Abstract
The ability of highresolution NMR spectroscopy to readout the response of molecular interactions at multiple atomic sites presents a unique capability to define thermodynamic equilibrium constants and kinetic rate constants for complex, multiplestep biological interactions. Nonetheless, the extraction of the relevant equilibrium binding and rate constants requires the appropriate analysis of not only a readout that follows the equilibrium concentrations of typical binding titration curves, but also the lineshapes of NMR spectra. To best take advantage of NMR data for characterizing molecular interactions, we developed NmrLineGuru, a software tool with a userfriendly graphical user interface (GUI) to model twostate, threestate, and fourstate binding processes. Application of NmrLineGuru is through standalone GUIs, with no dependency on other software and no scripted input. NMR spectra can be fitted or simulated starting with userspecified input parameters and a chosen kinetic model. The ability to both simulate and fit NMR spectra provides the user the opportunity to not only determine the binding parameters that best reproduce the measured NMR spectra for the selected kinetic model, but to also query the possibility that alternative models agree with the data. NmrLineGuru is shown to provide an accurate, quantitative analysis of complex molecular interactions.
Introduction
NMR is a powerful technique to study molecular structure, dynamics and kinetics without the need for chemical modification. Due to its atomlevel resolution, it is particularly useful to study molecular interactions involving multistate equilibrium and can be used to simultaneously extract thermodynamics and kinetics parameters of each binding step^{1,2,3,4,5}. In contrast, the readout of other labelfree techniques, such as isothermal titration calorimetry, contains averaged information of multiple binding steps and/or provides estimates of only thermodynamics parameters^{6,7}.
To study binding interactions by NMR, a titration experiment is usually performed. At each titration point, an NMRobservable molecule (P) is mixed with its binding partner (L) at a certain ratio and 1D or 2D NMR spectra are recorded. The changes of chemical shifts, peak widths, and peak intensities observed during this process are then used to extract thermodynamics and kinetics parameters.
NMR titration data exhibit different behavior depending on the binding process and exchange regimes set by the relative values of the on/off kinetic rates and chemical shift frequencies of the various molecular species. For the fastexchange regime, the observed chemical shifts are a weighted average of the two exchanging states and thus thermodynamic parameters can be extracted directly from the normalized chemical shifts as for any titration binding curve^{1,8}. For the slowexchange regime, the peak intensities of exchanging states are proportional to their population and thus can be used to extract thermodynamic parameters^{1,6}. However, if the exchange falls in the intermediate regime or involves multiple binding steps or both thermodynamics and kinetics parameters are wanted, a lineshape analysis using the whole peak envelope is necessary.
Although lineshape analysis can extract both thermodynamics and kinetics parameters for multistate equilibrium binding models and all types of exchange regimes, the calculation steps are more complicated by involving both the equilibrium binding constants and kinetics rate constants. This complication limits the wide application of NMR lineshape analysis method.
Many published works involving NMR lineshape analysis utilized homewritten scripts which cannot be easily adopted^{2,3}. There are also several published software packages for NMR lineshape analysis which are summarized in Table 1. All the listed NMR lineshape analysis software packages require MATLAB installation, which is a commercial computing environment with expensive licensing fees. In addition, the MATLAB language syntax changes in different versions and older versions (required for older software) are harder to obtain and use as the compatible operating systems become obsolete. In addition, none of the listed software packages is fully based on a graphical user interface (GUI) for both lineshape simulation and fitting; running the scriptbased simulation or fitting requires a certain level of programming knowledge for MATLAB.
Based on our previous work in NMR lineshape analysis utilizing multistate equilibrium models^{3}, we developed NmrLineGuru, a standalone and userfriendly NMR lineshape software containing six GUIs for simulating and fitting NMR lineshape with two, three, and fourstate binding models. These GUIs have no dependency on other software; NmrLineGuru is developed in the MATLAB environment, but does not require separate installation of MATLAB. NmrLineGuru aims to be extremely userfriendly for nonexperts and timesaving with the hope of promoting the application of NMR lineshape analysis in research.
