J. Phys. Chem. 1996, 100, 2667-2674
2667
Structural Dynamics of PMP-D2: An Experimental and Theoretical Study†,⊥ Georges Mer,‡ Annick Dejaegere,‡,§ Roland Stote,§ Bruno Kieffer,‡ and Jean-Franc¸ ois Lefe` vre*,‡ Laboratoire de Chimie Biophysique, CNRS, URA 422, Institut Le Bel, UniVersite´ Louis Pasteur, 4 Rue Blaise Pascal, 67000 Strasbourg, France, and Ecole Supe´ rieure de Biotechnologie de Strasbourg, CNRS, UPR 9003, Bd Se´ bastien Brant, 67400 Illkirch-Graffenstaden, France ReceiVed: September 22, 1995X
PMP-D2 is a 35 residue polypeptide cross-linked by three disulfide bridges. Its three-dimensional structure has been previously determined (Mer et al. Biochemistry 1994, 33, 15397-15407). Further investigation of its structure identified a crucial interaction between W25 and K10 and a double salt bridge between the positively charged K10 and the negatively charged E2 and D13. Chemical shift calculations reveal some discrepancies with experimental data concerning the structure. Heteronuclear relaxation studies, which observed broadening of K10 side chain proton resonances, and molecular dynamics simulations subsequently suggest that these discrepancies are due to slow conformational exchange in the molecule. The heteronuclear relaxation studies and visual inspection of the three-dimensional structure suggest that the residues which exhibit slow exchange form a network and move in a concerted manner.
Introduction PMP-D2 is a 35 residue protein, with three disulfide bridges, found in the brain, the hemolymph, and the fat body of the insect Locusta migratoria (L. migratoria). It has the following sequence:1
Besides its recognized inhibitory activity of Ca2+ channels,2 it is suspected that PMP-D2 also inhibits serine proteinases. Indeed, its solution structure, determined by NMR,3 reveals an extended loop structure (between C27 and C32) similar to that found in serine proteinase inhibitors.4 However, this activity was not detectable against elastase and R-chymotrypsin; a proteinase specific of the insect is still under investigation. Small polypeptides like PMP-D2 are useful for studying fundamental aspects of protein structure and dynamics. Small polypeptides like PMP-D2 are also amenable to molecular simulation calculations which can enlighten experimental results on internal dynamics. In the present paper, amino acids essential for stabilizing the core of PMP-D2 by hydrophobic interactions and amino acids which form a structurally important salt bridge are identified. Chemical shift calculations reveal some discrepancies with experimental data concerning the structure; heteronuclear relaxation studies and molecular dynamics simulations subsequently suggest that these discrepancies are due to slow conformational exchange in the molecule. Materials and Methods (A) NMR Spectroscopy. All NMR experiments were recorded at 500.13 (1H) and 125.76 MHz (13C) on a Bruker * Author to whom correspondence should be addressed. † This paper is dedicated to Martin Karplus on the occasion of his 65th birthday. ‡ Ecole Supe ´ rieure de Biotechnologie de Strasbourg. § Universite ´ Louis Pasteur. ⊥ Abbreviations: CPMG, Carr-Purcell-Meiboom-Gill; CSA, chemical shift anisotropy; DSS, 2,2-dimethyl-2-silapentane-5-sulfonate; FID, free induction decay. GARP, globally optimized alternating-phase rectangular pulses; HSQC, heteronuclear single-quantum correlation; INEPT, insensitive nuclei enhancement by polarization transfer; NMR, nuclear magnetic resonance; NOE, nuclear Overhauser enhancement; rmsd, root mean square deviation. X Abstract published in AdVance ACS Abstracts, January 15, 1996.
