Jochen Heil

Quantum Chemistry in Solution by Combining 3D Integral Equation Theory with a Cluster Embedding Approach

Free energy changes associated with chemical reactions in solution are treated by integral equation theory in the form of the 3D reference interaction site model (RISM) in combination with quantum-chemical calculations via an embedded cluster approach (EC-RISM). The electronic structure of the solute is computed self-consistently with the solvent structure by mapping the charge distribution of the solvent onto a set of discrete background point charges that are added to the molecular Hamiltonian. The EC-RISM procedure yields chemical accuracy in free energy predictions for several benchmark systems without adjusting empirical parameters. We apply the method to the standard reaction free energy for the gauche-trans equilibrium of 1,2-dichloroethane in water and to pKa shift calculations for trifluoroacetic acid/acetic acid and 4-nitroaniline/aniline in water.

Targeting Drug Resistance in EGFR with Covalent Inhibitors: A Structure-Based Design Approach.

Receptor tyrosine kinases represent one of the prime targets in cancer therapy, as the dysregulation of these elementary transducers of extracellular signals, like the epidermal growth factor receptor (EGFR), contributes to the onset of cancer, such as non-small cell lung cancer (NSCLC). Strong efforts were directed to the development of irreversible inhibitors and led to compound CO-1686, which takes advantage of increased residence time at EGFR by alkylating Cys797 and thereby preventing toxic effects. Here, we present a structure-based approach, rationalized by subsequent computational analysis of conformational ligand ensembles in solution, to design novel and irreversible EGFR inhibitors based on a screening hit that was identified in a phenotype screen of 80 NSCLC cell lines against approximately 1500 compounds. Using protein X-ray crystallography, we deciphered the binding mode in engineered cSrc (T338M/S345C), a validated model system for EGFR-T790M, which constituted the basis for further rational design approaches. Chemical synthesis led to further compound collections that revealed increased biochemical potency and, in part, selectivity toward mutated (L858R and L858R/T790M) vs nonmutated EGFR. Further cell-based and kinetic studies were performed to substantiate our initial findings. Utilizing proteolytic digestion and nano-LC-MS/MS analysis, we confirmed the alkylation of Cys797.

Non-continuum solvation using the EC-RISM method applied to predict tautomer ratios, pKa and enantiomeric excess of alkylation reactions.

The three-dimensional “reference interaction site model” (3D-RISM) integral equation theory is a statistical-mechanical approach to predict liquid state structural and thermodynamic features. It is based on approximate solute-solvent correlation functions to be computed on a 3D grid as a function of the interaction potential between the solute and the solvent sites, circumventing the need of costly sampling of explicit solvent degrees of freedom. In combination with quantum-chemical calculations within the embedded cluster (EC-)RISM framework [1] the theory allows for studying chemical reactions in solution with an accuracy not reached by traditional continuum solvation methods. In particular, it improves upon dielectric continuum solvation by taking solvent granularity into account and also provides a means towards physically cavity formation and dispersion free Energies without introducing artificial boundaries and empirically fitted radii. We outline the general framework and show application examples from pKa and tautomeric ratio estimation [2] as well as enantiomeric excess prediction for stereoselective alkylation reactions in organic solvent.

Three-Dimensional RISM Integral Equation Theory for Polarizable Solute Models.

Modeling solute polarizability is a key ingredient for improving the description of solvation phenomena. In recent years, polarizable molecular mechanics force fields have emerged that circumvent the limitations of classical fixed charge force fields by the ability to adapt their electrostatic potential distribution to a polarizing environment. Solvation phenomena are characterized by the solutes excess chemical potential, which can be computed by expensive fully atomistic free energy simulations. The alternative is to employ an implicit solvent model, which poses a challenge to the formulation of the solute-solvent interaction term within a polarizable framework. Here, we adapt the three-dimensional reference interaction site model (3D RISM) integral equation theory as a solvent model, which analytically yields the chemical potential, to the polarizable AMOEBA force field using an embedding cluster (EC-RISM) strategy. The methodology is analogous to our earlier approach to the coupling of a quantum-chemical solute description with a classical 3D RISM solvent. We describe the conceptual physical and algorithmic basis as well as the performance for several benchmark cases as a proof of principle. The results consistently show reasonable agreement between AMOEBA and quantum-chemical free energies in solution in general and allow for separate assessment of energetic and solvation-related contributions. We find that, depending on the parametrization, AMOEBA reproduces the chemical potential in better agreement with reference quantum-chemical calculations than the intramolecular energies, which suggests possible routes toward systematic improvement of polarizable force fields.

Acidity in DMSO from the embedded cluster integral equation quantum solvation model.

