Effect of dental tissue conditioners and matrix metalloproteinase inhibitors on type I collagen microstructure analyzed by Fourier transform infrared spectroscopy

This study aimed to evaluate the chemical interaction of collagen with some substances usually applied in dental treatments to increase the durability of adhesive restorations to dentin. Initially, the similarity between human dentin collagen and type I collagen obtained from commercial bovine membranes of Achilles deep tendon was compared by the Attenuated Total Reflectance technique of Fourier Transform Infrared (ATR-FTIR) spectroscopy. Finally, the effects of application of 35% phosphoric acid, 0.1M ethylenediaminetetraacetic acid (EDTA), 2% chlorhexidine, and 6.5% proanthocyanidin solution on microstructure of collagen and in the integrity of its triple helix were also evaluated by ATR-FTIR. It was observed that the commercial type I collagen can be used as an efficient substitute for demineralized human dentin in studies that use spectroscopy analysis. The 35% phosphoric acid significantly altered the organic content of amides, proline and hydroxyproline of type I collagen. The surface treatment with 0.1M EDTA, 2% chlorhexidine, or 6.5% proanthocyanidin did not promote deleterious structural changes to the collagen triple helix. The application of 6.5% proanthocyanidin on collagen promoted hydrogen bond formation. (c) 2012 Wiley Periodicals, Inc. J Biomed Mater Res Part B: Appl Biomater, 2012.

Análise vibracional de compostos de coordenação de niquel(II): uma abordagem ao ensino dos grupos pontuais

This paper presents an IR and Raman experiment executed during the teaching of the course "Chemical Bonds" for undergraduated students of Science and Technology and Chemistry at the Federal University of ABC, in order to facilitate and encourage the teaching and learning of group theory. Some key aspects of this theory are also outlined. We believe that student learning was more significant with the introduction of this experiment, because there was an increase in the discussions level and in the performance during evaluations. This work also proposes a multidisciplinary approach to include the use of quantum chemistry tools.

Classical bifurcation in a quadrupolar NMR system

The Josephson junction model is applied to the experimental implementation of classical bifurcation in a quadrupolar nuclear magnetic resonance system. There are two regimes, one linear and one nonlinear, which are implemented by the radio-frequency and the quadrupolar terms of the Hamiltonian of a spin system, respectively. These terms provide an explanation of the symmetry breaking due to bifurcation. Bifurcation depends on the coexistence of both regimes at the same time in different proportions. The experiment is performed on a lyotropic liquid crystal sample of an ordered ensemble of 133Cs nuclei with spin I = 7/2 at room temperature. Our experimental results confirm that bifurcation happens independently of the spin value and of the physical system. With this experimental spin scenario, we confirm that a quadrupolar nuclei system could be described analogously to a symmetric two-mode Bose-Einstein condensate.

Theoretical studies of mononuclear non-heme iron active sites

The quantum chemical investigations presented in this thesis use hybrid density functional theory to shed light on the catalytic mechanisms of mononuclear non-heme iron oxygenases, accommodating a ferrous ion in their active sites. More specifically, the dioxygen activation process and the subsequent oxidative reactions in the following enzymes were studied: tetrahydrobiopterin-dependent hydroxylases, naphthalene 1,2-dioxygenase and α-ketoglutarate-dependent enzymes. In light of many experimental efforts devoted to the functional mimics of non-heme iron oxygenases, the reactivity of functional analogues was also examined. The computed energetics and the available experimental data served to assess the feasibility of the reaction mechanisms investigated. Dioxygen activation in tetrahydrobiopterin- and α-ketoglutarate-dependent enzymes were found to involve a high-valent iron-oxo species, which was then capable of substrate hydroxylation. In the case of naphthalene 1,2-dioxygenase, the reactivity of an iron(III)-hydroxperoxo species toward the substrate was investigated and compared to the biomimetic counterpart.

