Multiscale Simulation of Receptor-Drug Association Kinetics: Application to Neuraminidase Inhibitors.

A detailed understanding of the drug-receptor association process is of fundamental importance for drug design. Due to the long time scales of typical binding kinetics, the atomistic simulation of the ligand traveling from bulk solution into the binding site is still computationally challenging. In this work, we apply a multiscale approach of combined Molecular Dynamics (MD) and Brownian Dynamics (BD) simulations to investigate association pathway ensembles for the two prominent H1N1 neuraminidase inhibitors oseltamivir and zanamivir. Including knowledge of the approximate binding site location allows for the selective confinement of detailed but expensive MD simulations and application of less demanding BD simulations for the diffusion controlled part of the association pathway. We evaluate a binding criterion based on the residence time of the inhibitor in the binding pocket and compare it to geometric criteria that require prior knowledge about the binding mechanism. The method ranks the association rates of both inhibitors in qualitative agreement with experiment and yields reasonable absolute values depending, however, on the reaction criteria. The simulated association pathway ensembles reveal that, first, ligands are oriented in the electrostatic field of the receptor. Subsequently, a salt bridge is formed between the inhibitor's carboxyl group and neuraminidase residue Arg368, followed by adopting the native binding mode. Unexpectedly, despite oseltamivir's higher overall association rate, the rate into the intermediate salt-bridge state was found to be higher for zanamivir. The present methodology is intrinsically parallelizable and, although computationally demanding, allows systematic binding rate calculation on selected sets of potential drug molecules.

Thermodynamics and Kinetics of Nucleobase Stacking Oligomerization Revealed by Molecular Dynamics Simulations.

The aggregation of N6N9-dimethyladenine in aqueous solution into stacked oligomers represents an important model system for oligomerization processes. Molecular dynamics simulations allowed us to extract statistically converged stacking thermodynamics as well as converged association and dissociation kinetics. The simulations confirm an oligomerization mechanism according to a random isodesmic stacking model without significant cooperative effects. Multiple oligomerization and dissociation events were used to characterize stacking and unstacking processes and intermediate states in atomic detail. Standard three-point rigid body water force field models lead to significantly accelerated dynamics and an underestimation of enthalpic and entropic contributions. The fully flexible SPCFW water model yielded close agreement with the experimental equilibrium constant, entropy contribution, and, importantly, kinetic observables. In addition, the performance of several other water models was systematically tested in stacking dimerization simulations indicating that the realistic prediction of thermodynamics and kinetics will likely benefit from the use of flexible water models.

Subnanometre enzyme mechanics probed by single-molecule force spectroscopy.

Enzymes are molecular machines that bind substrates specifically, provide an adequate chemical environment for catalysis and exchange products rapidly, to ensure fast turnover rates. Direct information about the energetics that drive conformational changes is difficult to obtain. We used subnanometre single-molecule force spectroscopy to study the energetic drive of substrate-dependent lid closing in the enzyme adenylate kinase. Here we show that in the presence of the bisubstrate inhibitor diadenosine pentaphosphate (AP5A), closing and opening of both lids is cooperative and tightly coupled to inhibitor binding. Surprisingly, binding of the substrates ADP and ATP exhibits a much smaller energetic drive towards the fully closed state. Instead, we observe a new dominant energetic minimum with both lids half closed. Our results, combining experiment and molecular dynamics simulations, give detailed mechanical insights into how an enzyme can cope with the seemingly contradictory requirements of rapid substrate exchange and tight closing, to ensure efficient catalysis.

Substrate Binding Specifically Modulates Domain Arrangements in Adenylate Kinase.

The enzyme adenylate kinase (ADK) features two substrate binding domains that undergo large-scale motions during catalysis. In the apo state, the enzyme preferentially adopts a globally open state with accessible binding sites. Binding of two substrate molecules (AMP + ATP or ADP + ADP) results in a closed domain conformation, allowing efficient phosphoryl-transfer catalysis. We employed molecular dynamics simulations to systematically investigate how the individual domain motions are modulated by the binding of substrates. Two-dimensional free-energy landscapes were calculated along the opening of the two flexible lid domains for apo and holo ADK as well as for all single natural substrates bound to one of the two binding sites of ADK. The simulations reveal a strong dependence of the conformational ensembles on type and binding position of the bound substrates and a nonsymmetric behavior of the lid domains. Altogether, the ensembles suggest that, upon initial substrate binding to the corresponding lid site, the opposing lid is maintained open and accessible for subsequent substrate binding. In contrast, ATP binding to the AMP-lid induces global domain closing, preventing further substrate binding to the ATP-lid site. This might constitute a mechanism by which the enzyme avoids the formation of a stable but enzymatically unproductive state.

