A multistep transversal linearization (MTL) method in non-linear dynamics through a Magnus characterization

A new form of a multi-step transversal linearization (MTL) method is developed and numerically explored in this study for a numeric-analytical integration of non-linear dynamical systems under deterministic excitations. As with other transversal linearization methods, the present version also requires that the linearized solution manifold transversally intersects the non-linear solution manifold at a chosen set of points or cross-section in the state space. However, a major point of departure of the present method is that it has the flexibility of treating non-linear damping and stiffness terms of the original system as damping and stiffness terms in the transversally linearized system, even though these linearized terms become explicit functions of time. From this perspective, the present development is closely related to the popular practice of tangent-space linearization adopted in finite element (FE) based solutions of non-linear problems in structural dynamics. The only difference is that the MTL method would require construction of transversal system matrices in lieu of the tangent system matrices needed within an FE framework. The resulting time-varying linearized system matrix is then treated as a Lie element using Magnus’ characterization [W. Magnus, On the exponential solution of differential equations for a linear operator, Commun. Pure Appl. Math., VII (1954) 649–673] and the associated fundamental solution matrix (FSM) is obtained through repeated Lie-bracket operations (or nested commutators). An advantage of this approach is that the underlying exponential transformation could preserve certain intrinsic structural properties of the solution of the non-linear problem. Yet another advantage of the transversal linearization lies in the non-unique representation of the linearized vector field – an aspect that has been specifically exploited in this study to enhance the spectral stability of the proposed family of methods and thus contain the temporal propagation of local errors. A simple analysis of the formal orders of accuracy is provided within a finite dimensional framework. Only a limited numerical exploration of the method is presently provided for a couple of popularly known non-linear oscillators, viz. a hardening Duffing oscillator, which has a non-linear stiffness term, and the van der Pol oscillator, which is self-excited and has a non-linear damping term.

Characterization of anomalous relaxation using the time-fractional Bloch equation and multiple echo T2 *-weighted magnetic resonance imaging at 7T

PURPOSE To study the utility of fractional calculus in modeling gradient-recalled echo MRI signal decay in the normal human brain. METHODS We solved analytically the extended time-fractional Bloch equations resulting in five model parameters, namely, the amplitude, relaxation rate, order of the time-fractional derivative, frequency shift, and constant offset. Voxel-level temporal fitting of the MRI signal was performed using the classical monoexponential model, a previously developed anomalous relaxation model, and using our extended time-fractional relaxation model. Nine brain regions segmented from multiple echo gradient-recalled echo 7 Tesla MRI data acquired from five participants were then used to investigate the characteristics of the extended time-fractional model parameters. RESULTS We found that the extended time-fractional model is able to fit the experimental data with smaller mean squared error than the classical monoexponential relaxation model and the anomalous relaxation model, which do not account for frequency shift. CONCLUSIONS We were able to fit multiple echo time MRI data with high accuracy using the developed model. Parameters of the model likely capture information on microstructural and susceptibility-induced changes in the human brain.

Hydrothermal synthesis and structural characterization of novel alpha-Keggin unit-supported Cu(II)- and Mn(II)-bipyridine complexes from a tri-lacunary precursor

Blue [{Cu(2,2'-bipy)(2)}(2){alpha-SiW12O40}] (bipy = bipyridyl) (1) and pale yellow [Mn(2,2'-bipy)(3)](2)[alpha-SiW12O40] (2) have been synthesized hydrothermally and characterized by IR spectroscopy and single crystal X-ray structure analysis. In 1, the [alpha-SiW12O40](4-) ion acts as a bridge between the two [{Cu(2,2'-bipy)(2)](2+) moieties via coordination through the terminal oxygen atoms, while in 2, the [Mn(2,2'-bipy)(3)](2+) ion balances the charge on the polyoxo anion without forming any covalent bond. To the best of our knowledge, this is the first example of transition metal-mediated transformation of [alpha-SiW9O34](10-) to [alpha-SiW12O40](4-).

