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Follow Peak Intensity Series for Rate Calculations etc
The purpose of this system is to expedite the extraction of peak intensity data from series of related experiments and subsequently fit a selected function to the data to extract parameters such as relaxation rates or NOE decay. The general idea is that the user sets up an “NMR series” that contains an array of experiments, or a single experiment stacked into separate planes (e.g. a pseudo 3D), where each experiment or plane in the series represents a different value for some time or frequency measurement being investigated. Examples of this include T1, T2 & T1rho delay times for estimating relaxation rates and NOE mixing times. It should be noted that this system is specifically designed for the extraction of parameters derived from spectrum peak intensities where the position of related peaks across a series do not move significantly. For following peak movements and chemical shift changes the Follow Shift Changes tool may be used.
The layout of the popup window is split into two tabs to reduce clutter. The first tab allows the user to setup and adjust all of the options used to perform the peak intensity extraction and function fitting. The second tab is used to actually perform the operations and display the results on a table of peak groups. Each group corresponds to a series of peaks, usually with a common resonance assignment, with one peak for each time value (i.e. per experiment or plane).
The general idea is that the user selects a reference peak list, which will determine the location and assignment identities of the peaks being analysed. For proteins this reference is often a 15N HSQC peak list, in which case the analysis operates on peak groups that correspond to amides of individual residues. The reference need not be part of the series of analysed experiments, but naturally peak locations should match. Also, the user chooses an NMR series that has been setup elsewhere with the relevant experiments or planes and their corresponding time parameters. The [Edit NMR Series] button will open the NMR Series popup window to create and adjust such series. The “Fitting Function” option is adjusted to say what kind of curve should be fitted to the peak intensity data (often this is a two-parameter exponential). The “Rate Type” and “Coherence Type” options are only used if results are stored in the CCPN project as a measurement list and do not affect the initial analysis. The Error Method determines how the errors in the parameters of the fitted function (e.g. error in relaxation rate) will be calculated.
The “covariance” error method can be used if the measurement errors are normally distributed (which is often a reasonable assumption). For each parameter the error (standard deviation) estimate is the square root of (the chi squared value times the covariance matrix diagonal term for that parameter). Reference: section 15.6, “Confidence Limits on Estimated Model Parameters” in Numerical Recipes, second edition.
The “bootstrap” error method uses repeated sampling to provide an estimate of the error. If there are N (x, y) points to be fit then each sampling takes N of those (x, y), but with replacement allowed, so some of the (x, y) might be repeated and some might be left out. For each sampling the best fit is calculated and that determines the parameters for this specific sampling, which in turn allows an estimate of the error (standard deviation) over all samplings. Analysis uses 1000 samples. Reference: “Bootstrap Methods for Standard Errors, Confidence Intervals and Other Measures of Statistical Accuracy”, B. Efron and R. Tibshirani, Statistical Science, 1986, Vol. 1, No. 1, 54-77.
The “jiggling” error method uses repeated sampling but here the (x, y) are both sampled from a normal distribution with mean the actual value and standard deviation the estimated data errors. There is no real scientific basis for this estimate, so probably best avoided.
The peak picking and search tolerance sections control how peaks are grouped together so that their intensities may be analysed. The basic process is that each reference peak position is used to locate a corresponding peak in each plane/experiment of the series. How exactly this is done depends on which options are checked. If a peak, at the right point of the NMR series, has the same assignment as the reference peak then that peak is used in preference to any others, irrespective of location. If a peak with a matching assignment cannot be found, the position of the reference peak is then used to locate the peaks for its group. When looking for peaks based on location the system checks to see if there are any existing, picked peaks in the series that are close to the reference (within the search tolerances). If no existing peaks are found for a point in the series then, should the “Pick new peaks” option be set, an attempt is made to pick a new peak extremum within the stated tolerances. If there is no extremum to pick, then the system may still add a “non-maxima” peak at exactly the reference position; useful where peak intensities dip into the noise levels, but are still helpful in a function fit. Also, having the “Assign groups?” option set means that after the first peak grouping, peaks will be linked via assignment and subsequent peak searches are not generally required.
The peak grouping and function fitting is performed using the [Group & Fit Peaks] function. After the initial grouping the intensity curve fitting may be redone with via one of the “Re-fit” buttons; this useful if the fitting function is changed. When the curve fitting is done the parameter results from the fit, e.g. the “A” and “B” from an “A exp(-Bx)” equation, are immediately made available from the results table. Also, where relevant, any time constant values (one divided by the rate) are also presented. In the “Peak Groups & Analysis” table the user can see the fit results and analyse or adjust the peak groups. It is commonplace to look through all the intensity curves for each of the peak groups by using [Show Fit Graph]; here the user can check how well the curve-fit worked and whether any adjustments (e.g. in peak picking) need to be made or groups removed. See the Fit Graph documentation for details about how the resultant popup window operates. The “Y” value of the curves naturally come from the selected type of peak intensity and the “X” values come from those that were entered for the experimental points/planes in the NMR series. When the results have been checked, if the data is of a kind that corresponds to the “Rate Type” in the settings, then the user may save the values of the time constant, like T1 or T2, in a measurement list within the CCPN project using the “Make List” function. Alternatively the results may be used by directly exporting the fitted parameters from the table.
