Distance geometry and related methods for protein structure determination from NMR data

The method of choice to reveal the conformation of protein molecules in atomic detail has been X-ray single-crystal analysis. Since the first structural analysis of diffraction patterns, computer calculations have been an important tool in these studies (Blundell & Johnson, 1976). As is described by Sheldrick (1985), it has been taken for granted that a necessary first step in the determination of a protein structure would be writing computer programs to fit structure factors. In contrast the combined use of the structural analysis of NMR data and computer calculations has been quite limited. An early attempt of such structural calculations was the quantitative determination of mononucleotide conformations in solution using lanthanide ion shifts (Barry et al. 1971

Efficient minimization of multipole electrostatic potentials in torsion space

The development of models of macromolecular electrostatics capable of delivering improved fidelity to quantum mechanical calculations is an active field of research in computational chemistry. Most molecular force field development takes place in the context of models with full Cartesian coordinate degrees of freedom. Nevertheless, a number of macromolecular modeling programs use a reduced set of conformational variables limited to rotatable bonds. Efficient algorithms for minimizing the energies of macromolecular systems with torsional degrees of freedom have been developed with the assumption that all atom-atom interaction potentials are isotropic. We describe novel modifications to address the anisotropy of higher order multipole terms while retaining the efficiency of these approaches. In addition, we present a treatment for obtaining derivatives of atom-centered tensors with respect to torsional degrees of freedom. We apply these results to enable minimization of the Amoeba multipole electrostatics potential in a system with torsional degrees of freedom, and validate the correctness of the gradients by comparison to finite difference approximations. In the interest of enabling a complete model of electrostatics with implicit treatment of solvent-mediated effects, we also derive expressions for the derivative of solvent accessible surface area with respect to torsional degrees of freedom

Boundary value approaches to molecular dynamics simulation

The focus of the research of this dissertation is the mathematical modeling of and use of numerical methods for the study of the dynamics of conformational transitions of biomolecules like proteins and small peptides. While an IV-AA-MDS approach could be considered for this purpose, the focus of this dissertation is a related approach that is called boundary value all-atom molecular dynamics simulation (BV-AA-MDS) in this dissertation. This approach includes the application of a numerical method to seek numerical solutions to two-point boundary value problems (BVP\u27s) for systems of 2nd-order nonlinear ordinary differential equations (ODE\u27s).;In this dissertation, the mathematical framework of AA-MDS, BV-AA-MDS and some numerical methods for BV-AA-MDS---single shooting, multiple shooting, finite differences methods, and stochastic difference equation methods---are described. Important computational limitations of AA-MDS, BV-AA-MDS, and MS for BV-AA-MDS are highlighted and reasons for considering these approaches and methods despite the computational limitations will be provided.;Also, in this dissertation, the application of multiple shooting to BVP\u27s for ODE\u27s corresponding to transitions between two molecular conformations specified by two sets of internal coordinates is proposed. Strategies and issues related to definition of boundary conditions, assignment of initial parameters, and convergence are investigated. Results from the study of transitions between local minima of the potential energy surface of an alanine dipeptide are presented. Implications of the methods and results of this work for application of multiple shooting to the study of conformational transitions in larger systems are discussed.;Defining boundary conditions corresponding to sets of internal coordinates of local minima leads to what is defined to be a full set of 6n boundary conditions, i.e. R = 6n. And, defining parameters of the multiple shooting method as the initial conditions on each subinterval leads to what is defined to be a full set of 6nN parameters. To apply multiple shooting with a full set of parameters to a BVP with a full set of boundary conditions, the number of atoms in the molecule must be limited to avoid excessive computational cost. In this dissertation, for the case of single shooting, an alternate boundary value simulation approach is presented that involves a reduced set of boundary conditions and a reduced set of parameters. We also propose an approach for use a reduced parameter set that is based on an application of principles of normal mode analysis. We provide results from the application of these approaches to the study of transitions between potential energy wells for an alanine dipeptide.;In this dissertation, all-atom distance matrix interpolation (AA-DMI) methods are described. These are methods for generating position trajectories that satisfy certain types of boundary conditions are less computationally demanding than boundary value approaches to AA-MDS, but do provide atomically detailed trajectories. These methods involve an optimization problem with an objective function derived by interpolation of interatomic distances between their values in one conformation and their values in another conformation. Results are presented from the study of conformational transitions of an alanine dipeptide. Future directions of research are discussed. (Abstract shortened by UMI.

