Author: bugman
Date: Fri Oct 11 17:47:29 2013
New Revision: 21077
URL: http://svn.gna.org/viewcvs/relax?rev=21077&view=rev
Log:
Added the 'MQ NS CPMG 2-site' model to the relax user manual.
This is the 2-site numeric solution for multi-quantum CPMG-type data.
This follows the tutorial for adding relaxation dispersion models at:
http://wiki.nmr-relax.com/Tutorial_for_adding_relaxation_dispersion_models_to_relax#The_relax_manual.
Modified:
branches/relax_disp/docs/latex/bibliography.bib
branches/relax_disp/docs/latex/dispersion.tex
branches/relax_disp/docs/latex/relax.tex
Modified: branches/relax_disp/docs/latex/bibliography.bib
URL:
http://svn.gna.org/viewcvs/relax/branches/relax_disp/docs/latex/bibliography.bib?rev=21077&r1=21076&r2=21077&view=diff
==============================================================================
--- branches/relax_disp/docs/latex/bibliography.bib (original)
+++ branches/relax_disp/docs/latex/bibliography.bib Fri Oct 11 17:47:29 2013
@@ -3484,6 +3484,140 @@
year = 1997
}
+@Article{Korzhnev04a,
+ Author = {Korzhnev, D. M. and Kloiber, K. and Kanelis, V. and
+ Tugarinov, V. and Kay, L. E.},
+ Title = {Probing slow dynamics in high molecular weight
+ proteins by methyl-{TROSY} {NMR} spectroscopy:
+ application to a 723-residue enzyme.},
+ Journal = jacs,
+ Volume = {126},
+ Number = {12},
+ Pages = {3964-3973},
+ abstract = {A new CPMG-based multiple quantum relaxation
+ dispersion experiment is presented for measuring
+ millisecond dynamic processes at side-chain methyl
+ positions in high molecular weight proteins. The
+ experiment benefits from a methyl-TROSY effect in which
+ cancellation of intramethyl dipole fields occurs,
+ leading to methyl (13)C-(1)H correlation spectra of
+ high sensitivity and resolution (Tugarinov, V.; Hwang,
+ P. M.; Ollerenshaw, J. E.; Kay, L. E. J. Am. Chem. Soc.
+ 2003, 125, 10420-10428). The utility of the methodology
+ is illustrated with an application to a highly
+ deuterated, methyl-protonated sample of malate synthase
+ G, an 82 kDa enzyme consisting of a single polypeptide
+ chain. A comparison of the sensitivity obtained using
+ the present approach relative to existing HSQC-type
+ (13)C single quantum dispersion experiments shows a
+ gain of a factor of 5.4 on average, significantly
+ increasing the range of applications for this
+ methodology.},
+ authoraddress = {Protein Engineering Network Centres of Excellence and
+ the Departments of Medical Genetics, Biochemistry, and
+ Chemistry, University of Toronto, Toronto, Ontario,
+ Canada M5S 1A8.},
+ keywords = {Carbon Isotopes ; Malate Synthase/*chemistry ; Models,
+ Chemical ; Models, Molecular ; Molecular Weight ;
+ Nuclear Magnetic Resonance, Biomolecular/*methods ;
+ Protein Conformation ; Thermodynamics},
+ language = {eng},
+ medline-aid = {10.1021/ja039587i [doi]},
+ medline-crdt = {2004/03/25 05:00},
+ medline-da = {20040324},
+ medline-dcom = {20040707},
+ medline-edat = {2004/03/25 05:00},
+ medline-fau = {Korzhnev, Dmitry M ; Kloiber, Karin ; Kanelis, Voula ;
+ Tugarinov, Vitali ; Kay, Lewis E},
+ medline-is = {0002-7863 (Print) ; 0002-7863 (Linking)},
+ medline-jid = {7503056},
+ medline-jt = {Journal of the American Chemical Society},
+ medline-lr = {20061115},
+ medline-mhda = {2004/07/09 05:00},
+ medline-own = {NLM},
+ medline-pl = {United States},
+ medline-pmid = {15038751},
+ medline-pst = {ppublish},
+ medline-pt = {Journal Article ; Research Support, Non-U.S. Gov't},
+ medline-rn = {0 (Carbon Isotopes) ; EC 2.3.3.9 (Malate Synthase)},
+ medline-sb = {IM},
+ medline-so = {J Am Chem Soc. 2004 Mar 31;126(12):3964-73.},
+ medline-stat = {MEDLINE},
+ url =
{http://eutils.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?cmd=prlinks&dbfrom=pubmed&retmode=ref&id=15038751},
+ doi = {10.1021/ja039587i},
+ year = 2004
+}
+
+@Article{Korzhnev04b,
+ Author = {Korzhnev, D. M. and Kloiber, K. and Kay, L. E.},