AbstractThe embedded cluster reference interaction site model (EC-RISM) is applied to the prediction of acidity constants of organic molecules in dimethyl sulfoxide (DMSO) solution. EC-RISM is based on a self-consistent treatment of the solute’s electronic structure and the solvent’s structure by coupling quantum-chemical calculations with three-dimensional (3D) RISM integral equation theory. We compare available DMSO force fields with reference calculations obtained using the polarizable continuum model (PCM). The results are evaluated statistically using two different approaches to eliminating the proton contribution: a linear regression model and an analysis of pKa shifts for compound pairs. Suitable levels of theory for the integral equation methodology are benchmarked. The results are further analyzed and illustrated by visualizing solvent site distribution functions and comparing them with an aqueous environment. FigureSolvent site distribution of DMSO around 3-methylphenole and pKa regression result for the EC-RISM quantum solvation model

Structure and thermodynamics of nondipolar molecular liquids and solutions from integral equation theory

ABSTRACT Solvent-induced solute polarisation of nondipolar solvents originates mainly from specific directional interactions and higher electrostatic multipole moments. Popular continuum solvation models such as the polarisable continuum models ignore such interactions and, therefore, cannot adequately model solvation effects on electronic structure in these environments. Important examples of nondipolar solvents that are indistinguishable by continuum methods are benzene and hexafluorobenzene. Both substances have very similar macroscopic properties, while solutes dissolved in either benzene or hexafluorobenzene behave differently due to their inverted electrostatic quadrupole moments and slightly different size. As a first step towards a proper and computationally feasible description of nondipolar molecular solvents, we present here integral equation theory results based on various forms of the reference interaction site model coupled to quantum-chemical calculations for benzene and hexafluorobenzene solutions of small molecules. We analyse solvation structures, also in comparison with molecular dynamics simulations, and show that predictions of transfer Gibbs energies, which define partition constants, benefit substantially from considering the exact, wave function-derived electrostatic field distribution beyond a simple point charge solute model in comparison with experimental data. Moreover, by constructing artificial uncharged and charge-inverted toy models of the solvents, it is possible to dissect the relative importance of dispersion and quadrupolar electrostatic effects on the partitioning equilibria. Such insight can help to design specifically optimised solvents to control solubility and selectivity for a wide range of applications.

Thermodynamic Characterization of Hydration Sites from Integral Equation-Derived Free Energy Densities: Application to Protein Binding Sites and Ligand Series

Water molecules play an essential role for mediating interactions between ligands and protein binding sites. Displacement of specific water molecules can favorably modulate the free energy of binding of protein-ligand complexes. Here, the nature of water interactions in protein binding sites is investigated by 3D RISM (three-dimensional reference interaction site model) integral equation theory to understand and exploit local thermodynamic features of water molecules by ranking their possible displacement in structure-based design. Unlike molecular dynamics-based approaches, 3D RISM theory allows for fast and noise-free calculations using the same detailed level of solute-solvent interaction description. Here we correlate molecular water entities instead of mere site density maxima with local contributions to the solvation free energy using novel algorithms. Distinct water molecules and hydration sites are investigated in multiple protein-ligand X-ray structures, namely streptavidin, factor Xa, and factor VIIa, based on 3D RISM-derived free energy density fields. Our approach allows the semiquantitative assessment of whether a given structural water molecule can potentially be targeted for replacement in structure-based design. Finally, PLS-based regression models from free energy density fields used within a 3D-QSAR approach (CARMa - comparative analysis of 3D RISM Maps) are shown to be able to extract relevant information for the interpretation of structure-activity relationship (SAR) trends, as demonstrated for a series of serine protease inhibitors.

Structure and thermodynamics of nonaqueous solvation by integral equation theory

Electronic structure theory under the influence of apolar solvents suffers from substantial methodical difficulties since in this case the solvent-induced solute polarization originates mainly from specific directional interactions and higher electric multipoles. Continuum solvation models based on the dielectric solvent response such as the PCM approach ignore such interactions and can therefore not adequately model solvation effects in nonaqueous environments. The “embedded cluster reference interaction site model” (EC-RISM) [1] retains the granularity of the solvent and represents a microscopically more detailed and therefore improved approach towards solvation modeling. EC-RISM is based on a self-consistent solution of solvent distribution functions described by a 3D integral equation theory and solute electronic structure by mapping the solvent charge distribution onto discrete, solute-embedding point charges. In aqueous solution EC-RISM theory is capable of calculating pKa shifts [1] and tautomer ratios relatively fast and with high accuracy [2]. Here we outline the strength of the integral equation model by studying benzene and hexafluorobenzene solutions. In particular, the thermodynamics of differential solvation is quantified for organic compounds dissolved in these media. Moreover, it is shown that the respective solvent structures around particular solutes differ strongly, possibly leading to changes in the thermodynamic stability scale of various isomers which are not reproduced by the PCM model.