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Shortcut: GYRATION

Module	colvar
Description	Usage
Calculate the radius of gyration, or other properties related to it.
output value	type
the radius that was computed from the weights	scalar

Input

The atoms that serve as the input for this action are specified using one or more of the keywords in the following table.

Keyword	Type	Description
ATOMS	atoms	the group of atoms that you are calculating the Gyration Tensor for

Further details and examples

Calculate the radius of gyration, or other properties related to it.

The radius of gyration is calculated using:

$s_{\rm Gyr}=\Big ( \frac{\sum_i^{n} w_i \vert {r}_i -{r}_{\rm COM} \vert ^2 }{\sum_i^{n} w_i} \Big)^{1/2}$

with the position of the center ${r}_{\rm COM}$ given by:

${r}_{\rm COM}=\frac{\sum_i^{n} {r}_i\ w_i }{\sum_i^{n} w_i}$

In these expressions $r_i$ indicates the position of atom $i$ and $w_i$ is the weight for atom $i$ . The following input shows how you can calculate the expressions for a set of atoms by using PLUMED:

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

w: CONSTANTCreate a constant value that can be passed to actions More details VALUESthe numbers that are in your constant value=1,2,2,3,4
The CONSTANT action with label w calculates the following quantities: Quantity    Description  
w.value the constant value that was read from the plumed inputg: GYRATIONCalculate the radius of gyration, or other properties related to it. More details ATOMSthe group of atoms that you are calculating the Gyration Tensor for=1-5 TYPE The type of calculation relative to the Gyration Tensor you want to perform=RADIUS WEIGHTSwhat weights should be used when calculating the center=w
The GYRATION action with label g calculates the following quantities: Quantity    Description  
g.value the radius that was computed from the weightsPRINTPrint quantities to a file. More details ARGthe labels of the values that you would like to print to the file=g FILEthe name of the file on which to output these quantities=colvar

In the above input the weights in the expressions above are set equal to the eleemnts of a constant vector, w. A more common approach is to use the masses of the atoms as in the input below:

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

gThe GYRATION action with label g calculates the following quantities: Quantity    Type    Description  
g scalar the radius of gyration: GYRATIONCalculate the radius of gyration, or other properties related to it. More details ATOMSthe group of atoms that you are calculating the Gyration Tensor for=1-5 TYPE The type of calculation relative to the Gyration Tensor you want to perform=RADIUS MASS_WEIGHTED set the masses of all the atoms equal to one
# This input is equivalent
# g: GYRATION ATOMS=1-5 TYPE=RADIUS WEIGHTS=@Masses
PRINTPrint quantities to a file. More details ARGthe labels of the values that you would like to print to the file=g FILEthe name of the file on which to output these quantities=colvar

or to set all the input weights equal to one as is done in the input below;

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

gThe GYRATION action with label g calculates the following quantities: Quantity    Type    Description  
g scalar the radius of gyration: GYRATIONCalculate the radius of gyration, or other properties related to it. More details ATOMSthe group of atoms that you are calculating the Gyration Tensor for=1-5 TYPE The type of calculation relative to the Gyration Tensor you want to perform=RADIUS
PRINTPrint quantities to a file. More details ARGthe labels of the values that you would like to print to the file=g FILEthe name of the file on which to output these quantities=colvar

Notice that in the first input above GYRATION is a shortcut and that in the second two inputs it is not. This is because there is a faster (non-shortcutted) version that can be used for these two more-commonplace inputs. The shortcut input is still useful as it allows one to do less comonplace analyses such as this one where a clustering is performed and the radius of gyration for the largest cluster is determined.

