Grand Canonical Free-Energy Calculations of Protein−Ligand Binding

Baseline Comparisons of Complementary Sampling Methods for Assembly Driven by Short-Ranged Pair Potentials toward Fast and Flexible Hybridization

This work measures baseline sampling characteristics that highlight fundamental differences between sampling methods for assembly driven by short-ranged pair potentials. Such granular comparison is essential for fast, flexible, and accurate hybridization of complementary methods. Besides sampling speed, efficiency, and accuracy of uniform grid coverage, other sampling characteristics measured are (i) accuracy of covering narrow low energy regions that have low effective dimension (ii) ability to localize sampling to specific basins, and (iii) flexibility in sampling distributions. As a proof of concept, we compare a recently developed geometric methodology EASAL (Efficient Atlasing and Search of Assembly Landscapes) and the traditional Monte Carlo (MC) method for sampling the energy landscape of two assembling trans-membrane helices, driven by short-range pair potentials. By measuring the above-mentioned sampling characteristics, we demonstrate that EASAL provides localized and accurate coverage of crucial regions of the energy landscape of low effective dimension, under flexible sampling distributions, with much fewer samples and computational resources than MC sampling. EASAL's empirically validated theoretical guarantees permit credible extrapolation of these measurements and comparisons to arbitrary number and size of assembling units. Promising avenues for hybridizing the complementary advantages of the two methods are discussed.

Atlasing of Assembly Landscapes using Distance Geometry and Graph Rigidity

This Article describes a novel geometric methodology for analyzing free energy and kinetics of assembly driven by short-range pair-potentials in an implicit solvent and provides a proof-of-concept illustration of its unique capabilities. An atlas is a labeled partition of the assembly landscape into a roadmap of maximal, contiguous, nearly-equipotential-energy conformational regions or macrostates, together with their neighborhood relationships. The new methodology decouples the roadmap generation from sampling and produces: (1) a queryable atlas of local potential energy minima, their basin structure, energy barriers, and neighboring basins; (2) paths between a specified pair of basins, each path being a sequence of conformational regions or macrostates below a desired energy threshold; and (3) approximations of relative path lengths, basin volumes (configurational entropy), and path probabilities. Results demonstrating the core algorithm's capabilities and high computational efficiency have been generated by a resource-light, curated open source software implementation EASAL (Efficient Atlasing and Search of Assembly Landscapes, ACM Trans. Math. Softw. 2018 44, 1-48. 10.1145/3204472; see software, Efficient Atlasing and Search of Assembly Landscapes, 2016. https://bitbucket.org/geoplexity/easal; video, Video Illustrating the opensource software EASAL, 2016. https://cise.ufl.edu/~sitharam/EASALvideo.mpeg; and user guide, EASAL software user guide, 2016. https://bitbucket.org/geoplexity/easal/src/master/CompleteUserGuide.pdf). Running on a laptop with Intel(R) Core(TM) i7-7700@3.60 GHz CPU with 16GB of RAM, EASAL atlases several hundred thousand conformational regions or macrostates in minutes using a single compute core. Subsequent path and basin computations each take seconds. A parallelized EASAL version running on the same laptop with 4 cores gives a 3× speedup for atlas generation. The core algorithm's correctness, time complexity, and efficiency-accuracy trade-offs are formally guaranteed using modern distance geometry, geometric constraint systems and combinatorial rigidity. The methodology further links the shape of the input assembling units to a type of intuitive and queryable bar-code of the output atlas, which in turn determine stable assembled structures and kinetics. This succinct input-output relationship facilitates reverse analysis and control toward design. A novel feature that is crucial to both the high sampling efficiency and decoupling of roadmap generation from sampling is a recently developed theory of convex Cayley (distance-based) custom parametrizations specific to assembly, as opposed to folding. Representing microstates with macrostate-specific Cayley parameters, to generate microstate samples, avoids gradient-descent search used by all prevailing methods. Further, these parametrizations convexify conformational regions or macrostates. This ratchets up sampling efficiency, significantly reducing number of repeated and discarded samples. These features of the new stand-alone methodology can also be used to complement the strengths of prevailing methodologies including Molecular Dynamics, Monte Carlo, and Fast Fourier Transform based methods.