Molecular Characterization of Fibrotic Scarring in Kidneys with Congenital Nephrotic Syndrome of the Finnish type

Congenital nephrotic syndrome of the Finnish type (NPHS1, CNF) is an autosomal recessive disease, enriched in the Finnish population. NPHS1 is caused by a mutation in the NPHS1 gene. This gene encodes for nephrin, which is a major structural component of the slit diaphragm connecting podocyte foot processes in the glomerular capillary wall. In NPHS1, the genetic defect in nephrin leads to heavy proteinuria already in the newborn period. Finnish NPHS1 patients are nephrectomized at infancy, and after a short period of dialysis the patients receive a kidney transplant, which is the only curative therapy for the disease. In this thesis, we examined the cellular and molecular mechanisms leading to the progression of glomerulosclerosis and tubulointerstitial fibrosis in NPHS1 kidneys. Progressive mesangial expansion in NPHS1 kidneys is caused by mesangial cell hyperplasia and the accumulation of extracellular matrix proteins. Expansion of the extracellular matrix was caused by the normal mesangial cell component, collagen IV. However, no significant changes in mesangial cell phenotype or extracellular matrix component composition were observed. Endotheliosis was the main ultrastructural lesion observed in the endothelium of NPHS1 glomeruli. The abundant expression of vascular endothelial growth factor and its transcription factor hypoxia inducible factor-1 alpha were in accordance with the preserved structure of the endothelium in NPHS1 kidneys. Hypoperfusion of peritubular capillaries and tubulointerstitial hypoxia were evident in NPHS1 kidneys, indicating that these may play an important role in the rapid progression of fibrosis in the kidneys of NPHS1 patients. Upregulation of Angiotensin II was obvious, emphasizing its role in the pathophysiology of NPHS1. Excessive oxidative stress was evident in NPHS1 kidneys, manifested as an increase expression of p22phox, superoxide production, lipid oxide peroxidation and reduced antioxidant activity. In conclusion, our data indicate that mesangial cell proliferation and the accumulation of extracellular matrix accumulation are associated with the obliteration of glomerular capillaries, causing the reduction of circulation in peritubular capillaries. The injury and rarefaction of peritubular capillaries result in impairment of oxygen and nutrient delivery to the tubuli and interstitial cells, which correlates with the fibrosis, tubular atrophy and oxidative stress observed in NPHS1 kidneys.

Characterization of Failure Modes in CFRP Composites - An ANN Approach

Carbon fiber reinforced polymer (CFRP) composite specimens with different thickness, geometry, and stacking sequences were subjected to fatigue spectrum loading in stages. Another set of specimens was subjected to static compression load. On-line acoustic Emission (AE) monitoring was carried out during these tests. Two artificial neural networks, Kohonen-self organizing feature map (KSOM), and multi-layer perceptron (MLP) have been developed for AE signal analysis. AE signals from specimens were clustered using the unsupervised learning KSOM. These clusters were correlated to the failure modes using available a priori information such as AE signal amplitude distributions, time of occurrence of signals, ultrasonic imaging, design of the laminates (stacking sequences, orientation of fibers), and AE parametric plots. Thereafter, AE signals generated from the rest of the specimens were classified by supervised learning MLP. The network developed is made suitable for on-line monitoring of AE signals in the presence of noise, which can be used for detection and identification of failure modes and their growth. The results indicate that the characteristics of AE signals from different failure modes in CFRP remain largely unaffected by the type of load, fiber orientation, and stacking sequences, they being representatives of the type of failure phenomena. The type of loading can have effect only on the extent of damage allowed before the specimens fail and hence on the number of AE signals during the test. The artificial neural networks (ANN) developed and the methods and procedures adopted show significant success in AE signal characterization under noisy environment (detection and identification of failure modes and their growth).

Cyclic AMP in Mycobacteria: Characterization and Functional Role of the Rv1647 Ortholog in Mycobacterium smegmatis{triangledown}

