Automated NMR relaxation dispersion data analysis using NESSY
© Bieri and Gooley; licensee BioMed Central Ltd. 2011
Received: 12 July 2011
Accepted: 27 October 2011
Published: 27 October 2011
Proteins are dynamic molecules with motions ranging from picoseconds to longer than seconds. Many protein functions, however, appear to occur on the micro to millisecond timescale and therefore there has been intense research of the importance of these motions in catalysis and molecular interactions. Nuclear Magnetic Resonance (NMR) relaxation dispersion experiments are used to measure motion of discrete nuclei within the micro to millisecond timescale. Information about conformational/chemical exchange, populations of exchanging states and chemical shift differences are extracted from these experiments. To ensure these parameters are correctly extracted, accurate and careful analysis of these experiments is necessary.
The software introduced in this article is designed for the automatic analysis of relaxation dispersion data and the extraction of the parameters mentioned above. It is written in Python for multi platform use and highest performance. Experimental data can be fitted to different models using the Levenberg-Marquardt minimization algorithm and different statistical tests can be used to select the best model. To demonstrate the functionality of this program, synthetic data as well as NMR data were analyzed. Analysis of these data including the generation of plots and color coded structures can be performed with minimal user intervention and using standard procedures that are included in the program.
NESSY is easy to use open source software to analyze NMR relaxation data. The robustness and standard procedures are demonstrated in this article.
KeywordsProtein dynamics software cpmg conformational/chemical exchange μs-ms motion van't Hoff transition state theory
Proteins are responsible for many different and important biochemical functions, such as ligand binding, signaling or catalysis [1–4]. Many of these events occur on the μs-ms timescale making the detection and interpretation of these motions critical for understanding their biological significance. Advances in solution Nuclear Magnetic Resonance (NMR) of biomolecules have enabled the measurement of protein dynamics on different timescales. Relaxation experiments measuring the two relaxation rates R1 (the longitudinal relaxation rate) and R2 (the transverse relaxation rate) as well as the steady state heteronuclear NOE are used to detect motion within ps-ns . However, detection of these motions is limited by the molecular tumbling of the molecule, which is on the order of ns. Recent developments in 15N/13C relaxation-compensated Carr-Purcell-Meiboom-Gill (CPMG) and R1ρ rotating-frame relaxation dispersion experiments [6–9] have enabled measurement of protein dynamics on the μs-ms timescale. From these experiments the exchange contribution to transverse relaxation (R ex ), exchange constant (k ex ), chemical shift differences between exchanging states (δω) and the population of individual states can be extracted. Consequently, relaxation dispersion experiments are commonly used to investigate changes in dynamics caused by ligand binding , to discover limiting events during enzyme catalysis , to follow protein folding and intermediate states as well as to detect functionally important hidden states . Furthermore, it has been proposed that a detailed understanding of the dynamical behavior of a protein at atomic resolution may help identify novel drug target sites .
Here, we present a novel software (NESSY) that is designed for simple and automated analysis of relaxation dispersion data. Data can be fitted to two states and at one or more field strengths. Model selection protocols are included for the selection of the best models and Monte Carlo simulations are used to estimate errors of extracted parameters. Furthermore, publication quality 2D and 3D plots and color coded structures are easily created.
where T CPMG is the constant CPMG time, I(0) is the intensity of the peak in the reference spectrum and I(v CPMG ) is the intensity of the peak at the CPMG frequency, vCPMG. Then, data are fitted to different models, which can be selected individually. These models are divided on the basis of no exchange (model 1), two-site fast (model 2) and two-site slow (model 3) exchange.
No exchange: model 1
where is the effective transverse relaxation rate at infinite vCPMG.
Two-state exchange: model 2 and 3
Where k a-b and k b-a are the forward and backward exchange rates, respectively, between the states A and B.
and p a and p b are the populations of the two state models (p a is the major conformation, p a + p b = 1), ke xis the chemical/conformational exchange (kex = k a-b + k b-a ) constant and δω is the chemical shift difference between states. In eq. (4) only , k ex and Φ can be extracted, as p b and, δω cannot be uniquely determined.
