from the fluorescence data is shown as the dashed curve in Fig. 4 A, and the corresponding parameters are included in Table 4. Evidently, the spectral density curve and the corresponding parameters agree very well with the data obtained from NMR on the same system.

View larger version (29K): [in this window] [in a new window]   FIGURE 6   FAD of the side chain of Tyr7 in 5 mM motilin at 35°C in 30% (v/v) HFP. Experimental data and a fitted two-component curve are shown. The residuals show the weighted differences between experimentally determined I  I and the values obtained for the fitted model as described previously (Kawato et al., 1977; Kouyama et al., 1989). The two-component model had the parameters shown in Table 4. The fluorescence lifetimes were evaluated from the isotropic fluorescence decay (I + 2I) and were as follows: F1 = 0.00292, 1 = 4.03 ns; F2 = 0.0123, 2 = 1.33 ns; and F3 = 0.00439, 3 = 0.28 ns. Data acquisition started before the laser pulse, and the zero time point was determined during fitting.

More complex dynamic models

The six parameters of a three-component model (Eq. 9) were fitted to the FAD data:

(9)

The best-fitting values are A₁ = 0.10, ₁ = 2.2 ns, A₂ = 0.050, ₂ = 0.42 ns, A₃ = 0.15, and ₃ = 0.029 ns. Also for this model the sum of the amplitudes is less than the theoretical value of 2/5. The amplitudes were rescaled so that their sum becomes unity. The result is included in Table 4. The small bulge visible in the residuals at the beginning of the curve when fitting the two-component model to the FAD data (Fig. 6) disappears when the three-component model is used.

A careful inspection of the fit of the model-free spectral density function to the SSDM data points (Fig. 4 A) reveals certain deviations between the model and the data. The spectral density function corresponding to a three-component model (Eq. 10) was fitted to the spectral density data points:

(10)

The sum of the amplitudes was scaled to be unity. The results are shown in Figs. 4 B and 5 and in Table 4. This three-component model is analogous to the three-step model of Clore et al. (1990), but the parameters of the above three-component model (Eq. 10) were used for easier comparison with the FAD results. The three components are shown in Fig. 7. One can see that the fastest component is very close to constant over the entire frequency range studied. This implies that the time constant, and the amplitude of this component should be considered as effective parameters only, and assigning a specific physical meaning to them should only be done with great caution. If the term corresponding to the fastest motions in Eq. 10 makes a negligible contribution to the spectral densities at all frequencies within the studied range, this term can be omitted when fitting to SDM data. The resulting spectral density function resembles the model-free spectral density function, if one would allow the sum of the two remaining amplitudes to take values less than unity. An equivalent expression would be obtained if the internuclear distance were allowed to vary:

(11)

Here S² and (1  S²) correspond to A₁ and A₂ in Table 4, respectively. The results from fitting the parameters of Eq. 11 to the SSDM data are also shown in Table 4. A best-fitting internuclear distance of 1.16 Å was obtained. This long distance corresponds to fast internal motions of considerable amplitude, probably including also librations of the tyrosine ring relative to the molecular frame, for example, fluctuations of the ² angle. Furthermore, when using a variable internuclear distance with a large fitted value, the order parameter, the global rotational correlation time, and the effective internal correlation time all increase compared with the results obtained when using a fixed internuclear distance of 1.09 Å (Table 4).

View larger version (17K): [in this window] [in a new window]   FIGURE 7   The three-component model is shown together with the SSDM data. The sum of the components is shown as the solid curve and the individual components as dashed curves. It is clear that the fastest component is effectively constant over the accessible frequency range.

	DISCUSSION

TOP ABSTRACT INTRODUCTION THEORY MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

SDM is a consistent method to analyze the dynamics of a molecule. As a first step the experimental rates are converted to spectral densities, which allows a check of the consistency of the measured rates. It was at this stage that the inconsistencies of the transverse anti-phase rates were discovered. Taking the anti-phase rate at face value, it gave rise to negative J(_H) values, and the effect on J(0) was to increase it significantly. With the SSDM, where the transverse anti-phase rate was omitted, all used rates were consistent and gave a very precise picture of the spectral densities representative of the ¹³C-H vectors in -position in the tyrosine ring.

The results of the SSDM could be fitted to a three-parameter dynamic model by the model-free approach to allow comparison with the fluorescence results. Care was taken to ensure that NMR and fluorescence measurements were made on identical samples. One question about the comparison of the two methods is related to the fact that in the FAD experiment the rotational correlation function of the excitation dipole of the excited state is studied, whereas the NMR experiments are sensitive to the dynamical properties of the electronic ground state. Recent theoretical calculations (Kushwaha and Mishra, 2000) indicate that the geometries of the ground state and the lowest singlet state are similar, i.e., with only a 0.02-Å shortening of the carbon-oxygen distance and a 0.025-Å lengthening of the C-C bonds upon excitation. The changes outside the aromatic ring are even smaller, indicating that the effect does not spread to the other parts of the polypeptide. It therefore seems reasonable to assume that the dynamic parameters are very similar for the ground and excited states of the aromatic ring.

When the tyrosine residue is excited from the ground state to the lowest-lying singlet state, i.e., the transition relevant to this case, some electron density moves from the -carbon, the -carbon, and the hydroxyl oxygen to the - and -carbons (Smolyar and Wong, 1999). This redistribution of electrons is in agreement with a transition moment in the plane of the ring, orthogonal to the symmetry axis (Hooker and Schellman, 1970) (see Fig. 2). One should note that the environment of the aromatic ring is not symmetric, a reason that the symmetry arguments might not be strictly valid. The small changes of the properties of the aromatic ring might lead to small changes in the energy landscape and consequently the dynamic behavior. The experimental data indicate that these effects are not significant in the case of the tyrosine residue in motilin, however.