0022-3654/96/20100-2667$12.00/0
AMX 500 spectrometer. Relaxation experiments and temperature studies were performed on a single 10 mM PMP-D2 sample in D2O at pH ≈ 3. The pH was measured with a glass electrode and was not corrected for isotope effects. pH titration experiments were performed on a 2 mM sample in 90%/10% H2O/D2O. Both samples contained an internal reference of DSS. pH Titration Experiments. Solutions at different pH values were prepared by addition of small amounts of 1 M HCl or 1 M NaOH. The ionization constants, pKa, or apparent pKa, were calculated from nonlinear fits of the pH dependence, from pH 2 to pH 6, of the experimental chemical shifts δ(H) to the following equation:5
δ(H) )
δHA + 10(pH-pKa)δA1 + 10(pH-pKa)
(1)
δHA and δA- are the chemical shifts of the fully protonated and fully deprotonated species, respectively. Heteronuclear Relaxation. Methine 13C assignments were determined from the previously assigned 1H resonances,3 using a 13C-1H HSQC experiments,6 and are available on request. Relaxation experiments were performed at natural 13C abundance. The temperature was set to 30 °C. The measured relaxation parameters included the spin-lattice 13C relaxation rate constants RC(Cz), the in-phase spin-spin relaxation rate constants RC(Cx,y), and the cross-relaxation rate constants RC(HzfCz) obtained from the heteronuclear NOE enhancements. The pulse sequences used for these measurements have been adapted from those reported by Peng and Wagner.7,8 The relaxation period to obtain RC(Cx,y) values consists of a CPMG spin-echo sequence.9,10 Suppression of 12C-bound proton resonances is performed by storing the carbon signals of interest along the z-axis and applying a pulse field gradient. In addition, a spin-lock purge of 2 ms is applied before acquisition. The residual H2O signal is suppressed by a weak presaturation. Proton decoupling is achieved by applying the GARP11 scheme to the 13C spins during signal detection in all experiments. All two-dimensional spectra were acquired with spectral widths of 6024 and 4000 Hz in the 1H and 13C dimensions, respectively. They consisted of 128 increments in the 13C © 1996 American Chemical Society
2668 J. Phys. Chem., Vol. 100, No. 7, 1996
Mer et al.
dimension with 2048 complex points per FID. Quadrature detection in t1 was achieved by time-proportional phase incrementation of the initial pulse.12 The RC(Cz) values were obtained with 10 delays of 5, 30, 60, 100, 200, 400, 600, 800, 1200, and 2000 ms. The 5, 30, and 60 ms spectra were recorded in duplicate to get an estimate of the experimental uncertainties in the peak intensities (Vide infra). During the relaxation period, proton saturation was achieved by means of 90° pulses, spaced 5 ms apart in order to ensure a monoexponential behavior by suppressing cross-relaxation due to the heteronuclear dipolar interaction and the effects of dipolar-CSA cross-correlation.13 The spectra were acquired with 48 scans per increment. The recovery delay was set to 5 s. For RC(Cx,y) measurements, 11 spectra were recorded with delays of 3, 9, 20, 30, 40, 60, 80, 100, 150, 200, and 250 ms. The 3 ms spectrum was acquired in triplicate. The spectra were acquired with 64 scans per increment. The recovery delay was set to 3.5 s. The heteronuclear NOE enhancements were obtained by recording three spectra with proton saturation during the recovery delay of 4.8 s and three spectra without saturation during this delay. The spectra were acquired with 192 scans per increment. Spectra were processed using the program FELIX (version 2.1 from Biosym Technologies, San Diego). Prior to Fourier transform, free induction decays along t2 were zero-filled to 4096 real points and apodized with an exponential function. Along t1, the interferograms were zero-filled to 2048 real points and filtered by a 60°-shifted sine-squared window function. Relaxation rate constants and heteronuclear NOE enhancements were calculated from resonance intensities. For RC(Cz) and RC(Cx,y) calculations, data were fitted to a three and two parameter exponential decay, respectively, by means of a simplex algorithm.
I(t) ) I∞ + (I0 - I∞) exp{-RC(Cz)t}
(2)
I(t) ) I0 exp{-RC(Cx,y)t}
(3)
where I0 is the initial value of the resonance intensity and I∞ is the steady-state value. The heteronuclear NOE enhancements η and, consequently, the cross-relaxation rate constants were obtained from
η)
(
Isat.
Iunsat.