Inclusion of enclosed hydration effects in the binding free energy estimation of dopamine D3 receptor complexes

Confined hydration and conformational flexibility are some of the challenges encountered for the rational design of selective antagonists of G-protein coupled receptors. We present a set of C3-substituted (-)-stepholidine derivatives as potent binders of the dopamine D3 receptor. The compounds are characterized biochemically, as well as by computer modeling using a novel molecular dynamics-based alchemical binding free energy approach which incorporates the effect of the displacement of enclosed water molecules from the binding site. The free energy of displacement of specific hydration sites is obtained using the Hydration Site Analysis method with explicit solvation. This work underscores the critical role of confined hydration and conformational reorganization in the molecular recognition mechanism of dopamine receptors and illustrates the potential of binding free energy models to represent these key phenomena.

Enhanced Monte Carlo Methods for Modeling Proteins Including Computation of Absolute Free Energies of Binding

The generation of a complete ensemble of geometrical configurations is required to obtain reliable estimations of absolute binding free energies by alchemical free energy methods. Molecular dynamics (MD) is the most popular sampling method, but the representation of large biomolecular systems may be incomplete owing to energetic barriers that impede efficient sampling of the configurational space. Monte Carlo (MC) methods can possibly overcome this issue by adapting the attempted movement sizes to facilitate transitions between alternative local-energy minima. In this study, we present an MC statistical mechanics algorithm to explore the protein-ligand conformational space with emphasis on the motions of the protein backbone and side chains. The parameters for each MC move type were optimized to better reproduce conformational distributions of 18 dipeptides and the well-studied T4-lysozyme L99A protein. Next, the performance of the improved MC algorithms was evaluated by computing absolute free energies of binding for L99A lysozyme with benzene and seven analogs. Results for benzene with L99A lysozyme from MD and the optimized MC protocol were found to agree within 0.6 kcal/mol, while a mean unsigned error of 1.2 kcal/mol between MC results and experiment was obtained for the seven benzene analogs. Significant advantages in computation speed are also reported with MC over MD for similar extents of configurational sampling.

Rigorous Free Energy Calculations in Structure-Based Drug Design

Structure-based drug design could benefit greatly from computational methodologies that accurately predict the binding affinity of small compounds to target biomolecules. However, the current scoring functions used to rank compounds in virtual screens by docking are not sufficiently accurate to guide reliably the design of tight binding ligands. Thus, there is strong interest in methodologies based on molecular simulations of protein-ligand complexes which are perceived to be more accurate and, with advances in computing power, amenable to routine use. This report provides an overview of the technical details necessary to understand, execute and analyze binding free energy calculations, using free energy perturbation or thermodynamic integration methods. Examples of possible applications in structure-based drug design are discussed. Current methodological limitations are highlighted as well as a number of ongoing developments to improve the scope, reliability, and practicalities of free energy calculations. These efforts are paving the way for a more common use of free energy calculations in molecular design.

Water Sites, Networks, And Free Energies with Grand Canonical Monte Carlo

Water molecules play integral roles in the formation of many protein-ligand complexes, and recent computational efforts have been focused on predicting the thermodynamic properties of individual waters and how they may be exploited in rational drug design. However, when water molecules form highly coupled hydrogen-bonding networks, there is, as yet, no method that can rigorously calculate the free energy to bind the entire network or assess the degree of cooperativity between waters. In this work, we report theoretical and methodological developments to the grand canonical Monte Carlo simulation technique. Central to our results is a rigorous equation that can be used to calculate efficiently the binding free energies of water networks of arbitrary size and complexity. Using a single set of simulations, our methods can locate waters, estimate their binding affinities, capture the cooperativity of the water network, and evaluate the hydration free energy of entire protein binding sites. Our techniques have been applied to multiple test systems and compare favorably to thermodynamic integration simulations and experimental data. The implications of these methods in drug design are discussed.

Protein binding site analysis for drug discovery using a computational fragment-based method

One of the most powerful tools for designing drug molecules is an understanding of the target protein's binding site. Identifying key amino acids and understanding the electronic, steric, and solvation properties of the site enables the design of potent ligands. Of equal importance for the success of a drug discovery program is the evaluation of binding site druggability. Determining, a priori, if a particular binding site has the appropriate character to bind drug-like ligands saves research time and money.While there are a variety of experimental and computational techniques to identify and characterize binding sites, the focus of this chapter is on Binding Site Analysis (BSA) using virtual fragment simulations. The methodology of the technique is described, along with examples of successful application to drug discovery programs. BSA both indicates if a protein is a viable target for drug discovery and provides a roadmap for designing ligands. Using a computational fragment-based method is a effective means of understanding of a binding site.

