ADAPTIVE_PATH

This is part of the mapping module

Compute path collective variables that adapt to the lowest free energy path connecting states A and B.

The Path Collective Variables developed by Branduardi and co-workers [28] 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:

\[ s = i_2 + \textrm{sign}(i_2-i_1) \frac{ \sqrt{( \mathbf{v}_1\cdot\mathbf{v}_2 )^2 - |\mathbf{v}_3|^2(|\mathbf{v}_1|^2 - |\mathbf{v}_2|^2) } }{2|\mathbf{v}_3|^2} - \frac{\mathbf{v}_1\cdot\mathbf{v}_3 - |\mathbf{v}_3|^2}{2|\mathbf{v}_3|^2} \]

In this expression \(\mathbf{v}_1\) and \(\mathbf{v}_3\) are the vectors connecting the current position to the closest and second closest node of the path, respectfully and \(i_1\) and \(i_2\) are the projections of the closest and second closest frames of the path. \(\mathbf{v}_2\), meanwhile, is the vector connecting the closest frame to the second closest frame. The distance from the path, \(z\) is calculated using:

\[ z = \sqrt{ \left[ |\mathbf{v}_1|^2 - |\mathbf{v}_2| \left( \frac{ \sqrt{( \mathbf{v}_1\cdot\mathbf{v}_2 )^2 - |\mathbf{v}_3|^2(|\mathbf{v}_1|^2 - |\mathbf{v}_2|^2) } }{2|\mathbf{v}_3|^2} - \frac{\mathbf{v}_1\cdot\mathbf{v}_3 - |\mathbf{v}_3|^2}{2|\mathbf{v}_3|^2} \right) \right]^2 } \]

Notice that these are the definitions of \(s\) and \(z\) that are used by PATH when the GPATH option is employed. The reason for this is that the adaptive path method implemented in this action was inspired by the work of Diaz and Ensing in which these formula were used [82]. To learn more about how the path is adapted we strongly recommend reading this paper.

Examples

The input below provides an example that shows how the adaptive path works. The path is updated every 50 steps of MD based on the data accumulated during the preceding 50 time steps.

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

d1: DISTANCE ATOMSthe pair of atom that we are calculating the distance between. =1,2 COMPONENTS( default=off ) calculate the x, y and z components of the distance separately and
store them as label.x,  The DISTANCE action with label d1 calculates the following quantities:

 Quantity   
 Description  
d1.x
the x-component of the vector connecting the two atoms
d1.y
the y-component of the vector connecting the two atoms
d1.z
the z-component of the vector connecting the two atoms


pp: ADAPTIVE_PATH TYPEcompulsory keyword ( default=OPTIMAL-FAST )
the manner in which distances are calculated. =EUCLIDEAN FIXEDcompulsory keyword 
the positions in the list of input frames of the two path nodes whose positions remain
fixed during the path optimization =2,5 UPDATEcompulsory keyword 
the frequency with which the path should be updated =50 WFILEfile on which to write out the path =out-path.pdb WSTRIDEfrequency with which to write out the path =50 REFERENCEcompulsory keyword 
a pdb file containing the set of reference configurations =mypath.pdb The ADAPTIVE_PATH action with label pp calculates the following quantities:

 Quantity   
 Description  
pp.gspath
the position on the path calculated using trigonometry
pp.gzpath
the distance from the path calculated using trigonometry


PRINT ARGthe input for this action is the scalar output from one or more other actions. =d1.x,d1.y,pp.* FILEthe name of the file on which to output these quantities =colvar The PRINT action with label 

In the case above the distance between frames is calculated based on the \(x\) and \(y\) components of the vector connecting atoms 1 and 2. As such an extract from the input reference path (mypath.pdb) would look as follows:

REMARK ARG=d1.x,d1.y d1.x=1.12 d1.y=-.60
END
REMARK ARG=d1.x,d1.y d1.x=.99 d1.y=-.45
END
REMARK ARG=d1.x,d1.y d1.x=.86 d1.y=-.30
END
REMARK ARG=d1.x,d1.y d1.x=.73 d1.y=-.15
END
REMARK ARG=d1.x,d1.y d1.x=.60 d1.y=0
END
REMARK ARG=d1.x,d1.y d1.x=.47 d1.y=.15
END

Notice that one can also use RMSD frames in place of arguments like those above.

Glossary of keywords and components

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
FIXED	the positions in the list of input frames of the two path nodes whose positions remain fixed during the path optimization
HALFLIFE	( default=-1 ) the number of MD steps after which a previously measured path distance weighs only 50% in the average. This option may increase convergence by allowing to forget the memory of a bad initial guess path. The default is to set this to infinity
UPDATE	the frequency with which the path should be updated
TOLERANCE	( default=1E-6 ) the tolerance to use for the path updating algorithm that makes all frames equidistant
FMT	( default=f ) the format to use for output files

Options

NUMERICAL_DERIVATIVES	( default=off ) calculate the derivatives for these quantities numerically
SERIAL	( default=off ) do the calculation in serial. Do not use MPI
LOWMEM	( default=off ) lower the memory requirements
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.
WFILE	file on which to write out the path
WSTRIDE	frequency with which to write out the path