The Hamilton-Jacobi equation revisited

A new analysis of the nature of the solutions of the Hamilton-Jacobi equation of classical dynamics is presented based on Caratheodory’s theorem concerning canonical transformations. The special role of a principal set of solutions is stressed, and the existence of analogous results in quantum mechanics is outlined.

Symmetries and constraints in generalized Hamiltonian dynamics

A general analysis of symmetries and constraints for singular Lagrangian systems is given. It is shown that symmetry transformations can be expressed as canonical transformations in phase space, even for such systems. The relation of symmetries to generators, constraints, commutators, and Dirac brackets is clarified.

A Note on Easily Testable Realizations for Logic Functions

It is shown that at most, n + 3 tests are required to detect any single stuck-at fault in an AND gate or a single faulty EXCLUSIVE OR (EOR) gate in a Reed-Muller canonical form realization of a switching function.

On the stabilization of uniformly decoupled systems by state variable feedback

Conditions under which the asymptotic stabilization of uniformly decoupled time-varying multivariate systems is possible are explored. This is accomplished by developing a canonical form for integrator uniformly decoupled system in which the coefficient matrices have a simple structure. The procedures developed rely on certain conditions on the given system and yield explicit expressions for the stabilization compensators.

Structural and Functional Studies on Trimeric Autotransporters

Trimeric autotransporters are a family of secreted outer membrane proteins in Gram-negative bacteria. These obligate homotrimeric proteins share a conserved C-terminal region, termed the translocation unit. This domain consists of an integral membrane β-barrel anchor and associated α-helices which pass through the pore of the barrel. The α-helices link to the extracellular portion of the protein, the passenger domain. Autotransportation refers to the way in which the passenger domain is secreted into the extracellular space. It appears that the translocation unit mediates the transport of the passenger domain across the outer membrane, and no external factors, such as ATP, ion gradients nor other proteins, are required. The passenger domain of autotransporters contains the specific activities of each protein. These are usually related to virulence. In trimeric autotransporters, the main function of the proteins is to act as adhesins. One such protein is the Yersinia adhesin YadA, found in enteropathogenic species of Yersinia. The main activity of YadA from Y. enterocolitica is to bind collagen, and it also mediates adhesion to other molecules of the extracellular matrix. In addition, YadA is involved in serum resistance, phagocytosis resistance, binding to epithelial cells and autoagglutination. YadA is an essential virulence factor of Y. enterocolitica, and removal of this protein from the bacteria leads to avirulence. In this study, I investigated the YadA-collagen interaction by studying the binding of YadA to collagen-mimicking peptides by several biochemical and biophysical methods. YadA bound as tightly to the triple-helical model peptide (Pro-Hyp-Gly)10 as to native collagen type I. However, YadA failed to bind a similar peptide that does not form a collagenous triple helix. As (Pro-Hyp-Gly)10 does not contain a specific sequence, we concluded that a triple-helical conformation is necessary for YadA binding, but no specific sequence is required. To further investigate binding determinants for YadA in collagens, I examined the binding of YadA to a library of collagen-mimicking peptides that span the entire triple-helical sequences of human collagens type II and type III. YadA bound promiscuously to many but not all peptides, indicating that a triple-helical conformation alone is not sufficient for binding. The high-binding peptides did not share a clear binding motif, but these peptides were rich in hydroxyproline residues and contained a low number of charged residues. YadA thus binds collagens without sequence specificity. This strategy of promiscuous binding may be advantageous for pathogenic bacteria. The Eib proteins from Escherichia coli are immunoglobulin (Ig)-binding homologues of YadA. I showed conclusively that recombinant EibA, EibC, EibD and EibF bind to IgG Fc. I crystallised a fragment of the passenger domain of EibD, which binds IgA in addition to IgG. The structure has a YadA-like head domain and an extended coiled-coil stalk. The top half of the coiled-coil is right-handed with hendecad periodicity, whereas the lower half is a canonical left-handed coiled-coil. At the transition from right- to left-handedness, a small β-sheet protrudes from each monomer. I was able to map the binding regions for IgG and IgA using truncations and site-directed mutagenesis to the coiled-coil stalk and identified residues critical for Ig binding.

