Pseudocontact shift analysis - Revision history

Kuprov: Normalise sequential blank lines

2026-04-25T11:28:54Z

Normalise sequential blank lines

Kuprov: /* Example 4b. Reconstructing PCS tag distributions in proteins */

2018-07-04T12:13:29Z

‎Example 4b. Reconstructing PCS tag distributions in proteins

Kuprov: /* Example 4b. Reconstructing PCS tag distributions in proteins */

2018-06-29T10:07:55Z

‎Example 4b. Reconstructing PCS tag distributions in proteins

Suturina: /* Distributed paramagnetic centre model */

2017-01-06T11:06:06Z

‎Distributed paramagnetic centre model

Suturina: /* Using hyperfine tensors from electronic structure theory */

2017-01-06T11:03:55Z

‎Using hyperfine tensors from electronic structure theory

Suturina: /* Point dipole approximation */

2017-01-06T10:56:14Z

‎Point dipole approximation

Admin: /* Example 4b. Reconstructing PCS tag distributions in proteins */

2017-01-02T09:50:41Z

‎Example 4b. Reconstructing PCS tag distributions in proteins

Admin: /* Example 4b. Reconstructing PCS tag distributions in proteins */

2017-01-01T17:57:56Z

‎Example 4b. Reconstructing PCS tag distributions in proteins

Admin: /* Example 4b. Reconstructing PCS tag distributions in proteins */

2017-01-01T17:52:59Z

‎Example 4b. Reconstructing PCS tag distributions in proteins

Admin: /* Example 4b. Reconstructing PCS tag distributions in proteins */

2017-01-01T17:51:25Z

‎Example 4b. Reconstructing PCS tag distributions in proteins

@@ Line 11: / Line 11: @@
 ==Point dipole approximation==
 This is historically the first and the simplest approach. It is based on the point dipole approximation for the electron. The expression for the pseudocontact shift for a nucleus at position <math>\mathbf{r}</math> relative to the electron with a magnetic susceptibility tensor <math>\mathbf{\chi }</math> is:
 <center><math>\sigma =\frac{1}{4\pi {{r}^{3}}}\text{Tr}\left[ \left( \frac{\mathbf{r}\otimes {{\mathbf{r}}^{\text{T}}}}{{{r}^{2}}}-\frac{1}{3} \right)\cdot \mathbf{\chi } \right]</math></center>
 This approach is valid for the distances at which the paramagnetic centre may be viewed as a point - typically at least 10 Angstroms away. The PCS of any nuclei located at closer distances would not fit this model. The ''Spinach'' function that calculates pseudocontact shifts from user-specified coordinates and electron susceptibility tensors is [[ppcs.m]]. The function that extracts the paramagnetic centre position and the susceptibility tensor from user-specified nuclear coordinates and pseudocontact shifts using the point electron model is [[ippcs.m]].
 Note that the magnetic susceptibility tensor may be estimated from the g-tensor for S=1/2 using the following expression:
 <center><math>{\chi _i} = {\mu _0}\mu _B^2\frac{{g_i^2}}{{4{k_B}T}} \approx 1.9571\frac{{g_i^2}}{{T[K]}}[{{Å}^3}]</math></center>
 The function that performs this estimation for an arbitary g-tensor is [[g2chi.m]]. The resulting estimate is only valid at high temperature.
@@ Line 135: / Line 131: @@
 ==Magnetic multipole approximation==
 The next level of theory that improves on the point dipole approximation is based on the spherical harmonic expansion of the electron probability density:
 <center><math>\rho \left( \mathbf{r} \right)=\sum\limits_{l,m}{\alpha _{l}^{m}\left( r \right)Y_{l}^{m}\left( \theta ,\varphi  \right)}</math></center>
 It works for nuclei positioned outside the bounding sphere of the electron probability density. PCS calculation is performed using [[lpcs.m]] function and the fitting is performed using [[ilpcs.m]] function. In both cases, the list of <math>l</math> ranks to be included into the expansion must be supplied by the user.
@@ Line 193: / Line 187: @@
 Spinach has two electronic structure theory package parsers: [[gparse.m]] for outputs from ''Gaussian'' and [[oparse.m]] for outputs from ''ORCA''. Both extract hyperfine tensors from the logs produced by the program. The function [[hfc2pcs.m]] then computes PCS by multiplying the traceless part of the hyperfine tensor by the traceless part of the susceptibility tensor and taking the trace of the result. To keep the traces (and therefore the contact part of the full paramagnetic shift), use [[hfc2pms.m]] function. The general equation is:
 <center><math>\sigma _{\text{CS}}^{\left( k \right)}+\sigma _{\text{PCS}}^{\left( k \right)}=-\frac{1}{3}\text{Tr}\left[ \frac{{{\mathbf{A}}^{\left( k \right)}}\cdot \boldsymbol{\chi }}{{{\mu }_{0}}{{\gamma }_{\text{e}}}\gamma _{\text{n}}^{\left( k \right)}\hbar } \right]</math></center>
 See http://dx.doi.org/10.1039/C4CP03106G for further information. Note that this method essentially requires the molecule to be rigid; realistically, it is only applicable to small molecules, for which it is strongly recommended.
@@ Line 345: / Line 337: @@
 to obtain your new susceptibility tensor. If it is significantly different from the previous one, repeat Steps 6 and 7 until self-consistency is achieved.
 ''Version 1.9, authors: [[Elizaveta Suturina]], [[Ilya Kuprov]]''

