Author: bugman
Date: Sun Dec 8 23:05:40 2013
New Revision: 21872
URL: http://svn.gna.org/viewcvs/relax?rev=21872&view=rev
Log:
Complete reworking of the 'NS R1rho 2-site' dispersion model.
The original code of Nikolai Skrynnikov and Martin Tollinger has been
modified to match the
behaviour of Dmitry Korzhnev's cpmg_fit software. The equations from
Korzhnev et al., JACS 2005
(http://dx.doi.org/10.1021/ja0446855) have been used for the initial
magnetisation and the R1rho'
calculation. All equations have been added to the manual to clarify the
model.
Modified:
trunk/docs/latex/bibliography.bib
trunk/docs/latex/dispersion.tex
trunk/docs/latex/dispersion_models.tex
trunk/lib/dispersion/ns_r1rho_2site.py
trunk/target_functions/relax_disp.py
Modified: trunk/docs/latex/bibliography.bib
URL:
http://svn.gna.org/viewcvs/relax/trunk/docs/latex/bibliography.bib?rev=21872&r1=21871&r2=21872&view=diff
==============================================================================
--- trunk/docs/latex/bibliography.bib (original)
+++ trunk/docs/latex/bibliography.bib Sun Dec 8 23:05:40 2013
@@ -3868,7 +3868,81 @@
year = 2004
}
-@Article{Korzhnev05,
+@Article{Korzhnev05a,
+ Author = {Korzhnev, D. M. and Orekhov, V. Y. and Kay, L. E.},
+ Title = {Off-resonance {R}(1rho) {NMR} studies of exchange
+ dynamics in proteins with low spin-lock fields: an
+ application to a {F}yn {SH}3 domain.},
+ Journal = jacs,
+ Volume = {127},
+ Number = {2},
+ Pages = {713-721},
+ abstract = {An (15)N NMR R(1rho) relaxation experiment is
+ presented for the measurement of millisecond time scale
+ exchange processes in proteins. On- and off-resonance
+ R(1rho) relaxation profiles are recorded one residue at
+ a time using a series of one-dimensional experiments in
+ concert with selective Hartmann-Hahn polarization
+ transfers. The experiment can be performed using low
+ spin-lock field strengths (values as low as 25 Hz have
+ been tested), with excellent alignment of magnetization
+ along the effective field achieved. Additionally,
+ suppression of the effects of cross-correlated
+ relaxation between dipolar and chemical shift
+ anisotropy interactions and (1)H-(15)N scalar coupled
+ evolution is straightforward to implement, independent
+ of the strength of the (15)N spin-locking field. The
+ methodology is applied to study the folding of a G48M
+ mutant of the Fyn SH3 domain that has been
+ characterized previously by CPMG dispersion
+ experiments. It is demonstrated through experiment that
+ off-resonance R(1rho) data measured at a single
+ magnetic field and one or more spin-lock field
+ strengths, with amplitudes on the order of the rate of
+ exchange, allow a complete characterization of a
+ two-site exchange process. This is possible even in the
+ case of slow exchange on the NMR time scale, where
+ complementary approaches involving CPMG-based
+ experiments fail. Advantages of this methodology in
+ relation to other approaches are described.},
+ authoraddress = {Protein Engineering Network Centers of Excellence and
+ Department of Medical Genetics, The University of
+ Toronto, Toronto, Ontario, Canada M5S 1A8.},
+ keywords = {Nitrogen Isotopes ; Nuclear Magnetic Resonance,
+ Biomolecular/*methods ; Protein Folding ;
+ Proto-Oncogene Proteins/*chemistry ; Proto-Oncogene
+ Proteins c-fyn ; src Homology Domains ; src-Family
+ Kinases/*chemistry},
+ language = {eng},
+ medline-aid = {10.1021/ja0446855 [doi]},
+ medline-crdt = {2005/01/13 09:00},
+ medline-da = {20050112},
+ medline-dcom = {20050303},
+ medline-edat = {2005/01/13 09:00},
+ medline-fau = {Korzhnev, Dmitry M ; Orekhov, Vladislav Yu ; 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 = {2005/03/04 09:00},
+ medline-own = {NLM},
+ medline-pl = {United States},
+ medline-pmid = {15643897},
+ medline-pst = {ppublish},
+ medline-pt = {Journal Article ; Research Support, Non-U.S. Gov't},
+ medline-rn = {0 (Nitrogen Isotopes) ; 0 (Proto-Oncogene Proteins) ;
+ EC 2.7.10.2 (Proto-Oncogene Proteins c-fyn) ; EC
+ 2.7.10.2 (src-Family Kinases)},
+ medline-sb = {IM},
+ medline-so = {J Am Chem Soc. 2005 Jan 19;127(2):713-21.},
+ medline-stat = {MEDLINE},
+ url =
{http://eutils.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?cmd=prlinks&dbfrom=pubmed&retmode=ref&id=15643897},
+ doi = {10.1021/ja0446855},
+ year = 2005
+}
+
+@Article{Korzhnev05b,
Author = {Korzhnev, D. M. and Neudecker, P. and Mittermaier, A.