Results and Discussion
Models and interface
NmrLineGuru aims to be extremely friendly for nonexperienced users. It currently supports the most commonly used two, three, and fourstate binding models. For each model, there are two singlewindow GUI applications, one for simulating and the other for fitting 1D NMR lineshape data. Figure 1 shows screenshots of the 2 and 3state GUIs as examples (see Supporting Information Fig. S1 for the 4state GUIs). The input fields on each GUI are grouped and arranged by logical order to facilitate use. Default parameters are filled in by example, and to enable oneclick simulation or fitting.
Overview of the workflow
The general workflow of NmrLineGuru is shown in Fig. 2. Users are expected to provide only the minimal amount of information in the singlewindow GUI and the GUI will handle the subsequent steps automatically.
The simulation GUIs take the default or userprovided thermodynamic, kinetic, and resonance parameters to generate 1D NMR lineshape data for the userspecified concentrations of each species in a given titration series according to the selected model. The generated data can contain arbitrary noise and any number of points as requested by the user. The results will be automatically plotted, displayed, and saved in various formats (png, eps, fig, and txt) according to user preference.
The fitting GUIs read in the userprovided lineshape data to search for the bestmatch thermodynamic and kinetic parameters. The input can be data from the simulation GUIs, experimental data from 1D NMR spectra, or 1D slices from 2D HSQC experiments. The input format (detailed in online tutorials) is simple twocolumn text files that can be generated or converted from most NMRspectrum software packages. For the users’ convenience, a plugin for data export is provided and integrated in the NMRFAM^{9} distribution of Sparky (Goddard TD & Kneller DG, University of California, San Francisco), the most popular NMR spectra visualization tool^{9}. After reading the lineshape data and initial parameters, the fitting GUIs automatically normalize the input data, perform a Lorentzian fit to estimate resonance parameters, iteratively search the bestfit dynamic and kinetic parameters within the userspecified range of values, perform Monte Carlo error estimation, and output the results as plots and tables. Automatic global fitting will be performed if multiple datasets are found in the input data directory.
Example 2state simulations and fittings
The 2state simulation GUI simulates the singlestep binding process (P + L ↔ PL) with arbitrary parameters. Figure 3 shows example 2state simulations using the prefilled default parameters (300 μM [P_{total}]; 0–900 μM [L_{total}]; 10 μM K_{D}; NMR frequencies ω_{0} = 0, 500 s^{−1} for P and PL, respectively; all line widths dω = 100 s^{−1}) with different k_{off} values ranging from 0.01 to 100 × Δω (5–50000 s^{−1}) to highlight the effects of exchange kinetics on NMR lineshape. For a 2state binding system (free P and bound PL), the exchange rate is k_{ex} = k_{on} [L] + k_{off}, which is dominated by k_{off} at low ligand concentration. As expected, the generated lineshapes show canonical slowexchange behavior (Fig. 3b) when k_{off} ≪ Δω and fastexchange behavior (Fig. 3f) when k_{off} ≫ Δω. For moderate k_{off} values (0.1–10 × Δω), the resonances broaden to various extent and shows intermediateslow or intermediatefast behavior (Fig. 3c–e).
These simulated 2state lineshape data (50 data points sampled on each line with random noise, and signal/noise ≈50; a typical signal/noise level of 50–100 was seen in our NMR titration studies, such as the 29 kD Syk tSH2 constructs^{3,7}) are fitted with the 2state fitting GUI (Fig. 3 and Table 2). In all cases, the GUI correctly determines the K_{D} value. k_{off} values are determined for the range of 0.1–10 × Δω, and cannot be determined for values ≥ 100 × Δω, which is above the fastexchange limit (i.e. spectrum appearance becomes insensitive to the k_{off} values above the limit).
