Long-Range Residual Dipolar Couplings: A Tool for Determining the Configuration of Small Molecules.

Together with NOE and J coupling, one-bond residual dipolar coupling (RDC), which reports on the three-dimensional orientation of an internuclear vector in the molecular frame, plays an important role in the conformation and configuration analysis of small molecules in solution by NMR spectroscopy. When the molecule has few C-H bonds, or too many bonds are in parallel, the available RDCs may not be sufficient to obtain the alignment tensor used for structure elucidation. Long-range RDCs that connect nuclei over multiple bonds are normally not parallel to the single bonds and therefore complement one-bond RDCs. Herein we present a method for extracting the long-range RDC of a chosen proton or group of protons to all remotely connected carbon atoms, including non-protonated carbon atoms. Alignment tensors fitted directly to the total long-range couplings (T=J+D) enabled straightforward analysis of both the long-range and one-bond RDCs for strychnine.

relax: the analysis of biomolecular kinetics and thermodynamics using NMR relaxation dispersion data.

UNLABELLED: Nuclear magnetic resonance (NMR) is a powerful tool for observing the motion of biomolecules at the atomic level. One technique, the analysis of relaxation dispersion phenomenon, is highly suited for studying the kinetics and thermodynamics of biological processes. Built on top of the relax computational environment for NMR dynamics is a new dispersion analysis designed to be comprehensive, accurate and easy-to-use. The software supports more models, both numeric and analytic, than current solutions. An automated protocol, available for scripting and driving the graphical user interface (GUI), is designed to simplify the analysis of dispersion data for NMR spectroscopists. Decreases in optimization time are granted by parallelization for running on computer clusters and by skipping an initial grid search by using parameters from one solution as the starting point for another -using analytic model results for the numeric models, taking advantage of model nesting, and using averaged non-clustered results for the clustered analysis. AVAILABILITY AND IMPLEMENTATION: The software relax is written in Python with C modules and is released under the GPLv3+ license. Source code and precompiled binaries for all major operating systems are available from http://www.nmr-relax.com. CONTACT: edward@nmr-relax.com.

Challenge of large-scale motion for residual dipolar coupling based analysis of configuration: the case of fibrosterol sulfate A.

Fibrosterol sulfate A is a polysulfated bis-steroid with an atypical side chain. Due to the flexibility of the linker, large-scale motions that change dramatically the shape of the entire molecule are expected. Such motions pose major challenges to the structure elucidation and the correct determination of configuration. In this study, we will describe the determination of the relative configuration of fibrosterol sulfate A through a residual dipolar coupling based multiple alignment tensor analysis complemented by molecular dynamics. For completeness, we applied also the single tensor approach which is unreliable due to the large-scale motions and compare the results.

relaxGUI: a new software for fast and simple NMR relaxation data analysis and calculation of ps-ns and µs motion of proteins.

Investigation of protein dynamics on the ps-ns and µs-ms timeframes provides detailed insight into the mechanisms of enzymes and the binding properties of proteins. Nuclear magnetic resonance (NMR) is an excellent tool for studying protein dynamics at atomic resolution. Analysis of relaxation data using model-free analysis can be a tedious and time consuming process, which requires good knowledge of scripting procedures. The software relaxGUI was developed for fast and simple model-free analysis and is fully integrated into the software package relax. It is written in Python and uses wxPython to build the graphical user interface (GUI) for maximum performance and multi-platform use. This software allows the analysis of NMR relaxation data with ease and the generation of publication quality graphs as well as color coded images of molecular structures. The interface is designed for simple data analysis and management. The software was tested and validated against the command line version of relax.

Bijvoet in solution reveals unexpected stereoselectivity in a Michael addition.

The absolute configuration of small crystallizable molecules can be determined with anomalous X-ray diffraction as shown by Bijvoet in 1951. For the majority of compounds that can neither be crystallized nor easily be converted into crystallizable derivatives, stereocontrolled organic synthesis is still required to establish their absolute configuration. In this contribution, a new fundamental methodology for resolving the absolute configuration will be presented that does not require crystallization. With residual dipolar coupling enhanced NMR spectroscopy, ensembles of a limited number of structures are created reflecting the correct conformations and relative configuration. Subsequently, from these ensembles, optical rotation dispersion (ORD) spectra are predicted by DFT calculations and compared to experimental results. The combination of these two steps reveals the absolute configuration of a flexible molecule in solution, which is a big challenge to chiroptical methods and DFT in the absence of NMR spectroscopy. Here the absolute stereochemistry of the product of a new Michael addition, synthesized via a niobium(V) chiral enolate, will be elucidated by using the new methodology.