+ Title = {Multiple-quantum relaxation dispersion {NMR}
+ spectroscopy probing millisecond time-scale dynamics in
+ proteins: theory and application.},
+ Journal = jacs,
+ Volume = {126},
+ Number = {23},
+ Pages = {7320-7329},
+ abstract = {New relaxation dispersion experiments are presented
+ that probe millisecond time-scale dynamical processes
+ in proteins. The experiments measure the relaxation of
+ (1)H-(15)N multiple-quantum coherence as a function of
+ the rate of application of either (1)H or (15)N
+ refocusing pulses during a constant time relaxation
+ interval. In contrast to the dispersion profiles
+ generated from more conventional (15)N((1)H)
+ single-quantum relaxation experiments that depend on
+ changes in (15)N((1)H) chemical shifts between
+ exchanging states, (1)H-(15)N multiple-quantum
+ dispersions are sensitive to changes in the chemical
+ environments of both (1)H and (15)N spins. The
+ resulting multiple-quantum relaxation dispersion
+ profiles can, therefore, be quite different from those
+ generated by single-quantum experiments, so that an
+ analysis of both single- and multiple-quantum profiles
+ together provides a powerful approach for obtaining
+ robust measures of exchange parameters. This is
+ particularly the case in applications to protonated
+ proteins where other methods for studying exchange
+ involving amide proton spins are negatively influenced
+ by contributions from neighboring protons. The
+ methodology is demonstrated on protonated and
+ perdeuterated samples of a G48M mutant of the Fyn SH3
+ domain that exchanges between folded and unfolded
+ states in solution.},
+ authoraddress = {Protein Engineering Network Centres of Excellence and
+ the Department of Medical Genetics, University of
+ Toronto, Toronto, Ontario, Canada M5S 1A8.},
+ keywords = {*Magnetic Resonance Spectroscopy ; Protein Folding ;
+ Proto-Oncogene Proteins/*chemistry/*metabolism ;
+ Proto-Oncogene Proteins c-fyn ; Time Factors ; src
+ Homology Domains},
+ language = {eng},
+ medline-aid = {10.1021/ja049968b [doi]},
+ medline-crdt = {2004/06/10 05:00},
+ medline-da = {20040609},
+ medline-dcom = {20040923},
+ medline-edat = {2004/06/10 05:00},
+ medline-fau = {Korzhnev, Dmitry M ; Kloiber, Karin ; Kay, Lewis E},
+ medline-is = {0002-7863 (Print) ; 0002-7863 (Linking)},
+ medline-jid = {7503056},
+ medline-jt = {Journal of the American Chemical Society},
+ medline-lr = {20091119},
+ medline-mhda = {2004/09/24 05:00},
+ medline-own = {NLM},
+ medline-pl = {United States},
+ medline-pmid = {15186169},
+ medline-pst = {ppublish},
+ medline-pt = {Journal Article ; Research Support, Non-U.S. Gov't},
+ medline-rn = {0 (Proto-Oncogene Proteins) ; EC 2.7.10.2
+ (Proto-Oncogene Proteins c-fyn)},
+ medline-sb = {IM},
+ medline-so = {J Am Chem Soc. 2004 Jun 16;126(23):7320-9.},
+ medline-stat = {MEDLINE},
+ url =
{http://eutils.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?cmd=prlinks&dbfrom=pubmed&retmode=ref&id=15186169},
+ doi = {10.1021/ja049968b},
+ year = 2004
+}
+
@Article{KullbackLeibler51,
Author = {Kullback, S. and Leibler, R. A.},
Title = {On information and sufficiency},
Modified: branches/relax_disp/docs/latex/dispersion.tex
URL:
http://svn.gna.org/viewcvs/relax/branches/relax_disp/docs/latex/dispersion.tex?rev=21077&r1=21076&r2=21077&view=diff
==============================================================================
--- branches/relax_disp/docs/latex/dispersion.tex (original)
+++ branches/relax_disp/docs/latex/dispersion.tex Fri Oct 11 17:47:29 2013
@@ -112,6 +112,14 @@
\begin{description}
\item[`NS R1rho 2-site':]\index{relaxation dispersion!NS R1rho 2-site model}
The model for 2-site exchange using 3D magnetisation vectors. It has the
parameters $\{\Ronerhoprime, \dots, \pA, \dw, \kex\}$. See
Section~\ref{sect: dispersion: NS R1rho 2-site model} on page~\pageref{sect:
dispersion: NS R1rho 2-site model}.
