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CHAPTER 15: nD Analysis Workwindow

This chapter describes the nD Analysis workwindow. The individual input fields are explained, along with standard settings for the analysis of routine spectra. (To display all the input fields available in this workwindow, select from the Edit menu [Preferences...]. Set Mode: [Full NMRanalyst], [Show All Input Fields] switches, and click [OK].) The analysis performed by this workwindow is the heart of the NMRanalyst software. The corresponding analyze program determines the correlation information from two- and three-dimensional spectra. Using the output of the 1D Analysis and FFT workwindows, the analyze program searches all multidimensional signal regions to find spin systems of interest. See CHAPTER 12: "Using the Workwindows" for a general description of the function and use of a workwindow.

15.1 Input Files

Specify in the F1 through F2 (F1 through F3 for 3D) input fields the file with resonance positions along each axis of the multidimensional spectrum. For homo nuclear 2D spectra (DQF-COSY, INADEQUATE, NOESY, ROESY, and TOCSY), only the F2 1D Analysis Output File input field is displayed, since the indirectly determined F1 resonance frequencies are identical to the directly acquired ones. For 2D heteronuclear spectrum types (ADEQUATE, HETCOR, HMBC, N15_HMBC, HSQC, COUPLED_HSQC, and N15_HSQC), both the F1 and the F2 resonances have to be specified. For 3D spectra, the general heteronuclear spectrum type is assumed. If several axes of the multidimensional spectrum show the same possible resonance frequencies, specify the same 1D line list in the corresponding input fields. (Key: Fn1DF1,..., Fn1DF3)

The label of the input field changes with the dimensionality of the selected spectrum type. Specify in this input field the name of the phase-sensitive multidimensional spectrum created by the FFT workwindow. (Key: FnCube)

15.2 Output Files

Specify a name for the nD Analysis workwindow output file. For each examined multidimensional spectral region, the initial, best-fit, and error values (marginal standard deviations) of possible correlation patterns are written to this file. (Key: FnBond)

For the optimal detection of correlations in multidimensional spectra, NMRanalyst fits a simulation of the expected spin-system to the experimental data. The simulated spectrum containing all best-fit spin systems is hence a natural way to present the analysis results.

When the [Add Correlations] or [Add Diagonal Resonances] switch is selected, NMRanalyst writes 2D and 3D spectral simulations in its internal format. If no file name is specified in this input field, the file name from the 2D FFT Output File input field is used with a ".sim" postfix. The 2D and 3D spectral simulations can be displayed by the nmrplot program described in CHAPTER 4: "Tutorial II: Setting Analysis Parameters". (Key: FnSim)

15.3 Analysis Parameters

Specify which correlation areas the analyze program should examine. Up to 999,999 correlation areas can be examined. For a given number of 1D resonances, n, the maximum number of correlation areas in 2D homonuclear spectra is: n(n-1)/2. The number of possible multidimensional heteronuclear correlations is the product of resonances in all specified 1D input files. Leave this input field empty to have all correlation areas examined.

Specific correlation areas can be examined by listing in this input field a sequence of correlation numbers and/or ranges of correlation numbers separated by spaces, commas, tabs, colons, semicolons, or any combination thereof. A range of correlation numbers is specified by the first and last number of the range separated by a dash. For example, the input 2 10-50 3 specifies that correlation numbers 2 and 3 as well as 10 through 50 should be examined. (Key: BondNo)

NMRanalyst fits a spin system model to the data. By default, only the Threshold: Precision (for DQF-COSY, HMBC, and N15_HMBC called Agreements) value (described below) is used to keep noise patterns from being misinterpreted as correlations. This Thresholds: Integral allows specifying the minimal integral a simulated spin system has to reach before being identified as a correlation. To determine this threshold, analyze the dataset and display the determined integral distribution (see the Report workwindow Integral Distribution field description). Choose a value above the main integral distribution as described below.

