Shortcut: PAMM

Module	pamm
Description	Usage
Probabilistic analysis of molecular motifs.

Details and examples

Probabilistic analysis of molecular motifs.

Probabilistic analysis of molecular motifs (PAMM) was introduced in the papers in the bibliography. The essence of this approach involves calculating some large set of collective variables for a set of atoms in a short trajectory and fitting this data using a Gaussian Mixture Model. The idea is that modes in these distributions can be used to identify features such as hydrogen bonds or secondary structure types.

The assumption within this implementation is that the fitting of the Gaussian mixture model has been done elsewhere by a separate code. You thus provide an input file to this action which contains the means, covariance matrices and weights for a set of Gaussian kernels, $\{\phi\}$ . The values and derivatives for the following set of quantities is then computed:

$s_k = \frac{ \phi_k}{ \sum_i \phi_i }$

Each of the $\phi_k$ is a Gaussian function that acts on a set in quantities calculated that might be calculated using a TORSION, DISTANCE or ANGLE action for example. These quantities are then inserted into the set of $n$ kernels that are in the the input file. This will be done for multiple sets of values for the input quantities and a final quantity will be calculated by summing the above $s_k$ values or some transformation of the above. This sounds less complicated than it is and is best understood by looking through the example given below, which can be expanded to show the full set of operations that PLUMED is performing.

\warning Mixing input variables that are periodic with variables that are not periodic has not been tested

Examples

In this example I will explain in detail what the following input is computing:

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

#SETTINGS MOLFILE=regtest/pamm/rt-pamm-periodic/M1d.pdb INPUTFILES=regtest/pamm/rt-pamm-periodic/2D-testc-0.75.pammp
MOLINFOThis command is used to provide information on the molecules that are present in your system. More details MOLTYPE what kind of molecule is contained in the pdb file - usually not needed since protein/RNA/DNA are compatible=protein STRUCTUREa file in pdb format containing a reference structure=regtest/pamm/rt-pamm-periodic/M1d.pdb Click here to see an extract from this file.
    ×  FILE: regtest/pamm/rt-pamm-periodic/M1d.pdb
    ATOM      1  CH3 ACE     1      -0.595   0.734   0.353  1.00  0.00           C  
ATOM      2  C   ACE     1       0.767   0.829  -0.308  1.00  0.00           C  
ATOM      3  O   ACE     1       0.968  -0.029  -1.182  1.00  0.00           O  
ATOM      4 1HH3 ACE     1      -0.561   0.034   1.174  1.00  0.00           H  
ATOM      5 2HH3 ACE     1      -0.893   1.700   0.729  1.00  0.00           H  
...
ATOM    380  H   NME    23      14.888 -21.273  -9.959  1.00  0.00           H  
ATOM    381 HH31 NME    23      17.241 -22.202 -11.437  1.00  0.00           H  
ATOM    382 HH32 NME    23      15.946 -23.378 -11.638  1.00  0.00           H  
ATOM    383 HH33 NME    23      15.734 -21.723 -12.191  1.00  0.00           H  
END
  
