UmbrellaIntegrate 0.41

Description:

UmbrellaIntegrate 0.41

Umbrella Integration[1] algorithm of calculating PMF using Python.

Dependence

Python3
Numpy
pandas for parsing metafile
Scipy for trapz integration



Usage:
See help:
python3 ubint.py -h

Input

Metafile
The <your-metafile> should be in fellowing form:
/path/to/your/window/file window_center spring_constant [temperature]
There is a variable of T in ubint.py, if the temperature
left blank in the metafile, the default temperature would be variable
T in the ubint.py, or you can set specific temperature for some
window.


Data file for each window
The data file of each window need to be a 2-column file with
time reaction_coordinate, the coordinate should be 1-dimensional.



Output
The output file is free_py.txt with 2-column
reaction_coordinate free_energy



Warning

Unit
I use kJ/mol in this program.


Spring constant K
In your simulation, the biased spring potential shoud be in form of
0.5 * K * (r - r0) ** 2, here K is the parameter set in your
<your-metafile>, for some simulation program, there is no 0.5 in
the biased spring potential.



Screen shots
Raw data was generated by Gaussian
distribution for
each window with MEAN=window_center and STD=0.8, the centers are
in range of 0.0 ~ 19.5 by step of 0.5, here is the result
compare with WHAM[2]:

Raw Data








Compare with WHAM




The zero point in WHAM is the minimum value and the zero point in UI
is 0.


TO DO
The UI algorithm with higher oder terms[3] of A(xi) is
ubint_ho_devel.py, the result is not ideal using previous data,
still in development.
Problems occurred at standard normal distributions, maybe the
quadruplicate term which even possesses a small value could cause a huge
deviation. I should try some systems with non-quadratic potentials.
The function ``exp(-beta(a1*xi+a2*xi^2+a3*xi^3+a4*xi^4))`` and its
integration (Normalization factor) give very large value (even inf),
this is unable to solve yet.

Results






Ref

Kästner, Johannes, and Walter Thiel. “Bridging the Gap between
Thermodynamic Integration and Umbrella Sampling Provides a Novel
Analysis Method: ‘Umbrella Integration.’” The Journal of Chemical
Physics 123, no. 14 (October 8, 2005): 144104. doi:10.1063/1.2052648.
http://membrane.urmc.rochester.edu/content/wham
Kästner, Johannes. “Umbrella Integration with Higher-Order Correction
Terms.” The Journal of Chemical Physics 136, no. 23 (June 21, 2012):
234102. doi:10.1063/1.4729373.