Protein Docking by the Underestimation of Free Energy Funnels in the Space of Encounter Complexes

Similarly to protein folding, the association of two proteins is driven by a free energy funnel, determined by favorable interactions in some neighborhood of the native state. We describe a docking method based on stochastic global minimization of funnel-shaped energy functions in the space of rigid body motions (SE(3)) while accounting for flexibility of the interface side chains. The method, called semi-definite programming-based underestimation (SDU), employs a general quadratic function to underestimate a set of local energy minima and uses the resulting underestimator to bias further sampling. While SDU effectively minimizes functions with funnel-shaped basins, its application to docking in the rotational and translational space SE(3) is not straightforward due to the geometry of that space. We introduce a strategy that uses separate independent variables for side-chain optimization, center-to-center distance of the two proteins, and five angular descriptors of the relative orientations of the molecules. The removal of the center-to-center distance turns out to vastly improve the efficiency of the search, because the five-dimensional space now exhibits a well-behaved energy surface suitable for underestimation. This algorithm explores the free energy surface spanned by encounter complexes that correspond to local free energy minima and shows similarity to the model of macromolecular association that proceeds through a series of collisions. Results for standard protein docking benchmarks establish that in this space the free energy landscape is a funnel in a reasonably broad neighborhood of the native state and that the SDU strategy can generate docking predictions with less than 5 � ligand interface Ca root-mean-square deviation while achieving an approximately 20-fold efficiency gain compared to Monte Carlo methods

MDM2 Case Study: Computational Protocol Utilizing Protein Flexibility Improves Ligand Binding Mode Predictions

Recovery of the P53 tumor suppressor pathway via small molecule inhibitors of onco-protein MDM2 highlights the critical role of computational methodologies in targeted cancer therapies. Molecular docking programs in particular, provide a quantitative ranking of predicted binding geometries based on binding free energy allowing for the screening of large chemical libraries in search of lead compounds for cancer therapeutics. This study found improved binding mode predictions of medicinal compounds to MDM2 using the popular docking programs AutoDock and AutoDock Vina, while adopting a rigid-ligand/flexible-receptor protocol. Crystal structures representing small molecule inhibitors bound to MDM2 were selected and a total of 12 rotatable bonds was supplied to each complex and distributed systematically between the ligand and binding site residues. Docking results were evaluated in terms of the top ranked binding free energy and corresponding RMSD values from the experimentally known binding site. Results show lowest RMSD values coincide with a rigid ligand, while the protein retained the majority of flexibility. This study suggests the future implementation of a rigid-ligand/flexible-receptor protocol may improve accuracy of high throughput screenings of potential cancer drugs targeting the MDM2 protein, while maintaining manageable computational costs

Constrained optimization applied to multiscale integrative modeling

Multiscale integrative modeling stands at the intersection between experimental and computational techniques to predict the atomistic structures of important macromolecules. In the integrative modeling process, the experimental information is often integrated with energy potential and macromolecular substructures in order to derive realistic structural models. This heterogeneous information is often combined into a global objective function that quantifies the quality of the structural models and that is minimized through optimization. In order to balance the contribution of the relative terms concurring to the global function, weight constants are assigned to each term through a computationally demanding process. In order to alleviate this common issue, we suggest to switch from the traditional paradigm of using a single unconstrained global objective function to a constrained optimization scheme. The work presented in this thesis describes the different applications and methods associated with the development of a general constrained optimization protocol for multiscale integrative modeling. The initial implementation concerned the prediction of symmetric macromolecular assemblies throught the incorporation of a recent efficient constrained optimizer nicknamed mViE (memetic Viability Evolution) to our integrative modeling protocol power (parallel optimization workbench to enhance resolution). We tested this new approach through rigorous comparisons against other state-of-the-art integrative modeling methods on a benchmark set of solved symmetric macromolecular assemblies. In this process, we validated the robustness of the constrained optimization method by obtaining native-like structural models. This constrained optimization protocol was then applied to predict the structure of the elusive human Huntingtin protein. Due to the fact that little structural information was available when the project was initiated, we integrated information from secondary structure prediction and low-resolution experiments, in the form of cryo-electron microscopy maps and crosslinking mass spectrometry data, in order to derive a structural model of Huntingtin. The structure resulting from such integrative modeling approach was used to derive dynamic information about Huntingtin protein. At a finer level of resolution, the constrained optimization protocol was then applied to dock small molecules inside the binding site of protein targets. We converted the classical molecular docking problem from an unconstrained single objective optimization to a constrained one by extracting local and global constraints from pre-computed energy grids. The new approach was tested and validated on standard ligand-receptor benchmark sets widely used by the molecular docking community, and showed comparable results to state-of-the-art molecular docking programs. Altogether, the work presented in this thesis proposed improvements in the field of multiscale integrative modeling which are reflected both in the quality of the models returned by the new constrained optimization protocol and in the simpler way of treating the uncorrelated terms concurring to the global scoring scheme to estimate the quality of the models

COMBINATORIAL LIBRARY DESIGN OF MUTATION-RESISTANT HIV PROTEASE INHIBITORS.

