Sample Scheduler for Non-Uniform Data Sets

General information: The Non-Uniform Sample Scheduler is designed for the creation of sample schedules to be used for collecting non-uniform NMR data sets. Data collected in this manner cannot be processed with conventional FT methods. Maximum Entropy reconstruction methods work very well with non-uniformly sampled data points and can give NMR spectra of the same high quality as FT methods, but with the distinct advantage of being able to sample non-uniformly. Sampling non-uniformly allows for shorter data acquisition times as not all points need be collected, higher resolution as farther data points can be collected without increasing the data collection time significantly, and allows for greater sensitivity per unit time as a greater percentage of the "early" data points are collected and relatively few "late" data points (where the signal is weak) need to be collected.

Synopsis of program: The program can create 1D sample schedules suitable for 2D NMR data sets or 2D sample schedules suitable for 3D NMR data sets. In both cases the acquisition dimension is sampled linearly as it takes no longer time to do so. Sample schedules can be forced to have a certain number of points in them or the total number of points can be dictated by the parameters. In general it is better to NOT force the total number of points to a specific value and simply adjust the parameters if you would like more or less sample points. The parameters; sweep width, force initial points, maximum increment, and decay constant, are the only parameters used when creating the sample schedule. The nucleus type and the sample factor are only used in conjunction with the molecular weight dialog box to guess suitable values for the decay constant and the maximum increment selected.

For a given molecular weight, sweep width(s), and nucleus type(s) the T2 relaxation rates (linewidths) are estimated. Correlation times are estimated from a plot of correlation time versus molecular weight at 25 deg C. for a large number of proteins that have had 15N relaxation analysis performed on them. These values are slightly higher than theoretical predictions likely due to the non-spherical nature of most proteins, and having an effective higher viscosity than water alone due to the high protein concentrations used in NMR studies. An additional 25% increase in the correlation time is used for samples in D2O due to the increase in viscosity of D2O as compared to H2O. All linewidth calculations assume a field strength of 600 MHz and an additional 1 Hz is added to the linewidth calculations to account for inhomogenity of the NMR instrument. The decay constant(s) on the form are set based on the linewidth calculations. The maximum increment for each of the dimensions is set to the T2 time multiplied by the sample factor. The theoretical maximum sensitivity is achieved at 1.26 time the T2 time. Sampling beyond 1.26 times the T2 time may increase resolution if the signal strength is strong enough, but will cause an overall decrease in sensitivity.

Sample schedules are created "randomly" but with a distribution that follows an exponential function based on the sweep width and decay constant. The initial points in any dimension can be forced to be sure these "early" points which have the highest signal strength are not skipped by chance. It is also possible to process a subset of the data that was collected uniformly with conventional FT methods first before trying maximum entropy methods on the entire data set. In all cases the first and last point of the schedule are always present. If the force total points checkbox is checked then the sample schedule will be created with the number of total points selected in the dialog box. If the force total points checkbox is not selected than each possible point in the schedule is treated independently based on its probability which is based on the decay constant, and sweep width when randomly choosing the points to be in the schedule. Even though it may be desirable to set the number of points in the schedule it is safer to leave the force total points checkbox off. If you desire a different percentage of the points to be kept in the schedule you are typically better off changing the exponent rather than simply forcing the total points to some value that may then lead to a poor sampling schedule.

Dimension: (top)

Toggle to switch between 2-dimensional and 3-dimensional experiments. For 2D a 1D schedule is created and for 3D a 2D schedule is created. The acquisition dimension is not used in generating the schedules and is only there to suggest the number of complex points to collect based on the information provided. When the 2-dimensional toggle is selected only the first two columns will appear (acquisition dimension and t1:first indirect). When the 3-dimensional toggle is selected all three columns will appear (acquisition dimension, t1:first indirect, and t2:second indirect).

Solvent: (top)

Toggle to switch between H₂O and D₂O. When D₂O is selected the calculated molecular correlation time is increased by 20% due to the increased viscosity of D₂O as compared to D₂O.

Start Schedule: (top)

Toggle to switch between starting the sample schedule at "one" or "zero". The Rowland NMR Toolkit requires that the sample schedule start at "one", where point "one" corresponds to the first increment with a delay time of zero. Other software packages work differently where the first increment is defined as point "zero" in the sample schedule.

Force Total Points: (top)

When checked the sample schedule will be created with the exact number of points entered on the total points text box. This checkbox must be selected when the constant time checkboxes are selected. When the constant time checkboxes are not selected it is generally more useful to leave this checkbox off and simply let the sample scheduler choose the number of points in the schedule on its own. If the number of points selected is too small or too large based on how long you want your experiment to run it is better to change the parameters such as max points and decay constants rather than forcing the total number of points to an exact number. When the force total points checkbox is off each possible point is treated independently based on its probability based on the input information. The force total points checkbox, when selected, can often take a very long time to create a schedule especially for very large schedules. Please be patient.

Seed: (top)

Points in the sample schedulers are created randomly using a random number generator. When use random seed is selected a true random seed is chosen. If you click refresh a new schedule will be created that is slightly different as the seed will be different. When manually define seed is selected the seed entered in the seed text box is used to seed the random number generator. When the refresh button is hit (or a new schedule is created using identical parameters) the identical sample schedule will be generated. The text box for seed must be entered when defining a manual seed, but is not necessary when using the random seed.

Molecular Weight: (top)

Enter the molecular weight of the molecule you are studying. Once the molecular weight is entered the rotational correlation time for the molecule is calculated based on an equation derived from experimental NMR data. These values are slightly larger than theoretical calculations. Based on this correlation time T2 relaxation times for the nucleus in the nucleus pull-down menu are calculated. These relaxation rates along with the sweep widths are then used to set initial guesses for the decay constants and the maximum increments. All of these calculations are done using JavaScript and will refresh when any of the linked parameters is changed.