The main result of this thesis is the development of a theory of semidefinite facial reduction for the Euclidean distance matrix completion problem. Our key result shows a close connection between cliques in the graph of the partial Euclidean distance matrix and faces of the semidefinite cone containing the feasible set of the semidefinite relaxation. We show how using semidefinite facial reduction allows us to dramatically reduce the number of variables and constraints required to represent the semidefinite feasible set. We have used this theory to develop a highly efficient algorithm capable of solving many very large Euclidean distance matrix completion problems exactly, without the need for a semidefinite optimization solver. For problems with a low level of noise, our SNLSDPclique algorithm outperforms existing algorithms in terms of both CPU time and accuracy. Using only a laptop, problems of size up to 40,000 nodes can be solved in under a minute and problems with 100,000 nodes require only a few minutes to solve.

The investigation and control of molecular properties is currently a dynamic research field. Here I present molecular level studies of porphyrin molecules adsorbed on metal surfaces via Low Temperature Scanning Tunneling Microscopy/Spectroscopy (STM/STS), supported by complementary X-ray absorption experiments. Intermolecular and molecule-surface interactions of tetrapyrdil porphyrin (TPyP) on Ag(111) and Cu(111) were investigated. TPyP self-assembles on Ag(111) over a wide sample temperature range into large, highly-ordered 2D chiral domains. By contrast, adsorption of TPyP on the more reactive Cu(111) leads to temperature dependent assemblies, governed decisively by the strong substrate influence. The increased metal-surface interactions on Cu(111) are accompanied by a conformational distortion of the porphyrin macrocycle. The TPyP’s pyridil groups were coordinated with single iron molecules, forming metal-organic complexes. Furthermore, the porphyrin’s macrocycle was metalated by exposing a layer of well-ordered TPyP to an iron atom beam, demonstrating a novel approach towards the fabrication of metallo-tetraaryl porphyrins performed in two dimensions under ultrahigh vacuum conditions. This method was similarly used to form lanthanideporphyrinates by coordinating tetraphenyl porphyrin (TPP) macrocycles with cerium. The influence of the metal center on the porphyrins’ electronic structure was investigated via STS for TPP, TPyP,Fe−TPyP, Fe−TPP, Ce−TPP, and Co−TPP, whereby the inhomogenous electron density distribution associated with individual frontier orbitals were imaged via dI/dV mapping. The symmetry and form of the molecular orbitals could be directly correlated to the saddle-shaped conformational adaptation for the case of Co −TPP.

The investigation and control of molecular properties is currently a dynamic research field. Here I present molecular level studies of porphyrin molecules adsorbed on metal surfaces via Low Temperature Scanning Tunneling Microscopy/Spectroscopy (STM/STS), supported by complementary X-ray absorption experiments. Intermolecular and molecule-surface interactions of tetrapyrdil porphyrin (TPyP) on Ag(111) and Cu(111) were investigated. TPyP self-assembles on Ag(111) over a wide sample temperature range into large, highly-ordered 2D chiral domains. By contrast, adsorption of TPyP on the more reactive Cu(111) leads to temperature dependent assemblies, governed decisively by the strong substrate influence. The increased metal-surface interactions on Cu(111) are accompanied by a conformational distortion of the porphyrin macrocycle. The TPyP’s pyridil groups were coordinated with single iron molecules, forming metal-organic complexes. Furthermore, the porphyrin’s macrocycle was metalated by exposing a layer of well-ordered TPyP to an iron atom beam, demonstrating a novel approach towards the fabrication of metallo-tetraaryl porphyrins performed in two dimensions under ultrahigh vacuum conditions. This method was similarly used to form lanthanideporphyrinates by coordinating tetraphenyl porphyrin (TPP) macrocycles with cerium. The influence of the metal center on the porphyrins’ electronic structure was investigated via STS for TPP, TPyP,Fe−TPyP, Fe−TPP, Ce−TPP, and Co−TPP, whereby the inhomogenous electron density distribution associated with individual frontier orbitals were imaged via dI/dV mapping. The symmetry and form of the molecular orbitals could be directly correlated to the saddle-shaped conformational adaptation for the case of Co −TPP. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

No description available.