Structure determination of proteins and peptides in solution: simulation, chirality and NMR studies

The study of protein fold is a central problem in life science, leading in the last years to several attempts for improving our knowledge of the protein structures. In this thesis this challenging problem is tackled by means of molecular dynamics, chirality and NMR studies. In the last decades, many algorithms were designed for the protein secondary structure assignment, which reveals the local protein shape adopted by segments of amino acids. In this regard, the use of local chirality for the protein secondary structure assignment was demonstreted, trying to correlate as well the propensity of a given amino acid for a particular secondary structure. The protein fold can be studied also by Nuclear Magnetic Resonance (NMR) investigations, finding the average structure adopted from a protein. In this context, the effect of Residual Dipolar Couplings (RDCs) in the structure refinement was shown, revealing a strong improvement of structure resolution. A wide extent of this thesis is devoted to the study of avian prion protein. Prion protein is the main responsible of a vast class of neurodegenerative diseases, known as Bovine Spongiform Encephalopathy (BSE), present in mammals, but not in avian species and it is caused from the conversion of cellular prion protein to the pathogenic misfolded isoform, accumulating in the brain in form of amiloyd plaques. In particular, the N-terminal region, namely the initial part of the protein, is quite different between mammal and avian species but both of them contain multimeric sequences called Repeats, octameric in mammals and hexameric in avians. However, such repeat regions show differences in the contained amino acids, in particular only avian hexarepeats contain tyrosine residues. The chirality analysis of avian prion protein configurations obtained from molecular dynamics reveals a high stiffness of the avian protein, which tends to preserve its regular secondary structure. This is due to the presence of prolines, histidines and especially tyrosines, which form a hydrogen bond network in the hexarepeat region, only possible in the avian protein, and thus probably hampering the aggregation.

