Chemical Shift Referencing and Temperature Calibration.

This document covers temperature and chemical shift calibration experiments that should be done in conjunction with protein spectra.  The document deals with correcting a systematic error that arises from the use of an external standard and the deuterium lock operating on deuterated water.  The error arises from the fact that the resonance frequency of water is temperature dependent.  The function of the deuterium lock is to compensate for instrumental drift in the field strength during and between experiments.  The lock continually alters the field to enforce a fixed resonance frequency of the internal deuterated water.  When comparing experiments done at different temperatures, the lock will have adjusted the field to cancel the intrinsic temperature shift of the deuterated water.  As a consequence, the resonance frequency for water will be falsely reported as the same at different temperatures, and the frequencies of all other signals will have an equal and opposite shift to that of water superimposed on their intrinsic temperature shifts.

To contrast with the problem created by external referencing, the temperature shift artifact does not affect internally referenced experiments.  For internal referencing, the standard 2,2-dimethylsilapentane-5-sulfonic acid (DSS) is included within the protein sample.  DSS has no intrinsic temperature (or pH) shift.  When comparing experiments at different temperatures, the DSS peak will artifactually be shifted along with the other signals by the operation of the deuterium lock.  However, during processing, the DSS peak of each experiment will be manually set as the zero point.  This will automatically subtract the artifactual shift on the ¹H axis from all other signals.  There may be shifts remaining for the other proton signals.  But these residual shifts reflect true and intrinsic properties of those nuclei, and there is no intention of removing those shifts from the data.  For ¹³C and ¹⁵N, there is generally no corresponding internal reference molecule.  An artificial internal zero point for the ¹³C and ¹⁵N axes is created by multiplying the DSS frequency by a characteristic ratio (see below).  Hence these reference points will indirectly be adjusted to subtract the deuterium lock artifact from the ¹³C and ¹⁵N axes.

However, most experiments are not internally referenced.  This is due to the fear that the DSS may bind to the protein and alter some of its signals.  Instead most experiments are externally referenced.  During external referencing there is no peak to manually set to the zero point.  Instead, the carrier frequency, which is at the center point of the spectrum, is initially taken as the zero point.  Then an offset is added that would cause the DSS peak to become zero if it were in the spectrum.  That requires knowing what the difference between the carrier and the DSS frequency should be under the conditions of each experiment.  The carrier frequency is set to the constant water resonance of water that is enforced by the deuterium lock  The deuterium lock will cause the apparent frequency where DSS would resonate if it were there to shift with temperature.  Hence one needs to know the apparent DSS frequency as a function of temperature in order to correctly process the data.

Temperature shifts in Hz are generally divided by the frequency of the zero point reference for that nucleus and expressed in ppm.  Temperature shifts expressed in ppm are the same when measured on instruments with different field strengths, and are also in the same units as the chemical shifts they are being used to correct.  See examples at the bottom.

There are two experimental issues involved in this problem.

1. An experiment is described that measures how close the thermistor that reports sample temperature is to the true temperature.  It consists of taking the spectrum of ethylene glycol, in which there are two peaks whose separation is highly temperature sensitive.  The thermistor can be off by several degrees C.  Obviously one can't choose the right temperature correction without knowing the true temperature of the experiment.  Best practice is to measure the offset of the thermistor from the true temperature first, and then set the experimental temperature to compensate.  This calibration is recommended to be performed about once every two weeks.  As a note on record keeping, I recommend using the settitle command during experiment set up to record the true temperature.  Otherwise the temperature correction factor tends to get misplaced before the data gets processed.
2. An experiment is described that measures the shift between DSS and water at a particular temperature.  These shifts should come out to be 4.742 ppm at 300K, with a temperature coefficient of - 0.0119 ppm/degree (Wishart et al., J. Biomol. NMR 6: 135-140).  There is also a 0.002 ppm shift per unit pH, and possibly salt effects.  To get the most accurate possible correction, one should put DSS into your experimental buffer and make the determination.  However, assuming an experimental precision on the order of 0.01 ppm for ¹H, only the temperature correction is relevant under typical experimental conditions.  Hence we use a standard consisting of DSS in water.  Doing this calibration instead of using the theoretical values is mainly an exercise in determining your own experimental accuracy.

Temperature calibration with ethylene glycol.

