Matrix Loop Research Articles

Integrable couplings, bi-integrable couplings and their Hamiltonian structures of the Giachetti-Johnson soliton hierarchy

On the basis of zero curvature equations from semi-direct sums of Lie algebras, we construct integrable couplings of the Giachetti–Johnson hierarchy of soliton equations. We also establish Hamiltonian structures of the resulting integrable couplings by the variational identity. Moreover, we obtain bi-integrable couplings of the Giachetti–Johnson hierarchy and their Hamiltonian structures by applying a class of non-semisimple matrix loop algebras consisting of triangular block matrices. Copyright © 2014 John Wiley & Sons, Ltd.

Non-Semisimple Lie Algebras of Block Matrices and Applications to Bi-Integrable Couplings

AbstractWe propose a class of non-semisimple matrix loop algebras consisting of 3 × 3 block matrices, and form zero curvature equations from the presented loop algebras to generate bi-integrable couplings. Applications are made for the AKNS soliton hierarchy and Hamiltonian structures of the resulting integrable couplings are constructed by using the associated variational identities.

Tri-integrable Couplings by Matrix Loop Algebras

Abstract We create a class of non-semisimple matrix loop algebras, and use the associated zero curvature equations to construct tri-integrable couplings. An application is made for the AKNS equations as an illustrative example. Hamiltonian structures of the resulting tri-integrable couplings are furnished by the variational identities over the presented matrix loop algebras, which implies the commutativity of the sequences of symmetries and conserved functionals.

A Block Matrix Loop Algebra and Bi-Integrable Couplings of the Dirac Equations

AbstractA non-semisimple matrix loop algebra is presented, and a class of zero curvature equations over this loop algebra is used to generate bi-integrable couplings. An illustrative example is made for the Dirac soliton hierarchy. Associated variational identities yield bi-Hamiltonian structures of the resulting bi-integrable couplings, such that the hierarchy of bi-integrable couplings possesses infinitely many commuting symmetries and conserved functionals.

Exploring the Conformational Dynamics of the Bovine ADP/ATP Carrier in Mitochondria

The mitochondrial ADP/ATP carrier catalyzes the transport of ADP and ATP across the mitochondrial inner membrane by switching between two different conformations. They can be blocked by two inhibitors: carboxyatractyloside (CATR) and bongkrekic acid (BA). Our understanding of the ADP/ATP transport process is largely based on analysis of structural differences between the individual inhibited states. The X-ray crystallographic three-dimensional structure of bovine ADP/ATP carrier isoform 1 (bAnc1p) complexed with CATR was determined, but the structure of the BA-carrier complex remains unknown. We recently investigated the conformational dynamics of bAnc1p in detergent solution using hydrogen/deuterium exchange and mass spectrometry (HDX-MS). This study shed light on some features of ADP/ATP translocation, but the mechanism itself and the organization of bAnc1p in the membrane required further investigation. This paper describes the first study of bAnc1p in the mitochondria on the whole-protein scale using HDX-MS. Membrane-embedded bAnc1p was deuterated and purified under HDX-MS-compatible conditions. Our results for the carrier in the mitochondrial inner membrane differed from those published for the carrier in a detergent solution. These differences were mainly in the upper half of the cavity that globally showed a limited H/D exchange whatever the complex analyzed and at the level of the matrix loops that were less accessible to the solvent in the BA-carrier complex than in the CATR-carrier complex. They are discussed with respect to published data for bAnc1p and have provided new insights into the conformation of the matrix loops of the bovine carrier in complex with BA in mitochondria.