No / We describe a series of experiments designed to investigate the conformational transition that highly-branched polymers with ligands undergo when interacting with bacteria, a process that may provide a new sensing mechanism for bacterial detection. Fluorescent highly-branched poly(N-isopropyl acrylamide)s (HB-PNIPAM) were prepared by sequential self-condensing radical copolymerizations, using anthrylmethyl methacrylate (AMMA) and fluorescein-O-acrylate (FA) as fluorescent comonomers and 4-vinylbenzyl pyrrole carbodithioate as a branch forming monomer. Differences in reactivity necessitated to first copolymerize AMMA then react with FA in a separate sequential monomer feed step. Modifications of the chain ends produced vancomycin-functional derivatives (HB-PNIPAM-Van). The AMMA and FA labels allow probing of the conformational behaviour of the polymers in solution via Forster resonance energy transfer experiments. It was shown that interaction of this polymer's end groups with Staphylococcus aureus induced a macromolecular collapse. The data thus provide conclusive evidence for a conformational transition that is driven by binding to a bacterium.

"An apparatus for the delivery of radiation to the tip-sample interface of an Atomic Force Microscope (AFM) is demonstrated. The Pulsed Light Delivery System (PLDS) was fabricated to probe photoinduced conformational changes of molecules using an AFM. The PLDS is 67 mm long, 59 mm wide, and 21 mm high, leaving clearance to mount the PLDS and a microscope slide coated with a thin film of photoactive molecules beneath the cantilever tip of a stand-alone AFM. The PLDS is coupled into a fiber pigtailed Nd:Yag frequency doubled laser, operating at a wavelength of 532 nm. The radiation delivered to a sample through the PLDS can be configured for continuous or pulsed mode. The maximum continuous wave (CW) power delivered was 0.903 mW and the minimum pulse width was 12.3 ms (maximal 401 ms), corresponding to a minimal energy of 0.150 nJ (maximal 362 nJ), and had a cycle duration of 10.0 ms. The PLDS consists of micro-optical components 3.0 mm and smaller in diameter. The optical design was inspired by the three-beam pick-up method used in CD players, which could provide a method to focus the pulse of light onto the sample layer. In addition, the system can be easily modified for different operational parameters (pulse width, wavelength, and power). As proof that the prototype design works, we observed a photoinduced ‘bimetallic’ bending of the cantilever, as evidenced by observing no photoinduced bending when a reflective-coated cantilever was replaced by an uncoated cantilever. Using the apparatus will allow investigation of many different types of molecules exhibiting photoinduced isomerization."

Molecular recognition, defined as the specific interactions between two or more molecules, is at the center of many biological processes including catalysis, signal transduction, gene regulation and allostery. Allosteric regulation is the modification of function caused by an intermolecular interaction. Allosteric proteins modify their activity in response to a biological signal that is often transmitted through the interaction with a small effector molecule. Therefore, determination of the origins of intermolecular interactions involved in molecular recognition and allostery are essential for understanding biological processes. Classically, molecular recognition and allosteric regulation have been associated to structural changes of the system. NMR spectroscopic methods have indicated that changes in protein dynamics may also contribute to molecular recognition and allostery. This thesis is an investigation of the contributions of both structure and dynamics in molecular binding phenomena. In chapter I, I describe molecular recognition, allostery and examples of allostery and cooperativity. Then I discuss the contribution of protein dynamics to function with a special focus on allosteric regulation. Lastly I introduce the hemoglobin homodimer, HbI of Scapharca inaequivalvis and the mRNA binding protein TIS11d. Chapter II is the primary focus of this thesis on the contribution of protein dynamics to allostery in the dimeric hemoglobin of scapharca inaequivalvis, HbI. Thereafter I concentrate on the mechanism of adenine recognition of the Tristetraprolin-like (TTP) protein TIS11d; this study is detailed in Chapter III. In Chapter IV I discuss broader impacts and future directions of my research. This thesis presents an example of the use of protein NMR spectroscopy to probe ligand binding. The studies presented in this thesis emphasize the importance of dynamics in understanding protein function. Measurements of protein motions will be an element of future studies to understand protein function in health and disease.