Sistemi liquido cristallini complessi: simulazioni al calcolatore e studi ESR

The aim of this PhD thesis was to study at a microscopic level different liquid crystal (LC) systems, in order to determine their physical properties, resorting to two distinct methodologies, one involving computer simulations, and the other spectroscopic techniques, in particular electron spin resonance (ESR) spectroscopy. By means of the computer simulation approach we tried to demonstrate this tool effectiveness for calculating anisotropic static properties of a LC material, as well as for predicting its behaviour and features. This required the development and adoption of suitable molecular models based on a convenient intermolecular potentials reflecting the essential molecular features of the investigated system. In particular, concerning the simulation approach, we have set up models for discotic liquid crystal dimers and we have studied, by means of Monte Carlo simulations, their phase behaviour and self­-assembling properties, with respect to the simple monomer case. Each discotic dimer is described by two oblate Gay­Berne ellipsoids connected by a flexible spacer, modelled by a harmonic "spring" of three different lengths. In particular we investigated the effects of dimerization on the transition temperatures, as well as on the characteristics of molecular aggregation displayed and the relative orientational order. Moving to the experimental results, among the many experimental techniques that are typically employed to evaluate LC system distinctive features, ESR has proved to be a powerful tool in microscopic scale investigation of the properties, structure, order and dynamics of these materials. We have taken advantage of the high sensitivity of the ESR spin probe technique to investigate increasingly complex LC systems ranging from devices constituted by a polymer matrix in which LC molecules are confined in shape of nano- droplets, as well as biaxial liquid crystalline elastomers, and dimers whose monomeric units or lateral groups are constituted by rod-like mesogens (11BCB). Reflection-mode holographic-polymer dispersed liquid crystals (H-PDLCs) are devices in which LCs are confined into nanosized (50­-300 nm) droplets, arranged in layers which alternate with polymer layers, forming a diffraction grating. We have determined the configuration of the LC local director and we have derived a model of the nanodroplet organization inside the layers. Resorting also to additional information on the nanodroplet size and shape distribution provided by SEM images of the H-PDLC cross-section, the observed director configuration has been modeled as a bidimensional distribution of elongated nanodroplets whose long axis is, on the average, parallel to the layers and whose internal director configuration is a uniaxial quasi- monodomain aligned along the nanodroplet long axis. The results suggest that the molecular organization is dictated mainly by the confinement, explaining, at least in part, the need for switching voltages significantly higher and the observed faster turn-off times in H-PDLCs compared to standard PDLC devices. Liquid crystal elastomers consist in cross-linked polymers, in which mesogens represent the monomers constituting the main chain or the laterally attached side groups. They bring together three important aspects: orientational order in amorphous soft materials, responsive molecular shape and quenched topological constraints. In biaxial nematic liquid crystalline elastomers (BLCEs), two orthogonal directions, rather than the one of normal uniaxial nematic, can be controlled, greatly enhancing their potential value for applications as novel actuators. Two versions of a side-chain BLCEs were characterized: side­-on and end­-on. Many tests have been carried out on both types of LCE, the main features detected being the lack of a significant dynamical behaviour, together with a strong permanent alignment along the principal director, and the confirmation of the transition temperatures already determined by DSC measurements. The end­-on sample demonstrates a less hindered rotation of the side group mesogenic units and a greater freedom of alignment to the magnetic field, as already shown by previous NMR studies. Biaxial nematic ESR static spectra were also obtained on the basis of Molecular Dynamics generated biaxial configurations, to be compared to the experimentally determined ones, as a mean to establish a possible relation between biaxiality and the spectral features. This provides a concrete example of the advantages of combining the computer simulation and spectroscopic approaches. Finally, the dimer α,ω-bis(4'-cyanobiphenyl-4-yl)undecane (11BCB), synthesized in the "quest" for the biaxial nematic phase has been analysed. Its importance lies in the dimer significance as building blocks in the development of new materials to be employed in innovative technological applications, such as faster switching displays, resorting to the easier aligning ability of the secondary director in biaxial phases. A preliminary series of tests were performed revealing the population of mesogenic molecules as divided into two groups: one of elongated straightened conformers sharing a common director, and one of bent molecules, which display no order, being equally distributed in the three dimensions. Employing this model, the calculated values show a consistent trend, confirming at the same time the transition temperatures indicated by the DSC measurements, together with rotational diffusion tensor values that follow closely those of the constituting monomer 5CB.

Hochgenaue Berechnungen von Energien und molekularen Eigenschaften mit Hilfe der Coupled-Cluster-Theorie