• Use edte to set the temperature given best available information to achieve the true temperature at which you wish to operate.
• Load the sample and leave some time for equilibration.
• Turn SWEEP off.  There is no deuterium upon which to operate a lock, and the frequency shifts that are part of the lock operation will interfere with this spectrum.
• Shim the sample by maximizing integrated fid. This methods does not require the deuterium lock signal.  It may also be a good method for improving higher order shims on proteins samples, since the integrated area of the fid may be more sensitive to improvements in these shims than is the lock signal.
• Read (rsh) a suitable wilmad shim file, eg. aph_dss_wilmad.
• If you haven't already set up a specialized dataset for the dss calibration, do so now by selecting calib1h and using edc to save it by a different name, eg. oned_ethgly.xxx.
• Make it issue a rectangular pulse of 2 dB and 7 usec.
• Make TD (total data points) to 8K. This high value will increase the resolution by taking more data points.
• The exact settings for the 90 degree pulse width and the shimming are not particularly critical.
• Use gs and acqu to display a continuously acquired fid.
• Noting the integrated fid value displayed in the info window, adjust the shims in the usual order to maximize this value.
• Type stop to end the continuous acquisitions when your are through shimming.
• Tune and match the proton probe as usual.
• Measure the chemical shift between the two peaks in the ethylene glycol spectrum.
• Take the spectrum (zg), fourier transform (ef), and phase.
• Set the right peak to 0.
• To zoom on the peak, left click to associate cursor with the spectrum (the cursor will seem to stick to the spectrum). Then middle click to the left and the right of the peak to zoom in on it.
• Click on <calibrate> and put the cursor at the peak tip and middle click. This will open a box into which to enter a 0.
• Zoom on the left peak in the same way, and position the cursor at the peak top.  Read the chemical shift from the information box.
• For 100% ethylene glycol, y = 4.5677 - 0.0097723 x, where x is temp. in Kelvin. and y is the chemical shift.
• In a separate shell type "bc -l" to get a calculator.
• If necessary, reset the temperature to get the desired true temperature given the measured bias. Leave some time for equilibration.
• Take several readings with some time in between to be sure that the sample is thermally equilibrated.  The thermistor comes to equilibrium before the sample does.

DSS standard.

A DSS sample in deuterated water is found in a wilmad tube in the flask of standards on the operator's table.

• Set the temperature and load the sample.
• Starting from a suitable shim files, eg. aph_dss_wilmad, shim using the lock signal as usual.
• Tune and match the proton probe as usual (remember to turn SWEEP back on).
• If you haven't already, make a specialized version of calib1h with edc (eg. 1d_dss.xxx) and set it to issue a rectangular pulse at 2 usec and 2 dB; set TD to 8K.
• Take spectrum (zg), transform (ef), and phase.
• The spectrum will have two tall peaks with 3 short peaks in between.  The one on the left is deuterated water (ie. ^[1]H in HDO); the one on the right is the relevant DSS resonance.  Ignore the short peaks.
• Zoom on the rightmost DSS peak. Click <utilities> and <O1>.  Position the cursor on the peak top and read the absolute frequency from the information window.  As an example, on the AMX500 at 300 K, I found 500.1312532.  Be careful not to middle click, else you will change a carrier frequency setting in the active dataset.
• Use <calibrate> to set this peak to zero, and then get the chemical shift to deuterated water as above.  For 300 K (true), I got 4.7396.  Remember that the theoretical value is 4.742, so I decide to be satisfied with my accuracy of 0.0024 ppm.  I will use 4.7396 as my center point shift for hydrogen.
• To get center positions for nitrogen or carbon, multiply the absolute DSS frequency by the relative chemical shift constant for that nuclei to get the extrapolated reference frequency.  The relative chemical shift constants are given in the Markley et al. paper cited above and are based on choosing reference values (ppm = 0) for the other nuclei at a constant proportion to the hydrogen DSS standard under all conditions.  The nitrogen reference is 0.10132918 times the hydrogen reference.  The carbon standard is 0.251449530 time the hydrogen reference.
• For nitrogen: Look in the pulse program and see on what channel nitrogen.  For hsqc_fb.ref, it is channel f3.  For example on the AMX500 I found the nitrogen carrier frequency as SFO3 = 50.683840.  Take the difference between the carrier and the nitrogen reference frequency and divide by the  reference frequency to get the center position for nitrogen. So for ^[15]N, the reference frequency is 500.1312532 * 0.101329118 =  50.677859.  The center position offset is (50.683840-50.677859)/50.677859 =118.05 ppm.
•  ^[13]C is calculated similarly except that the carrier frequency may be a little more complicated to identify.
• In some cases involving ^[13]C, The frequency is switched among several different frequencies.  If this is the case, there will be a list of frequencies listed specified by the parameter F2LIST.  The pulse program will advance through this list each time it executes an "O2" command, cycling back to the beginning of the list as necessary.  Only one of these frequencies will be used as the ^[13]C carrier with respect to evolution of the ^[13]C  magnetization in the indirect dimension.  The other frequencies are used for decoupling.  It may not be obvious to the casual user which frequency on the frequency list is the correct one to use for the carrier position.  In this case, there should be a comment in the header of the pulse program clarifying which frequency to use.  As a rule of thumb, always read the comments in the pulse program first.
• For example, suppose that you establish that the ^[13]C carrier was at = 125.764214.  500.1312532 * 0.251449530 = 125.757769.  (125.764214 - 125.757769)/125.757769 = 50.12 ppm
• During processing on the NIS system, you can check your pulse program and/or use uxgrep to look in parameter files for information about the appropriate carrier frequencies.
• Note: shifting towards a lower ppm is said to be shifting "upfield". Shifting towards higher ppm is said to be shifting "downfield".
• The error of indexing to the wrong temperature is 0.0119 ppm/degree for all nuclei.  For small temperature shifts, people often ignore correcting the carbon and nitrogen on the grounds that their resolution is less than the correction.