Computational chemists have successfully simulated many systems by applying the principles of quantum mechanics, while approximate molecular mechanical models have seen great utility in problems of biochemical interest. In recent years, a number of methods have been developed to combine the advantages of both techniques. In this study the so-called QM/MM method is developed and applied to the determination of the free energy of a simple Menshutkin S_N2 chemical reaction. This is an extremely demanding process, well beyond the computational capacity of an average workstation, and thus a Beowulf-class Linux cluster is constructed to perform the calculations, and tested for a variety of computational chemistry applications. A number of methods for improving the QM/MM approach are considered in this work. The Fluctuating Charge, or FlucQ, polarizable molecular mechanics force field is implemented in a flexible manner within the CHARMM package and tested for a variety of systems, including the S_N2 test case. Several drawbacks of the original method are addressed and overcome. Both molecular dynamics and Monte Carlo techniques are used within the QM/MM framework to investigate the S_N2 reaction, and the two methods are compared. Techniques are developed and tested to increase the efficiency of QM/MC calculations to the point where they become competitive with QM/MD. Extremely expensive QM treatments are shown to be required to obtain accurate energies for the Menshutkin reaction. A method is developed and tested, and compared with the traditional ONIOM technique, for dramatically reducing the computational time required to use these treatments for QM/MC simulations, paving the way for fully ab initio high basis set QM/MM simulation.

One of the central tasks for biomolecular modeling is to develop accurate and computationally cheap methods. In this dissertation, we present the development of a brand new polarizable force field—Polarizable Simulations with Second order Interaction Model (POSSIM) involving electrostatic polarization. The POSSIM framework combines accuracy of a polarizable force field and computational efficiency of the second-order approximation of the full-scale induced point dipole polarization formalism. POSSIM force field has been extended to include parameters for small molecules serving as models for peptide and protein side-chains. Parameters have been fitted to permit reproducing many-body energies, gas-phase dimerization energies and geometries and liquid-phase heats of vaporization and densities. Quantum mechanical and experimental data have been used as the target for the fitting. The resulting parameters can be used for simulations of the parameterized molecules themselves or their analogues. In addition to this, these force field parameters have been employed in further development of the POSSIM fast polarizable force field for proteins. The POSSIM framework has been expanded to include a complete polarizable force field for proteins. Most of the parameter fitting was done to high-level quantum mechanical data. Conformational geometries and energies for dipeptides have been reproduced within average errors of ca. 0.5 kcal/mol for energies of the conformers (for the electrostatically neutral residues) and 9.7º for key dihedral angles. We have also validated this force field by simulating an elastin-like polypeptide GVG(VPGVG)3 in aqueous solution. Elastin-like peptides with the (VPGVG)n motif are known to exhibit anomalous behavior of their radius of gyration that increases when temperature is lowered (the so called inverse temperature transition). We have simulated the system with the OPLS-AA and POSSIM force fields and demonstrated that our newly developed polarizable POSSIM parameters permit to capture the experimentally observed decrease of the radius of gyration with increasing temperature, while the fixed-charges OPLS-AA ones do not. Furthermore, our fitting of the force field parameters for the peptides and proteins has been streamlined compared with the previous generation of the complete polarizable force field and relied more on transferability of parameters for non-bonded interactions (including the electrostatic component). The resulting deviations from the quantum mechanical data are similar to those achieved with the previous generation, thus the technique is robust and the parameters are transferable. At the same time, the number of parameters used in this work was noticeably smaller than that of the previous generation of our complete polarizable force field for proteins, thus the transferability of this set can be expected to be greater and the danger of force field fitting artifacts is lower. Therefore, we believe that this force field can be successfully applied in a wide variety of applications to proteins and protein-ligand complexes.

