RDC

This is part of the isdb module

Calculates the (Residual) Dipolar Coupling between two atoms.

The Dipolar Coupling between two nuclei depends on the \(\theta\) angle between the inter-nuclear vector and the external magnetic field.

\[ D=D_{max}0.5(3\cos^2(\theta)-1) \]

where

\[ D_{max}=-\mu_0\gamma_1\gamma_2h/(8\pi^3r^3) \]

that is the maximal value of the dipolar coupling for the two nuclear spins with gyromagnetic ratio \(\gamma\). \(\mu\) is the magnetic constant and h is the Planck constant.

Common Gyromagnetic Ratios (C.G.S)

• H(1) 26.7513
• C(13) 6.7261
• N(15) -2.7116 and their products (this is what is given in input using the keyword GYROM)
• N-H -72.5388
• C-H 179.9319
• C-N -18.2385
• C-C 45.2404

In isotropic media DCs average to zero because of the rotational averaging, but when the rotational symmetry is broken, either through the introduction of an alignment medium or for molecules with highly anisotropic paramagnetic susceptibility, then the average of the DCs is not zero and it is possible to measure a Residual Dipolar Coupling (RDCs).

This collective variable calculates the Dipolar Coupling for a set of couple of atoms using the above definition.

In a standard MD simulation the average over time of the DC should then be zero. If one wants to model the meaning of a set of measured RDCs it is possible to try to solve the following problem: "what is the distribution of structures and orientations that reproduce the measured RDCs".

This collective variable can then be use to break the rotational symmetry of a simulation by imposing that the average of the DCs over the conformational ensemble must be equal to the measured RDCs [34] . Since measured RDCs are also a function of the fraction of aligned molecules in the sample it is better to compare them modulo a constant or looking at the correlation.

Alternatively if the molecule is rigid it is possible to use the experimental data to calculate the alignment tensor and the use that to back calculate the RDCs, this is what is usually call the Single Value Decomposition approach. In this case the code rely on the a set of function from the GNU Scientific Library (GSL). (With SVD forces are not currently implemented).

Replica-Averaged simulations can be performed using RDCs, ENSEMBLE, STATS and RESTRAINT . METAINFERENCE can be activated using DOSCORE and the other relevant keywords.

Additional material and examples can be also found in the tutorial ISDB: setting up a Metadynamics Metainference simulation

Examples

In the following example five N-H RDCs are defined and averaged over multiple replicas, their correlation is then calculated with respect to a set of experimental data and restrained. In addition, and only for analysis purposes, the same RDCs each single conformation are calculated using a Single Value Decomposition algorithm, then averaged and again compared with the experimental data.

Click on the labels of the actions for more information on what each action computes

#SETTINGS NREPLICAS=2
nh: RDC ...
   
GYROM
compulsory keyword ( default=1. )
Add the product of the gyromagnetic constants for the bond. 
=-72.5388 
   
SCALE
compulsory keyword ( default=1. )
Add the scaling factor to take into account concentration and other effects. 
=0.001 
   
ATOMS1
the couple of atoms involved in each of the bonds for which you wish to calculate
the RDC. 
=20,21 
   
ATOMS2
the couple of atoms involved in each of the bonds for which you wish to calculate
the RDC. 
=37,38 
   
ATOMS3
the couple of atoms involved in each of the bonds for which you wish to calculate
the RDC. 
=56,57 
   
ATOMS4
the couple of atoms involved in each of the bonds for which you wish to calculate
the RDC. 
=76,77 
   
ATOMS5
the couple of atoms involved in each of the bonds for which you wish to calculate
the RDC. 
=92,93 
   
...The RDC action with label nh calculates the following quantities:

 Quantity   
 Description  
nh.rdc-0
the calculated # RDC  This is the 0th of these quantities
nh.rdc-1
the calculated # RDC  This is the 1th of these quantities
nh.rdc-2
the calculated # RDC  This is the 2th of these quantities
nh.rdc-3
the calculated # RDC  This is the 3th of these quantities
nh.rdc-4
the calculated # RDC  This is the 4th of these quantities

erdc: ENSEMBLE 
ARG
the input for this action is the scalar output from one or more other actions. 
=nh.* The ENSEMBLE action with label erdc calculates the following quantities:

 Quantity   
 Description  
erdc.nh.rdc-0
the label of this action is set by user in the input. See documentation above.  This is the 0th of these quantities
erdc.nh.rdc-1
the label of this action is set by user in the input. See documentation above.  This is the 1th of these quantities
erdc.nh.rdc-2
the label of this action is set by user in the input. See documentation above.  This is the 2th of these quantities
erdc.nh.rdc-3
the label of this action is set by user in the input. See documentation above.  This is the 3th of these quantities
erdc.nh.rdc-4
the label of this action is set by user in the input. See documentation above.  This is the 4th of these quantities

st: STATS 
ARG
the input for this action is the scalar output from one or more other actions. 
=erdc.* 
PARAMETERS
the parameters of the arguments in your function 
=8.17,-8.271,-10.489,-9.871,-9.152 The STATS action with label st calculates the following quantities:

 Quantity   
 Description  
st.sqdevsum
the sum of the squared deviations between arguments and parameters
st.corr
the correlation between arguments and parameters
st.slope
the slope of a linear fit between arguments and parameters
st.intercept
the intercept of a linear fit between arguments and parameters

rdce: RESTRAINT 
ARG
the input for this action is the scalar output from one or more other actions. 
=st.corr 
KAPPA
compulsory keyword ( default=0.0 )
specifies that the restraint is harmonic and what the values of the force constants
on each of the variables are 
=0. 
SLOPE
compulsory keyword ( default=0.0 )
specifies that the restraint is linear and what the values of the force constants
on each of the variables are 
=-25000.0 
AT
compulsory keyword 
the position of the restraint 
=1. The RESTRAINT action with label rdce calculates the following quantities:

 Quantity   
 Description  
rdce.bias
the instantaneous value of the bias potential
rdce.force2
the instantaneous value of the squared force due to this bias potential

svd: RDC ...
   