CADASIL: molecular studies on the most common hereditary vascular dementing disorder

Cerebral Autosomal Dominant Arteriopathy with Subcortical Infarcts and Leukoencephalopathy (CADASIL) is the most common hereditary vascular dementia. CADASIL is a systemic disease of small and medium-sized arteries although the symptoms are almost exclusively neurological, including migraineous headache, recurrent ischemic episodes, cognitive impairment and, finally, subcortical dementia. CADASIL is caused by over 170 different mutations in the NOTCH3 gene, which encodes a receptor expressed in adults predominantly in the vascular smooth muscle cells. The function of NOTCH3 is not crucial for embryonic development but is needed after birth. NOTCH3 directs postnatal arterial maturation and helps to maintain arterial integrity. It is involved in regulation of vascular tone and in the wound healing of a vascular injury. In addition, NOTCH3 promotes cell survival by inducing expression of anti-apoptotic proteins. NOTCH3 is a membrane-spanning protein with a large extracellular domain (N3ECD) containing 34 epidermal growth factor-like (EGF) repeats and a smaller intracellular domain with six ankyrin repeats. All CADASIL mutations are located in the EGF repeats and the majority of the mutations cause gain or loss of one cysteine residue in one of these repeats leading to an odd number of cysteine residues, which in turn leads to misfolding of N3ECD. This misfolding most likely alters the maturation, targetting, degradation and/or function of the NOTCH3 receptor. CADASIL mutations do not seem to affect the canonical NOTCH3 signalling pathway. The main pathological findings are the accumulation of the NOTCH3 extracellular domain on degenerating vascular smooth muscle cells (VSMCs), accumulation of granular osmiophilic material (GOM) in the close vicinity of VSMCs as well as fibrosis and thickening of arterial walls. Narrowing of the arterial lumen and local thrombosis cause insufficient blood flow, mainly in small arteries of the cerebral white matter, resulting in tissue damage and lacunar infarcts. CADASIL is suspected in patients with a suggestive family history and clinical picture as well as characteristic white matter alterations in magnetic resonance imaging. A definitive verification of the diagnosis can be achieved by identifying a pathogenic mutation in the NOTCH3 gene or through the detection of GOM by electron microscopy. To understand the pathology underlying CADASIL, we have generated a unique set of cultured vascular smooth muscle cell (VSMC) lines from umbilical cord, placental, systemic and cerebral arteries of CADASIL patients and controls. Analyses of these VSMCs suggest that mutated NOTCH3 is misfolded, thus causing endoplasmic reticulum stress, activation of the unfolded protein response and increased production of reactive oxygen species. In addition, mutation in NOTCH3 causes alterations in actin cytoskeletal structures and protein expression, increased branching and abnormal node formation. These changes correlate with NOTCH3 expression levels within different VSMCs lines, suggesting that the phenotypic differences of SMCs may affect the vulnerability of the VSMCs and, therefore, the pathogenic impact of mutated NOTCH3 appears to vary in the arteries of different locations. Furthermore, we identified PDGFR- as an immediate downstream target gene of NOTCH3 signalling. Activation of NOTCH induces up-regulation of the PDGFR- expression in control VSMCs, whereas this up-regulation is impaired in CADASIL VSMCs and might thus serve as an alternative molecular mechanism that contributes to CADASIL pathology. In addition, we have established the congruence between NOTCH3 mutations and electron microscopic detection of GOM with a view to constructing a strategy for CADASIL diagnostics. In cases where the genetic analysis is not available or the mutation is difficult to identify, a skin biopsy is an easy-to-perform and highly reliable diagnostic method. Importantly, it is invaluable in setting guidelines concerning how far one should proceed with the genetic analyses.