HMBC and DQF-COSY resonances result from couplings which can be below the acquired digital F2 resolution. The spin system resonances overlap and largely cancel each other due to their opposite signs (anti-phase). For these spectrum types, the absolute value integral of resonances is tested against this Integral threshold. (Key: IntLimit)

or A detected pattern is reported as a correlation based on this threshold value. For DQF-COSY, HMBC, and N15_HMBC spectrum types, this is the agreement in percent between simulated and experimental spectra. For other spectrum types, it is the determined absolute value integral divided by its uncertainty (marginal standard deviation). The higher this value, the more likely the pattern is a genuine correlation signal.

By default, NMRanalyst chooses this value such that reported correlation signals have at least a 99.9% probability of being genuine correlations. This input field allows overwriting this default threshold. The Report workwindow provides a detection probability for each reported correlation. After the initial analysis of the spectrum, display the precisions.plot or agreements.plot. The used threshold is shown in the distribution plot as a vertical red line. Adjust its position to lie outside the Gaussian distribution of noise values. (Key: PInt)

This switch is displayed for the ADEQUATE, HETCOR, HMBC, N15_HMBC, HSQC, COUPLED_HSQC, and N15_HSQC spectrum types. Normally 2D spectra are acquired covering the full range of the corresponding atom. The ADEQUATE F1 range has to cover two carbon chemical shift ranges. This requires a considerable spectral resolution and the acquired F1 range is often chosen smaller allowing resonances outside the acquired range to alias back into the acquired range. Other spectrum types have similar F1 challenges. Select this switch to have NMRanalyst consider multiple F1 aliasing. Acquire aliased spectra such that aliased and non-aliased resonances do not fall at the same F1 frequencies. Otherwise, ambiguities in the correlation assignment may result. (Key: LAlias)

This switch is displayed for the INADEQUATE spectrum type. Overlapping correlation signals in multidimensional spectra can lead to ambiguous signal interpretations. Multiple Minima in the goodness-of-fit criterion for a single fitting area indicate that multiple correlations were found in this fitting area. This information is required to identify all ambiguities in the identified signal assignments.

For 2D INADEQUATE spectra, this switch is selected by default. The resonance frequency of a carbon atom in the 1D carbon spectrum and in the 2D INADEQUATE spectrum differs by up to 0.027 ppm due to isotope shifts caused by the neighboring 13C nucleus. In high resolution 2D INADEQUATE data (F2 resolution < 1 Hz), if the 1D carbon spectrum contains resonances less than 0.03 ppm apart, several bond patterns might be found in one fitting area. If there are no two carbon resonances 0.03 ppm or less apart, or if plotting is requested and should be limited to the strongest identified pattern in a fitting area, this button can be deselected to simplify the program output. (Key: MulMin)

To find a resonance along one axis in a multidimensional spectrum, the corresponding 1D resonance frequency is used as initial estimate. The 1D and nD resonance frequencies might differ somewhat. A search area in the multidimensional spectrum around the 1D resonance frequency can be specified. The number of starting points to use for the search inside this specified mapping range can be specified as well (see below). The program analyze knows the spectral resolution along each spectral axis as well as the approximate linewidth from the corresponding 1D resonance. So the automatically chosen number of mapping points is normally appropriate. When using generic line lists, the mapping range has to cover half the chosen distance between generated signals.

For 2D INADEQUATE spectra, the default mapping range is the 0.027 ppm maximum isotope shift1 times the Observe Frequency value specified in the FFT workwindow. For a 500 MHz spectrometer, the default mapping range for 2D INADEQUATE spectra is ±0.027ppm*125.697Hz/ppm = ±3.395 Hz. The actual value used by the program analyze is shown at the start of the program in the output line:

 Mapping Density: F-Range=+/-3.39 F-#Pts=1 J-Range=+/-10.00 J-#Pts=2

The default 2D INADEQUATE frequency range is sufficient only for accurate acquisition and referencing of the 1D and 2D spectra and in the absence of significant signal overlap in the 2D spectrum. For homonuclear and heteronuclear correlation spectra, the default mapping range is ±10 Hz.

