Knowledge-based energy functions for computational studies of proteins

This chapter discusses theoretical framework and methods for developing knowledge-based potential functions essential for protein structure prediction, protein-protein interaction, and protein sequence design. We discuss in some details about the Miyazawa-Jernigan contact statistical potential, distance-dependent statistical potentials, as well as geometric statistical potentials. We also describe a geometric model for developing both linear and non-linear potential functions by optimization. Applications of knowledge-based potential functions in protein-decoy discrimination, in protein-protein interactions, and in protein design are then described. Several issues of knowledge-based potential functions are finally discussed.Comment: 57 pages, 6 figures. To be published in a book by Springe

A Novel Empirical Free Energy Function That Explains And Predicts Protein–Protein Binding Affinities

A free energy function can be defined as a mathematical expression that relates macroscopic free energy changes to microscopic or molecular properties. Free energy functions can be used to explain and predict the affinity of a ligand for a protein and to score and discriminate between native and non-native binding modes. However, there is a natural tension between developing a function fast enough to solve the scoring problem but rigorous enough to explain and predict binding affinities. Here, we present a novel, physics-based free energy function that is computationally inexpensive, yet explanatory and predictive. The function results from a derivation that assumes the cost of polar desolvation can be ignored and that includes a unique and implicit treatment of interfacial water-bridged interactions. The function was parameterized on an internally consistent, high quality training set giving R 2 =0.97 and Q 2 =0.91. We used the function to blindly and successfully predict binding affinities for a diverse test set of 31 wild-type protein–protein and protein–peptide complexes (R 2 =0.79, rmsd=1.2 kcal mol−1). The function performed very well in direct comparison with a recently described knowledge-based potential and the function appears to be transferable. Our results indicate that our function is well suited for solving a wide range of protein/peptide design and discovery problems

Prediction of hot spot residues at protein-protein interfaces by combining machine learning and energy-based methods

Background: Alanine scanning mutagenesis is a powerful experimental methodology for investigating the structural and energetic characteristics of protein complexes. Individual aminoacids are systematically mutated to alanine and changes in free energy of binding (Delta Delta G) measured. Several experiments have shown that protein-protein interactions are critically dependent on just a few residues ("hot spots") at the interface. Hot spots make a dominant contribution to the free energy of binding and if mutated they can disrupt the interaction. As mutagenesis studies require significant experimental efforts, there is a need for accurate and reliable computational methods. Such methods would also add to our understanding of the determinants of affinity and specificity in protein-protein recognition.Results: We present a novel computational strategy to identify hot spot residues, given the structure of a complex. We consider the basic energetic terms that contribute to hot spot interactions, i.e. van der Waals potentials, solvation energy, hydrogen bonds and Coulomb electrostatics. We treat them as input features and use machine learning algorithms such as Support Vector Machines and Gaussian Processes to optimally combine and integrate them, based on a set of training examples of alanine mutations. We show that our approach is effective in predicting hot spots and it compares favourably to other available methods. In particular we find the best performances using Transductive Support Vector Machines, a semi-supervised learning scheme. When hot spots are defined as those residues for which Delta Delta G >= 2 kcal/mol, our method achieves a precision and a recall respectively of 56% and 65%.Conclusion: We have developed an hybrid scheme in which energy terms are used as input features of machine learning models. This strategy combines the strengths of machine learning and energy-based methods. Although so far these two types of approaches have mainly been applied separately to biomolecular problems, the results of our investigation indicate that there are substantial benefits to be gained by their integration

Intuitive, But Not Simple: Including Explicit Water Molecules in Protein-Protein Docking Simulations Improves Model Quality

Characterizing the nature of interaction between proteins that have not been experimentally co-crystallized requires a computational docking approach that can successfully predict the spatial conformation adopted in the complex. In this work, the Hydropathic INTeractions (HINT) force field model was used for scoring docked models in a data set of 30 high-resolution crystallographically characterized “dry” protein-protein complexes, and was shown to reliably identify native-like models. However, most current protein-protein docking algorithms fail to explicitly account for water molecules involved in bridging interactions that mediate and stabilize the association of the protein partners, so we used HINT to illuminate the physical and chemical properties of bridging waters and account for their energetic stabilizing contributions. The HINT water Relevance metric identified the ‘truly’ bridging waters at the 30 protein-protein interfaces and we utilized them in “solvated” docking by manually inserting them into the input files for the rigid body ZDOCK program. By accounting for these interfacial waters, a statistically significant improvement of ~24% in the average hit-count within the top-10 predictions the protein-protein dataset was seen, compared to standard “dry” docking. The results also show scoring improvement, with medium and high accuracy models ranking much better than incorrect ones. These improvements can be attributed to the physical presence of water molecules that alter surface properties and better represent native shape and hydropathic complementarity between interacting partners, with concomitantly more accurate native-like structure predictions

Quantifying the Role of Water in Ligand-Protein Binding Processes

The aim of this thesis is to quantify the contributions of water thermodynamics to the binding free energy in protein-ligand complexes. Various computational tools were directly applied, implemented, benchmarked and discussed. An own implementation of the IFST formulation was developed to facilitate easy integration in workflows that are based on Schrödinger software. By applying the tool to a well-defined test set of congeneric ligand pairs, the potential of IFST for quantitative predictions in lead-optimization was assessed. Furthermore, FEP calculations were applied to an extended test set to validate if these simulations can accurately account for solvent displacement in ligand modifications. As a fast tool that has applications in virtual screening problems, we finally developed and validated a new scoring function that incorporates terms for protein and ligand desolvation. This resulted in total in three distinct studies, that all elucidated different aspects of water thermodynamics in CADD. These three studies are presented in the next section. In the conclusion, the results and implications of these studies are discussed jointly, as well with possible future developments. An additional study was focused on virtual screening and toxicity prediction at the androgen receptor, where distinguishing agonists and antagonists poses difficulties. We proposed and validated an approach based on MD simulations and ensemble docking to improve predictions of androgen agonists and antagonists

How interface geometry dictates water's thermodynamic signature in hydrophobic association

As a common view the hydrophobic association between molecular-scale binding partners is supposed to be dominantly driven by entropy. Recent calorimetric experiments and computer simulations heavily challenge this established paradigm by reporting that water's thermodynamic signature in the binding of small hydrophobic ligands to similar-sized apolar pockets is enthalpy-driven. Here we show with purely geometric considerations that this controversy can be resolved if the antagonistic effects of concave and convex bending on water interface thermodynamics are properly taken into account. A key prediction of this continuum view is that for fully complementary binding of the convex ligand to the concave counterpart, water shows a thermodynamic signature very similar to planar (large-scale) hydrophobic association, that is, enthalpy-dominated, and hardly depends on the particular pocket/ligand geometry. A detailed comparison to recent simulation data qualitatively supports the validity of our perspective down to subnanometer scales. Our findings have important implications for the interpretation of thermodynamic signatures found in molecular recognition and association processes. Furthermore, traditional implicit solvent models may benefit from our view with respect to their ability to predict binding free energies and entropies.Comment: accepted for publication in J. Stat. Phys., special issue on water&associated liquid