Monte Carlo Free Ligand Diffusion with Markov State Model Analysis and Absolute Binding Free Energy Calculations

Takahashi, Ryoji, Víctor A. Gil, and Victor Guallar  Journal of Chemical Theory and Computation 2014, 10, 282−288.

Contributed by +Jan Jensen

This study uses Monte Carlo (MC) sampling, and a Markov state model analysis of the resulting trajectories, to compute absolute binding free energies for four benzamidine ligands binding to trypsin that are in good agreement with experiment.  The measured binding free energies for the same ligand vary a bit and the mean absolute deviation ranges from 0.9 to 1.4 kcal/mol.

The binding free energy for each ligand is derived from a Markov state model analysis of 840 MC trajectories constructed using six different random initial ligand positions - all well away from the protein surface. Each MC trajectory is constructed using the protein energy landscape exploration (PELE) method. There are three kinds of PELE MC moves: (1) the ligand can be translated or rotated rigidly, (2) the internal ligand geometry can be changed using a ligand-specific rotamer library, and (3) all protein atoms are displaced along a randomly picked mode derived from an anisotropic network model followed by minimization of all all atoms except the $\alpha$-carbons.

After each move is made the side-chain orientations close to the ligands are sampled from a rotamer library followed my an OPLS-AA/SGB energy minimization of all atoms affected by the move. The resulting "super move" is accepted or rejected based on a Metropolis criterion.

The total simulation time for a ligand is about 1 week using 64 cores. However, the binding site of each ligand could be identified using only 20-30 trajectories in 5-10 CPU hours.  In fact, such a binding site search can be performed using the PELE web server developed by the authors.

With its use of "super moves" with extensive energy minimization this method strikes me as an excellent way to generate snapshots for QM/MM calculations and it seems to me it could be easily adapted to look at enzyme catalysis.


This work is licensed under a Creative Commons Attribution 4.0 International License.

Bulk Liquid Water at Ambient Temperature and Pressure from MP2 Theory

Mauro Del Ben, Mandes Schönherr, Jürg Hutter, and Joost VandeVondele. J. Phys. Chem. Lett. 2013, 4, 3753−3759. DOI: 10.1021/jz401931f
Contributed by François-Xavier Coudert.

Reprinted with permission from doi:10.1021/jz401931f
Copyright 2013 American Chemical Society.

Let's start with the obvious: molecular simulation of liquid water is a very challenging, yet very important, part of our field. While MP2 (second-order perturbation theory) gives a highly accurate description of water-water interactions in water clusters, it was so far too computationally expensive to perform decent-scale molecular dynamics and Monte Carlo simulations of bulk liquid water.

Well, no more. Using large HPC resources, in particular the European PRACE Research Infrastructure and the Swiss National Supercomputer Centre, Mauro Del Ben et al. report in J. Phys. Chem. Lett. the first “truly first-principles simulation of liquid water in the NpT ensemble”. They performed a isobaric-isothermal Monte Carlo simulation, at the MP2 level, of 64 water molecules in a periodic simulation cell, under ambient conditions. The resulting density and structure of the liquid water are quite good, and are contrasted in particular with the less-than-stellar densities yielded by DFT-based methods.

These results represent the latest step in a series of papers these past few years, harnessing the ever-growing power of HPC capabilities to test the validity of quantum chemical calculations for the description of bulk liquid water. Some of the earlier episodes can be read here:

• McGrath, M. J.; Siepmann, J. I.; Kuo, I.-F. W.; Mundy, C. J.; VandeVondele, J.; Hutter, J.; Mohamed, F.; Krack, M. “Isobaric−Isothermal Monte Carlo Simulations from First Principles: Application to Liquid Water at Ambient Conditions”. ChemPhysChem 2005, 6, 1894−1901.
• Schmidt, J.; VandeVondele, J.; Kuo, I.-F. W.; Sebastiani, D.; Siepmann, J. I.; Hutter, J.; Mundy, C. J. “Isobaric−Isothermal Molecular Dynamics Simulations Utilizing Density Functional Theory: An Assessment of the Structure and Density of Water at Near-Ambient Conditions”. J. Phys. Chem. B 2009, 113, 11959−11964.
• Jonchiere, R.; Seitsonen, A. P.; Ferlat, G.; Saitta, A. M.; Vuilleumier, R. “Van der Waals Effects in Ab Initio Water at Ambient and Supercritical Conditions”. J. Chem. Phys. 2011, 135, 154503.