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

c1The CONTACT_MATRIX action with label c1 calculates the following quantities: Quantity    Type    Description  
c1 matrix a matrix containing the weights for the bonds between each pair of atoms: CONTACT_MATRIXAdjacency matrix in which two atoms are adjacent if they are within a certain cutoff. More details GROUPspecifies the list of atoms that should be assumed indistinguishable=1-100 SWITCHthe input for the switching function that acts upon the distance between each pair of atoms. Options for this keyword are explained in the documentation for LESS_THAN.={RATIONAL R_0=0.1 D_MAX=0.5}
dfsThe DFSCLUSTERING action with label dfs calculates the following quantities: Quantity    Type    Description  
dfs vector vector with length that is equal to the number of rows in the input matrix.  Elements of this vector are equal to the cluster that each node is a part of: DFSCLUSTERINGFind the connected components of the matrix using the depth first search clustering algorithm. More details ARGthe input matrix=c1
wThe CLUSTER_WEIGHTS action with label w calculates the following quantities: Quantity    Type    Description  
w vector vector with elements that are one if the atom of interest is part of the required cluster and zero otherwise: CLUSTER_WEIGHTSSetup a vector that has one for all the atoms that form part of the cluster of interest and that has zero for all other atoms. More details CLUSTERSthe label of the action that does the clustering=dfs CLUSTER which cluster would you like to look at 1 is the largest cluster, 2 is the second largest, 3 is the the third largest and so on=1
gThe GYRATION action with label g calculates the following quantities: Quantity    Type    Description  
g scalar the radius that was computed from the weights: GYRATIONCalculate the radius of gyration, or other properties related to it. This action is a shortcut. More details ATOMSthe group of atoms that you are calculating the Gyration Tensor for=1-100 WEIGHTSwhat weights should be used when calculating the center=w TYPE The type of calculation relative to the Gyration Tensor you want to perform=RADIUS
# PLUMED interprets the command:
# g: GYRATION ATOMS=1-100 WEIGHTS=w TYPE=RADIUS
# as follows (Click the red comment above to revert to the short version of the input):
g_centThe ARGS2VATOM action with label g_cent calculates the following quantities: Quantity    Type    Description  
g_cent.x scalar the x coordinate of the virtual atom
g_cent.y scalar the y coordinate of the virtual atom
g_cent.z scalar the z coordinate of the virtual atom
g_cent.mass scalar the mass of the virtual atom
g_cent.charge scalar the charge of the virtual atom: CENTERCalculate the center for a group of atoms, with arbitrary weights. More details ATOMSthe group of atoms that you are calculating the Gyration Tensor for=1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100 WEIGHTSwhat weights should be used when calculating the center=w
g_distsThe DISTANCE action with label g_dists calculates the following quantities: Quantity    Type    Description  
g_dists.x vector the x-component of the vector connecting the two atoms
g_dists.y vector the y-component of the vector connecting the two atoms
g_dists.z vector the z-component of the vector connecting the two atoms: DISTANCECalculate the distance/s between pairs of atoms. More details COMPONENTS calculate the x, y and z components of the distance separately and store them as label ATOMS1the pair of atom that we are calculating the distance between=g_cent,1 ATOMS2the pair of atom that we are calculating the distance between=g_cent,2 ATOMS3the pair of atom that we are calculating the distance between=g_cent,3 ATOMS4the pair of atom that we are calculating the distance between=g_cent,4 ATOMS5the pair of atom that we are calculating the distance between=g_cent,5     # Action input conctinues with 95 further ATOMSn keywords, 
g_tensorThe MATRIX_PRODUCT action with label g_tensor calculates the following quantities: Quantity    Type    Description  
g_tensor matrix the product of the two input matrices: COVARIANCE_MATRIXCalculate a covariance matix More details ARGthe vectors of data from which we are calculating the covariance=g_dists.x,g_dists.y,g_dists.z WEIGHTSthis keyword takes the label of an action that calculates a vector of values=w
g_diag_elementsThe SELECT_WITH_MASK action with label g_diag_elements calculates the following quantities: Quantity    Type    Description  
g_diag_elements vector a vector/matrix of values that is obtained using a mask to select elements of interest: SELECT_COMPONENTSCreate a new value to hold a subset of the components that are in a vector or matrix More details ARGthe value from which we are selecting components=g_tensor COMPONENTSthe components in the input value that you woul like to build a new vector from=1.1,2.2,3.3
g_traceThe SUM action with label g_trace calculates the following quantities: Quantity    Type    Description  
g_trace scalar the sum of all the elements in the input vector: SUMCalculate the sum of the arguments More details ARGthe values input to this function=g_diag_elements PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
gThe CUSTOM action with label g calculates the following quantities: Quantity    Type    Description  
g scalar an arbitrary function: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=g_trace FUNCthe function you wish to evaluate=sqrt(x) PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
# --- End of included input ---

