Next Article in Journal
Macrocyclic Pyridyl Polyoxazoles: Structure-Activity Studies of the Aminoalkyl Side-Chain on G-Quadruplex Stabilization and Cytotoxic Activity
Next Article in Special Issue
The Involvement of Amino Acid Side Chains in Shielding the Nickel Coordination Site: An NMR Study
Previous Article in Journal / Special Issue
Nuclear Magnetic Resonance Approaches in the Study of 2-Oxo Acid Dehydrogenase Multienzyme Complexes—A Literature Review
Order Article Reprints
Font Type:
Arial Georgia Verdana
Font Size:
Aa Aa Aa
Line Spacing:
Column Width:

Measuring Dynamic and Kinetic Information in the Previously Inaccessible Supra-tc Window of Nanoseconds to Microseconds by Solution NMR Spectroscopy

Department for NMR-based Structural Biology, Max-Planck Institute for Biophysical Chemistry, Am Fassberg 11, D-37077 Göttingen, Germany
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Molecules 2013, 18(10), 11904-11937;
Received: 16 July 2013 / Revised: 28 August 2013 / Accepted: 17 September 2013 / Published: 26 September 2013
(This article belongs to the Special Issue NMR of Proteins and Small Biomolecules)


Nuclear Magnetic Resonance (NMR) spectroscopy is a powerful tool that has enabled experimentalists to characterize molecular dynamics and kinetics spanning a wide range of time-scales from picoseconds to days. This review focuses on addressing the previously inaccessible supra-τc window (defined as τc < supra-τc < 40 μs; in which τc is the overall tumbling time of a molecule) from the perspective of local inter-nuclear vector dynamics extracted from residual dipolar couplings (RDCs) and from the perspective of conformational exchange captured by relaxation dispersion measurements (RD). The goal of the first section is to present a detailed analysis of how to extract protein dynamics encoded in RDCs and how to relate this information to protein functionality within the previously inaccessible supra-τc window. In the second section, the current state of the art for RD is analyzed, as well as the considerable progress toward pushing the sensitivity of RD further into the supra-τc scale by up to a factor of two (motion up to 25 μs). From the data obtained with these techniques and methodology, the importance of the supra-τc scale for protein function and molecular recognition is becoming increasingly clearer as the connection between motion on the supra-τc scale and protein functionality from the experimental side is further strengthened with results from molecular dynamics simulations.

1. Introduction

One of the essential keystones for the existence of life rests in the intricate relationship between biomolecular function and structural dynamics. The biomolecular machines engaging in these indispensable processes possess internal structural dynamics on a wide range of time-scales. It is the relationship or connection between the time-scales of these fundamental biophysical phenomena and the time-scales of biomolecular dynamics that the technique of Nuclear Magnetic Resonance (NMR) spectroscopy is uniquely equipped to explore. NMR is a powerful technique whose observables are time-scale sensitive [1]. Given that the sample is tractable for NMR studies, the system can be explored in solution without chemical modification while maintaining atomic resolution.
A wide range of NMR experiments have been developed that report on a broad range of time-scales from picoseconds to more than seconds (Figure 1). Exchange Spectroscopy (Figure 1; EXSY) first demonstrated by Meier et al. in 1979 [2] is a NMR technique for investigating slow time-scale dynamics (~50 ms to more than seconds provided that the exchange process is not much slower than the longitudinal relaxation rate). Specifically slow processes can therefore be studied by EXSY on states of the density matrix with long longitudinal relaxation times [2]. EXSY was later applied to measure aromatic ring flips in BPTI [3], to monitor enzyme catalysis [4,5,6] and to follow folding processes [7,8]. NMR can also be implemented for the investigation of biophysical processes occurring so slowly that several free induction decays (FIDs) or even multidimensional spectra can be recorded while the system is pseudo-static. This type of experiment is called real-time NMR and utilizes the repetitious collection of NMR spectra. Real-time NMR has been applied to systems engaged in slow substrate turn-over events [9] and in folding processes [10]. Fast acquisition techniques [11,12,13] and hyperpolarization [14,15] have recently been invented with the goal of measuring faster kinetics as well as improving signal to noise. Additionally, the probed system adopts a range of distinctive structural configurations that may translate into differences in the NMR chemical shift. Depending on the time-scale for the structural changes, the chemical shift itself can also be used as a dynamic metric [16,17,18,19]. Chemical shifts have been predicted and used to report on sampled conformational sub-states from a recent 1 millisecond molecular dynamics (MD) trajectory of bovine pancreatic trypsin inhibitor (BPTI) [19,20]. Another important NMR parameter is the cross-correlated relaxation rate, which encapsulates the correlated nature of potentially synchronous inter-nuclear vector motion on time-scales spanning picoseconds to milliseconds [21,22,23,24,25].
In this review, we address the considerable progress that has been made to characterize the amplitude and time-scale of inter-nuclear vector dynamics within a window that remained as a “blind-spot” for NMR. This window covers about four orders of magnitude and ranges between the overall tumbling time of a molecule (τc) to 40 μs (Figure 1), but as we will see has been extended to ~25 μs [26] (Section 3). This previously inaccessible time window has been defined as the supra-τc range [27,28]. The use of experiments that report on motions faster than τc will also be mentioned as well as the experiments denoted in Figure 1 as rotating frame longitudinal relaxation (R) and Carr-Purcell-Meiboom-Gill (CPMG) experiments, which rely on the characterization of conformational exchange. The extraction of dynamical content from residual dipolar couplings (RDCs) and the measuring of kinetics from conformational exchange has implications for understanding the mechanisms of molecular recognition and protein function within the supra-τc scale.
Figure 1. The accessible time-scale for NMR observables and the respective limits for some NMR experiments.
Figure 1. The accessible time-scale for NMR observables and the respective limits for some NMR experiments.
Molecules 18 11904 g001

2. Dynamic Content of the Supra-τc Range

2.1. Introduction to Residual Dipolar Couplings

An essential NMR parameter that provides both structural and dynamic information including the supra-τc scale is the residual dipolar coupling (RDC) between two nuclear magnetic moments [29,30]. The beginnings of the RDC field can be traced back to 1963 when Saupe and Englert aligned benzene with p-azoxyanisole [31]. From here, the theoretical background for the analysis of RDCs for the extraction of structural and dynamic parameters has a rich history of development. Though this review does not aim to provide a detailed account concerning the history of the RDC field, nevertheless, we refer the reader to a comprehensive, yet not exhaustive, list of the pioneering work from Saupe [32,33], Snyder [34], MacLean and co-workers [35,36,37], Emsley and co-workers [38,39,40,41,42,43,44], and Pines and co-workers [45,46] toward the advancement of the theoretical underpinnings regarding solute alignment under anisotropic conditions.
In respect to biomolecules, thirty-two years passed from the initial report from Saupe and Englert [17] until Tolman and coworkers reported the first investigation of aligning cyanometmyoglobin, which possesses a paramagnetic center, in a magnetic field [47]. At the same time, Bolton and co-workers aligned a dodecamer of DNA in a magnetic field due to magnetic susceptibility of the unlabeled DNA [48]. A year later, Bax and colleagues described RDCs for the diamagnetic protein ubiquitin taken from changes in N-HN splitting resulting from varying magnetic susceptibility anisotropy at different static field strengths [49]. These couplings were quite small, on the order of 0.2 Hz, and an alternative method for measuring RDCs was proposed where the protein is dissolved in a partially anisotropic environment, the first being bicelles [9]. Since then, a multitude of alignment media have been described in the literature, including but not limited to filamentous phages [50,51,52], a mixture of cetylpyridinium bromide/chloride hexanol [53,54], a mixture of alkyl poly(ethylene glycol) and hexanol [55], a stretched [56,57] or a compressed polyacrylamide gel [58], and purple membrane fragments [59,60]. The advantage of these types of alignment media is that the strength of alignment is more under the experimentalist’s control, producing RDC values several orders of magnitude higher than in the case of magnetic susceptibility anisotropy. For more information on the specifics of the different types of alignment media that are currently available, the reader is referred to the following reviews [61,62,63].
In the anisotropic media, all possible orientations for an inter-nuclear vector are populated with unequal probability, resulting in the dipolar couplings (D) no longer averaging to zero, with values on the order of 1/1000 the value of the maximal dipolar coupling. From an experimental standpoint, the RDC adds together with J-coupling, requiring two measurements to extract the RDCs: one in isotropic conditions to determine the J-coupling and one in anisotropic conditions to determine the (J + D)-coupling. Reviewed in several places, schemes for measuring the RDCs either rely on measuring the peak splitting in a coupled HSQC or the (J + D)- or J- coupling modulated peak intensity [61,64,65,66].
The main focus of this section is two-fold. First, a theoretical framework for utilizing RDCs in the determination of structural and dynamic properties for inter-nuclear vectors is described in detail. The measured RDCs encode a unique signature of the extent of supra-τc motion and methodology has been developed toward extracting this information in a robust manner. The second half of this section concentrates on some of the effort that has been invested in linking these amplitudes of supra-τc motion to biophysical phenomena, specifically molecular recognition. In particular, long MD trajectories, accelerated molecular dynamics simulations, and RDC restrained molecular dynamics simulations provide a more global picture of how these experimentally derived local dynamics could be relevant for function and stability.

2.2. Alignment Tensor Determination

Partial alignment of a protein results in the observed resonance splitting (Hz) for two nuclear spins to possess a contribution from the secular part of the magnetic dipole interaction:
Molecules 18 11904 i002
Molecules 18 11904 i003
where μ0 is the permeability of vacuum, γi and γj are the gyromagnetic ratios of nuclei i and j, ℏ is Planck’s constant, rij is the distance between nuclei i and j, and θk is the angle between the inter-nuclear vector formed by nuclear spin pair k and the magnetic field (B0). The important concept to note from Equation (1) is that the magnitude of Molecules 18 11904 i004 depends on Molecules 18 11904 i005, which is ensemble averaged over the time-scale covered by the RDC measurement (denoted by the angular brackets). The time-averaged or ensemble averaged information covers up to the millisecond time-scale or roughly 1/D, spanning the supra-τc scale [30].
We will first consider the simplest case, theoretical analysis of a rigid molecule. In the absence of inter-nuclear vector dynamics, the instantaneous orientation of B0 relative to each inter-nuclear vector within a protein or molecule can be defined in the molecular frame (MF), which is an arbitrary frame of reference usually given by the PDB coordinates. Each inter-nuclear vector can be defined by three angles, βx, βy, and βz, between the vector and the respective MF axes. In a similar fashion, the vector parallel to B0 can be expressed by three angles representing the instantaneous orientation of B0 relative to the MF axes, αx, αy, and αz. Within the MF, Equation (1) can be expressed as:
Molecules 18 11904 i006
where B ∙ 〈A〉 is the scalar product of two vectors representing the inter-nuclear orientations (B) and the B0 orientations (〈A〉). Both 〈A〉 and B contain 5 independent terms and are related to a 3 × 3 second rank Cartesian order tensor as follows [32,33,34]
Molecules 18 11904 i007
where the averaged orientation of B0 in the MF is given by:
Molecules 18 11904 i008
Molecules 18 11904 i009
where the orientation of the inter-nuclear vector in the MF is described by:
Molecules 18 11904 i010
The term δmn represents the Kronecker delta function, l is the alignment condition, and m,n = x, y, z. When a set of RDCs have been measured for a protein and the structural coordinates of the protein are known from a crystal or NMR structure, then Singular Value Decomposition (SVD) is typically used to calculate an exact solution for the alignment tensor, 〈A [67]. Here, SVD of B is performed in order to obtain the pseudo-inverse of B, B+. With B+, the following equation determines 〈A〉 through left multiplication of Equation (3) with B+:
Molecules 18 11904 i011
The SVD approach requires that the RDC measurement includes at least five inter-nuclear vectors sampling at least five independent orientations, leading to a nonsingular B matrix and thus B+ B = 1, or the identity matrix.
The calculated alignment tensor can be recast into a symmetric 3 x 3 second rank Cartesian order tensor, (〈A(2)〉) and then redefined in a principal axis system (PAS), termed the alignment frame (AF), where Equation (1) becomes [61]:
Molecules 18 11904 i012
In Equation (9), the magnitude of the alignment tensor is Molecules 18 11904 i013, the rhombicity is Molecules 18 11904 i014, Molecules 18 11904 i015 are the polar angles defining the inter-nuclear vector in the AF, and Molecules 18 11904 i016 are the eigenvalues resulting from the diagonalization of 〈A(2)〉. From the eigenvectors ( Molecules 18 11904 i017), the Euler angles describing the rotation of 〈A〉 and B into the PAS are defined:
Molecules 18 11904 i018
In the case where multiple RDC sets are available for a given biomolecule, Joel Tolman developed a compact matrix formalism to calculate alignment tensor information in a more intuitive manner [68]. When K RDCs are measured under L alignments, then Equation (3) becomes:
D = BA
where D is a K x L matrix, B is a K x 5 matrix, and 〈A〉 is a 5 x L matrix. In Equation (11), the term Molecules 18 11904 i021 is included in 〈A〉. The rows of B are defined by Equation (6) and the columns of A are given by Equation (4). As with the SVD approach to a single alignment media, the calculation of 〈A〉 for all alignment media at once requires a nonsingular B matrix:
A〉 = B+D
where B+ is the pseudo-inverse of B. As mentioned above, each alignment tensor can be rotated into a PAS and the five parameters describing the alignment, {Da, R, α, β, γ}l, can be extracted with Equations (9) and (10). It should be mentioned that several programs exist for the calculation of alignment tensor information, such as PALES [69,70] and REDCAT [71].

