ADAPTIVE_PATH

	This is part of the mapping module
	It is only available if you configure PLUMED with ./configure –enable-modules=mapping . Furthermore, this feature is still being developed so take care when using it and report any problems on the mailing list.

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 [24] 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 [66]. 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

contract shortcuts

d1: DISTANCE 
ATOMS
the 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 
TYPE
compulsory keyword ( default=OPTIMAL-FAST )
the manner in which distances are calculated. 
=EUCLIDEAN 
FIXED
compulsory keyword 
the positions in the list of input frames of the two path nodes whose positions remain
fixed during the path optimization 
=2,5 
UPDATE
compulsory keyword 
the frequency with which the path should be updated 
=50 
WFILE
file on which to write out the path 
=out-path.pdb 
WSTRIDE
compulsory keyword 
frequency with which to write out the path 
=50 
REFERENCE
compulsory 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.s
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

Description of components



 Quantity   
 Keyword   
 Description    

 gspath  
 GPATH   
the position along the path calculated using the geometric formula   

 gzpath  
 GPATH   
the distance from the path calculated using the geometric formula   

 spath  
 GPATH   
the position along the path calculated using the geometric formula   

 zpath  
 GPATH   
the distance from the path calculated using the geometric formula   

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 percent 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   

 WSTRIDE  
frequency with which to write out the path   

Options



 NOPBC  
( default=off ) ignore the periodic boundary conditions when calculating distances   

 NOSPATH  
( default=off ) do not calculate the spath CV   

 NOZPATH  
( default=off ) do not calculate the zpath CV   

 GPATH  
( default=off ) calculate the trigonometric path  



 ARG  
the list of arguments you would like to use in your definition of the path   

 COEFFICIENTS  
the coefficients of the displacements along each argument that should be used when calculating the euclidean distance   

 PROPERTY  
read in path coordinates by finding option with this label in remark of pdb frames   

 WFILE  
file on which to write out the path   







  


    
   
    
     1.8.17