A referencing difference between the 1D and the multidimensional spectra can be compensated for by analyzing the multidimensional spectrum with the Map F? Frequencies ± values greater than their default values. The referencing of the multidimensional spectral axes can then be corrected by the average determined frequency shift. However, an increased input value slows the analysis significantly, and increases the number of ambiguous signal assignments. Keeping the acquisition conditions of the 1D and the multidimensional spectra identical and acquiring the 2D spectrum with sufficient resolution to limit signal overlap problems is preferable. (Key: RangeF1, ..., RangeF3, RangeF1U, ..., RangeF3U)

Depending on the selected spectrum type, up to three spectral dimensions (F1 through F3) can be mapped. The specified frequency ranges are mapped using the number of mapping points specified in these F1 through F3 input fields. The density of mapping points is dF=Range/#points, where "Range" is twice the value specified in the previous input field and "#points" is the value specified in this input field. The smallest mapping point value is Pmin = Pmid - Range/2 + dF/2, and the largest mapping point value is Pmax = Pmid + Range/2 - dF/2, where "Pmid" is the estimated parameter value. The mapping points are optimally positioned in the mapping range. NMRanalyst currently supports a maximum of 20 specified mapping points. (Key: MapF1, ..., MapF3)

This field is only shown for INADEQUATE, HMBC, N15_HMBC, COUPLED_HSQC, and DQF-COSY spectral analyses supporting the determination of scalar coupling constants. The coupling constant of a two-spin system is difficult to estimate from prior knowledge. See the description of the Estimated Coupling Constant input field below. The mapped coupling constant range should be chosen to cover all possible deviations from the initial estimates.

A 2D INADEQUATE experiment can reliably detect coupling constants ±10 Hz around the set coupling constant (JCC) used in the pulse sequence. The default mapping range depends on the estimated coupling constant. For an estimated coupling constant under 50 Hz, the mapping range is ±10 Hz. For a coupling constant above 50 Hz, the default mapping range is ±15 Hz. For a DQF-COSY spectrum, the default value is ± the Estimated Coupling Constant value (described below) minus two Hz. For COUPLED_HSQC, the default value is ±30 Hz (Key: RangeJ, RangeJU)

Only the INADEQUATE, HMBC, N15_HMBC, COUPLED_HSQC, and DQF-COSY spectral analyses support the determination of scalar coupling constants and display this input field. Specify in this input field how many mapping points should be used to examine the Map Coupling Constant ± range. A maximum number of 100 mapping points are accepted by NMRanalyst. For a detailed discussion of this input field, see the description for the # F2 Mapping Points input field. (Key: MapJ)

Only the INADEQUATE, HMBC, N15_HMBC, COUPLED_HSQC, and DQF-COSY spectral analyses support the determination of scalar coupling constants and display this input field. For the regression analysis of INADEQUATE spectral regions, a one-bond carbon-carbon coupling constant (1JCC) needs to be estimated. The default estimate for 1JCC is chosen on the basis of possible hybridization of the carbons involved as follows: sp3-sp3, 35 Hz, sp3-sp2, 45 Hz; sp2-sp2, 60 Hz.2 The INADEQUATE pulse sequence contains a coupling constant parameter (often called JCC) for which the data acquisition provides the optimal detection. This JCC value -- or any other value assumed to give a good initial 1JCC estimate -- can be specified in this input field.

By default, the regression analysis of DQF-COSY spectral regions uses a proton-proton coupling constant of 7 Hz (vicinal coupling for unfixed conformation), and for the analysis of HMBC and N15_HMBC spectra a long-range CH coupling constant of 8 Hz (typical HMBC pulse sequence optimization). Mapping of the coupling constant can be used to overcome inaccuracies in the specified or the default initial coupling constants.