2.3. Model Free Analysis and Direct Interpretation of Dipolar Couplings

In reality, the molecules under investigation are not static and ensemble averaging of the RDC observable must also be considered. To calculate the dynamical content from the RDC data, five orthogonal alignment media must be measured for the system under investigation. This requirement is in analogy to the determination of an alignment tensor, where at least five orthogonal inter-nuclear vectors are necessary to define the five independent elements of each alignment tensor. The dynamical content contained within the RDC data is encapsulated by a generalized order parameter, Molecules 18 11904 i022, which possesses dynamic information on the picosecond to millisecond time-scale, which includes the supra-τc range (Figure 1). Within the framework of ensemble averaging, Equations (11) and (12) become:
D = 〈B〉〈A
A〉 = 〈B+D
There are two principal schemes for extracting the structural and dynamic content from RDC data measured in at least five linearly independent alignment media, namely the Model Free Analysis (MFA) [72] and the Direct Interpretation of Dipolar Couplings (DIDC) [68]. Before delving into the details concerning these model free approaches, we discuss a necessary caveat for the implementation of this methodology and how to assess the quality of the RDC data, as well as the sampling of the five-dimensional space.
The fundamental assumption for both the MFA and DIDC approaches is that the internal protein dynamics for each inter-nuclear vector is uncorrelated with alignment tensor. Thus, a single average alignment tensor can be utilized for each medium. Molecular dynamics simulations indicate that this assumption is true for secondary structural elements, yet 〈B〉 and 〈A〉 dynamics may be correlated for the most mobile regions of a protein [73,74]. In the case of intrinsically disordered proteins [75,76], multi-domain proteins [77,78], and extended nucleic acid structures [48,79], internal conformational dynamics couples with the alignment tensor. After realizing that even intrinsically disordered proteins exhibit RDCs [80,81], Blackledge and co-workers have developed strategies for interpreting RDCs measured for intrinsically disordered proteins and the reader is referred to the following papers on the subject [82,83,84]. RDCs measured for multi-domain proteins report on both inter-nuclear vector dynamics and inter-domain dynamics that result in changes in molecular alignment [85]. One avenue to de-correlate these two processes is to use internal paramagnetic alignment where one domain is preferentially aligned in the magnetic field [78,86]. Though the focus of this section is assessing inter-nuclear vector dynamics via RDCs obtained from external alignment media, we direct the interested reader to these papers on utilizing paramagnetic tagging for the determination of structure, inter-domain orientation and dynamics with RDCs from the groups of Ubbink [87,88], Bertini [78,89,90], Otting [91,92], Byrd [93,94], and Schwalbe [95,96]. As for aligning extended nucleic acid structures, such as RNA, the laboratory of Al-Hashimi has developed a novel strategy of elongating RNA helices [97]. In this situation, the extended RNA structure dominates the molecular alignment and the internal dynamics of the RNA helix no longer contributes to the overall alignment of the biomolecule [98].
When analyzing RDC data, a fundamental assumption that is made concerns the uncorrelatedness of the inter-nuclear dynamics and the alignment process; hence the averages of 〈B〉 and 〈A〉 are independent of each other. This assumption can be tested with the Self-Consistency of Dipolar Couplings Analysis (SECONDA) [99,100]. SECONDA attempts to quantitate the degree of structural heterogeneity for the measured protein over at least 6 different alignment media. The analysis only requires RDC data as input, without structural data or alignment tensor information. In principal, perfectly homogenous behavior suggests that the internal structural dynamics are not influenced by the variations in the alignment process, in temperature or in pH. Furthermore, the homogeneity can be quantified on a per residue basis. A covariance matrix is created from the RDC data and from a principal component analysis or SVD of the covariance matrix the degree of structural heterogeneity is assessed from the resulting singular values. The first five singular values contain the structural and dynamic content encompassed within the RDC data. The other singular values indicate the degree of structural and dynamic heterogeneity, noise, and systematic errors resulting in singular values that are not equal to zero. The SECONDA gap is a measure of the self-consistency and homogeneity of the RDC data set, which is the ratio of the 5th and 6th singular value.
The degree in which the five dimensional space is being sampled can be quantified from SVD [68,101]. SVD of the five independent elements of each alignment tensor within 〈A〉 yields five singular values. The ratio of the first to the fifth singular value indicates the strength of the contribution from the strongest and weakest dimensions being sampled by the RDC data. This parameter is called the condition number. A value of one indicates that each dimension is being sampled equally. In the case of ubiquitin where 36 RDC data sets were available the average condition number was 6.3 [102]. Residues 22, 31, 46, 69, and 73 were removed from this 36 RDC data set, since they possessed condition numbers larger than 10.
We will focus our discussion on the extraction of structural and dynamic content from RDC data on the similar nature of both the MFA and DIDC analysis and how they are unified within the context of the standard tensorial analysis [103]. Beginning with the MFA, five independent alignment media are necessary to calculate the five independent elements of the RDC tensor for each inter-nuclear vector, as well as a priori knowledge of the protein structure [72,101]. With the alignment tensor information, the averages over the second rank spherical harmonics describing the mean orientations of the vectors, contained within the RDC tensor, provide the desired structural and dynamic content. The alignment tensor parameters taken from the alignment frame (AF), {Da, R, α, β, γ}l, are used to construct the 〈F〉 matrix which is needed to derive the five dynamically averaged second order spherical harmonics:
Molecules 18 11904 i023
Molecules 18 11904 i024
Molecules 18 11904 i025
Utilizing the following relationships,
Molecules 18 11904 i026
Molecules 18 11904 i027
Equation (9) is reformulated in terms of dynamically averaged second order spherical harmonics
Molecules 18 11904 i028
The 〈F〉 matrix functions in a similar way to 〈A〉 and relates the measured RDCs to the spherical harmonics defined in the MF by a Wigner rotation from the MF to the AF:
Molecules 18 11904 i029
Molecules 18 11904 i030
In analogy to the component definition from Equations (13) and (14), 〈Y〉 is a K x 5 matrix containing the dynamically averaged spherical harmonics in the MF and 〈F〉 is a 5 x L matrix containing the alignment tensor information. Refined structural coordinates are determined directly from the RDCs and alignment information:
Yrefined = DnormalizedF+
In order to normalize the contributions of each alignment condition to the calculation of refined structural coordinates, Dnormalized represents Molecules 18 11904 i033 which results in the condition number being lower than in the unnormalized case. In other words, this normalization helps to even out the contributions of each RDC set to the calculation of 〈Y〉refined. Each row of 〈Y〉refined is used to determine Molecules 18 11904 i034:
Molecules 18 11904 i035
From the dynamically averaged spherical harmonics, the dynamically averaged orientations for each inter-nuclear vector, Molecules 18 11904 i036, can be obtained. Maximizing Molecules 18 11904 i037 places the z-axis of the vector’s axis system, termed the vector frame (VF), in the center of the inter-nuclear vector’s orientational distribution:
Molecules 18 11904 i038
The terms Molecules 18 11904 i040 vanish in the VF and Molecules 18 11904 i041 possesses information on the amplitude of anisotropy, ηk, and the orientation of anisotropic motions, Molecules 18 11904 i042:
Molecules 18 11904 i043
Molecules 18 11904 i044
It should be noted that Molecules 18 11904 i034 is the same in any frame, thus:
Molecules 18 11904 i045
which is equivalent to Equation (24).
With the DIDC approach, structural input is not required in the calculation of the inter-nuclear vector’s structural and dynamic content [68]. In concordance with Equation (23):
Brefined = DA+ + B[1 – 〈A〉〈A>〉+]
where 〈Brefined can be calculatedwithout extracting each set of {Da, R, α, β, γ}l. A key difference between the MFA and DIDC is the requirement of normalizing D and 〈A〉. In the current implementation of DIDC, these parameters are not normalized, which will lead to some discrepancies between RDC analysis utilizing the MFA and the DIDC. Neglecting this normalization will lead to a disproportionate contribution of the stronger alignment media to the calculation of the refined structural coordinates. We propose the following modification of Equation (29) for the DIDC approach when seeking a direct correspondence between both methods:
Molecules 18 11904 i046
where Dnormalized and 〈Anormalized represent the RDCs and alignment tensors divided by Molecules 18 11904 i047.
The unification of both the MFA and the DIDC is readily apparent when looking at the relationship between 〈B〉 and 〈Y〉. Recalling Equation (6), the following relationships are established in order to construct Molecules 18 11904 i048 [34]:
Molecules 18 11904 i049
Molecules 18 11904 i050
Molecules 18 11904 i051
Molecules 18 11904 i052
Molecules 18 11904 i053
In 2012, Meirovitch et al. made the following connection between maximizing Molecules 18 11904 i037 and defining each inter-nuclear vector in a unique principal axis system [103]. The resulting eigenvalues ( Molecules 18 11904 i054 contain the dynamic information for each vector Molecules 18 11904 i055, while the eigenvectors, Molecules 18 11904 i056, encompass the bond orientations Molecules 18 11904 i057 and the direction of the anisotropic local motion Molecules 18 11904 i058. The following equations detail how the dynamic parameters are calculated from Molecules 18 11904 i059. The Saupe order parameters are defined as:
Molecules 18 11904 i060
Molecules 18 11904 i061
Molecules 18 11904 i062
Molecules 18 11904 i063
For each inter-nuclear vector, Molecules 18 11904 i057 and Molecules 18 11904 i064 are extracted from the transpose of the resulting Molecules 18 11904 i065 matrix:
Molecules 18 11904 i066
Both the MFA and DIDC methods have been incorporated into iterative schemes with the goal of improving the accuracy of the alignment tensor calculation by reducing the effects of the structural noise, termed the Self-Consistent RDC based MFA (SCRM) [102], iterative DIDC [104] and the Optimized RDC-based Iterative and Unified Model-free analysis (ORIUM) [89]. The iterative schemes achieve this by using the refined dynamically averaged coordinates as input for additional runs of either MFA or DIDC. Interestingly, ORIUM is the only iterative procedure that can begin with random coil input as the starting structural coordinates and extract the same structural and dynamic information calculated from an x-ray structure used as the beginning structural input [105]. This result shows that the iterative ORIUM scheme tolerates a significant amount of structural noise and has the potential be implemented in refinement of conformational ensembles.
A final consideration when determining the dynamic parameters from RDC data is that the actual magnitude of Molecules 18 11904 i047 or D a,l is not known, which will lead to Molecules 18 11904 i022 values being only relative in nature to the true absolute value [27,72]. The other alignment tensor parameters {R, α, β, γ}l are unaffected by the reduction in the magnitude of D a,l. The correct scaling parameter, termed Soverall, is crucial for distinguishing sub- and supra-τc motion. All three iterative schemes have addressed this issue in different manners. In the iterative DIDC, order parameters are scaled relative to the largest Molecules 18 11904 i069 leaving one order parameter equal to one [68,104]. Sub- and supra-tc motion happening for each vector equally will not be detected by this approach, which will underestimate the motion. With the MFA/SCRM procedure, Molecules 18 11904 i069 is scaled relative to the Lipari-Szabo order parameters ( Molecules 18 11904 i070 calculated for each residue [27,102], as long as Molecules 18 11904 i071 are available for the inter-nuclear vectors being analyzed. This approach as been successfully applied to ubiquitin, however, supra-tc motion affecting all nuclei equally will not be picked up by this method. Finally, ORIUM uses the inter-nuclear vector’s motional variance, which is directly related to the resulting eigenvalues calculated from diagonalization of Molecules 18 11904 i048 into a local axis system. By definition, variance cannot be negative, and therefore, a uniform scaling parameter, Soverall, is necessary to insure that the variance for each inter-nuclear vector about each of the three principal axes is positive. The advantage of this method is that Soverall is derived based on variances of a single type of RDC without needing Molecules 18 11904 i071 as a constraint, and hence does not possess any time-scale bias. Yet, it should be noted that Soverall determined by this procedure could underestimate motion if there is a uniform sub- or supra-tc motion affecting all inter-nuclear vectors equally.

2.4. Gaussian Axial Fluctuation Model

Brüschweiler and co-workers developed a model, termed the Gaussian Axial Fluctuation model (GAF), describing rotational motion of the peptide plane around the axis defined by Cα(i-1) and Cα(i) [106,107,108]. The original observation for this type of motion comes from NMR spin relaxation measurements as well as molecular dynamics simulations, where crankshaft type motions along this axis were observed. Blackledge and co-workers have adapted this model for the use with RDC data, which spans up to the millisecond time-scale [109,110,111]. The amount of this motion is encapsulated in the angular standard deviation (σ) about three orthogonal axes defined by the peptide plane. In the simplest formulation, considering motion about the axis defined by Cα(i-1) and Cα(i), the model is considered (ortho-GAF) and σ is incorporated into Equation (6) as follows:
Molecules 18 11904 i072
Molecules 18 11904 i073.
Here, α, β, γ represent the Euler angles describing the transformation into the peptide plane’s frame, where the z-axis points along the direction of the N-HN bond and the x-axis orthogonal to the peptide plane. This rotation is similar to putting the N-HN bond in the local principal axis system described above. It should be noted that the Cα(i-1) and Cα(i) axis is tilted away from the y axis by 11 degrees.
As is this case with RDCs measured in alignment media with unknown absolute magnitude, the GAF method also requires a scaling factor, which has been addressed with the structure-free (SF) GAF approach [112]. The methodology treats each peptide plane as an independent entity, the only requirement being the starting coordinates for a representative peptide plane. RDC data measured in multiple alignment media for the N-HN, C'N, C'- HN, and C'-Cα were used to fit for the residue specific α, β, γ, σz, σyx and the alignment condition specific Molecules 18 11904 i074. This procedure was most effective when using the full 3D-GAF model. For ubiquitin, a comparison of Molecules 18 11904 i022 derived from the SCRM [102] approach of constraining with Molecules 18 11904 i071 with the SF-GAF method Molecules 18 11904 i022 displayed remarkable agreement.

