Journal club (Bernhard Knapp): MMPBSA Binding Free Energy Calculations

This week’s topic of the Journalclub was about Molecular Mechanics Poisson−Boltzmann Surface Area (MMPBSA) binding free energy calculations between ligand and receptor using Molecular Dynamics simultions (MD). As an example I selected:

David W. Wright, Benjamin A. Hall, Owain A. Kenway, Shantenu Jha, and Peter V. Coveney. Computing Clinically Relevant Binding Free Energies of HIV-1 Protease Inhibitors. J Chem Theory Comput. Mar 11, 2014; 10(3): 1228–1241

The first question is: Why do we need such rather complex and computationally expensive approaches if other (e.g. empirical) scoring functions can do similar things? The main challenges thereby is that simple scoring functions often do not work very well for systems where they were not calibrated on (e.g. Knapp et al. 2009 (http://www.ncbi.nlm.nih.gov/pubmed/19194661)). The reasons for that are manifold. MD-based approaches can improve two major limitations of classical docking/scoring functions:

1) Proteins are not static. Ligand as well as receptor can undergo various slightly different configurations even for one binding site. Therefore the view of scoring one ligand configuration against one receptor configuration is not the whole picture. The first improvement is to consider a lot of different configurations for one position score of the ligand:

multipleReceptorLigand.png

2) A more physics based scoring function can be more reliable than a simple and run-time efficient scoring function. On the basis of the MD simulations a variety of different terms can be deduced. These include:

dG_formula

– MM stands for Molecular Mechanics. It’s internal energy includes bond stretch, bend, and torsion. The electrostatic part is calculated using a Coulomb potential while the Van der Waals term is calculated using a Lennard-Jones potential.
– PB stands for Poisson−Boltzmann. It covers the polar solvation part i.e. the electrostatic free energy of solvation.
– SA stands for Surface Area. It covers the non-polar solvation part via a surface tension weighted solvent accessible surface area calculation.
– TS stands for the entropy loss of the system. This term is necessary because the non-polar solvation incorporates an estimate of the entropy changes implicitly but does not account for an entropy change upon receptor/ligand formation in vacuo. This term is calculated on the basis of a normal mode analysis.

If all these terms are calculated for each single frame of the MD simulations and those single values are averaged an estimate of the binding free energy of the complex can be obtained. However, this estimate might not represent the actual mean of the spatial distribution. Therefore at least 50 replica MD simulations are needed per investigated complex. In this aspect replica means an identically parameterized simultion of the same complex where only the inital forces are assinged randomly.

On the basis of the described MMPBSA-TS approach in combination with 50 replicas the authors achieve a reasonable correlation (0.63) for the 9 FDA-approved HIV-1
protease inhibitors with know experimental binding affinities. If the two largest complexes are excluded the correlation improves to an excellent value (0.93).

In a current study we are using the same methodology for peptide/MHC interactions. This system is completely different from the protease inhibitor study of Wright et al.: The ligands are peptides and the binding site is a groove consisting of two alpha-helices. The methods was applied as it is (without calibration or any kind of training). Prelimiary data still shows a high correlation with experimental values for the peptide/MHC system. This indicates that this MMPBSA approach can yield reliable predictions for very different systems without further modification.

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