GMCT and GCEM form a pair of programs for studying the binding thermodynamics of macromolecular receptors. GCEM is a program for the automated preparation of the necessary input for GMCT from a continuum electrostatics / molecular mechanics model. The software allows a detailed modeling of complex ligandreceptor systems in structure based calculations. The primary targets of the software are biomolecular receptors like proteins that bind or transfer protons, electrons or other smallmolecule ligands. The software might, however, also be useful for studying polyelectrolytes in a broader sense or other systems like Ising or Potts models. The properties of large systems can be studied using a variety of modern simulation methods. This makes the software ideally suited to study the thermodynamics of ligand binding and charge transfer processes in bioenergetic complexes and other complex biomolecular systems.
The receptor modelThe image on the right shows a schematic view of the receptor model of GMCT with all possible features at the example of a membraneintrinsic receptor. The image gives explanations on mouseover if your browser supports SVG.


Our software rests on a general formulation of binding theory in terms of electrochemical potentials, instead of not directly comparable quantities like pH value and reduction potential. This formulation increases the transparency of calculation results by making them particularly easy to interpret. A detailed derivation of the formalism can be found in → this thesis. The essentials of the formalism can be displayed below.
Observables and thermodynamic functions of the system are determined by the partition functions of involved substates of the system or the overall system. The partition function of the system is given by \[ \partitionf = \sum\limits_{\ms{n}}^{\Nstates} \exp\left[\beta \Gmicro{\ms{n}} \right] \] where the sum runs over all microstates \(\ms{n}\) of the system. The partition function of a substate \(a\) is given by the sum over all microstates of the system that are compatible with the definition of the substate \[ \partitionf_{a} = \sum\limits_{\ms{n}}^{\Nstates} \delta_{\ms{n},a} \exp\left[\beta \Gmicro{\ms{n}} \right] \] where \(\delta_{\ms{n},a}\) is equal to \(1\) if the microstate is compatible with the definition of the substate \(a\) and equal to \(0\) otherwise. The definition of substate \(a\) could, for example, state that a certain site binds two protons. The probability of observing substate \(a\) in equilibrium is given by \[ p_{a} = \frac{\partitionf_{a}}{\partitionf_{\phantom{a}}} \] The free energy difference between two substates \(a\) and \(b\) of a system is determined by their partition functions \[ \Delta G_{a \rightarrow b} = \beta^{1}\ln\left[\frac{\partitionf_{b}}{\partitionf_{a}}\right] \] One could, for example, be interested in the free energy cost of increasing the number of protons bound to a certain site from one to two.
An analytical calculation of thermodynamic properties and observables is in practice impracticable already for systems of moderate size, because the number of possible microstates grows exponentially with the number of sites. Simulation methods make it possible to accomplish such calculations even for large systems, like the protein complexes occurring in bioenergetics, in acceptable time. Monte Carlo (MC) simulation methods are often particularly efficient.
Currently, GMCT offers two basic MC methods: Metropolis MC and WangLandau MC. Unique features of GMCT are accurate and efficient free energy calculation methods that can be used to calculate free energy differences for freely definable transformations and for the calculation of free energy measures of cooperativity. Namely, the free energy perturbation method, thermodynamic integration, the nonequilibrium work method and the Bennett acceptance ratio method have been implemented. The coupling between events in molecular systems can be quantified with covariances or free energy measures of cooperativity.
A variety of modern Monte Carlo simulation methods can be used to study overall properties of the receptor as well as properties of individual sites. The description of the system in terms of discrete microstates of the receptor and chemical potentials of the ligands renders the simulations computationally very inexpensive relative to allatom simulations. This computational efficiency enables very accurate calculations of receptor properties with low statistical uncertainty.
Properties of binding processes that can be calculated are for example binding probabilities (titration curves), binding free energies and binding constants. These properties can be computed from a microscopic viewpoint for studying the behavior of separate sites or groups of sites in the receptor or from a macroscopic viewpoint for studying the overall behavior of the receptor. Midpoint reduction potentials \(\mathcal{E}_{1/2}\) and \(\mathrm{p}K_{1/2}\) values can be derived from computed titration curves. Binding free energies can be expressed in terms of thermodynamically defined reduction potentials and \(\mathrm{p}K_{\mathrm{a}}\) values. The free energy calculation methods can also be used to study charge transfer reactions, conformational transitions and any other process that can be described within the receptor model of GMCT .
A particularly interesting feature of GMCT is the possibility to calculate free energy measures of cooperativity that can be used to study the coupling of different processes in the receptor. An example of special interest in our lab is the coupling between binding and transfer processes of charged ligands in bioenergetic protein complexes.
GMCT can also be helpful in setting up and complementing molecular dynamics (MD) simulations. The preparation of a protein structure for MD simulations does often require the specification of protonation states and tautomeric states occupied by titratable residues. This information can be obtained from Metropolis MC calculations with GMCT . In addition, protonation state calculations can be used to assess whether the modeling of a protein or other polyelectrolyte could require a constantpH MD method.
GMCT and the continuum electrostatics / molecular mechanics model of GCEM are described in →this paper. See the subdirectory doc of the GMCT distribution for detailed documentation, including the theoretical basis of both programs (basically comprises the above mentioned paper with more detail at some points plus a detailed description of all programs). Information about the extended MEAD library utilized by GCEM and usage of the program can be found →here. Examples for the usage of GMCT can be found in the directory examples of the GMCT distribution. Examples for the usage of GCEM can be found in the directory examples/gcem of the MEAD distribution.
GMCT
version 1.2.4 fixes compilation issues with newer compilers
(GCC >= 7, Clang 8, ICC 2018).
The MEAD distribution was updated to version 2.3.5 which fixes
compilation issues with newer compilers.
Version 2.3.2 fixed a critical bug that caused
segfaults in calculations with very big and/or fine grids.
Details can be found on the
web page of the distribution.
The software is free software
in the sense of the definition given by the Free Software Foundation.
GMCT
and
GCEM
are distributed under the terms of the
GNU Affero General Public License as published by the
Free Software Foundation; either version 3, or (at your option) any later version.
For more details, see the documentation of
GMCT
found in the directory doc of the distribution.
MEAD
is distributed under the terms of the
GNU General Public License as published by the
Free Software Foundation; either version 1, or (at your option) any later version.
For more details, see the files README, INSTALLATION and COPYING of the distribution.
GMCT  download gmct1.2.4.tar.bz2 
GCEM is part of an extended version of the program suite MEAD.  download my_mead2.3.5.tar.bz2 
Your opinion and hints are very welcome. Please provide detailed information about the program input and output when reporting a bug. Often, running a program with a higher verbosity level (set the parameter blab to 3) helps to clarify the source of an error.
© 20112019 TRU, Computational Biochemistry Group, University of Bayreuth