Mitochondrial ADP/ATP Carrier: Preventing Conformational Changes by Point Mutations Inactivates Nucleotide Transport Activity

The mitochondrial ADP/ATP carrier (Ancp) is a paradigm of the mitochondrial carrier family (MCF); its members allow metabolic fluxes between mitochondria and the cytosol. The members of the MCF share numerous structural and functional characteristics. Ancp is very specifically inhibited by two classes of compounds, which stabilize the carrier in two different conformations involved in nucleotide transport. Resolution of the atomic structure of the bovine Ancp, in complex with one of its specific inhibitors, is that of the carrier open toward the intermembrane space. To gain insights into the interconversion from one conformation to the other, we introduced point mutations in the yeast carrier at positions Cys73 in the first matrix loop and Tyr97 and Gly298 in transmembrane helices 2 and 6. We demonstrate in this paper that they impair stabilization of the carrier in one conformation or the other, resulting in an almost complete inactivation of nucleotide transport in both cases. The results are discussed on the basis of the atomic structure of the conformation open to the cytosol. These mutant proteins could afford convenient tools for undertaking structural studies of both conformations of the yeast carrier.

Loop algebras and bi-integrable couplings

A class of non-semisimple matrix loop algebras consisting of triangular block matrices is introduced and used to generate bi-integrable couplings of soliton equations from zero curvature equations. The variational identities under non-degenerate, symmetric and ad-invariant bilinear forms are used to furnish Hamiltonian structures of the resulting bi-integrable couplings. A special case of the suggested loop algebras yields nonlinear bi-integrable Hamiltonian couplings for the AKNS soliton hierarchy.

Prognostic associations of insulin-like growth factor-1 receptor in primary uveal melanoma

Objective To study the association between immunoreactivity for insulin-like growth factor-1 receptor (IGF-1R) in primary ciliary body and choroidal melanoma and metastatic death in a consecutive, population-based data set. Design Retrospective, consecutive, population-based cohort study. Participants A total of 167 patients with choroidal and ciliary body melanoma, enucleated from 1972 to 1981, with long-term survival data. Methods Specimens were immunostained by using the avidin-biotinylated peroxidase complex method and polyclonal antibodies to IGF-1R. The percentage of tumour area that was immunopositive was recorded. Survival was assessed by Cox multivariate regression analysis. Results The tumour area could be reliably measured from 129 (78%) of the 167 choroidal or ciliary body melanomas. More heavy pigmentation ( p = 0.001), larger number of macrophages ( p = 0.003) and higher microvascular density ( p = 0.060) were associated with a higher percentage of tumour area that was immunopositive for IGF-1R, the reverse being true of extrascleral extension ( p = 0.049). No significant association was observed with ciliary body extension, largest basal tumour diameter, cell type, mean diameter of the 10 largest nucleoli, and presence of extravascular matrix loops and networks ( p = 0.61-0.96). The percentage of tumour area that was immunopositive for IGF-1R was not associated with survival. Conclusions In our data set, immunoreactivity for IGF-IR did not independently predict metastasis from primary uveal melanoma. Partial loss of antigenicity can not be ruled out as a confounding factor because no frozen sections were available. Results of previous studies have likewise been variable, suggesting that immunohistochemical determination of IGF-1R from formalin-fixed, paraffin-embedded specimens is not practical as a routine test.

Exploring Interactions between the 49 kDa and ND1 Subunits in Mitochondrial NADH-Ubiquinone Oxidoreductase (Complex I) by Photoaffinity Labeling

Quinazolines are strong inhibitors of NADH-ubiquinone oxidoreductase (complex I) from bovine heart mitochondria. Using a photoreactive quinazoline, [(125)I]AzQ, and bovine heart submitochondrial particles (SMPs), we demonstrated previously that [(125)I]AzQ binds at the interface of the 49 kDa and ND1 subunits in complex I; it labeled a site in the N-terminal (Asp41-Arg63) region of the 49 kDa subunit, suggesting that this region contacts the ND1 subunit [Murai, M., et al. (2009) Biochemistry 48, 688-698]. The labeled region of ND1 could not be identified because it is highly hydrophobic, and the SMPs did not yield sufficient amounts of labeled protein. Here, we describe how photoaffinity labeling of isolated complex I by [(125)I]AzQ yielded sufficient material for identification of the labeled region of the ND1 subunit. The inhibition of the isolated enzyme by AzQ is comparable to that of SMPs. Our results reveal that the labeled site in ND1 is between Asp199 and Lys262, mostly likely in the third matrix loop that connects the fifth and sixth transmembrane helices. Thus, our results reveal new information about the interface between the hydrophilic and hydrophobic domains of complex I, a region that is thought to be important for ubiquinone reduction and energy transduction.