The MOLINFO action with label  calculates somethingpsiThe TORSION action with label psi calculates the following quantities: Quantity    Type    Description  
psi vector the TORSION for each set of specified atoms: TORSIONCalculate one or multiple torsional angles. More details ATOMS1the four atoms involved in the torsional angle=@psi-2the four atoms that are required to calculate the psi dihedral for residue 2. Click here for more information.  ATOMS2the four atoms involved in the torsional angle=@psi-3the four atoms that are required to calculate the psi dihedral for residue 3. Click here for more information.  ATOMS3the four atoms involved in the torsional angle=@psi-4the four atoms that are required to calculate the psi dihedral for residue 4. Click here for more information. 
phiThe TORSION action with label phi calculates the following quantities: Quantity    Type    Description  
phi vector the TORSION for each set of specified atoms: TORSIONCalculate one or multiple torsional angles. More details ATOMS1the four atoms involved in the torsional angle=@phi-2the four atoms that are required to calculate the phi dihedral for residue 2. Click here for more information.  ATOMS2the four atoms involved in the torsional angle=@phi-3the four atoms that are required to calculate the phi dihedral for residue 3. Click here for more information.  ATOMS3the four atoms involved in the torsional angle=@phi-4the four atoms that are required to calculate the phi dihedral for residue 4. Click here for more information. 
p: PAMMProbabilistic analysis of molecular motifs. This action is a shortcut and it has hidden defaults. More details ...
  ARGthe vectors from which the pamm coordinates are calculated=phi,psi MEAN calculate the mean of all the quantities
  CLUSTERSthe name of the file that contains the definitions of all the clusters=regtest/pamm/rt-pamm-periodic/2D-testc-0.75.pammp Click here to see an extract from this file.
    ×  FILE: regtest/pamm/rt-pamm-periodic/2D-testc-0.75.pammp
    #! FIELDS height phi psi sigma_phi_phi sigma_phi_psi sigma_psi_phi sigma_psi_psi 
#! SET kerneltype von-misses
      2.97197455E-0001     -1.91983118E+0000      2.25029540E+0000      2.45960237E-0001     -1.30615381E-0001     -1.30615381E-0001      2.40239117E-0001  
      2.29131448E-0002      1.39809354E+0000      9.54585380E-0002      9.61755708E-0002     -3.55657919E-0002     -3.55657919E-0002      1.06147253E-0001  
      5.06676398E-0001     -1.09648066E+0000     -7.17867907E-0001      1.40523052E-0001     -1.05385552E-0001     -1.05385552E-0001      1.63290557E-0001  
  
...
The PAMM action with label p calculates the following quantities: Quantity    Description  
p.mean the mean of the colvarsp: PAMMProbabilistic analysis of molecular motifs. This action is a shortcut and uses the defaults shown here. More details ...
  ARGthe vectors from which the pamm coordinates are calculated=phi,psi MEAN calculate the mean of all the quantities
  CLUSTERSthe name of the file that contains the definitions of all the clusters=regtest/pamm/rt-pamm-periodic/2D-testc-0.75.pammp Click here to see an extract from this file.
    ×  FILE: regtest/pamm/rt-pamm-periodic/2D-testc-0.75.pammp
    #! FIELDS height phi psi sigma_phi_phi sigma_phi_psi sigma_psi_phi sigma_psi_psi 
#! SET kerneltype von-misses
      2.97197455E-0001     -1.91983118E+0000      2.25029540E+0000      2.45960237E-0001     -1.30615381E-0001     -1.30615381E-0001      2.40239117E-0001  
      2.29131448E-0002      1.39809354E+0000      9.54585380E-0002      9.61755708E-0002     -3.55657919E-0002     -3.55657919E-0002      1.06147253E-0001  
      5.06676398E-0001     -1.09648066E+0000     -7.17867907E-0001      1.40523052E-0001     -1.05385552E-0001     -1.05385552E-0001      1.63290557E-0001  
  
