Data Analysis : Follow Shift Changes

Follow Chemical Shift Changes During Titrations

This system is desined to efficently extract changing peak position data, which for example may occur during a titration experiment, and then fit the chemical shift changes to an equation curve for the extraction of parameters that relate to the peak movements. This analysis may be used to measure such things as dissociation constants (e.g. Kd) and temperature coeffients; where the position of or more peaks in a group of related spectra changes according to some experimental condition. Many kinds of experimental condition may be varied, but series with changing in concentration (e.g. ligand), temperature or pH are commonplace. This system is closely related to the Follow Intensity Changes tool, but here the peak grouping and function fitting is for peak locations that do move, rather than stay in the same place and change intensity.

The general idea is that the user sets up an “NMR series” that contains an array of experiments where each experiment is point in the series and represents a different value for a parameter (like concentration) being investigated. Based initially on the reference peak positions, trajectories where picked peak positions move in the different experiments are tracked by finding the peak groups that best fits the stated function which relates chemical shift to series parameter. It should be noted that NMR series that are comprised of experiment planes stacked into a higher-dimensionality “pseudo-nD” experiment cannot be used in this analysis. The reason for this relates to the way that experiments link to chemical shift lists in the CCPN data model; there is no meachanism to record a changing chemical shift within a single experiment.

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 follow the peak positions as they form “trajectories” and do the function fitting. The second tab is used to display the results on a table of peak groups, where each group corresponds to a series of peaks which have common assignemnts, with one peak for each experiment.

The general idea is that the user selects a reference peak list, which will give assignment identities to the peak groups being analysed. Typically the reference peak list will be from an experiment in the NMR series, so that the the positions of the peaks, as they move in the different experiments, cross or end at the reference position. For proteins this reference will often be a 15N HSQC peak list, in which case the analysis operates on peak groups that correspond to amides of individual residues.

The user chooses an NMR series that has been setup in the NMR Series popup, accessible using the [Edit NMR Series] button. For the anlysis to proceed properly the selected NMR series will need to contain all of the experiments that form part of the titration/analysis and the vaues of the condition being studied (e.g. concentration) must be correctly set. The “Data List Type” and corresponding unit indicate what kind of experimental condition/parameter, as dictated by the NMR series, will be fitted to chemical shift distance. The “Fitting Function” option is adjusted to say what kind of curve should be fitted to the peak intensity data; the linear “Ax + B” is common for temperature coefficents while the elaborate “A((B+4x-sqrt((B+4x)^2-(4x)^2))/4x - C)” is often used to measure dissociation constants. The Error Method determines how the errors in the parameters of the fitted function (e.g. error in Kd 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 groups that are analysed for the fit of experimental parameter to chemical shift distance may be manually specified by giving a common assignment to peaks that derive from the same resonances. Alternatively, an automatic method is used to find peaks which are not assigned. This automation follows the positions of peaks in their trajectories, choosing the best combination of peaks that a) roughly follows a straight line and b) fits the selected fuction equation, in terms of the expected chemical shift distance for the experiment. 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. Peak positions may be tracked in one or more spectrum dimensions, according to the “Followed Dimensions” selection. When multiple dimensions are used, chemical shift difference for dissimilar istopes are combined using the “Shift Weighting” values. The “Max Step Size” value are important for the automated peak grouping, given that they limit which peaks are considered when going from one experiment to the next. When step sizes are too large the grouping calculation can take a long time. When step sizes are too small peaks will be missed and grouping may fail.

The peak grouping and function fitting is performed using the [Group & Fit Peaks] function. After the initial grouping the 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 “Ax + B” equation, are immediately made available from the results table. Also, where relevant, any Kd values are also presented; this requires that the binding site concentration was specified. 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 come from the (isotope weigted) chemical shift distance for each peak of the group along the trajectory from its start point 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, they may be used by directly exporting the fitted parameters from the table.

Caveats & Tips

Each peak group need not contain the same number of peaks if data is missing.

Peaks must be picked in all of the analysed experiments beforehand for this system to function.

Choosing an assigned reference peak list that is postioned in the centre of the moving peak trajectories will give the quickest and most reliable peak groupings; the trajectory search radius is minimised.

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, for example using the “propagate” assignment option, thus connecting peaks together.

It is expected that each experiment of the analysed series, because peaks move position significantly, will be linked to a separate chemical shift record; so that there is a shift value for each condition point. If the experiments of a series do no not use separate shift list the user will be propted to set this up.