)
-1
γC RC(HzfCz) ) ηRC(Cz) γH
(4)
where Isat. and Iunsat. are the resonance intensities with and without proton saturation, respectively. The uncertainties in peak intensities were calculated from Monte Carlo simulations as previously described.7,14,15 The errors were in the range of 10%, for RC(Cz) and RC(Cx,y), and 40% for the heteronuclear NOE enhancements. Spectral Density Function Calculation. The spectral density function, J(ω), was calculated under the assumption that the values of J(ω) at high frequency are very similar.16-18 The three relaxation rate constants, RC(Cz), RC(Cx), and RC(HzfCz) are related to the three values of the spectral density function, J(0), J(ωC), and 〈J(ωH)〉 by
[
][
][ ]
RC(Cz) J(0) 0 E 7A RC(Cx) ) 2E/3 E/2 13A/2 J(ωX) 〈J(ωH)〉 0 0 5A RC(HzfCz)
A)
( )
∆2ωX2 µ0 2γH2γX2p2 , B ) , E ) 3A + B 4π 4r 6 3 XH
(7)
µ0 is the permeability of vacuum (4π × 10-7) used here in order to express A in MKSA units, and ∆ is the chemical shift anisotropy (20 ppm for carbon). The values of J(ω) can be obtained from eq 6 by inverting the matrix C:
J ) C-1‚R
(8)
Translational Diffusion Measurement. The diffusion constant of the molecule was measured through the decay of double quantum magnetization with a spin-echo type sequence including two magnetic field gradients19,41 applied symmetrically around the 180° pulse (P180) in the z direction and of the same intensity (Gz ) 30 G‚cm-1) and duration (δ ) 2 ms):
d1 - S1 - d2 - t1 - δ(Gz) - t2 - P180 - t2 - δ(Gz) - t1 d2(gz) - S2 - acquisition S1 ) P90 - d3 - P180 - d3 - P90 is used to produce double quantum coherence. The maximum efficiency of the sequence is obtained when the delay d3 is set to 1/4JHH. However, in order to avoid important loss of magnetization, d3 was set to only 12 ms. The sequence S2 ) P90 - d2 - d5 - P180 - d4 d2(2gz) - P90 converts double quantum coherence into antiphase magnetization and refocuses it. The gradients gz (-3 G‚cm-1, 2 ms) select for double quantum coherence, avoiding phase cycling. The delay d2 + d5 was also set to 12 ms. The total duration of the spin-echo sequence (τ) was kept constant and equal to 100 ms. The delay between the two GZ gradients (∆ ) 2t2) is incremented, while t1 is decremented. The magnetization reads19
[
)]
τ δ M(∆) ) M0 exp - - (pγGzδ)2Dt ∆ T2 3
(
(9)
T2 is the transverse relaxation rate of the proton, and Dt the translational diffusion constant of the molecule; p is the coherence order. In our case, the coherence order p equals 2, which allows for a reasonable decrease of the magnetization. Indeed, for single quantum transition, the molecule does not diffuse enough to affect the magnetization during the spin-echo sequence. Several double quantum coherences were followed in the spectra, and Dt was obtained by a fit of eq 9. The gradient strengths were calibrated by imaging a hole of known length in a Teflon phantom. The correlation time for the rotational Brownian motion is deduced from the translational diffusion constant using the classical hydrodynamic equations.20 (B) Computational Methods. Calculation of Chemical Shifts. The empirical model developed by O ¨ sapay and Case21,22 was used to calculate the proton chemical shifts in PMP-D2. This model calculates the difference in proton chemical shifts between random coil and folded conformations of proteins. This difference is decomposed into the following contributions:
(5)
∆δ ) δprotein - δrandom coil ) δrc + δm + δel - δconstant
(6)
In eq 10, rc, m, and el refer to ring current, peptide group anisotropy, and electrostatic interactions, respectively. Longrange contributions to the chemical shift are thus assumed to be responsible for the difference between the random coil and
which is equivalent to
R ) C‚J
where A and B are functions of the dipolar and the chemical shift anisotropy interactions:
(10)
Structural Dynamics of PMP-D2
J. Phys. Chem., Vol. 100, No. 7, 1996 2669
Figure 1. Stereoview of the PMP-D2 structure. The side chains of E2, K10, D13, and W25 are represented, as well as the three disulfide bridges C4-C19, C17-C27, and C14-C32. The amino acids involved in slow motions are shown in grey.