 REGULARISE don't allow the denominator to be smaller then this value=0.001 KERNELS which kernels are we computing the PAMM values for=all
...
# PLUMED interprets the command:
# p: PAMM ...
#   ARG=phi,psi MEAN
#   CLUSTERS=regtest/pamm/rt-pamm-periodic/2D-testc-0.75.pammp
# ...
# as follows (Click the red comment above to revert to the short version of the input):
p_kernel-1The CUSTOM action with label p_kernel-1 calculates the following quantities: Quantity    Type    Description  
p_kernel-1 vector the vector obtained by doing an element-wise application of an arbitrary function to the input vectors: KERNELTransform a set of input coordinates using a kernel function More details NORMALIZED would you like the kernel function to be normalized ARGthe arguments that should be used as input to this method=phi,psi NUMBER if there are multiple sets of kernel parameters in the input file which set of kernel parameters would you like to read in here=1 REFERENCEthe file from which to read the kernel parameters=regtest/pamm/rt-pamm-periodic/2D-testc-0.75.pammp Click here to see an extract from this file.
    ×  FILE: regtest/pamm/rt-pamm-periodic/2D-testc-0.75.pammp
    #! FIELDS height phi psi sigma_phi_phi sigma_phi_psi sigma_psi_phi sigma_psi_psi 
#! SET kerneltype von-misses
      2.97197455E-0001     -1.91983118E+0000      2.25029540E+0000      2.45960237E-0001     -1.30615381E-0001     -1.30615381E-0001      2.40239117E-0001  
      2.29131448E-0002      1.39809354E+0000      9.54585380E-0002      9.61755708E-0002     -3.55657919E-0002     -3.55657919E-0002      1.06147253E-0001  
      5.06676398E-0001     -1.09648066E+0000     -7.17867907E-0001      1.40523052E-0001     -1.05385552E-0001     -1.05385552E-0001      1.63290557E-0001  
  
 WEIGHT the weight to multiply this kernel function by=0.297197 TYPE the type of kernel to use=von-misses
p_kernel-2The CUSTOM action with label p_kernel-2 calculates the following quantities: Quantity    Type    Description  
p_kernel-2 vector the vector obtained by doing an element-wise application of an arbitrary function to the input vectors: KERNELTransform a set of input coordinates using a kernel function More details NORMALIZED would you like the kernel function to be normalized ARGthe arguments that should be used as input to this method=phi,psi NUMBER if there are multiple sets of kernel parameters in the input file which set of kernel parameters would you like to read in here=2 REFERENCEthe file from which to read the kernel parameters=regtest/pamm/rt-pamm-periodic/2D-testc-0.75.pammp Click here to see an extract from this file.
    ×  FILE: regtest/pamm/rt-pamm-periodic/2D-testc-0.75.pammp
    #! FIELDS height phi psi sigma_phi_phi sigma_phi_psi sigma_psi_phi sigma_psi_psi 
#! SET kerneltype von-misses
      2.97197455E-0001     -1.91983118E+0000      2.25029540E+0000      2.45960237E-0001     -1.30615381E-0001     -1.30615381E-0001      2.40239117E-0001  
      2.29131448E-0002      1.39809354E+0000      9.54585380E-0002      9.61755708E-0002     -3.55657919E-0002     -3.55657919E-0002      1.06147253E-0001  
      5.06676398E-0001     -1.09648066E+0000     -7.17867907E-0001      1.40523052E-0001     -1.05385552E-0001     -1.05385552E-0001      1.63290557E-0001  
  
 WEIGHT the weight to multiply this kernel function by=0.0229131 TYPE the type of kernel to use=von-misses
p_kernel-3The CUSTOM action with label p_kernel-3 calculates the following quantities: Quantity    Type    Description  
p_kernel-3 vector the vector obtained by doing an element-wise application of an arbitrary function to the input vectors: KERNELTransform a set of input coordinates using a kernel function More details NORMALIZED would you like the kernel function to be normalized ARGthe arguments that should be used as input to this method=phi,psi NUMBER if there are multiple sets of kernel parameters in the input file which set of kernel parameters would you like to read in here=3 REFERENCEthe file from which to read the kernel parameters=regtest/pamm/rt-pamm-periodic/2D-testc-0.75.pammp Click here to see an extract from this file.
    ×  FILE: regtest/pamm/rt-pamm-periodic/2D-testc-0.75.pammp
    #! FIELDS height phi psi sigma_phi_phi sigma_phi_psi sigma_psi_phi sigma_psi_psi 
#! SET kerneltype von-misses
      2.97197455E-0001     -1.91983118E+0000      2.25029540E+0000      2.45960237E-0001     -1.30615381E-0001     -1.30615381E-0001      2.40239117E-0001  
      2.29131448E-0002      1.39809354E+0000      9.54585380E-0002      9.61755708E-0002     -3.55657919E-0002     -3.55657919E-0002      1.06147253E-0001  
      5.06676398E-0001     -1.09648066E+0000     -7.17867907E-0001      1.40523052E-0001     -1.05385552E-0001     -1.05385552E-0001      1.63290557E-0001  
  