and Orekhov, V. Y. and Kay, L. E.},
Title = {Multiple-site exchange in proteins studied with a
Modified: trunk/docs/latex/dispersion.tex
URL:
http://svn.gna.org/viewcvs/relax/trunk/docs/latex/dispersion.tex?rev=21872&r1=21871&r2=21872&view=diff
==============================================================================
--- trunk/docs/latex/dispersion.tex (original)
+++ trunk/docs/latex/dispersion.tex Sun Dec 8 23:05:40 2013
@@ -666,8 +666,8 @@
in which
\begin{subequations}
\begin{align}
- \delta_A &= \omegaA - \omegarf, \\
- \delta_B &= \omegaB - \omegarf, \\
+ \delta_A &= \omegaA - \omegarf, \label{eq: deltaA}\\
+ \delta_B &= \omegaB - \omegarf, \label{eq: deltaB} \\
\aveomega &= \pA\omegaA + \pB\omegaB, \\
\aveoffset &= \aveomega - \omegarf, \\
\omega_\textrm{Aeff}^2 &= \omegaone^2 + \delta_A^2, \\
@@ -769,6 +769,31 @@
It is selected by setting the model to `NS R1rho 2-site'.
The simple constraint $\pA > \pB$ is used to halve the optimisation space,
as both sides of the limit are mirror image spaces.
+For this model, the equations from \citet{Korzhnev05a} have been used. The
$\Ronerho$ value for state A magnetisation is defined as
+\begin{equation}
+ \Ronerho = - \frac{1}{T_\textrm{relax}} \cdot \ln \left( M_0^T \cdot
e^{R \cdot T_\textrm{relax}} \cdot M_0 \right),
+\end{equation}
+
+where
+\begin{align}
+ M_0 &= \begin{pmatrix} \sin{\theta} \\ 0 \\ 0 \\ 0 \\ \cos{\theta} \\
0 \end{pmatrix}, \\
+ \theta &= \arctan \left( \frac{\omegaone}{\aveoffset} \right).
+\end{align}
+
+The relaxation evolution matrix is defined as
+\begin{equation}
+ R = -\begin{pmatrix}
+ \Ronerhoprime+\kAB & -\kBA & \delta_A & 0
& 0 & 0 \\
+ -\kAB & \Ronerhoprime+\kBA & 0 &
\delta_B & 0 & 0 \\
+ -\delta_A & 0 & \Ronerhoprime+\kAB &
-\kBA & \omegaone & 0 \\
+ 0 & -\delta_B & -\kAB &
\Ronerhoprime+\kBA & 0 & \omegaone \\
+ 0 & 0 & -\omegaone & 0
& \Rone+\kAB & -\kBA \\
+ 0 & 0 & 0 &
-\omegaone & -\kAB & \Rone+\kBA \\
+ \end{pmatrix},
+\end{equation}
+
+where $\delta_{A,B}$ is defined in Equations~\ref{eq: deltaA} and~\ref{eq:
deltaB}.
+
% The analytic MMQ CPMG models.
@@ -832,7 +857,7 @@
\begin{itemize}
\item \bibentry{Korzhnev04a}
\item \bibentry{Korzhnev04b}
-\item \bibentry{Korzhnev05}
+\item \bibentry{Korzhnev05b}
\end{itemize}
@@ -855,7 +880,7 @@
\label{sect: dispersion: NS MMQ 2-site model}
\index{relaxation dispersion!NS MMQ 2-site model|textbf}
-This is the numerical model for 2-site exchange for proton-heteronuclear SQ,
ZQ, DQ and MQ CPMG data, as derived in
\citep{Korzhnev04a,Korzhnev04b,Korzhnev05}.