The emergence of HIV strains that are resistant to current HIV protease inhibitors in the past few years has become a major concern in AIDS treatment. The goal of this project is to design a combinatorial library of potential lead compounds that can bind to both the wild-type and mutant proteases and that can resist further mutations. A recent crystallographic study of complexes of HIV protease with its substrates has provided structural insights into the differential recognition of the substrates and inhibitors. It has been proposed that clinical resistance is a consequence of inhibitors failure to stay within the consensus substrate volume. In this work, we devised a quantitative indicator of the degree to which a candidate ligand falls outside the consensus substrate volume, and determined its correlation with the inhibitor's sensitivity to clinically relevant resistant mutations. The validation of this hypothesis has encouraged us to use this strategy in our design of a combinatorial library of inhibitors. The compounds in a typical combinatorial library are built around a common structural scaffold possessing multiple connection points where substituents can be added by reliable synthetic steps. As the number of compounds encompassed by such a combinatorial scheme frequently exceeds what can actually be synthesized and tested, virtual screening methods are sought to shortlist the compounds. Even though these methods require only seconds to minutes of CPU time per compound, exhaustive screening of an entire virtual combinatorial library is computationally demanding. We therefore implemented a simple algorithm of combining substituents that have been optimized independently for the substituent sites. This method was compared with Genetic Algorithm, a global optimization method and was found equally efficient. This simple method was hence chosen for the design process. A combinatorial library based on these ideas and methods has been synthesized and tested. It includes four compounds with nanomolar inhibition constants. Two of them were shown to have retained affinity against a panel of treatment-resistant mutations

On deep generative modelling methods for protein-protein interaction

Proteins form the basis for almost all biological processes, identifying the interactions that proteins have with themselves, the environment, and each other are critical to understanding their biological function in an organism, and thus the impact of drugs designed to affect them. Consequently a significant body of research and development focuses on methods to analyse and predict protein structure and interactions. Due to the breadth of possible interactions and the complexity of structures, \textit{in sillico} methods are used to propose models of both interaction and structure that can then be verified experimentally. However the computational complexity of protein interaction means that full physical simulation of these processes requires exceptional computational resources and is often infeasible. Recent advances in deep generative modelling have shown promise in correctly capturing complex conditional distributions. These models derive their basic principles from statistical mechanics and thermodynamic modelling. While the learned functions of these methods are not guaranteed to be physically accurate, they result in a similar sampling process to that suggested by the thermodynamic principles of protein folding and interaction. However, limited research has been applied to extending these models to work over the space of 3D rotation, limiting their applicability to protein models. In this thesis we develop an accelerated sampling strategy for faster sampling of potential docking locations, we then address the rotational diffusion limitation by extending diffusion models to the space of $SO(3)$ and finally present a framework for the use of this rotational diffusion model to rigid docking of proteins

Dynamics of the Acetylcholinesterase Tetramer

Acetylcholinesterase rapidly hydrolyzes the neurotransmitter acetylcholine in cholinergic synapses, including the neuromuscular junction. The tetramer is the most important functional form of the enzyme. Two low-resolution crystal structures have been solved. One is compact with two of its four peripheral anionic sites (PAS) sterically blocked by complementary subunits. The other is a loose tetramer with all four subunits accessible to solvent. These structures lacked the C-terminal amphipathic t-peptide (WAT domain) that interacts with the proline-rich attachment domain (PRAD). A complete tetramer model (AChEt) was built based on the structure of the PRAD/WAT complex and the compact tetramer. Normal mode analysis suggested that AChEt could exist in several conformations with subunits fluctuating relative to one another. Here, a multiscale simulation involving all-atom molecular dynamics and Cα-based coarse-grained Brownian dynamics simulations was carried out to investigate the large-scale intersubunit dynamics in AChEt. We sampled the ns-μs timescale motions and found that the tetramer indeed constitutes a dynamic assembly of monomers. The intersubunit fluctuation is correlated with the occlusion of the PAS. Such motions of the subunits “gate” ligand-protein association. The gates are open more than 80% of the time on average, which suggests a small reduction in ligand-protein binding. Despite the limitations in the starting model and approximations inherent in coarse graining, these results are consistent with experiments which suggest that binding of a substrate to the PAS is only somewhat hindered by the association of the subunits