Modeling Symmetric Macromolecular Structures in Rosetta3

Symmetric protein assemblies play important roles in many biochemical processes. However, the large size of such systems is challenging for traditional structure modeling methods. This paper describes the implementation of a general framework for modeling arbitrary symmetric systems in Rosetta3. We describe the various types of symmetries relevant to the study of protein structure that may be modeled using Rosetta's symmetric framework. We then describe how this symmetric framework is efficiently implemented within Rosetta, which restricts the conformational search space by sampling only symmetric degrees of freedom, and explicitly simulates only a subset of the interacting monomers. Finally, we describe structure prediction and design applications that utilize the Rosetta3 symmetric modeling capabilities, and provide a guide to running simulations on symmetric systems

Modeling and simulation of intrinsically disordered proteins

This work is primarily about the development, validation and application of computer simulation models for intrinsically disordered proteins, both in solution and in the presence of uniformly charged, ideal surfaces. The models in question are either coarse-grained or atomistic in nature, and their applications are dependent on the specific purpose of each study. Both, Metropolis Monte Carlo and molecular dynamics simulations were employed to execute them.In regard to the coarse-grained models, it was found that a simple physical model can be used to mimic the properties of flexible proteins, helping to understand how and why these proteins adsorb to surfaces under certain conditions. The same model later shown that two disordered proteins from different sources (saliva and milk) possess similar structural and thermodynamic properties in solution and when adsorbed to surfaces, thus being hypothesized that it may be possible to use one of them as a substitute for the other under a pharmaceutical context.After a first indication that the atomistic models used until recently for the simulation of well-folded proteins may not be applicable to their disordered counterparts, it was then confirmed - by evaluating several such models against experimental evidence - that these models do indeed produce overly collapsed IDP conformational ensembles. New models, favoring protein–water over protein–protein interactions, were then shown to effectively produce more extended conformations, which are in much better agreement with each other and with experimental evidence. One of the new atomistic models was then used to perform the structural characterization of a disordered peptide conjugated to a small molecule, which has been shown to possess promising therapeutical applications. The value of computer simulations is well illustrated in this study, as the insight obtainable from experiment was limited and it was only through the analysis of the simulations that a possible link between the average conjugate structure and its increased antifungal activity is established

Application of computer simulation approaches to study the structure and properties of polymeric systems

