The Filling Potential Method:  A Method for Estimating the Free Energy Surface for Protein−Ligand Docking

Abstract

We developed a molecular simulation method suitable for estimation of binding free energy, called the filling potential method, based on the concept of the Taboo search, which is a type of self-avoiding random walk consisting of a cycle of local-minimum searches and transition state searches. The filling potential method is an umbrella potential sampling method, and enables the ligand molecule to drift from its local minima automatically. In the case of the filling potential method, the umbrella potential is a combination of Gaussian-type repulsive potentials, which are located on the trajectory of the ligand. Without setting the reaction coordinates a priori, this method searches for and determines the suitable reaction coordinates by successive generation of umbrella potentials based on its trajectory analysis. The weighted histogram analysis for these trajectories gives the binding free energy of the ligand to the receptor protein. It was applied to the complex of thermolysin and its inhibitors in explicit water, and the free energy surfaces with the stable binding state and the energy barrier were examined. The calculated binding free energies agreed well with the experimental results.

A virtual-system coupled multicanonical molecular dynamics simulation: Principles and applications to free-energy landscape of protein–protein interaction with an all-atom model in explicit solvent

“…Therefore, the conformational ensemble in the Native complex drawn to show two quantities: e a1 · e a2 and e b1 · e b2 . Red arrows are inter-Cα atomic vectors from 11 Lys to 17 Cys of the two molecules. Blue arrows are those from 2 Arg to that of 7 Ser for the two molecules.…”

“…where Z mc is the partition function: (11) ensures that P mc (E R , E V ) converges to the two-dimensional distribution g(E R , E V ) after a long simulation. However, twodimensional convergence is generally more time consuming than one-dimensional convergence:…”

“…Weight w was set to a small value: 0.006 kcal/mol Å 2 . The restraints were applied to 14 residue pairs: 1 Lys- 17 Cys, 1 Lys- 18 His, 2 Arg- 17 Cys, 2 Arg- 18 His, 3 Cys- 17 Cys, 4 Ser- 17 Cys, 5 Cys- 13 Cys, 5 Cys- 14 Val, 8 Leu- 14 Val, 10 Asp- 14 Val, 11 Lys- 15 Tyr, 12 Glu- 16 Phe, 13 Cys- 17 Cys, and 14 Val- 18 His. The distances for these pairs are smaller than 7.0 Å in the native structure.…”

“…Recently, generalized ensemble methods have been developed for sampling large-scale motions of polypeptides. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] A multicanonical Monte Carlo sampling, was introduced to study a physical system, a two-dimensional Potts model, 16 and was subsequently applied to biological systems. [17][18][19] Nakajima et al extended the multicanonical sampling to molecular dynamics (MD), which solves the equations of motion in a Cartesian coordinate space.…”

Enhanced sampling simulations to construct free-energy landscape of protein–partner substrate interaction

“…If the binding site is known in advance, this method can therefore be selected. Similar to reducing sampling space, there is a method to sample the conformations and FEL along a certain binding pathway: the filling potential method (Fukunishi et al 2003). Application of the confinement method without any knowledge of the binding site has also been reported with the use of the replica exchange method (Anselmi and Pisabarro 2015), where the ligand resides inside a receptorshaped closed surface larger than the receptor surface.…”