2.5. Supra-τc Dynamics Determined from RDCs is linked to Molecular Recognition

The potential linkage of experimentally extracted inter-nuclear vector dynamics within the supra-τc range to molecular recognition has been investigated for three proteins: ubiquitin (SCRM [102]/SF-GAF [54]/ORIUM [105]), GB3 (iterative DIDC [45]/3D-GAF [111], ORIUM [105]) and SH3 (3D-GAF [113]). Amplitudes of supra-τc motion can be readily quantified from knowledge of Molecules 18 11904 i022 and Molecules 18 11904 i071:
Molecules 18 11904 i075
For all three proteins, additional motions resulting from slower time-scale dynamics are present. Furthermore, in the case of ubiquitin, there exists a significant amount of motion for the side-chain methyl groups [114], while such studies have not yet been conducted for the other two proteins. The connection to molecular recognition rests in the observation that for some residues possessing significant Molecules 18 11904 i076 are involved with binding to interaction partners. When considering the interacting partners SH3 and ubiquitin, they both appear to possess a significant amount of supra-τc motion at their respective binding interfaces [102,113].
Molecular dynamics (MD) simulations restrained with or validated against RDC data is an approach to develop an ensemble of structures that best represents the ground state ensemble of the protein. Recently, RDC data was used as a restraint in MD simulations of ubiquitin. A principal component analysis of the resulting ensemble demonstrated that ubiquitin samples the same conformational space as all conformers captured to date in crystal structures of ubiquitin complexes [28]. These findings support the concept of conformational selection, specifically that amplitudes of motion or dynamics resulting from conformational inter-conversion on the supra-τc scale are limiting the on-rates for complex formation [115]. For ubiquitin, a majority of these conformational dynamics are concentrated in a single collective mode described by a pincer-like motion. To alleviate the entropic costs associated with sampling conformers along the pincer-like trajectory, another ubiquitin conformational ensemble predicts a significant amount of correlated motions, determined from long range ϕ/ψ dihedral correlations [116]. These findings demonstrate the power of using RDC data to refine ensembles containing dynamic information on the supra-τc scale.
Accelerated molecular dynamics (AMD) is another strategy for utilizing RDC data in the generation of a conformational ensemble possessing dynamics up to the millisecond time-scale [117]. In AMD, the energy barriers between the many conformational states of a protein ensemble are lowered, allowing the AMD simulation to cover conformational space that potentially exists on longer time-scales. From here, a canonical ensemble can be generated from a Boltzmann reweighting of each ensemble member. The AMD approach has been employed with several protein systems, including GB3 [118], ubiquitin [119], thrombin [120,121], and IκBα [122]. In all cases, the AMD ensembles were cross-validated with RDC data, then order parameters were calculated. Supra-τc motion is also present with the AMD method, suggesting, at least for systems as large as thrombin and IκBα, a common time-scale of supra-τc motion may be present for all proteins.
As this section has demonstrated, RDC data encompasses important information regarding the amplitudes of motion spanning the supra-τc scale. The next step is to assign a specific rate to this motion. Are these dynamics related to conformational inter-conversion within the ground state ensemble and, if so, what is the time-scale of this process? A powerful technique to potentially answer this question comes from relaxation dispersion measurements. The next section reviews the progress that has been made linking RDC extracted supra-τc scale dynamics to a specific rate describing the actual process of conformational inter-conversion.

3. Kinetics from the Supra-τc Range

3.1. Sub-τc Relaxation is Limited to the Overall Tumbling Time

Conventional NMR relaxation focuses on backbone 15N nuclei and we will limit our discussion to this nucleus type [123,124], although, a plethora of experiments have been developed that can probe the relaxation processes of other nuclei [125,126,127,128,129,130]. Commonly applied NMR experiments measure the longitudinal and transverse relaxation rates, R1 and R2,0, respectively [124]. These intrinsic relaxation parameters report on local oscillating magnetic fields that are generated due to dipolar interactions between the 15N nucleus and its attached amide proton (dipole-dipole coupling) and from magnetic fields generated due to a nucleus electron cloud’s orientation with the static magnetic field (chemical shift anisotropy) [131]. These local magnetic fields are reoriented because of molecular tumbling which for proteins occurs in the nanosecond range and demarcated by the characteristic lifetime called the overall rotational correlation time (τc). These relaxation rates are described by spectral density type functions that are evaluated at characteristic frequencies, which report on transitions that drive nuclei back to equilibrium. These frequencies occur at zero, ωH/N, and ωH ± ωN where ωX is the Larmor frequency for either 1H or 15N nuclei [131,132,133]. However, since these relaxation rates depend on fluctuations of dipolar couplings that are averaged by the molecular reorientation occurring with the correlation time τc, only motions up to that time are accessible, i.e. motions that are slower than the inverse correlation time are not reflected in these relaxation rates. This range of motion faster than the inverse correlation time is called the sub-τc window. The experiments that probe these relaxation rates function by probing inphase coherences of the type Nx,y and Nz for R2,0 and R1, respectively [1,134], from which the longevity of these coherences is queried by observing their rate of decay which is extracted using a two parameter exponential decay function [135].
A broad range of information can be retrieved from the measurement of relaxation rates. The ratio of R2,0 and R1 can be used to determine τc itself [124], and many insights into local molecular flexibility can be attained by performing a Model-Free analysis (MF) [136,137]. The MF formalism allows the extraction of an order parameter that quantifies the spatial flexibility of a given inter-nuclear vector. This parameter can also be used as a proxy for conformational entropy [138,139,140,141]. An extended MF formalism has been developed for the characterization of internal motion occurring from two distinct time-scales within the sub-τc range [142]. The local and overall rotational anisotropy [143] of a macromolecule and the orientations of modular proteins [144,145] can also be ascertained from such data. Although insight into motion from the sub-τc range has given input into finer molecular motions, some biologically relevant processes cannot be assessed with these types of measurements due to the time-scale limitation.
The kinetic characterization for biologically relevant processes like protein folding [146,147,148,149], enzymatic turnover events [150,151,152,153,154], and molecular recognition [155,156,157] are inaccessible by conventional sub-τc relaxation techniques. Instead, NMR based relaxation dispersion (RD) experiments have emerged as a successful tool to explore these processes [1,158,159,160]. Fifty years ago, the concept of RD was applied for the measurement of the proton transfer rate between trimethylammonium and trimethylamine [161]. The success of these experiments is directly related to their ability to exploit the phenomenon of conformational exchange. Conformational exchange occurs when the electronic environment of a nucleus is perturbed due to its own motion or from its surroundings. This motion in turn modulates a nuclei’s isotropic chemical shift (ω) thereby causing the generation of alternatively populated coherences [159,162]. These variously populated states also interconvert with a given lifetime (τex) whose smallest observable value is limited by the experimental conditions. The effect of conformational exchange creates a dephasing in the transverse plane that is appended to R2,0. This dephasing creates an effective transverse relaxation rate, R2,eff = R2,0 + Rex where Rex is a contribution of relaxation due to conformational exchange.
The lifetime for a conformational exchange event is governed by the chemical shift time-scale [163]. Traditionally, the process is defined to be either in the slow, intermediate, or fast regime. These regimes are separated based on the inverse ratio of the product between the chemical shift difference between populated states (Δω) and τex ((Δω·τex)−1) which for slow, intermediate, and fast processes take on the values of < 1, ≈ 1, and > 1, respectively [163]. For processes that may take place in the supra-τc range (10s of μs and faster) motion is in the fast regime and therefore a given resonance position will represent a population weight of all assumed states. Since conformational exchange is governed by perturbations in ω, the line width of an NMR lineshape is affected during a period of free-precession. Assuming a two-state model, the contribution to the line width due to fast exchange is Molecules 18 11904 i077 in which pA is the population of the major state (pB = 1 – pA) [159,162]. The next section explores how RD experiments work to disentangle these parameters that modify transverse relaxation.

3.2. Relaxation Dispersion Experiments

The two most commonly invoked RD experiments are the transverse-rotating frame relaxation (R) [160,164] and Carr-Purcell-Meiboom-Gill (CPMG) [165,166] experiments. CPMG experiments have grown large popularity to be able to study lowly populated intermediates for some systems [147,157,167]. However, RD can also be used to probe the ground states of a protein as well [115]. Other methods have also been proposed for RD experiments [168,169]. Although, the dependence of conformational exchange differs between the R and CPMG techniques [1,170], the phenomenological concept is the same. In both cases a relaxation rate is monitored as a function of the rate at which a given magnetization coherence can be refocused. CPMG experiments vary the degree of refocusing by changing 180° pulse repetition rates [171,172,173,174], and R experiments use radio frequency pulses with varying amplitudes and frequency offsets that effectively constrain (spin-lock) a given magnetization coherence [160]. The amplitude of a given spin-lock pulse is denoted as νRF. However, due to technical limitations, CPMG experiments, when performed on 15N nuclei, permit the observation of motions with a τex of up to ~150 μs [135]. R experiments were limited to a time resolution of 40 μs, but now νRF values permit the observation of kinetic events up to 25 μs (vide infra) which has made this NMR experiment a well suited candidate to access kinetic information from the supra-τc range.
Figure 2. Illustrative schematic describing transverse rotating frame experiments (R) for the measurement of two-state conformational exchange events for NMR active nuclei. As states A and B interconvert with some lifetime (τex) they have a phase separation of Δω. The length of each vector (arrow tipped lines) denotes the effective field that each populated coherence possesses. The effective field, or length of each vector, is governed by experimental parameters, namely the offset (Ω) and νRF, where Ω is the difference between the resonance frequency for a given nucleus and the frequency at which νRF is applied. The effective field can be calculated as Molecules 18 11904 i078 (rad s−1). The incomplete refocusing of state B (vector diagram on the left) leads to a dephasing of the magnetization, which translates to a larger relaxation rate. Upon sufficient refocusing of both magnetization vectors (vector diagram on the right) the relaxation rate decreases to R2,0. The cones directly reflect the size of the nutation generated from the applied spin-lock field. In the fast regime, the dependence of R2,eff with an increasing νRF gives a Lorentzian profile [Equation (44)]. If no conformational exchange exists, then R2,eff remains constant for all applied νRF values.
Figure 2. Illustrative schematic describing transverse rotating frame experiments (R) for the measurement of two-state conformational exchange events for NMR active nuclei. As states A and B interconvert with some lifetime (τex) they have a phase separation of Δω. The length of each vector (arrow tipped lines) denotes the effective field that each populated coherence possesses. The effective field, or length of each vector, is governed by experimental parameters, namely the offset (Ω) and νRF, where Ω is the difference between the resonance frequency for a given nucleus and the frequency at which νRF is applied. The effective field can be calculated as Molecules 18 11904 i078 (rad s−1). The incomplete refocusing of state B (vector diagram on the left) leads to a dephasing of the magnetization, which translates to a larger relaxation rate. Upon sufficient refocusing of both magnetization vectors (vector diagram on the right) the relaxation rate decreases to R2,0. The cones directly reflect the size of the nutation generated from the applied spin-lock field. In the fast regime, the dependence of R2,eff with an increasing νRF gives a Lorentzian profile [Equation (44)]. If no conformational exchange exists, then R2,eff remains constant for all applied νRF values.
Molecules 18 11904 g002

3.3. Off/On-Resonance R

Off- and on-resonance R experiments have been applied to a variety of topics related to the study of internal molecular motions such as hinge and loop displacements [175,176], fast folding events [177], structural configurations that can be assumed in solution by DNA/RNA [178,179], and molecular recognition events [115]. R experiments can be used as a type of RD experiment because they create “dispersion” by monitoring a nuclei specific relaxation rate as a function of the amplitude of a spin-lock field (νRF) and/or by manipulation of the offset frequency (Ω). The transverse rotating frame relaxation rate is dependent on the intrinsic R1, R2,0, and if conformational exchange exists Rex. In the off-resonance R scenario, populated coherences are rotated away from the static magnetic field by some tilt angle (θ), where the magnetization is locked and thereby begins to precess with the applied field (Figure 2). The tilt angle is an experimentally controlled parameter, θ = tan−1(νRF/Ω) where νRF and Ω are the amplitude of the employed spin-lock (Hz) and the frequency difference between the resonance position of a given nuclei and the frequency at which νRF is applied, respectively. The overall magnitude of a spin-lock field is called the effective field ( Molecules 18 11904 i080(rad·s−1)). If an interconversion event exists, then assuming a two-state process, the populated coherences will be differentially spin-locked (Figure 2). At this point, the alternatively populated coherence is not sufficiently refocused and dephasing leads to an elevated effective relaxation rate (R2,eff) (Figure 2). As ωeff is sufficiently increased to encompass the exchanging magnetization vectors, the relaxation rate decreases to R2,0 or to the point at which the exchange contribution to R2,eff is quenched (Figure 2).
The equation that describes off-resonance R is given in Figure 2. In order to isolate the effect of conformational exchange, it is convenient to visualize the contribution of Rex by either converting off-resonance R data to R2,eff (Figure 2) or by performing R experiments on-resonance (θ = π/2) whereby the dependence of R1 and the tilt angle are removed. If motion exists in the fast regime, then this creates an addendum to R that is given by:
Molecules 18 11904 i082
However when the motion is fast, then information between the populations and Δω cannot be separated and therefore only the product is retained. This is called the conformational amplitude of the process and is denoted as Фex. Comparing the dependence of Rex between R and CPMG type experiments it can be seen that their dependence is similar (Figure 3). The 180° pulse repetition rate (νCPMG) can be equated to νRF using relations derived from Ishima et al. ( Molecules 18 11904 i083) [180].
Figure 3. Dependence of Rex monitored by R (solid black line) and CPMG (dashed black line) experiments. The dashed black line was created using the Carver-Richards model [181] which is applicable for CPMG experiments, and the solid black curve calculated using Equation (44). The exchange parameters τex, pB, and Δω, were set to 150 μs, 5 %, and 61 Hz, respectively.
Figure 3. Dependence of Rex monitored by R (solid black line) and CPMG (dashed black line) experiments. The dashed black line was created using the Carver-Richards model [181] which is applicable for CPMG experiments, and the solid black curve calculated using Equation (44). The exchange parameters τex, pB, and Δω, were set to 150 μs, 5 %, and 61 Hz, respectively.
Molecules 18 11904 g003
It is also important to note that, similar to CPMG experiments, theoretical formalisms and experiments have been reported in which R can be applied outside of the fast regime [182,183,184]. Still conventional 15N CPMG experiments are limited to motions around 150 μs (νCPMG ~ 1 kHz) [135]. Taken together, since supra-τc motion can reside past this limit, R can be used in hopes of gaining access to the kinetics from this time-scale.