Cytogenetics and prognosis for uveal melanoma in Korean patients

To determine the rate of mortality for uveal melanoma in the Korean population and assess whether it correlates with cytogenetic data, and clinical and histopathological factors. A retrospective review of medical files from 33 uveal melanoma patients who underwent enucleation at Yonsei University, Seoul, Korea, between January, 1994 and December, 2009 was performed. Dual-colour fluorescence in situ hybridization was performed using centromeric probes for chromosome 3 and 8 in archived patient tissues. The mean age of patients was 53.2 years (range; 29-78), and the mean largest basal diameter was 11.8 mm (range; 6.0-18.1). Of the 20 tissue blocks with available cytogenetic data, there was monosomy 3 in seven (35%) and polysomy 8 in four (20%). The presence of monosomy 3 (p < 0.001), polysomy 8 (p < 0.001), ciliary body involvement (p < 0.001), a mitotic rate ≥5/40 high-power fields (p = 0.006), closed extravascular matrix loop (p = 0.025), large basal tumour diameter (p = 0.029) and epithelioid cellularity (p = 0.038) predicted melanoma-related mortality. The median time from enucleation to liver metastasis was 16 months (range; 10-70), and the median survival after metastasis was 5 months (range; 1-9). The Kaplan--Meier survival curve estimated the metastatic death rate to be 22% for 5 years and 30% for 10 years. Korean patients with uveal melanoma are younger and appear to exhibit no worse prognosis than Caucasian. Cytogenetic abnormality of chromosome 3 and 8 highly predicted metastatic death.

Microstructure formation in neutron-irradiated V-1.6Y alloy at 800 °C

Microstructure formation in V-1.6Y during neutron irradiation at 800°C was examined with transmission electron microscopy. Faulted vacancy loops were observed in the coarse grains several micrometers in diameter without dispersed Y2O3 particles. The habit plane of the faulted vacancy loop is close to {116}. Formation of faulted vacancy loops in the vanadium matrix could be induced by oxygen picked up from the environment during irradiation. Denuded zone of faulted vacancy loops was observed around both helical dislocations and grain boundaries.

Infiltrating macrophages in extratumoural tissues after brachytherapy of uveal melanoma

To compare distribution of macrophages in extratumoural ocular tissues in enucleated eyes with irradiated and nonirradiated uveal melanomas to find out how irradiation affects distribution of macrophages so as to gain insight into their potential routes of migration and changes in local inflammatory responses. Thirty-four matched pairs of primarily enucleated nonirradiated and secondarily enucleated irradiated eyes with choroidal and ciliary body melanoma were stained with mAb PG-M1, and the extratumoural immunopositive elements were counted under the microscope. Main outcome variables were the number of macrophages in the sclera underlying the tumour, in the choroid adjacent to the tumour, and in the ciliary body. The number of macrophage aggregates in the anterior ipsi- and contralateral episclera adjacent to the limbus was also counted. Macrophages were more numerous within the sclera under the tumour in irradiated eyes when compared to primarily enucleated eyes (median 1514 versus 619/mm², p = 0.0001), and more aggregates of episcleral macrophages adjacent to the limbus were found after irradiation (ipsilateral side, median 132 versus 0, p = 0.0034; contralateral side, median 79 versus 0, p = 0.014). In primarily enucleated eyes, increasing numbers of tumour-infiltrating macrophages were associated with presence of higher numbers of macrophages in the ciliary body (p = 0.003) and the adjacent choroid (p = 0.044), whereas in the irradiated eyes, increasing numbers of tumour-infiltrating macrophages (p = 0.010) and increasing extent of necrosis (p < 0.001) were associated with higher numbers of intrascleral macrophages underlying the tumour. Resident macrophages are present in extratumoural tissues in eyes with uveal melanoma. Brachytherapy may alter their route of migration and increase the number of macrophages in the sclera and episclera. Histopathologically detectable episcleral aggregates of macrophages adjacent to the limbus are detected predominantly after irradiation, a population of which is clinically visible as episcleral deposits after irradiation.