Mycobacterial genomes are endowed with many eukaryote-like nucleotide cyclase genes encoding proteins that can synthesize 3',5'-cyclic AMP (cAMP). However, the roles of cAMP and the need for such redundancy in terms of adenylyl cyclase genes remain unknown. We measured cAMP levels in Mycobacterium smegmatis during growth and under various stress conditions and report the first biochemical and functional characterization of the MSMEG_3780 adenylyl cyclase, whose orthologs in Mycobacterium tuberculosis (Rv1647) and Mycobacterium leprae (ML1399) have been recently characterized in vitro. MSMEG_3780 was important for producing cAMP levels in the logarithmic phase of growth, since the {Delta}MSMEG_3780 strain showed lower intracellular cAMP levels at this stage of growth. cAMP levels decreased in wild-type M. smegmatis under conditions of acid stress but not in the {Delta}MSMEG_3780 strain. This was correlated with a reduction in MSMEG_3780 promoter activity, indicating that the effect of the reduction in cAMP levels on acid stress was caused by a decrease in the transcription of MSMEG_3780. Complementation of the {Delta}MSMEG_3780 strain with the genomic integration of MSMEG_3780 or the Rv1647 gene could restore cAMP levels during logarithmic growth. The Rv1647 promoter was also acid sensitive, emphasizing the biochemical and functional similarities in these two adenylyl cyclases. This study therefore represents the first detailed biochemical and functional analysis of an adenylyl cyclase that is important for maintaining cAMP levels in mycobacteria and underscores the subtle roles that these genes may play in the physiology of the organism.

RNA triphosphatase and guanylyl transferase activities are associated with the RNA polymerase protein L of rinderpest virus

Rinderpest virus (RPV) large (L) protein is an integral part of the ribonucleoprotein (RNP) complex of the virus that is responsible for transcription and replication of the genome. Previously, we have shown that recombinant L protein coexpressed along with P protein (as the L-P complex) catalyses the synthesis of all viral mRNAs in vitro and the abundance of mRNAs follows a gradient of polarity, similar to the occurrence in vivo. In the present work, we demonstrate that the viral mRNAs synthesized in vitro by the recombinant L or purified RNP are capped and methylated at the N-7 guanine position. RNP from the purified virions, as well as recombinant L protein, shows RNA triphosphatase (RTPase) and guanylyl transferase (GT) activities. L protein present in the RNP complex catalyses the removal of gamma-phosphate from triphosphate-ended 25 nt RNA generated in vitro representing the viral N-terminal mRNA 5' sequence. The L protein forms a covalent enzyme-guanylate intermediate with the GMP moiety of GTP, whose formation is inhibited by the addition of pyrophosphate; thus, it exhibits characteristics of cellular GTs. The covalent bond between the enzyme and nucleotide is acid labile and alkali stable, indicating the presence of phosphoamide linkage. The C-terminal region (aa 1717-2183) of RPV L protein alone exhibits the first step of GT activity needed to form a covalent complex with GMP, though it lacks the ability to transfer GMP to substrate RNA. Here, we describe the biochemical characterization of the newly found RTPase/GT activity of L protein.

Characterization of hot deformation behavior of Zr-1Nb-1Sn alloy

The hot deformation behavior of beta-quenched Zr-1 Nb-1Sn was studied in the temperature range 650-1050 degrees C and strain rate range 0.001-100 s(-1) using processing maps. These maps revealed three different domains: a domain of dynamic recovery at temperatures <700 degrees C and at strain rates <3 x 10(-3) s(-1), a domain of dynamic recrystallization in the temperature range 750-950 C-degrees and at strain rates <10(-2) S-1 with a peak at 910 degrees C and 10(-3) S-1 (in alpha + beta phase field), and a domain of large-grain superplasticity in the beta phase field at strain rates <10(-2) s(-1). In order to identify the rate controlling mechanisms involved in these domains, kinetic analysis was carried out to determine the various activation parameters. In addition, the processing maps showed a regime of flow instability spanning both alpha + beta and beta phase fields. The hot deformation behavior of Zr 1Nb-1Sn was compared with that of Zr, Zr-2.5Nb and Zircaloy-2 to bring out the effects of alloy additions. (C) 2006 Elsevier BN. All rights reserved.

Characterization of mouse neuronal Ca2+/calmodulin kinase II inhibitor alpha

We have overexpressed an 8.5-kDa mouse Ca2+/calmodulin kinase II inhibitor a protein (mCaMKIIN alpha) in Escherichia coli and demonstrate that the recombinant protein is a potent inhibitor of Ca2+/calmodulin kinase 11 (CaMKII) in vitro. However, antibodies raised against recombinant mCaMKIIN alpha. react with an similar to 37-kDa protein present in mouse brain. The pattern of expression of the similar to 37-kDa protein is similar to that of mCaMKIIN alpha mRNA as both are expressed in normal but not Japanese encephalitis virus (JEV)-infected mouse brain. Subcellular localization studies indicate that the similar to 37-kDa protein is present in the post-synaptic density (PSD) where mCaMKII alpha is known to perform key regulatory functions. We conclude that the similar to 37-kDa protein identified in this study is mCaMKIIN alpha. and its localization in the PSD indicates a novel role for this protein in the regulation of neuronal CaMKII alpha. (c) 2007 Elsevier B.V. All rights reserved.