Example 3state simulations and fittings
The 3state simulation GUI can simulate any [L]dependent binding followed by a [L]independent step such as ligand isomerization or ligandinduced protein conformational change (Fig. 4a). Figure 4 displays example 3state simulations (300 μM [P_{total}]; 0–900 μM [L_{total}]; 10 μM K_{D}; 1 K_{eq}; NMR frequencies ω_{0} = 0, 500, 1000 s^{−1} for P, PL and P′L, respectively; all line widths dω = 100 s^{−1}) for fast or slow binding coupled with fast or slow isomerization (see Table 3 for k_{off} and k_{rev} values). For simplification, intermediate exchange is not illustrated for either step. For this 3state binding system (free P, bound PL and isomerized P′L), the isomerization step lacks dependency on ligand concentration so species PL and P′L form at a constant ratio defined by the equilibrium constant K_{eq} = [PL]/[P′L]. Coupled with the [L]dependent exchange between P and PL, this system has interesting behavior. When the isomerization step is slow exchange (Fig. 3c,e), PL and P′L resonances are separate peaks; the system can appear like 2state exchange between P and PL or P′L depending on K_{eq}. When the isomerization step is fast exchange (Fig. 3d,f), PL and P′L resonances show up as one peak; the system looks like 2state exchange between P and the PL/P′Ldegenerate peak. The behavior therefore can be deceptive and careful inspection of the spectra is needed when investigating the detailed binding mechanism^{1}.
The combined fitting and simulation capability of NmrLineGuru enables facile consideration of different binding models. The simulated 3state lineshape data (50 data points on each line with noise, signal/noise ≈50) were fitted with the 2 and 3state fitting GUIs. The results are summarized in Table 3. As required, the 3state model fits well with all the lineshape data (Supporting Information Fig. S2), and gives correct thermodynamic and kinetic parameters within 95% confidence intervals for most values. The difference in K_{D} estimated from resonance in Fig. 4c and the actual value is less than a factor of two, which is typically considered to be within experimental error in practice. Interestingly, the 2state model agrees well with the lineshape data when the isomerization is in fast exchange (Fig. 4d,f and Supporting Information Fig. S3). When both steps are in slow exchange, and the resonances for P and PL are selected for the 2state fitting, ignoring the P′L resonance, the lineshapes are well fitted (Fig. 4c and Supporting Information Fig. S3). But for the case where ligand binding is in fast exchange and isomerization is slow (Fig. 4e), fitting is poor even though the P′L resonance is ignored and deviations in fitting the NMR lineshapes are sufficient to suspect an incorrect model. Nevertheless, even for the cases where the lineshapes are well fitted, the K_{D} and k_{off} values are inaccurate, especially when both the binding and isomerization steps are in slow exchange (Table 3). In part, the apparent good fit of the lineshapes is due to the normalization step imposed in the fitting algorithm.
Example 4state simulations and fittings
The 4state simulation GUI can simulate any system with two independent or coupled binding sites and arbitrary binding affinities (Fig. 5a). Figure 5 shows example 4state simulations for two independent binding sites with similar binding affinities (300 μM [P_{total}]; 0–900 μM [L_{total}]; 10 μM K_{D} for all binding steps; NMR frequencies ω_{0} = 0, 400, 600, 1000 s^{−1} for P, PL, LP and LPL, respectively; all line widths dω = 100 s^{−1}), and disparate kinetic rate constants (see Table 4). Lineshape simulations are only shown for the limiting conditions of fast or slow exchange. When binding to both sites is in slow exchange, the NMR lineshape shows four resonances for the free, two singly ligated (LP and PL) and doubly ligated (LPL) forms of the protein (Fig. 5c), with the peak intensity for P gradually decreasing, that for LP and PL increasing and then decreasing, and that for LPL gradually increasing, which directly reflects the population change shown in Fig. 5b. When one of the two sites is in fast exchange, the NMR lineshape is dominated by the rapid kinetics for binding either free protein or protein ligated at the alternate site, and the spectrum looks like two fastexchange binding processes in that the line frequency appears to follow the equilibrium concentration; however, the peak intensity for free P decreases and that for the ligated form increases (Fig. 5d,e). When both sites are in fast exchange, the NMR lineshape is collapsed into a single resonance at all titration points and looks like a 2state binding system (Fig. 5f).
