## Purpose of MEAD and our extensions

This page describes our extensions to the molecular electrostatics software suite MEAD. The original version of MEAD was written by Donald Bashford and can be found → here.

MEAD consists of a library of C++ objects and some applications that use these objects for modeling electrostatic properties of molecules. MEAD is an acronym for macroscopic electrostatics with atomic detail. That is, macroscopic continuum electrostatics is applied at a molecular scale, partitioning the system in regions with different dielectric constants (molecule, solvent, membrane, ...). Solvent regions can contain mobile ions. The electrostatic potential is computed according to the linearized Poisson-Boltzmann equation. Despite its simplicity, this model can be used to compute molecular properties with very good accuracy (pKa values, binding constants, electrostatic solvation energies, ...).

Our extensions allow a detailed modeling of (biological) macromolecules including the possibility to account for a membrane environment with an electrostatic trans-membrane potential. Further extensions allow the visualization of electrostatic potentials, charge distributions, electrolyte distributions and dielectric distributions. The data can be given out as three-dimensional volumetric data in OpenDX format, or within a cut plane or along a line in ASCII format for plotting with your favorite software. The figure below shows the trans-membrane potential across the ammonia transporter Amt-1 from Archaeoglobus fulgidus as an example application for the visualization extensions.

The trans-membrane potential distribution across the ammonium transporter Amt-1. The figure was taken from → this paper. The structure of Amt-1 is described in Andrade, Susana L. A.; Dickmanns, Antje; Ficner, Ralph and Einsle, Oliver, 2005, PNAS, 102, 14994-14999. The extracellular side is shown at the top and the intracellular side at the bottom. The horizontal black lines indicate the boundaries of the membrane core and headgroup regions. The dark outer contour of Amt-1 denotes a projection of the solvent accessible surface of a transporter trimer into a plane perpendicular to the membrane. The lighter inner contour shows a projection of a slice of Amt-1 of 5 A thickness into the same projection plane. The slice shows the trans-membrane pore including putative ammonia positions, the twin-histidine motive and the Phe-gate. a) The trans-membrane potential is plotted in a slice plane cutting through the transporter's trans-membrane pore. The potential is projected into a plane perpendicular to the membrane, while the slice plane is slightly tilted relative to the membrane normal to follow the course of the trans-membrane pore. The values at the white contours denote the fraction of the trans-membrane potential at the respective coordinate. It can be seen that the membrane potential distribution within the protein does not show a simple linear dependency on the z coordinate. b) The mobile source charge distribution of the trans-membrane potential in the same slice and projection planes as in a). Darker red or blue shades denote higher negative or positive charge density, respectively. It can be seen that most of the unbalanced charge is concentrated close to the membrane and in the depressions of the protein surface.

• A lipid membrane can be represented by three dielectric slabs that model the hydrophobic, ion-inaccessible core region and the hydrophilic headgroup regions that can be penetrated by mobile ions. Regions within the membrane boundaries that are not part of the protein or the membrane can be specified (e.g., water filled protein cavities or a channel through the membrane).
• The protein interior can comprise different dielectric regions that can be used, for example, to account for protein regions that are modeled classically and such that are modeled with a quantum chemical approach. In addition there can be regions that model protein cavities or channels.
• The solvent phase(s) are modeled by separate dielectric regions that can also contain mobile ions.

## Documentation

The documentation for the original MEAD package is the file README found in the root directory of the distribution. Below, you can find the information from this README file and information about our changes and additional application programs. Example calculations with all necessary input files can be found in the subdirectory "examples" of the distribution.

The MEAD library is best explored by looking at the source code. The best starting point may be to look at some of the simpler programs like potential or solvate and then one of the solver programs (my_xyz_solver). Don't start with multiflex or GCEM, because these programs and the objects used by them are too complex for a start. A brief outline of the design of the MEAD library can be found in → this paper.

The calculation of binding properties with a continuum electrostatics/molecular mechanics model is described in a short version on the page about GMCT & GCEM . A more detailed description is given in → this thesis. Parts of this description are included in the user manual of GMCT (found in the directory doc of the distribution) and the → corresponding paper. See → this paper for a review of titration calculations with continuum electrostatics within a classical two-state model.

#### General information on MEAD usage

Here, you find information on general options and input files common to all MEAD programs

#### GCEM

GCEM is a program for the automated preparation of the necessary input for GMCT from a continuum electrostatics / molecular mechanics model.

#### my_2diel_solver

This program computes the electrostatic potential and the corresponding electrostatic energy terms of a site in a two-dielectric environment. Additional features enable the use of this program for visualization purposes and as helper program for GCEM.

#### my_3diel_solver

This program computes the electrostatic potential of a site in a three-dielectric environment and the corresponding electrostatic energy terms. Additional features enable the use of this program for visualization purposes and as helper program for GCEM.

#### my_Ndiel_solver

This program computes the electrostatic potential of a site in an environment with an arbitrary number of dielectric and electrolyte regions and the corresponding electrostatic energy terms. Additional features enable the use of this program for visualization purposes and as helper program for GCEM.

#### my_memb_solver

This program computes the electrostatic potential and the corresponding electrostatic energy terms of a site in a environment that models a lipid membrane, the receptor and the solvent phases above and below the membrane with up to 6 dielectric and 2 electrolyte regions. Additional features enable the use of this program for visualization purposes and as helper program for GCEM.

#### my_membpot_solver

This program computes the electrostatic trans-membrane potential and the corresponding electrostatic energy terms in a environment that models a lipid membrane, the protein and the solvent phases above and below the membrane with up to 6 dielectric and 2 electrolyte regions (same as for my_memb_solver). Additional features enable the use of this program for visualization purposes and as helper program for GCEM.

#### get-curves-gmct

This program analyzes the output of GMCT and extracts information as for example net binding probabilities of sites summed over all instances, and $$\mathrm{p}K_{1/2}$$ values. The MEAD library is only used for reading and writing of instance structures from the GCEM input.

#### pqr2SolvAccVol

This program computes an analytical representation of the solvent (in)accessible volume of a molecular structure and writes it to a binary or ASCII file which can be read by the programs my_xyz_solver to avoid time-consuming recomputation of the volume.

#### pqr2IonAccVol

This program computes an analytical representation of the ion inaccessible volume (solvent inaccessible volume with Stern layer radius as probe radius and extended by the Stern layer radius) of a molecular structure and writes it to a binary or ASCII file which can be read by the programs my_xyz_solver to avoid time-consuming recomputation of the volume.

#### pqr2crv

This program computes a projection of the solvent inaccessible volume of a molecular structure or a slice thereof into a user defined plane for visualization purposes. An example is shown in the above figure showing the trans-membrane potential distribution across Amt-1.

#### potential

This program calculates the electrostatic potential due to the charge distribution of molname

#### solvate

This program calculates the electrostatic solvation energy of a molecule in a solvent.

#### solinprot

Solinprot calculates the electrostatic part of the transfer energy for bringing a compound from the bulk solvent to a molecular environment.

#### multiflex

Multiflex is a program for the automated preparation of the necessary input for continuum electrostatic calculations on binding equilibria within a traditional two-state model.

#### redti

This program calculates titration curves with an approximate analytical method (reduced site method).