Measuring 15N T1 and T2 relaxation times (Varian): Difference between revisions

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== '''Correlation Time and NMR Measurement Time Prediction''' ==
=== Experimental Setup  ===


=== '''Experimental Setup''' ===
Run the <tt>HTP_t1t2_setup</tt> script to setup the following experiments:


Run the <tt>HTP_t1t2_setup</tt> script to setup the following experiments:
*2D [15N, 1H] HSQC, ~1.5h for SN analysis  
* 2D [15N, 1H] HSQC, ~1.5h for SN analysis
**<tt>NHonly='n' C13refoc='y' ni=256 f1180='n' phase=1,2 nt=8 ss=32</tt>  
** <tt>NHonly='n' C13refoc='y' ni=256 f1180='n' phase=1,2 nt=8 ss=32</tt>
*1D 15N T1, ~30 min  
* 1D 15N T1, ~30 min
**<tt>ni=1 phase=1 T1='y' f1180='n' NHonly='n' C13refoc='n' ss=256 nt=128</tt>  
** <tt>ni=1 phase=1 T1='y' f1180='n' NHonly='n' C13refoc='n' ss=256 nt=128</tt>
**<tt>relaxT=0.1, 0.2, 0.3, 0.4, 0.7, 1.0, 1.5, 2.0</tt>  
** <tt>relaxT=0.1, 0.2, 0.3, 0.4, 0.7, 1.0, 1.5, 2.0</tt>
*1D 15N T2, ~30 min  
* 1D 15N T2, ~30 min  
**<tt>ni=1 phase=1 T2='y' f1180='n' NHonly='n' C13refoc='n' ss=256 nt=128</tt>  
** <tt>ni=1 phase=1 T2='y' f1180='n' NHonly='n' C13refoc='n' ss=256 nt=128</tt>
**<tt>relaxT=0.01,0.03,0.05,0.07,0.09,0.11,0.13,0.15,0.17 maxrelaxT=0.17</tt>
** <tt>relaxT=0.01,0.03,0.05,0.07,0.09,0.11,0.13,0.15,0.17 maxrelaxT=0.17</tt>


Key points to consider:


Key issues:
*For most proteins it is recommended to run T1 and T2 experiments for at least 30 min each to achieve adequate S/N on a room-temperature probe. Short measurement times may lead to underestimated tc values. With cryogenic probes or very concentrated (&gt; 1 mM) samples the minimum measurement time may be smaller.  
* For most proteins it is recommended to run T1 and T2 experiments for at least 30 min each to achieve adequate S/N on a room-temperature probe. Short measurement times may lead to underestimated tc values. With cryogenic probes or very concentrated (> 1 mM) samples the minimum measurement time may be smaller.
*Short <tt>d1</tt> delays (~1 s) may lead to incorrect integral for the first T1 point. However, long d1 values may lead to a large residual water line and non-uniform baseline, especially on a cryoprobe. See what works best for the particular sample and spectrometer.  
* Short <tt>d1</tt> delays (~1 s) may lead to incorrect integral for the first T1 point. However, long d1 values may lead to a large residual water line and non-uniform baseline, especially on a cryoprobe. See what works best for the particular sample and spectrometer.
*<tt>relaxT</tt> must be given as a multiple of 10 ms for T1 and '''odd''' multiple of 10 ms for T2.  
* <tt>relaxT</tt> must be given as a multiple of 10 ms for T1 and '''odd''' multiple of 10 ms for T2.
*<tt>maxrelaxT</tt> is not used in T1 measurements.  
* <tt>maxrelaxT</tt> is not used in T1 measurements.
*Avoid sampling T2 points beyond 250 ms - it may cause excessive sample heating.  
* Avoid sampling T2 points beyond 250 ms - it may cause excessive sample heating.
*Intermediate tc values (between monomer and dimer) may indicate transient dimerization. Dilution studies are then required.  
* Intermediate tc values (between monomer and dimer) may indicate transient dimerization. Dilution studies are then required.
*The tc value is calculated under assumption of isotropic tumbling. For example, if a protein consists of long parallel a-helices the reported tc will indicate a larger molecular weight.
* The tc value is calculated under assumption of isotropic tumbling. For example, if a protein consists of long parallel a-helices the reported tc will indicate a larger molecular weight.