3.4. Off-Resonance R in Super-Cooled Conditions

Kinetics from the supra-τc range measured by off-resonance R was recently performed on the protein ubiquitin free in solution [115]. This study characterized a rapid microsecond process within the ground-state ensemble of ubiquitin whose rate of conformer interconversion has implications for its molecular recognition process [115,185,186]. At high temperatures, ubiquitin does not report on having an exchange contribution to R [70]. The authors hypothesized that if the motion escaped detection at higher temperatures then by lowering the temperature the lifetime of motion would increase making it accessible by off-resonance R. Experiments were performed by super-cooling the sample to 265 K whereby significant RD was detected and a τex of 120 μs was determined [115]. Following the temperature dependence of this motion, an Arrhenius extrapolation identified that the motion at physiological temperatures is between 1 and 19 μs. This motion has been attributed to the interconversion between distinct ubiquitin conformers and was corroborated with predicted Фex values from the RDC derived ensembles [28,116], as well as measurements in solution using dielectric relaxation spectroscopy [115,187]. Although dielectric relaxation does not maintain atomic resolution like RD experiments, an Arrhenius extrapolation of the conformer interconversion lifetime is not required. Even with this milestone of measuring RD at super-cooled temperatures, only limited information with respect to the expansiveness of this motion could be attained because only a few sites within ubiquitin were detectable.

3.5. Exceeding the Limit with Cryogenically Cooled Probeheads

A prime limitation in RD experiments is the minimum accessible time-scale. Equation (44) has a Lorentzian form and therefore the smallest lifetime that can be observed is limited to the natural line width of a Lorentzian, which is controlled by ωeffex ≈ 1eff). For the observation of exchange events, ωeff depends on both νRF and Ω. Since these are both experimentally controlled parameters, they can be changed, but a compromise has to be made with respect to the tilt angle. A caveat emerges in which larger Ω values will cause the R value to be dominated by R1 (cos2(θ) approaches 1), which in turn minimizes the contribution of Rex. Thus, increases in νRF, instead of Ω, would provide a means of further extending R based RD techniques into the supra-τc range.
Recently, the previous limitations were exceeded through the use of hardware that is found in many NMR based laboratories, the cryogenically cooled probehead (cryo-probehead). A Bruker QCI S3 cryo-probehead was demonstrated to be capable of safely withstanding νRF values up to 6.4 kHz and represents an improvement by a factor of three from what was previously accepted [26]. This larger attainable spin-lock field strength permits a time resolution for motion up to 25 μs. On-resonance R experiments for 15N nuclei within ubiquitin that had been previously shown to have dispersion were performed as validation for the use of large amplitude νRF [115,185]. Additional advantages also emerged when a cryo-probehead was used for RD measurements. Since a major aspect in relaxation experiments is to attain sufficient signal to noise that minimizes the errors in the obtained rates, measurement with a helium cooled NMR coil and pre-amplifier fulfills exactly this requirement via a noise reduction in those electronic components. Therefore, R rates could be monitored with increased precision. Given the increased precision in the measured rates, the errors in the extracted exchange parameters also decreased. More importantly, the implementation of on-resonance experiments removes any contribution from R1 and tilt angle to the measured rate. Thus, any observed conformational exchange is solely modulated by νRF. The on-resonance RD measurement allows for a more complete sampling of the Rex contribution. Furthermore, a 15N site that undergoes smaller amplitude motion within the supra-τc range can be detected. The use of large amplitude spin-lock field strengths also purported more accurate intrinsic relaxation rates because exchange events up to 25 μs could be removed from R2,eff [26]. The application of more efficient quenching of conformational exchange has been recently demonstrated for the measurement of veracious intrinsic relaxation rates that supplement constant time CPMG type RD experiments [171]. An experiment was created (HEROINE) in which the same averaged coherence is monitored, but large amplitude νRF are employed permitting more accurate and precise kinetics to be extracted from CT-CPMG data even when motion is in the fast regime [188] ((τex·ω)-1 > 3) The use of large νRF may also be extended to nuclei with a larger gyromagnetic ratio (γ) as the achievable νRF scales with this value (νRF = γBRF/2π) and even larger νRF could then potentially be applied [189,190,191]. Ultimately, large amplitude νRF based R appears to be a promising approach to the further quantification of kinetics from the supra-τc range.

3.6. Experimental Aspects for Kinetic Measurements in the Supra-τc Range

Experimental outlines for the execution of off/on-resonance R experiments for 15N nuclei have been given in many reviews and texts [132,135,159,160,192], but details pertaining to super-cooled and large amplitude νRF measurements will be discussed here. Initially demonstrated by Szyperski and coworkers, super-cooled relaxation measurements can be used to probe sub-τc events [193,194]. Under super-cooled conditions, the surface tension of the water increases resulting in a lower freezing point for a liquid solution. The NMR sample is initially centrifugated for a sufficient time in order to remove any potential nucleation points for ice formation. The samples can be placed into 1 mm NMR tubes, which are then filled with the liquid samples and subsequently flame sealed. Approximately ten to twelve 1 mm NMR tubes can be placed into a 5 mm tube, which is then inserted in the NMR magnet. Cooling to the desired temperature should be done in small increments and the sample given sufficient time in between temperature decrements for equilibration. As the temperature decreases, the line broadening of the NMR peaks is increased due to an increase in τc and/or due to slowing down the rates of conformational exchange processes. In order to enhance the sensitivity, R based RD can be performed by either querying the narrower doublet for 15N nuclei [195,196] or by a conventional pulse sequence equipped with a TROSY [197,198] readout to maximize the longevity of the NMR signal. Additionally, TROSY is without decoupling during acquisition and therefore the overall heating canbe reduced.
For the measurement of large amplitude νRF, the proper calibration of useable spin-lock field strengths must be ascertained. Continuous wave (CW) off-resonance decoupling experiments are a facile way to determine these amplitudes. CW-fields are applied off-resonance during the acquisition of a two-dimensional correlation experiment (e.g., [1H, 15N]-HSQC) that will cause some amount of partial decoupling. This partial decoupling translates to an effective scalar coupling value which can be correlated with respect to the Ω of a given resonance position [160,192]. A linear correlation between the scalar coupling values and Ω yields a line whose slope is νRF [26,160]. The collection of enough points during the acquisition period provides a way to determine the spin-lock amplitudes and lengths that can be safely applied on a given probehead. Of extreme importance is the utilization of recycle delays that are long enough to ensure a duty cycle that does not exceed 5% and that maintain the NMR coil temperature and preamp power reserve at a stable level. Heating due to the electric field component of a radio-frequency pulse can be differential between different experiments. Temperature compensation schemes should be implemented, which not only considers the length that νRF is applied, but also the amplitude of νRF in order to equalize the temperature between experiments [199]. The relative change in the temperature can be determined from 1HN temperature coefficients.
The acquisition of RD data can be conducted by varying νRF and/or Ω. With a given configuration, signal intensities are tracked by measuring their time dependence either by observing a full exponential decay or with two-point sampling schemes. Error estimation and application of different sampling techniques have been previously discussed [135,173,200]. Discerning possible dispersion profiles can be done by following particular selection criteria (i.e. minimum differences in relaxation rates) [147]. From here, the analysis of dispersion data is conducted by standard minimization protocols [132,135], in which the data are fit to models that are with and without conformational exchange contributions. Statistical tests, such as F-tests [201], can be applied in order to identify the better fitting model.

4. Conclusions and Outlook

The dynamic characterization of motions from the supra-τc range has been made possible by the careful dissemination of RDC data collected in unique alignment conditions [102,104,113]. The analysis of such information relies on model dependent (GAF; Section 2.4) [109,110,111] and model independent techniques (MFA, DIDC, SCRM and ORIUM; Section 2.3) [68,72,101,102,104,105]. Insight from such data has highlighted molecular motions related to molecular recognition for ubiquitin [28] and TAR-RNA [202], which were only realized with the inclusion of RDC data. RD is also emerging as an experimental tool to capture the kinetics from the supra-τc range [26,115]. Further methodological advancement will be required to try to completely sample this four orders of magnitude time window, however motion as fast as ~25 μs can be accessed with atomic resolution [26] based on variance of 15N chemical shifts and even faster for nuclei with a larger gyromagnetic ratio. The harmony between experiment and computer simulation can also aid in accelerating studies of protein dynamics from supra-τc range. The RDC-derived ensembles [28,115,116] have shown that they faithfully include structural variances within the supra-τc range, and can also be used to have predictive power in identifying sites that may undergo conformational exchange that could be detectable by RD. Additionally, long MD trajectories and AMD type simulations have been able to identify supra-τc motion for the backbone of BPTI [20] and for example thrombin [120,121], respectively. A major goal for the future will be to see these experimental and computational techniques applied to an increased number of other biological macromolecules in order to enhance our understanding of the complex behavior displayed by biological macromolecules within the supra-τc window.


This paper is dedicated to Richard R. Ernst on the occasion of his 80th birthday. This work has been supported by the Max Planck Society and the EU (ERC grant agreement number 233227). We would like to acknowledge Mikael Akke and Nils Alexander Lakomek for helpful discussions. We would also like to acknowledge Helena Kovacs, Roberto Seydoux, Klemens Kessler, Detlef Moskau and Rainer Kümmerle at Bruker BioSpin AG for the helpful discussions pertaining to cryo-probehead technology.

Conflicts of Interest

The authors declare no conflict of interest.


