effective (potential derived) charges for macromolecules in solvent

version 2.00

EMBL, Heidelberg

Mon Jan 19 11:11:11 MET 1998

Revised version integrated into SDA 7, October 2013, MM.

R.R. Gabdoulline & R.C. Wade. Effective charges for macromolecules in solvent
J.Phys.Chem. (1996) 100, 3868-3878


In order to study protein-protein and protein-DNA association, the electrostatic forces and interaction free energies for two macromolecules at different mutual orientations and separations need to be evaluated. Realistic systems typically consist of thousands of atomic charges in an environment with a non-uniform dielectric permittivity and a solvent of non-zero ionic strength. Consequently, accurate evaluations of electrostatic forces and energies for such systems are only computationally feasible for a limited number of macromolecule positions. Here, we show that, by representing each molecule by a small number of effective charges in a uniform dielectric, intermolecular electrostatic interactions can be calculated simply and with high accuracy. The effective charges are derived by fitting them to reproduce the molecular electrostatic potential calculated by numerical solution of the finite-difference linearized Poisson-Boltzmann equation. The derived charges are expected to be useful in applications such as the simulation of the diffusional encounter of proteins where they will provide improved accuracy over the commonly-used test charge approximation.

Effective charges for macromolecules in solvent: what they are and when to use them
How to generate effective charges

BEFORE using the programs the user should have 2 files and know 2 parameters:

Version 2.00 notes.
Version 2 allows the charges to be fitted for an angular region of the potential. The user needs to specify coordinates of 2 points (x1dir(3) and x2dir(3)) and the restriction angle (angleg, in grad) in the file "angular.restriction". Then any points forming an angle larger than angleg to the vector (x2dir-x1dir) are omitted from the fitting procedure. Note, that the order of the 2 points in this input file makes a difference. If there are no data in the file "angular.restriction", the fitting procedure does not perform angular restriction.

There are 4 programs for effective charges generation:


usage: ecm_mksites file.pdb [file.tcha]

reads in pdb file, locates the sites for effective charges, assigns them the test charge value and writes to the output file in a PDB format with charges given in the last column. The output file is optional.

comment: Only test charges for OE* OD* NZ NE* atoms of Glu, Asp, Lys, Arg, and N & O* of NTR and CTR terminal residues are coded in the current program. The user may use the add_atoms to overwritte or provide new definitions.


usage: ecm_expand ecm.in

Expands the electrostatic potential of a macromolecule as given by a set of effective charges in uniform solvent. The resultant effective charges are given in the last column of a PDB format file output in "echa_file". In addition, the matrix for Coulomb-Coulomb, Coulomb-grid, grid-grid overlaps is written in file "matrix". (This is the most expensive part to compute.) The file "matrix" will be used by the subsequent regularization programs under this name. Standard output contains information about the performance of ecm_expand. This includes a simple graphics display of a cross-section of the region over which the potential fitting is performed. The user should check that this bears some resemblance to the shape of the protein under study.

It prints out the properties of the matrix equation for expansion. Namely, it exhaustively probes regularization of the matrix equation in the fitting problem equating the last N principal components of charges to the values derived from test charges. The output gives the N-dependence of the deviations (RMSD, see the definitions below) of the effective charge values from those of the test charges, the fitting error, the maximum deviation of any one effective charge from the respective test charge value (RM1D), the square root of the fitting error, and the sum of all the effective charges.



Advice: If the fitting results are satisfactory, don't go further. However, save the file "matrix" if you want to probe different regularizations later.

You can check the correctness of the assigned charges by loading the output file into a molecular visualization program and colouring the atom types by temperature factor, which reflects the effective charge in this file


usage: ecm_mkreglev [-reg_level 25] [-reg_charge 1.0] (automatically reads from file "matrix")

To use for generating effective charges at a given iteration (reg_level) OR at a charge value (reg_charge), i.e., uses only one of these two options. You have to choose this level according to the iteration regularization generated by the previous program.


usage: ecm_all -fp p1_noh.pdb -fg ep.grd -is 150. -rc 1.0 -fe p1_noh.echa

Execute all previous steps in one process. This tool accepts only arguments in command line (no input file is needed).

Usage examples

To generate effective charges with intermediate steps:

In one step:

A step-by-step procedure is described in the tutorial (section 4.) and examples of usage are given in preapre_grids_and_ecm/ subfolders of the examples.

Notes about effective charges regularization

The left graph in the figure below shows the meaning of optimization when using regularized charges.

In this example, 47 charge sites were used to fit the potential over distances 5-8 Angstroms from the van der Waals surface of the macromolecule in file "1brsA.pdb".

Automated optimization is difficult even in this case. The error increase with optimization level allows at least the 3 above mentioned optimum choices.

If one wants to use more sites, the curve would look different. An example is given in the right graph in the figure below, where 92 charge sites are used.
Here, regularization at level 40 allows approximation of the potential within an error of 14% and with RMSD deviation of charges 0.55 (RM1D - 1.6). The smallest fit error is 10%, compared to 20% in the previous case.

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