=== '''Correlation Time Measurement''' ===
=== Calculating rotational correlation time  ===


Based on the Stokes's law, the isotropic rotational correlation time for approximately spherical globular proteins is a function of the effective hydrodynamic radius of the protein, which provides a simple way to check the oligomerizaiton status of protein in solution. Here is the basic law: the correlation time in nanoseconds is approximately half of the value of the protein's molecular weight in kilodaltons.
*Process the data in Buffalo.VNMR with <tt>wft</tt> and adjust the phase for pure absorption.
*Invoke <tt>dc</tt> to correct baseline shift and slope. Expand the spectrum first for better results.
*Invoke <tt>dscale</tt> and <tt>setref</tt> to make sure the ppm scale is correct - required for the <tt>tc</tt> macro.
*Display all spectra with <tt>dssh</tt> and check that
**baseline is flat and uniform in all 1D spectra.  
**Spectral intensity follows an exponential decay.
*Run <tt>tc([T1exp, T2exp, [ppm1, ppm2]])</tt>, where the first two arguments are T1 and T2 experiment numbers, and the last two optional arguments specify the integration range in ppm. By default, integration is performed over the range between 10.5 ppm and 8.5 ppm to exclude signals from side-chain CONH2 groups (6 - 7 ppm) and unfolded segments (8 ppm). If called with no arguments it will prompt for experiment numbers and use the default integration range.


A protein's rotational correlation time (Tauc) can be quickly estimated from average 15N T1 and T2 relaxation times.
<br> The <tt>tc</tt> macro requires <tt>t1a</tt>, <tt>t2a</tt> and <tt>intav</tt> macros. The <tt>intav</tt> macro performs integration and stores the integral values in the <tt>fp.out</tt> file. <tt>t1a</tt> and <tt>t2a</tt> macros extract T<sub>1</sub> and T<sub>2</sub> relaxation times from the exponential fitting to the data in <tt>fp.out</tt>. Manual phase and drift correction (<tt>dc</tt>) of 1D spectra should be performed first to get accurate results.  


Rotational correlation time τ<sub>c</sub> is then calculated as


To calculate Tauc:
:<math>\tau_c\approx\frac{1}{4\pi\nu_N}\sqrt{6\frac{T_1}{T_2}-7}</math>,
* Process the data in Buffalo.VNMR with <tt>wft</tt> and adjust the phase for pure absorption.
* Invoke <tt>dc</tt> to correct baseline shift and slope. You can expand the spectrum for better results.
* Invoke <tt>dscale</tt> and <tt>setref</tt> to make sure the ppm scale is correct - required for the <tt>tc</tt> macro.
* Display all spectra with <tt>dssh</tt> and check that
** baseline is flat and uniform across points.
** Spectral intensity follows an exponential decay.
* Run <tt>tc([T1exp, T2exp, [ppm1, ppm2]])</tt>, where the first two arguments are T1 and T2 experiment numbers, and the last two optional arguments specify the integration range in ppm. By default, integration is performed over the range between 10.5 ppm and 8.5 ppm to exclude signals from side-chain CONH2 groups (6 - 7 ppm) and unfolded parts (8 ppm).


where ν<sub>N</sub> is the <sup>15</sup>N resonance frequency.


==== '''Tc macro'''  ====
The reported error range is from simple error propagation of the exponential fit error and is rather crude. Strictly speaking, such simple error propagation does not apply here, because the expected error distribution for τ<sub>c</sub> is asymmetric.  
 
The [[NESG:%ATTACHURL%/tc|tc]] macro is invoked by typing <tt>tc([T1exp, T2exp, [ppm1, ppm2]])</tt> at the [[NESG:VnmR|VNMR]] prompt. <tt>T1exp</tt> and <tt>T2exp</tt> are the experiment numbers of T1 and T2 experiments, respectively. As an option, the integration range in ppm can be specified with the third and fourth arguments. The default integration range is chosen between 10.5 and 8.5 ppm to avoid the resonances from side chain -CONH2 groups and backbone amides from unfolded regions. If called with no arguments [[NESG:%ATTACHURL%/tc|tc]] will prompt for experiment numbers and use the default integration range.
 
Tc macro requires <tt>t1a</tt>, <tt>t2a</tt> and <tt>intav</tt> macros. The <tt>intav</tt> macro performs integration stores the integral values in the <tt>fp.out</tt> file. <tt>t1a</tt> and <tt>t2a</tt> macros extract T1 and T2 relaxation times from the exponential fitting to the data in <tt>fp.out</tt>. Manual phase and drift correction (<tt>dc</tt>) of 1D spectra should be performed first to get accurate results.
 
τ_c is then calculated as
 
  τ_c = sqrt(6 * (T1 / T2) - 7) / (2 ω(N)),
 
where ω(N) is the 15N frequency. This formula is derived from equation (8) in [http://pubs.acs.org/cgi-bin/archive.cgi/bichaw/1989/28/i23/pdf/bi00449a003.pdf Kay, Torchia and Bax, Biochemistry '''1989''', 28, p8972-8979] by keeping only J(0) and J(ω(N)) terms and neglecting all higher frequencies. The complete equation (8) cannot be solved analytically for τ_c, and the simplified formula presented here should yield accurate results for systems with τ_c &gt;&gt; 0.5 ns.
 