These simulated 4state lineshape data (50 data points on each line with noise, signal/noise ≈50) were fitted with the 2 or 4state fitting GUI. The 2state model cannot fit any of the lineshape data, not even those from Fig. 5f which look like 2state exchange (Fig. 5e,f; Supporting Information Fig. S4). In contrast, the 4state model fits well with all lineshape data (Supporting Information Fig. S5) and gives correct values for all K_{D} parameters and most of the k_{off} parameters (Table 4). There are two k_{off} parameters which cannot be determined from the 4state fitting due to reaching the fastexchange limit (“UB” in Table 4).
Experimental lineshape data for Syk tSH2 binding with NIHP
The GUIs were used to examine data reported for the interaction between Syk tandem SH2 domain and tyrosyl phosphorylated peptides^{3}. In previous work, the necessity and power of using NMR lineshape analysis to effectively extract dynamic and kinetic information was recognized^{3}. NmrLineGuru is demonstrated here to analyze data on this interaction.
The Syk tandem SH2 domain fragment (tSH2) contains two SH2 domains and either domain can bind to a phosphotyrosine peptide, NIHP [AcPD(pY)EPIRKGNH_{2}], with a sequence derived from the CD3ε chain of the T cell receptor. tSH2 was titrated with NIHP and the binding process was monitored by ^{15}N^{1}H HSQC experiments (Fig. 6a,b). Although the lineshapes look like 2state exchange, it is demonstrated that the 2state model cannot fit the data (Fig. 6c,d). The lineshapes of resonances from both domains (protondimension slices for G32, L37, H61, A74, F106, D175, G184, and G210; nitrogendimension slices for L52, Y73, L192, C205, and S244) are then globally fitted with the 4state model assuming two independent binding sites and the 4state model fits the data well (Fig. 6e,f). The fitted equilibrium dissociation constants are 730 ± 20 and 69 ± 4 µM and the fitted off rates are 1800 ± 300 and 380 ± 20 s^{−1} (mean ± SD of fitted values from two independent experiments), for the N and Cterminal SH2 domains binding NIHP, respectively.
Comparison of the fitted parameters by IDAP, TITAN, and NmrLineGuru
The experimental lineshape data^{10} for E22A CsnN174 chitosanase binding with the chitosan hexamer substrate (GlcN)_{6} were used to compare the fitting quality of NmrLineGuru to two other packages, IDAP^{1,2} and TITAN^{12}. Data from multiple peaks were globally fitted in all three cases. Example lineshapes and fittings by NmrLineGuru are shown in Fig. 7 and the fitted parameters are summarized in Table 5 (fitted values with IDAP and TITAN are from reference^{10}).
The lineshape behavior shown in Fig. 7, especially that of W28, resembles the simulation in Fig. 4e whereby one peak shifts and decreases intensity, and another peak gradually appears. This behavior indicates that the underlying mechanism is fast ligand binding coupled with slow isomerization, consistent with the reported analysis^{10}. Global fitting of the selected 1D spectral slices by NmrLineGuru gives similar thermodynamic and kinetic parameters to those from IDAP and TITAN; the differences shown in Table 5 are considered negligible. The off rate of the ligand binding step is too fast to be accurately determined, which for NmrLineGuru is reported as beyond fastexchange limit.