Influence of Hydrophilic Surface Specificity on the Structural Properties of Confined Water

The influence of chemical specificity of hydrophilic surfaces on the structure of confined water in the subnanometer regime is investigated using grand canonical Monte Carlo Simulations. The structural variations for water confined between hydroxylated silica surfaces are contrasted with water confined between mica surfaces. Although both surfaces are hydrophilic, our Study shows that hydration of potassium ions on the mica surface has a strong influence on the water Structure and solvation force response of confined water. In contrast to the disrupted hydrogen bond network observed for water confined between Mica Surfaces, water between silica surfaces retains its hydrogen bond network displaying bulklike structural features down to surface separations as small as 0.45 nm. Hydrogen bonding of all invariant contact water layer with the surface silanol groups aids in maintaining a constant number of hydrogen bonds per water molecule for the silica surfaces. As a consequence water depletion and rearrangement upon decreasing confinement is a strong function of the hydrophilic surface specificity, particularly at smaller separations. An oscillatory solvation force response is only observed for water confined between Silica surfaces, and bulklike features are observed for both Surfaces above a surface separation of about 1.2 nm. We evaluate and contrast the water density, dipole moment distributions, pi pair correlation functions, and solvation forces as a function of the surface separation.

Ethyl 4-(4-chlorophenyl)-6-methyl-2-thioxo-1,2,3,4-tetrahydropyrimidine-5-carboxylate

In the title compound, C14H15ClN2O2S, the tetrahydropyrimidine ring adopts a twisted boat conformation with the carbonyl group in an s-trans conformation with respect to the C C double bond of the six-membered tetrahydropyrimidine ring. The molecular conformation is determined by an intramolecular C-H center dot center dot center dot pi interaction. The crystal structure is further stabilized by intermolecular N-H center dot center dot center dot O molecular chains and centrosymmetric N-H center dot center dot center dot S dimers.

Sostdc1 Plays an Essential Role in Mammalian Tooth Patterning : Insight into the Rodent Dental Evolution

This thesis work focuses on the role of TGF-beta family antagonists during the development of mouse dentition. Tooth develops through an interaction between the dental epithelium and underlying neural crest derived mesenchyme. The reciprocal signaling between these tissues is mediated by soluble signaling molecules and the balance between activatory and inhibitory signals appears to be essential for the pattern formation. We showed the importance of Sostdc1 in the regulation of tooth shape and number. The absence of Sostdc1 altered the molar cusp patterning and led to supernumerary tooth formation both in the molar and incisor region. We showed that initially, Sostdc1 expression is in the mesenchyme, suggesting that dental mesenchyme may limit supernumerary tooth induction. We tested this in wild-type incisors by minimizing the amount of mesenchymal tissue surrounding the incisor tooth germs prior to culture in vitro. The cultured teeth phenocopied the extra incisor phenotype of the Sostdc1-deficient mice. Furthermore, we showed that minimizing the amount of dental mesenchyme in cultured Sostdc1-deficient incisors caused the formation of additional de novo incisors that resembled the successional incisor development resulting from activated Wnt signaling. Sostdc1 seemed to be able to inhibit both mesenchymal BMP4 and epithelial canonical Wnt signaling, which thus allows Sostdc1 to restrict the enamel knot size and regulate the tooth shape and number. Our work emphasizes the dual role for the tooth mesenchyme as a suppressor as well as an activator during tooth development. We found that the placode, forming the thick mouse incisor, is prone to disintegration during initiation of tooth development. The balance between two mesenchymal TGF-beta family signals, BMP4 and Activin is essential in this regulation. The inhibition of BMP4 or increase in Activin signaling led to the splitting of the large incisor placode into two smaller placodes resulting in thin incisors. These two signals appeared to have different effects on tooth epithelium and the analysis of the double null mutant mice lacking Sostdc1 and Follistatin indicated that these TGF-beta inhibitors regulate the mutual balance of BMP and Activin in vivo. In addition, this work provides an alternative explanation for the issue of incisor identity published in Science by Tucker et al. in 1998 and proposes that the molar like morphology that can be obtained by inhibiting BMP signaling is due to partial splitting of the incisor placodes and not due to change in tooth identity from the incisor to the molar. This thesis work presents possible molecular mechanisms that may have modified the mouse dental pattern during evolution leading to the typical rodent dentition of modern mouse. The rodent dentition is specialized for gnawing and consists of two large continuously growing incisors and toothless diastema region separating the molars and incisors. The ancestors of rodents had higher number of more slender incisors together with canines and premolars. Additionally, murine rodents, which include the mouse, have lost their ability for tooth replacement. This work has revealed that the inhibitory molecules appear to play a role in the tooth number suppression by delineating the spatial and temporal action of the inductive signals. The results suggest that Sostdc1 plays an essential role in several stages of tooth development through the regulation of both the BMP and Wnt pathway. The work shows a dormant sequential tooth forming potential present in wild type mouse incisor region and gives a new perspective on tooth suppression by dental mesenchyme. It reveals as well a novel mechanism to create a large mouse incisor through the regulation of mesenchymal balance between inductive and inhibitory signals.