ADP/ATP mitochondrial carrier MD simulations to shed light on the structural–dynamical events that, after an additional mutation, restore the function in a pathological single mutant

Molecular dynamics simulations of the wild type bovine ADP/ATP mitochondrial carrier, and of the single Ala113Pro and double Ala113Pro/Val180Met mutants, embedded in a lipid bilayer, have been carried out for 30ns to shed light on the structural-dynamical changes induced by the Val180Met mutation restoring the carrier function in the Ala113Pro pathologic mutant. Principal component analysis indicates that, for the three systems, the protein dynamics is mainly characterized by the motion of the matrix loops and of the odd-numbered helices having a conserved proline in their central region. Analysis of the motions shows a different behaviour of single pathological mutant with respect of the other two systems. The single mutation induces a regularization and rigidity of the H3 helix, lost upon the introduction of the second mutation. This is directly correlated to the salt bridge distribution involving residues Arg79, Asp134 and Arg234, hypothesized to interact with the substrate. In fact, in the wild type simulation two stable inter-helices salt bridges, crucial for substrate binding, are present almost over all the simulation time. In line with the impaired ADP transport, one salt interaction is lost in the single mutant trajectory but reappears in the double mutant simulation, where a salt bridge network matching the wild type is restored. Other important structural-dynamical properties, such as the trans-membrane helices mobility, analyzed via the principal component analysis, are similar for the wild type and double mutant while are different for the single mutant, providing a mechanistic explanation for their different functional properties.

家族性lecithin:cholesterol acyltransferase欠損症の一例

Lecithin: cholesterol acyltransferase (LCAT) is an enzyme that catalyzes the esterifying reaction of cholesterol in plasma high density lipoprotein (HDL). Deficiency of LCAT is a rare hereditary disease characterized by several clinical symptoms such as proteinuria, corneal opacity, and anemia due to a shortened life span of erythrocytes. In this communication, we report a case of 40 year-old female patient of LCAT deficiency. She visited a hospital for work-up of proteinuria, corneal opacity and anemia. Activity of her serum LCAT was found to be extremely low, and characteristic changes in plasma lipids due to deficiency of LCAT was observed: those were marked decreases in HDL-cholesterol, degree of esterification in serum cholesterol, and apoprotein A-I, A-II, B and C-II levels. The diagnosis of LCAT deficiency was finally made. We studied about histopathological changes in the patient's kidney, and erythrocyte membrane lipid composition and fluidity. Histopathological findings in renal biopsy were follows: a) Light microscopy showed spherical deposits stained with periodic acid-Schiff in mesangial matrix and adjacent capillary loops, and hyaline deposits in arterioles, b) Electron microscopy showed vacuoles in mesangial matrix and along the glomerular basement membranes. In erythrocyte membrane lipids, increase of cholesterol to phospholipid molar ratio was evident, being accompanied by changes in phospholipid fractions: increase of phosphatidylcholine, and decreases of phosphatidylethanolamine, sphingomyelin and lysophosphatidylcholine. In phospholipid acyl chains, increase of C18:2 and decreased of C18:1 were evident in the patient. Erythrocyte membrane fluidity was found to be decreased in the patient in a measurement by pyrene, probably being related to the changes in membrane lipid composition.(ABSTRACT TRUNCATED AT 250 WORDS)