@@ Line 280: / Line 280: @@
       parameters.plot={'diagnostics','density','molecule','tightzoom','box'};
       parameters.box_cent=[### ### ###];
-      parameters.box_size=[ 25.0 25.0 25.0];
+      parameters.box_size=[25.0 25.0 25.0];
       parameters.margins=50*ones(1,6);
       parameters.confine=[2.0 12.0];
@@ Line 315: / Line 315: @@
       % Result arrays
-      err=zeros(30,1); reg=zeros(30,1);
+      err=zeros(1,30); reg=zeros(1,30);
       % Run a parallel loop

@@ Line 288: / Line 288: @@
       parameters.xyz=xyz;
       parameters.chi=chi;
       parameters.gpu=0;
@@ Line 297: / Line 298: @@
 *The sixth line switches off source sharpening - a penalty functional that drives values below average to zero and values above average to infinity. Increase the coefficient if you have minor low-amplitude clouds in your solution, but remember that this algorithm is hard to justify on physical grounds.
 * Lines 7-10 simply provide the information we already have from the previous sections.
 * The last line may be used to enable GPU processing if you have an NVidia GPU. It assumes that you have no NVidia GPUs in the system. If you do, set the value to 1; the calculations would go faster on any serious gaming card and ''massively'' faster if you have a Tesla coprocessor installed.

@@ Line 235: / Line 235: @@
      pad_size=2; [density,ext]=[[ocparse.m|ocparse]]('cu_porph_sd80.spindens.3d',pad_size);
-* Charnock-Kuprov equation is solved:
+* PCS from distributed density is computed:
      % Solve Kuprov equation

← Older revision		Revision as of 11:03, 6 January 2017
Line 195:		Line 195:


−	<center><math>\sigma _{\text{CS}}^{\left( k \right)}+\sigma _{\text{PCS}}^{\left( k \right)}=-\frac{1}{3}\text{Tr}\left[ \frac{{{\mathbf{A}}^{\left( k \right)}}\cdot \~~mathbf~~{\chi }}{{{\mu }_{0}}{{\gamma }_{\text{e}}}\gamma _{\text{n}}^{\left( k \right)}\hbar } \right]</math></center>	+	<center><math>\sigma _{\text{CS}}^{\left( k \right)}+\sigma _{\text{PCS}}^{\left( k \right)}=-\frac{1}{3}\text{Tr}\left[ \frac{{{\mathbf{A}}^{\left( k \right)}}\cdot \boldsymbol{\chi }}{{{\mu }_{0}}{{\gamma }_{\text{e}}}\gamma _{\text{n}}^{\left( k \right)}\hbar } \right]</math></center>

← Older revision		Revision as of 10:56, 6 January 2017
Line 18:		Line 18:
	This approach is valid for the distances at which the paramagnetic centre may be viewed as a point - typically at least 10 Angstroms away. The PCS of any nuclei located at closer distances would not fit this model. The ''Spinach'' function that calculates pseudocontact shifts from user-specified coordinates and electron susceptibility tensors is [[ppcs.m]]. The function that extracts the paramagnetic centre position and the susceptibility tensor from user-specified nuclear coordinates and pseudocontact shifts using the point electron model is [[ippcs.m]].		This approach is valid for the distances at which the paramagnetic centre may be viewed as a point - typically at least 10 Angstroms away. The PCS of any nuclei located at closer distances would not fit this model. The ''Spinach'' function that calculates pseudocontact shifts from user-specified coordinates and electron susceptibility tensors is [[ppcs.m]]. The function that extracts the paramagnetic centre position and the susceptibility tensor from user-specified nuclear coordinates and pseudocontact shifts using the point electron model is [[ippcs.m]].