  1. Palmer III, A.G. NMR characterization of the dynamics of biomacromolecules. Chem. Rev. 2004, 104, 3623–3640. [Google Scholar] [CrossRef]
  2. Meier, B.H.; Ernst, R.R. Elucidation of Chemical-Exchange Networks by 2-Dimensional NMR-Spectroscopy — Heptamethylbenzenonium Ion. J. Am. Chem. Soc. 1979, 101, 6441–6442. [Google Scholar] [CrossRef]
  3. Wagner, G.; Bodenhausen, G.; Müller, N.; Rance, M.; Sørensen, O.W.; Ernst, R.R.; Wüthrich, K. Exchange of two-spin order in nuclear magnetic resonance: Separation of exchange and cross-relaxation processes. J. Am. Chem. Soc. 1985, 107, 6440–6446. [Google Scholar] [CrossRef]
  4. Chapman, B.E.; Stewart, I.M.; Bulliman, B.T.; Mendz, G.L.; Kuchel, P.W. 31P Magnetization Transfer in the Phosphoglyceromutase-Enolase Coupled Enzyme-System. Eur. Biophys. J. 1988, 16, 187–191. [Google Scholar]
  5. Kuchel, P.W.; Bulliman, B.T.; Chapman, B.E. Mutarotase equilibrium exchange kinetics studied by 13C-NMR. Biophys. Chem. 1988, 32, 89–95. [Google Scholar] [CrossRef]
  6. Mendz, G.L.; Robinson, G.; Kuchel, P.W. Direct quantitative-analysis of enzyme-catalyzed reactions by two-dimensional nuclear-magnetic-resonance spectroscopy–Adenylate kinase and phosphoglyceromutase. J. Am. Chem. Soc. 1986, 108, 169–173. [Google Scholar] [CrossRef]
  7. Farrow, N.A.; Zhang, O.W.; Forman-Kay, J.D.; Kay, L.E. A Heteronuclear correlation experiment for simultaneous determination of 15N longitudinal decay and chemical-exchange rates of systems in slow equilibrium. J. Biomol. NMR 1994, 4, 727–734. [Google Scholar] [CrossRef]
  8. Wider, G.; Neri, D.; Wüthrich, W. Studies of slow conformational equilibria in macromolecules by exchange of heteronuclear longitudinal 2-spin-order in a 2D difference correlation experiment. J. Biomol. NMR 1991, 1, 93–98. [Google Scholar] [CrossRef]
  9. Haupt, C.; Patzschke, R.; Weininger, U.; Gröger, S.; Kovermann, M.; Balbach, J. Transient enzyme-substrate recognition monitored by real-time NMR. J. Am. Chem. Soc. 2011, 133, 11154–11162. [Google Scholar]
  10. Zeeb, M.; Balbach, J. Protein folding studied by real-time NMR spectroscopy. Methods 2004, 34, 65–74. [Google Scholar] [CrossRef]
  11. Schanda, P.; Brutscher, B. Very fast two-dimensional NMR spectroscopy for real-time investigation of dynamic events in proteins on the time scale of seconds. J. Am. Chem. Soc. 2005, 127, 8014–8015. [Google Scholar] [CrossRef]
  12. Frydman, L.; Scherf, T.; Lupulescu, A. The acquisition of multidimensional NMR spectra within a single scan. Proc. Nat. Acad. Sci. USA 2002, 99, 15858–15862. [Google Scholar] [CrossRef]
  13. Rennella, E.; Cutuil, T.; Schanda, P.; Ayala, I.; Forge, V.; Brutscher, B. Real-time NMR characterization of structure and dynamics in a transiently populated protein folding intermediate. J. Am. Chem. Soc. 2012, 134, 8066–8069. [Google Scholar] [CrossRef]
  14. Bowen, S.; Hilty, C. Time-resolved dynamic nuclear polarization enhanced NMR spectroscopy. Angew. Chem. Int. Edit. 2008, 47, 5235–5237. [Google Scholar] [CrossRef]
  15. Harris, T.; Giraudeau, P.; Frydman, L. Kinetics from indirectly detected hyperpolarized NMR spectroscopy by using spatially selective coherence transfers. Chem. Eur. J. 2011, 17, 697–703. [Google Scholar] [CrossRef]
  16. Berjanskii, M.V.; Wishart, D.S. A simple method to predict protein flexibility using secondary chemical shifts. J. Am. Chem. Soc. 2005, 127, 14970–14971. [Google Scholar] [CrossRef]
  17. Li, D.W.; Brüschweiler, R. Certification of molecular dynamics trajectories with NMR chemical shifts. J. Phys. Chem. Lett. 2010, 1, 246–248. [Google Scholar] [CrossRef]
  18. Robustelli, P.; Stafford, K.A.; Palmer, A.G. Interpreting protein structural dynamics from NMR chemical shifts. J. Am. Chem. Soc. 2012, 134, 6365–6374. [Google Scholar] [CrossRef]
  19. Xue, Y.; Ward, J.M.; Yuwen, T.R.; Podkorytov, I.S.; Skrynnikov, N.R. Microsecond time-scale conformational exchange in proteins: Using long molecular dynamics trajectory to simulate NMR relaxation dispersion data. J. Am. Chem. Soc. 2012, 134, 2555–2562. [Google Scholar] [CrossRef]
  20. Shaw, D.E.; Maragakis, P.; Lindorff-Larsen, K.; Piana, S.; Dror, R.O.; Eastwood, M.P.; Bank, J.A.; Jumper, J.M.; Salmon, J.K.; Shan, Y.B.; Wriggers, W. Atomic-level characterization of the structural dynamics of proteins. Science 2010, 330, 341–346. [Google Scholar] [CrossRef]
  21. Reif, B.; Hennig, M.; Griesinger, C. Direct measurement of angles between bond vectors in high-resolution NMR. Science 1997, 276, 1230–1233. [Google Scholar] [CrossRef]
  22. Vögeli, B. Comprehensive description of NMR cross-correlated relaxation under anisotropic molecular tumbling and correlated local dynamics on all time scales. J. Chem. Phys. 2010, 133, 014501:1–014501:13. [Google Scholar]
  23. Vugmeyster, L.; Pelupessy, P.; Vugmeister, B.E.; Abergel, D.; Bodenhausen, G. Cross-correlated relaxation in NMR of macromolecules in the presence of fast and slow internal dynamics. C.R. Phys. 2004, 5, 377–386. [Google Scholar] [CrossRef]
  24. Pelupessy, P.; Ravindranathan, S.; Bodenhausen, G. Correlated motions of successive amide N-H bonds in proteins. J. Biomol. NMR 2003, 25, 265–280. [Google Scholar] [CrossRef]
  25. Vögeli, B.; Yao, L.S. Correlated dynamics between protein hn and hc bonds observed by NMR cross relaxation. J. Am. Chem. Soc. 2009, 131, 3668–3678. [Google Scholar] [CrossRef]
  26. Ban, D.; Gossert, A.D.; Giller, K.; Becker, S.; Griesinger, C.; Lee, D. Exceeding the limit of dynamics studies on biomolecules using high spin-lock field strengths with a cryogenically cooled probehead. J. Magn. Reson. 2012, 221, 1–4. [Google Scholar] [CrossRef]
  27. Lakomek, N.A.; Carlomagno, T.; Becker, S.; Griesinger, C.; Meiler, J. A thorough dynamic interpretation of residual dipolar couplings in ubiquitin. J. Biomol. NMR 2006, 34, 101–115. [Google Scholar] [CrossRef]
  28. Lange, O.F.; Lakomek, N.A.; Farés, C.; Schröder, G.F.; Walter, K.F.; Becker, S.; Meiler, J.; Grubmüller, H.; Griesinger, C.; de Groot, B.L. Recognition dynamics up to microseconds revealed from an RDC-derived ubiquitin ensemble in solution. Science 2008, 320, 1471–1475. [Google Scholar] [CrossRef]
  29. Tjandra, N.; Bax, A. Direct measurement of distances and angles in biomolecules by NMR in a dilute liquid crystalline medium. Science 1997, 278, 1111–1114. [Google Scholar] [CrossRef]
  30. Tolman, J.R.; Flanagan, J.M.; Kennedy, M.A.; Prestegard, J.H. NMR evidence for slow collective motions in cyanometmyoglobin. Nat. Struct. Mol. Biol. 1997, 4, 292–297. [Google Scholar] [CrossRef]
  31. Saupe, A.; Englert, G. High-resolution nuclear magnetic resonance spectra of orientated molecules. Phys. Rev. Lett. 1963, 11, 462–464. [Google Scholar] [CrossRef]
  32. Saupe, A. Kernresonanzen in kristallinen flüssigkeiten und in kristallinflussigen lösungen. I. Z. Naturforsch. A 1964, A 19, 161–171. [Google Scholar]
  33. Saupe, A. Recent results in field of liquid crystals. Angew. Chem. Int. Edit. 1968, 7, 97–118. [Google Scholar] [CrossRef]
  34. Snyder, L.C. Analysis of nuclear magnetic resonance spectra of molecules in liquid-crystal solvents. J. Chem. Phys. 1965, 43, 4041–4050. [Google Scholar] [CrossRef]
  35. Gayathri, C.; Bothner-By, A.A.; van Zijl, P.C.M.; Maclean, C. Dipolar magnetic-field effects in NMR-spectra of liquids. Chem. Phys. Lett. 1982, 87, 192–196. [Google Scholar] [CrossRef]
  36. Lohman, J.A.B.; Maclean, C. Alignment Effects on High-Resolution NMR-spectra, Induced by the magnetic-field. Chem. Phys. 1978, 35, 269–274. [Google Scholar] [CrossRef]
  37. van Zijl, P.C.M.; Ruessink, B.H.; Bulthuis, J.; Maclean, C. NMR of partially aligned liquids–Magnetic-susceptibility anisotropies and dielectric-properties. Acc. Chem. Res. 1984, 17, 172–180. [Google Scholar] [CrossRef]
  38. Celebre, G.; Longeri, M.; Emsley, J.W. The Nature of the internal rotational barrier in benzyl-chloride - an interpretation of the dipolar coupling-constants obtained from the analysis of the proton NMR-spectra of samples dissolved in liquid-crystal solvents. Mol. Phys. 1988, 64, 715–723. [Google Scholar] [CrossRef]
  39. Celebre, G.; Longeri, M.; Emsley, J.W. An investigation by NMR-spectroscopy of the dependence on internal motion of the orientational ordering of ethoxybenzene and 4-fluoroethoxybenzene when dissolved in a nematic solvent. Liq. Cryst. 1989, 6, 689–700. [Google Scholar] [CrossRef]
  40. Counsell, C.J.R.; Emsley, J.W.; Luckhurst, G.R.; Sachdev, H.S. Orientational order in the 4-n-alkyloxy-4'-cyanobiphenyls–a comparison between experiment and theory. Mol. Phys. 1988, 63, 33–47. [Google Scholar] [CrossRef]
  41. Emsley, J.W.; Foord, E.K.; Gandy, P.J.F.; Turner, D.L.; Zimmermann, H. Assignment of the quadrupolar splittings in fully deuteriated alkyl chains of liquid-crystalline compounds–the case of 4-n-hexyloxy-4'-cyanobiphenyl. Liq. Cryst. 1994, 17, 303–309. [Google Scholar] [CrossRef]
  42. Emsley, J.W.; Heaton, N.J.; Kimmings, M.K.; Longeri, M. The conformation and orientational order of 1-ethoxy-4-chlorobenzene dissolved in a nematic liquid-crystal. Mol. Phys. 1987, 61, 433–442. [Google Scholar] [CrossRef]
  43. Emsley, J.W.; Luckhurst, G.R. The effect of internal motion on the orientational order parameters for liquid-crystalline systems. Mol. Phys. 1980, 41, 19–29. [Google Scholar] [CrossRef]
  44. Emsley, J.W.; Luckhurst, G.R.; Stockley, C.P. The deuterium and proton-(Deuterium) NMR-spectra of the partially deuteriated nematic liquid-crystal 4-n-pentyl-4'-cyanobiphenyl. Mol. Phys. 1981, 44, 565–580. [Google Scholar] [CrossRef]
  45. Rosen, M.E.; Rucker, S.P.; Schmidt, C.; Pines, A. 2-Dimensional proton NMR-studies of the conformations and orientations of n-alkanes in a liquid-crystal solvent. J. Phys. Chem. 1993, 97, 3858–3866. [Google Scholar] [CrossRef]
  46. Sinton, S.W.; Zax, D.B.; Murdoch, J.B.; Pines, A. Multiple-quantum NMR-study of molecular-structure and ordering in a liquid-crystal. Mol. Phys. 1984, 53, 333–362. [Google Scholar] [CrossRef]
  47. Tolman, J.R.; Flanagan, J.M.; Kennedy, M.A.; Prestegard, J.H. Nuclear magnetic dipole interactions in field-oriented proteins–information for structure determination in solution. Proc. Nat. Acad. Sci. USA 1995, 92, 9279–9283. [Google Scholar] [CrossRef]
  48. Kung, H.C.; Wang, K.Y.; Goljer, I.; Bolton, P.H. Magnetic alignment of duplex and quadruplex DNAs. J. Magn. Reson. Ser. B 1995, 109, 323–325. [Google Scholar] [CrossRef]
  49. Tjandra, N.; Grzesiek, S.; Bax, A. Magnetic field dependence of nitrogen-proton J splittings in N-15-enriched human ubiquitin resulting from relaxation interference and residual dipolar coupling. J. Am. Chem. Soc. 1996, 118, 6264–6272. [Google Scholar] [CrossRef]
  50. Clore, G.M.; Starich, M.R.; Gronenborn, A.M. Measurement of residual dipolar couplings of macromolecules aligned in the nematic phase of a colloidal suspension of rod-shaped viruses. J. Am. Chem. Soc. 1998, 120, 10571–10572. [Google Scholar] [CrossRef]
  51. Hansen, M.R.; Mueller, L.; Pardi, A. Tunable alignment of macromolecules by filamentous phage yields dipolar coupling interactions. Nat. Struct. Mol. Biol. 1998, 5, 1065–1074. [Google Scholar] [CrossRef]
  52. Hansen, M.R.; Rance, M.; Pardi, A. Observation of long-range H-1-H-1 distances in solution by dipolar coupling interactions. J. Am. Chem. Soc. 1998, 120, 11210–11211. [Google Scholar] [CrossRef]
  53. Barrientos, L.G.; Dolan, C.; Gronenborn, A.M. Characterization of surfactant liquid crystal phases suitable for molecular alignment and measurement of dipolar couplings. J. Biomol. NMR 2000, 16, 329–337. [Google Scholar] [CrossRef]