Efficient calculation of relative binding free energies by umbrella sampling perturbation.

An important task of biomolecular simulation is the calculation of relative binding free energies upon chemical modification of partner molecules in a biomolecular complex. The potential of mean force (PMF) along a reaction coordinate for association or dissociation of the complex can be used to estimate binding affinities. A free energy perturbation approach, termed umbrella sampling (US) perturbation, has been designed that allows an efficient calculation of the change of the PMF upon modification of a binding partner based on the trajectories obtained for the wild type reference complex. The approach was tested on the interaction of modified water molecules in aqueous solution and applied to in silico alanine scanning of a peptide-protein complex. For the water interaction test case, excellent agreement with an explicit PMF calculation for each modification was obtained as long as no long range electrostatic perturbations were considered. For the alanine scanning, the experimentally determined ranking and binding affinity changes upon alanine substitutions could be reproduced within 0.1-2.0 kcal/mol. In addition, good agreement with explicitly calculated PMFs was obtained mostly within the sampling uncertainty. The combined US and perturbation approach yields, under the condition of sufficiently small system modifications, rigorously derived changes in free energy and is applicable to any PMF calculation.

Evaluation of Generalized Born Model Accuracy for Absolute Binding Free Energy Calculations.

Generalized Born (GB) implicit solvent models are widely used in molecular dynamics simulations to evaluate the interactions of biomolecular complexes. The continuum treatment of the solvent results in significant computational savings in comparison to an explicit solvent representation. It is, however, not clear how accurately the GB approach reproduces the absolute free energies of biomolecular binding. On the basis of induced dissociation by means of umbrella sampling simulations, the absolute binding free energies of small proline-rich peptide ligands and a protein receptor were calculated. Comparative simulations according to the same protocol were performed by employing an explicit solvent model and various GB-type implicit solvent models in combination with a nonpolar surface tension term. The peptide ligands differed in a key residue at the peptide-protein interface, including either a nonpolar, a neutral polar, a positively charged, or a negatively charged group. For the peptides with a neutral polar or nonpolar interface residue, very good agreement between the explicit solvent and GB implicit solvent results was found. Deviations in the main separation free energy contributions are smaller than 1 kcal/mol. In contrast, for peptides with a charged interface residue, significant deviations of 2-4 kcal/mol were observed. The results indicate that recent GB models can compete with explicit solvent representations in total binding free energy calculations as long as no charged residues are present at the binding interface.

Adaptive Biasing Combined with Hamiltonian Replica Exchange to Improve Umbrella Sampling Free Energy Simulations.

The accurate calculation of potentials of mean force for ligand-receptor binding is one of the most important applications of molecular simulation techniques. Typically, the separation distance between ligand and receptor is chosen as a reaction coordinate along which a PMF can be calculated with the aid of umbrella sampling (US) techniques. In addition, restraints can be applied on the relative position and orientation of the partner molecules to reduce accessible phase space. An approach combining such phase space reduction with flattening of the free energy landscape and configurational exchanges has been developed, which significantly improves the convergence of PMF calculations in comparison with standard umbrella sampling. The free energy surface along the reaction coordinate is smoothened by iteratively adapting biasing potentials corresponding to previously calculated PMFs. Configurations are allowed to exchange between the umbrella simulation windows via the Hamiltonian replica exchange method. The application to a DNA molecule in complex with a minor groove binding ligand indicates significantly improved convergence and complete reversibility of the sampling along the pathway. The calculated binding free energy is in excellent agreement with experimental results. In contrast, the application of standard US resulted in large differences between PMFs calculated for association and dissociation pathways. The approach could be a useful alternative to standard US for computational studies on biomolecular recognition processes.