For COUPLED_HSQC, a 1JCH value of 150 Hz is assumed. Alkyne protons have a 240-250 Hz coupling constant and are not detected by this value. Increase this value to 245 Hz for their detection. (Key: UsrJcc, UsrJccU)

This input field is displayed for the ADEQUATE, HMBC, N15-HMBC, HSQC, COUPLED_HSQC, and N15_HSQC spectrum types. These spectra can contain ridges in F1 or sinc wiggles for underdigitized signals. This threshold for ridge volume vs. correlation volume is used to avoid the misinterpretation of such ridges as correlations. The default value for HMBC and N15_HMBC is 5.5, for COUPLED_HSQC and N15_HSQC 5, and for other spectrum types 10. To increase the effectiveness of this ridge suppression, increase the specified Map F1 Frequencies ± mapping range. (Key: Ridge)







These switches indicate which parameter values are to be optimized during the Mapping stage for the selected spectrum type. In addition to the selected switches, the chemical shifts in F1 through F3 are mapped if appropriate, and for DQF-COSY, HMBC, N15_HMBC, COUPLED_HSQC, and INADEQUATE spectra the coupling constant is mapped as well. The [2 Integrals] and [4 Integrals] switches are mutually exclusive. When the Detection: [F1 Relaxation] switch (described below) is selected, the resonance frequency in F1 direction is also optimized to overcome possible inaccuracies in the relaxation time caused by this resonance frequency.

For the initial analysis of a dataset, the phase switches should be selected until the phase functions are determined. Once phase functions are determined, these switches can be deselected so that the response surface can be mapped rapidly in a linear fashion. The [F? Phase] and [F? Relaxation] switches select the optimization of non-linear parameters which are time consuming to optimize. (Key: Map1, ..., Map8. Not accessible from interface: MapF1A, MapF2A, MapF1F)








The mapping step described above is optimized to rapidly identify possible correlation signals. The detection step described here further optimizes the spin system descriptions. These final parameter values are reported in the analyze program output and are used for spectral simulations.

The switches indicate which combination of parameter values is optimized during the Detection stage for the selected spectrum type. Every spin system identified during the Mapping stage is further refined based on the selected Detection parameters, before deciding if the found pattern is a valid correlation signal. In addition to the selected switches, the chemical shifts in F1 through F3 are always refined if appropriate, and for DQF-COSY, HMBC, N15_HMBC, COUPLED_HSQC, and INADEQUATE spectra the coupling constant is refined as well.

The [2 Couplings] switch for DQF-COSY spectra determines an independent F1 and F2 coupling constant. The DQF-COSY active coupling spin system is symmetrical and can be described by a single coupling constant. But when an overlapping passive coupling is present, a single coupling constant could be determined as large as the sum of the active and the passive coupling. Selecting the [2 Couplings] switch safeguards against this misinterpretation.

The HSQC, COUPLED_HSQC, and 3D_SPECTRUM spectral types can encode further spin system information by creating signals in positive and negative absorption. Select the [± Integral] switch if positive and negative integrals are expected in the spectral absorption mode. When phases are locked, spin systems with negative integrals are only recognized as correlations, if this switch is selected.

The analyze program optimizes the selected Detection parameters and decides whether or not a valid correlation signal was found according to the adjusted values. When a valid correlation signal is detected, a summary line for this fitting area is shown like:

 # 5 C 2 C 15  CORRELATION:  Fa= 2.166  Fb= .814  J= 7.02

If no potential correlation signal can be found in the fitting area, the summary line looks as follows:

 # 71 C 9 C 15  No correlation detected: No pattern found

When more than one potential correlation signal results from the optimization of the selected Detection parameters, each of these signal patterns is examined further. In case no detected correlations result from the potential patterns, the signal pattern leading to the smallest sum-of-square residuals is listed in the summary line with an explanation why this pattern is not a valid correlation signal. The most frequently encountered reason for rejection of a possible correlation signal is an insufficient parameter precision. If only the overall integral of a spin system is determined (no [? Integrals] switch selected), the corresponding correlation area summary line may read:

 #  3 C  6 C 13  No correlation detected: dI1

When the phase functions are locked (as indicated by unselected phase switches in the Detection section), patterns can be rejected based on an inappropriate sign of the determined integral parameters. Note that the anti-phase character of DQF-COSY and 2D INADEQUATE spectral spin systems has already been incorporated in the analysis model, and hence all determined integral parameters should be positive. When the phase functions are not locked, a sign difference between I1 and I2 and between I3 and I4 can also be used to reject a pattern. Whenever a negative sign of an integral value is encountered, the summary line of the fitting area shows the I_neg indicator as in:

 # 89 C  6 C 14  No correlation detected: I_neg dI1 dI2 dI3

To assign for example a 2D correlation signal to a pair of 1D resonances, the range given in the Map F2 Frequencies ± input field described above is used to decide whether or not the pattern under consideration can result from the two 1D resonances corresponding to the current fitting area. The indicators Fa and Fb are used in summary lines to indicate that an identified pattern does not meet this requirement:

 # 65 C  6 C  9  No correlation detected: Fa Fb

Finally, when the optimization of a relaxation time is requested in the Detection section, a determined negative time rejects the corresponding pattern. This condition is shown in the summary line by the T2_neg indicator as in:

 # 52 C 14 C 17  No correlation detected: T2_neg

Initial parameter values should be optimized only if the corresponding values are clearly determined by the data. (Key: Bnd1, ..., Bnd8. Not accessible from interface: BndF1A, BndF2A, BndF1F)

If the phase switches in the Detection section are selected, the analyze program determines phase values for each identified correlation pattern. The report program, which is controlled by the Report workwindow, can interpolate the determined phase values of each spectral dimension by a linear phase function, which can be entered in these input fields. Input fields without a specified phase value default to zero.

It is important to understand the determination and use of phase functions. When specifying the phase function without locking the phase parameters, a slight speed advantage is achieved during the analysis, because better starting values for the phases are available. The time determining step in the analysis is the mapping of the response surface for each fitting area. Using default parameters, this mapping is designed to detect even bad deviations of real correlation patterns from initial parameter estimates. If the phase function in any direction is unknown, the mapping of the response surface has to be performed in a slow nonlinear way. So it is advantageous, though not required, to determine approximate phase functions and to lock the phase parameters during the mapping step in order to perform the response surface mappings in a linear way. The linear analysis is about ten times faster than a nonlinear approach. A further advantage of locking phase functions is that during the mapping step fewer patterns are considered to be potential correlations.

During the detection step, locked phase functions provide a powerful filter to increase the distinction between correlation and noise patterns. For step-by-step instructions on how to determine and use phase functions, see CHAPTER 4: "Tutorial II: Setting Analysis Parameters". (Key: F1Pse0, F1Pse1, F2Pse0, F2Pse1, F3Pse0, F3Pse1)

15.4 Select Plot Data to be Saved

The plotting switches in this section should be unselected when analyzing whole datasets. Plot generation slows down the analysis and consumes disk space. Created plots can be displayed by the Graphic workwindow.

These two switches allow creating a simulated spectrum. When the [Add Correlations] and [Add Diagonal Resonances] switches are selected, the simulated best-fit patterns of each analyzed correlation is added to the simulated spectrum. The [Add Diagonal Resonances] switch can be selected to add such signals to the simulated spectrum. (Key: Add2PF, DiagPF)

This switch allows saving the analyzed spectral region. For 2D fitting areas a surface ("carpet") plot and for 3D spectra an isosurface plot are created. This type of plots provides the greatest detail available on each correlation. The plot contains the phase corrected experimental, simulated, and residual spectral data for one spectral region. All phase components of the hypercomplex data are saved and the desired phase component can be selected when displaying the data. (Key: CorrPlot)

15.5 Automatically Running Report After nD Analysis

Selecting this [RUN REPORT WORKWINDOW AFTER SUCCESSFUL ANALYSIS] automatically starts the Report workwindow after the nD Analysis workwindow runs to completion. This auto-run functionality is a feature of the NMRanalyst user interface and hence does not apply to a backgrounded analyze computing program. (Key: ARunReport)

1Hansen, P.E. "Isotope Effects on Nuclear Shielding", in Annual Reports on NMR Spectroscopy; Webb, G.A., Ed.; Academic Press: New York, 1983; Vol. 15, pp 105-234.

2Wray, V. Prog. Nucl. Magn. Reson. Spectrosc. 1979, 13, 177.

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