G-quadruplexes (GQs) are highly stable noncanonical nucleic acid structures that form in the DNA of human cells and play fundamental roles in maintaining genomic stability and regulating gene expression. These unique structures exert broad influence over biologically important processes and can modulate cell survival and human health. In fact, mutations, hyper-stability, and dissociation of GQs are implicated in neurodegenerative disease, mental retardation, premature-aging conditions, and various cancers. As such, GQs are novel drug targets. GQ-targeting therapeutics are developed to influence the folding and genetic interactions of GQs that are implicated in diseased states. To do so requires a greater understanding of GQ structure and dynamics and molecular dynamics (MD) simulations are well suited to provide these fundamental insights. Previous MD simulations of GQs have provided limited information due to inaccuracies in their models, namely the nonpolarizable nature of their force fields (FFs). The cutting-edge Drude polarizable FF models electronic degrees of freedom, allowing charge distribution to change in response to its environment. This is an important component for modeling ion-ion and ion-DNA interactions and can influence the overall stability of GQ structures. The work herein employs the Drude polarizable FF to 1) describe the role of electronic structure on the dynamics and folded stability of GQs, 2) determine the impact of ion interaction on GQ stability, and 3) characterize the role of G-hairpin motifs in GQ intermediates. Such fundamental investigations will help clarify GQs role in healthy and diseased states and transform our understanding of noncanonical DNA, improving human health, therapeutic design, and fundamental science. / Doctor of Philosophy / Human health and disease are influenced by unique nucleic acid structures called G-quadruplexes (GQs). GQs form when DNA or RNA fold into a square-shaped structure that is stabilized by ion interactions and special hydrogen bonding patterns. These GQ structures exert broad influence over normal biological processes, but also play a role in neurodegeneration, intellectual disabilities, premature-aging conditions, and various cancers, many of which are chemotherapeutic resistant. As such, modulating GQ structures, or their interactions with proteins, is a promising therapeutic approach. However, a greater understanding of GQ folding, folded structure, and interactions with other biomolecules is needed to do so. Computational techniques such as molecular dynamics (MD) simulations use experimental data and fundamental biophysics to gain new insights on these properties and inform novel drug design. In this project, we explored the dynamics of several distinct GQ structures and folding intermediates with state-of-the-art MD simulation methods. In doing so, we provided new insight on their structural features as well as their interactions with extended DNA sequences and different ion types, which serve as fundamental information for future structural or computer-aided drug design studies.

Le but de cette thèse est une revisite du potentiel SIBFA. Ceci inclut un travail et une réflexion sur la méthodologie de cette approche avec une implémentation proposant une utilisation plus large. De plus, une nouvelle calibration de champ de forces raffiné est permise aujourd’hui. En effet, la décomposition d’énergie intermoléculaire SAPT donne accès à toutes les composantes avec rigueur. La reproduction des résultats ab-initio par un potentiel analytique laisse entrevoir des applications prometteuses. Au-delà du coup de calcul considérablement réduit par rapport aux méthodes de chimie quantique, son intégration dans un code de dynamique moléculaire ouvre les portes à de nombreuses études encore plus prometteuses hors de portée de la chimie quantique. Enfin l’optimisation de ce code, avec une parallélisation bien étudiée, en feront un outil majeur de la biochimie. Dans une première partie, nous introduirons les notions et principes essentiels à la dynamique moléculaire. Un premier chapitre exposera la mécanique classique utilisé dans les programmes les plus distribués et utilisés. Un second chapitre introduira les méthodes permettant un meilleur traitement des interactions non-covalentes essentielles dans les études de complexes ligand-récepteur. Une seconde partie abordera de manière plus concrète la stratégie d’implémentation de SIBFA dans Tinker. Celle-ci s’organisera autour de trois chapitres, traitant chaque composante énergétique intermoléculaire. L’objectif de cette thèse est de proposer un socle solide autour du traitement des interactions non covalentes dans le cadre des champs de forces polarisables de dernières générations et de présenter le modèle d’eau hybride AMOEBA/SIBFA. / The purpose of this thesis is to revisit the potential of SIBFA (Sum of Interactions Between Fragments Ab initio computed) [...]