The study at the nanoscopic level of the polymeric systems is a keystone for a deeper understanding of their internal structure and properties, not only at nanometric scale but also at macroscopic level. The disciplines involved in this scientific field are diverse, including areas such as chemistry, physics, material science, biology and statistics among others. The aforementioned fields converge in a scientific and technologic central branch called nanotechnology. In the last decades, nanotechnology based on polymeric systems has aroused a great interest among the scientific community, as is clearly evidenced by the huge amount of scientific publications and applications developed within this area. However, the experimental complexity for the development of new devices and the economical limitations devoted to this end are barriers that let us think about the use of alternative approaches in this scientific field. In the face of this endeavors, the application of computer simulation methodologies to must be taken into account. The principal focus of this Thesis is the study at the atomic and molecular level of some polymeric systems through theoretical methodologies based on quantum and classical mechanics formalisms. Such methods allow us to support and understand some chemical and physical observables as well as to analyze and describe these systems at their structural level. Within the framework of the application of the atomic and molecular simulation methodologies, this Thesis could be divided mainly in three main research lines: Conducting Polymers, Polymeric Cation Exchange Membranes, and Dendrimers and Dendronized Polymers The first one focusses on evaluating the detection ability of different conducting polymers when they interact with dopamine or morphine with the final aim of developing a sensor based on these materials. The examination of conducting polymers sensitivity to the analyte detection was carried out via inspection of their ability to form secondary interactions (i.e. weak and strong hydrogen bonds, p-stacking interactions), which was examined using quantum mechanical calculations. Second line is devoted to the application of atomistic molecular dynamics simulation for the investigation of the influence of the electric field strength and the temperature in the dynamical and structural properties of cationic exchange membranes. These investigations were focused on the analysis of hydronium transport mechanism, internal structural rearrangements of the membrane and the characteristics of the hydration shell surrounding the diffused hydronium ions. The last working line of this Thesis is centered on the study at electronic and atomic level of dendritic molecules and dendronized polymers through both quantum and classical mechanics formalisms. The structural properties and molecular interactions occurring in a particular class of dendronized polymers were analyzed. On one side, through a characterization of the inter and intramolecular non bonded interactions of two interacting polymer chains in an attempt to relate atomistic information to the rheological response of these large cylindrical-shape objects. On the other side, studying the internal structure and solvent absorption ability of these systems positively charged and comparing them with their neutral analogues. Finally, studies of both dendrimers and dendronized polymers based on all-thiophene dendrons trough quantum mechanics and molecular dynamics were performed. The electronic properties of symmetric and unsymmetric all-thiophene dendrimers containing up to 45 thiophene rings in neutral and oxidized state was investigated. On the other hand, the internal organization of second and third generation macromonomers and dendronized polymers based on all-thiophene dendrons was studied using density functional theory calculations and classical molecular dynamics simulations, respectively.El estudio a nivel nanoscópico de sistemas poliméricos es un punto clave para la comprensión de su estructura atómica y de sus propiedades, no solamente a escala nanométrica sino también a nivel macroscópico. Las disciplinas involucradas en este campo son diversas e incluyen áreas tales como la química, física, ciencia de materiales y estadística, entre otras. Todos estos campos convergen en una rama científica y tecnológica denominada nanotecnología. En los últimos años, el uso de sistemas poliméricos dentro del campo de la nanotecnología ha suscitado un gran interés dentro de la comunidad científica, tal como queda manifiesto debido al gran número de publicaciones científicas y aplicaciones desarrolladas. Sin embargo tanto el grado de complejidad que implica el desarrollo de nuevos dispositivos dentro de esta disciplina como las limitaciones económicas existentes para estos fines, han hecho que los métodos de simulación molecular sean una herramienta clave para continuar avanzando en esta línea de investigación. El propósito de esta Tesis es el estudio de algunos sistemas poliméricos a nivel atómico y molecular mediante métodos teóricos basados en mecánica cuántica y clásica. Dichos métodos nos han permitido corroborar y entender propiedades físico-químicas a la vez que analizar y describir estos sistemas a nivel estructural. Dentro del marco de la aplicación de métodos de simulación atomístico y molecular, esta tesis puede dividirse en tres líneas de trabajo: Polímeros Conductores, Membranas Poliméricas de Intercambio Catiónico, y Polímeros Dendríticos. En la primera línea se ha evaluado, a partir de estudios cuánticos, la capacidad de detección de diversos polímeros conductores al interactuar con morfina o dopamina; con el objetivo final de desarrollar sensores basados en dichos materiales. Los análisis de sensibilidad de estos polímeros para la detección de dichos analitos se llevaron a cabo mediante el estudio de la capacidad que presentan estos sistemas para formar interacciones secundarias (i.e. puentes de hidrógeno y p-stacking). En segundo lugar se han llevado a cabo estudios atomísticos basados en dinámica molecular para estudiar la influencia de la intensidad del campo eléctrico y de la temperatura en las propiedades dinámicas y estructurales que tienen lugar en membranas de intercambio catiónico. Estas investigaciones se centraron en el análisis de los mecanismos de transporte de los iones hidronio, los cambios sufridos a nivel estructural dentro de la membrana y la caracterización de la capa de hidratación que rodea los a los iones difundidos. La última línea de trabajo está centrada en el estudio tanto a nivel electrónico como atomístico de moléculas dendríticas y polímeros dendronizados mediante mecánica cuántica y clásica. Se llevaron a cabo análisis de las propiedades estructurales así como de las interacciones moleculares que tienen lugar en una clase particular de polímeros dendronizados. Por un lado, mediante la caracterización de las interacciones inter e intramoleculares de dos cadenas poliméricas interpenetradas con el objetivo de establecer la relación existente entre la información atomística obtenida y las propiedades viscoelásticas propias de estos objetos cilíndricos. Por otro lado, mediante un estudio comparativo de estos sistemas en estado neutro y cargado para determinar como la distribución de carga afecta a su estructura interna y a su capacidad de absorción en disolución. Finalmente, se han estudiado dendrímeros y polímeros dendronizados basados en dendrones de tiofeno. Se investigaron propiedades electrónicas de estructuras simétricas y asimétricas de dendrímeros con hasta 45 anillos de tiofeno en estado neutro y oxidado. Además, se analizó la organización interna de macromonómeros basados en dendrones de tiofeno de 2ª y 3ª generación así como de sus correspondientes polímeros mediante cálculos de teoría de funcional de densidad y mediante simulaciones de dinámica molecular, respectivamente.Postprint (published version

Molecular simulations of conformational transitions in biomolecules using a novel computational tool

