A Multifaceted Approach to the Interpretation of NMR Order Parameters: A Case Study of a Dynamic α-Helix

Structural characterization of the interaction of α-synuclein nascent chains with the ribosomal surface and trigger factor

The ribosome is increasingly becoming recognized as a key hub for integrating quality control processes associated with protein biosynthesis and cotranslational folding (CTF). The molecular mechanisms by which these processes take place, however, remain largely unknown, in particular in the case of intrinsically disordered proteins (IDPs). To address this question, we studied at a residue-specific level the structure and dynamics of ribosome-nascent chain complexes (RNCs) of α-synuclein (αSyn), an IDP associated with Parkinson's disease (PD). Using solution-state nuclear magnetic resonance (NMR) spectroscopy and coarse-grained molecular dynamics (MD) simulations, we find that, although the nascent chain (NC) has a highly disordered conformation, its N-terminal region shows resonance broadening consistent with interactions involving specific regions of the ribosome surface. We also investigated the effects of the ribosome-associated molecular chaperone trigger factor (TF) on αSyn structure and dynamics using resonance broadening to define a footprint of the TF-RNC interactions. We have used these data to construct structural models that suggest specific ways by which emerging NCs can interact with the biosynthesis and quality control machinery.

Time-averaged order parameter restraints in molecular dynamics simulations

A method is described that allows experimental S(2) order parameters to be enforced as a time-averaged quantity in molecular dynamics simulations. The two parameters that characterize time-averaged restraining, the memory relaxation time and the weight of the restraining potential energy term in the potential energy function used in the simulation, are systematically investigated based on two model systems, a vector with one end restrained in space and a pentapeptide. For the latter it is shown that the backbone N-H order parameter of individual residues can be enforced such that the spatial fluctuations of quantities depending on atomic coordinates are not significantly perturbed. The applicability to realistic systems is illustrated for the B3 domain of protein G in aqueous solution.

Synergistic applications of MD and NMR for the study of biological systems

Modern biological sciences are becoming more and more multidisciplinary. At the same time, theoretical and computational approaches gain in reliability and their field of application widens. In this short paper, we discuss recent advances in the areas of solution nuclear magnetic resonance (NMR) spectroscopy and molecular dynamics (MD) simulations that were made possible by the combination of both methods, that is, through their synergistic use. We present the main NMR observables and parameters that can be computed from simulations, and how they are used in a variety of complementary applications, including dynamics studies, model-free analysis, force field validation, and structural studies.

The disordered C-terminus of the RNA polymerase II phosphatase FCP1 is partially helical in the unbound state

Intrinsically disordered proteins (IDPs) lack unique 3D structures under native conditions and yet retain critical functions. Recycling of RNA Polymerase II after transcription is promoted by an interaction between the winged helix domain of RAP74, a component of the general transcription factor IIF (TFIIF), and the C-terminus of the TFIIF-associating CTD phosphatase (FCP1). Sixteen residues from the C-terminus of FCP1 form an α-helix in the complex, but the protein is otherwise agreed in the literature to be intrinsically disordered. Here we show through CD and recently developed carbon-detected NMR that, although FCP1 is intrinsically disordered, the above 16 residues composing the RAP74 binding surface form nascent α-helical structure in the unbound state. We further show retention of general FCP1 disorder and the nascent helical content in HeLa extract, establishing cellular relevance. The conformational bias observed leads to a mechanistic proposal for FCP1's transition from a disordered ensemble to an ordered conformation upon binding.

NMR order parameters calculated in an expanding reference frame: identifying sites of short- and long-range motion

NMR order parameters are calculated from molecular dynamics computer simulations of ubiquitin and the apo (Ca(2+)-free) state of calbindin D(9k). Calculations are performed in an expanding reference frame so as to discriminate between the effects of short- and long-range motions. This approach reveals that the dominant contributions to the order parameters are short-range. Longer-range contributions are limited to specific sites, many of which have been recognized in previous studies of correlated motions. These sites are identified on the basis of an effective reorientational number, n ( eff ). Not only does this parameter identify sites of short- and long-range motion, it also provides a way of evaluating the separability condition that is key to the Lipari-Szabo model-free method. When analyzed in conjunction with the Prompers-Brüschweiler separability index, the n ( eff ) values indicate that longer-range motions play a more prominent role in apo calbindin than they do in ubiquitin.