Cette thèse porte sur deux projets visant au développement de nouvelles approches pour simuler les dynamiques moléculaire et électronique avec application à des biomolécules étendues. Dans la première partie nous cherchons à améliorer significativement la précision des simulations des propriétés rédox des protéines. Dans ce contexte, l'objectif est de recourir à de champ de force reposant sur une description multipolaire des interactions électrostatiques (AMOEBA) pour estimer les potentiels redox d'hémoprotéines. Nous avons dérivé des paramètres pour AMOEBA afin de décrire précisément les interactions électrostatiques avec l'hème. Une amélioration très encourageante est obtenue par rapport aux champs de forces standard. Le second projet vise à développer de nouvelles méthodes pour étudier la dynamique des électrons dans des biomolécules à l'échelle attoseconde en incluant les effets d'environnement. Nous avons conçu un couplage original entre la théorie de la fonctionnelle de la densité dépendant du temps (RT-TDDFT) et un modèle de mécanique moléculaire polarisable (MMpol). Une implémentation efficace et robuste de cette méthode a été réalisée dans le logiciel deMon2k. L'utilisation de techniques d'ajustements de densités électroniques auxiliaires permet de réduire drastiquement le coût de calcul des propagations RT-TDDFT/MMpol. La méthode est appliquée à l'analyse de la dissipation d'énergie dans l'environnement d'un peptide excité par un impulsion laser. / This thesis involves two projects devoted to the development of advanced approaches for simulating molecular and electron dynamics in extended biomolecules. The first project aims at significantly improving the accuracy of redox potentials of proteins by numerical simulations. A sophisticated force field relying on a multipolar description of electrostartic interactions (AMOEBA) is used to perform molecular dynamics simulations onheme proteins. We derived parameters for AMOEBA to accurately describe electrostatic interactions with hemein both ferrous and ferric states. Very encouraging improvements are obtained compared to the standard force fields. The second project aims at developing original approaches for simulating ultrafast electron dynamics in biomolecules in contact to polarizable environments. We devised acombination of Real-time Time-Dependent Density Functional Theory (RT-TDDFT) and polarizable Molecular Mechanics (MMpol). An efficient and robust implementation of this method has been realized in deMon2k software. Density fitting techniques allow to reduce the computational cost of RT-TDDFT/MMpol propagations. The methodology is applied to understand the mechanisms of energy dissipation of a peptide excited by a laser pulse.

La spectroscopie de dissociation par absorption de photons infrarouges (IRPD) permet d’obtenir les signatures vibrationnelles d’espèces chargées en phase gazeuse, telles que de petits peptides ou des ions hydratés dans des agrégats d’eau. L’attribution des modes de vibration pour établir une relation entre le spectre expérimental et une structure moléculaire est une tâche délicate et nécessite le recours à la modélisation moléculaire.Ce manuscrit présente un ensemble d’outils théoriques pour le calcul et l’attribution de spectres vibrationnels, basée principalement sur la dynamique moléculaire classique et le champ de forces polarisable AMOEBA, ainsi que son application à des ions gazeux de tailles diverses. Les ions hydratés dans des agrégats d’eau M(H2O)n (n allant de 6 à 100) sont caractérisés par une dynamique importante, et leur spectre expérimental ne peut pas être décrit par une seule structure. La signature des peptides évolue avec la température et les effets d’anharmonicité dynamique. Ils peuvent également être le siège de mécanismes de transfert de proton, présentant une signature vibrationnelle très caractéristique.La surface d’énergie potentielle de ces systèmes est explorée par la dynamique moléculaire classique en trajectoires individuelles ou avec échange de répliques, afin d’engendrer des structures énergétiquement stables. Pour les plus petits systèmes, les méthodes quantiques DFT et post-HF sont utilisées pour confirmer les structures de plus basse énergie, calculer leurs spectres IR statiques et proposer des attributions des modes de vibration. Pour les plus systèmes de plus grandes tailles, c’est-à-dire les ions dans des gouttes d’eau de plusieurs dizaines de molécules, la simulation des spectres IR à température finie est basée sur la transformée de Fourier de la fonction d’autocorrélation du moment dipolaire (DACF), calculée pour une trajectoire de dynamique moléculaire