Coupled-Cluster-Theorie (CC) ist in der heutigen Quantenchemie eine der erfolgreichsten Methoden zur genauen Beschreibung von Molekülen. Die in dieser Arbeit vorgestellten Ergebnisse zeigen, daß neben den Berechnungen von Energien eine Reihe von Eigenschaften wie Strukturparameter, Schwingungsfrequenzen und Rotations-Schwingungs-Parameter kleiner und mittelgrofler Moleküle zuverlässig und präzise vorhergesagt werden können. Im ersten Teil der Arbeit wird mit dem Spin-adaptierten Coupled-Cluster-Ansatz (SA-CC) ein neuer Weg zur Verbesserung der Beschreibung von offenschaligen Systemen vorgestellt. Dabei werden zur Bestimmung der unbekannten Wellenfunktionsparameter zusätzlich die CC-Spingleichungen gelöst. Durch dieses Vorgehen wird gewährleistet, daß die erhaltene Wellenfunktion eine Spineigenfunktion ist. Die durchgeführte Implementierung des Spin-adaptierten CC-Ansatzes unter Berücksichtigung von Einfach- und Zweifachanregungen (CCSD) für high-spin Triplett-Systeme wird ausführlich erläutert. Im zweiten Teil werden CC-Additionsschemata vorgestellt, die auf der Annahme der Additivität von Elektronenkorrelations- und Basissatzeffekten basieren. Die etablierte Vorgehensweise, verschiedene Beiträge zur Energie mit an den Rechenaufwand angepassten Basissätzen separat zu berechnen und aufzusummieren, wird hier auf Gradienten und Kraftkonstanten übertragen. Für eine Beschreibung von Bindungslängen und harmonischen Schwingungsfrequenzen mit experimenteller Genauigkeit ist die Berücksichtigung von Innerschalenkorrelationseffekten sowie Dreifach- und Vierfachanregungen im Clusteroperator der Wellenfunktion nötig. Die Basissatzkonvergenz wird dabei zusätzlich mit Extrapolationsmethoden beschleunigt. Die quantitative Vorhersage der Bindungslängen von 17 kleinen Molekülen, aufgebaut aus Atomen der ersten Langperiode, ist so mit einer Genauigkeit von wenigen Hundertstel Pikometern möglich. Für die Schwingungsfrequenzen dieser Moleküle weist das CC-Additionsschema basierend auf den berechneten Kraftkonstanten im Vergleich zu experimentellen Ergebnissen einen mittleren absoluten Fehler von 3.5 cm-1 und eine Standardabweichung von 2.2 cm-1 auf. Darüber hinaus werden zur Unterstützung von experimentellen Untersuchungen berechnete spektroskopische Daten einiger größerer Moleküle vorgelegt. Die in dieser Arbeit vorgestellten Untersuchungen zur Isomerisierung von Dihalogensulfanen XSSX (X= F, Cl) oder die Berechnung von Struktur- und Rotations-Schwingungs-Parametern für die Moleküle CHCl2F und CHClF2 zeigen, daß bereits störungstheoretische CCSD(T)-Näherungsmethoden qualitativ gute Vorhersagen experimenteller Resultate liefern. Desweiteren werden Diskrepanzen von experimentellen und berechneten Bindungsabständen bei den Molekülen Borhydrid- und Carbenylium durch die Berücksichtigung des elektronischen Beitrages zum Trägheitsmoment beseitigt.

Isoxazolidines and oxazines: preliminary studies for the synthesis of N,O-heterocyclic systems via an organocatalyzed 1,3-Dipolar Cycloaddiction and a tandem reaction mediated by TEMPO salts

This thesis is the result of the study of two reactions leading to the formation of important heterocyclic compounds of potential pharmaceutical interest. The first study concerns the reaction of (1,3)-dipolar cycloaddition between nitrones and activated olefins by hydrogen bond catalysis of thioureas derivatives leading to the formation of a five-membered cyclic adducts, an interesting and strategic synthetic intermediate, for the synthesis of benzoazepine. The second project wants to explore the direct oxidative C(sp3)-H α-alkylation of simple amides with subsequent addition of an olefin and cyclization in order to obtain the corresponding oxazine. Both reactions are still under development.

Synthesis and Supramolecular Architectures of Lipophilic Derivatives of Guanine

Self-assembly relies on the association of pre-programmed building blocks through non-covalent interactions to give complex supramolecular architectures. Previous studies provided evidence for the unique self-assembly properties of semi-synthetic lipophilic guanosine derivatives which can sequestrate ions from an aqueous phase, carry them into an organic phase where they promote the generation of well-defined supramolecular assemblies. In the presence of cations lipophilic guanosines form columnar aggregates while in their absence they generate supramolecular ribbons. The aim of this thesis has been the synthesis of guanine derivatives, in particular N9-alkylated guanines and a guanosine functionalized as a perchlorotriphenylmetil moiety (Gace-a-HPTM) in order to observe their supramolecular behaviour in the absence of sugar (ribose or deoxyribose) and in the presence of a bulky and chiral substituent respectively. By using guanine instead of guanosine, while maintaining all the hydrogen bond acceptor and donor groups required for supramolecular aggregation, the steric hindrance to supramolecular aggregation is notably reduced because (i.e. guanines with groups in N9 different from sugar are expected to have a greatest conformational freedom even in presence of bulky groups in C8). Supramolecular self-assembly of these derivatives has been accomplished in solutions by NMR and CD spectroscopy and on surface by STM technique. In analogy with other guanosine derivatives, also N9-substituted guanines and GAceHPTM form either ribbon-like aggregates or cation-templated G-quartet based columnar structures.