Characterization of LRRTM and NGR gene families: Expression and functions

Some leucine-rich repeat (LRR) -containing membrane proteins are known regulators of neuronal growth and synapse formation. In this work I characterize two gene families encoding neuronal LRR membrane proteins, namely the LRRTM (leucine-rich repeat, transmembrane neuronal) and NGR (Nogo-66 receptor) families. I studied LRRTM and NGR family member's mRNA tissue distribution by RT-PCR and by in situ hybridization. Subcellular localization of LRRTM1 protein was studied in neurons and in non-neuronal cells. I discovered that LRRTM and NGR family mRNAs are predominantly expressed in the nervous system, and that each gene possesses a specific expression pattern. I also established that LRRTM and NGR family mRNAs are expressed by neurons, and not by glial cells. Within neurons, LRRTM1 protein is not transported to the plasma membrane; rather it localizes to endoplasmic reticulum. Nogo-A (RTN4), MAG, and OMgp are myelin-associated proteins that bind to NgR1 to limit axonal regeneration after central nervous system injury. To better understand the functions of NgR2 and NgR3, and to explore the possible redundancy in the signaling of myelin inhibitors of neurite growth, I mapped the interactions between NgR family and the known and candidate NgR1 ligands. I identified high-affinity interactions between RTN2-66, RTN3-66 and NgR1. I also demonstrate that Rtn3 mRNA is expressed in the same glial cell population of mouse spinal cord white matter as Nogo-A mRNA, and thus it could have a role in myelin inhibition of axonal growth. To understand how NgR1 interacts with multiple structurally divergent ligands, I aimed first to map in more detail the nature of Nogo-A:NgR1 interactions, and then to systematically map the binding sites of multiple myelin ligands in NgR1 by using a library of NgR1 expression constructs encoding proteins with one or multiple surface residues mutated to alanine. My analysis of the Nogo-A:NgR1 -interactions revealed a novel interaction site between the proteins, suggesting a trivalent Nogo-A:NgR1-interaction. Our analysis also defined a central binding region on the concave side of NgR1's LRR domain that is required for the binding of all known ligands, and a surrounding region critical for binding MAG and OMgp. To better understand the biological role of LRRTMs, I generated Lrrtm1 and Lrrtm3 knock out mice. I show here that reporter genes expressed from the targeted loci can be used for maping the neuronal connections of Lrrtm1 and Lrrtm3 expressing neurons in finer detail. With regard to LRRTM1's role in humans, we found a strong association between a 70 kb-spanning haplotype in the proposed promoter region of LRRTM1 gene and two possibly related phenotypes: left-handedness and schizophrenia. Interestingly, the responsible haplotype was linked to phenotypic variability only when paternally inherited. In summary, I identified two families of neuronal receptor-like proteins, and mapped their expression and certain protein-protein interactions. The identification of a central binding region in NgR1 shared by multiple ligands may facilitate the design and development of small molecule therapeutics blocking binding of all NgR1 ligands. Additionally, the genetic association data suggests that allelic variation upstream of LRRTM1 may play a role in the development of left-right brain asymmetry in humans. Lrrtm1 and Lrrtm3 knock out mice developed as a part of this study will likely be useful for schizophrenia and Alzheimer s disease research.