Virtual fragment preparation for computational fragment-based drug design

Fragment-based drug design (FBDD) has become an important component of the drug discovery process. The use of fragments can accelerate both the search for a hit molecule and the development of that hit into a lead molecule for clinical testing. In addition to experimental methodologies for FBDD such as NMR and X-ray Crystallography screens, computational techniques are playing an increasingly important role. The success of the computational simulations is due in large part to how the database of virtual fragments is prepared. In order to prepare the fragments appropriately it is necessary to understand how FBDD differs from other approaches and the issues inherent in building up molecules from smaller fragment pieces. The ultimate goal of these calculations is to link two or more simulated fragments into a molecule that has an experimental binding affinity consistent with the additive predicted binding affinities of the virtual fragments. Computationally predicting binding affinities is a complex process, with many opportunities for introducing error. Therefore, care should be taken with the fragment preparation procedure to avoid introducing additional inaccuracies.This chapter is focused on the preparation process used to create a virtual fragment database. Several key issues of fragment preparation which affect the accuracy of binding affinity predictions are discussed. The first issue is the selection of the two-dimensional atomic structure of the virtual fragment. Although the particular usage of the fragment can affect this choice (i.e., whether the fragment will be used for calibration, binding site characterization, hit identification, or lead optimization), general factors such as synthetic accessibility, size, and flexibility are major considerations in selecting the 2D structure. Other aspects of preparing the virtual fragments for simulation are the generation of three-dimensional conformations and the assignment of the associated atomic point charges.

Strategies to calculate water binding free energies in protein-ligand complexes

Water molecules are commonplace in protein binding pockets, where they can typically form a complex between the protein and a ligand or become displaced upon ligand binding. As a result, it is often of great interest to establish both the binding free energy and location of such molecules. Several approaches to predicting the location and affinity of water molecules to proteins have been proposed and utilized in the literature, although it is often unclear which method should be used under what circumstances. We report here a comparison between three such methodologies, Just Add Water Molecules (JAWS), Grand Canonical Monte Carlo (GCMC), and double-decoupling, in the hope of understanding the advantages and limitations of each method when applied to enclosed binding sites. As a result, we have adapted the JAWS scoring procedure, allowing the binding free energies of strongly bound water molecules to be calculated to a high degree of accuracy, requiring significantly less computational effort than more rigorous approaches. The combination of JAWS and GCMC offers a route to a rapid scheme capable of both locating and scoring water molecules for rational drug design.

Sampling of Organic Solutes in Aqueous and Heterogeneous Environments Using Oscillating Excess Chemical Potentials in Grand Canonical-like Monte Carlo-Molecular Dynamics Simulations

Solute sampling of explicit bulk-phase aqueous environments in grand canonical (GC) ensemble simulations suffer from poor convergence due to low insertion probabilities of the solutes. To address this, we developed an iterative procedure involving Grand Canonical-like Monte Carlo (GCMC) and molecular dynamics (MD) simulations. Each iteration involves GCMC of both the solutes and water followed by MD, with the excess chemical potential (μ_ex) of both the solute and the water oscillated to attain their target concentrations in the simulation system. By periodically varying the μ_ex of the water and solutes over the GCMC-MD iterations, solute exchange probabilities and the spatial distributions of the solutes improved. The utility of the oscillating-μ_ex GCMC-MD method is indicated by its ability to approximate the hydration free energy (HFE) of the individual solutes in aqueous solution as well as in dilute aqueous mixtures of multiple solutes. For seven organic solutes: benzene, propane, acetaldehyde, methanol, formamide, acetate, and methylammonium, the average μ_ex of the solutes and the water converged close to their respective HFEs in both 1 M standard state and dilute aqueous mixture systems. The oscillating-μ_ex GCMC methodology is also able to drive solute sampling in proteins in aqueous environments as shown using the occluded binding pocket of the T4 lysozyme L99A mutant as a model system. The approach was shown to satisfactorily reproduce the free energy of binding of benzene as well as sample the functional group requirements of the occluded pocket consistent with the crystal structures of known ligands bound to the L99A mutant as well as their relative binding affinities.