 WEIGHT the weight to multiply this kernel function by=0.506676 TYPE the type of kernel to use=von-misses
p_kernel-4The CUSTOM action with label p_kernel-4 calculates the following quantities: Quantity    Type    Description  
p_kernel-4 vector the vector obtained by doing an element-wise application of an arbitrary function to the input vectors: KERNELTransform a set of input coordinates using a kernel function More details NORMALIZED would you like the kernel function to be normalized ARGthe arguments that should be used as input to this method=phi,psi NUMBER if there are multiple sets of kernel parameters in the input file which set of kernel parameters would you like to read in here=4 REFERENCEthe file from which to read the kernel parameters=regtest/pamm/rt-pamm-periodic/2D-testc-0.75.pammp Click here to see an extract from this file.
    ×  FILE: regtest/pamm/rt-pamm-periodic/2D-testc-0.75.pammp
    #! FIELDS height phi psi sigma_phi_phi sigma_phi_psi sigma_psi_phi sigma_psi_psi 
#! SET kerneltype von-misses
      2.97197455E-0001     -1.91983118E+0000      2.25029540E+0000      2.45960237E-0001     -1.30615381E-0001     -1.30615381E-0001      2.40239117E-0001  
      2.29131448E-0002      1.39809354E+0000      9.54585380E-0002      9.61755708E-0002     -3.55657919E-0002     -3.55657919E-0002      1.06147253E-0001  
      5.06676398E-0001     -1.09648066E+0000     -7.17867907E-0001      1.40523052E-0001     -1.05385552E-0001     -1.05385552E-0001      1.63290557E-0001  
  
 WEIGHT the weight to multiply this kernel function by=0.00838236 TYPE the type of kernel to use=von-misses
p_kernel-5The CUSTOM action with label p_kernel-5 calculates the following quantities: Quantity    Type    Description  
p_kernel-5 vector the vector obtained by doing an element-wise application of an arbitrary function to the input vectors: KERNELTransform a set of input coordinates using a kernel function More details NORMALIZED would you like the kernel function to be normalized ARGthe arguments that should be used as input to this method=phi,psi NUMBER if there are multiple sets of kernel parameters in the input file which set of kernel parameters would you like to read in here=5 REFERENCEthe file from which to read the kernel parameters=regtest/pamm/rt-pamm-periodic/2D-testc-0.75.pammp Click here to see an extract from this file.
    ×  FILE: regtest/pamm/rt-pamm-periodic/2D-testc-0.75.pammp
    #! FIELDS height phi psi sigma_phi_phi sigma_phi_psi sigma_psi_phi sigma_psi_psi 
#! SET kerneltype von-misses
      2.97197455E-0001     -1.91983118E+0000      2.25029540E+0000      2.45960237E-0001     -1.30615381E-0001     -1.30615381E-0001      2.40239117E-0001  
      2.29131448E-0002      1.39809354E+0000      9.54585380E-0002      9.61755708E-0002     -3.55657919E-0002     -3.55657919E-0002      1.06147253E-0001  
      5.06676398E-0001     -1.09648066E+0000     -7.17867907E-0001      1.40523052E-0001     -1.05385552E-0001     -1.05385552E-0001      1.63290557E-0001  
  