The comparison of the calculated spectral density curves obtained from NMR relaxation and fluorescence results, which are shown in Fig. 4 A with corresponding parameters in Table 4, indicate that the two methods give very similar results in terms of dynamic parameters. The closely coinciding values of S² and _m give credibility to these parameters, whether they are obtained by FAD or NMR.

Also for the more complex three-component model (Eqs. 10 and 11), a close agreement between the parameters estimated from the FAD and SSDM results is obtained (Fig. 4 B; Table 4). A different problem arises when the validity of the dynamic models in the present case is questioned. Our old results from NMR relaxation were measured under almost identical conditions but with the ¹³C label instead placed on the C of Leu¹⁰. A direct comparison (Table 3) of the spectral densities evaluated at three different magnetic fields in that study, and those found here, shows that with the Leu¹⁰ label, J(0) was determined to be ~1.0 ns rad¹, whereas 0.3-0.4 ns rad¹ was determined here for J(0). The spectral densities at higher frequencies are more similar in the two measurements. The difference in J(0) causes the rather big difference in evaluated overall rotational correlation times (_M = 3.1 ns for the Leu¹⁰-labeled sample, which should be compared with the value of 1.7 ns according to the fit here of the model-free spectral density function). The striking deviation between the two values might be because of different sample conditions as indicated from preliminary translational diffusion measurements, where D_t = 1.2 10¹⁰ m²/s for the sample labeled in the tyrosine side chain and D_t = 0.7 10¹⁰ m²/s for the sample labeled in Leu¹⁰ (data not shown).

If conformational exchange is included in the dynamic model, more parameters are allowed and the fit to the experimental spectral densities is improved (Fig. 6). The agreement between the fluorescence and NMR results remains about the same (Table 4). The statistical evidence for the inclusion of an exchange term is weak. Comparing with the data from the Leu¹⁰-labeled peptide, we observe that in that case the J(0) value varies much less with the magnetic field and not in a monotonous manner as in the present case (cf. Table 3, this work, and Table 2 in Jarvet et al., 1996). Therefore, we conclude that the present result shows at least one remaining possible systematic error, the uncertainty of whether the exchange should be considered or not. The variation in the dynamic parameters indicates the uncertainty associated with this error.

Another source of a systematic error is the question of the internuclear C-H distance r_CH. We have used the standard value 1.09 Å for evaluation of the spectral densities (Table 3). When the internuclear distance was treated as an adjustable parameter in the model-free spectral density function a best-fitting value of 1.16 Å was obtained. This result is compatible with earlier reports stating that increased internuclear distances give better fits to NMR results (Llinas et al., 1977; Dill and Allerhand, 1979). It is also compatible with the estimates of the internuclear distances by solid-state NMR. Recently, effective distances of 1.12 ± 0.02 and 1.15 ± 0.05 Å were reported for the nonequivalent  carbon-proton pairs of L-tyrosine-HCl (De Paul et al., 2000). The effects of increasing the assumed internuclear distance on the model-free parameters are increasing, in particular the internal correlation time and the order parameter, but also to a lesser degree the rotational correlation time (Table 4). This is a second indication of how a systematic error may influence the dynamic parameters. The presently available NMR instrumentation is not sufficient to cover the large frequency range that would be needed to determine the r_CH parameter accurately. The fastest component found using the three-component model makes a nonnegligible contribution to the spectral density at the highest frequency (Fig. 7). This raises the question of the validity of Eq. 11 in this particular case.

The estimated values of the correlation time for local motion, _e (Table 4), should also be commented on. In the FAD evaluation using the two-component fit, this parameter (then called ₂) describes an average of all the rapid processes that can be measured. The observation that the sum of the two amplitudes is less than 0.4 is partly because the excitation and emission dipole vectors do not coincide, but could also suggest that there are even more rapid processes occurring, which are not accounted for by the two exponentials. In NMR, the _e parameter is not measured accurately in the experiments available with present-day magnets. The highest frequency where the spectral density is evaluated in the present study is 1000 MHz (the sum of the carbon and proton frequencies at an 18-T magnetic field), corresponding to a correlation time of 1/2 × 10⁹ s, i.e., on the order of 200 ps. There is obviously no real information about processes with faster motions than this to be obtained from NMR relaxation measurements using spectrometers with 800-MHz or lower proton frequencies; i.e., these processes can be treated only with one average or effective parameter.

In the three-component model, two of the time constants fall within the frequency range accessible by SDM (Fig. 7). The fastest component represents fast dynamics of considerable amplitude. Several physical models can account for the observed results. One example of a model compatible with the experimental results is to associate the slowest component with overall tumbling. The intermediate component may be associated with transitions between different rotameric states of the tyrosine side chain, involving the dihedral angles ₁ and ₂, which should occur on the sub-nanosecond time scale. The fastest component could then be associated with wobbling motions of the C-H bond vector of considerable amplitude. The types of motion associated with the intermediate and fast components have been observed for a surface-exposed tyrosine residue in a molecular dynamics simulation of glutaredoxin in explicit water (L. Nilsson, Karolinska Institutet, Stockholm, personal communication) and for phenylalanine side chains in antamanide in Langev