In calculating the gyration radius you first calculate the GYRATION_TENSOR. Instad of computing the radius from this tensor you can instead compute the trace of the tensor by using the following input:

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

w: CONSTANTCreate a constant value that can be passed to actions More details VALUESthe numbers that are in your constant value=1,2,2,3,4
The CONSTANT action with label w calculates the following quantities: Quantity    Description  
w.value the constant value that was read from the plumed inputg: GYRATIONCalculate the radius of gyration, or other properties related to it. More details ATOMSthe group of atoms that you are calculating the Gyration Tensor for=1-5 TYPE The type of calculation relative to the Gyration Tensor you want to perform=TRACE WEIGHTSwhat weights should be used when calculating the center=w
The GYRATION action with label g calculates the following quantities: Quantity    Description  
g.value the radius that was computed from the weightsPRINTPrint quantities to a file. More details ARGthe labels of the values that you would like to print to the file=g FILEthe name of the file on which to output these quantities=colvar

You can also calculate the largest, middle and smallest principal moments of the tensor:

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

w: CONSTANTCreate a constant value that can be passed to actions More details VALUESthe numbers that are in your constant value=1,2,2,3,4
# This computes the largest principal moment
The CONSTANT action with label w calculates the following quantities: Quantity    Description  
w.value the constant value that was read from the plumed inputl: GYRATIONCalculate the radius of gyration, or other properties related to it. More details ATOMSthe group of atoms that you are calculating the Gyration Tensor for=1-5 TYPE The type of calculation relative to the Gyration Tensor you want to perform=GTPC_1 WEIGHTSwhat weights should be used when calculating the center=w
# This computes the middle principal moment
The GYRATION action with label l calculates the following quantities: Quantity    Description  
l.value the radius that was computed from the weightsm: GYRATIONCalculate the radius of gyration, or other properties related to it. More details ATOMSthe group of atoms that you are calculating the Gyration Tensor for=1-5 TYPE The type of calculation relative to the Gyration Tensor you want to perform=GTPC_2 WEIGHTSwhat weights should be used when calculating the center=w
# This computes the smallest principal moment
The GYRATION action with label m calculates the following quantities: Quantity    Description  
m.value the radius that was computed from the weightss: GYRATIONCalculate the radius of gyration, or other properties related to it. More details ATOMSthe group of atoms that you are calculating the Gyration Tensor for=1-5 TYPE The type of calculation relative to the Gyration Tensor you want to perform=GTPC_3 WEIGHTSwhat weights should be used when calculating the center=w
The GYRATION action with label s calculates the following quantities: Quantity    Description  
s.value the radius that was computed from the weightsPRINTPrint quantities to a file. More details ARGthe labels of the values that you would like to print to the file=l,m,s FILEthe name of the file on which to output these quantities=colvar

From these principal moments you can calculate the Asphericiry, Acylindricity, or the Relative Shape Anisotropy by using the following input:

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

w: CONSTANTCreate a constant value that can be passed to actions More details VALUESthe numbers that are in your constant value=1,2,2,3,4
# This computes the Asphericiry
The CONSTANT action with label w calculates the following quantities: Quantity    Description  
w.value the constant value that was read from the plumed inputl: GYRATIONCalculate the radius of gyration, or other properties related to it. More details ATOMSthe group of atoms that you are calculating the Gyration Tensor for=1-5 TYPE The type of calculation relative to the Gyration Tensor you want to perform=ASPHERICITY WEIGHTSwhat weights should be used when calculating the center=w
# This computes the Acylindricity
The GYRATION action with label l calculates the following quantities: Quantity    Description  
l.value the radius that was computed from the weightsm: GYRATIONCalculate the radius of gyration, or other properties related to it. More details ATOMSthe group of atoms that you are calculating the Gyration Tensor for=1-5 TYPE The type of calculation relative to the Gyration Tensor you want to perform=ACYLINDRICITY WEIGHTSwhat weights should be used when calculating the center=w
# This computes the Relative Shape Anisotropy
The GYRATION action with label m calculates the following quantities: Quantity    Description  
m.value the radius that was computed from the weightss: GYRATIONCalculate the radius of gyration, or other properties related to it. More details ATOMSthe group of atoms that you are calculating the Gyration Tensor for=1-5 TYPE The type of calculation relative to the Gyration Tensor you want to perform=KAPPA2 WEIGHTSwhat weights should be used when calculating the center=w
The GYRATION action with label s calculates the following quantities: Quantity    Description  
s.value the radius that was computed from the weightsPRINTPrint quantities to a file. More details ARGthe labels of the values that you would like to print to the file=l,m,s FILEthe name of the file on which to output these quantities=colvar