folded state chemical shift, while local diamagnetic and paramagnetic contributions are assumed to be identical in the random coil and folded protein. The ring current, peptide group anisotropy, and electrostatic contributions have been calibrated against experimental data.21 The δconstant term in eq 10 was originally introduced as a fitting parameter; it reflects in part anisotropy and electrostatic effects which are present in the random coil peptide. The random coil reference chemical shifts are taken from the work of Bundi and Wu¨thrich.23 The model has been shown to give satisfactory results for carbon-attached protons,21 while the results for nitrogen-attached hydrogen are not as satisfying.21 Molecular Dynamics Simulation. Molecular dynamics simulations of PMP-D2 in solution were done using version 23 of CHARMM,24 with the CHARMM22 all-atom potential function.25 The initial structure of PMP-D2 was taken from a set of twelve structures which best satisfied the experimental constraints.3 The protein was solvated with a sphere of TIP3P water25,26 (radius of 25 Å), and water overlapping the protein was deleted. The SHAKE algorithm27 was used to constrain bonds between hydrogens and heavy atoms, and a deformable boundary potential was used to constrain the water molecules to the sphere.28,29 The remaining water was equilibrated around the fixed peptide for 7.5 ps followed by an unconstrained energy minimization (except for SHAKE constraints) of the solvated protein using the steepest descent algorithm.24 The system was equilibrated at 300 K for 20 ps, and the simulations continuted for another 200 ps. A 12 Å group-based cutoff was used, the nonbonded interactions were truncated with a switching function24 between 8.0 and 11.0 Å; and a time step of 2 fs was used in all dynamics calculations. The calculation was repeated for three different structures of PMP-D2; the systems contained a total of 6509-6524 atoms. Results and Discussion (A) Architecture of PMPD2. PMP-D2 folds in three β-strands (Figure 1) and is maintained by a unique disulfide
bridge pattern which has been found so far only in pheromones from Euplotes raikoVi.30 Three cysteins located in or near the central strand are bridged to the third strand (C17-C27) and the C-terminal part (C14-C32) and to the N-terminal end (C19-C4). The loop connecting the first to the second strand appears ill defined, while the structure seems more rigid between the second and the third strands. The C-terminal end, between C27 and C32, adopts mainly an extended structure which is canonical for proteinase inhibitory loops.4 During the process of determining the solution structure of PMP-D2, it was noted that lysine 10 is connected to tryptophan 25 by 21 NOEs.3 It was further assessed that the interaction between the aromatic moiety of W25 and the hydrophobic part of the lysine side chain is essential for the folding of the protein. A mutant, where W25 is replaced by an alanine, showed no evidence of secondary and tertiary structure in its proton NMR spectrum (data not shown). Furthermore, in PMP-C, a peptide analogous to PMP-D2, this hydrophobic core is maintained by a double compensatory mutation: K10 and W25 in PMP-D2 are replaced in PMP-C by F10 and A26, respectively.31 This hydrophobic core element is closed by two salt bridges involving the charged groups of E2, K10, and D13, as presented in the three-dimensional structure of PMP-D2 (Figure 1). This was inferred from the pH dependence of K10 Hγ and Hδ resonances, which titrate with an apparent acidic pKa of 3.5 (data not shown). PMP-D2 only contains four amino acids which titrate in the acidic range: E1, E2, D13, and the C-terminal residue A35. The influence of A35 on K10 could be ruled out because of the 25 Å distance between the ammonium and the C-terminal end. The apparent pKa value of K10 is intermediate between that of D13 measured on its own amide proton (pKa ) 3.3) and that of E2 measured through its influence on the side chain NH of W25 (pKa ) 3.8). This observation suggests the existence of a double interaction: K10-D13 and K10E2. An interaction between residues 2 and 10 is also found in PMP-C, which is related to PMP-D2 and has a very similar structure.31 In PMP-C, numerous NOEs indicate that residues
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Figure 2. Difference between calculated and observed chemical shifts for each residue in PMP-D2. Two methods are used to calculate the difference: in one, the difference between observed and calculated shifts for each proton is averaged over the 12 NMR structures; shown (×) is the by residue average of the absolute value of the proton averages. By taking the absolute value, cancellation between different protons is avoided. In the second method (O), the difference between the observed and calculated chemical shifts for each proton is averaged over the 12 NMR structures; these values are then averaged by residue, and the rmsd from the residue average is used as a measure of the error.