Biomolecular electrostatics and solvation: a computational perspective

An understanding of molecular interactions is essential for insight into biological systems at the molecular scale. Among the various components of molecular interactions, electrostatics are of special importance because of their long-range nature and their influence on polar or charged molecules, including water, aqueous ions, proteins, nucleic acids, carbohydrates, and membrane lipids. In particular, robust models of electrostatic interactions are essential for understanding the solvation properties of biomolecules and the effects of solvation upon biomolecular folding, binding, enzyme catalysis, and dynamics. Electrostatics, therefore, are of central importance to understanding biomolecular structure and modeling interactions within and among biological molecules. This review discusses the solvation of biomolecules with a computational biophysics view toward describing the phenomenon. While our main focus lies on the computational aspect of the models, we provide an overview of the basic elements of biomolecular solvation (e.g. solvent structure, polarization, ion binding, and non-polar behavior) in order to provide a background to understand the different types of solvation models.

In silico and intuitive predictions of CYP46A1 inhibition by marketed drugs with subsequent enzyme crystallization in complex with fluvoxamine

Cytochrome P450 46A1 (cholesterol 24-hydroxylase) is an important brain enzyme that may be inhibited by structurally distinct pharmaceutical agents both in vitro and in vivo. To identify additional inhibitors of CYP46A1 among U.S. Food and Drug Administration-approved therapeutic agents, we used in silico and intuitive predictions and evaluated some of the predicted binders in the enzyme and spectral binding assays. We tested a total of 298 marketed drugs for the inhibition of CYP46A1-mediated cholesterol hydroxylation in vitro and found that 13 of them reduce CYP46A1 activity by >50%. Of these 13 inhibitors, 7 elicited a spectral response in CYP46A1 with apparent spectral K(d) values in a low micromolar range. One of the identified tight binders, the widely used antidepressant fluvoxamine, was cocrystallized with CYP46A1. The structure of this complex was determined at a 2.5 Å resolution and revealed the details of drug binding to the CYP46A1 active site. The NH(2)-containing arm of the Y-shaped fluvoxamine coordinates the CYP46A1 heme iron, whereas the methoxy-containing arm points away from the heme group and has multiple hydrophobic interactions with aliphatic amino acid residues. The CF(3)-phenyl ring faces the entrance to the substrate access channel and has contacts with the aromatic side chains. The crystal structure suggests that only certain drug conformers can enter the P450 substrate access channel and reach the active site. Once inside the active site, the conformer probably further adjusts its configuration and elicits the movement of the protein side chains.

Protein flexibility in docking and surface mapping

Structure-based drug design has become an essential tool for rapid lead discovery and optimization. As available structural information has increased, researchers have become increasingly aware of the importance of protein flexibility for accurate description of the native state. Typical protein-ligand docking efforts still rely on a single rigid receptor, which is an incomplete representation of potential binding conformations of the protein. These rigid docking efforts typically show the best performance rates between 50 and 75%, while fully flexible docking methods can enhance pose prediction up to 80-95%. This review examines the current toolbox for flexible protein-ligand docking and receptor surface mapping. Present limitations and possibilities for future development are discussed.

Protein-ligand binding free energies from exhaustive docking

We explore the use of exhaustive docking as an alternative to Monte Carlo and molecular dynamics sampling for the direct integration of the partition function for protein-ligand binding. We enumerate feasible poses for the ligand and calculate the Boltzmann factor contribution of each pose to the partition function. From the partition function, the free energy, enthalpy, and entropy can be derived. All our calculations are done with a continuum solvation model that includes solving the Poisson equation. In contrast to Monte Carlo and molecular dynamics simulations, exhaustive docking avoids (within the limitations of a discrete sampling) the question of "Have we run long enough?" due to its deterministic complete enumeration of states. We tested the method on the T4 lysozyme L99A mutant, which has a nonpolar cavity that can accommodate a number of small molecules. We tested two electrostatic models. Model 1 used a solute dielectric of 2.25 for the complex apoprotein and free ligand and 78.5 for the solvent. Model 2 used a solute dielectric of 2.25 for the complex and apoprotein but 1.0 for the free ligand. For our test set of eight molecules, we obtain a reasonable correlation with a Pearson r(2) = 0.66 using model 1. The trend in binding affinity ranking is generally preserved with a Kendall τ = 0.64 and Spearman ρ = 0.83. With model 2, the correlation is improved with a Pearson r(2) = 0.83, Kendall τ = 0.93, and Spearman ρ = 0.98. This suggests that the energy function and sampling method adequately captured most of the thermodynamics of binding of the nonpolar ligands to T4 lysozyme L99A.