The reported error range is from simple error propagation of the exponential fit error and is rather crude. Strictly speaking, such simple error propagation does not apply here, because the expected error distribution for τ_c is asymmetric.  


To install tc macro:  
To install tc macro:  
Line 58: Line 46:
#Download [[Media:Tc_macro.tar|tc_macro.tar]] into the user maclib directory (<tt>~/vnmrsys/maclib/</tt>)  
#Download [[Media:Tc_macro.tar|tc_macro.tar]] into the user maclib directory (<tt>~/vnmrsys/maclib/</tt>)  
#Unpack it with <tt>tar xvf tc_macro.tar</tt>
#Unpack it with <tt>tar xvf tc_macro.tar</tt>
=== '''Measurement Time Prediction''' ===
The minimum measurement time of (4,3)D GFT experiments can be reliably predicted from the S/N distribution of a 2D [15N, 1H] HSQC and the rotational correlation time tau_c. First, you need to generate an integrated peaklist.
==== '''Peak Integration in 2D [15N, 1H] HSQC'''  ====
Having processed 2D (15N, 1H) HSQC as described in data process, one can do the peak picking and integration of 2D (15N, 1H) HSQC manualy or semi-automaticlly as following:
*Peak picking and integration by using program XEASY
##Use command <tt>ns</tt> to load the spectrum
##Use <tt>ls</tt> to load the corresponding sequence file (optional)
##Use <tt>in</tt> to automatic pick peaks with total peak number slightly more than expected by select adjust contour level; then manually remove side-chain amide peaks
##Use <tt>mn</tt> to measure noise level, and use <tt>tw</tt> to display the noise level value. Normally the value of 2.5 times of standard deviation ( ~250 if the noise level has been normalized ) is taken as noise level.
##Use <tt>ip</tt> to choose peak height (m) as integration mode, and use "ii" to integrate the whole spectrum. An [[NESG:XEASY|XEASY]] external program "PeakintI" can be used to obtain more accurate peak height values, which is discribed below.
##Use <tt>wp</tt> to save the peak list.
*More accurate peak height measurement by using program [[NESG:PeakintI|PeakintI]].<br> Type command: <br><br> <tt>peakintI ../data/NHsqc6001 nhsqcsa_b.peaks 250 -i -t 2 2 0.1 </tt><br><br> where the <tt>nhsqcsa_b.peaks</tt> is the input peak list and the output file will be <tt>inhsqcsa_b.peaks</tt>.
*Combing atom name informaiton in the peak list for S/N distribution (optional). <br>
**by using [[NESG:UBNMR|UBNMR]], please check [[NESG:UBNMR|UBNMR]] macro
**by using script '''sim''', run macro '''comb_yang''' by typing <tt>sim comb_yang</tt>
==== '''S/N distribution analysis for 2D (15N, 1H) HSQC'''  ====
The SN distribution of resonances in a NMR spectra can be fit to the Gaussian distribution:
    [[Image:Sn_nhsqc.jpg]]
<br><tt>f= a*exp(-0.5*((ln(SN_i)-ln(SN_0))/b)^2) </tt><br> where <tt>SN_0</tt> is the most populated S/N observed, <tt>f is the expected population at a certern SN value SN_i</tt>, <tt>a and b</tt> are contants.
The SN of NHSQC <tt>SN_0</tt> can be obtained as following:
#Calculate <tt>ln(SN)</tt> for each peak from the peak height and noise level, e.g. by using EXCEL
#Obtain SN distribution (<tt>population v.s. ls(SN)</tt>) by using Sigma-Plot
#By using Sigma-Plot, fitting SN distribution to Gaussian distribution and obtain <tt>SN_0</tt>, constant <tt>a and b</tt>.
==== '''Calculation of Measurement Time'''  ====
The SN distribution of resonances in other NMR spectra can also be fit to the Gaussian distribution as in 2D (15N, 1H) NHSQC:<br><br> <tt>f= a*exp(-0.5*((ln(SN_i)-ln(SN_0))/b)^2)</tt> <br><br> where <tt>SN_0</tt> is the most populated SN observed, <tt>f</tt> is the expected population at a certain SN value <tt>SN_i</tt>, <tt>a</tt> and <tt>b</tt> are constants. Based on this equation, one can calculate the expected SN_0 for a required peak detection yield.
Assuming that a peak shall have at least SN value of 2 in order to be observed or detected, and the average b for (4,3) GFT experiments is 0.8; if 95% peak detection yield is required, the exptected SN_0 is:<br><br><tt>SN_0=exp(ln2+1.644*b)=7.4 </tt><br><br>
    [[Image:Sn2.jpg]]
NMR measurement time of (4,3) GFT HNNCABCA, (4,3)D GFT CABCAcoNHN and (4,3)D HABCABCONHN can be calculated from the following equation:<br><br> <tt>T_43d= ((SN_43d* Tauc^2)/(SN_2d*A))^2 </tt><br> where <tt>T_43d</tt> is the required time for (4,3) GFT experiment, <tt>SN_43d</tt> is the expected SN value of (4,3)D GFT experiments, <tt>SN_2d</tt> is the SN per hour of 2D (15N, 1H) HSQC. =A= is constant, which has value of 0.8639 for (4,3) GFT HNNCABCA, 1.6019 for (4,3)D GFT CABCAcoNHN and 1.0153 for (4,3)D HABCABCONHN.
    [[Image:Sn3.jpg]]
One can use [[NESG:UBNMR|UBNMR]] to run the measurement time predition by the following command: <br><br><br> <tt>predict T2d SN2d Tc</tt><br>where
*<tt>T2d</tt> is the acquisition time of 2D [15N,1H] HSQC in hours
*<tt>SN2d</tt> is the SN distribution average of 2D [15N,1H] HSQC
*<tt>Tc</tt> is the rotational correlation time of protein in nanoseconds.
<br>