Tyrosine phosphorylation by Src within the cavity of the adenine nucleotide translocase 1 regulates ADP/ATP exchange in mitochondria

Phosphorylation of adenine nucleotide translocator 1 (ANT1) at residue Y194, which is part of the aromatic ladder located within the lumen of the carrier, critically regulates mitochondrial metabolism. Recent data support the concept that members of the Src family of nonreceptor tyrosine kinases are constitutively present in mitochondria and key to regulation of mitochondrial function. Herein, we demonstrate that site mutations of ANT1 (Y190-->F190, Y194-->F194) mimicking dephosphorylation of the aromatic ladder resulted in loss of oxidative growth and ADP/ATP exchange activity in respiration-incompetent yeast expressing mutant chimeric yN-hANT1. ANT1 is phosphorylated at Y194 by the Src family kinase members Src and Lck, and increased phosphorylation is tightly linked to reduced cell injury in preconditioned protected vs. unprotected cardiac mitochondria. Molecular dynamics simulations find the overall structure of the phosphorylated ANT1 stable, but with an increased steric flexibility in the region of the aromatic ladder, matrix loop m2, and four helix-linking regions. Combined with an analysis of the putative cytosolic salt bridge network, we reason that the effect of phosphorylation on transport is likely due to an accelerated transition between the main two conformational states (c<-->m) of the carrier during the transport cycle. Since "aromatic signatures" are typical for other mitochondrial carrier proteins with important biological functions, our results may be more general and applicable to these carriers.

Two Residues of a Conserved Aromatic Ladder of the Mitochondrial ADP/ATP Carrier Are Crucial to Nucleotide Transport

The mitochondrial ADP/ATP carrier is the paradigm of the mitochondrial carrier family (MCF), whose members are crucial for cross-talks between mitochondria, where cell energy is mainly produced, and the cytosol, where cell energy is mainly consumed. These carriers share structural and functional characteristics. Resolution of the 3D structure of the beef mitochondrial ADP/ATP carrier, in a complex with one of its specific inhibitors, revealed interesting features and suggested the involvement of some particular residues in substrate binding and transfer from the outside to the inside of mitochondria. To ascertain the role of these residues, namely, Y186, Y190, F191, and Y194, they were mutated into alanine in the yeast mitochondrial ADP/ATP carrier at equivalent positions (Y203, Y207, F208, and Y211). Two residues, Y203 and F208, appeared to be crucial for transport activity but not for substrate binding per se, indicating their involvement in the substrate transfer process through the carrier. Furthermore, it was possible to show that these mutations precluded conformational changes of the matrix loop m2, whose movements were demonstrated to participate in substrate transport by the wild-type carrier. Therefore, these aromatic residues may be involved in substrate gliding, and they may also confer specificity toward adenine nucleotides for the ADP/ATP carrier as compared with the MCF members.

What is the significance of vortex vein invasion in uveal melanoma?

To correlate vortex vein invasion with established prognostic factors for uveal melanoma. Enucleated eyes with a confirmed histopathological diagnosis of uveal melanoma with vortex vein invasion were identified, over a 10-year period. Established uveal melanoma prognostic factors, with tumour genetics were correlated with vortex vein invasion and patient survival. Microscopic vortex vein involvement was present in 29 of 244 (11.9%) uveal melanomas. Of 29, 6 (20.7%) tumours had macroscopic evidence of vortex vein invasion. Of 29, 14 (48.3%) tumours also showed evidence of non-vortex vein, 'direct' scleral invasion. 23 (79.3%) of 29 melanomas involved only the choroid. The mean maximum diameter of tumours with vortex vein invasion was 15.8 mm and the mean thickness was 9.7 mm. The uveal melanoma was a discrete nodule in 27 of 29 (93.1%) cases. Histologically, 8 of 29 tumours (27.6%) were spindle cell, 19 of 29 (65.5%) were mixed cell, and 2 of 29 (6.9%) were epithelioid cell type. Of 29, 22 (75.9%) uveal melanomas with vortex vein invasion contained extracellular matrix networks and loops. Genetic abnormalities correlated with poor prognosis were seen in 25 of 29 (86.2%) tumours with vortex vein invasion. Liver metastasis was confirmed in 19 of 29 (65.5%) patients with vortex vein invasion. No patients with uveal melanomas showing vortex vein invasion suffered orbital recurrence of disease following enucleation. The trends show that vortex vein invasion is associated with a choroidal location, large tumour size, spindle cell bias, presence of extracellular matrix loops/networks and genetic markers. A higher proportion of patients with vortex vein invasion progress to develop liver metastasis compared with the general uveal melanoma population.