L’objectif de cette thèse est d’analyser et prédire les conformations d’un système moléculaire en combinant la théorie des graphes et la chimie computationnelle.Dans le cadre des simulations de dynamique moléculaire, une molécule peut avoir une ou plusieurs conformations au cours du temps. Dans les trajectoires de simulation de dynamique moléculaire, on peut avoir des trajectoires n’explorant qu’une seule conformation ou des trajectoires explorant plusieurs conformations, donc plusieurs transitions entre conformations sont observées. L’exploration de ces conformations dépend du temps de la simulation et de l'énergie (température) fixée dans le système. Pour avoir une bonne exploration des conformations d’un système moléculaire, il faut générer et analyser plusieurs trajectoires à différentes énergies. Notre objectif est de proposer un algorithme universel qui permet d’analyser la dynamique conformationnelle de ces trajectoires d’une façon rapide et automatique. Les trajectoires fournissent les positions cartésiennes des atomes du système moléculaire à des intervalles de temps réguliers. Chaque intervalle contenant un ensemble de positions est appelé image. L’algorithme utilise des règles de géométrie (distances, angles, etc.) sur les positions pour trouver les liaisons (liaisons covalentes, liaisons hydrogène et interactions électrostatiques) créées entre les atomes, permettant par la suite d’obtenir le graphe mixte qui modélise une conformation. Nous ne considérons un changement conformationnel que s’il y a un changement dans les liaisons calculées à partir des positions données. L’algorithme permet de donner l’ensemble des conformations explorées sur une ou plusieurs trajectoires, la durée d’exploration de chaque conformation, ainsi que le graphe de transitions qui contient tous les changements conformationnels observés.Les conformations se caractérisent par une énergie appelée énergie potentielle. Cette énergie est représentée par une courbe appelée surface d’énergie potentielle. En chimie théorique et computationnelle, certains s’intéressent à trouver des points particuliers sur cette surface. Il s'agit des minima qui représentent les conformations les plus stables et des maxima ou états de transition qui représentent les points de passage d'une conformation à une autre. En effet, d'une part, la conformation la plus stable est celle de plus basse énergie. D'autres part, pour aller d’une conformation à une autre il faut une énergie supplémentaire, le point maximum représente l'état de transition. Les méthodes développées pour calculer ces points nécessitent une connaissance de l’énergie potentielle ce qui est coûteux en temps et en calculs. Notre objectif est de proposer une méthode alternative en utilisant des mesures ah doc basées sur des propriétés des graphes qu’on a utilisées dans le premier algorithme et sans faire appel à la géométrie ni aux calculs moléculaires. Ces mesures permettent de générer des conformations avec un classement énergétique ainsi de définir le coût énergétique de chaque transition permise. Les conformations possibles avec les transitions représentent respectivement les sommets et les arcs de ce qu’on appelle le “graphe des possibles”. Les hypothèses utilisées dans le modèle proposé est que seules les liaisons hydrogène peuvent changer entre les conformations et que le nombre de liaisons hydrogène présentes dans le système permet de déterminer son coût énergétique.L’algorithme d'analyser des trajectoires a été testé sur trois types de systèmes moléculaires en phase gazeuse de taille et de complexité croissantes. Bien que la complexité théorique de l’algorithme est exponentielle (tests d’isomorphisme) les résultats ont montré que l’algorithme est rapide (quelques secondes). De plus, cet algorithme peut être facilement adapté et appliqué à d’autres systèmes. Pour la prédiction conformationnelle, le modèle proposé a été testé sur des peptides isolés. / This PhD is part of transdisciplinary works, combining graph theory and computational chemistry.In molecular dynamics simulations, a molecular system can adopt different conformations over time. Along a trajectory, one conformation or more can thus be explored. This depends on the simulation time and energy within the system. To get a good exploration of the molecular conformations, one must generate and analyse several trajectories (this can amount to thousands of trajectories). Our objective is to propose an automatic method that provides rapid and efficient analysis of the conformational dynamics explored over these trajectories. The trajectories of interest here are in cartesian coordinates of the atoms that constitute the molecular system, recorded at regular time intervals (time-steps). Each interval containing a set of positions is called a snapshot. At each snapshot, our developed algorithm uses geometric rules (distances, angles, etc.) to compute bonds (covalent bonds, hydrogen bonds and any other kind of intermolecular criterium) formed between atoms in order to get the mixed graph modelling one given conformation. Within our current definitions, a conformational change is characterized by either a change in the hydrogen bonds or in the covalent bonds. One choice or the other depends on the underlying physics and chemistry of interest. The proposed algorithm provides all conformations explored along one or several trajectories, the period of time for the existence of each one of these conformations, and also provides the graph of transitions that shows all conformational changes that have been observed during the trajectories. A user-friendly interface has been developed, that can de distributed freely.Our proposed algorithm for analysing the trajectories of molecular dynamics simulations has been tested on three kinds of gas phase molecular systems (peptides, ionic clusters). This model can be easily adapted and applied to any other molecular systems as well as to condensed matter systems, with little effort. Although the theoretical complexity of the algorithm is exponential (isomorphism tests), results have shown that the algorithm is rapid.We have also worked on computationally low cost graph methods that can be applied in order to pre-characterize specific conformations/points on a potential energy surface (it describes the energy of a system in terms of positions of the atoms). These points are the minima on the surface, representing the most stable conformations of a molecular system, and the maxima on that surface, representing transition states between two conformers. Our developed methods and algorithms aim at getting these specific points, without the prerequisite knowledge/calculation of the potential energy surface by quantum chemistry methods (or even by classical representations). By avoiding an explicit calculation of the potential energy surface by quantum chemistry methods, one saves computational time and effort. We have proposed an alternative method using ad doc measures based on properties of the graphs (already used in the first part of the PhD), without any knowledge of energy and/or molecular calculations. These measures allow getting the possible conformations with a realistic energy classification, as well as transition states, at very low computational cost. The algorithm has been tested on gas phase peptides.