Spectroscopic signatures from first principles calculations: from surface adsorbates to liquids and polymers

In dieser Arbeit werden drei wasserstoffverbrückte Systeme in der kondensierten Phase mit Hilfe von first-principles-Elektronenstruktur-Rechnungen untersucht, die auf der Dichtefunktionaltheorie (DFT) unter periodischen Randbedingungen basieren. Ihre lokalen Konformationen und Wasserstoffbrückenbindungen werden mittels ab-initio Molekulardynamiksimulationen berechnet und weiterhin durch die Bestimmung ihrer spektroskopischen Parameter charakterisiert. Der Schwerpunkt liegt dabei auf lokalen Strukturen und auf schnellen Fluktuationen der Wasserstoffbrückenbindungen, welche von zentraler Bedeutung für die physikalischen und chemischen Eigenschaften der betrachteten Systeme sind. Die für die lokalen, instantanen Konformationen berechneten Spektren werden verwendet, um die physikalischen Prozesse, die hinter den untersuchten Phänomenen stehen, zu erklären: die Wasseradsorption auf metallischen Oberflächen, die Ionensolvatisierung in wässrigen Lösungen und der Protonentransport in protonleitenden Polymeren, welche Prototypen von Membranen für Brennstoffzellen sind. Die Möglichkeit der Vorhersage spektroskopischer Parameter eröffnet vielfältige Möglichkeiten des Dialogs zwischen Experimenten und numerischen Simulationen. Die in dieser Arbeit vorgestellten Ergebnisse zeigen, dass die Zuverlässigkeit dieser theoretischen Berechnungen inzwischen für viele experimentell relevante Systeme ein quantitatives Niveau erreicht hat.

Large-scale coupled-cluster calculations

Coupled-cluster theory provides one of the most successful concepts in electronic-structure theory. This work covers the parallelization of coupled-cluster energies, gradients, and second derivatives and its application to selected large-scale chemical problems, beside the more practical aspects such as the publication and support of the quantum-chemistry package ACES II MAB and the design and development of a computational environment optimized for coupled-cluster calculations. The main objective of this thesis was to extend the range of applicability of coupled-cluster models to larger molecular systems and their properties and therefore to bring large-scale coupled-cluster calculations into day-to-day routine of computational chemistry. A straightforward strategy for the parallelization of CCSD and CCSD(T) energies, gradients, and second derivatives has been outlined and implemented for closed-shell and open-shell references. Starting from the highly efficient serial implementation of the ACES II MAB computer code an adaptation for affordable workstation clusters has been obtained by parallelizing the most time-consuming steps of the algorithms. Benchmark calculations for systems with up to 1300 basis functions and the presented applications show that the resulting algorithm for energies, gradients and second derivatives at the CCSD and CCSD(T) level of theory exhibits good scaling with the number of processors and substantially extends the range of applicability. Within the framework of the ’High accuracy Extrapolated Ab initio Thermochemistry’ (HEAT) protocols effects of increased basis-set size and higher excitations in the coupled- cluster expansion were investigated. The HEAT scheme was generalized for molecules containing second-row atoms in the case of vinyl chloride. This allowed the different experimental reported values to be discriminated. In the case of the benzene molecule it was shown that even for molecules of this size chemical accuracy can be achieved. Near-quantitative agreement with experiment (about 2 ppm deviation) for the prediction of fluorine-19 nuclear magnetic shielding constants can be achieved by employing the CCSD(T) model together with large basis sets at accurate equilibrium geometries if vibrational averaging and temperature corrections via second-order vibrational perturbation theory are considered. Applying a very similar level of theory for the calculation of the carbon-13 NMR chemical shifts of benzene resulted in quantitative agreement with experimental gas-phase data. The NMR chemical shift study for the bridgehead 1-adamantyl cation at the CCSD(T) level resolved earlier discrepancies of lower-level theoretical treatment. The equilibrium structure of diacetylene has been determined based on the combination of experimental rotational constants of thirteen isotopic species and zero-point vibrational corrections calculated at various quantum-chemical levels. These empirical equilibrium structures agree to within 0.1 pm irrespective of the theoretical level employed. High-level quantum-chemical calculations on the hyperfine structure parameters of the cyanopolyynes were found to be in excellent agreement with experiment. Finally, the theoretically most accurate determination of the molecular equilibrium structure of ferrocene to date is presented.