Optimisation of NMR dynamic models I. Minimisation algorithms and their performance within the model-free and Brownian rotational diffusion spaces.

The key to obtaining the model-free description of the dynamics of a macromolecule is the optimisation of the model-free and Brownian rotational diffusion parameters using the collected R (1), R (2) and steady-state NOE relaxation data. The problem of optimising the chi-squared value is often assumed to be trivial, however, the long chain of dependencies required for its calculation complicates the model-free chi-squared space. Convolutions are induced by the Lorentzian form of the spectral density functions, the linear recombinations of certain spectral density values to obtain the relaxation rates, the calculation of the NOE using the ratio of two of these rates, and finally the quadratic form of the chi-squared equation itself. Two major topological features of the model-free space complicate optimisation. The first is a long, shallow valley which commences at infinite correlation times and gradually approaches the minimum. The most severe convolution occurs for motions on two timescales in which the minimum is often located at the end of a long, deep, curved tunnel or multidimensional valley through the space. A large number of optimisation algorithms will be investigated and their performance compared to determine which techniques are suitable for use in model-free analysis. Local optimisation algorithms will be shown to be sufficient for minimisation not only within the model-free space but also for the minimisation of the Brownian rotational diffusion tensor. In addition the performance of the programs Modelfree and Dasha are investigated. A number of model-free optimisation failures were identified: the inability to slide along the limits, the singular matrix failure of the Levenberg-Marquardt minimisation algorithm, the low precision of both programs, and a bug in Modelfree. Significantly, the singular matrix failure of the Levenberg-Marquardt algorithm occurs when internal correlation times are undefined and is greatly amplified in model-free analysis by both the grid search and constraint algorithms. The program relax ( http://www.nmr-relax.com ) is also presented as a new software package designed for the analysis of macromolecular dynamics through the use of NMR relaxation data and which alleviates all of the problems inherent within model-free analysis.

Optimisation of NMR dynamic models II. A new methodology for the dual optimisation of the model-free parameters and the Brownian rotational diffusion tensor.

Finding the dynamics of an entire macromolecule is a complex problem as the model-free parameter values are intricately linked to the Brownian rotational diffusion of the molecule, mathematically through the autocorrelation function of the motion and statistically through model selection. The solution to this problem was formulated using set theory as an element of the universal set [formula: see text]-the union of all model-free spaces (d'Auvergne EJ and Gooley PR (2007) Mol BioSyst 3(7), 483-494). The current procedure commonly used to find the universal solution is to initially estimate the diffusion tensor parameters, to optimise the model-free parameters of numerous models, and then to choose the best model via model selection. The global model is then optimised and the procedure repeated until convergence. In this paper a new methodology is presented which takes a different approach to this diffusion seeded model-free paradigm. Rather than starting with the diffusion tensor this iterative protocol begins by optimising the model-free parameters in the absence of any global model parameters, selecting between all the model-free models, and finally optimising the diffusion tensor. The new model-free optimisation protocol will be validated using synthetic data from Schurr JM et al. (1994) J Magn Reson B 105(3), 211-224 and the relaxation data of the bacteriorhodopsin (1-36)BR fragment from Orekhov VY (1999) J Biomol NMR 14(4), 345-356. To demonstrate the importance of this new procedure the NMR relaxation data of the Olfactory Marker Protein (OMP) of Gitti R et al. (2005) Biochem 44(28), 9673-9679 is reanalysed. The result is that the dynamics for certain secondary structural elements is very different from those originally reported.

Probing the flexibility of the DsbA oxidoreductase from Vibrio cholerae--a 15N - 1H heteronuclear NMR relaxation analysis of oxidized and reduced forms of DsbA.

We have determined the structure of the reduced form of the DsbA oxidoreductase from Vibrio cholerae. The reduced structure shows a high level of similarity to the crystal structure of the oxidized form and is typical of this class of enzyme containing a thioredoxin domain with an inserted alpha-helical domain. Proteolytic and thermal stability measurements show that the reduced form of DsbA is considerably more stable than the oxidized form. NMR relaxation data have been collected and analyzed using a model-free approach to probe the dynamics of the reduced and oxidized states of DsbA. Akaike's information criteria have been applied both in the selection of the model-free models and the diffusion tensors that describe the global motions of each redox form. Analysis of the dynamics reveals that the oxidized protein shows increased disorder on the pico- to nanosecond and micro- to millisecond timescale. Many significant changes in dynamics are located either close to the active site or at the insertion points between the domains. In addition, analysis of the diffusion data shows there is a clear difference in the degree of interdomain movement between oxidized and reduced DsbA with the oxidized form being the more rigid. Principal components analysis has been employed to indicate possible concerted movements in the DsbA structure, which suggests that the modeled interdomain motions affect the catalytic cleft of the enzyme. Taken together, these data provide compelling evidence of a role for dynamics in the catalytic cycle of DsbA.