Transplant-insert-constrain-relax-assemble (TICRA): protein-ligand complex structure modeling and application to kinases

We introduce TICRA (transplant-insert-constrain-relax-assemble), a method for modeling the structure of unknown protein-ligand complexes using the X-ray crystal structures of homologous proteins and ligands with known activity. We present results from modeling the structures of protein kinase-inhibitor complexes using p38 and Lck as examples. These examples show that the TICRA method may be used prospectively to create and refine models for protein kinase-inhibitor complexes with an overall backbone rmsd of less than 0.75 Å for the kinase domain, when compared to published X-ray crystal structures. Further refinement of the models of the kinase domains of p38 and Lck in complex with their cognate ligands from the published crystal structures was able to improve the rmsd's of the model complexes to below 0.5 Å. Our results show that TICRA is a useful approach to the problem of structure-based drug design in cases where little structural information is available for the target proteins and the binding mode of active compounds is unknown.

The measured and calculated affinity of methyl- and methoxy-substituted benzoquinones for the Q(A) site of bacterial reaction centers

Quinones play important roles in mitochondrial and photosynthetic energy conversion acting as intramembrane, mobile electron, and proton carriers between catalytic sites in various electron transfer proteins. They display different affinity, selectivity, functionality, and exchange dynamics in different binding sites. The computational analysis of quinone binding sheds light on the requirements for quinone affinity and specificity. The affinities of 10 oxidized, neutral benzoquinones were measured for the high affinity Q(A) site in the detergent-solubilized Rhodobacter sphaeroides bacterial photosynthetic reaction center. Multiconformation Continuum Electrostatics was then used to calculate their relative binding free energies by grand canonical Monte Carlo sampling with a rigid protein backbone, flexible ligand, and side chain positions and protonation states. Van der Waals and torsion energies, Poisson-Boltzmann continuum electrostatics, and accessible surface area-dependent ligand-solvent interactions are considered. An initial, single cycle of GROMACS backbone optimization improves the match with experiment as do coupled-ligand and side-chain motions. The calculations match experiment with an root mean square deviation (RMSD) of 2.29 and a slope of 1.28. The affinities are dominated by favorable protein-ligand van der Waals rather than electrostatic interactions. Each quinone appears in a closely clustered set of positions. Methyl and methoxy groups move into the same positions as found for the native quinone. Difficulties putting methyls into methoxy sites are observed. Calculations using a solvent-accessible surface area-dependent implicit van der Waals interaction smoothed out small clashes, providing a better match to experiment with a RMSD of 0.77 and a slope of 0.97.

The rational design of a novel potent analogue of the 5'-AMP-activated protein kinase inhibitor compound C with improved selectivity and cellular activity

We have designed and synthesized analogues of compound C, a non-specific inhibitor of 5'-AMP-activated protein kinase (AMPK), using a computational fragment-based drug design (FBDD) approach. Synthesizing only twenty-seven analogues yielded a compound that was equipotent to compound C in the inhibition of the human AMPK (hAMPK) α2 subunit in the heterotrimeric complex in vitro, exhibited significantly improved selectivity against a subset of relevant kinases, and demonstrated enhanced cellular inhibition of AMPK.

Prediction of protein-ligand binding affinity by free energy simulations: assumptions, pitfalls and expectations

Many limitations of current computer-aided drug design arise from the difficulty of reliably predicting the binding affinity of a small molecule to a biological target. There is thus a strong interest in novel computational methodologies that claim predictions of greater accuracy than current scoring functions, and at a throughput compatible with the rapid pace of drug discovery in the pharmaceutical industry. Notably, computational methodologies firmly rooted in statistical thermodynamics have received particular attention in recent years. Yet free energy calculations can be daunting to learn for a novice user because of numerous technical issues and various approaches advocated by experts in the field. The purpose of this article is to provide an overview of the current capabilities of free energy calculations and to discuss the applicability of this technology to drug discovery.