For groups where the peaks do not move significantly, between experiments in the series, a curve will still be fitted to the trajectory. This is because the value fitted is a weighted chemical shift distance, from one position to the next in the trajectory, and distances will always be positive, including when points double-black (within the “Shift Error” tolerance).

If the peak grouping is taking a significant amount of time, consider reducing the “Max Step Size” values; but still leave vales large enough to jump from one experiment to the next.

The fit of the equation curve to the chemical shift changes is naturally limited to how many experimental points there are in the series and how well spread they are. For example when measuring ligand Kd values, where possible, if is best to have some experiments at low concentration and some at high concentration, near saturation.

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 for resonance which don’t move significantly enough for analysis.

Main Panel

button Clone: Clone popup window

button Help: Show popup help document

button Close: Close popup

Settings

Allows the user to setup how resonance trajectories are followed and which experiments to analyse

Experiment Setup

pulldown Reference Peak List: Selects which peak list is the source of assignments and representative positions for peak group trajectories (need not be at the end of the trajectory)

pulldown NMR Experiment Series: Selects which series of NMR experiments to perform the peak-following and equation fitting analysis for

Function Fitting

pulldown Fitting Function: Selects which kind of parameterised equation to use in the fitting of chemical shift distance to NMR series value

pulldown Followed Dimensions: Selects which dimensions of the spectra to follow chemical shifts for; can use different isotope types given the stated weightings

pulldown Error method: Selects how errors in the fit of the selected equation to the chemical shift data are estimated

float 4.0: The amount of grace, in data points, for grouping resonance locations that do not move significantly; allows trajectories to backtrack a little

check Assign groups?: Whether to assign all peaks in the same group to the same resonances; where possible inherited from the reference peak list

float Min F2/F1 Grad: The lower limit of the chemical shift trajectory gradient; difference in second dimension over difference in first dimension

check Ignore Zero Merit Peaks?: When grouping peaks along resonance trajectories, whether to ignore peaks with zero figure-of-merit value

float Max F2/F1 Grad: The upper limit of the chemical shift trajectory gradient; difference in second dimension over difference in first dimension

Isotope Parameters

float 1.0: The scaling factor for 1H dimensions, used to give equivalency to ppm distances for different kinds of isotope

float 0.15: The scaling factor for 15N dimensions, used to give equivalency to ppm distances for different kinds of isotope; default is relative to a 1H weight of 1.0

float 0.1: The scaling factor for 13C dimensions, used to give equivalency to ppm distances for different kinds of isotope; default is relative to a 1H weight of 1.0

float 0.05: The 1H ppm difference limit, within which each subsequent point along a resonance trajectory may be found; to make peak groups

float 0.5: The 15N ppm difference limit, within which each subsequent point along a resonance trajectory may be found; to make peak groups

float 0.5: The 13C ppm difference limit, within which each subsequent point along a resonance trajectory may be found; to make peak groups

Peak Groups & Analysis

The peaks that have been grouped into resonance trajectories, and the various equation parameters estimated for each

Table 1
# Number of the peak group
Assign F1 The assignment of the reference peak for the group in the F1 dimension
Assign F2 The assignment of the reference peak for the group in the F2 dimension
Traj Dist The isotope-weighted chemical shift path length; following each pair of points in the trajectory of the peak group
Shift Dist The isotope-weighted chemical shift distance between the first and last point in the peak group
Fit Error The error in the goodness fo fit of the selected graph to the observed chemical shift data
Num Peaks The number of peaks contained in the analysis group
Fitted Function The kind of function used in the graph fitting, to extract parameters, for this group
Fit Param A The estimated value of parameter “A”, obtained by fitting the selected equation to the chemical shift data
Fit Param B The estimated value of parameter “B”, obtained by fitting the selected equation to the chemical shift data
Param Error A The estimated error, using the selected method, in fit parameter “A”
Param Error B The estimated error, using the selected method, in fit parameter “B”

button Remove Selected Groups: Documentation missing

button Re-fit Selected: Documentation missing

button Show Fit Graph: Documentation missing

button Show Peaks: Documentation missing

button Group & Fit Peaks: Documentation missing

button Re-fit All Groups: Documentation missing

button Edit NMR Series: Documentation missing

button Export Shifts: Documentation missing

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