NESSY also automatically calculates the exchange contribution to transverse relaxation, R ex , where for fast exchange, R ex = Φ/k ex , and slow exchange, R ex = p a p b k ex /(1 + (k ex /δω) 2 ).
Optimization and Model Selection
Model selection is performed using AICc (Akaike information criteria with second order correction for small sample size) by default, but other tests, such as AIC or F-test are included as well . Uncertainties are estimated using 500 (default value, but user controlled) Monte Carlo simulations.
Extracted dynamics parameters of synthetic relaxation dispersion data.
Model 2, original
Model 2, ± 2%
Model 2, ± 5%
Model 2, ± 8%
Model 2, ± 10%
Model 3, original
Model 3, ± 2%
Model 3, ± 5%
Model 3, ± 8%
Model 3, ± 10%
Carr-Purcell-Meiboom-Gill (CPMG) relaxation dispersion experiments of a 0.3 mM PCTX1 sample (kindly provided by Prof. G. King, University of Queensland, Australia) were recorded on a Bruker 600 MHz AVANCE III spectrometer. Experiments were acquired at 298 K using 0.08 s constant CPMG period (TCPMG) as a single scanned interleaved pseudo 3D experiment. Relaxation dispersion profiles were obtained by recording spectra with varying CPMG pulse frequencies (νCPMG) (25, 2× 50, 75, 100, 2× 150, 2× 200, 300, 500, 600, 700, 900, 1000, 1500 and 2000 Hz). Spectra were processed in NMRPipe  and intensities extracted using CcpNmr .
Model selection of synthetic relaxation dispersion data.
Model 2, 2% error
Model 2, 5% error
Model 2, 8% error
Model 2, 10% error
Model 3, 2% error
Model 3, 5% error
Model 3, 8% error
Model 3, 10% error
The parameters k ex , p b and δω that were extracted for model 3 matched the initial parameters used to generate the synthetic data within the order of the introduced error (Table 1). As expected, introducing larger errors into the synthetic data sets produced larger errors for the extracted parameters (calculated by Monte Carlo Simulations).
Fitting relaxation dispersion experiments of PCTX1 at 600 MHz
Global fit to synthetic data
Model selection of global fit of synthetic relaxation dispersion data.
Extracted dynamic parameters of global fit of relaxation dispersion data.
Fit to Model 2
Fit to Model 3
The software presented in this article permits the automated data analysis of relaxation dispersion experiments. The user has the opportunity to choose to fit to the entire data set or individually selected residues. In addition, data from two or more magnetic fields can be globally fitted. During global fits, field dependency of δω is taken into account. Multiple residues can be grouped and analyzed simultaneously using built-in cluster analysis (individual or global fit).
Maximum flexibility of data entry has been included. For example, peak lists containing peak intensities that are created by any other software can be imported; protein sequences are read either from PDB files, retrieved from the internet using UniProt identifier http://www.expasy.ch or can be added manually; CPMG frequencies are read directly from Bruker VD (variable delay) lists. Furthermore, NESSY is linked to the Bruker Protein Dynamic Center (PDC, starting with version 1.1, http://www.bruker-biospin.com, in collaboration with Dr. Klaus-Peter Neidig) so that projects can be exported in PDC and directly read into NESSY for extended data analysis. In addition, NMRView  tables can be imported directly.
During the calculation, NESSY produces plots and CSV files (text files compatible with Excel and OpenOffice) of the profiles and the individual fits for each calculated residue as well as the extracted values (such as R 2 , k ex and p b ) and statistics (χ 2 and AICc) for each model. In addition, color coded structures for selected models, k ex and R ex are created (structures are drawn using Pymol). Furthermore, NESSY offers tools to create custom made 2D and 3D plots in different formats and styles suitable for publication (see Figures 2 to 6).
