Utilizing dipole-dipole cross-correlated relaxation for the measurement of angles between pairs of opposing CαHα-CαHα bonds in anti-parallel ß-sheets.

Dipole-dipole cross-correlated relaxation (CCR) between two spin pairs is rich with macromolecular structural and dynamic information on inter-nuclear bond vectors. Measurement of short range dipolar CCR rates has been demonstrated for a variety of inter-nuclear vector spin pairs in proteins and nucleic acids, where the multiple quantum coherence necessary for observing the CCR rate is created by through-bond scalar coupling. In principle, CCR rates can be measured for any pair of inter-nuclear vectors where coherence can be generated between one spin of each spin pair, regardless of both the distance between the two spin pairs and the distance of the two spins forming the multiple quantum coherence. In practice, however, long range CCR (lrCCR) rates are challenging to measure due to difficulties in linking spatially distant spin pairs. By utilizing through-space relaxation allowed coherence transfer (RACT), we have developed a new method for the measurement of lrCCR rates involving CαHα bonds on opposing anti-parallel ß-strands. The resulting lrCCR rates are straightforward to interpret since only the angle between the two vectors modulates the strength of the interference effect. We applied our lrCCR measurement to the third immunoglobulin-binding domain of the streptococcal protein G (GB3) and utilize published NMR ensembles and static NMR/X-ray structures to highlight the relationship between the lrCCR rates and the CαHα-CαHα inter-bond angle and bond mobility. Furthermore, we employ the lrCCR rates to guide the selection of sub-ensembles from the published NMR ensembles for enhancing the structural and dynamic interpretation of the data. We foresee this methodology for measuring lrCCR rates as improving the generation of structural ensembles by providing highly accurate details concerning the orientation of CαHα bonds on opposing anti-parallel ß-strands.

Standard tensorial analysis of local ordering in proteins from residual dipolar couplings.

Residual dipolar couplings (RDCs) in proteins arise from independent external medium-related and internal protein-related ordering of the spin-bearing probe. Griesinger et al. developed a method for treating RDCs in proteins. The global ordering is given in the standard manner by a rank 2 tensor specified in a known molecular frame, MF. The local ordering is described by the spherical harmonic ensemble averages, , m = 0, ±1, ±2, also given in MF. From these quantities, a method we call mf-RDC derives the squared generalized order parameter (S(rdc)(2)), the amplitude (direction) of the anisotropic disorder, η (Φ'), and an approximation, (N−H)(eff), to the average probe orientation, i.e., to the local director. (N−H)(eff) is determined through a frame transformation where is maximized. Φ' is associated with a subsequent frame transformation where is maximized. The mf-RDC method was applied previously to N−H and C−C(methyl) sites in ubiquitin. In this study, we convert the respective 's into a Saupe tensor, which is diagonalized. This is the standard procedure. It yields the eigenvalues, S(xx), S(yy), and S(zz), and the Principal Axis System (PAS) of the rank 2 local ordering tensor, S(l). S(rdc)(2), η, and Φ' can be recast as S(xx), S(yy), and S(zz). The mf-RDC frame transformations are not the same as the conventional Wigner rotation. The standard tensorial analysis provides new information. The contribution of local ordering rhombicity to S(rdc)(2) is evaluated. For the α-helix of ubiquitin, the main local ordering axis is assigned as C(i−1)(α) − C(i)(α); for the methyl sites, it is associated with the C−C(methyl) axis, as in mf-RDC. Ordering strength correlates with methyl type. The strength (rhombicity) of S(l) associated with picosecond−nanosecond local motions is reduced moderately (substantially) by nanosecond−millisecond local motions. A scheme for analyzing experimental RDCs based on the standard tensorial perspective, which allows for arbitrary orientation of the local director in the protein and of the PAS of S(l) in the probe, is formulated.

Thermal coefficients of the methyl groups within ubiquitin.

Physiological processes such as protein folding and molecular recognition are intricately linked to their dynamic signature, which is reflected in their thermal coefficient. In addition, the local conformational entropy is directly related to the degrees of freedom, which each residue possesses within its conformational space. Therefore, the temperature dependence of the local conformational entropy may provide insight into understanding how local dynamics may affect the stability of proteins. Here, we analyze the temperature dependence of internal methyl group dynamics derived from the cross-correlated relaxation between dipolar couplings of two CH bonds within ubiquitin. Spanning a temperature range from 275 to 308 K, internal methyl group dynamics tend to increase with increasing temperature, which translates to a general increase in local conformational entropy. With this data measured over multiple temperatures, the thermal coefficient of the methyl group order parameter, the characteristic thermal coefficient, and the local heat capacity were obtained. By analyzing the distribution of methyl group thermal coefficients within ubiquitin, we found that the N-terminal region has relatively high thermostability. These results indicate that methyl groups contribute quite appreciably to the total heat capacity of ubiquitin through the regulation of local conformational entropy.