 WEIGHT the weight to multiply this kernel function by=0.134976 TYPE the type of kernel to use=von-misses
p_kernel-6The CUSTOM action with label p_kernel-6 calculates the following quantities: Quantity    Type    Description  
p_kernel-6 vector the vector obtained by doing an element-wise application of an arbitrary function to the input vectors: KERNELTransform a set of input coordinates using a kernel function More details NORMALIZED would you like the kernel function to be normalized ARGthe arguments that should be used as input to this method=phi,psi NUMBER if there are multiple sets of kernel parameters in the input file which set of kernel parameters would you like to read in here=6 REFERENCEthe file from which to read the kernel parameters=regtest/pamm/rt-pamm-periodic/2D-testc-0.75.pammp Click here to see an extract from this file.
    ×  FILE: regtest/pamm/rt-pamm-periodic/2D-testc-0.75.pammp
    #! FIELDS height phi psi sigma_phi_phi sigma_phi_psi sigma_psi_phi sigma_psi_psi 
#! SET kerneltype von-misses
      2.97197455E-0001     -1.91983118E+0000      2.25029540E+0000      2.45960237E-0001     -1.30615381E-0001     -1.30615381E-0001      2.40239117E-0001  
      2.29131448E-0002      1.39809354E+0000      9.54585380E-0002      9.61755708E-0002     -3.55657919E-0002     -3.55657919E-0002      1.06147253E-0001  
      5.06676398E-0001     -1.09648066E+0000     -7.17867907E-0001      1.40523052E-0001     -1.05385552E-0001     -1.05385552E-0001      1.63290557E-0001  
  
 WEIGHT the weight to multiply this kernel function by=0.0262405 TYPE the type of kernel to use=von-misses
p_kernel-7The CUSTOM action with label p_kernel-7 calculates the following quantities: Quantity    Type    Description  
p_kernel-7 vector the vector obtained by doing an element-wise application of an arbitrary function to the input vectors: KERNELTransform a set of input coordinates using a kernel function More details NORMALIZED would you like the kernel function to be normalized ARGthe arguments that should be used as input to this method=phi,psi NUMBER if there are multiple sets of kernel parameters in the input file which set of kernel parameters would you like to read in here=7 REFERENCEthe file from which to read the kernel parameters=regtest/pamm/rt-pamm-periodic/2D-testc-0.75.pammp Click here to see an extract from this file.
    ×  FILE: regtest/pamm/rt-pamm-periodic/2D-testc-0.75.pammp
    #! FIELDS height phi psi sigma_phi_phi sigma_phi_psi sigma_psi_phi sigma_psi_psi 
#! SET kerneltype von-misses
      2.97197455E-0001     -1.91983118E+0000      2.25029540E+0000      2.45960237E-0001     -1.30615381E-0001     -1.30615381E-0001      2.40239117E-0001  
      2.29131448E-0002      1.39809354E+0000      9.54585380E-0002      9.61755708E-0002     -3.55657919E-0002     -3.55657919E-0002      1.06147253E-0001  
      5.06676398E-0001     -1.09648066E+0000     -7.17867907E-0001      1.40523052E-0001     -1.05385552E-0001     -1.05385552E-0001      1.63290557E-0001  
  
