Improved estimation of ligand–macromolecule binding affinities by linear response approach using a combination of multi-mode MD simulation and QM/MM methods

Abstract

Structure-based predictions of binding affinities of ligands binding to proteins by coordination bonds with transition metals, covalent bonds, and bonds involving charge re-distributions are hindered by the absence of proper force fields. This shortcoming affects all methods which use force-field-based molecular simulation data on complex formation for affinity predictions. One of the most frequently used methods in this category is the Linear Response (LR) approach of Åquist, correlating binding affinities with van der Waals and electrostatic energies, as extended by Jorgensen's inclusion of solvent-accessible surface areas. All these terms represent the differences, upon binding, in the ensemble averages of pertinent quantities, obtained from molecular dynamics (MD) or Monte Carlo simulations of the complex and of single components. Here we report a modification of the LR approach by: (1) the replacement of the two energy terms through the single-point QM/MM energy of the time-averaged complex structure from an MD simulation; and (2) a rigorous consideration of multiple modes (mm) of binding. The first extension alleviates the force-field related problems, while the second extension deals with the ligands exhibiting large-scale motions in the course of an MD simulation. The second modification results in the correlation equation that is nonlinear in optimized coefficients, but does not lead to an increase in the number of optimized coefficients. The application of the resulting mm QM/MM LR approach to the inhibition of zinc-dependent gelatinase B (matrix metalloproteinase 9) by 28 hydroxamate ligands indicates a significant improvement of descriptive and predictive abilities.

Ligand-Binding Affinity Estimates Supported by Quantum-Mechanical Methods

“…They also treated averages over each 25 ps simulation as a separate binding mode. 350 The results were somewhat improved for the pure MM approach (R 2 = 0.84, most likely owing to the increased number of fitting parameters), but not for the QM/MM-LIE approach (R 2 = 0.90). They also used the original approach to study the binding of the same ligands to a related protein, MMP3.…”

Mechanisms of Proteolytic Enzymes and Their Inhibition in QM/MM Studies

“…The specificity of most MMPs is surprisingly similar, which makes it very difficult to design the much desired inhibitors that target individual MMPs, which are involved in cancer. Thus, the binding of inhibitors to various metalloproteases was investigated using QM/MM approaches since around the year 2000, e.g., for MMP1, MMP3, MMP9, carboxypeptidase A, and glutamate carboxypeptidase II [ 58 , 59 , 60 , 61 , 62 , 63 , 64 , 65 , 66 , 67 ]. A comparative study on MMP1-3, MMP8, MMP9, and MMP13 confirmed the good correlation of computed and experimental free binding energies of inhibitors, while a cross-docking matrix gave hints to rational design of more specific MMP inhibitors [ 68 ].…”

Modeling Soft Supramolecular Nanostructures by Molecular Simulations

“…Other interesting example of application relates to protein-ligand interactions [103][104][105][106][107], which are typically pursued by significant conformational and energetic changes. These Representative conformation of the complex between PAZ domain of the human argonaute 2 (hAgo2) and the chemically modified siRNAs at 3′ overhang, obtained from the last nanoseconds of the MD production runs.…”

“…One possible alternative relies on the assumption that the change in the binding free-energy resulting, for e.g. from a mutation of a ligand bounded to a protein, complies a linear response scheme [104], with parameters estimated from training sets of protein-ligand complexes, and used for predicting binding affinities of new ligands. Another strategy is the computational design of the ligand in free and bound states.…”