Conclusion
We describe six standalone and userfriendly GUIs for both simulating and fitting 1D NMR lineshape data using the common 2, 3, or 4state binding models. Accuracy in fitting the NMR data was demonstrated with simulated and experimental data, including global fitting of multiple peak lineshapes. These GUIs require the minimal amount of user input and handle most of the workflow in an automatic way. Aiming for nonexperienced users, these GUIs can help to promote the wide use of the NMR lineshape analysis method, which is powerful and unique in studying dynamics and kinetics for multistate binding systems.
Methods
Code development
The GUIs are developed in MATLAB R2014a (The MathWorks, Inc.) and compiled into standalone applications for both Windows and Linux. The lowlevel 1D NMR lineshape data I/O APIs (including the Sparky plugin) are from IDAP^{1,2} (Integrative Data Analysis Platform, http://lineshapekin.net).
NMR lineshape for an exchange system
The NMR transverse magnetization for an equilibrium system of N spins in chemical exchange is generally described by the matrix form of the BlochMcConnell equations^{2,11}. The spectrum intensity at angular frequency ω is given by the sum of real components of the following complex vector S:
where P is a complex vector of length N and Ω is a N × N complex matrix. The elements of P are the relative spin populations, p_{i}, defined by the kinetic rate constants \({k}_{ij}^{\ast }\)
Ω is given by
M is a diagonal matrix with the following element M_{ii} for spin i
where \({R}_{2}^{i}\) and \({\omega }_{0}^{i}\) are the transverse relaxation rate and intrinsic resonance frequency of spin i. \({R}_{2}^{i}\) and \({\omega }_{0}^{i}\) are provided by user input for simulations, or obtained by fitting the given resonance peaks to a Lorentzian function (assuming the peak centers at ω_{0} with a line width 2R_{2}), or searched as fitting parameters during fitting procedures. K is the N × N exchange matrix with the following elements from kinetic rate constants:
Theory for 2state binding and lineshape analysis
The 2state binding model contains only one binding step between P and L to form PL, assuming P and PL are the NMRdetectable species. The system contains one equilibrium dissociation constant, K_{D}:
The total concentration of protein and ligand of each titration point is:
From Eqs (7–9), the relationship between [L], [P_{total}], [L_{total}], and K_{D} can be solved as:
With given values of [P_{total}], [L_{total}], and varying values for K_{D}, the value of [L] is solved analytically. Once [L] is known, the concentrations of other species in the system are determined based on Eqs (7–9):
The NMR lineshape calculation requires an additional parameter to describe the 2state system, the off rate k_{off}. The corresponding on rate is:
The predicted lineshape for a nucleus at a given titration point is described in Eqs (1–6). The following matrices are now
Theory for the 3 state binding and lineshape
The 3state binding model (Fig. 4a) contains an intermolecular binding step between the free P and L to form PL, and an intramolecular (concentration independent) isomerization step for PL to form P′L. These two steps are described by the equilibrium dissociation constant K_{D} and equilibrium isomerization constant K_{eq}:
The total concentration of protein and ligand of each titration point is expressed as
From Eqs (16–19), the relationship between [L], [P_{total}], [L_{total}], K_{D}, and K_{eq} is
With given values of [P_{total}], [L_{total}], K_{D}, K_{eq}, the value of [L] can be solved analytically. Once [L] is known, the concentrations of other species in the system could be determined as follows based on Eqs (16–19):
The lineshape analysis requires two more parameters to describe the 3state system: the off rate for the binding process (k_{off}) and the reverse rate for the isomerization process (k_{rev}). The corresponding on rate and forward rate are:
The predicted lineshape for a nucleus at a given titration point is described in Eqs (1–6). The following matrices are now
Theory for the 4 state binding and lineshape
The 4state binding model (Fig. 5a) contains four binding steps described by four equilibrium dissociation constants:
