Cone Domains Research Articles

Degeneration of the spectral gap with negative Robin parameter

AbstractThe spectral gap of the Neumann and Dirichlet Laplacians are each known to have a sharp positive lower bound among convex domains of a given diameter. Between these cases, for each positive value of the Robin parameter, an analogous sharp lower bound on the spectral gap is conjectured. In this paper, we show that the extension of this conjecture to negative Robin parameters fails by proving that the spectral gap of double cone domains are exponentially small, for each fixed parameter value.

Structural Investigation of Allosteric Regulation in Class III Ribonucleotide Reductases

Ribonucleotide reductases (RNRs) are essential enzymes that use radical‐based chemistry to catalyze the reduction of ribonucleotides to deoxyribonucleotides. Each RNR class uses a different cofactor to generate a catalytically‐essential thiyl radical species in the enzyme active site. Anaerobic (class III) RNRs employ an oxygen‐sensitive glycyl radical cofactor installed within the glycyl radical domain (GRD) that is adjacent to the active site, whereas aerobic (class Ia) RNRs employ long‐range radical transfer between the catalytic subunit and a di‐iron/tyrosyl radical cofactor housed in the b2 subunit. To maintain intracellular nucleotide pool balance, RNRs are allosterically regulated. For the prototypical class Ia RNRs from Escherichia coli, this allosteric activity regulation involves dATP binding to the N‐terminus of the catalytic subunit in a region known as the ‘cone domain’, resulting in an association between the cone domain and the b2 subunit that prevents radical transfer between subunits. Despite not requiring a b2 subunit, some class III RNRs (e.g. Streptococcus thermophilus)have a cone domain and are allosterically inhibited by dATP. In this study, we investigate allosteric activity regulation for such a class III RNR, the class III RNR from Streptococcus thermophilus(StNrdD). We use a newly developed LC‐MS/MS based activity assay to show that dATP downregulates StNrdD activity and ATP upregulates activity as is true for class Ia RNRs. Using crystallography, we obtain structural data showing that ATP and dATP both bind to the cone domain, and that both the cone domain and GRD are flexible. In particular, in one monomer of StNrdD dimer, the cone domain contacts the GRD, and both domains are ordered, and in the other monomer, the cone domain is positioned away from the GRD and the GRD is disordered. These observations led us to hypothesize that the cone domains of class III RNRs, like those of class Ia RNR, regulate activity through promotion or inhibition of the radical transfer step, but instead of controlling the position of b2, the position of the GRD is allosterically regulated. In this presentation, we show the data described above and show recent cryogenic electron microscopy of ATP‐bound and dATP‐bound states of StNrdD, which reveals differential positioning of the cone domains in the presence of these allosteric effectors. We also present our current thinking about the mechanism of allosteric regulation of activity in a class III RNR.

Biochemical Characterization of a Human Ribonucleotide Reductase (HsRNR) Variant Lacking Activity Regulation

Ribonucleotide reductase (RNR) is responsible for the synthesis of deoxyribonucleotides used in DNA synthesis and repair. Class Ia RNRs are composed of two dimeric subunits: a catalytic subunit (α2) which contains the active site and two allosteric regulation sites, and radical generating (β2) subunit housing the diferric‐tyrosyl radical cofactor. The two subunits form an α2β2 heterotetrametric complex that allows the radical to travel from β to α subunit for catalysis. RNR activity is regulated by the binding of ATP/dATP to an N‐terminal cone domain. Human RNRs (HsRNRs) are class Ia enzymes that form a homohexameric α6in the presence of either dATP or ATP. Although, both α6 assemblies are morphologically identical, only the α6‐ATP can be disturbed by the addition of β to form the α2β2 complex necessary for catalysis. Recent studies have shown that α subunits contact each other via their cone domains in the α6 rings, but it is unknown if the cone domains contact β2 in the α2β2 active complex. Here, we aim to probe the role of the cone domains in catalysis through biochemical and biophysical studies of an α subunit variant lacking the cone domain. We used site‐directed mutagenesis to delete residues 2‐92 of α, and expressed and purified the variant a protein. The variant protein was used for HPLC‐MS based activity assays of HsRNR. Preliminary results show the cone domain is important for catalysis. Understanding more about RNR’s structure and activity regulation can facilitate development of new cancer therapies.

Oblique derivative problems for elliptic equations on conical domains

We study the oblique derivative problem for uniformly elliptic equations on cone domains. Under the assumption of axi-symmetry of the solution, we find sufficient conditions on the angle of the oblique vector for Hölder regularity of the gradient to hold up to the vertex of the cone. The proof of regularity is based on the application of carefully constructed barrier methods or via perturbative arguments. In the case that such regularity does not hold, we give explicit counterexamples. We also give a counterexample to regularity in the absence of axi-symmetry. Unlike in the equivalent two-dimensional problem, the gradient Hölder regularity does not hold for all axi-symmetric solutions, but rather the qualitative regularity properties depend on both the opening angle of the cone and the angle of the oblique vector in the boundary condition.