The function of biological macromolecules is inherently linked to their complex conformational behaviour. As a consequence, the corresponding potential energy landscape encompasses multiple minima. Some of the intermediate structures between the initial and final states can be characterized by experimental techniques. Computer simulations can explore the dynamics of individual states and bring these together to rationalize the overall process. A novel method based on atomistic structure-based potentials in combination with the empirical valence bond theory (EVB-SBP) has been developed and implemented in the Amber package. The method has been successfully applied to explore various biological processes. The first application of the EVB-SBP approach involves the study of base flipping in B-DNA. The use of simple structurebased potentials are shown to reproduce structural ensembles of stable states obtained by using more accurate force field simulations. Umbrella sampling in conjunction with the energy gap reaction coordinate enables the study of alternative molecular pathways efficiently. The main application of the method is the study of the switching mechanism in a short bistable RNA. Molecular pathways, which connect the two stable states, have been elucidated, with particular interest to the characterisation of the transition state ensemble. In addition, NMR experiments have been performed to support the theoretical findings. Finally, a recent study of large-scale conformational transitions in protein kinases shows the general applicability of the method to different biomolecules

Molecular Simulation Studies on the Prion Protein Variants: Insights into the Intriguing Effects of Mutations

Prion diseases, or transmissible spongiform encephalopathies (TSE), are a group of rare fatal neurodegenerative maladies that affect humans and animals. The fundamental breakthrough in TSE research was the discovery of the "prion"\u23afproteinaceous infectious particle\u23af and the verification of the \u201cprotein-only\u201d hypothesis, which states that prions could self-propagate by converting the cellular prion protein (PrPC) into the scrapie form, PrPSc (or prions), and lead to neurodegeneration without using any nucleic acids. The concept of prions may unify neurodegenerative diseases under a common pathogenic mechanism. Indeed, growing evidence shows that TSE may share similar pathogenesis with common neurodegenerative syndromes such as Alzheimer\u2019s disease and Parkinson\u2019s disease, for which there are currently no cure. Today, PrP is one of the most studied models for protein misfolding mechanism and TSE serve as an excellent model for studying many other neurodegenerative diseases. Understanding the molecular mechanism of the PrP misfolding process may profoundly influence the development of diagnostics and effective therapies for neurodegenerative diseases in general. Investigating human (Hu) PrP TSE-linked mutations (more than 50 currently identified mutations, linked to ~15% of the cases) may be very instrumental in this respect, as it can provide hints on the molecular basis of the PrPC\u2192PrPSc conversion. These mutations cause spontaneous TSE, which are likely due to modifications in the native structure of PrPC. They are located all over the structure. Polymorphisms (i.e. non-pathogenic, naturally occurring mutations) in the PrP gene have been found to influence the etiology and neuropathology of the disease in both humans and sheep. In transgenic (Tg) mice, artificial mutations can determine the susceptibility to the infection of different prion strains. Intriguingly, mouse (Mo) PrP containing artificial mutations (denoted MoPrP chimera, hereinafter) have very different effects in vitro: some MoPrP chimera were found to resist PrPSc infection, whereas some others did not; some of the resistant MoPrP chimeras even exhibited a protective effect (known as the dominant-negative effect) over the co-expressed endogenous wild-type (WT) MoPrPC. Most mutations are located in the folded globular domain (GD) while fewer are located in the intrinsically disordered N-terminal domain (N-term). The N-term of PrPC has been suggested to serve multiple functions in vivo, which likely relies on the structural flexibility of this domain. Therefore, characterizing the structural features of the N-term is central for investigating not only the mutations in this domain, but also the physiological role of the N-term. Based on previous studies in our lab, in this thesis we first applied molecular dynamics simulations to studying the impact of all the known Hu TSE-linked mutations in HuPrPC GD. We next applied the same approach to study the GD structure of MoPrP chimeras which contain one or two residues from Hu or sheep PrP sequence. By studying these PrP variants, we aim to identify the structural determinants of the mutants that may play a role in the PrPC\u2192PrPSc conversion. Our calculations discovered that these mutants exhibit different structural features from those of the WT PrP GD mainly in two common regions that are likely the \u201chot spots\u201d in the protein misfolding process. These features can be classified into different types that are correlated to the types of mutants (i.e. pathogenic, resistant or dominant-negative), thus hinting to the molecular mechanisms of PrPSc formation and propagation. We have then predicted the structure of the entire PrP N-term and the impact of the Hu TSE-linked mutations in this domain using a novel Monte Carlo-based simulation approach, PROFASI. PROFASI has already shown to provide structural predictions in a disordered protein such as \u3b1-synuclein. Our results are consistent with available experimental data and therefore firmly allow us to provide the first overview on the structural determinants of all Hu TSE-linked mutations in PrP