Methyl dynamics of a Ca2+-calmodulin-peptide complex from NMR/SRLS

We developed the slowly relaxing local structure (SRLS) approach for analyzing NMR spin relaxation in proteins. SRLS accounts for dynamical coupling between the tumbling of the protein and the local motion of the probe and for general tensorial properties. It is the generalization of the traditional model-free (MF) method, which does not account for mode-coupling and treats only simple tensorial properties. SRLS is applied herein to ²H relaxation of ¹³CDH₂ groups in the complex of Ca(2+)-calmodulin with the peptide smMLCKp. Literature data comprising ²H T₁ and T₂ acquired at 14.1 and 17.6 T, and 288, 295, 308, and 320 K, are used. We find that mode-coupling is a small effect for methyl dynamics. On the other hand, general tensorial properties are important. In particular, it is important to allow for the asymmetry of the local spatial restrictions, which can be represented in SRLS by a rhombic local ordering tensor with components S(0)(2) and S(2)(2). The principal axes frame of this tensor is obviously different from the axial frames of the magnetic tensors. Here, we find that -0.2 ≤ S(0)(2) ≤ 0.5 and -0.4 ≤ S(2)(2) ≤ 0. MF features a single "generalized" order parameter, S, confined to the 0-0.316 range; the local geometry is inherently simple. The parameter S is inaccurate, having absorbed unaccounted for effects, notably S(2)(2) ≠ 0. We find that the methionine methyls (the other methyl types) reorient with rates of 8.6 × 10⁹ to 21.4 × 10⁹ (0.67 × 10⁹ to 6.5 × 10⁹) 1/s. The corresponding activation energies are 10 (10-27) kJ/mol. By contrast, MF yields inaccurate effective local motional correlation times, τ(e), with nonphysical temperature dependence. Thus, the problematic S- and τ(e)-based MF picture of methyl dynamics has been replaced with an insightful physical picture based on a local ordering tensor related to structural features, and a local diffusion tensor that yields accurate activation energies.

Entropy localization in proteins

The configurational entropy of a protein is under physiological conditions a major contributor to the free energy. Its quantitative characterization is therefore an important step toward the understanding of protein function. The configurational entropy of the oncoprotein MDM2, whose determination is a challenge by experiment alone, is studied here by means of 0.4 μs molecular dynamics computer simulations in both the presence and absence of the p53-peptide ligand. By characterizing protein motions in dihedral angle space, it is found that the motional amplitudes change considerably upon ligand binding while correlations between dihedral angle motions are remarkably well conserved. This applies for backbone and side-chain dihedral angle pairs at both short- and long-range distance to the binding site. As a direct consequence, the change of the configurational entropy can be decomposed into a sum of local contributions. This significantly facilitates the understanding of the relationship between protein dynamics and thermodynamics, which is important, for example, in the context of protein-ligand and protein-protein interactions. The findings also have implications for the direct derivation of entropy changes from site-specific dynamics measurements as afforded by NMR spectroscopy.

Interpretation of biomolecular NMR spin relaxation parameters

Biomolecular nuclear magnetic resonance (NMR) spin relaxation experiments provide exquisite information on the picosecond to nanosecond timescale motions of bond vectors. Spin-lattice (T1) and spin-spin (T2) relaxation times and the steady-state nuclear Overhauser effect (NOE) are the first set of parameters extracted from typical 15N or 13C NMR relaxation experiments. Therefore, verifying that T1, T2, and NOE are consistent with theoretical predictions is an important step before carrying out the more detailed model-free and reduced spectral density mapping analyses commonly employed. In this mini-review, we discuss the essential motional parameters used to describe biomolecular dynamics in the context of a variety of examples of folded and intrinsically disordered proteins and peptides in aqueous and membrane mimetic environments. Estimates of these parameters can be used as input for an online interface, introduced herein, allowing plotting of trends of T1, T2, and NOE with magnetic field strength. The plots may serve as a first-check to the spectroscopist preparing to embark on a detailed NMR relaxation analysis.

The physical basis of model-free analysis of NMR relaxation data from proteins and complex fluids

NMR relaxation experiments have provided a wealth of information about molecular motions in macromolecules and ordered fluids. Even though a rigorous theory of spin relaxation is available, the complexity of the investigated systems often makes the interpretation of limited datasets challenging and ambiguous. To allow physically meaningful information to be extracted from the data without commitment to detailed dynamical models, several versions of a model-free (MF) approach to data analysis have been developed. During the past 2 decades, the MF approach has been used in the vast majority of all NMR relaxation studies of internal motions in proteins and other macromolecules, and it has also played an important role in studies of colloidal systems. Although the MF approach has been almost universally adopted, substantial disagreement remains about its physical foundations and range of validity. It is our aim here to clarify these issues. To this end, we first present rigorous derivations of the three well-known MF formulas for the time correlation function relevant for isotropic solutions. These derivations are more general than the original ones, thereby substantially extending the range of validity of the MF approach. We point out several common misconceptions and explain the physical significance of the approximations involved. In particular, we discuss symmetry requirements and the dynamical decoupling approximation that plays a key role in the MF approach. We also derive a new MF formula, applicable to anisotropic fluids and solids, including microcrystalline protein samples. The so-called slowly relaxing local structure (SRLS) model has been advanced as an alternative to the MF approach that does not require dynamical decoupling of internal and global motions. To resolve the existing controversy about the relative merits of the SRLS model and the MF approach, we formulate and solve a planar version of the SRLS model. The analytical solution of this model reveals the unphysical consequences of the symmetrical two-body Smoluchowski equation as applied to protein dynamics, thus refuting the widely held belief that the SRLS model is more accurate than the MF approach. The different results obtained by analyzing data with these two approaches therefore do not indicate the importance of dynamical coupling between internal and global motions. Finally, we explore the two principal mechanisms of dynamical coupling in proteins: torque-mediated and friction-mediated coupling. We argue by way of specific analytically solvable models that torque-mediated coupling (which the SRLS model attempts to capture) is unimportant because the relatively slow internal motions that might couple to the global motion tend to be intermittent (jumplike) in character, whereas friction-mediated coupling (which neither the SRLS model nor the MF approach incorporates) may be important for proteins with unstructured parts or flexibly connected domains.