Lastly, you can calculate the largest, middle and smallest principal radii of gyration by using the following input:

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

w: CONSTANTCreate a constant value that can be passed to actions More details VALUESthe numbers that are in your constant value=1,2,2,3,4
# This computes the largest principal radius of gyration
The CONSTANT action with label w calculates the following quantities: Quantity    Description  
w.value the constant value that was read from the plumed inputl: GYRATIONCalculate the radius of gyration, or other properties related to it. More details ATOMSthe group of atoms that you are calculating the Gyration Tensor for=1-5 TYPE The type of calculation relative to the Gyration Tensor you want to perform=RGYR_1 WEIGHTSwhat weights should be used when calculating the center=w
# This computes the middle principal radius of gyration
The GYRATION action with label l calculates the following quantities: Quantity    Description  
l.value the radius that was computed from the weightsm: GYRATIONCalculate the radius of gyration, or other properties related to it. More details ATOMSthe group of atoms that you are calculating the Gyration Tensor for=1-5 TYPE The type of calculation relative to the Gyration Tensor you want to perform=RGYR_2 WEIGHTSwhat weights should be used when calculating the center=w
# This computes the smallest principal radius of gyration
The GYRATION action with label m calculates the following quantities: Quantity    Description  
m.value the radius that was computed from the weightss: GYRATIONCalculate the radius of gyration, or other properties related to it. More details ATOMSthe group of atoms that you are calculating the Gyration Tensor for=1-5 TYPE The type of calculation relative to the Gyration Tensor you want to perform=RGYR_3 WEIGHTSwhat weights should be used when calculating the center=w
The GYRATION action with label s calculates the following quantities: Quantity    Description  
s.value the radius that was computed from the weightsPRINTPrint quantities to a file. More details ARGthe labels of the values that you would like to print to the file=l,m,s FILEthe name of the file on which to output these quantities=colvar

By expanding the shortcuts in the inputs above or by reading the papers cited below you can see how these quantities are computed from the GYRATION_TENSOR. Notice, however, that as with the radius if you use the masses or a vector of ones as weights a faster implemention of this colvar that calculates these quantities directly will be used.

A note on periodic boundary conditions

Calculating the radius of gyration is normally used to determine the shape of a molecule so all the specified atoms would normally be part of the same molecule. When computing this CV it is important to ensure that the periodic boundaries are calculated correctly. There are two ways that you can manage periodic boundary conditions when using this action. The first and simplest is to reconstruct the molecule similarly to the way that WHOLEMOLECULES operates. This reconstruction of molecules has been done automatically since PLUMED 2.2. If for some reason you want to turn it off you can use the NOPBC flag.

An alternative approach to handling PBC is to use the PHASES keyword. This keyword instructs PLUMED to use the PHASES option when computing the position of the center using the CENTER command. Distances of atoms from this center are then computed using PBC as usual.

References

More information about how this action can be used is available in the following articles: - J. Vymětal, J. Vondrášek, Gyration- and Inertia-Tensor-Based Collective Coordinates for Metadynamics. Application on the Conformational Behavior of Polyalanine Peptides and Trp-Cage Folding. The Journal of Physical Chemistry A. 115, 11455–11465 (2011)

Syntax

The following table describes the keywords and options that can be used with this action

Keyword	Type	Default	Description
ATOMS	input	none	the group of atoms that you are calculating the Gyration Tensor for
TYPE	compulsory	RADIUS	The type of calculation relative to the Gyration Tensor you want to perform
NOPBC	optional	false	ignore the periodic boundary conditions when calculating distances
WEIGHTS	optional	not used	what weights should be used when calculating the center
PHASES	optional	false	use trigonometric phases when computing position of center of mass
MASS	optional	false	calculate the center of mass
MASS_WEIGHTED	optional	false	set the masses of all the atoms equal to one
UNORMALIZED	optional	false	do not divide by the sum of the weights

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