The user may fit the peak intensity data outside of Analysis by exporting the values for the individual intensities (and any fitted parameters) using the [Export Data] button at the bottom right. This will produce an aligned, whitespace-separated plain text file that aims to be easy to analyse with external programs and scripts. If the fitting functions that are available in CCPN are not required, or cause problems, the fitting function may be set to “<None>”, which means that the peaks are still grouped and that their intensities are available for export.
Caveats & Tips
Each peak group need not contain the same number of peaks if data is missing.
A subset of peaks in a series may be analysed by reducing the number of peaks in the reference peak list. For example the user could make a copy of an HSQC peak list and then remove and peak locations that are not required in the analysis, e.g. for side chain NH2 peaks or severely overlapped peaks.
Any peak picking done by the system uses the same spectrum peak finding parameters as is normally used in Analysis. Such parameters may be adjusted via the Peak Finding popup.
If there are problems with grouping peaks together the user may assign all peaks that ought to go in the same group to the same resonances, thus connecting peaks together.
As with all analyses based upon peak intensity, the user should be cautious in regions of spectra where peaks are severely overlapped. In such cases using peak “height” rather than “volume” integral may help to a degree.
The user should be cautious of manually copying or importing peaks into an intensity series from other spectra. Potentially both the peak position and intensity might not reflect the real data in the series. Accordingly, for copied peaks the user should recalculate intensities and check that the peak positions are at extrema, re-centring (<Ctrl> + <p>) as required. Alternatively, the automated series picking is normally adequate if the reference peak list matches reasonably and the picking PPM tolerances are appropriate.
The NMR series that will be considered by this system are currently limited to the following types: “delay time”, “time”,”num delays”, “mixing time” and “pulsing frequency”.
Documentation missing
Reference Peak List: Selects the peak list used to confer assignments and groupings to analysed peaks
NMR Experiment Series: The NMR series that carries details of which experiments to follow and their sampled conditions (e.g. delay times)
Fitting Function: Selects the type of graph to fit to the peak intensities within each grouping
Intensity Type: Whether to fit to peak heights or volume integrals
Error Method: Selects which method is used to estimate errors in the graph fitting
Rate Type: The type of rate experiment performed; important for storage in CCPN project
Coherence Type: Sets which sub-type of rate experiment was performed
Total diffusion time (s): The total diffusion time in seconds between NMR gradients (from pulse sequence)
Gradient length (s): The duration of the gradient in the pulse sequence
Full gradient stength (G/cm): The maximum gradient strength (i.e. at 100%); used if relative gradient strengths have been entered
Bipolar separation (s): The short time interval between bipolar gradients, if bipolar gradients were used
Pick new peaks?: Whether to pick new peaks, according to the reference peaks, should none of the right assignment be found
Pick non-maxima peaks? (At reference position): Whether to pick new peaks at exactly the reference position, if no extremum exists
Assign groups?: Whether to assign newly picked peaks, using the reference assignment for the group
Skip zero merit peaks?: Whether to exclude peaks from analysis if they have figure-of-merit set to zero
Use noise threshold for finding maxima?: Whether to search for peaks above a special noise threshold, rather than the regular pick level.
Threshold intensity: When searching for peaks, the minimum spectrum intensity level to consider. Below this level peaks may still be picked at the exact reference position.
Table 1 | |
Dimension | Spectrum dimension for tolerance setting |
Tolerance | Maximum ppm distance to group or pick peaks, relative to reference position (Editable) |
Documentation missing
Table 2 | |
# | Peak group row number |
Assign F1 | Assignment in F1 dimension, from reference peak list, for group |
Assign F2 | Assignment in F2 dimension, from reference peak list, for group |
Time Constant | Time constant, e.g. T1 or T2; one over the decay rate for exponential fits |
TC Error | Estimated error in the time constant |
Fit Error | Error in the fit of the peak intensities to the fitting function |
Num Peaks | Number of peaks in groups |
Function | Function used to fit to peak intensities |
Fit Param A | Parameter “A” from the graph fitting equation |
Fit Param B | Parameter “B” from the graph fitting equation |
Param Error A | Estimated error in parameter “A”, according to selected error method |
Param Error B | Estimated error in parameter “B”, according to selected error method |
Remove Selected Groups: Remove the selected peak groups from the table
Re-fit Selected: Redo the intensity graph fitting for the selected groups
Show Fit Graph: Show a graph of peak intensities and the fitted function
Show Peaks: Show a table of peaks within the selected groups
Make T1 List: Save the results as a data list in the CCPN project, using selected type options
Group & Fit Peaks: Search for peaks near to reference positions to create peak groups
Re-fit All Groups: Perform graph fitting for the intensities of peaks in all groups
Edit NMR Series: Edit the selected NMR experiment series, e.g. to setup delay times
Export Data: Export the results as a flat text file