Toward a predictive understanding of slow methyl group dynamics in proteins.

The development of the most recent generation of molecular mechanics force fields promises an increasingly predictive understanding of the protein dynamics-function relationship. Based on extensive validation against various types of experimental data, the AMBER force field ff99SB was benchmarked in recent years as a favorable force field for protein simulations. Recent improvements of the side chain and backbone potentials, made by different groups, led to the ff99SB-ILDN and ff99SBnmr1 force fields, respectively. The combination of these potentials into a unified force field, termed ff99SBnmr1-ILDN, was used in this study to perform a microsecond time scale molecular dynamics simulation of free ubiquitin in explicit solvent for validation against an extensive set of experimental NMR methyl group residual dipolar couplings. Our results show a high level of consistency between the experimental data and the values predicted from the molecular dynamics trajectory reflecting a systematically improved performance of ff99SBnmr1-ILDN over the original ff99SB force field. Moreover, the unconstrained ff99SBnmr1-ILDN MD ensemble achieves a similar level of agreement as the recently introduced EROS ensemble, which was constructed based on a large body of NMR data as constraints, including the methyl residual dipolar couplings. This suggests that ff99SBnmr1-ILDN provides a high-quality representation of the motions of methyl-bearing protein side chains, which are sensitive probes of protein-protein and protein-ligand interactions.

Weak long-range correlated motions in a surface patch of ubiquitin involved in molecular recognition.

Long-range correlated motions in proteins are candidate mechanisms for processes that require information transfer across protein structures, such as allostery and signal transduction. However, the observation of backbone correlations between distant residues has remained elusive, and only local correlations have been revealed using residual dipolar couplings measured by NMR spectroscopy. In this work, we experimentally identified and characterized collective motions spanning four ß-strands separated by up to 15 Å in ubiquitin. The observed correlations link molecular recognition sites and result from concerted conformational changes that are in part mediated by the hydrogen-bonding network.

Accessing ns-micros side chain dynamics in ubiquitin with methyl RDCs.

This study presents the first application of the model-free analysis (MFA) (Meiler in J Am Chem Soc 123:6098-6107, 2001; Lakomek in J Biomol NMR 34:101-115, 2006) to methyl group RDCs measured in 13 different alignment media in order to describe their supra-tau (c) dynamics in ubiquitin. Our results indicate that methyl groups vary from rigid to very mobile with good correlation to residue type, distance to backbone and solvent exposure, and that considerable additional dynamics are effective at rates slower than the correlation time tau (c). In fact, the average amplitude of motion expressed in terms of order parameters S (2) associated with the supra-tau (c) window brings evidence to the existence of fluctuations contributing as much additional mobility as those already present in the faster ps-ns time scale measured from relaxation data. Comparison to previous results on ubiquitin demonstrates that the RDC-derived order parameters are dominated both by rotameric interconversions and faster libration-type motions around equilibrium positions. They match best with those derived from a combined J-coupling and residual dipolar coupling approach (Chou in J Am Chem Soc 125:8959-8966, 2003) taking backbone motion into account. In order to appreciate the dynamic scale of side chains over the entire protein, the methyl group order parameters are compared to existing dynamic ensembles of ubiquitin. Of those recently published, the broadest one, namely the EROS ensemble (Lange in Science 320:1471-1475, 2008), fits the collection of methyl group order parameters presented here best. Last, we used the MFA-derived averaged spherical harmonics to perform highly-parameterized rotameric searches of the side chains conformation and find expanded rotamer distributions with excellent fit to our data. These rotamer distributions suggest the presence of concerted motions along the side chains.

Residual dipolar couplings as a tool to study molecular recognition of ubiquitin.

RDCs (residual dipolar couplings) in NMR spectroscopy provide information about protein dynamics complementary to NMR relaxation methods, especially in the previously inaccessible time window between the protein correlation time tau(c) and 50 micros. For ubiquitin, new modes of motion of the protein backbone could be detected using RDC-based techniques. An ensemble of ubiquitin based on these RDC values is found to comprise all different conformations that ubiquitin adopts upon binding to different recognition proteins. These conformations in protein-protein complexes had been derived from 46 X-ray structures. Thus, for ubiquitin recognition by other proteins, conformational selection rather than induced fit seems to be the dominant mechanism.