I2 and F10 are in close proximity to one another. Moreover, the K10-E2 interaction in PMP-D2 is confirmed by the heteronuclear relaxation of 13CR carbons (Vide infra). The CRHR vector of E2 is shown to experience a slow exchange, suggesting that the motion of this residue is restricted. In the previous structure determination,3 the chemical shifts of the amide and R protons of the N-terminal sequence were indicative of a nonrandom structure, but no NOEs could be observed constraining this sequence with respect to the rest of the molecule. The K10-E2 salt bridge removes this ambiguity, and the structure was further refined by introducing an upper distance constraint of 5 Å between K10 and E2 as well as between K10 and D13 charged groups. The resulting refined structures are those used in the chemical shift and the molecular dynamics calculations (Vide infra). (B) Calculation of Chemical Shifts. It has long been recognized that proton chemical shifts carry conformational information, for example, on secondary structure.32 There have recently been several attempts to develop methods for calculating chemical shifts.21,33-37 The goal of these calculations is to assess the quality of NMR determined structures38 and to use the calculated chemical shifts in structure refinement.35,39,40 Using 12 refined NMR structures of PMP-D2, the chemical shift for each carbon-attached proton was calculated using the empirical model discussed in Material and Methods. These results were averaged to give a mean value of the calculated chemical shift for each of the 148 protons in the protein. The overall average difference between calculated and observed chemical shifts is 0.08 ppm, with an rmsd of 0.34 ppm around the mean. These values are coherent with those recently reported,38 where it was shown that good quality NMR structures have an rmsd of 0.3 ppm. The published study38 uses a model similar to the O ¨ sapay and Case model21,22 but where the parameters have been derived independently. It thus appears that both approaches give similar results for the overall rmsd between calculated and experimental shifts. The average difference between the calculated and observed chemical shifts on each of the 12 structures was also calculated to check if some of the structures in the family give a better agreement with the calculated chemical shifts. The lowest rmsd between calculated and observed shifts is 0.33, and the largest is 0.41;
individual structures generally have a larger rms difference between calculated and experimental shifts compared to the value obtained by averaging over all the structures. This is coherent with the idea that the protein actually samples several of the conformations identified by NMR. The differences between calculated and observed chemical shifts were also calculated on a residue by residue basis to examine whether there were local problems in the NMR structures. These results are displayed in Figure 2, where it is clear that the calculated chemical shifts of some residues in PMP-D2 are quite different from the corresponding experimental values, e.g., K10, T16, C17, T18, C19, T20, G26, C32, and to a lesser extent P6, Q8, and V9. Interestingly, independent tests have shown that several of these residues are undergoing slow conformational motions (Vide infra) and were, therefore, less accurately defined in the structure. For example, K10 is involved in salt bridges with E2 and D13, and these residues exhibit slow conformational exchange. The R carbons of residues 16, 18, 19, and 32 have also been shown to undergo slow conformational motion. There are, of course, several shortcomings of the models used for chemical shifts calculations, such as, e.g., the neglect of van der Waals contributions to chemical shift, the fact that the electrostatic contributions come solely from backbone atom charges. Some of the discrepancies between calculated and experimental shifts could, therefore, arise from the model itself. The results presented here nevertheless support the claim38 that chemical shifts calculations are a useful independent test of the quality of NMR structures and point to the region of the protein where the conformation may be ill defined. In the present case, these discrepancies may be due to slow conformational exchange as revealed by experiments discussed below. (C) Intermediate Exchange Detected in K10 Side Chain Proton Resonances. The resonances of K10 γ and δ protons are upfield shifted [δ(0.73, 1.02) and γ(0.38, 0.51)] and are easily observed in a one-dimensional proton spectrum (Figure 3a). These resonances shift widely with temperature and remain broad from 5 to 80 °C, suggesting an exchange in the intermediate range. Recall that, as stated above, the side chain of K10 is close to the aromatic ring of W25 and therefore exposes its protons to a strong ring current effect. A slight
Structural Dynamics of PMP-D2
J. Phys. Chem., Vol. 100, No. 7, 1996 2671
δ(T) )
Figure 3. (a, top) Chemical shift variation of K10 Hγ protons as a function of temperature. V24 methyl resonances are indicated for comparison. (b, bottom) Fit of the temperature dependence of K10 Hγ chemical shift (O) according to eq 13.