PARAMETERIZATION OF AN ENERGY MODEL FOR SCORING OF ANTI-HIV DRUGS AND A COMPUTATIONAL METHOD OF LEAD COMPOUND OPTIMIZATION FOR DRUG DISCOVERY

This project aims to parameterize an energy model with the goal of developing a fast method for predicting binding affinities of HIVP inhibitors. This method will be used for in silico compound screening to discover new potential anti-HIV drug candidates. The project also aims to develope a method of optimizing the charges of local parts of a ligand while keeping the rest of the charges roughly constant, rather than attempting to modify all of the ligand's charges towards an optimum, as done in previous approaches. The method developed here will also be computationally faster than existing approaches

Robust Search Methods for Rational Drug Design Applications

The main topic of this thesis is the development of computational search methods that are useful in drug design applications. The emphasis is on exhaustiveness of the search method such that it can guarantee a certain level of geometric accuracy. In particular, the following two problems are addressed: (i) Prediction of binding mode of a drug molecule to a receptor and (ii) prediction of crystal structures of drug molecules. Predicting the binding mode(s) of a drug molecule to a target receptor is pivotal in structure-based rational drug design. In contrast to most approaches to solve this problem, the idea in this work is to analyze the search problem from a computational perspective. By building on top of an existing docking tool, new methods are proposed and relevant computational results are proven. These methods and results are applicable for other place-and-join frameworks as well. A fast approximation scheme for the docking of rigid fragments is described that guarantees certain geometric approximation factors. It is also demonstrated that this can be translated into an energy approximation for simple scoring functions. A polynomial time algorithm is developed for the matching phase of the docked rigid fragments. It is demonstrated that the generic matching problem is NP-hard. At the same time the optimality of the proposed algorithm is proven under certain scoring function conditions. The matching results are also applicable for some of the fragment-based de novo design methods. On the practical side, the proposed method is tested on 829 complexes from the PDB. The results show that the closest predicted pose to the native structure has the average RMS deviation of 1.06 °A. The prediction of crystal structures of small organic molecules has significantly improved over the last two decades. Most of the new developments, since the first blind test held in 1999, have occurred in the lattice energy estimation subproblem. In this work, a new efficient systematic search method that avoids random moves is proposed. It systematically searches through the space of possible crystal structures and conducts search space cuts based on statistics collected from the structural databases. It is demonstrated that the fast search method for rigid molecules can be extended to include flexible molecules as well. Also, the results of some prediction experiments are provided showing that in most cases the systematic search generates a structure with less than 1.0°A RMSD from the experimental crystal structure. The scoring function that has been developed for these experiments is described briefly. It is also demonstrated that with a more accurate lattice energy estimation function, better results can be achieved with the proposed robust search method

Optimización multi-objetivo en las ciencias de la vida.