GYROM
compulsory keyword ( default=1. )
Add the product of the gyromagnetic constants for the bond. 
=-72.5388 
   
SVD
( default=off ) Set to TRUE if you want to back calculate using Single Value Decomposition
(need GSL at compilation time). 
 
   
ATOMS1
the couple of atoms involved in each of the bonds for which you wish to calculate
the RDC. 
=20,21 
COUPLING1
Add an experimental value for each coupling (needed by SVD and useful for \ref STATS).
=8.17 
   
ATOMS2
the couple of atoms involved in each of the bonds for which you wish to calculate
the RDC. 
=37,38 
COUPLING2
Add an experimental value for each coupling (needed by SVD and useful for \ref STATS).
=-8.271 
   
ATOMS3
the couple of atoms involved in each of the bonds for which you wish to calculate
the RDC. 
=56,57 
COUPLING3
Add an experimental value for each coupling (needed by SVD and useful for \ref STATS).
=-10.489 
   
ATOMS4
the couple of atoms involved in each of the bonds for which you wish to calculate
the RDC. 
=76,77 
COUPLING4
Add an experimental value for each coupling (needed by SVD and useful for \ref STATS).
=-9.871 
   
ATOMS5
the couple of atoms involved in each of the bonds for which you wish to calculate
the RDC. 
=92,93 
COUPLING5
Add an experimental value for each coupling (needed by SVD and useful for \ref STATS).
=-9.152 
   
...The RDC action with label svd calculates the following quantities:

 Quantity   
 Description  
svd.rdc-0
the calculated # RDC  This is the 0th of these quantities
svd.rdc-1
the calculated # RDC  This is the 1th of these quantities
svd.rdc-2
the calculated # RDC  This is the 2th of these quantities
svd.rdc-3
the calculated # RDC  This is the 3th of these quantities
svd.rdc-4
the calculated # RDC  This is the 4th of these quantities
svd.exp-0
the experimental # RDC  This is the 0th of these quantities
svd.exp-1
the experimental # RDC  This is the 1th of these quantities
svd.exp-2
the experimental # RDC  This is the 2th of these quantities
svd.exp-3
the experimental # RDC  This is the 3th of these quantities
svd.exp-4
the experimental # RDC  This is the 4th of these quantities
svd.Sxx
Tensor component
svd.Syy
Tensor component
svd.Szz
Tensor component
svd.Sxy
Tensor component
svd.Sxz
Tensor component
svd.Syz
Tensor component

esvd: ENSEMBLE 
ARG
the input for this action is the scalar output from one or more other actions. 
=(svd\.rdc-.*) The ENSEMBLE action with label esvd calculates the following quantities:

 Quantity   
 Description  
esvd.svd.rdc-0
the label of this action is set by user in the input. See documentation above.  This is the 0th of these quantities
esvd.svd.rdc-1
the label of this action is set by user in the input. See documentation above.  This is the 1th of these quantities
esvd.svd.rdc-2
the label of this action is set by user in the input. See documentation above.  This is the 2th of these quantities
esvd.svd.rdc-3
the label of this action is set by user in the input. See documentation above.  This is the 3th of these quantities
esvd.svd.rdc-4
the label of this action is set by user in the input. See documentation above.  This is the 4th of these quantities

st_svd: STATS 
ARG
the input for this action is the scalar output from one or more other actions. 
=esvd.* 
PARAMETERS
the parameters of the arguments in your function 
=8.17,-8.271,-10.489,-9.871,-9.152 The STATS action with label st_svd calculates the following quantities:

 Quantity   
 Description  
st_svd.sqdevsum
the sum of the squared deviations between arguments and parameters
st_svd.corr
the correlation between arguments and parameters
st_svd.slope
the slope of a linear fit between arguments and parameters
st_svd.intercept
the intercept of a linear fit between arguments and parameters

PRINT 
ARG
the input for this action is the scalar output from one or more other actions. 
=st.corr,st_svd.corr,rdce.bias 
FILE
the name of the file on which to output these quantities 
=colvar The PRINT action with label 

Glossary of keywords and components

Description of components

By default this Action calculates the following quantities. These quantities can be referenced elsewhere in the input by using this Action's label followed by a dot and the name of the quantity required from the list below.

Quantity	Description
score	the Metainference score
sigma	uncertainty parameter
sigmaMean	uncertainty in the mean estimate
neff	effective number of replicas
acceptSigma	MC acceptance for sigma values
rdc	the calculated # RDC

In addition the following quantities can be calculated by employing the keywords listed below

Quantity	Keyword	Description
acceptScale	SCALEDATA	MC acceptance for scale value
acceptFT	GENERIC	MC acceptance for general metainference f tilde value
weight	REWEIGHT	weights of the weighted average
biasDer	REWEIGHT	derivatives with respect to the bias
scale	SCALEDATA	scale parameter
offset	ADDOFFSET	offset parameter
ftilde	GENERIC	ensemble average estimator
exp	SVD/COUPLING	the experimental # RDC
Sxx	SVD	Tensor component
Syy	SVD	Tensor component
Szz	SVD	Tensor component
Sxy