movement of the lysine with respect to the tryptophan may induce a large chemical shift variation of K10 proton resonances. Assuming a simple two state model (A and B), the chemical shift δ(T) observed at one temperature (T) can be directly related to the population of each state (R and 1 - R, respectively):
δ(T) ) RδA + (1 - R)δB
(11)
Expressing R as a function of the equilibrium thermodynamic parameters, e.g., the equilibrium constant (K ) k1/k-1) and the enthalpy (∆H) and the entropy (∆S) variations
R)
1 1 ) 1 + K 1 + e-∆H/RT e∆S/R
lead to the expression
(12)
δAe-∆S/R + δBe-∆H/RT e-∆S/R + e-∆H/RT
(13)
A nonlinear fit performed on the above expression to the variation of chemical shift as a function of temperature of one proton γ of K10 (Figure 3b) yields ∆H ) 2.8 kcal‚mol-1, ∆S ) 5.4 cal‚mol-1‚K-1, δA ) 0.02 ppm, and δB ) 3.61 ppm. This large variation in chemical shift (δB - δA ) 3.6 ppm) is likely because it originates from variation of the tryptophan ring current effect as stated above. The random coil value of the chemical shift for this proton is 1.45 ppm. The rate of exchange is of the order of the chemical shift difference, 1800 s-1, and is in the intermediate range, corresponding to a rather slow motion on the scale of molecular dynamics. Slow exchange is not only observed on K10; the heteronuclear relaxation experiments described below reveal that several other residues in the molecule also exhibit slow exchange. (D) Spectral Density Function at Zero Frequency Reveals Slow Conformational Exchange. The relaxation rate of longitudinal and in phase transverse magnetization of CR, as well as of the magnetization transfer rate from HR to CR (via steady state NOEs) were measured for all residues except for those with overlapping peaks in the heteronuclear 2D map (E1, C4, and W25) and for glycines (G7, G23, G26, and G31) because polarization transfer delays were tuned to JCH coupling. The three relaxation rates were translated into values of the spectral density function (J(ω)) at zero and the 13C and 1H frequencies (Figure 4a), according to the reduced spectral density function approach (see Material and Methods). As expected, the spectral density function decreases from low to high frequency. While J(ωC) remains quite insensitive to the structure of the peptide, J(0) varies widely with the sequence and, for many residues, in a noncontinuous manner. This behavior can generally be used to diagnose exchange processes acting on the adiabatic part of the transverse relaxation which relates to J(0). In proteins where no exchange processes in the intermediate range take place, J(0) appears as a more or less continuous function. It is quite constant along a helix or a β-strand and decreases smoothly within loops or free terminal ends as one gets further away from the more structured elements. The effect of anisotropy is quite small as it will be seen below. The wide variation of J(0) does not allow the determination of the correlation time τC, which characterizes the overall tumbling of the protein, from the slope and the intercept of J(ωC) as a function of J(0).16 Therefore, τc was determined from the translational diffusion constant Dt, measured with a pulsed field gradients enhanced spin-echo experiment41 (see Material and Methods). Given the prolate ellipsoidal shape of the molecule, with an axial ratio of 2, the value of Dt translates into correlation times of 2.81 or 1.96 ns for vectors aligned with the major or the minor axis, respectively.41 The same molecule with a spherical shape would have a correlation time of 2 ns. Knowing the three-dimensional structure of the protein,3 the maximum value of J(0), assuming a rigid molecule, was calculated for each vector, according to its orientation in the molecule (see Figure 4a). As can be seen, the variation of J(0) due to the anisotropy is much less than the observed one. The continuous behavior of the J(0) function with respect to the sequence can be used to extract the exchange components. Excluding the highest values of J(0) (>0.8 ns in Figure 4b), a polynomial fit of degree 3 was performed on the remaining points. J(0) values above the fitting curve were further removed and a second fit was performed (Figure 4b). The resulting curve can be considered as a base line containing the dynamic behavior of the CR-HR vectors along the sequence. The exchange
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Mer et al.
Figure 4. Spectral density function for CR-HR and exchange rate constant. (a) The values of the spectral density function are plotted as a function of the sequence. High, middle, and low values correspond to J(0), J(ωC), and 〈J(ωH)〉, respectively for CR-HR (O) and Cβ-Hβ (*) vectors. The solid lines represent the maximum values of J(0) and J(ωC) calculated for a rigid ellipsoid, taking into account the orientation of the CR-HR vectors. (b) J(0) values (O) and the polynomial fit on the lowest values (solid line). (c) Exchange rate constants. (d) Order parameters.