Gabapentin: A Stereochemically Constrained gamma Amino Acid Residue in Hybrid Peptide Design

Nature has used the all-alpha-polypeptide backbone of proteins to create a remarkable diversity of folded structures. Sequential patterns of 20 distinct amino adds, which differ only in their side chains, determine the shape and form of proteins. Our understanding of these specific secondary structures is over half a century old and is based primarily on the fundamental elements: the Pauling alpha-helix and beta-sheet. Researchers can also generate structural diversity through the synthesis of polypeptide chains containing homologated (omega) amino acid residues, which contain a variable number of backbone atoms. However, incorporating amino adds with more atoms within the backbone introduces additional torsional freedom into the structure, which can complicate the structural analysis. Fortunately, gabapentin (Gpn), a readily available bulk drug, is an achiral beta,beta-disubstituted gamma amino add residue that contains a cyclohexyl ring at the C-beta carbon atom, which dramatically limits the range of torsion angles that can be obtained about the flanking C-C bonds. Limiting conformational flexibility also has the desirable effect of increasing peptide crystallinity, which permits unambiguous structural characterization by X-ray diffraction methods. This Account describes studies carried out in our laboratory that establish Gpn as a valuable residue in the design of specifically folded hybrid peptide structures. The insertion of additional atoms into polypeptide backbones facilitates the formation of intramolecular hydrogen bonds whose directionality is opposite to that observed in canonical alpha-peptide helices. If hybrid structures mimic proteins and biologically active peptides, the proteolytic stability conferred by unusual backbones can be a major advantage in the area of medicinal chemistry. We have demonstrated a variety of internally hydrogen-bonded structures in the solid state for Gpn-containing peptides, including the characterization of the C-7 and C-9 hydrogen bonds, which can lead to ribbons in homo-oligomeric sequences. In hybrid alpha gamma sequences, district C-12 hydrogen-bonded turn structures support formation of peptide helices and hairpins in longer sequences. Some peptides that include the Gpn residue have hydrogen-bond directionality that matches alpha-peptide helices, while others have the opposite directionality. We expect that expansion of the polypeptide backbone will lead to new classes of foldamer structures, which are thus far unknown to the world of alpha-polypeptides. The diversity of internally hydrogen-bonded structures observed in hybrid sequences containing Gpn shows promise for the rational design of novel peptide structures incorporating hybrid backbones.

Pi-turns in proteins and peptides: Classification, conformation, occurrence, hydration and sequence.

The i + 5-->i hydrogen bonded turn conformation (pi-turn) with the fifth residue adopting alpha L conformation is frequently found at the C-terminus of helices in proteins and hence is speculated to be a "helix termination signal." An analysis of the occurrence of i + 5-->i hydrogen bonded turn conformation at any general position in proteins (not specifically at the helix C-terminus), using coordinates of 228 protein crystal structures determined by X-ray crystallography to better than 2.5 A resolution is reported in this paper. Of 486 detected pi-turn conformations, 367 have the (i + 4)th residue in alpha L conformation, generally occurring at the C-terminus of alpha-helices, consistent with previous observations. However, a significant number (111) of pi-turn conformations occur with (i + 4)th residue in alpha R conformation also, generally occurring in alpha-helices as distortions either at the terminii or at the middle, a novel finding. These two sets of pi-turn conformations are referred to by the names pi alpha L and pi alpha R-turns, respectively, depending upon whether the (i + 4)th residue adopts alpha L or alpha R conformations. Four pi-turns, named pi alpha L'-turns, were noticed to be mirror images of pi alpha L-turns, and four more pi-turns, which have the (i + 4)th residue in beta conformation and denoted as pi beta-turns, occur as a part of hairpin bend connecting twisted beta-strands. Consecutive pi-turns occur, but only with pi alpha R-turns. The preference for amino acid residues is different in pi alpha L and pi alpha R-turns. However, both show a preference for Pro after the C-termini. Hydrophilic residues are preferred at positions i + 1, i + 2, and i + 3 of pi alpha L-turns, whereas positions i and i + 5 prefer hydrophobic residues. Residue i + 4 in pi alpha L-turns is mainly Gly and less often Asn. Although pi alpha R-turns generally occur as distortions in helices, their amino acid preference is different from that of helices. Poor helix formers, such as His, Tyr, and Asn, also were found to be preferred for pi alpha R-turns, whereas good helix former Ala is not preferred. pi-Turns in peptides provide a picture of the pi-turn at atomic resolution. Only nine peptide-based pi-turns are reported so far, and all of them belong to pi alpha L-turn type with an achiral residue in position i + 4. The results are of importance for structure prediction, modeling, and de novo design of proteins.