 WEIGHT the weight to multiply this kernel function by=0.00361413 TYPE the type of kernel to use=von-misses
p_ksumThe COMBINE action with label p_ksum calculates the following quantities: Quantity    Type    Description  
p_ksum vector the vector obtained by doing an element-wise application of a linear combination to the input vectors: COMBINECalculate a polynomial combination of a set of other variables. More details PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO ARGthe values input to this function=p_kernel-1,p_kernel-2,p_kernel-3,p_kernel-4,p_kernel-5,p_kernel-6,p_kernel-7 PARAMETERS the parameters of the arguments in your function=-0.001,0,0,0,0,0,0
p-1The CUSTOM action with label p-1 calculates the following quantities: Quantity    Type    Description  
p-1 vector the vector obtained by doing an element-wise application of an arbitrary function to the input vectors: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=p_kernel-1,p_ksum FUNCthe function you wish to evaluate=x/y PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
p-1_meanThe MEAN action with label p-1_mean calculates the following quantities: Quantity    Type    Description  
p-1_mean scalar the MEAN of the elements in the input value: MEANCalculate the arithmetic mean of the elements in a vector More details ARGthe vector/matrix/grid whose elements shuld be added together=p-1 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
p-2The CUSTOM action with label p-2 calculates the following quantities: Quantity    Type    Description  
p-2 vector the vector obtained by doing an element-wise application of an arbitrary function to the input vectors: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=p_kernel-2,p_ksum FUNCthe function you wish to evaluate=x/y PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
p-2_meanThe MEAN action with label p-2_mean calculates the following quantities: Quantity    Type    Description  
p-2_mean scalar the MEAN of the elements in the input value: MEANCalculate the arithmetic mean of the elements in a vector More details ARGthe vector/matrix/grid whose elements shuld be added together=p-2 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
p-3The CUSTOM action with label p-3 calculates the following quantities: Quantity    Type    Description  
p-3 vector the vector obtained by doing an element-wise application of an arbitrary function to the input vectors: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=p_kernel-3,p_ksum FUNCthe function you wish to evaluate=x/y PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
p-3_meanThe MEAN action with label p-3_mean calculates the following quantities: Quantity    Type    Description  
p-3_mean scalar the MEAN of the elements in the input value: MEANCalculate the arithmetic mean of the elements in a vector More details ARGthe vector/matrix/grid whose elements shuld be added together=p-3 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
p-4The CUSTOM action with label p-4 calculates the following quantities: Quantity    Type    Description  
p-4 vector the vector obtained by doing an element-wise application of an arbitrary function to the input vectors: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=p_kernel-4,p_ksum FUNCthe function you wish to evaluate=x/y PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
p-4_meanThe MEAN action with label p-4_mean calculates the following quantities: Quantity    Type    Description  
p-4_mean scalar the MEAN of the elements in the input value: MEANCalculate the arithmetic mean of the elements in a vector More details ARGthe vector/matrix/grid whose elements shuld be added together=p-4 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
p-5The CUSTOM action with label p-5 calculates the following quantities: Quantity    Type    Description  
p-5 vector the vector obtained by doing an element-wise application of an arbitrary function to the input vectors: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=p_kernel-5,p_ksum FUNCthe function you wish to evaluate=x/y PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
p-5_meanThe MEAN action with label p-5_mean calculates the following quantities: Quantity    Type    Description  
p-5_mean scalar the MEAN of the elements in the input value: MEANCalculate the arithmetic mean of the elements in a vector More details ARGthe vector/matrix/grid whose elements shuld be added together=p-5 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
p-6The CUSTOM action with label p-6 calculates the following quantities: Quantity    Type    Description  
p-6 vector the vector obtained by doing an element-wise application of an arbitrary function to the input vectors: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=p_kernel-6,p_ksum FUNCthe function you wish to evaluate=x/y PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
p-6_meanThe MEAN action with label p-6_mean calculates the following quantities: Quantity    Type    Description  
p-6_mean scalar the MEAN of the elements in the input value: MEANCalculate the arithmetic mean of the elements in a vector More details ARGthe vector/matrix/grid whose elements shuld be added together=p-6 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
p-7The CUSTOM action with label p-7 calculates the following quantities: Quantity    Type    Description  
p-7 vector the vector obtained by doing an element-wise application of an arbitrary function to the input vectors: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=p_kernel-7,p_ksum FUNCthe function you wish to evaluate=x/y PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
p-7_meanThe MEAN action with label p-7_mean calculates the following quantities: Quantity    Type    Description  
p-7_mean scalar the MEAN of the elements in the input value: MEANCalculate the arithmetic mean of the elements in a vector More details ARGthe vector/matrix/grid whose elements shuld be added together=p-7 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
# --- End of included input --- PRINTPrint quantities to a file. More details ARGthe labels of the values that you would like to print to the file=p-1_mean,p-2_mean FILEthe name of the file on which to output these quantities=colvar