Note that only the first three equilibrium dissociation constants are independent parameters while the fourth becomes a function of the first three. The total concentration of protein and ligand of each titration point is expressed as
From Eqs (28–33), the relationship between [L], [P_{total}], [L_{total}], \({K}_{{\rm{D}}}^{{\rm{A}}1}\), \({K}_{{\rm{D}}}^{{\rm{B}}1}\) and \({K}_{{\rm{D}}}^{{\rm{A}}2}\) is
With given values of [P_{total}], [L_{total}], \({K}_{{\rm{D}}}^{{\rm{A}}1}\), \({K}_{{\rm{D}}}^{{\rm{B}}1}\) and \({K}_{{\rm{D}}}^{{\rm{A}}2}\), the value of [L] can be solved analytically with symbolic linear algebra software, such as Maxima (a Computer Algebra System, version 5.42.2, http://maxima.sourceforge.net). Once [L] is known, the concentrations of other species in the system are known from Eqs (28–33):
The lineshape analysis requires four more parameters to describe the 4state system: the off rates for the four binding process: \({k}_{{\rm{off}}}^{{\rm{A1}}}\), \({k}_{{\rm{off}}}^{B1}\), \({k}_{{\rm{off}}}^{A2}\), and \({k}_{{\rm{off}}}^{{\rm{B2}}}\). The corresponding on rate is
where i denotes any of the four binding steps. The predicted lineshape for a nucleus at a given titration point is described in Eqs (1–6). The following matrices are now
Fittingspecific algorithms
The fitting GUIs search the bestfit values of unknown thermodynamic and kinetic parameters based on the input lineshape data. The unknown parameters (e.g. K_{D}, k_{off}) are assigned to the initial values from user selection and then iteratively refined by an optimization algorithm to match the experimental data, such that the following target function (sum of squared errors between the experimentally determined and the predicted lineshape data) is minimized:
where \({S}_{i,j}^{pred}({\omega }_{k})\) and \({S}_{i,j}^{expt}({\omega }_{k})\,\)are the predicted and experimental spectrum intensity of resonance i at titration point j at frequency \({\omega }_{k}\), respectively; a_{i} and b_{i} are the intensity and baseline correction factors for resonance i to compensate the normalization errors, if any, introduced during the normalization process of the experimental lineshape data.
If selected by the user in the interface, fitting errors of the bestfit values are determined by Monte Carlo resampling, in which a random noise is generated based on the spectrum noise level input with the experimental data and added to each of the input lineshape data points. The resampling and fitting procedure is repeated a minimum of 50 times and until convergence to determine the 95% confidence intervals of the fitted parameters. To determine experimental errors, multiple experiments should be performed and processed independently. The variance from experimental errors is generally larger than that from fitting errors^{3}. If multiple experimental datasets are available, results from their independent fitting should be used to determine uncertainty for the fitted parameters.
Data availability
The datasets generated during and/or analyzed during the current study are available in the online tutorials from NmrLineGuru GitHub wiki (https://github.com/stonefonly/NmrLineGuru/wiki) or from the corresponding author.
Code availability
The compiled GUIs and related documents are available from NmrLineGuru GitHub repo (https://github.com/stonefonly/NmrLineGuru). The software has been preinstalled in NMRbox (https://www.nmrbox.org). For academic use, this work should be cited. For commercial use or source code request, please contact us directly.
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Acknowledgements
This work was supported by NIH R01GM039478.
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C.F. developed the GUIs and fitting/simulation code, contributed to the research design and wrote the manuscript. E.K. developed 1D NMR lineshape data APIs (including the Sparky plugin) and contributed to the written manuscript. C.B.P. contributed to the research design and the written manuscript.
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Feng, C., Kovrigin, E.L. & Post, C.B. NmrLineGuru: Standalone and UserFriendly GUIs for Fast 1D NMR Lineshape Simulation and Analysis of MultiState Equilibrium Binding Models. Sci Rep 9, 16023 (2019). https://doi.org/10.1038/s41598019524518
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DOI: https://doi.org/10.1038/s41598019524518
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