Set theory formulation of the model-free problem and the diffusion seeded model-free paradigm.

Model-free analysis of NMR relaxation data, which describes the motion of individual atoms, is a problem intricately linked to the Brownian rotational diffusion of the macromolecule. The diffusion tensor parameters strongly influence the optimisation of the various model-free models and the subsequent model selection between them. Finding the optimal model of the dynamics of the system among the numerous diffusion and model-free models is hence quite complex. Using set theory, the entirety of this global problem has been encapsulated by the universal set Ll, and its resolution mathematically formulated as the universal solution Ll. Ever since the original Lipari and Szabo papers the model-free dynamics of a molecule has most often been solved by initially estimating the diffusion tensor. The model-free models which depend on the diffusion parameter values are then optimised and the best model is chosen to represent the dynamics of the residue. Finally, the global model of all diffusion and model-free parameters is optimised. These steps are repeated until convergence. For simplicity this approach to Ll will be labelled the diffusion seeded model-free paradigm. Although this technique suffers from a number of problems many have been solved. All aspects of the diffusion seeded paradigm and its consequences, together with a few alternatives to the paradigm, will be reviewed through the use of set notation.

Model-free model elimination: a new step in the model-free dynamic analysis of NMR relaxation data.

Model-free analysis is a technique commonly used within the field of NMR spectroscopy to extract atomic resolution, interpretable dynamic information on multiple timescales from the R1, R2, and steady state NOE. Model-free approaches employ two disparate areas of data analysis, the discipline of mathematical optimisation, specifically the minimisation of a chi2 function, and the statistical field of model selection. By searching through a large number of model-free minimisations, which were setup using synthetic relaxation data whereby the true underlying dynamics is known, certain model-free models have been identified to, at times, fail. This has been characterised as either the internal correlation times, tau(e), tau(f), or tau(s), or the global correlation time parameter, local tau(m), heading towards infinity, the result being that the final parameter values are far from the true values. In a number of cases the minimised chi2 value of the failed model is significantly lower than that of all other models and, hence, will be the model which is chosen by model selection techniques. If these models are not removed prior to model selection the final model-free results could be far from the truth. By implementing a series of empirical rules involving inequalities these models can be specifically isolated and removed. Model-free analysis should therefore consist of three distinct steps: model-free minimisation, model-free model elimination, and finally model-free model selection. Failure has also been identified to affect the individual Monte Carlo simulations used within error analysis. Each simulation involves an independent randomised relaxation data set and model-free minimisation, thus simulations suffer from exactly the same types of failure as model-free models. Therefore, to prevent these outliers from causing a significant overestimation of the errors the failed Monte Carlo simulations need to be culled prior to calculating the parameter standard deviations.

The use of model selection in the model-free analysis of protein dynamics.

Model-free analysis of NMR relaxation data, which is widely used for the study of protein dynamics, consists of the separation of the global rotational diffusion from internal motions relative to the diffusion frame and the description of these internal motions by amplitude and timescale. Five model-free models exist, each of which describes a different type of motion. Model-free analysis requires the selection of the model which best describes the dynamics of the NH bond. It will be demonstrated that the model selection technique currently used has two significant flaws, under-fitting, and not selecting a model when one ought to be selected. Under-fitting breaks the principle of parsimony causing bias in the final model-free results, visible as an overestimation of S2 and an underestimation of taue and Rex. As a consequence the protein falsely appears to be more rigid than it actually is. Model selection has been extensively developed in other fields. The techniques known as Akaike's Information Criteria (AIC), small sample size corrected AIC (AICc), Bayesian Information Criteria (BIC), bootstrap methods, and cross-validation will be compared to the currently used technique. To analyse the variety of techniques, synthetic noisy data covering all model-free motions was created. The data consists of two types of three-dimensional grid, the Rex grids covering single motions with chemical exchange [S2,taue,Rex], and the Double Motion grids covering two internal motions [S f 2,S s 2,tau s ]. The conclusion of the comparison is that for accurate model-free results, AIC model selection is essential. As the method neither under, nor over-fits, AIC is the best tool for applying Occam's razor and has the additional benefits of simplifying and speeding up model-free analysis.