  54. Prosser, R.S.; Losonczi, J.A.; Shiyanovskaya, I.V. Use of a novel aqueous liquid crystalline medium for high-resolution NMR of macromolecules in solution. J. Am. Chem. Soc. 1998, 120, 11010–11011. [Google Scholar] [CrossRef]
  55. Rückert, M.; Otting, G. Alignment of biological macromolecules in novel nonionic liquid crystalline media for NMR experiments. J. Am. Chem. Soc. 2000, 122, 7793–7797. [Google Scholar] [CrossRef]
  56. Chou, J.J.; Gaemers, S.; Howder, B.; Louis, J.M.; Bax, A. A simple apparatus for generating stretched polyacrylamide gels, yielding uniform alignment of proteins and detergent micelles. J. Biomol. NMR 2001, 21, 377–382. [Google Scholar] [CrossRef]
  57. Sass, H.J.; Musco, G.; Stahl, S.J.; Wingfield, P.T.; Grzesiek, S. Solution NMR of proteins within polyacrylamide gels: Diffusional properties and residual alignment by mechanical stress or embedding of oriented purple membranes. J. Biomol. NMR 2000, 18, 303–309. [Google Scholar]
  58. Tycko, R.; Blanco, F.J.; Ishii, Y. Alignment of biopolymers in strained gels: A new way to create detectable dipole-dipole couplings in high-resolution biomolecular NMR. J. Am. Chem. Soc. 2000, 122, 9340–9341. [Google Scholar] [CrossRef]
  59. Koenig, B.W.; Hu, J.S.; Ottiger, M.; Bose, S.; Hendler, R.W.; Bax, A. NMR measurement of dipolar couplings in proteins aligned by transient binding to purple membrane fragments. J. Am. Chem. Soc. 1999, 121, 1385–1386. [Google Scholar] [CrossRef]
  60. Sass, J.; Cordier, F.; Hoffmann, A.; Cousin, A.; Omichinski, J.G.; Lowen, H.; Grzesiek, S. Purple membrane induced alignment of biological macromolecules in the magnetic field. J. Am. Chem. Soc. 1999, 121, 2047–2055. [Google Scholar] [CrossRef]
  61. Bax, A.; Kontaxis, G.; Tjandra, N. Dipolar couplings in macromolecular structure determination. Methods Enzymol. 2001, 339, 127–174. [Google Scholar] [CrossRef]
  62. Chen, K.; Tjandra, N. The use of residual dipolar coupling in studying proteins by NMR. Top. Curr. Chem. 2012, 326, 47–67. [Google Scholar] [CrossRef]
  63. Tolman, J.R.; Ruan, K. NMR residual dipolar couplings as probes of biomolecular dynamics. Chem. Rev. 2006, 106, 1720–1736. [Google Scholar] [CrossRef]
  64. Bax, A.; Vuister, G.W.; Grzesiek, S.; Delaglio, F.; Wang, A.C.; Tschudin, R.; Zhu, G. Measurement of Homonuclear and Heteronuclear J-Couplings from Quantitative J-Correlation. Methods Enzymol. 1994, 239, 79–105. [Google Scholar] [CrossRef]
  65. Prestegard, J.H.; Al-Hashimi, H.M.; Tolman, J.R. NMR structures of biomolecules using field oriented media and residual dipolar couplings. Quart. Rev. Biophys. 2000, 33, 371–424. [Google Scholar] [CrossRef]
  66. Prestegard, J.H.; Mayer, K.L.; Valafar, H.; Benison, G.C. Determination of protein backbone structures from residual dipolar couplings. Methods Enzymol. 2005, 394, 175–209. [Google Scholar] [CrossRef]
  67. Losonczi, J.A.; Andrec, M.; Fischer, M.W.F.; Prestegard, J.H. Order matrix analysis of residual dipolar couplings using singular value decomposition. J. Magn. Reson. 1999, 138, 334–342. [Google Scholar] [CrossRef]
  68. Tolman, J.R. A novel approach to the retrieval of structural and dynamic information from residual dipolar couplings using several oriented media in biomolecular NMR spectroscopy. J. Am. Chem. Soc. 2002, 124, 12020–12030. [Google Scholar] [CrossRef]
  69. Zweckstetter, M. NMR: Prediction of molecular alignment from structure using the PALES software. Nat. Protoc. 2008, 3, 679–690. [Google Scholar] [CrossRef]
  70. Zweckstetter, M.; Bax, A. Prediction of sterically induced alignment in a dilute liquid crystalline phase: Aid to protein structure determination by NMR. J. Am. Chem. Soc. 2000, 122, 3791–3792. [Google Scholar] [CrossRef]
  71. Valafar, H.; Prestegard, J.H. REDCAT: A residual dipolar coupling analysis tool. J. Magn. Reson. 2004, 167, 228–241. [Google Scholar] [CrossRef]
  72. Meiler, J.; Prompers, J.J.; Peti, W.; Griesinger, C.; Brüschweiler, R. Model-free approach to the dynamic interpretation of residual dipolar couplings in globular proteins. J. Am. Chem. Soc. 2001, 123, 6098–6107. [Google Scholar] [CrossRef]
  73. Louhivuori, M.; Otten, R.; Lindorff-Larsen, K.; Annila, A. Conformational fluctuations affect protein alignment in dilute liquid crystal media. J. Am. Chem. Soc. 2006, 128, 4371–4376. [Google Scholar] [CrossRef]
  74. Salvatella, X.; Richter, B.; Vendruscolo, M. Influence of the fluctuations of the alignment tensor on the analysis of the structure and dynamics of proteins using residual dipolar couplings. J. Biomol. NMR 2008, 40, 71–81. [Google Scholar] [CrossRef]
  75. Bernadó, P.; Blanchard, L.; Timmins, P.; Marion, D.; Ruigrok, R.W.H.; Blackledge, M. A structural model for unfolded proteins from residual dipolar couplings and small-angle x-ray scattering. Proc. Nat. Acad. Sci. USA 2005, 102, 17002–17007. [Google Scholar] [CrossRef]
  76. Bertoncini, C.W.; Jung, Y.S.; Fernández, C.O.; Hoyer, W.; Griesinger, C.; Jovin, T.M.; Zweckstetter, M. Release of long-range tertiary interactions potentiates aggregation of natively unstructured alpha-synuclein. Proc. Nat. Acad. Sci. USA 2005, 102, 1430–1435. [Google Scholar] [CrossRef]
  77. Rodriguez-Castañeda, F.; Haberz, P.; Leonov, A.; Griesinger, C. Paramagnetic tagging of diamagnetic proteins for solution NMR. Magn. Reson. Chem. 2006, 44, S10–S16. [Google Scholar] [CrossRef]
  78. Bertini, I.; Del Bianco, C.; Gelis, I.; Katsaros, N.; Luchinat, C.; Parigi, G.; Peana, M.; Provenzani, A.; Zoroddu, M.A. Experimentally exploring the conformational space sampled by domain reorientation in calmodulin. Proc. Nat. Acad. Sci. USA 2004, 101, 6841–6846. [Google Scholar] [CrossRef]
  79. Zhang, Q.; Throolin, R.; Pitt, S.W.; Serganov, A.; Al-Hashimi, H.M. Probing motions between equivalent RNA domains using magnetic field induced residual dipolar couplings: Accounting for correlations between motions and alignment. J. Am. Chem. Soc. 2003, 125, 10530–10531. [Google Scholar]
  80. Louhivuori, M.; Pääkkönen, K.; Fredriksson, K.; Permi, P.; Lounila, J.; Annila, A. On the origin of residual dipolar couplings from denatured proteins. J. Am. Chem. Soc. 2003, 125, 15647–15650. [Google Scholar] [CrossRef]
  81. Shortle, D.; Ackerman, M.S. Persistence of native-like topology in a denatured protein in 8 M urea. Science 2001, 293, 487–489. [Google Scholar] [CrossRef]
  82. Ozenne, V.; Bauer, F.; Salmon, L.; Huang, J.R.; Jensen, M.R.; Segard, S.; Bernadó, P.; Charavay, C.; Blackledge, M. Flexible-meccano: a tool for the generation of explicit ensemble descriptions of intrinsically disordered proteins and their associated experimental observables. Bioinformatics 2012, 28, 1463–1470. [Google Scholar] [CrossRef]
  83. Jensen, M.R.; Houben, K.; Lescop, E.; Blanchard, L.; Ruigrok, R.W.H.; Blackledge, M. Quantitative conformational analysis of partially folded proteins from residual dipolar couplings: Application to the molecular recognition element of Sendai virus nucleoprotein. J. Am. Chem. Soc. 2008, 130, 8055–8061. [Google Scholar] [CrossRef]
  84. Nodet, G.; Salmon, L.; Ozenne, V.; Meier, S.; Jensen, M.R.; Blackledge, M. Quantitative description of backbone conformational sampling of unfolded proteins at amino acid resolution from NMR residual dipolar couplings. J. Am. Chem. Soc. 2009, 131, 17908–17918. [Google Scholar] [CrossRef]
  85. Skrynnikov, N.R.; Goto, N.K.; Yang, D.W.; Choy, W.Y.; Tolman, J.R.; Mueller, G.A.; Kay, L.E. Orienting domains in proteins using dipolar couplings measured by liquid-state NMR: Differences in solution and crystal forms of maltodextrin binding protein loaded with beta-cyclodextrin. J. Mol. Biol. 2000, 295, 1265–1273. [Google Scholar] [CrossRef]
  86. Koehler, J.; Meiler, J. Expanding the utility of NMR restraints with paramagnetic compounds: Background and practical aspects. Prog. Nucl. Magn. Reson. Spectros. 2011, 59, 360–389. [Google Scholar] [CrossRef]
  87. Xu, X.F.; Keizers, P.H.J.; Reinle, W.; Hannemann, F.; Bernhardt, R.; Ubbink, M. Intermolecular dynamics studied by paramagnetic tagging. J. Biomol. NMR 2009, 43, 247–254. [Google Scholar] [CrossRef]
  88. Xu, X.F.; Reinle, W.G.; Hannemann, F.; Konarev, P.V.; Svergun, D.I.; Bernhardt, R.; Ubbink, M. Dynamics in a pure encounter complex of two proteins studied by solution scattering and paramagnetic NMR spectroscopy. J. Am. Chem. Soc. 2008, 130, 6395–6403. [Google Scholar] [CrossRef]
  89. Barbieri, R.; Bertini, I.; Lee, Y.M.; Luchinat, C.; Velders, A.H. Structure-independent cross-validation between residual dipolar couplings originating from internal and external orienting media. J. Biomol. NMR 2002, 22, 365–368. [Google Scholar] [CrossRef]
  90. Bertini, I.; Gupta, Y.K.; Luchinat, C.; Parigi, G.; Peana, M.; Sgheri, L.; Yuan, J. Paramagnetism-based NMR restraints provide maximum allowed probabilities for the different conformations of partially independent protein domains. J. Am. Chem. Soc. 2007, 129, 12786–12794. [Google Scholar]
  91. Pintacuda, G.; Keniry, M.A.; Huber, T.; Park, A.Y.; Dixon, N.E.; Otting, G. Fast structure-based assignment of 15N HSQC spectra of selectively 15N-labeled paramagnetic proteins. J. Am. Chem. Soc. 2004, 126, 2963–2970. [Google Scholar]
  92. Otting, G. Protein NMR using paramagnetic ions. Annu. Rev. Biophys. 2010, 39, 387–405. [Google Scholar] [CrossRef]
  93. Gaponenko, V.; Altieri, A.S.; Li, J.; Byrd, R.A. Breaking symmetry in the structure determination of (large) symmetric protein dimers. J. Biomol. NMR 2002, 24, 143–148. [Google Scholar] [CrossRef]
  94. Gaponenko, V.; Sarma, S.P.; Altieri, A.S.; Horita, D.A.; Li, J.; Byrd, R.A. Improving the accuracy of NMR structures of large proteins using pseudocontact shifts as long-range restraints. J. Biomol. NMR 2004, 28, 205–212. [Google Scholar] [CrossRef]
  95. Wöhnert, J.; Franz, K.J.; Nitz, M.; Imperiali, B.; Schwalbe, H. Protein alignment by a coexpressed lanthanide-binding tag for the measurement of residual dipolar couplings. J. Am. Chem. Soc. 2003, 125, 13338–13339. [Google Scholar] [CrossRef]
  96. Barthelmes, K.; Reynolds, A.M.; Peisach, E.; Jonker, H.R.A.; DeNunzio, N.J.; Allen, K.N.; Imperiali, B.; Schwalbe, H. Engineering Encodable Lanthanide-Binding Tags into Loop Regions of Proteins. J. Am. Chem. Soc. 2011, 133, 808–819. [Google Scholar] [CrossRef]
  97. Zhang, Q.; Sun, X.Y.; Watt, E.D.; Al-Hashimi, H.M. Resolving the motional modes that code for RNA adaptation. Science 2006, 311, 653–656. [Google Scholar] [CrossRef]
  98. Zhang, Q.; Stelzer, A.C.; Fisher, C.K.; Al-Hashimi, H.M. Visualizing spatially correlated dynamics that directs RNA conformational transitions. Nature 2007, 450, 1263–1267. [Google Scholar] [CrossRef]
  99. Hus, J.C.; Brüschweiler, R. Principal component method for assessing structural heterogeneity across multiple alignment media. J. Biomol. NMR 2002, 24, 123–132. [Google Scholar] [CrossRef]
  100. Hus, J.C.; Peti, W.; Griesinger, C.; Brüschweiler, R. Self-consistency analysis of dipolar couplings in multiple alignments of ubiquitin. J. Am. Chem. Soc. 2003, 125, 5596–5597. [Google Scholar]
  101. Peti, W.; Meiler, J.; Brüschweiler, R.; Griesinger, C. Model-free analysis of protein backbone motion from residual dipolar couplings. J. Am. Chem. Soc. 2002, 124, 5822–5833. [Google Scholar] [CrossRef]
  102. Lakomek, N.A.; Walter, K.F.; Farés, C.; Lange, O.F.; de Groot, B.L.; Grubmüller, H.; Brüschweiler, R.; Munk, A.; Becker, S.; Meiler, J.; et al. Self-consistent residual dipolar coupling based model-free analysis for the robust determination of nanosecond to microsecond protein dynamics. J. Biomol. NMR 2008, 41, 139–155. [Google Scholar] [CrossRef]