The best place to start our explanation is to look at the contents of the 2D-testc-0.75.pammp file, which you can do by clicking on the links in the annotated input above. This files contains the parameters of two two-dimensional Gaussian functions. Each of these Gaussian kernels has a weight, $w_k$ , a vector that specifies the position of its center, $\mathbf{c}_k$ , and a covariance matrix, $\Sigma_k$ . The $\phi_k$ functions that we use to calculate our PAMM components are thus:

$\phi_k = \frac{w_k}{N_k} \exp\left( -(\mathbf{s} - \mathbf{c}_k)^T \Sigma^{-1}_k (\mathbf{s} - \mathbf{c}_k) \right)$

In the above $N_k$ is a normalization factor that is calculated based on $\Sigma$ . The vector $\mathbf{s}$ is a vector of quantities that are calculated by the input TORSION actions. This vector must be two dimensional and in this case each component is the value of a torsion angle. If we look at the two TORSION actions in the above we are calculating the $\phi$ and $\psi$ backbone torsional angles in a protein (Note the use of MOLINFO to make specification of atoms straightforward). We thus calculate the values of our 2 $\{ \phi \}$ kernels 3 times. The first time we use the $\phi$ and $\psi$ angles in the second residue of the protein, the second time it is the $\phi$ and $\psi$ angles of the third residue of the protein and the third time it is the $\phi$ and $\psi$ angles of the fourth residue in the protein. The final two quantities that are output by the print command, p.mean-1 and p.mean-2, are the averages over these three residues for the quantities:

$s_1 = \frac{ \phi_1}{ \phi_1 + \phi_2 }$

and

$s_2 = \frac{ \phi_2}{ \phi_1 + \phi_2 }$

There is a great deal of flexibility in this input. We can work with, and examine, any number of components, we can use any set of collective variables and compute these PAMM variables and we can transform the PAMM variables themselves in a large number of different ways when computing these sums. Furthermore, by expanding the shortcuts in the example above we can obtain insight into how the PAMM method operates.

Output components

This action can calculate the values in the following table when the associated keyword is included in the input for the action. These values can be referenced elsewhere in the input by using this Action's label followed by a dot and the name of the value required from the list below.

Name	Type	Keyword	Description
lessthan	scalar	LESS_THAN	the number of colvars that have a value less than a threshold
morethan	scalar	MORE_THAN	the number of colvars that have a value more than a threshold
altmin	scalar	ALT_MIN	the minimum value of the cv
min	scalar	MIN	the minimum colvar
max	scalar	MAX	the maximum colvar
between	scalar	BETWEEN	the number of colvars that have a value that lies in a particular interval
highest	scalar	HIGHEST	the largest of the colvars
lowest	scalar	LOWEST	the smallest of the colvars
sum	scalar	SUM	the sum of the colvars
mean	scalar	MEAN	the mean of the colvars

Full list of keywords

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

Keyword	Type	Default	Description
ARG	compulsory	none	the vectors from which the pamm coordinates are calculated
CLUSTERS	compulsory	none	the name of the file that contains the definitions of all the clusters
REGULARISE	compulsory	0.001	don't allow the denominator to be smaller then this value
KERNELS	compulsory	all	which kernels are we computing the PAMM values for

deprecated keywords

The keywords in the following table can still be used with this action but have been deprecated

Keyword	Description
LESS_THAN	calculate the number of variables that are less than a certain target value
MORE_THAN	calculate the number of variables that are more than a certain target value
ALT_MIN	calculate the minimum value
MIN	calculate the minimum value
MAX	calculate the maximum value
BETWEEN	calculate the number of values that are within a certain range
HIGHEST	this flag allows you to recover the highest of these variables
HISTOGRAM	calculate a discretized histogram of the distribution of values
LOWEST	this flag allows you to recover the lowest of these variables
SUM	calculate the sum of all the quantities
MEAN	calculate the mean of all the quantities

References

More information about how this action can be used is available in the following articles:

Quantity	Type	Description
psi	vector	the TORSION for each set of specified atoms