Studies of pure rotational spectra of isolated molecules and molecular adducts using pulsed jet Fourier transform microwave (PJ-FTM) spectroscopy

This thesis focuses on studying molecular structure and internal dynamics by using pulsed jet Fourier transform microwave (PJ-FTMW) spectroscopy combined with theoretical calculations. Several kinds of interesting chemical problems are investigated by analyzing the MW spectra of the corresponding molecular systems. First, the general aspects of rotational spectroscopy are summarized, and then the basic theory on molecular rotation and experimental method are described briefly. ab initio and density function theory (DFT) calculations that used in this thesis to assist the assignment of rotational spectrum are also included. From chapter 3 to chapter 8, several molecular systems concerning different kind of general chemical problems are presented. In chapter 3, the conformation and internal motions of dimethyl sulfate are reported. The internal rotations of the two methyl groups split each rotational transition into several components line, allowing for the determination of accurate values of the V3 barrier height to internal rotation and of the orientation of the methyl groups with respect to the principal axis system. In chapter 4 and 5, the results concerning two kinds of carboxylic acid bi-molecules, formed via two strong hydrogen bonds, are presented. This kind of adduct is interesting also because a double proton transfer can easily take place, connecting either two equivalent or two non-equivalent molecular conformations. Chapter 6 concerns a medium strong hydrogen bonded molecular complex of alcohol with ether. The dimer of ethanol-dimethylether was chosen as the model system for this purpose. Chapter 7 focuses on weak halogen…H hydrogen bond interaction. The nature of O-H…F and C-H…Cl interaction has been discussed through analyzing the rotational spectra of CH3CHClF/H2O. In chapter 8, two molecular complexes concerning the halogen bond interaction are presented.

Monte-Carlo simulation of hard spherocylinders under confinement

When a liquid crystal is confined to a cavity its director field becomes subject to competing forces: on the one hand, the surface of the cavity orients the director field (``surface anchoring''), on the other hand deformations of the director field cost elastic energy. Hence the equilibrium director field is determined by a compromise between surface anchoring and elasticity. One example of a confined liquid crystal that has attracted particular interest from physicists is the nematic droplet. In this thesis a system of hard rods is considered as the simplest model for nematic liquid crystals consisting of elongated molecules. First, systems of hard spherocylinders in a spherical geometry are investigated by means of canonical Monte Carlo simulations. In contrast to previous simulation work on this problem, a continuum model is used. In particular, the effects of ordering near hard curved walls are studied for the low-density regime. With increasing density, first a uniaxial surface film forms and then a biaxial surface film, which eventually fills the entire cavity. We study how the surface order, the adsorption and the shape of the director field depend on the curvature of the wall. We find that orientational ordering at a curved wall in a cavity is stronger than at a flat wall, while adsorption is weaker. For densities above the isotropic-nematic transition, we always find bipolar configurations. As a next step, an extension of the Asakura-Oosawa-Vrij model for colloid-polymer mixtures to anisotropic colloids is considered. By means of computer simulations we study how droplets of hard, rod-like particles optimize their shape and structure under the influence of the osmotic compression caused by the presence of spherical particles that act as depletion agents. At sufficiently high osmotic pressures the rods that make up the drops spontaneously align to turn them into uniaxial nematic liquid crystalline droplets. The nematic droplets or ``tactoids'' that so form are not spherical but elongated, resulting from the competition between the anisotropic surface tension and the elastic deformation of the director field. In agreement with recent theoretical predictions we find that sufficiently small tactoids have a uniform director field, whilst large ones are characterized by a bipolar director field. From the shape and director-field transformation of the droplets we estimate the surface anchoring strength.