+This is the numerical model for 2-site exchange for proton-heteronuclear SQ,
ZQ, DQ and MQ CPMG data, as derived in
\citep{Korzhnev04a,Korzhnev04b,Korzhnev05b}.
It is selected by setting the model to `NS MMQ 2-site'.
The simple constraint $\pA > \pB$ is used to halve the optimisation space,
as both sides of the limit are mirror image spaces.
Different sets of equations are used for the different data types.
@@ -958,7 +983,7 @@
\begin{itemize}
\item \bibentry{Korzhnev04a}
\item \bibentry{Korzhnev04b}
-\item \bibentry{Korzhnev05}
+\item \bibentry{Korzhnev05b}
\end{itemize}
@@ -969,7 +994,7 @@
\label{sect: dispersion: NS MMQ 3-site linear model}
\index{relaxation dispersion!NS MMQ 3-site linear model|textbf}
-This is the numerical model for 3-site exchange for proton-heteronuclear SQ,
ZQ, DQ and MQ CPMG data, as derived in
\citep{Korzhnev04a,Korzhnev04b,Korzhnev05}.
+This is the numerical model for 3-site exchange for proton-heteronuclear SQ,
ZQ, DQ and MQ CPMG data, as derived in
\citep{Korzhnev04a,Korzhnev04b,Korzhnev05b}.
As this model is linear, the assumption that $\kAC$~= $\kCA$~= 0 has been
made.
To simplify the optimisation space for the model, the assumption
$\RtwozeroA$~= $\RtwozeroB$~= $\RtwozeroC$~= $\Rtwozero$ has also been made.
@@ -1045,7 +1070,7 @@
\label{sect: dispersion: NS MMQ 3-site model}
\index{relaxation dispersion!NS MMQ 3-site model|textbf}
-This is the numerical model for 3-site exchange for proton-heteronuclear SQ,
ZQ, DQ and MQ CPMG data, as derived in
\citep{Korzhnev04a,Korzhnev04b,Korzhnev05}.
+This is the numerical model for 3-site exchange for proton-heteronuclear SQ,
ZQ, DQ and MQ CPMG data, as derived in
\citep{Korzhnev04a,Korzhnev04b,Korzhnev05b}.
However it has been extended to allow the $A \leftrightarrow C$ transition.
To simplify the optimisation space for the model as in the `NS MMQ 3-site
linear' model, the assumption $\RtwozeroA$~= $\RtwozeroB$~= $\RtwozeroC$~=
$\Rtwozero$ has been made.
Modified: trunk/docs/latex/dispersion_models.tex
URL:
http://svn.gna.org/viewcvs/relax/trunk/docs/latex/dispersion_models.tex?rev=21872&r1=21871&r2=21872&view=diff
==============================================================================
--- trunk/docs/latex/dispersion_models.tex (original)
+++ trunk/docs/latex/dispersion_models.tex Sun Dec 8 23:05:40 2013
@@ -55,10 +55,10 @@
\cline{1-1}
\\[-5pt]
MMQ CR72 & Analytic & 2 & $\{\Rtwozero, \dots, \pA, \dw,
\dwH, \kex\}$ & $\pA > \pB$ &
\citet{Korzhnev04a} \\
-NS MMQ 2-site & Numeric & 2 & $\{\Rtwozero, \dots, \pA, \dw,
\dwH, \kex\}$ & $\pA > \pB$ & \citet{Korzhnev05}
\\
-NS MMQ 3-site linear & Numeric & 3 & $\{\Rtwozero, \dots, \pA, \pB,
\dwAB, \dwBC,$ & $\pA > \pB$ and $\pB > \pC$ & \citet{Korzhnev05}
\\
+NS MMQ 2-site & Numeric & 2 & $\{\Rtwozero, \dots, \pA, \dw,
\dwH, \kex\}$ & $\pA > \pB$ &
\citet{Korzhnev05b} \\
+NS MMQ 3-site linear & Numeric & 3 & $\{\Rtwozero, \dots, \pA, \pB,
\dwAB, \dwBC,$ & $\pA > \pB$ and $\pB > \pC$ &
\citet{Korzhnev05b} \\
& & & $\dwHAB, \dwHBC, \kexAB,
\kexBC\}$ \\
-NS MMQ 3-site & Numeric & 3 & $\{\Rtwozero, \dots, \pA, \pB,
\dwAB, \dwBC,$ & $\pA > \pB$ and $\pB > \pC$ & \citet{Korzhnev05}
\\
+NS MMQ 3-site & Numeric & 3 & $\{\Rtwozero, \dots, \pA, \pB,
\dwAB, \dwBC,$ & $\pA > \pB$ and $\pB > \pC$ &
\citet{Korzhnev05b} \\
& & & $\dwHAB, \dwHBC, \kexAB,
\kexBC, \kexAC\}$ \\
% R1rho-type models.
