Guidelines for Free-Energy Calculations Involving Charge Changes.

The Coulomb interactions in molecular simulations are inherently approximated due to the finite size of the molecular box sizes amenable to current-day compute power. Several methods exist for treating long-range electrostatic interactions, yet these approaches are subject to various finite-size-related artifacts. Lattice-sum methods are frequently used to approximate long-range interactions; however, these approaches also suffer from artifacts which become particularly pronounced for free-energy calculations that involve charge changes. The artifacts, however, also affect the sampling when plain simulations are performed, leading to a biased ensemble. Here, we investigate two previously described model systems to determine if artifacts continue to play a role when overall neutral boxes are considered, in the context of both free-energy calculations and sampling. We find that ensuring that no net-charge changes take place, while maintaining a neutral simulation box, may be sufficient provided that the simulation boxes are large enough. Addition of salt to the solution (when appropriate) can further alleviate the remaining artifacts in the sampling or the calculated free-energy differences. We provide practical guidelines to avoid finite-size artifacts.

Charge-Changing Perturbations and Path Sampling via Classical Molecular Dynamic Simulations of Simple Guest-Host Systems.

Currently, two different methods dominate the field of biomolecular free-energy calculations for the prediction of binding affinities. Pathway methods are frequently used for large ligands that bind on the surface of a host, such as protein-protein complexes. Alchemical methods, on the other hand, are preferably applied for small ligands that bind to deeply buried binding sites. The latter methods are also widely known to be heavily artifacted by the representation of electrostatic energies in periodic simulation boxes, in particular, when net-charge changes are involved. Different methods have been described to deal with these artifacts, including postsimulation correction schemes and instantaneous correction schemes (e.g., co-alchemical perturbation of ions). Here, we use very simple test systems to show that instantaneous correction schemes with no change in the system net charge lower the artifacts but do not eliminate them. Furthermore, we show that free energies from pathway methods suffer from the same artifacts.

Toward Automated Free Energy Calculation with Accelerated Enveloping Distribution Sampling (A-EDS).

Free-energy perturbation (FEP) methods are commonly used in drug design to calculate relative binding free energies of different ligands to a common host protein. Alchemical ligand transformations are usually performed in multiple steps which need to be chosen carefully to ensure sufficient phase-space overlap between neighboring states. With one-step or single-step FEP techniques, a single reference state is designed that samples phase-space not only representative of a full transformation but also ideally resembles multiple ligand end states and hence allows for efficient multistate perturbations. Enveloping distribution sampling (EDS) is one example for such a method in which the reference state is created by a mathematical combination of the different ligand end states based on solid statistical mechanics. We have recently proposed a novel approach to EDS which enables efficient barrier crossing between the different end states, termed accelerated EDS (A-EDS). In this work, we further simplify the parametrization of the A-EDS reference state and demonstrate the automated calculation of multiple free-energy differences between different ligands from a single simulation in three different well-described drug design model systems.

GroScore: Accurate Scoring of Protein-Protein Binding Poses Using Explicit-Solvent Free-Energy Calculations.

Protein-protein docking algorithms promise a potential relief for the mismatch between the number of experimentally determined complex structures and the number of relevant protein interactions in an organism. To distinguish correctly from wrongly generated poses, it is necessary to score complexes according to their structural similarity to the real complex, which is usually done by computing interaction energies of some sort. Here, we explore the potential of free-energy calculations with statistical-mechanical foundation in the context of molecular dynamics (MD) simulations with explicit solvent to score a large number of complex poses. We introduce an adaptive sampling scheme which ensures that most sampling time is spent on the most promising poses. Our approach is illustrated by scoring of all targets in the CAPRI Score_set, a scoring benchmark set, and three additional CAPRI targets, together consisting of more than 22 000 poses. Our scoring scheme shows a performance that is competitive with the most successful approaches that were previously reported. All necessary scripts to run the automated scoring pipeline are available in the Supporting Information for this paper.

An antibody with Fab-constant domains exchanged for a pair of CH3 domains.

