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Crystallography. --- Conformational analysis --- Crystal lattices --- Crystallography --- Crystallographies --- Leptology --- Physical sciences --- Mineralogy --- Crystals --- Crystallography, Mathematical --- Lattice theory --- Twinning (Crystallography) --- Analysis, Conformational --- Molecular rotation --- Lattices --- Conformational analysis. --- Crystal lattices. --- Molecular structure --- Molecular crystals --- Lattice dynamics

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The aim of these lecture notes is to propose a systematic framework for geometry and analysis on metric spaces. The central notion is a partition (an iterated decomposition) of a compact metric space. Via a partition, a compact metric space is associated with an infinite graph whose boundary is the original space. Metrics and measures on the space are then studied from an integrated point of view as weights of the partition. In the course of the text: It is shown that a weight corresponds to a metric if and only if the associated weighted graph is Gromov hyperbolic. Various relations between metrics and measures such as bilipschitz equivalence, quasisymmetry, Ahlfors regularity, and the volume doubling property are translated to relations between weights. In particular, it is shown that the volume doubling property between a metric and a measure corresponds to a quasisymmetry between two metrics in the language of weights. The Ahlfors regular conformal dimension of a compact metric space is characterized as the critical index of p-energies associated with the partition and the weight function corresponding to the metric. These notes should interest researchers and PhD students working in conformal geometry, analysis on metric spaces, and related areas.

Geometry. --- Mathematical analysis. --- Analysis (Mathematics). --- Hyperbolic geometry. --- Measure theory. --- Topology. --- Analysis. --- Hyperbolic Geometry. --- Measure and Integration. --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Lebesgue measure --- Measurable sets --- Measure of a set --- Algebraic topology --- Integrals, Generalized --- Measure algebras --- Rings (Algebra) --- Hyperbolic geometry --- Lobachevski geometry --- Lobatschevski geometry --- Geometry, Non-Euclidean --- 517.1 Mathematical analysis --- Mathematical analysis --- Mathematics --- Euclid's Elements --- Conformational analysis. --- Analysis, Conformational --- Molecular rotation

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Nucleic Acids. --- 577.323 --- 547.963.32 --- Biopolymers --- Conformational analysis --- Nucleic acids --- Spectrum analysis --- Analysis, Spectrum --- Spectra --- Spectrochemical analysis --- Spectrochemistry --- Spectroscopy --- Chemistry, Analytic --- Interferometry --- Optics --- Radiation --- Wave-motion, Theory of --- Absorption spectra --- Light --- Spectroscope --- Polynucleotides --- Biomolecules --- Analysis, Conformational --- Molecular rotation --- Bioactive polymers --- Biological polymers --- Natural polymers --- Naturally occurring polymers --- Polymers --- Acids, Nucleic --- Physics and physical chemistry of nucleic acids --- Qualitative --- Biopolymers. --- Conformational analysis. --- Nucleic acids. --- Spectrum analysis. --- 547.963.32 Nucleic acids --- 577.323 Physics and physical chemistry of nucleic acids --- Nucleic Acids --- Spectrometry --- Nucleic Acid --- Acid, Nucleic --- Analytical chemistry --- Molecular structure. --- Nuclear magnetic resonance. --- Circular dichroism --- Conformation --- Molecular vibration

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Speci?c binding of a ligand to a receptor is a key step in a variety of biol- ical processes, such as immune reactions, enzyme cascades, or intracellular transport processes. The ligand-receptor terminology implies that the rec- tor molecule is signi?cantly larger than the ligand, and the term bioactive conformation  usually characterizes the conformation of a ligand when it is bound to a receptor. In a more general sense, bioactive conformation applies toanymoleculeinabiologicallyrelevantboundstateregardlessofsizecons- erations. Mostofthecontributions tothisbookaddressligandsthat aremuch smaller than their receptors. X-ray crystallography and high resolution NMR spectroscopy are the two main experimental techniques used to study bioactive conformations. The- fore,the twovolumes ofthisbookcover approachesthat use either ofthetwo techniques, or a combination thereof. The combination of X-ray crystallog- phy and NMR spectroscopy is particularly useful when a crystal structure of areceptorprotein,butnotofthereceptorprotein-ligandcomplex,isavailable. Anumberofexperimentaltechniquestoanalyzethebioactiveconformationof aligandwithNMRarebasedontheobservationoftheresonancesignalsofthe free ligand that is in exchange with the bound ligand. Several chapters focus onsuchapproachesthat rangefromclassical transferredNOEexperiments, totransferred dipolar couplings,toSTD (saturation transfer difference) NMR techniques. Incaseswhere tightbinding inthesub-nanomolar rangeprevents the analysis of the bioactive conformation via free ligand signals, the ligand- proteincomplexhas tobeanalyzed withproteinNMR-based techniques orby crystallography.Sincethisareahasbeenthesubjectofmanyreviewsandmo- graphsitwill not be covered here in particular detail. As a unifying theme, all contributionstargetthequestionofhowmolecular recognitionofbiologically active molecules is achieved on the atomic scale. Depending on the research topic the results from these studies have a strong impact not only in basic research but also in several ?elds of application ranging frompharmaceutical applications tothe use of biomolecules as, for example, cryoprotectants.

Chemistry. --- Organic Chemistry. --- Biochemistry, general. --- Physical Chemistry. --- Medicinal Chemistry. --- Analytical Chemistry. --- Analytical biochemistry. --- Chemistry, Organic. --- Physical organic chemistry --- Biochemistry. --- Chimie --- Biochimie analytique --- Chimie organique --- Chimie organique physique --- Biochimie --- Conformational analysis --- Bioactive compounds --- Ligand binding (Biochemistry) --- Molecular Conformation --- Binding Sites --- Ligands --- Nuclear Magnetic Resonance, Biomolecular --- Protein Binding --- Analysis --- Chemistry --- Biochemistry --- Physical Sciences & Mathematics --- 577.354.3 --- Chemoreception --- 577.354.3 Chemoreception --- Conformational analysis. --- Analysis. --- Binding, Ligand (Biochemistry) --- Analysis, Conformational --- Biologically active compounds --- Compounds, Bioactive --- Compounds, Biologically active --- Compounds, Physiologically active --- Physiologically active compounds --- Analytical chemistry. --- Organic chemistry. --- Physical chemistry. --- Medicinal chemistry. --- Dye-ligand affinity chromatography --- Radioligand assay --- Molecular rotation --- Chemicals --- Chemistry, Physical organic. --- Analytic biochemistry --- Chemistry, Analytic --- Chemistry, Physical organic --- Chemistry, Organic --- Chemistry, Physical and theoretical --- Biological chemistry --- Chemical composition of organisms --- Organisms --- Physiological chemistry --- Biology --- Medical sciences --- Organic chemistry --- Composition --- Bioanalytic chemistry --- Bioanalytical chemistry --- Analytical chemistry --- Analysis, Chemical --- Analytic chemistry --- Chemical analysis --- Chemistry, Medical and pharmaceutical --- Chemistry, Pharmaceutical --- Drug chemistry --- Drugs --- Medical chemistry --- Medicinal chemistry --- Pharmacochemistry --- Chemistry, Theoretical --- Physical chemistry --- Theoretical chemistry --- Bioactive compounds - Analysis