Modified: trunk/lib/dispersion/ns_r1rho_2site.py
URL:
http://svn.gna.org/viewcvs/relax/trunk/lib/dispersion/ns_r1rho_2site.py?rev=21872&r1=21871&r2=21872&view=diff
==============================================================================
--- trunk/lib/dispersion/ns_r1rho_2site.py (original)
+++ trunk/lib/dispersion/ns_r1rho_2site.py Sun Dec 8 23:05:40 2013
@@ -81,8 +81,10 @@
# Repetitive calculations (to speed up calculations).
Wa = omega # Larmor frequency [s^-1].
Wb = omega + dw # Larmor frequency [s^-1].
+ W = pA*Wa + pB*Wb # Population-averaged Larmor frequency
[s^-1].
dA = Wa - offset # Offset of spin-lock from A.
dB = Wb - offset # Offset of spin-lock from B.
+ d = W - offset # Offset of spin-lock from
population-average.
# Loop over the time points, back calculating the R2eff values.
for i in range(num_points):
@@ -90,23 +92,15 @@
R = rr1rho_3d(R1=r1, Rinf=r1rho_prime, pA=pA, pB=pB, wA=dA, wB=dB,
w1=spin_lock_fields[i], k_AB=k_AB, k_BA=k_BA)
# The following lines rotate the magnetization previous to spin-lock
into the weff frame.
- # A new M0 is obtained: M0 = [sin(thetaA)*pA sin(thetaB)*pB 0 0
cos(thetaA)*pA cos(thetaB)*pB].
- thetaA = atan(spin_lock_fields[i]/dA)
- thetaB = atan(spin_lock_fields[i]/dB)
- M0[0] = sin(thetaA) * pA
- M0[1] = sin(thetaB) * pB
- M0[4] = cos(thetaA) * pA
- M0[5] = cos(thetaB) * pB
+ theta = atan(spin_lock_fields[i]/d)
+ M0[0] = sin(theta)
+ M0[4] = cos(theta)
# This matrix is a propagator that will evolve the magnetization
with the matrix R.
Rexpo = matrix_exponential(R*relax_time)
# Magnetization evolution.
- Moft = dot(Rexpo, M0)
- MAx = Moft[0].real / pA
- MAy = Moft[2].real / pA
- MAz = Moft[4].real / pA
- MA = sqrt(MAx**2 + MAy**2 + MAz**2) # For spin A, is equal to 1
if nothing happens (no relaxation).
+ MA = dot(M0, dot(Rexpo, M0))
# The next lines calculate the R1rho using a two-point
approximation, i.e. assuming that the decay is mono-exponential.
if MA <= 0.0 or isNaN(MA):
Modified: trunk/target_functions/relax_disp.py
URL:
http://svn.gna.org/viewcvs/relax/trunk/target_functions/relax_disp.py?rev=21872&r1=21871&r2=21872&view=diff
==============================================================================
--- trunk/target_functions/relax_disp.py (original)
+++ trunk/target_functions/relax_disp.py Sun Dec 8 23:05:40 2013
@@ -1500,10 +1500,6 @@
k_BA = pA * kex
k_AB = pB * kex
- # This is a vector that contains the initial magnetizations
corresponding to the A and B state transverse magnetizations.
- self.M0[0] = pA
- self.M0[1] = pB
-
# Chi-squared initialisation.
chi2_sum = 0.0
r21872 - in /trunk: docs/latex/ lib/dispersion/ target_functions/