No description available.

La géométrie moléculaire, également connue sous le nom de conformation, est la représentation la plus intrinsèque et la plus informative des molécules. Cependant, prédire des conformations stables à partir de graphes moléculaires reste un problème difficile et fondamental en chimie et en biologie computationnelles. Les méthodes expérimentales et computationelles traditionnelles sont généralement coûteuses et chronophages. Récemment, nous avons assisté à des progrès considérables dans l'utilisation de l'apprentissage automatique, en particulier des modèles génératifs, pour accélérer cette procédure. Cependant, les approches actuelles basées sur les données n'ont généralement pas la capacité de modéliser des distributions complexes et ne tiennent pas compte de caractéristiques géométriques importantes. Dans cette thèse, nous cherchons à construire des modèles génératifs basés sur des principes pour la génération de conformation moléculaire qui peuvent surmonter les problèmes ci-dessus. Plus précisément, nous avons proposé des modèles de diffusion basés sur les flux, sur l'énergie et de débruitage pour la génération de structures moléculaires. Cependant, il n'est pas trivial d'appliquer ces modèles à cette tâche où la vraisemblance des géométries devrait avoir la propriété importante d'invariance par rotation par de translation. Inspirés par les progrès récents de l'apprentissage des représentations géométriques, nous fournissons à la fois une justification théorique et une mise en œuvre pratique sur la manière d'imposer cette propriété aux modèles. Des expériences approfondies sur des jeux de données de référence démontrent l'efficacité de nos approches proposées par rapport aux méthodes de référence existantes. / Molecular geometry, also known as conformation, is the most intrinsic and informative representation of molecules. However, predicting stable conformations from molecular graphs remains a challenging and fundamental problem in computational chemistry and biology. Traditional experimental and computational methods are usually expensive and time-consuming. Recently, we have witnessed considerable progress in using machine learning, especially generative models, to accelerate this procedure. However, current data-driven approaches usually lack the capacity for modeling complex distributions and fail to take important geometric features into account. In this thesis, we seek to build principled generative models for molecular conformation generation that can overcome the above problems. Specifically, we proposed flow-based, energy-based, and denoising diffusion models for molecular structure generation. However, it's nontrivial to apply these models to this task where the likelihood of the geometries should have the important property of rotational and translation invariance. Inspired by the recent progress of geometric representation learning, we provide both theoretical justification and practical implementation about how to impose this property into the models. Extensive experiments on common benchmark datasets demonstrate the effectiveness of our proposed approaches over existing baseline methods.