-- AlexEletski - 03 Mar 2008
-- AlexEletski - 03 Mar 2008

Latest revision as of 21:36, 16 December 2009

Experimental Setup

Run the HTP_t1t2_setup script to setup the following experiments:

  • 2D [15N, 1H] HSQC, ~1.5h for SN analysis
    • NHonly='n' C13refoc='y' ni=256 f1180='n' phase=1,2 nt=8 ss=32
  • 1D 15N T1, ~30 min
    • ni=1 phase=1 T1='y' f1180='n' NHonly='n' C13refoc='n' ss=256 nt=128
    • relaxT=0.1, 0.2, 0.3, 0.4, 0.7, 1.0, 1.5, 2.0
  • 1D 15N T2, ~30 min
    • ni=1 phase=1 T2='y' f1180='n' NHonly='n' C13refoc='n' ss=256 nt=128
    • relaxT=0.01,0.03,0.05,0.07,0.09,0.11,0.13,0.15,0.17 maxrelaxT=0.17

Key points to consider:

  • For most proteins it is recommended to run T1 and T2 experiments for at least 30 min each to achieve adequate S/N on a room-temperature probe. Short measurement times may lead to underestimated tc values. With cryogenic probes or very concentrated (> 1 mM) samples the minimum measurement time may be smaller.
  • Short d1 delays (~1 s) may lead to incorrect integral for the first T1 point. However, long d1 values may lead to a large residual water line and non-uniform baseline, especially on a cryoprobe. See what works best for the particular sample and spectrometer.
  • relaxT must be given as a multiple of 10 ms for T1 and odd multiple of 10 ms for T2.
  • maxrelaxT is not used in T1 measurements.
  • Avoid sampling T2 points beyond 250 ms - it may cause excessive sample heating.
  • Intermediate tc values (between monomer and dimer) may indicate transient dimerization. Dilution studies are then required.
  • The tc value is calculated under assumption of isotropic tumbling. For example, if a protein consists of long parallel a-helices the reported tc will indicate a larger molecular weight.

Calculating rotational correlation time

  • Process the data in Buffalo.VNMR with wft and adjust the phase for pure absorption.
  • Invoke dc to correct baseline shift and slope. Expand the spectrum first for better results.
  • Invoke dscale and setref to make sure the ppm scale is correct - required for the tc macro.
  • Display all spectra with dssh and check that
    • baseline is flat and uniform in all 1D spectra.
    • Spectral intensity follows an exponential decay.
  • Run tc([T1exp, T2exp, [ppm1, ppm2]]), where the first two arguments are T1 and T2 experiment numbers, and the last two optional arguments specify the integration range in ppm. By default, integration is performed over the range between 10.5 ppm and 8.5 ppm to exclude signals from side-chain CONH2 groups (6 - 7 ppm) and unfolded segments (8 ppm). If called with no arguments it will prompt for experiment numbers and use the default integration range.


The tc macro requires t1a, t2a and intav macros. The intav macro performs integration and stores the integral values in the fp.out file. t1a and t2a macros extract T1 and T2 relaxation times from the exponential fitting to the data in fp.out. Manual phase and drift correction (dc) of 1D spectra should be performed first to get accurate results.

Rotational correlation time τc is then calculated as

<math>\tau_c\approx\frac{1}{4\pi\nu_N}\sqrt{6\frac{T_1}{T_2}-7}</math>,

where νN is the 15N resonance frequency.

The reported error range is from simple error propagation of the exponential fit error and is rather crude. Strictly speaking, such simple error propagation does not apply here, because the expected error distribution for τc is asymmetric.

To install tc macro:

  1. Download tc_macro.tar into the user maclib directory (~/vnmrsys/maclib/)
  2. Unpack it with tar xvf tc_macro.tar

-- AlexEletski - 03 Mar 2008

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