We have designed a complete antibody-like construct where the CH1 and Cκ domains are exchanged for a pair of the CH3 domains and efficient pairing of the heavy and light variable domain is achieved using "Knobs-into-Holes" strategy. This construct, composed of only naturally occurring immunoglobulin sequences without artificial linkers, expressed at a high level in mammalian cells, however exhibited low solubility. Rational mutagenesis aimed at the amino acid residues located at the interface of the variable domains and the exchanged CH3 domains was applied to improve the biophysical properties of the molecule. The domain-exchanged construct, including variable domains of the HER2/neu specific antibody trastuzumab, was able to bind to the surface of the strongly HER2/neu positive cell line SK-BR3 4-fold weaker than trastuzumab, but could nevertheless incite a more potent response in an antibody-dependent cell cytotoxicity (ADCC) reporter assay with FcγRIIIa-overexpressing T-cells. This could be explained with a stronger binding to the FcγRIIIa. Importantly, the novel construct could mediate a specific ADCC effect with natural killer cells similar to the parental antibody.

Accelerated Enveloping Distribution Sampling: Enabling Sampling of Multiple End States while Preserving Local Energy Minima.

Enveloping distribution sampling (EDS) is an efficient approach to calculate multiple free-energy differences from a single molecular dynamics (MD) simulation. However, the construction of an appropriate reference-state Hamiltonian that samples all states efficiently is not straightforward. We propose a novel approach for the construction of the EDS reference-state Hamiltonian, related to a previously described procedure to smoothen energy landscapes. In contrast to previously suggested EDS approaches, our reference-state Hamiltonian preserves local energy minima of the combined end-states. Moreover, we propose an intuitive, robust and efficient parameter optimization scheme to tune EDS Hamiltonian parameters. We demonstrate the proposed method with established and novel test systems and conclude that our approach allows for the automated calculation of multiple free-energy differences from a single simulation. Accelerated EDS promises to be a robust and user-friendly method to compute free-energy differences based on solid statistical mechanics.

Designing Fcabs: well-expressed and stable high affinity antigen-binding Fc fragments.

Fc fragment with antigen-binding (Fcab) is a novel construct which can be selected to recognize specifically a wide variety of target proteins. We describe the selection and affinity maturation of Fcab clones targeting VEGF, an important pro-angiogenesis factor. To investigate the extent of engineering permissible to Fcabs we applied targeted mutagenesis to all three C-terminal loop structures and the C-terminus of the CH3 domain to isolate high-affinity binders by directed evolution and yeast display. The matured clone, CT6, binds to VEGF with low nanomolar affinity and inhibits VEGF-stimulated proliferation of human umbilical vein endothelial cells in vitro. Molecular dynamics simulations were performed to address flexibility of the molecular structure of CT6 and to approximate a structural ensemble in aqueous solution. Significantly higher RMSF levels of CT6 in comparison to wild-type Fc were limited to the elongated CD-loop in the CH3 domain, while the overall structural integrity was retained. This allowed the Fcab to replace the Fc portion of a mAb, in which both the CH3 and Fab are capable of antigen engagement: a construct called mAb2 was assembled with CT6 and the Fab of bevacizumab. This bispecific molecule showed more potent antagonistic activity than bevacizumab in vitro. Further evaluation for the potential of the CT6 Fcab in targeted therapy is warranted due to the possibility of being combined with other therapeutically meaningful targets.

Simulation of Reversible Protein-Protein Binding and Calculation of Binding Free Energies Using Perturbed Distance Restraints.

Virtually all biological processes depend on the interaction between proteins at some point. The correct prediction of biomolecular binding free-energies has many interesting applications in both basic and applied pharmaceutical research. While recent advances in the field of molecular dynamics (MD) simulations have proven the feasibility of the calculation of protein-protein binding free energies, the large conformational freedom of proteins and complex free energy landscapes of binding processes make such calculations a difficult task. Moreover, convergence and reversibility of resulting free-energy values remain poorly described. In this work, an easy-to-use, yet robust approach for the calculation of standard-state protein-protein binding free energies using perturbed distance restraints is described. In the binding process the conformations of the proteins were restrained, as suggested earlier. Two approaches to avoid end-state problems upon release of the conformational restraints were compared. The method was evaluated by practical application to a small model complex of ubiquitin and the very flexible ubiquitin-binding domain of human DNA polymerase ι (UBM2). All computed free energy differences were closely monitored for convergence, and the calculated binding free energies had a mean unsigned deviation of only 1.4 or 2.5 kJ·mol-1 from experimental values. Statistical error estimates were in the order of thermal noise. We conclude that the presented method has promising potential for broad applicability to quantitatively describe protein-protein and various other kinds of complex formation.