Regio- e stereocontrollo nell'addizione viniloga di alchilidenossindoli a nitrostireni via organocatalisi.

The topic of this work is the simultaneous activation, promoted by 9-epi-NH2-DHQA-TU, of alkylideneoxindole and nistirene derivatives, respectively via base catalysis and hydrogen-bond catalysis. The chosen substrates, of high biological interest, are used as starting materials for a vinylogous Michael addition where we wish to control the stereochemistry of the two asymmetric carbons far away from the active site, respectively in γ and δ position. Due to the particular structure of the starting oxindoles, it is hereby presented the first variant of this reaction performed at its highest level of stereochemical complexity. It is possible as a matter of fact, to generate 24 isomers of the product. Specifically, given that the nucleophilic attack can occur from various, non equivalent regions of the starting molecule, our main goal was to achieve a complete regio- and stereocontrol of the reaction. We have verified that the reported organocatalyzed vinylogous reaction represents a valid integration of the metal-catalyzed one, since it affords highly stereochemically complex products in good to high yields and excellent optical purity.

Mathematical aspects of Feynman integrals

In the present dissertation we consider Feynman integrals in the framework of dimensional regularization. As all such integrals can be expressed in terms of scalar integrals, we focus on this latter kind of integrals in their Feynman parametric representation and study their mathematical properties, partially applying graph theory, algebraic geometry and number theory. The three main topics are the graph theoretic properties of the Symanzik polynomials, the termination of the sector decomposition algorithm of Binoth and Heinrich and the arithmetic nature of the Laurent coefficients of Feynman integrals.rnrnThe integrand of an arbitrary dimensionally regularised, scalar Feynman integral can be expressed in terms of the two well-known Symanzik polynomials. We give a detailed review on the graph theoretic properties of these polynomials. Due to the matrix-tree-theorem the first of these polynomials can be constructed from the determinant of a minor of the generic Laplacian matrix of a graph. By use of a generalization of this theorem, the all-minors-matrix-tree theorem, we derive a new relation which furthermore relates the second Symanzik polynomial to the Laplacian matrix of a graph.rnrnStarting from the Feynman parametric parameterization, the sector decomposition algorithm of Binoth and Heinrich serves for the numerical evaluation of the Laurent coefficients of an arbitrary Feynman integral in the Euclidean momentum region. This widely used algorithm contains an iterated step, consisting of an appropriate decomposition of the domain of integration and the deformation of the resulting pieces. This procedure leads to a disentanglement of the overlapping singularities of the integral. By giving a counter-example we exhibit the problem, that this iterative step of the algorithm does not terminate for every possible case. We solve this problem by presenting an appropriate extension of the algorithm, which is guaranteed to terminate. This is achieved by mapping the iterative step to an abstract combinatorial problem, known as Hironaka's polyhedra game. We present a publicly available implementation of the improved algorithm. Furthermore we explain the relationship of the sector decomposition method with the resolution of singularities of a variety, given by a sequence of blow-ups, in algebraic geometry.rnrnMotivated by the connection between Feynman integrals and topics of algebraic geometry we consider the set of periods as defined by Kontsevich and Zagier. This special set of numbers contains the set of multiple zeta values and certain values of polylogarithms, which in turn are known to be present in results for Laurent coefficients of certain dimensionally regularized Feynman integrals. By use of the extended sector decomposition algorithm we prove a theorem which implies, that the Laurent coefficients of an arbitrary Feynman integral are periods if the masses and kinematical invariants take values in the Euclidean momentum region. The statement is formulated for an even more general class of integrals, allowing for an arbitrary number of polynomials in the integrand.