\end{description}
+
+
+For the MQ CPMG-type experiments, the numeric models currently supported are:
+
+\begin{description}
+\item[`MQ NS CPMG 2-site':]\index{relaxation dispersion!MQ NS CPMG 2-site
model} The reduced model for 2-site exchange using 2D magnetisation vectors
whereby the simplification $\RtwozeroA = \RtwozeroB$ is assumed. It has the
parameters $\{\Rtwozero, \dots, \pA, \dw, \dwH, \kex\}$. See
Section~\ref{sect: dispersion: MQ NS CPMG 2-site} on page~\pageref{sect:
dispersion: MQ NS CPMG 2-site}.
+\end{description}
+
% Dispersion model summary.
@@ -158,6 +166,7 @@
$\pA$ & - & Population of state A
& - \\
$\pB$ & - & Population of state B
& - \\
$\dw$ & - & Chemical shift
difference between the two states & rad.s$^{-1}$
(stored as ppm) \\
+$\dwH$ & - & Proton chemical shift
difference between the two states (for MQ data) & rad.s$^{-1}$
(stored as ppm) \\
$\Phiex$ & $\pA\pB\dw^2$ & Fast exchange factor
& rad$^2$.s$^{-2}$
(stored as ppm$^2$) \\
$\PhiexB$ & See \ref{eq: disp phiexB} on page \pageref{eq: disp
phiexB} & Fast exchange factor between sites A and B & rad$^2$.s$^{-2}$
(stored as ppm$^2$) \\
$\PhiexC$ & See \ref{eq: disp phiexC} on page \pageref{eq: disp
phiexC} & Fast exchange factor between sites A and C & rad$^2$.s$^{-2}$
(stored as ppm$^2$) \\
@@ -647,10 +656,101 @@
The simple constraint $\pA > \pB$ is used to halve the optimisation space,
as both sides of the limit are mirror image spaces.
+% The numeric MQ CPMG models.
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\section{The numeric MQ CPMG models}
+\label{sect: dispersion: numeric MQ CPMG models}
+\index{relaxation dispersion!Numeric MQ CPMG model|textbf}
+
+\begin{sidewaystable}
+\begin{center}
+\caption{The analytic and numerical models for MQ CPMG-type experiments
currently supported within relax}
+\begin{tabular}{lllcll}
+\toprule
+Model code & Solution & Sites & Parameters
& Restriction & Reference \\
+\midrule
+R2eff & - & - & $\{\Rtwoeff, \cdots\}$
& Fixed relaxation time period & - \\
+R2eff & - & - & $\{\Rtwoeff, I_0, \cdots\}$
& Variable relaxation time period & - \\
+No Rex & Closed & 0 & $\{\Rtwozero, \cdots\}$
& - & - \\
+MQ NS CPMG 2-site & Numeric & 2 & $\{\Rtwozero, \dots, \pA, \dw,
\dwH, \kex\}$ & $\pA > \pB$ &
\citet{Korzhnev04a} \\
+\bottomrule
+\label{table: CPMG dispersion models}
+\end{tabular}
+\end{center}
+\end{sidewaystable}
+
+
+% MQ NS CPMG 2-site model.
+%~~~~~~~~~~~~~~~~~~~~~~~~~
+
+\subsection{The MQ NS CPMG 2-site model}
+\label{sect: dispersion: MQ NS CPMG 2-site model}
+\index{relaxation dispersion!MQ NS CPMG 2-site model|textbf}
+
+This is the numerical model for 2-site exchange using 2D magnetisation
vectors, as derived by \citep{Korzhnev04a}.
+It is selected by setting the model to `MQ NS CPMG 2-site'.
+The simple constraint $\pA > \pB$ is used to halve the optimisation space,
as both sides of the limit are mirror image spaces.
+The equation for the exchange process is
+\begin{equation}
+ \Rtwoeff = - \frac{1}{T}
+ \log \left\{ Re \left[ \frac{0.5}{\pA}
+ \begin{pmatrix}1&0\end{pmatrix} \cdot \left(
\mathbf{AB} + \mathbf{CD} \right) \cdot \begin{pmatrix}\pA\\\pB\end{pmatrix}
+ \right] \right\},
+\end{equation}
+
+where $T$ is the constant time interval, and the matrices $\mathbf{A}$,
$\mathbf{B}$, $\mathbf{C}$, and $\mathbf{D}$ are differentially defined.