Synthesis, spectral characterization, in-vitro microbiological evaluation and cytotoxic activities of novel macrocyclic bis hydrazone

A macrocyclic hydrazone Schiff base was synthesized by reacting 1,4-dicarbonyl phenyl dihydrazide with 2,6-diformyl-4-methyl phenol and a series of metal complexes with this new Schiff base were synthesized by reaction with Co(II), Ni(II) and Cu(II) metal salts. The Schiff base and its complexes have been characterized by elemental analyses, IR, H-1 NMR, UV-vis, FAB mass, ESR spectra, fluorescence, thermal, magnetic and molar conductance data. The analytical data reveal that the Co(II), Ni(II) and Cu(II) complexes possess 2:1 metal-ligand ratios. All the complexes are non-electrolytes in DMF and DMSO due to their low molar conductance values. Infrared spectral data suggest that the hydrazone Schiff base behaves as a hexadentate ligand with NON NON donor sequence towards the metal ions. The ESR spectral data shows that the metal-ligand bond has considerable covalent character. The electrochemical behavior of the copper(II) complex was investigated by cyclic voltammetry. The Schiff base and its complexes have also been screened for their antibacterial (Escherichia coli, Staphylococcus aureus, Shigella dysentery, Micrococcus, Bacillus subtilis, Bacillus cereus and Pseudomonas aeruginosa) and antifungal activities (Aspergillus niger, Penicillium and Candida albicans) by MIC method. The brine shrimp bioassay was also carried out to study their in-vitro cytotoxic properties. (C) 2009 Elsevier Masson SAS. All rights reserved.

Molecular characterization of mitochondrial ataxias : with emphasis on MIRAS and IOSCA

Uusi hermoston rappeumasairaus MIRAS: Suomessa kantajia joka 125. väestöstä Tässä väitöskirjatyössä on kuvattu uusi peittyvästi periytyvä hermoston rappeumasairaus, MIRAS (mitochondrial recessive ataxia syndrome), ja sen geenitausta. Tauti osoittautui tutkimuksessamme Suomen yleisimmäksi perinnölliseksi ataksiasairaudeksi. Tutkimuksessa on tutkittu perinnöllisiä aivosairauksia, joissa yhtenä oireena on ataksia (kävelyn epävarmuus, tasapainovaikeus ja liikkeiden haparointi), sekä lukuisia muita aivojen toimintahäiriöstä johtuvia oireita. Seuloessamme suomalaisilta ataksiapotilailta MIRAS-geenivirhettä, 27 potilasta sai diagnoosin aikaisemmin tuntemattomalle, etenevälle ataksiasairaudelleen. Tutkimuksen tuloksena kyseisen geenivirheen DNA-diagnostiikka on otettu käyttöön suomalaisissa ja eurooppalaisissa laboratorioissa, ja toista sataa potilasta ympäri maailman on saanut diagnoosin. Suomen väestössä joka 125. kantaa MIRAS geenivirhettä, mutta taudin saa vain, jos perii geenivirheen molemmilta vanhemmiltaan. MIRAS on taudinkuvaltaan vaihteleva, mutta vaikea etenevä neurologinen sairaus. Useilla potilailla esiintyvät oireet ovat ataksia, puheen puuromaisuus (dysartria), ääreishermorappeuma (neuropatia), pakkoliikkeet, psykiatriset oireet sekä vaikea epilepsia. Erityisen tärkeää MIRAS-taudin tunnistaminen on siihen liittyvän epilepsian hoitopäätöksessä: valproaatti-lääkitys voi aiheuttaa MIRAS-potilaille vaikean maksavaurion. Väitöskirjatyön tuloksena selvisi, että kaikki suomalaiset, norjalaiset, belgialaiset, englantilaiset, australialaiset ja uusi-seelantilaiset MIRAS potilaat olivat kaukaista sukua samalle, tuhansia vuosia sitten eläneelle eurooppalaiselle esivanhemmalle. Ataksiasairauksien tautimekanismeja selvitimme tutkimalla MIRAS-ataksiaa ja sitä muistuttavaa IOSCA sairautta (infantile onset spinocerebellar ataxia), jonka aiheuttaa peittyvästi periytyvä geenivirhe Twinkle-geenissä. Tutkimuksessa löydettiin myös uusi, Twinkle-geenin geenivirheestä johtuva taudinkuva: vaikea-asteinen, varhaisella iällä alkava aivosairaus, jossa on lisäksi viitteitä maksasairaudesta. Löysimme potilaiden aivoista muutoksia mitokondrioiden eli solun voimalaitosten perimän määrässä. Nämä tulokset antavat arvokasta lisätietoa ataksiasairauksien taustalla olevista muutoksista, joiden ymmärtäminen on välttämätön edellytys hoitomahdollisuuksien tutkimiselle tulevaisuudessa.