Synthetic data as well as experimental NMR CPMG relaxation dispersion data were analyzed using NESSY. The quality of fits of the synthetic data was assessed by comparing original values to those extracted from data analysis (Table 1 and 2, Figure 2). For choosing the best fitting model NESSY evaluates the need and benefit for describing the experimental data with more parameters by using AICc, AIC or F-test. By default, model selection is performed using AICc to avoid over fitting, as more parameters (more complex models) may give better fits. The advantage of using AICc (and AIC) compared to F-test is that data do not have to be normally distributed. As relaxation dispersion experiments usually consist of 15 to 20 data sets, normal distribution of data cannot be assumed. For the synthetic data the correct model was consistently chosen and the extracted values were statistically similar to the initial values. To demonstrate usability of NESSY for NMR data, two signals of PCTX1 were analyzed (Figures 3 and 4). One signal experienced slow-limit and the other fast-limit chemical exchange. In the case of slow exchange, the minor populated conformation was present at 0.8%, which is in accordance with the NMR spectra, where only one peak is visible.
To be able to unambiguously distinguish between fast and slow exchange and to extract populations and shift differences, experiments should be collected at two or more different magnetic fields . NESSY supports global fitting at multiple field strengths, while taking the field dependency of δω into account. Synthetic data for models 2 and 3 at two different static frequencies (600 and 800 MHz) were created and analyzed. Data were fitted to models 1 to 3 and in each case the correct model was chosen for both global fits (Tables 3 and 4, Figure 5).
In this article, the main features of NESSY have been presented, such as curve fitting, model selection and data presentation of relaxation dispersion experiments. Nevertheless, NESSY is not limited to these functions. As relaxation dispersion experiments enable the extraction of populations of individual states, NESSY offers tools to calculate the free energy (ΔG) between states. For data that fit best to fast exchange models, the populations of each state cannot be extracted, as k ex and δω cannot be uniquely determined. An integrated function in NESSY is to calculate the populations for residues with known chemical shift differences, such as observed in ligand binding experiments. If a series of experiments are recorded over a temperature range, the temperature dependence of ΔG can be used to extract entropy (ΔS) and enthalpy (ΔH) changes using van't Hoff analysis. NESSY supports automatic van't Hoff analysis of both linear and non-linear models . Furthermore, NESSY can calculate activation energy barriers using transition state theory and the Eyring equation and generate energy landscape plots.
Taken together, we present user-friendly software for NMR relaxation dispersion (15N/13C) data analysis that requires minimal user intervention. In addition, NESSY can be used to analyze biophysical experiments, such as van't Hoff and transition state theory analysis and to create publication quality 2D and 3D plots. Due to its flexibility, users can choose between different relaxation dispersion models and statistical tests for model selection. Results generated by NESSY are aimed to be usable for publication. Tables can be produced directly using CSV files; 2D and 3D plots are created during or after analysis and color coded structures can be directly used in publications. Note that each figure display in this article was created in NESSY. This software is open source and freely available from http://nessy.biochem.unimelb.edu.au. NESSY comes with a detailed manual and tutorial. For additional help, questions can be addressed at the NESSY mailing list (firstname.lastname@example.org).
Availability and requirements
Project name: NESSY
Project home page: http://nessy.biochem.unimelb.edu.au
Operating system(s): Platform independent
Programming language: Python
Other requirements: Scipy, Numpy, wxPython, Matplotlib (None for compiled binaries)
License: GNU GPL v3
Any restrictions to use by non-academics: None
Akaike's Information Criteria
Akaike's Information Criteria with second order correction for small sample size
NMR Relaxation Dispersion Spectroscopy Analysis Software
Nuclear Magnetic Resonance
Nuclear Overhauser Effect.
This work was supported by the Australian Research Council (ARC) and an equipment grant of the Rowden White Foundation (University of Melbourne). M.B. is a recipient of Swiss National Science Foundation (SNF) fellowships. The authors also thank Edward d'Auvergne for the comprehensive literature review about the hidden radian unit, which can be accessed in the NESSY help menu.
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