+When $n$ is even, they are defined as
+\begin{subequations}
+\begin{align}
+ \mathbf{A} &= \left( \mathbf{M_1} \mathbf{M_2} \mathbf{M_2} \mathbf{M_1}
\right)^{\frac{n}{2}}, \\
+ \mathbf{B} &= \left( \mathbf{M_2}^* \mathbf{M_1}^* \mathbf{M_1}^*
\mathbf{M_2}^* \right)^{\frac{n}{2}}, \\
+ \mathbf{C} &= \left( \mathbf{M_2} \mathbf{M_1} \mathbf{M_1} \mathbf{M_2}
\right)^{\frac{n}{2}}, \\
+ \mathbf{D} &= \left( \mathbf{M_1}^* \mathbf{M_2}^* \mathbf{M_2}^*
\mathbf{M_1}^* \right)^{\frac{n}{2}},
+\end{align}
+\end{subequations}
+
+and when $n$ is odd, they are defined as
+\begin{subequations}
+\begin{align}
+ \mathbf{A} &= \left( \mathbf{M_1} \mathbf{M_2} \mathbf{M_2} \mathbf{M_1}
\right)^{\frac{n-1}{2}} \mathbf{M_1} \mathbf{M_2}, \\
+ \mathbf{B} &= \left( \mathbf{M_1}^* \mathbf{M_2}^* \mathbf{M_2}^*
\mathbf{M_1}^* \right)^{\frac{n-1}{2}} \mathbf{M_1}^* \mathbf{M_2}^*, \\
+ \mathbf{C} &= \left( \mathbf{M_2} \mathbf{M_1} \mathbf{M_1} \mathbf{M_2}
\right)^{\frac{n-1}{2}} \mathbf{M_2} \mathbf{M_1}, \\
+ \mathbf{D} &= \left( \mathbf{M_2}^* \mathbf{M_1}^* \mathbf{M_1}^*
\mathbf{M_2}^* \right)^{\frac{n-1}{2}} \mathbf{M_2}^* \mathbf{M_1}^*.
+\end{align}
+\end{subequations}
+
+The $\mathbf{M}$ matrices are defined as:
+\begin{equation}
+ \mathbf{M_j} = \exp(\mathbf{m_j}\delta),
+\end{equation}
+
+where $2\delta$ is the spacing between successive 180$^\circ$ pulses and
where
+\begin{subequations}
+\begin{align}
+ \mathbf{m_1} &= \begin{pmatrix}
+ -\pB\kex - \RtwoDQA & \pA\kex \\
+ \pB\kex & - \pA\kex -i(\dwH + \dw) \RtwoDQB
+ \end{pmatrix}, \\
+ \mathbf{m_2} &= \begin{pmatrix}
+ -\pB\kex - \RtwoZQA & \pA\kex \\
+ \pB\kex & - \pA\kex -i(\dwH - \dw) \RtwoZQB
+ \end{pmatrix},
+\end{align}
+\end{subequations}
+
+The references for this model are:
+\begin{itemize}
+\item \bibentry{Korzhnev04a}
+\item \bibentry{Korzhnev04b}
+\end{itemize}
+
+
% Script UI.
%%%%%%%%%%%%
+\newpage
\section{Analysing dispersion in the prompt/script UI mode}
Before reading this section, please read Chapter~\ref{ch: data model}
covering the relax data model first. It will explain many of the concepts
used within the following example script.
Modified: branches/relax_disp/docs/latex/relax.tex
URL:
http://svn.gna.org/viewcvs/relax/branches/relax_disp/docs/latex/relax.tex?rev=21077&r1=21076&r2=21077&view=diff
==============================================================================
--- branches/relax_disp/docs/latex/relax.tex (original)
+++ branches/relax_disp/docs/latex/relax.tex Fri Oct 11 17:47:29 2013
@@ -165,6 +165,10 @@
\newcommand{\RtwozeroA}{\mathrm{R}_{2A}^0}
\newcommand{\RtwozeroB}{\mathrm{R}_{2B}^0}
\newcommand{\RtwozeroC}{\mathrm{R}_{2C}^0}
+\newcommand{\RtwoDQA}{\mathrm{R}_{2,DQ}^A}
+\newcommand{\RtwoDQB}{\mathrm{R}_{2,DQ}^B}
+\newcommand{\RtwoZQA}{\mathrm{R}_{2,ZQ}^A}
+\newcommand{\RtwoZQB}{\mathrm{R}_{2,ZQ}^B}
\newcommand{\tex}{\tau_\textrm{ex}}
\newcommand{\taucpmg}{\tau_\textrm{CPMG}}
r21077 - in /branches/relax_disp/docs/latex: bibliography.bib dispersion.tex relax.tex