  103. Meirovitch, E.; Lee, D.; Walter, K.F.; Griesinger, C. Standard tensorial analysis of local ordering in proteins from residual dipolar couplings. J. Phys. Chem. B 2012, 116, 6106–6117. [Google Scholar] [CrossRef]
  104. Yao, L.; Vögeli, B.; Torchia, D.A.; Bax, A. Simultaneous NMR study of protein structure and dynamics using conservative mutagenesis. J. Phys. Chem. B 2008, 112, 6045–6056. [Google Scholar]
  105. Sabo, T.M.; Smith, C.A.; Ban, D.; Mazur, A.; Lee, D.; Griesinger, C. ORIUM: Optimized RDC-based iterative and unified model-free analysis. J. Biomol. NMR 2013, in press. [Google Scholar]
  106. Bremi, T.; Brüschweiler, R. Locally anisotropic internal polypeptide backbone dynamics by NMR relaxation. J. Am. Chem. Soc. 1997, 119, 6672–6673. [Google Scholar] [CrossRef]
  107. Brüschweiler, R.; Wright, P.E. NMR order parameters of biomolecules–A new analytical representation and application to the gaussian axial fluctuation model. J. Am. Chem. Soc. 1994, 116, 8426–8427. [Google Scholar] [CrossRef]
  108. Lienin, S.F.; Bremi, T.; Brutscher, B.; Brüschweiler, R.; Ernst, R.R. Anisotropic intramolecular backbone dynamics of ubiquitin characterized by NMR relaxation and MD computer simulation. J. Am. Chem. Soc. 1998, 120, 9870–9879. [Google Scholar] [CrossRef]
  109. Bernadó, P.; Blackledge, M. Local dynamic amplitudes on the protein backbone from dipolar couplings: Toward the elucidation of slower motions in biomolecules. J. Am. Chem. Soc. 2004, 126, 7760–7761. [Google Scholar] [CrossRef]
  110. Bernadó, P.; Blackledge, M. Anisotropic small amplitude peptide plane dynamics in proteins from residual dipolar couplings. J. Am. Chem. Soc. 2004, 126, 4907–4920. [Google Scholar] [CrossRef]
  111. Bouvignies, G.; Bernadó, P.; Meier, S.; Cho, K.; Grzesiek, S.; Brüschweiler, R.; Blackledge, M. Identification of slow correlated motions in proteins using residual dipolar and hydrogen-bond scalar couplings. Proc. Nat. Acad. Sci. USA 2005, 102, 13885–13890. [Google Scholar] [CrossRef]
  112. Salmon, L.; Bouvignies, G.; Markwick, P.; Lakomek, N.; Showalter, S.; Li, D.W.; Walter, K.; Griesinger, C.; Brüschweiler, R.; Blackledge, M. Protein conformational flexibility from structure-free analysis of nmr dipolar couplings: Quantitative and absolute determination of backbone motion in ubiquitin. Angew. Chem. Int. Edit. 2009, 48, 4154–4157. [Google Scholar] [CrossRef]
  113. Salmon, L.; Pierce, L.; Grimm, A.; Roldan, J.L.O.; Mollica, L.; Jensen, M.R.; van Nuland, N.; Markwick, P.R.L.; McCammon, J.A.; Blackledge, M. Multi-timescale conformational dynamics of the sh3 domain of cd2-associated protein using NMR spectroscopy and accelerated molecular dynamics. Angew. Chem. Int. Edit. 2012, 51, 6103–6106. [Google Scholar] [CrossRef]
  114. Farés, C.; Lakomek, N.A.; Walter, K.F.A.; Frank, B.T.C.; Meiler, J.; Becker, S.; Griesinger, C. Accessing ns-μs side chain dynamics in ubiquitin with methyl RDCs. J. Biomol. NMR 2009, 45, 23–44. [Google Scholar] [CrossRef]
  115. Ban, D.; Funk, M.; Gulich, R.; Egger, D.; Sabo, T.M.; Walter, K.F.; Fenwick, R.B.; Giller, K.; Pichierri, F.; de Groot, B.L.; et al. Kinetics of conformational sampling in ubiquitin. Angew. Chem. Int. Ed. Engl. 2011, 50, 11437–11440. [Google Scholar] [CrossRef]
  116. Fenwick, R.B.; Esteban-Martín, S.; Richter, B.; Lee, D.; Walter, K.F.; Milovanovic, D.; Becker, S.; Lakomek, N.A.; Griesinger, C.; Salvatella, X. Weak long-range correlated motions in a surface patch of ubiquitin involved in molecular recognition. J. Am. Chem. Soc. 2011, 133, 10336–10339. [Google Scholar] [CrossRef]
  117. Hamelberg, D.; Mongan, J.; McCammon, J.A. Accelerated molecular dynamics: A promising and efficient simulation method for biomolecules. J. Chem. Phys. 2004, 120, 11919–11929. [Google Scholar] [CrossRef]
  118. Markwick, P.R.L.; Bouvignies, G.; Blackledge, M. Exploring multiple timescale motions in protein GB3 using accelerated molecular dynamics and NMR spectroscopy. J. Am. Chem. Soc. 2007, 129, 4724–4730. [Google Scholar] [CrossRef]
  119. Markwick, P.R.L.; Bouvignies, G.; Salmon, L.; McCammon, J.A.; Nilges, M.; Blackledge, M. Toward a unified representation of protein structural dynamics in solution. J. Am. Chem. Soc. 2009, 131, 16968–16975. [Google Scholar]
  120. Fuglestad, B.; Gasper, P.M.; Tonelli, M.; McCammon, J.A.; Markwick, P.R.L.; Komives, E.A. The Dynamic Structure of Thrombin in Solution. Biophys. J. 2012, 103, 79–88. [Google Scholar] [CrossRef]
  121. Gasper, P.M.; Fuglestad, B.; Komives, E.A.; Markwick, P.R.L.; McCammon, J.A. Allosteric networks in thrombin distinguish procoagulant vs. anticoagulant activities. Proc. Nat. Acad. Sci. USA 2012, 109, 21216–21222. [Google Scholar]
  122. Cervantes, C.F.; Markwick, P.R.L.; Sue, S.C.; McCammon, J.A.; Dyson, H.J.; Komives, E.A. Functional dynamics of the folded ankyrin repeats of iκbα revealed by nuclear magnetic resonance. Biochemistry 2009, 48, 8023–8031. [Google Scholar] [CrossRef]
  123. Farrow, N.A.; Muhandiram, R.; Singer, A.U.; Pascal, S.M.; Kay, C.M.; Gish, G.; Shoelson, S.E.; Pawson, T.; Forman-Kay, J.D.; Kay, L.E. Backbone dynamics of a free and phosphopeptide-complexed Src homology 2 domain studied by 15N NMR relaxation. Biochemistry 1994, 33, 5984–6003. [Google Scholar] [CrossRef]
  124. Kay, L.E.; Torchia, D.A.; Bax, A. Backbone dynamics of proteins as studied by 15N inverse detected heteronuclear NMR spectroscopy: Application to staphylococcal nuclease. Biochemistry 1989, 28, 8972–8979. [Google Scholar] [CrossRef]
  125. Cordier, F.; Brutscher, B.; Marion, D. Measurement of 13Cα-13CO cross-relaxation rates in 15N- /13C -labelled proteins. J. Biomol. NMR 1996, 7, 163–168. [Google Scholar]
  126. Daragan, V.A.; Mayo, K.H. Motional model analyses of protein and peptide dynamics using 13C and 15N-NMR relaxation. Prog. Nucl. Magn. Reson. Spectrosc. 1997, 31, 63–105. [Google Scholar] [CrossRef]
  127. Muhandiram, D.R.; Yamazaki, T.; Sykes, B.D.; Kay, L.E. Measurement of 2H T1 and T relaxation times in uniformly 13C-labeled and fractionally 2H-labeled proteins in solution. J. Am. Chem. Soc. 1995, 117, 11536–11544. [Google Scholar] [CrossRef]
  128. Palmer III, A.G.; Rance, M.; Wright, P.E. Intramolecular motions of a zinc finger DNA-binding domain from XFIN characterized by proton-detected natural abundance 13C heteronuclear NMR spectroscopy. J. Am. Chem. Soc. 1991, 113, 4371–4380. [Google Scholar] [CrossRef]
  129. Yamazaki, T.; Muhandiram, R.; Kay, L.E. NMR experiments for the measurement of carbon relaxation properties in highly enriched, uniformly 13C, 15N-labeled proteins: Application to 13Cα carbons. J. Am. Chem. Soc. 1994, 116, 8266–7278. [Google Scholar] [CrossRef]
  130. Zeng, L.; Fischer, M.W.F.; Zuiderweg, E.R.P. Study of protein dynamics in solution by measurement of 13Cα-13CO NOE and 13CO longitudinal relaxation. J. Biomol. NMR 1996, 7, 157–162. [Google Scholar]
  131. Cavanagh, J.; Fairbrother, W.J.; Palmer III, A.G.; Rance, M.; Skelton, N.J. Principles and Practice: Protein NMR Spectroscopy, 2nd ed.; Elsevier: London, United Kingdom, 2007. [Google Scholar]
  132. Korzhnev, D.M.; Billeter, M.; Arseniev, A.S.; Orekhov, V.Y. NMR studies of Brownian tumbling and internal motions in proteins. Prog. Nucl. Magn. Reson. Spectros. 2001, 38, 197–266. [Google Scholar] [CrossRef]
  133. Lüginbuhl, P.; Wüthrich, K. Semi-classical nuclear spin relaxation theory revisted for use with biological macromolecules. Prog. Nucl. Magn. Reson. Spectros. 2002, 40, 199–247. [Google Scholar] [CrossRef]
  134. Palmer III, A.G. NMR probes of molecular dynamics: Overview and comparison with other techniques. Annu. Rev. Biophys. Biomol. Struct. 2001, 30, 129–155. [Google Scholar] [CrossRef]
  135. Ishima, R. Recent developments in 15N NMR relaxation studies that probe protein backbone dynamics. Top. Curr. Chem. 2012, 326, 99–122. [Google Scholar]
  136. Lipari, G.; Szabo, A. Model-free approach to the interpretation of nuclear magnetic resonance relaxtion in macromolecules. 1. Theory and range of validity. J. Am. Chem. Soc. 1982, 104, 4546–4559. [Google Scholar] [CrossRef]
  137. Lipari, G.; Szabo, A. Model-Free approach to the interpretation of nuclear magnetic-resonance relaxation in macromolecules. 2. Analysis of experimental results. J. Am. Chem. Soc. 1982, 104, 4559–4570. [Google Scholar] [CrossRef]
  138. Yang, D.; Kay, L.E. Contributions to conformational entropy arising from bond vector fluctuations measured from NMR-derived order parameters: application to protein folding. J. Mol. Biol. 1996, 263, 369–382. [Google Scholar]
  139. Akke, M.; Brüschweiler, R.; Palmer, A.G., 3rd. NMR order parameters and free energy: an analytical approach and its application to cooperative Ca2+ binding by calbindin D9k. J. Am. Chem. Soc. 1993, 115, 9832–9833. [Google Scholar] [CrossRef]
  140. Lee, A.L.; Kinnear, S.A.; Wand, A.J. Redistribution and loss of side chain entropy upon formation of a calmodulin-peptide complex. Nat. Struct. Biol. 2000, 7, 72–77. [Google Scholar] [CrossRef]
  141. Sabo, T.M.; Bakhtiari, D.; Walter, K.F.A.; McFeeters, R.L.; Giller, K.; Becker, S.; Griesinger, C.; Lee, D. Thermal coefficients of the methyl groups within ubiquitin. Protein Sci. 2012, 21, 562–570. [Google Scholar] [CrossRef]
  142. Clore, G.M.; Szabo, A.; Bax, A.; Kay, L.E.; Driscoll, P.C.; Gronenborn, A.M. Deviations from the simple two-paramter model-free approach to the interpretation of nitrogen-15 nuclear magnetic relaxation of proteins. J. Am. Chem. Soc. 1990, 112, 4989–4991. [Google Scholar] [CrossRef]
  143. Tjandra, N.; Feller, S.E.; Pastor, R.W.; Bax, A. Rotational diffusion anisotropy of human ubiquitin from 15N NMR relaxation. J. Am. Chem. Soc. 1995, 117, 12562–12566. [Google Scholar] [CrossRef]
  144. Baber, J.L.; Szabo, A.; Tjandra, N. Analysis of slow interdomain motion of macromolecules using NMR relaxation data. J. Am. Chem. Soc. 2001, 123, 3953–3959. [Google Scholar] [CrossRef]
  145. Brüschweiler, R.; Liao, X.; Wright, P.E. Long-range motional restrictions in a multidomain zinc-finger protein from anisotropic tumbling. Science 1995, 268, 886–889. [Google Scholar]
  146. Jackson, S.E. How do small single-domain proteins fold? Fold. Des. 1998, 3, R81–R91. [Google Scholar] [CrossRef]
  147. Korzhnev, D.M.; Salvatella, X.; Vendruscolo, M.; Di Nardo, A.A.; Davidson, A.R.; Dobson, C.M.; Kay, L.E. Low-populated folding intermediates of Fyn SH3 characterized by relaxation dispersion NMR. Nature 2004, 430, 586–590. [Google Scholar] [CrossRef]
  148. Kubelka, J.; Hofrichter, J.; Eaton, W.A. The protein folding ‘speed limit’. Curr. Opin. Struct. Biol. 2004, 14, 76–88. [Google Scholar] [CrossRef]
  149. Neira, J.L. NMR as a tool to identify and characterize protein folding intermediates. Arch. Biochem. Biophys. 2013, 531, 90–99. [Google Scholar] [CrossRef]
  150. Bhabha, G.; Lee, J.; Ekiert, D.C.; Gam, J.; Wilson, I.A.; Dyson, H.J.; Benkovic, S.J.; Wright, P.E. A dynamic knockout reveals that conformational fluctuations influence the chemical step of enzyme catalysis. Science 2011, 332, 234–238. [Google Scholar] [CrossRef]
  151. Boehr, D.D.; McElheny, D.; Dyson, H.J.; Wright, P.E. The dynamic energy landscape of dihydrofolate reductase catalysis. Science 2006, 313, 1638–1642. [Google Scholar]
  152. Eisenmesser, E.Z.; Millet, O.; Labeikovsky, W.; Korzhnev, D.M.; Wolf-Watz, M.; Bosco, D.A.; Skalicky, J.J.; Kay, L.E.; Kern, D. Intrinsic dynamics of an enzyme underlies catalysis. Nature 2005, 438, 117–121. [Google Scholar] [CrossRef]
