Developed by Fabian Zeller and Manuel P. Luitz (2017).

BrownianDynamics (BD) is a software package for the simulation of association events of ligand molecules to their receptor with Brownian Dynamics. Within this approach, the receptor and ligand are treated as rigid molecules. The receptor is kept fixed at the origin of the coordinate system while the ligand can diffuse around it. The diffusive motions of the ligand account for the relative translational and rotational diffusion of both, receptor and ligand. To account for the long-range electrostatic interactions between ligand and receptor, the electrostatic field around the receptor has to be calculated first with the Adaptive Poisson Boltzmann Solver. At the beginning of a BD simulation, the ligand is randomly positioned on a sphere-shell around the receptor. The simulation is terminated when either the ligand diffuses into the binding region (fulfills the binding criterion) or when the ligand moves away from the receptor by more than a threshold distance. Final ligand/receptor configurations of trajectories that reach the binding criterion are stored. From the fraction of trajectories with ligands reaching the binding site the binding rate ("on" rate) of ligand and receptor can be estimated. The binding criterion can be either defined as center of mass (COM) distances between selected ligand/receptor atoms or as the distance root mean square deviation (drmsd) between selected ligand/receptor atoms. The latter allows not only to define the interactive patch on the receptor surface but also to define the orientation between ligand and receptor for a successful binding event.

You need the tools apbs and pdb2pqr which can be installed on a Ubuntu system with:

$ apt-get install apbs pdb2pqr

BD itself will need parmed and numpy which are available with python pip:

$ pip install numpy parmed

Assume we have two pdb files receptor.pdb and ligand.pdb in our working directory and we want to calculate the association rate of the ligand into a roughly define reaction surface around the receptors binding site. Before we can perform the BD run we need to prepare pqr files from the pdb files that include partial charges for each atom. We can do this with the pdb2pqr tool:

$ pdb2pqr --ff amber receptor.pdb receptor.pqr
$ pdb2pqr --ff amber ligand.pdb ligand.pqr

The --ff amber option specifies that we want to use partial charges from the amber forcefield. Next we need to calculate the electrostatic field by solving the Poisson Boltzmann equation around the receptor. We use the APBS software package to perform the PB calculations. A sample apbs.in configuration file is provide with the BD sources, the documentation can be found at here. The sample config should normally work for you just recheck the input file path for the receptor.pqr so that apbs can find it. Run the apbs program as follows:

$ apbs apbs.in

This will generate a file pot.dx containing the electrostatic potential on a 3D grid. After having calculated the electrostatic field, we can start the BD simulation.

$ ./BrownianDynamics/BrownianDynamics.py -c template.conf

Finally we can calculate the "on" rate from bulk state to the reaction surface (S. H. Northrup et al., J. Chem. Phys. 80 (4), 15 February 1984).

$ ./BrownianDynamics/BD_rate.py -c template.conf

A sample configuration file template.conf is provided as a starting point. The syntax is based on the python module ConfigParser.