The size and conformational complexity of proteins and other large systems represent major challenges for today's methods of quantum chemistry.This thesis is centered around the development of new computational tools to gain molecular-level insight into electronic transitions in such systems. To meet this challenge, we focus on the polarizable embedding (PE) model, which takes advantage of the fact that many electronic transitions are localized to a smaller part of the entire system.This motivates a partitioning of the large system into two regions that are treated at different levels of theory:The smaller part directly involved in the electronic process is described using accurate quantum-chemical methods, while the effects of the rest of the system, the environment, are incorporated into the Hamiltonian of the quantum region in an effective manner. This thesis presents extensions of the PE model with theaim of expanding its range of applicability to describe electronic transitions in large molecular systemsin the optical and X-ray regions. The developments cover both improvements with regardto the quantum region as well as the embedding potential representing the environment.Regarding the former, a damped linear response formulation has been implemented to allow for calculations of absorption spectra of large molecular systems acrossthe entire frequency range. A special feature of this development is its abilityto address core excitations that are otherwise not easily accessible.Another important development presented in this thesis is the coupling of the PE model to a multi-configuration self-consistent-field description of the quantum region and its further combination with response theory. In essence, this extends the PE model to the study of electronic transitions in large systems that are prone to static correlation --- a situation that is frequently encountered in biological systems. In addition to the direct environmental effects on the electronic structure of the quantum region, another important component of the description of electronic transitions in large molecular systems is an accurate account of the indirect effects of the environment, i.e., the geometrical distortions in the quantum region imposed by the environment. In thisthesis we have taken the first step toward the inclusion of geometry distortions in the PE frameworkby formulating and implementing molecular gradients for the quantum region. To identify critical points related to the environment description, we perform a theoretical analysis of the PE model starting from a full quantum-mechanicaltreatment of a composite system. Based on this, we present strategies for an accurate yet efficient construction of the embedding potentialcovering both the calculation of ground state and transition properties. The accurate representation of the environment makes it possible to reduce the size of the quantum region without compromising the overall accuracy of the final results. This further enables use of highly accurate quantum-chemical methods despite their unfavorable scaling with the size of the system. Finally, some examples of applications will be presented to demonstrate how the PE model may be applied as a tool to gain insight into and rationalize the factors influencing electronic transitions in large molecular systems of increasing complexity. / <p>The dissertation was awarded the best PhD thesis prize 2016 by the Danish Academy of Natural Sciences.</p><p></p><p>QC 20170209</p>

This dissertation presents a study of the molecular mechanism underlying the highly efficient solar energy conversion processes that occur in the Photosystem I (PS I) reaction centers in plants and bacteria. The primary electron donor P700 is at the heart of solar energy conversion process in PS I and the aim is to obtain a better understanding of the electronic and structural organization of P700 in the ground and excited states. Static Fourier Transform Infra-Red (FTIR) difference spectroscopy (DS) in combination with site directed mutagenesis and Density Functional Theory (DFT) based vibrational frequency simulations were used to investigate how protein interactions such as histidine ligation and hydrogen bonding modulate this organization. (P700+-P700) FTIR DS at 77K were obtained from a series of mutants from the cyanobacterium Synechocystis sp. 6803 (S. 6803) where the amino acid residues near the C=O groups of the two chlorophylls of P700 where specifically changed. (P700+-P700) FTIR DS was also obtained for a set of mutants from C. reinhardtii where the axial ligand to A0-, the primary electron acceptor in PS I was modified. The FTIR DS obtained from these mutants provides information on the axial ligands, the hydrogen bonding status as well as the polarity of the environment of specific functional groups that are part of the chlorophyll molecules that constitute P700. Assignment of the FTIR bands to vibrational modes in specific types of environment is very difficult. In order to assist the assignment of the difference bands in experimental spectra DFT based vibrational mode frequency calculations were undertaken for Chl-a and Chl-a+ model molecular systems under different set of conditions; in the gas phase, in solvents using the Polarizable Continuum Model (PCM), in the presence of explicit solvent molecules using QM/MM methods, and in the presence of axial ligands and hydrogen bonds. DFT methods were also used to calculate the charge, spin and redox properties of Chl-a/Chl-a’ dimer models that are representative of P700, the primary electron donor in PS I.