  153. Boehr, D.D.; Dyson, H.J.; Wright, P.E. An NMR perspective on enzyme catalysis. Chem. Rev. 2006, 106, 3055–3079. [Google Scholar] [CrossRef]
  154. Wang, L.; Pang, Y.; Holder, T.; Brender, J.R.; Kurochkin, A.V.; Zuiderweg, E.R.P. Functional dynamics in the active site of the ribonuclease binase. Proc. Nat. Acad. Sci. USA 2001, 98, 7684–7689. [Google Scholar]
  155. Janin, J. The kinetics of protein-protein recognition. Protein. Struct. Funct. Genet. 1997, 28, 153–161. [Google Scholar] [CrossRef]
  156. McCammon, J.A. Theory of biomolecular recognition. Curr. Opin. Struct. Biol. 1998, 8, 245–249. [Google Scholar] [CrossRef]
  157. Sugase, K.; Dyson, H.J.; Wright, P.E. Mechanism of coupled folding and binding of an intrinsically disordered protein. Nature 2007, 447, 1021–1025. [Google Scholar] [CrossRef]
  158. Neudecker, P.; Lundström, P.; Kay, L.E. Relaxation dispersion NMR spectroscopy as a tool for detailed studies of protein folding. Biophys. J. 2009, 96, 2045–2054. [Google Scholar] [CrossRef]
  159. Palmer III, A.G.; Kroenke, C.D.; Loria, J.P. Nuclear magnetic resonance methods for quantifying microsecond-to-millisecond motions in biological macromolecules. Methods Enzymol. 2001, 339, 204–238. [Google Scholar] [CrossRef]
  160. Palmer III, A.G.; Massi, F. Characterization of the dynamics of biomacromolecules using rotating-frame spin relaxation NMR spectroscopy. Chem. Rev. 2006, 106, 1700–1719. [Google Scholar] [CrossRef]
  161. Luz, Z.; Meiboom, S. Nuclear magnetic resonance study of the protolysis of trimethylammonium ion in aqueous solution-order of the reaction with respect to solvent. J. Chem. Phys. 1963, 39, 366–370. [Google Scholar] [CrossRef]
  162. Wennerström, H. Nuclear magnetic relaxation induced by chemical exchange. Mol. Phys. 1972, 24, 69–80. [Google Scholar] [CrossRef]
  163. Millet, O.; Loria, J.P.; Kroenke, C.D.; Pons, M.; Palmer, A.G., 3rd. The static magnetic field dependence of chemical exchange linebroadening defines the NMR chemical shift time scale. J. Am. Chem. Soc. 2000, 122, 2867–2877. [Google Scholar] [CrossRef]
  164. Deverell, C.; Morgan, R.E.; Strange, J.H. Studies of chemical exchange by nuclear magnetic relaxation in the rotating frame. Mol. Phys. 1970, 18, 553–559. [Google Scholar] [CrossRef]
  165. Carr, H.Y.; Purcell, E.M. Effects of diffusion on free precession in nuclear magnetic resonance experiments. Phys. Rev. 1954, 54, 630–638. [Google Scholar] [CrossRef]
  166. Meiboom, S.; Gill, S. Modified spin-echo method for measuring nuclear relaxation times. Rev. Sci. Instrum. 1958, 29, 688–691. [Google Scholar] [CrossRef]
  167. Korzhnev, D.M.; Religa, T.L.; Banachewicz, W.; Fersht, A.R.; Kay, L.E. A transient and low-populated protein-folding intermediate at atomic resolution. Science 2010, 329, 1312–1316. [Google Scholar] [CrossRef]
  168. Mangia, S.; Traaseth, N.J.; Veglia, G.; Garwood, M.; Michaeli, S. Probing slow protein dynamics by adiabatic R and R NMR experiments. J. Am. Chem. Soc. 2010, 132, 9979–9981. [Google Scholar] [CrossRef]
  169. Traaseth, N.J.; Chao, F.; Masterson, L.R.; Mangia, S.; Garwood, M.; Michaeli, S.; Seelig, B.; Veglia, G. Heteronuclear adiabatic relaxation dispersion (HARD) for quantitative analysis of conformational dynamics in proteins. J. Magn. Reson. 2012, 219, 75–82. [Google Scholar] [CrossRef]
  170. Davis, D.G.; Perlman, M.E.; London, R.E. Direct measurements of the dissociation-rate constant for inhibitor-enzyme complexes via the T and T2 (CPMG) methods. J. Magn. Reson. 1994, 104, 266–275. [Google Scholar] [CrossRef]
  171. Loria, J.P.; Rance, M.; Palmer III, A.G. A relaxation-compensated carr-purcell-meiboom-gill sequence for characterizing chemical exchange by nmr spectroscopy. J. Am. Chem. Soc. 1999, 121, 2331–2332. [Google Scholar] [CrossRef]
  172. Mulder, F.A.A.; Skrynnikov, N.R.; Hon, B.; Dahlquist, F.W.; Kay, L.E. Measurement of slow (micro- to millisecond) time scale dynamics in protein side chains by 15N relaxation dispersion NMR spectroscopy: Application to Asn and Gln residues in a cavity mutant of T4 lysozyme. J. Am. Chem. Soc. 2001, 123, 967–975. [Google Scholar]
  173. Skrynnikov, N.R.; Mulder, F.A.; Hon, B.; Dahlquist, F.W.; Kay, L.E. Probing slow time scale dynamics at methyl-containing side chains in proteins by relaxation dispersion NMR measurements: application to methionine residues in a cavity mutant of T4 lysozyme. J. Am. Chem. Soc. 2001, 123, 4556–4566. [Google Scholar] [CrossRef]
  174. Tollinger, M.; Skrynnikov, N.R.; Mulder, F.A.; Forman-Kay, J.D.; Kay, L.E. Slow dynamics in folded and unfolded states of an SH3 domain. J. Am. Chem. Soc. 2001, 123, 11341–11352. [Google Scholar]
  175. Akke, M.; Liu, J.; Cavanagh, J.; Erickson, H.P.; Palmer III, A.G. Pervasive conformational fluctuations on microsecond time scales in a fibronectin type III domain. Nat. Struct. Biol. 1998, 5, 55–59. [Google Scholar] [CrossRef]
  176. Akke, M.; Palmer III, A.G. Monitoring macromolecular motions on microsecond to Milliesecond time scales by R-R1 constant relaxation time NMR spectrosocpy. J. Am. Chem. Soc. 1996, 118, 911–912. [Google Scholar] [CrossRef]
  177. Vugmeyster, L.; Kroenke, C.D.; Picart, F.; Palmer III, A.G.; Raleigh, P. 15N R1r measurements allow the determination of ultrafast protein folding rates. J. Am. Chem. Soc. 2000, 122, 5387–5388. [Google Scholar] [CrossRef]
  178. Dethoff, E.A.; Petzold, K.; Chugh, J.; Casiano-Negroni, A.; Al-Hashimi, H.M. Visualizing transient low-populated structures of RNA. Nature 2012, 491, 724–728. [Google Scholar]
  179. Nikolova, E.N.; Kim, E.; Wise, A.A.; O'Brien, P.J.; Andricioaei, I.; Al-Hashimi, H.M. Transient hoogsteen base pairs in canonical duplex DNA. Nature 2011, 470, 498–502. [Google Scholar] [CrossRef]
  180. Ishima, R.; Torchia, D.A. Estimating the time scale of chemical exchange of proteins from measurements of transverse relaxation rates in solution. J. Biomol. NMR 1999, 14, 369–372. [Google Scholar] [CrossRef]
  181. Carver, J.P.; Richards, R.E. A general two-site solution for the chemical exchange produced dependence of T2 upon the Carr-Purcell pulse separation. J. Magn. Reson. 1972, 6, 89–105. [Google Scholar]
  182. Korzhnev, D.M.; Orekhov, V.Y.; Dahlquist, F.W.; Kay, L.E. Off-resonance R relaxation outside of the fast exchange limit: An experimental study of a cavity mutant of T4 lysozyme. J. Biomol. NMR 2003, 26, 39–48. [Google Scholar] [CrossRef]
  183. Korzhnev, D.M.; Orekhov, V.Y.; Kay, L.E. Off-resonance R NMR studies of exchange dynamics in proteins with low spin-lock fields: an application to a Fyn SH3 domain. J. Am. Chem. Soc. 2005, 127, 713–721. [Google Scholar] [CrossRef]
  184. Trott, O.; Palmer, A.G., 3rd. R relaxation outside of the fast-exchange limit. J. Magn. Reson. 2002, 154, 157–160. [Google Scholar] [CrossRef]
  185. Massi, F.; Grey, M.J.; Palmer, A.G., 3rd. Microsecond timescale backbone conformational dynamics in ubiquitin studied with NMR R relaxation experiments. Protein Sci. 2005, 14, 735–742. [Google Scholar] [CrossRef]
  186. Salvi, N.; Ulzega, S.; Ferrage, F.; Bodenhausen, G. Timescales of slow motions in ubiquitin explored by heteronuclear double resonance. J. Am. Chem. Soc. 2012, 134, 2481–2484. [Google Scholar] [CrossRef]
  187. Wolf, M.; Gulich, R.; Lunkenheimer, P.; Loidl, A. Relaxation dynamics of a protein solution investigated by dielectric spectroscopy. Biochim. Biophys. Acta 2012, 1824, 723–730. [Google Scholar] [CrossRef]
  188. Ban, D.; Mazur, A.; Carneiro, M.G.; Sabo, T.M.; Giller, K.; Koharudin, L.M.I.; Becker, S.; Gronenborn, A.M.; Griesinger, C.; Lee, D. Enhanced accuracy of kinetic information from CT-CMPG experiments by transverse rotating-frame spectroscopy. J. Biomol. NMR 2013, 57, 73–82. [Google Scholar] [CrossRef]
  189. Ishima, R.; Wingfield, P.T.; Stahl, S.J.; Kaufman, J.D.; Torchia, D.A. Using amide 1H and 15N transverse relaxation to detect millisecond time-scale motions in perdeuterated proteins: application to HIV-1 protease. J. Am. Chem. Soc. 1998, 120, 10534–10542. [Google Scholar] [CrossRef]
  190. Ishima, R.; Torchia, D.A. Extending the range of amide proton relaxation dispersion experiments in proteins using a constant-time relaxation-compensated CPMG approach. J. Biomol. NMR 2003, 25, 243–248. [Google Scholar] [CrossRef]
  191. Eichmüller, C.; Skrynnikov, N.R. A new amide proton R experiment permits accurate characterization of microsecond time-scale conformational exchange. J. Biomol. NMR 2005, 32, 281–293. [Google Scholar] [CrossRef]
  192. Desvaux, H.; Berthault, P. Study of dynamic processes in liquids using off-resonance rf irradiation. Prog. Nucl. Magn. Reson. Spectros. 1999, 35, 295–340. [Google Scholar] [CrossRef]
  193. Mills, J.L.; Szyperski, T. Protein dynamics in supercooled water: the search for slow motional modes. J. Biomol. NMR 2002, 23, 63–67. [Google Scholar] [CrossRef]
  194. Skalicky, J.J.; Sukumaran, D.K.; Mills, J.L.; Szyperski, T. Toward structural biology in supercooled water. J. Am. Chem. Soc. 2000, 122, 3230–3231. [Google Scholar] [CrossRef]
  195. Igumenova, T.I.; Palmer, A.G., III. Off-Resonance TROSY-selected R experiment with improved sensitivity for medium- and high-molecular wegith proteins. J. Am. Chem. Soc. 2006, 128, 8110–8111. [Google Scholar] [CrossRef]
  196. Kempf, J.G.; Jung, J.; Sampson, N.S.; Loria, J.P. Off-resonance TROSY (R-R1) for quantitation of fast exchange processes in large proteins. J. Am. Chem. Soc. 2003, 125, 12064–12065. [Google Scholar] [CrossRef]
  197. Pervushin, K.; Riek, R.; Wider, G.; Wüthrich, K. Attenuated T2 relaxation by mutual cancellation of dipole-dipole coupling and chemical shift anisotropy indicates an avenue to NMR structures of very large biological macromolecules in solution. Proc. Nat. Acad. Sci. USA 1997, 94, 12366–12371. [Google Scholar] [CrossRef]
  198. Nietlispach, D. Suppression of anti-TROSY lines in a sensitivity enhanced gradient selection TROSY scheme. J. Biomol. NMR 2005, 31, 161–166. [Google Scholar] [CrossRef]
  199. Wang, A.C.; Bax, A. Minimizing the effects of radio-frequency heating in multidimensional NMR experiments. J. Biomol. NMR 1993, 3, 715–720. [Google Scholar]
  200. Jones, J.A.; Hodgkinson, P.; Barker, A.L.; Hore, P.J. Optimal sampling strategies for the measurement of spin-spin relaxation times. J. Magn. Reson. 1996, 113, 25–34. [Google Scholar] [CrossRef]
  201. Burnham, K.P.; Anderson, D.R. Model Selection and Multi-Model Inference; Springer: New York, NY, USA, 2002. [Google Scholar]
  202. Al-Hashimi, H.M.; Gosser, Y.; Gorin, A.; Hu, W.D.; Majumdar, A.; Patel, D.J. Concerted motions in HIV-1 TAR RNA may allow access to bound state conformations: RNA dynamics from NMR residual dipolar couplings. J. Mol. Biol. 2002, 315, 95–102. [Google Scholar] [CrossRef]

Share and Cite

MDPI and ACS Style

Ban, D.; Sabo, T.M.; Griesinger, C.; Lee, D. Measuring Dynamic and Kinetic Information in the Previously Inaccessible Supra-tc Window of Nanoseconds to Microseconds by Solution NMR Spectroscopy. Molecules 2013, 18, 11904-11937.

AMA Style

Ban D, Sabo TM, Griesinger C, Lee D. Measuring Dynamic and Kinetic Information in the Previously Inaccessible Supra-tc Window of Nanoseconds to Microseconds by Solution NMR Spectroscopy. Molecules. 2013; 18(10):11904-11937.

Chicago/Turabian Style

Ban, David, T. Michael Sabo, Christian Griesinger, and Donghan Lee. 2013. "Measuring Dynamic and Kinetic Information in the Previously Inaccessible Supra-tc Window of Nanoseconds to Microseconds by Solution NMR Spectroscopy" Molecules 18, no. 10: 11904-11937.

Article Metrics

Back to TopTop