Johan Åqvist

The three-dimensional structure of retinol-binding protein.

The complex of retinol with its carrier protein, retinol‐binding protein (RBP) has been crystallized and its three‐dimensional structure determined using X‐ray crystallography. Its most striking feature is an eight‐stranded up‐and‐down beta barrel core that completely encapsulates the retinol molecule. The retinol molecule lies along the axis of the barrel with the beta‐ionone ring innermost and the tip of the isoprene tail close to the surface.

Ligand Binding Affinity Prediction by Linear Interaction Energy Methods

A recent method for estimating ligand binding affinities is extended. This method employs averages of interaction potential energy terms from molecular dynamics simulations or other thermal conformational sampling techniques. Incorporation of systematic deviations from electrostatic linear response, derived from free energy perturbation studies, into the absolute binding free energy expression significantly enhances the accuracy of the approach. This type of method may be useful for computational prediction of ligand binding strengths, e.g., in drug design applications.

Q: a molecular dynamics program for free energy calculations and empirical valence bond simulations in biomolecular systems.

A new molecular dynamics program for free energy calculations in biomolecular systems is presented. It is principally designed for free energy perturbation simulations, empirical valence bond calculations, and binding affinity estimation by linear interaction energy methods. Evaluation of ligand-binding selectivity and free energy profiles for nucleophile activation in two protein tyrosine phosphatases as well as absolute binding affinity estimation for a lysine-binding protein are given as examples.

Free Energy Calculations and Ligand Binding

Publisher Summary This chapter gives an overview of some different methods for calculating ligand binding free energies that are all based on force fields and conformational sampling. Many of these studies of protein–ligand binding in the mid-1980s showed a remarkable agreement between theory and experiment, which led to an explosion of activity in the field of free energy calculations. More recent investigations, however, have demonstrated that significantly longer simulations than those used in the original reports are often required obtaining reliable results in protein–ligand binding studies. The increasing number of applications of free energy calculations also showed that the use of these methods was not as straightforward as expected; therefore, much effort was spent on improving the methodology. The free energy perturbation (FEP)/thermodynamic integration (TI) type of method has not really fulfilled its promise of being able to open a major new avenue to structure-based drug design due to slow convergence and sampling difficulties. In particular, in this type of extrapolation process in which one may want to look at 20 or so new ligands, arriving at the correct end-points by long perturbation paths sometimes seems hopeless. It appears that a better solution to this problem can often be provided by automated docking of individual compounds, at least when they differ significantly from each other, and then to try to evaluate the binding energetic by a method that does not require the unphysical transformations involved in FEP/TI and related methods. The docking problem resembles the protein-folding one in many respects, and the only way to attack difficult cases seems to be by extensive conformational searching in combination with more reliable scoring methods.

A molecular dynamics study of the C-terminal fragment of the L7/L12 ribosomal protein: secondary structure motion in a 150 picosecond trajectory

A 150 picosecond molecular dynamics computer simulation of the C-terminal fragment of the L7/L12 ribosomal protein from Escherichia coli is reported. The molecular dynamics results are compared with the available high-resolution X-ray data in terms of atomic positions, distances and positional fluctuations. Good agreement is found between the molecular dynamics results and the X-ray data. The form and parameters of the interaction potential energy function and the procedures for deriving it are discussed. Some current misunderstandings concerning the ways of evaluating the efficiency of molecular dynamics algorithms and of application of bond-length constraints in protein simulations are cleared up. The 150 picosecond trajectory has been scanned in a search for correlated motions within and between secondary structure elements. The beta-strands have diffusional stretching modes, and uncorrelated transversal displacements. The dynamic analysis of alpha-helices shows a variety of features. The atomic fluctuations differ between the helix ends; this effect reflects long time-scale motions. Two alpha-helices, alpha A and alpha C, show diffusive longitudinal stretching modes. The third helix, alpha B, has a correlated asymmetric longitudinal stretching; the N-terminal part dominates this behaviour. Furthermore, alpha B presents a librational motion with respect to the other parts of the molecule with a frequency of approximately 5 cm-1. This motion is coupled to helix stretching. Interestingly, the regions of highly conserved residues contain the most mobile parts of the molecule.

The Linear Interaction Energy Method for Predicting Ligand Binding Free Energies

An overview of the simplified linear interaction energy (LIE) method for calculation of ligand binding free energies is given. This method is based on force field estimations of the receptor-ligand interactions and thermal conformational sampling. A notable feature is that the binding energetics can be predicted by considering only the intermolecular interactions between the ligand and receptor. The approximations behind this approach are examined and different parametrizations of the model are discussed. In general, LIE type of methods appear particularly useful for computational drug lead optimization.

Calculation of absolute binding free energies for charged ligands and effects of long‐range electrostatic interactions

A recently proposed molecular dynamics method for estimating binding free energies is applied to the complexation of two charged benzamidine inhibitors with trypsin. The difficulties with calculations of absolute binding energies for charged molecules, associated with long‐range electrostatic contributions, are discussed and it is shown how to deal with these effectively. In particular, energetic effects caused by the trunction of dipole‐dipole interactions in the medium surrounding the charged ligand are examined and found to be significant. Calculations of the absolute binding energy for benzamidine using the free energy perturbation approach are also reported. These simulations illustrate the typical problems associated with annihilation transformations of molecules bound inside proteins.

Mechanistic alternatives in phosphate monoester hydrolysis: What conclusions can be drawn from available experimental data?

Phosphate monoester hydrolysis reactions in enzymes and solution are often discussed in terms of whether the reaction pathway is associative or dissociative. Although experimental results for solution reactions have usually been considered as evidence for the second alternative, a closer thermodynamic analysis of observed linear free energy relationships shows that experimental information is consistent with the associative, concerted and dissociative alternatives.

Binding affinity prediction with different force fields: Examination of the linear interaction energy method

A systematic study of the linear interaction energy (LIE) method and the possible dependence of its parameterization on the force field and system (receptor binding site) is reported. We have calculated the binding free energy for nine different ligands in complex with P450cam using three different force fields (Amber95, Gromos87, and OPLS‐AA). The results from these LIE calculations using our earlier parameterization give relative free energies of binding that agree remarkably well with the experimental data. However, the absolute energies are too positive for all three force fields, and it is clear that an additional constant term (γ) is required in this case. Out of five examined LIE models, the same one emerges as the best for all three force fields, and this, in fact, corresponds to our earlier one apart from the addition of the constant γ, which is almost identical for the three force fields. Thus, the present free energy calculations clearly indicate that the coefficients of the LIE method are independent of the force field used. Their relation to solvation free energies is also demonstrated. The only free parameter of the best model is γ, which is found to depend on the hydrophobicity of the binding site. We also attempt to quantify the binding site hydrophobicity of four different proteins which shows that the ordering of γs for these sites reflects the fraction of hydrophobic surface area.

Exploring blocker binding to a homology model of the open hERG K+ channel using docking and molecular dynamics methods

Binding of blockers to the human voltage‐gated hERG potassium channel is studied using a combination of homology modelling, automated docking calculations and molecular dynamics simulations, where binding affinities are evaluated using the linear interaction energy method. A homology model was constructed based on the available crystal structure of the bacterial KvAP channel and the affinities of a series of sertindole analogues predicted using this model. The calculations reproduce the relative binding affinities of these compounds very well and indicate that both polar interactions near the intracellular opening of the selectivity filter as well as hydrophobic complementarity in the region around F656 are important for blocker binding. These results are consistent with recent alanine scanning mutation experiments on the blocking of the hERG channel by other compounds.