component can be calculated by subtracting this base line from the J(0) values. The results are plotted together with the amplitude of the variation of J(0) due to anisotropy in Figure 4c. Effects of exchange are mainly located around the six cysteins (E2, T5, K10, D13, C14, T16, T18, C19, T22, C27, T28, K30, C32). It should be noted that this effect can only manifest itself when the chemical shift varies with the conformational exchange:16
4π2∆ν2PAPBτex
J(0) ) J′(0) + C
1 + ω12τex2
(14)
where C is a constant, J′(0) is the fast motion contribution to the spectral density function, and ω1 is the spin-lock strength used during the measurement of the transverse magnetization relaxation. It is not possible to extract the characteristic exchange time (τex) from eq 14 with a single measurement of J(0) because it requires a knowledge of the populations of the different conformations (PA and PB) and of the variation in chemical shift (∆ν) between the conformers. (E) Amplitude of Fast Internal Motion: The Order Parameters. Utilizing the assumption that the spectral density function is a sum of contributions due to the overall tumbling (indice o) and internal motions (indice i), the order parameters (ao), analogous to the S2 of Lipari and Szabo,42,43 may be defined from
J′(0) ) aoJo(0) + ∑aiJi(0) i
J(ωC) ) aoJo(ωC) + ∑aiJi(0) i
〈J(ωH)〉 ) ao〈Jo(ωH)〉 + ∑ai〈Ji(ωH)〉
(15)
i
J′(0) are the values corrected for the exchange contribution as
defined in eq 14. The spectral density function for the overall tumbling is given a Lorentzian shape and is calculated by taking into account the anisotropy of the molecule. The above equation also contains the assumption that the spectral density function corresponding to the internal motions is flat at low frequency (at least up to the carbon frequency). The values of ao are plotted against the sequence in Figure 4d. As expected, it reflects the behaviour of J′(0). The N-terminus appears to be moderately mobile with an order parameter (0.45) which is slightly smaller than that found in the first β-strand (0.55). This observation reinforces the hypothesis of the formation of a salt bridge between the acidic group of E2 and the positively charged side chain group of K10 (Vide supra). Indeed, no NOE constraining the terminal end sequence (E1-C4) to the rest of the molecule was observed. However, the proton and carbon chemical shifts of these residues do not correspond to random structure. This analysis of the dynamics confirms that the motion in this leading sequence is similar to that of the first β-strand, implying that it is somehow anchored to the rest of the molecule. In the core of the protein (V9-G26), ao increases, going from the first to the last β-strand, suggesting an increasing rigidity of the molecule. Then, it begins to decrease within the inhibitory loop (C27-C32) and decreases further toward the C-terminus, which appears very mobile and unstructured. The spectral density function of Cβ-H vectors of threonines gives some insight into side chain dynamics (Figure 4a). Two of the threonines (T5 and T28) have high J(0) values which suggests that they also experience slow conformational exchange. In the other four threonines (T16, T18, T20, and T22), J(0) is lower for the Cβ-H than for the CR-H and well below the rigid body limit, thus reflecting the higher degree of freedom for the side chain compared to the backbone. (F) Molecular Dynamics Simulations. Besides exemplifying a number of basic molecular interactions responsible for protein stabilization, PMP-D2 exhibits an interesting range of dynamic motion. The simulations presented here are used to
Structural Dynamics of PMP-D2
J. Phys. Chem., Vol. 100, No. 7, 1996 2673 this residue exchanges slowly, yet the mean coordinate difference is relatively small. Conclusion
Figure 5. (a, top) Mean coordinate difference from the initial NMR structure calculated from the molecular dynamics simulations (given by the bars) and the rms fluctuations about the mean simulation structure (b) as a function of residue number. (b, bottom) Values of the exchange rate constants (×10-10) determined from NMR experiments (see text) as a function of residue number.
determine whether the protein remains in a stable conformation which resembles the NMR structure, thus complementing the chemical shift calculations in assessing the quality of the NMR structures. A detailed analysis of the dynamics of PMP-D2 using longer simulations will be presented elsewhere. Using the procedure outlined in Material and Methods, five different trajectories of PMP-D2 were generated, using three different initial structures and different initial starting conditions. Each simulation was longer than 200 ps; thus, the total simulation time was greater than 1 ns. The rms coordinate differences between the average structure from the simulations and the starting NMR structure range from 0.84 to 1.8 Å for the backbone atoms and from 3.5 to 5.3 Å for all heavy atoms in the core of the peptide, residues 4-30. The side chain atoms of many residues of this small protein extend into solvent and are, therefore, quite