   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  . 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 ...
GYROMcompulsory keyword ( default=1. )
Add the product of the gyromagnetic constants for the bond. =-72.5388
SCALEcompulsory keyword ( default=1. )
Add the scaling factor to take into account concentration and other effects. =0.001
ATOMS1the couple of atoms involved in each of the bonds for which you wish to calculate
the RDC. =20,21
ATOMS2the couple of atoms involved in each of the bonds for which you wish to calculate
the RDC. =37,38
ATOMS3the couple of atoms involved in each of the bonds for which you wish to calculate
the RDC. =56,57
ATOMS4the couple of atoms involved in each of the bonds for which you wish to calculate
the RDC. =76,77
ATOMS5the couple of atoms involved in each of the bonds for which you wish to calculate
the RDC. =92,93

...
erdc: ENSEMBLE ARGthe input for this action is the scalar output from one or more other actions. =nh.*
st: STATS ARGthe input for this action is the scalar output from one or more other actions. =erdc.* PARAMETERSthe parameters of the arguments in your function =8.17,-8.271,-10.489,-9.871,-9.152
rdce: RESTRAINT ARGthe input for this action is the scalar output from one or more other actions. =st.corr KAPPAcompulsory 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. SLOPEcompulsory 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 ATcompulsory keyword
the position of the restraint =1.
svd: RDC ...
GYROMcompulsory 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).
ATOMS1the couple of atoms involved in each of the bonds for which you wish to calculate
the RDC. =20,21 COUPLING1Add an experimental value for each coupling (needed by SVD and useful for \ref STATS).
=8.17
ATOMS2the couple of atoms involved in each of the bonds for which you wish to calculate
the RDC. =37,38 COUPLING2Add an experimental value for each coupling (needed by SVD and useful for \ref STATS).
=-8.271
ATOMS3the couple of atoms involved in each of the bonds for which you wish to calculate
the RDC. =56,57 COUPLING3Add an experimental value for each coupling (needed by SVD and useful for \ref STATS).
=-10.489
ATOMS4the couple of atoms involved in each of the bonds for which you wish to calculate
the RDC. =76,77 COUPLING4Add an experimental value for each coupling (needed by SVD and useful for \ref STATS).
=-9.871
ATOMS5the couple of atoms involved in each of the bonds for which you wish to calculate
the RDC. =92,93 COUPLING5Add an experimental value for each coupling (needed by SVD and useful for \ref STATS).
=-9.152

...
esvd: ENSEMBLE ARGthe input for this action is the scalar output from one or more other actions. =(svd\.rdc-.*)
st_svd: STATS ARGthe input for this action is the scalar output from one or more other actions. =esvd.* PARAMETERSthe parameters of the arguments in your function =8.17,-8.271,-10.489,-9.871,-9.152
PRINT ARGthe input for this action is the scalar output from one or more other actions. =st.corr,st_svd.corr,rdce.bias FILEthe name of the file on which to output these quantities =colvar

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