MSc (Chemistry) / Department of Chemistry

Les interactions protéine-protéine (IPPs) médient la signalisation cellulaire. Leur ingénierie peut fournir des informations et conduire au développement de molécules thérapeutiques. Les domaines PDZ sont des médiateurs importants de IPPs. Elles lient les 4--10 résidus C-terminaux de protéines cibles. Elles lient aussi les peptides correspondants, qui peuvent servir de systèmes modèles ou d'inhibiteurs. Nous avons développé deux approches computationnelles et les avons appliquées au domaine PDZ de la protéine Tiam1, un facteur d'échange pour la protéine Rac, impliqué dans la protrusion neuronale. Sa cible est la protéine Syndecan1. Des affinités expérimentales sont connues pour le peptide C-terminal, noté Sdc1, et plusieurs mutants; elles ont servi pour tester les calculs. Nous avons d'abord développé une méthode de dessin computationnel haut débit. Une simulation Monte Carlo est faite où les chaines latérales de la protéine et du peptide peuvent changer de conformères et certaines positions peuvent muter. Le solvant est implicite. Le paysage énergétique est aplati par la méthode adaptative de Wang-Landau, de sorte qu'un vaste ensemble de variantes est échantillonné. Effectuant des simulations distinctes du complexe et du peptide seul nous avons obtenu les énergies libres relatives d'association de 75,000 variantes en heure CPU sur une machine de bureau. Les valeurs sont compatibles avec les quelques données expérimentales disponibles. Ensuite, nous avons développé une approche beaucoup plus détaillée et réaliste. Soluté et solvant sont décrits par un champ de force atomique, qui représente explicitement la polarisation électronique: le champ de force Drude de Charmm. La polarisabilité peut être importante car les résidus de l'interface PDZ:peptide passent, lors de l'association, d'un environnement riche en solvant à un autre pauvre en solvant. Nous avons fait des simulations alchimiques d'énergie libre pour comparer quatre variantes du peptide qui diffèrent par une ou deux chaines latérales ioniques. Les résultats sont en bon accord avec l'expérience. Les champs de force additifs Charmm et Amber, qui représentent la polarisabilité implicitement, donnent un moins bon accord. Ces calculs sont le premier exemple de simulations alchimiques d'énergies libre d'association relatives protéine: ligand avec un champ de force polarisable. Enfin, pour une modélisation future de peptides phosphorylés, nous avons étendu le champ de force Drude pour inclure le méthyl phosphate et la phospho tyrosine. Il en résulte un excellent accord avec les affinités expérimentales phosphate: magnésium. / Protein-protein interactions (PPIs) regulate complex signaling networks in eukaryotic cells. Many binding events between several protein domains transfer information through communication pathways. Disrupting or altering the equilibrium between PPIs plays an important role inseveral diseases and the inibition of targeted PPIs is a recognized strategy for computational drug design. In the present thesis we focused on PDZ domains, which are among the most widespread signaling domains. PDZs recognize the 4-10 C-terminal amino acids of their target proteins as well as the corresponding peptides in isolation. We studied PDZ:peptide binding for the Tiam1 protein, which is a Rac GTP exchange factor involved in neuronal protrusion and axon guidance. Tiam1 activity modulates signaling for cell proliferation and migration, whose dysregulation increases growth of metastatic cancers. Its natural binder peptide is Syndecan1 (Sdc1), composed of 8 amino acids. Its last 5 Cter residues drive interactions in the binding pocket. Experimental affinities for several mutants of Sdc1 and in the protein domain constitute a complete dataset to study many ionic interactions with molecular simulations. These calculations are still challenging, despite the dramatic improvement of biomolecular modelling in the 1990's and 2000's. Upon binding, residues are transferred from a solvent-exposed environment to a solvent-poor one. This is expected to change the electron distribution within residues and nearby solvent molecules. Comparing ligands that differ by one or more ionic side-chain mutations, more sophisticated force fields where electronic polarizability is treated explicitly may be required. We developed and tested both Computational Protein Design (CPD) models and more precise free energy calculation methods based on polarizable molecular dynamics. We developed a general, high-througtput CPD protocol to optimize protein:peptide binding. The model has been implemented in on our in-house CPD package Proteus ( Simonson et al, 2014) and has been tested computing relative binding affinities for many variants of the Tiam1:Sdc1 complex. Monte Carlo sampling of equilibrium distributions of protein sequences is performed using an adaptive bias potential which flattens the energy landscape in sequence space and allows to estimate binding affinities for thousands of protein variants in limited CPU time (~1hour). We also improved our CPD implicit solvent model, implementing a more realistic description of the solute-solvent dielectric boundary. The new method, called Fluctuating Dielectric Boundary (FDB) showed a systematic improvement in the prediction of acid:base constants of several proteins. Promising results were also obtained for the complete sequence redesign of three PDZ domains. In the second part of this work we studied Tiam1:peptide affinities with more sophisticated models, based on free energy simulations with the Drude Polarizable Force field (DrudeFF). We first computed relative binding free energies for charge mutations in the Tiam1:Sdc1 complex, obtaining a clear improvement respect to equivalent calculations performed using two additive force fields. We applied the well-enstablished Dual Topology Approach: to our knowledge, this was the first example of such a calculation for a protein:peptide complex with uses the DrudeFF. Then we went on, developing the Drude polarizable models for methyl phosphate (MP) and phospho tyrosine (pTyr). We were interested in the change in binding affinity associated with phosphorylation of a Tyrosine residue of Sdc1, but Drude pTyr parameters were not yet developed. We tested our new phosphate parameters studying standard binding free energies between MP and magnesium (Mg2+) in water solution. Results showed a good agreement with experiment, improving previous calculations performed using additive force field

Dans cette thèse, les propriétés optiques de biomolécules importantes ont été étudiées en utilisant une approche théorique et, dans un cas, aussi expérimentale. La Théorie de la fonctionnelle de la densité (DFT) et la timedependent-DFT (TD-DFT) sont les principales méthodes de chimie quantique utilisées dans cette thèse. Plusieurs spectroscopies ont été étudiées (au niveau théorique et, dans certains cas, également au niveau expérimental) : absorption électronique linéaire (absorption à un photon, OPA) et non-linéaire (absorption à deux ou trois photons, TPA et 3PA), dichroïsme circulaire électronique (DCE) et spectroscopie de fluorescence. Les effets de l’environnement, particulièrement importants dans des systèmes biologiques, ont été pris en compte, pour les propriétés de l’état fondamental et des états excités en utilisant une méthode multi-échelles QM/MM appelée Polarizable Embedding (PE). L’échantillonnage des conformations a été pris en compte avec des simulations de dynamique moléculaire (MD) qui sont basées sur la mécanique classique. Deux thématiques ont été étudiées dans cette thèse : le cholestérol et le design in silico de ses analogues fluorescents ainsi que la caractérisation des coudes de type β dans différentes conformations grâce à la simulation des spectres DCE. La simulation de plus d’une spectroscopie a été importante dans l’étude des états excités du cholestérol dans des solutions organiques. Le design in silico a suggéré un nouveau stérol-polyénique (P-stérol) qui montre despropriétés optiques améliorées pour le mécanisme d’excitation à trois photons par rapport au déhydroergostérol (DHE), une sonde du cholestérol déjà très utilisée. Ce nouveau P-stérol a été suggéré pour la synthèse. L’étude des spectres de DCE des coudes β en différentes conformations a mené une double conclusion : même si deux allures de DCE pour les conformations des coudes β étudiées (4) ont été trouvées (dans la majorité des cas), la spectroscopie de DCE doit toujours être associée à d’autres techniques spectroscopiques dans la caractérisation en solution des coudes β. / In this thesis, the optical properties of important biomolecules were studied using a theoretical approach and, in one case, also an experimental one. Density Functional Theory (DFT) and time-dependent-DFT (TD-DFT), were the principal quantum chemical methods adopted in this thesis.Various spectroscopies were studied (theoretically and, in some cases, also experimentally) : linear (one-photon, OPA) and non-linear (two- and three-photon, TPA and 3PA) electronic absorption, electronic circular dichroism (ECD) and fluorescence spectroscopy. The environment effects, which are particularly important in biological systems, were taken into account, for both ground and excited states properties, using a multiscale QM/MM method called Polarizable Embedding (PE). The sampling of conformations was addressed by Molecular Dynamic (MD) simulations based on classical mechanics. Two topics were studied in this thesis: cholesterol and the in-silico design of its fluorescent analogues, and the characterization of β-turns in different conformations by simulations of their ECD spectra in aqueous solutions. The simulation of more than one spectroscopy resulted to be important when studying the electronic excited states of cholesterol in organic solutions. The in-silico design study suggested a novel polyene-sterol (P-sterol) which shows improved optical properties for the three-photon excitation mechanism with respect to dehydroergosterol (DHE), an already widely used cholesterol probe. This new P-sterol was thus suggested for synthesis. The achievement from the study of ECD spectra for different β-turn conformations is two-fold: even if two ECD patterns for the β-turn conformations studied (4) were found (in most of cases), ECD spectroscopy should be always associated with other spectroscopic techniques when trying to characterize the β-turn conformations in solutions.