flexible. The mean coordinate difference between the CR atoms of the initial NMR structure and the CR atoms of the simulation structures were calculated, as were the backbone rms coordinate fluctuations about the mean simulation structure; these results are compared to the values of the exchange rate, which reflect the motion of the CR atoms. In those regions of the protein where the CR atoms experimentally exhibit slow exchange (Figure 5, bottom), the CR atoms of the protein tended to drift further from their initial NMR structure during the molecular dynamics simulations (Figure 5, top), in particular, around residues 12 and 22, where the mean coordinate difference is 1.8 and 1.5 Å, respectively. Although residues 12 and 22 are found in the second and third loops, respectively, the increase in CR coordinates differences cannot be attributed to loop flexibility alone. Indeed, Figure 5 also shows that the rms fluctuations of the backbone are relatively constant: they do not vary around loop 2 (residues 11-14) and show only minor increases around loops 1 (residues 5-8) and 3 (residues 19-24). The regions which exhibit larger mean coordinate differences also correspond to the regions where a greater discrepancy was found between calculated and experimental chemical shifts. These results further support the idea that the structure is ill defined in several regions of the protein due to conformational averaging arising from slow exchange. An exception is found with T16; the NMR experiments show that
The structure of PMP-D2 is organized around a hydrophobic core defined by the interaction between W25 and K10 and is stabilized by two salt bridges between the positively charged K10 and the negatively charged E2 and D13. Three disulfide bridges add to the stability of the protein; however, they may also play a role in slow conformational exchange which is manifested by the broadening of the K10 side chain proton resonances and the unusually high values of the spectral density function at zero frequency, J(0), for some of the CR-HR vectors. The residues affected by the slow exchange are indicated in Figure 1. It can be seen that they form a network of interactions involving a disulfide bridge, hydrophobic and salt bridge interactions, and proximity in sequence. The major path in the network follows the route E2, K10, D13, C14, and C32. The other residues which exhibit slow exchange branch off of this network. For most of these residues, the chemical shifts calculated from the NMR structure largely disagree with the experimental data. When conformational motions are present, one can expect that chemical shifts calculated from NOE-derived structures would not necessarily agree with the experimental chemical shifts which are weighted averages of the chemical shifts characterizing each individual conformation. It was shown that, in relatively short molecular dynamics simulations, those regions of the protein where slow motion and chemical shift discrepancy exist were also regions where the structure tended to move further from the NOE-derived NMR structure. Via the network of interactions discussed above, it is possible that the slow exchange may be a concerted conformational motion involving the isomerization of one or several disulfide bridges, as already observed in BPTI.44,45 Such an equilibrium could be necessary in order to permit the protein to adapt to a receptor molecule. Acknowledgment. We thank Christine Kellenberger and He´le`ne Hietter for preparing PMP-D2 and for valuable discussions. The Institut de De´veloppement et des Ressources en Informatique Scientifique (IDRIS) provided an allocation of CRAY computer time which was used for this work. G.M. was supported by the program Cm2AO administered by the industrial organization, ORGANIBIO. R.S. was supported by a fellowship from the Fondation pour la Recherche Me´dicale. References and Notes (1) Nakakura, N.; Hietter, H.; van Dorsselaer, A.; Luu, B. Eur. J. Biochem. 1992, 204, 147. (2) Harding, L.; Scott, R. H.; Kellenberger, C.; Hietter, H.; Luu, B.; Beadle, D. J.; Bermudez, I. J. Recept. Res. 1995, 15, 355. (3) Mer, G.; Kellenberger, C.; Koehl, P.; Stote, R.; Sorokine, O.; Van Dorsselaer, A.; Luu, B.; Hietter, H.; Lefe`vre, J.-F. Biochemistry 1994, 33, 15397. (4) Bode, W.; Huber, R. Eur. J. Biochem. 1992, 204, 433. (5) Shrager, R. I.; Cohen, J. S.; Heller, S. R.; Sachs, D. H.; Schechter, A. N. Biochemistry 1972, 11, 541. (6) Bodenhausen, G.; Ruben, D. J. Chem. Phys. Lett. 1980, 69, 185. (7) Peng, J. W.; Wagner, G. Biochemistry 1992, 31, 8571. (8) Peng, J. W.; Wagner, G. J. Magn. Reson. 1992, 98, 308. (9) Carr, H. Y.; Purcell, E. M. Phys. ReV. 1954, 94, 630. (10) Meiboom, S.; Gill, D. ReV. Sci. Instrum. 1958, 29, 688. (11) Shaka, A. J.; Barker, P. B.; Freeman, R. J. Magn. Reson. 1985, 64, 547. (12) Marion, D.; Garbay-Jaureguiberry, C.; Roques, B. P. J. Magn. Reson. 1983, 53, 199. (13) Boyd, J.; Hommel, U.; Campbell, I. D. Chem. Phys. Lett. 1990, 175, 477. (14) Palmer, A. G., III; Rance, M.; Wright, P. E. J. Am. Chem. Soc. 1991, 113, 4371.
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