Bilayer in small bicelles revealed by lipid-protein interactions using NMR spectroscopy.

Intermolecular nuclear Overhauser effects (NOEs) between the integral outer membrane protein OmpX from Escherichia coli and small bicelles of dihexanoyl phosphatidylcholine (DHPC) and dimyristoyl phosphatidylcholine (DMPC) give insights into protein-lipid interactions. Intermolecular NOEs between hydrophobic tails of lipid and protein in the bicelles cover the surface area of OmpX forming a continuous cylindric jacket of approximately 2.7 nm in height. These NOEs originate only from DMPC molecules, and no NOEs from DHPC are observed. Further, these NOEs are mainly from methylene groups of the hydrophobic tails of DMPC, and only a handful of NOEs arise from methyl groups of the hydrophobic tails. The observed contacts indicate that the hydrophobic tails of DMPC are oriented parallel to the surface of OmpX and thus DMPC molecules form a bilayer in the vicinity of the protein. Thus, a bilayer exists in the small bicelles not only in the absence of but also in the presence of a membrane protein. In addition, the number of NOEs between the polar head groups of lipid molecules and protein is increased in the bicelles compared with those in micelles. This observation may be due to the closely packed head groups of the bilayer. Moreover, irregularity of hydrophobic interactions in the middle of the bilayer environment was observed. This observation together with the interactions between polar head groups and proteins gives a possible rationale for structural and functional differences of membrane proteins solubilized in micelles and in bilayer systems and hints at structural differences between protein-free and protein-loaded bilayers.

Self-consistent residual dipolar coupling based model-free analysis for the robust determination of nanosecond to microsecond protein dynamics.

Residual dipolar couplings (RDCs) provide information about the dynamic average orientation of inter-nuclear vectors and amplitudes of motion up to milliseconds. They complement relaxation methods, especially on a time-scale window that we have called supra-tau(c) (tau(c) < supra-tau(c) < 50 micros). Here we present a robust approach called Self-Consistent RDC-based Model-free analysis (SCRM) that delivers RDC-based order parameters-independent of the details of the structure used for alignment tensor calculation-as well as the dynamic average orientation of the inter-nuclear vectors in the protein structure in a self-consistent manner. For ubiquitin, the SCRM analysis yields an average RDC-derived order parameter of the NH vectors 0.72 +/- 0.02 compared to = 0.778 +/- 0.003 for the Lipari-Szabo order parameters, indicating that the inclusion of the supra-tau(c) window increases the averaged amplitude of mobility observed in the sub-supra-tau(c) window by about 34%. For the beta-strand spanned by residues Lys48 to Leu50, an alternating pattern of backbone NH RDC order parameter S2(rdc)(NH) = (0.59, 0.72, 0.59) was extracted. The backbone of Lys48, whose side chain is known to be involved in the poly-ubiquitylation process that leads to protein degradation, is very mobile on the supra-tau(c) time scale (S2(rdc)(NH) = 0.59 +/- 0.03), while it is inconspicuous (S2(LS)(NH)= 0.82) on the sub-tau(c) as well as on micros-ms relaxation dispersion time scales. The results of this work differ from previous RDC dynamics studies of ubiquitin in the sense that the results are essentially independent of structural noise providing a much more robust assessment of dynamic effects that underlie the RDC data.

Recognition dynamics up to microseconds revealed from an RDC-derived ubiquitin ensemble in solution.

Protein dynamics are essential for protein function, and yet it has been challenging to access the underlying atomic motions in solution on nanosecond-to-microsecond time scales. We present a structural ensemble of ubiquitin, refined against residual dipolar couplings (RDCs), comprising solution dynamics up to microseconds. The ensemble covers the complete structural heterogeneity observed in 46 ubiquitin crystal structures, most of which are complexes with other proteins. Conformational selection, rather than induced-fit motion, thus suffices to explain the molecular recognition dynamics of ubiquitin. Marked correlations are seen between the flexibility of the ensemble and contacts formed in ubiquitin complexes. A large part of the solution dynamics is concentrated in one concerted mode, which accounts for most of ubiquitin's molecular recognition heterogeneity and ensures a low entropic complex formation cost.