−	Note that the magnetic susceptibility tensor may be estimated from the g-tensor using the following expression:	+	Note that the magnetic susceptibility tensor may be estimated from the g-tensor for S=1/2 using the following expression:

@@ Line 332: / Line 332: @@
       % Solve and refine the grid
       for n=[64 128 256]
-          [source_cube,ranges]=ipcs(parameters,n,0.125);
+          [source_cube,ranges]=[[ipcs.m|ipcs]](parameters,n,0.125);
           parameters.guess=source_cube;
       end
@@ Line 340: / Line 340: @@
 . '''Refine the effective susceptibility tensor.''' Optionally, ''Spinach'' can now use your probability density to update the susceptibility tensor that you have obtained from the multipolar fit. Run the following call:
-      [chi,~]=chi_eff(source_cube,ranges,xyz,expt_pcs);
+      [chi,~]=[[chi_eff.m|chi_eff]](source_cube,ranges,xyz,expt_pcs);
 to obtain your new susceptibility tensor. If it is significantly different from the previous one, repeat Steps 6 and 7 until self-consistency is achieved.

← Older revision		Revision as of 17:57, 1 January 2017
Line 343:		Line 343:

	to obtain your new susceptibility tensor. If it is significantly different from the previous one, repeat Steps 6 and 7 until self-consistency is achieved.		to obtain your new susceptibility tensor. If it is significantly different from the previous one, repeat Steps 6 and 7 until self-consistency is achieved.
		+
		+
		+	''Version 1.9, authors: [[Elizaveta Suturina]], [[Ilya Kuprov]]''

@@ Line 311: / Line 311: @@
       % Regularisation parameter array
       lam=10.^linspace(-2.0,2.0,30);
-−
       % Result arrays
       err=zeros(30,1); reg=zeros(30,1);
-−
       % Run a parallel loop
       parfor n=1:30 %#ok<*PFOUS,*PFBNS>
@@ Line 320: / Line 320: @@
           reg(n)=reg(n)/lam(n);
       end
-−
       % L-curve analysis
       figure(); S=[[lcurve.m|lcurve]](lam,err,reg,'log');

← Older revision		Revision as of 17:51, 1 January 2017
Line 327:		Line 327:
	The optimum value of the regularisation parameter corresponds to the point of maximum curvature on the L-curve. A typical example appears in Figure 8 below.		The optimum value of the regularisation parameter corresponds to the point of maximum curvature on the L-curve. A typical example appears in Figure 8 below.
	[[File:lcurve.png\|center\|frame\|'''Figure 8.''' A typical L-curve with the maximum curvature point indicated by a red circle.]]		[[File:lcurve.png\|center\|frame\|'''Figure 8.''' A typical L-curve with the maximum curvature point indicated by a red circle.]]
		+
		+	6. '''Run the accurate reconstruction.''' Use the optimal value of the Tikhonov regularisation parameter to run the reconstruction on a finer grid. An iterative approach is suggested, for example:
		+
		+	% Solve and refine the grid
		+	for n=[64 128 256]
		+	[source_cube,ranges]=ipcs(parameters,n,0.125);
		+	parameters.guess=source_cube;
		+	end
		+
		+	At the end of the calculation (very long if you don't have a Tesla card) you will obtain a high quality reconstruction.
		+
		+	7. '''Refine the effective susceptibility tensor.''' Optionally, ''Spinach'' can now use your probability density to update the susceptibility tensor that you have obtained from the multipolar fit. Run the following call:
		+
		+	[chi,~]=chi_eff(source_cube,ranges,xyz,expt_pcs);
		+
		+	to obtain your new susceptibility tensor. If it is significantly different from the previous one, repeat Steps 6 and 7 until self-consistency is achieved.