New Matrix Loop Algebra and Its Application

A new matrix Lie algebra and its corresponding Loop algebra are constructed firstly, as its application, the multi-component TC equation hierarchy is obtained, then by use of trace identity the Hamiltonian structure of the above system is presented. Finally, the integrable couplings of the obtained system is worked out by the expanding matrix Loop algebra.

Modelling life history strategies with capture-recapture data: Evolutionary demography of the water skink Eulamprus tympanum

Matrix population models, elasticity analysis and loop analysis can potentially provide powerful techniques for the analysis of life histories. Data from a capture–recapture study on a population of southern highland water skinks (Eulamprus tympanum) were used to construct a matrix population model. Errors in elasticities were calculated by using the parametric bootstrap technique. Elasticity and loop analyses were then conducted to identify the life history stages most important to fitness. The same techniques were used to investigate the relative importance of fast versus slow growth, and rapid versus delayed reproduction. Mature water skinks were long-lived, but there was high immature mortality. The most sensitive life history stage was the subadult stage. It is suggested that life history evolution in E. tympanum may be strongly affected by predation, particularly by birds. Because our population declined over the study, slow growth and delayed reproduction were the optimal life history strategies over this period. Although the techniques of evolutionary demography provide a powerful approach for the analysis of life histories, there are formidable logistical obstacles in gathering enough high-quality data for robust estimates of the critical parameters.

A CD study of uncoupling protein-1 and its transmembrane and matrix-loop domains

Conformations of the prototypic UCP-1 (uncoupling protein-1) and its TM (transmembrane) and ML (matrix-loop) domains were studied by CD spectroscopy. Recombinant, untagged mouse UCP-1 and a hexahistidine-tagged version of the protein were obtained in high purity following their overexpression in Escherichia coli. The TM and ML domains of hamster UCP-1 were chemically synthesized. Conformations of both recombinant UCP-1 proteins were dominantly helical (40-50%) in digitonin micelles. Binding of the purine nucleotides GDP and GTP to UCP-1, detected in the near-UV CD region, supported the existence of the functional form of the protein in digitonin micelles. All individual TM and ML peptides, except the third ML domain, adopted helical structures in aqueous trifluoroethanol, which implies that, in addition to six TM segments, at least two of the ML domains of the UCP-1 can form helical structures in membrane interface regions. TM and ML domains interacted with vesicles composed of the main phospholipids of the inner membrane of mitochondria, phosphatidylcholine, phosphatidylethanolamine and cardiolipin, to adopt dominantly beta- and/or unordered conformations. Mixtures of UCP-1 peptide domains spontaneously associated in aqueous, phospholipid vesicles and digitonin micelle environments to form ordered conformations, which exhibited common features with the conformations of the full-length proteins. Thermal denaturations of UCP-1 and its nine-peptide-domain assembly in digitonin were co-operative but not reversible. Assembly of six TM domains in lipid bilayers formed ion-conducting units with possible helical bundle conformations. Consequently, covalent connection between peptide domains, tight domain interactions and TM potential are essential for the formation of the functional conformation of UCP-1.