   PATH
 This is part of the mapping module

Path collective variables with a more flexible framework for the distance metric being used.

The Path Collective Variables developed by Branduardi and co-workers  allow one to compute the progress along a high-dimensional path and the distance from the high-dimensional path. The progress along the path (s) is computed using:

$s = \frac{ \sum_{i=1}^N i \exp( -\lambda R[X - X_i] ) }{ \sum_{i=1}^N \exp( -\lambda R[X - X_i] ) }$

while the distance from the path (z) is measured using:

$z = -\frac{1}{\lambda} \ln\left[ \sum_{i=1}^N \exp( -\lambda R[X - X_i] ) \right]$

In these expressions $$N$$ high-dimensional frames ( $$X_i$$) are used to describe the path in the high-dimensional space. The two expressions above are then functions of the distances from each of the high-dimensional frames $$R[X - X_i]$$. Within PLUMED there are multiple ways to define the distance from a high-dimensional configuration. You could calculate the RMSD distance or you could calculate the ammount by which a set of collective variables change. As such this implementation of the path cv allows one to use all the difference distance metrics that are discussed in Distances from reference configurations. This is as opposed to the alternative implementation of path (PATHMSD) which is a bit faster but which only allows one to use the RMSD distance.

Compulsory keywords
 REFERENCE a pdb file containing the set of reference configurations TYPE ( default=OPTIMAL-FAST ) the manner in which distances are calculated. More information on the different metrics that are available in PLUMED can be found in the section of the manual on Distances from reference configurations LAMBDA the value of the lambda parameter for paths
Options
 NUMERICAL_DERIVATIVES ( default=off ) calculate the derivatives for these quantities numerically SERIAL ( default=off ) do the calculation in serial. Do not parallelize TIMINGS ( default=off ) output information on the timings of the various parts of the calculation DISABLE_CHECKS ( default=off ) disable checks on reference input structures. NOZPATH ( default=off ) do not calculate the zpath position NOSPATH ( default=off ) do not calculate the spath position
Examples

The following input instructs PLUMED to calculate the values of the path collective variables. The frames that make up this path are defined in the file all.pdb and all distances are measured using the OPTIMAL metric that is discussed in the manual page on RMSD.

p2: PATH REFERENCE=all.pdb LAMBDA=69087
PRINT ARG=p2.spath,p2.zpath STRIDE=1 FILE=colvar


If you wish to use collective variable values in the definition of your path you would use an input file with something like this:

d1: DISTANCE ATOMS=1,2
d2: DISTANCE ATOMS=3,4a
p2: PATH REFERENCE=mypath.pdb LAMBDA=2 TYPE=EUCLIDEAN
PRINT ARG=p2.spath,p2.zpath STRIDE=1 FILE=colvar


The corresponding pdb file containing the definitions of the frames in the path would then look like this:

DESCRIPTION: a defintiion of a PATH
REMARK TYPE=EUCLIDEAN
REMARK ARG=d1,d2
REMARK d1=1.0 d2=1.0
END
REMARK TYPE=EUCLIDEAN
REMARK ARG=d1,d2
REMARK d1=2.0 d2=2.0
END


For each frame in the path you must specify the arguments that should be used to calculate the distance between the instantaneous configuration of the system and the reference configurations together with the values that these arguments take in each of the reference configurations.