PyDHAMed

DHAMed -Dynamic Histogram Analysis extended to detailed balance

Input are transition counts between states/bins and biases (if any). Biases specify the differences in the potential energy functions in the different simulation windows/runs.

To run DHAMed from a list of count matrices and an array specfying the biases in each simulation (window) is required.

To see how DHAMed can be used to extract free energies from biased simulations look at the example Jupyter notebook provided. https://github.com/bio-phys/PyDHAMed/blob/master/pydhamed/cg-rna/cg_RNA_duplex_formation.ipynb

Installation

To install PyDHAMed clone or download the repository

git clone https://github.com/bio-phys/PyDHAMed.git 
cd PyDHAMed

Then install the dowloaded repository with pip:

pip install . 

PyDHAMed is now ready for use.

Inputs

The list of the individual count matrices C contain the transition counts between the different states (or bins in umbrella sampling). C[i,j] where i is the product state and j the reactent state. The first row contains thus all the transitions into state 0.The first column C[:,0] all transition out of state 0.

The bias array contains a bias value for each state and for each simulation (or window in umbrella sampling). The bias array has the shape N rows nwin columns and contains the bias acting on each state in each simulation (window). The bias NEEDS to be given in units to kB_T.

Most parameters besides count_list and bias_ar are only relevant for testing and further code developement.

To run DHAMed

# import DHAMed functions 
from pydhamed.optimize_dhamed import *
from pydhamed.determine_transition_counts import count_matrix

# determine transition counts for each trajectory
# Each frame in a trajectory needs to be assigned to one of the the n states
# of the system
for traj in traj_list:
  count_list.append(count_matrix(traj, n_states=n))

# Bias - need to specfiy the bias acting on each of the n states in the nwin simulation. 
bias_ar = np.zeros((n, nwin))
for i in range(n)
    bias_ar[i,:] = np.loadtxt("bias"+i)

# run optimization
og = run_dhamed(count_list, bias_ar)

DHAMed examples

Two example calculations are provided in the pydhamed folder.

Ion channel permeation:

Umbrella sampling simulations of ion permeation through a channel. Data from all-atom simulations are analyzed in this example Jupyter notebook. https://github.com/bio-phys/PyDHAMed/blob/master/pydhamed/glic-ion-channel/glic_ion_channel_permeation.ipynb

RNA duplex formation:

Umbrella sampling simulations of RNA duplex formation using a coarse-grained model https://github.com/bio-phys/PyDHAMed/blob/master/pydhamed/cg-rna/cg_RNA_duplex_formation.ipynb

References

Dynamic Histogram Analysis To Determine Free Energies and Rates from biased Simulations, L. S. Stelzl, A. Kells, E. Rosta, G. Hummer, J. Chem. Theory Comput., 2017, http://pubs.acs.org/doi/abs/10.1021/acs.jctc.7b00373