Molecular dynamics umbrella sampling

Figure 10. Classical adiabatic free energy curve (solid line) forthe Fe /Fe electron transfer at the water/Pt(lll) interface calculated using the Anderson-Newns Hamiltonian and the molecular dynamics umbrella sampling method. Also shown by the dashed line is the parabolic fit of the data. (Reprinted from Ref. 14.)...

Several mechanisms have been proposed, hi their study, van Gunsteren et al investigated two general acid-general base catalytic mechanisms in which one or the other of the two aspartates was protonated. The difference between the two is that in one case the initial proton transfer is to the carbonyl oxygen of the scissile peptide whereas in the other it is to the nitrogen. They performed molecular dynamics umbrella sampling simulations with a PM3/MM potential to... 

Umbrella sampling attempts to overcome the sampling problem by modifying the potenti function so that the unfavourable states are sampled sufficiently. The method can be use with both Monte Carlo and molecular dynamics simulations. The modification of tf potential function can be written as a perturbation ... 

With the characterized mechanism, the next key question is the origin of its catalytic power. A prerequisite for this investigation is to reliably compute free energy barriers for both enzyme and solution reactions. By employing on-the-fly Born-Oppenheimer molecular dynamics simulations with the ab initio QM/MM approach and the umbrella sampling method, we have determined free energy profiles for the methyl-transfer reaction catalyzed by the histone lysine methyltransferase SET7/9... 

To circumvent this problem avoiding such inefficient exploration of the configurational space, several methods have emerged. Two particularly useful approaches are the Umbrella Sampling and the Statistical Perturbation Theory. Both methods can be used either with Monte Carlo or with Molecular Dynamics simulations. 

Figure 9. The free energy curves for the Fe (aq) and Fe (aq) ions. The bold curves represent the result of umbrella sampling of the molecular dynamics calculation. Thin solid lines correspond to the best parabolic fit of the region near the bottom of each wall. (Reprinted from Ref. 12.)...

Figure 11. Solvent free energies for the electron transfer reaction Fe + e <- Fe in bulk water (top panel) and at the water/Pt(100) interface (bottom panel) at T = 300 K. In each panel, the solid line gives the results of umbrella sampling molecular dynamics, and the thin line is the best parabolic fit to the bottom region of each curve. (Adapted from Ref. 163.)...

All simulations were carried out with the GROM ACS molecular dynamics simulation program [23] with some modification to perform the umbrella sampling... 

QM-MM simulations were used to generate trajectories for the steered molecular dynamics calculation of the free energy profile for the conversion of two molecules (chorismate to prephenate) involved in the biosynthesis of amino acids. The results showed good agreement with those obtained from umbrella sampling. Only fair agreement with experiment was attributed to the accuracy of the density function theory calculations. 

Schmidt, R. K., Teo, B. and Brady, J. W. (1995). Use of umbrella sampling in the calculation of the potential of mean force for maltose in vacuum from molecular dynamics simulations. J. Phys. Chem., 99, 11339-11343. 

We then performed several metadynamics runs with different choices of w, 5s and tq and, since the exact free energy for the system has been computed by umbrella sampling explicitly, we estimate the error with (11). In total, we tested more than fifty different combinations of parameters, for a total of almost 200 ns of molecular dynamics. All the simulations are started from the same initial condition in which the naphthalene is inserted in the catenane, and are stopped when the system escapes this free energy minimum. 

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