Para conseguir este objetivo, en lugar de intentar incorporar nuevos algoritmos directamente en el código fuente de AutoDock, se utilizó un framework orientado a la resolución de problemas de optimización con metaheurísticas. Concretamente, se usó jMetal, que es una librería de código libre basada en Java. Ya que AutoDock está implementado en C++, se desarrolló una versión en C++ de jMetal (posteriormente distribuida públicamente). De esta manera, se consiguió integrar ambas herramientas (AutoDock 4.2 y jMetal) para optimizar la energía libre de unión entre compuesto químico y receptor. Después de disponer de una amplia colección de metaheurísticas implementadas en jMetalCpp, se realizó un detallado estudio en el cual se aplicaron un conjunto de metaheurísticas para optimizar un único objetivo minimizando la energía libre de unión, el cual es el resultado de la suma de todos los términos de energía de la función objetivo de energía de AutoDock 4.2. Por lo tanto, cuatro metaheurísticas tales como dos variantes de algoritmo genético gGA (Algoritmo Genético generacional) y ssGA (Algoritmo Genético de estado estacionario), DE (Evolución Diferencial) y PSO (Optimización de Enjambres de Partículas) fueron aplicadas para resolver el problema del acoplamiento molecular. Esta fase se dividió en dos subfases en las que se usaron dos conjuntos de instancias diferentes, utilizando como receptores HIV-proteasas con cadenas laterales de aminoacidos flexibles y como ligandos inhibidores HIV-proteasas flexibles. El primer conjunto de instancias se usó para un estudio de configuración de parámetros de los algoritmos y el segundo para comparar la precisión de las conformaciones ligando-receptor obtenidas por AutoDock y AutoDock+jMetalCpp. La siguiente fase implicó aplicar una formulación multi-objetivo para resolver problemas de acoplamiento molecular dados los resultados interesantes obtenidos en estudios previos existentes en los que dos objetivos como la energía intermolecular y la energía intramolecular fueron minimizados. Por lo tanto, se comparó y analizó el rendimiento de un conjunto de metaheurísticas multi-objetivo mediante la resolución de complejos flexibles de acoplamiento molecular minimizando la energía inter- e intra-molecular. Estos algoritmos fueron: NSGA-II (Algoritmo Genético de Ordenación No dominada) y su versión de estado estacionario (ssNSGA-II), SMPSO (Optimización Multi-objetivo de Enjambres de Partículas con Modulación de Velocidad), GDE3 (Tercera versión de la Evolución Diferencial Generalizada), MOEA/D (Algoritmo Evolutivo Multi-Objetivo basado en la Decomposición) y SMS-EMOA (Optimización Multi-objetivo Evolutiva con Métrica S). Después de probar enfoques multi-objetivo ya existentes, se probó uno nuevo. En concreto, el uso del RMSD como un objetivo para encontrar soluciones similares a la de la solución de referencia. Se replicó el estudio previo usando este conjunto diferente de objetivos. Por último, se analizó de forma detallada el algoritmo que obtuvo mejores resultados en los estudios previos. En concreto, se realizó un estudio de variantes del SMPSO minimizando la energía intermolecular y el RMSD. Este estudio proporcionó algunas pistas sobre cómo nuevos algoritmos basados en SMPSO pueden ser adaptados para mejorar los resultados de acoplamiento molecular para aquellas simulaciones que involucren ligandos y receptores flexibles. Esta tesis demuestra que la inclusión de técnicas metaheurísticas de jMetalCpp en la herramienta de acoplamiento molecular AutoDock incrementa las posibilidades a los usuarios de ámbito biológico cuando resuelven el problema del acoplamiento molecular. El uso de técnicas de optimización mono-objetivo diferentes aparte de aquéllas ampliamente usadas en las comunidades de acoplamiento molecular podría dar lugar a soluciones de mayor calidad. En nuestro caso de estudio mono-objetivo, el algoritmo de evolución diferencial obtuvo mejores resultados que aquellos obtenidos por AutoDock. También se propone diferentes enfoques multi-objetivo para resolver el problema del acoplamiento molecular, tales como la decomposición de los términos de la energía de unión o el uso del RMSD como un objetivo. Finalmente, se demuestra que el SMPSO, una metaheurística de optimización multi-objetivo de enjambres de partículas, es una técnica remarcable para resolver problemas de acoplamiento molecular cuando se usa un enfoque multi-objetivo, obteniendo incluso mejores soluciones que las técnicas mono-objetivo.Las herramientas de acoplamiento molecular han llegado a ser bastante eficientes en el descubrimiento de fármacos y en el desarrollo de la investigación de la industria farmacéutica. Estas herramientas se utilizan para elucidar la interacción de una pequeña molécula (ligando) y una macro-molécula (diana) a un nivel atómico para determinar cómo el ligando interactúa con el sitio de unión de la proteína diana y las implicaciones que estas interacciones tienen en un proceso bioquímico dado. En el desarrollo computacional de las herramientas de acoplamiento molecular los investigadores de este área se han centrado en mejorar los componentes que determinan la calidad del software de acoplamiento molecular: 1) la función objetivo y 2) los algoritmos de optimización. La función objetivo de energía se encarga de proporcionar una evaluación de las conformaciones entre el ligando y la proteína calculando la energía de unión, que se mide en kcal/mol. En esta tesis, se ha usado AutoDock, ya que es una de las herramientas de acoplamiento molecular más citada y usada, y cuyos resultados son muy precisos en términos de energía y valor de RMSD (desviación de la media cuadrática). Además, se ha seleccionado la función de energía de AutoDock versión 4.2, ya que permite realizar una mayor cantidad de simulaciones realistas incluyendo flexibilidad en el ligando y en las cadenas laterales de los aminoácidos del receptor que están en el sitio de unión. Se han utilizado algoritmos de optimización para mejorar los resultados de acoplamiento molecular de AutoDock 4.2, el cual minimiza la energía libre de unión final que es la suma de todos los términos de energía de la función objetivo de energía. Dado que encontrar la solución óptima en el acoplamiento molecular es un problema de gran complejidad y la mayoría de las veces imposible, se suelen utilizar algoritmos no exactos como las metaheurísticas, para así obtener soluciones lo suficientemente buenas en un tiempo razonable