classique. Cette méthode n’offrant pas d’accès direct aux modes normaux de vibration, nous avons implémenté une méthode d’attribution dynamique, basée sur la Driven Molecular Dynamics (DMD) et couplée au DACF. La combinaison AMOEBA/DACF/DMD a été utilisée pour reproduire et attribuer le spectre du dipeptide Ace-Phe-Ala-NH2, et ceux d’ions hydratés dans des agrégats d’eau.Enfin, la signature vibrationnelle d’un transfert de proton ne peut être décrite, ni par des méthodes statiques quantiques, ni par la dynamique classique. Sa modélisation a nécessité le développement d’un modèle Empirical Valence Bond (EVB) à deux états, couplé au champ de forces polarisable AMOEBA. Le modèle EVB a été implémenté dans la suite logicielle Tinker. Il permet de reproduire le comportement dynamique du transfert de proton au sein de petits peptides et de diacides déprotonés, ainsi que la signature spectroscopique observée expérimentalement.Une partie importante des applications de ces développements concerne des ions simples hydratés dans des nano-gouttelettes, et en particulier l’ion sulfate de grande importance environnementale. Nous avons pu reproduire de façon satisfaisante, pour la première fois, les spectres d’agrégats contenant jusqu’à 100 molécules d’eau. Le principal contributeur à cette spectroscopie expérimentale est l’équipe d’E. Williams à l’université de Californie à Berkeley. Nous avons établi avec eux une collaboration pour compléter ce travail en modélisant les spectres IR d’ions sulfates hydratés [SO4(H2O)n=9-36]2-, dont ils ont obtenu les signatures expérimentales. / Spectroscopy dissociation by absorption of infrared photons (IRPD) provides vibrational signatures of charged species in the gas phase, such as small peptides or hydrated ions in water clusters. The vibrational normal modes assignment to establish a relationship between the experimental spectrum and molecular structure is a delicate task and requires the use of molecular modeling.This manuscript presents a set of theoretical tools for calculation and assignment of vibrational spectra, based mainly on classical molecular dynamics and polarizable AMOEBA force field, and its application to gaseous ions of various sizes. Hydrated ions in water clusters M(H2O)n (n in 6-100 range) are characterized by a dynamic behavior, and their experimental spectrum can not be described by a single structure. The signature of peptides changes with temperature and dynamic anharmonicity effects. They can also be the site of proton transfer mechanisms, with a very characteristic vibrational signature.The potential energy surface of these systems is explored by classical molecular dynamics in individual trajectories or replica exchange to generate energetically stable structures. For smaller systems, quantum methods, as DFT and post-HF, are used to confirm the lowest energy structures, calculate their static IR and propose normal modes assignments. For larger systems, i.e ions in water drops of several tens of molecules, the simulation of IR spectra at finite temperature is based on the Fourier transform of the autocorrelation function of the dipole moment (DACF), calculated during a classical molecular dynamics trajectory. As this method does not allow direct access to the vibrational normal modes, we implemented a method of dynamic assigments, based on the Driven Molecular Dynamics (DMD) and coupled to the DACF. The combination AMOEBA /DACF / DMD was used to reproduce and assign the spectrum of the dipeptide Ace-Phe-Ala-NH2, and those of hydrated ions in water clusters.Finally, the vibrational signature of a proton transfer can not be described by quantum static methods or by classical dynamics. Its modeling required the development of a two states Empirical Valence Bond Model (EVB), coupled with AMOEBA polarizable force field. The two states EVB model was implemented in the software TINKER. It can reproduce the dynamic behavior of proton transfer in small peptides and deprotonated acids, as well as the spectroscopic signatures observed experimentally.An important part of the applications of these developments relates simple hydrated ions in nano-droplets, and in particular the sulfate ion of great environmental importance. We were able to reproduce satisfactorily, for the first time, the spectra of clusters containing up to 100 water molecules. The main contributor to this experimental spectroscopy is the team of E. Williams from the University of California of Berkeley. We have established cooperation with them to complete this work by modeling the IR spectra of hydrated sulfates ions [SO4(H2O) n=9-36]2-, for which they obtained experimental signatures.