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Three-dimensional integral equation theory for predicting protein-ligand binding affinities

Subject Area Theoretical Chemistry: Electronic Structure, Dynamics, Simulation
Biophysics
Term from 2009 to 2014
Project identifier Deutsche Forschungsgemeinschaft (DFG) - Project number 137795400
 
Final Report Year 2016

Final Report Abstract

Understanding and modeling the interaction between a protein and a ligand is an essential early step in drug discovery and development. In order to reproduce and predict both structural data such as binding modes and thermodynamic quantities like binding affinities, a computational model has to account for the complexity of the binding process. In practice this means that we have to consider the following issues: knowledge about structures and protonation as well as tautomerization states, definition of interaction energy terms between the complex partners and between solutes and water/electrolyte as a solvent, adequate and sufficient reproduction of naturally fluctuating molecular geometries (sampling problem), conversion of sampled structures into a thermodynamic affinity expression (binding free energy), and, finally, benchmarking of model data with respect to appropriately chosen experimental reference quantities. Despite many well-known conceptual difficulties, molecular dynamics (MD) simulations with specific extensions to determine the binding free energy are de facto the most reliable theoretical method presently available for studying binding processes in solution, though at a high price to pay for the computational effort. We therefore proposed to develop and apply an alternative theoretical platform for answering all question related to complex formation, socalled liquid state theory in the form of the three-dimensional (3D) “reference interaction site model” (RISM) integral equation formalism. Briefly, 3D RISM theory represents one specific class of approximations within the family of liquid state theories that yields solute-solvent (uv) site distribution functions on a 3D grid for a given structural solute model and solute-solvent interaction potential. Such an approach can in principle compete with MD simulations in that thermodynamic quantities can be computed at a fraction of computational cost. However, a number of conceptual and technical problems needed to be addressed in the present project. We specifically focused on (a) the numerical problem to solve the integral equations efficiently, (b) the 3D RISM-based calculation of (local) binding free energy data in the form of the socalled “potential of mean force” (PMF) that defines the energy surfaces governing the binding process, and (c) the complete physicochemical characterization of small molecules with pharmaceutical relevance. Subproject (a) was tackled by developing and implementing novel theory and numerical approximations with particular emphasis on the problem of long-range (Coulomb) interactions which are problematic to handle on relatively small, finite 3D grids. While it was not yet possible to solve the ultimate goal, the molecular solute-solute equation in a numerically stable and physically plausible manner, we succeeded to lay the theoretical groundwork that, at the same time, improved the computational speed and numerical precision of 3D RISM calculations considerably. Part (b) was therefore restricted to benchmarking calculations on model cases comprising molecular hosts binding atomic, possibly charged, guest partners. It could be shown which kind of RISM-based theory agrees best with reference MD simulation. As an added value, it was possible to define and test so-called binding “free energy derivatives” (FED) with respect to complex interaction parameters, thus paving the way for rational design in “chemical property space”. Problem area (c) was addressed by coupling electronic structure calculations to integral equation theory in the form of the “embedded cluster” (EC-RISM) approach. We contributed to the full range of relevant questions, such as the prediction of acidity, tautomer preference, distribution coefficients, and conformational equilibria, in aqueous and non-aqueous phases as well as within bound configurations in a complex. The performance of the methodology was critically assessed by contributions to several blind prediction contests where a number of groups were asked to test their methods on unknown compounds, revealing concrete problem areas for further improvements. In summary, we have now established the conceptual and computational basis for addressing the next major step, molecular complexes on the basis of accurate small molecule properties.

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