Effect of deletion of Ghrelin-O-Acyltransferase on the pulsatile release of growth hormone in mice

Ghrelin, a gut hormone originating from the post-translational cleavage of preproghrelin, is the endogenous ligand of growth hormone secretagogue receptor 1a (GHS-R1a). Within the growth hormone (GH) axis, the biological activity of ghrelin requires octanoylation by ghrelin-O-acyltransferase (GOAT), conferring selective binding to the GHS-R1a receptor via acylated ghrelin. Complete loss of preproghrelin-derived signalling (through deletion of the Ghrl gene) contributes to a decline in peak GH release; however, the selective contribution of endogenous acyl-ghrelin to pulsatile GH release remains to be established. We assessed the pulsatile release of GH in ad lib. fed male germline goat−/− mice, extending measures to include mRNA for key hypothalamic regulators of GH release, and peripheral factors that are modulated relative to GH release. The amount of GH released was reduced in young goat−/− mice compared to age-matched wild-type mice, whereas pulse frequency and irregularity increased. Altered GH release did not coincide with alterations in hypothalamic Ghrh, Srif, Npy or Ghsr mRNA expression, or pituitary GH content, suggesting that loss of Goat does not compromise canonical mechanisms that contribute to pituitary GH production and release. Although loss of Goat resulted in an irregular pattern of GH release (characterised by an increase in the number of GH pulses observed during extended secretory events), this did not contribute to a change in the expression of sexually dimorphic GH-dependent liver genes. Of interest, circulating levels of insulin-like growth factor (IGF)-1 were elevated in goat−/− mice. This rise in circulating levels of IGF-1 was correlated with an increase in GH pulse frequency, suggesting that sustained or increased IGF-1 release in goat−/− mice may occur in response to altered GH release patterning. Our observations demonstrate that germline loss of Goat alters GH release and patterning. Although the biological relevance of altered GH secretory patterning remains unclear, we propose that this may contribute to sustained IGF-1 release and growth in goat−/− mice.

2-[2-(Cyclohexylcarbonyl)phenyl]-1-phenylethanone

The title diketone, C21H22O2, features a phenylene ring having benzoylmethyl and cyclohexanoyl substituents ortho to each other. The cyclohexyl ring adopts a chair conformation with the ketonic group occupying an equatorial position; the four-atom -C(O)-C ketonic unit is twisted out of the plane of the phenylene ring by 34.9 (1)degrees.

Ethyl 2,6-dichloro-4-phenylquinoline-3-carboxylate

In the title compound,C18H13Cl2NO2,the quinoline ring system is almost planar (r.m.s.deviation 0.009 angstrom), and the phenyl and carboxylate planes are twisted away from it by 59.2 (1)and 65.9 (2)degrees,respectively.

Ethyl 6-chloro-2-oxo-4-phenyl-1,2-dihydroquinoline-3-carboxylate

In the title compound,C18H14ClNO3,the dihydroquinolin-2-one ring system is almost planar (r.m.s.deviation = 0.033 angstrom).The carboxylate plane and the phenyl group are twisted away from the dihydroquinolin-2-one ring system by 50.3(1) and 64.9(1)degrees,respectively.In the crystal structure, inversion-related molecules form R-2(2)(8)dimers via pairs of N-H center dot center dot center dot O hydrogen bonds.