An endogenous dAMP ligand in Bacillus subtilis class Ib RNR promotes assembly of a noncanonical dimer for regulation by dATP

The high fidelity of DNA replication and repair is attributable, in part, to the allosteric regulation of ribonucleotide reductases (RNRs) that maintains proper deoxynucleotide pool sizes and ratios in vivo. In class Ia RNRs, ATP (stimulatory) and dATP (inhibitory) regulate activity by binding to the ATP-cone domain at the N terminus of the large α subunit and altering the enzyme's quaternary structure. Class Ib RNRs, in contrast, have a partial cone domain and have generally been found to be insensitive to dATP inhibition. An exception is the Bacillus subtilis Ib RNR, which we recently reported to be inhibited by physiological concentrations of dATP. Here, we demonstrate that the α subunit of this RNR contains tightly bound deoxyadenosine 5'-monophosphate (dAMP) in its N-terminal domain and that dATP inhibition of CDP reduction is enhanced by its presence. X-ray crystallography reveals a previously unobserved (noncanonical) α2 dimer with its entire interface composed of the partial N-terminal cone domains, each binding a dAMP molecule. Using small-angle X-ray scattering (SAXS), we show that this noncanonical α2 dimer is the predominant form of the dAMP-bound α in solution and further show that addition of dATP leads to the formation of larger oligomers. Based on this information, we propose a model to describe the mechanism by which the noncanonical α2 inhibits the activity of the B. subtilis Ib RNR in a dATP- and dAMP-dependent manner.

Existence of global solutions in time for reaction-diffusion systems with inhomogeneous terms in cones

We consider nonnegative solutions of the initial-boundary value problems in cone domains for the reaction-diffusion systems with inhomogeneous terms dependent on space-time coordinates. In this paper we show the condition for the existence of global solutions. Our conditions for the global existence are optimal in view of our nonexistence results in 2009.

Microtubule-mediated Src Tyrosine Kinase Trafficking in Neuronal Growth Cones

Src family tyrosine kinases are important signaling enzymes in the neuronal growth cone, and they have been implicated in axon guidance; however, the detailed localization, trafficking, and cellular functions of Src kinases in live growth cones are unclear. Here, we cloned two novel Aplysia Src kinases, termed Src1 and Src2, and we show their association with both the plasma membrane and the microtubule cytoskeleton in the growth cone by live cell imaging, immunocytochemistry, and cell fractionation. Activated Src2 is enriched in filopodia tips. Interestingly, Src2-enhanced green fluorescent protein-positive endocytic vesicles and tubulovesicular structures undergo microtubule-mediated movements that are bidirectional in the central domain and mainly retrograde in the peripheral domain. To further test the role of microtubules in Src trafficking in the growth cone, microtubules were depleted with either nocodazole or vinblastine treatment, resulting in an increase in Src2 plasma membrane levels in all growth cone domains. Our data suggest that microtubules regulate the steady-state level of active Src at the plasma membrane by mediating retrograde recycling of endocytosed Src. Expression of constitutively active Src2 results in longer filopodia that protrude from smaller growth cones, implicating Src2 in controlling the size of filopodia and lamellipodia.

A note on four-point partial difference equations with variable coefficients

The aim of this note is to find the explicit solution of four-point linear partial difference equations with variable coefficients. Three-point and four-point cases in quadrant and cone domains are considered and the boundary conditions, allowing the existence and the uniqueness of the solution, are detailed. The adopted procedure is a double iteration and the solution consists of a product of series, whose number of factors may be reduced successively by means of the indefinite sum operator of the difference calculus.

Localization of unconventional myosins V and VI in neuronal growth cones

Class V and VI myosins, two of the six known classes of actin-based motor genes expressed in vertebrate brain (Class I, II, V, VI, IX, and XV), have been suggested to be organelle motors. In this report, the neuronal expression and subcellular localization of chicken brain myosin V and myosin VI is examined. Both myosins are expressed in brain during embryogenesis. In cultured dorsal root ganglion (DRG) neurons, immunolocalization of myosin V and myosin VI revealed a similar distribution for these two myosins. Both are present within cell bodies, neurites and growth cones. Both of these myosins exhibit punctate labeling patterns that are found in the same subcellular region as microtubules in growth cone central domains. In peripheral growth cone domains, where individual puncta are more readily resolved, we observe a similar number of myosin V and myosin VI puncta. However, less than 20% of myosin V and myosin VI puncta colocalize with each other in the peripheral domains. After live cell extraction, punctate staining of myosin V and myosin VI is reduced in peripheral domains. However, we do not detect such changes in the central domains, suggesting that these myosins are associated with cytoskeletal/organelle structures. In peripheral growth cone domains myosin VI exhibits a higher extractability than myosin V. This difference between myosin V and VI was also found in a biochemical growth cone particle preparation from brain, suggesting that a significant portion of these two motors has a distinct subcellular distribution.

Immunohistochemical Markers in Full-Thickness Embryonic Rabbit Retinal Transplants

Purpose: To examine immunohistochemical markers in straight, well-laminated retinal transplants with special attention paid to the interphotoreceptor matrix, the Müller cells and the ganglion cells as these three retinal components have been abnormal in transplants produced by previous methods. Methods: Nine rabbits underwent subretinal transplantation of a complete full-thickness embryonic neuroretina. After 31 or 49 days, the transplants were stained for light microscopy and processed for immunohistochemistry. Results: Six of 9 eyes contained transplants with straight, well-laminated regions with all light-microscopic characteristics of a normal retina. In the outer segment region, the expression of peanut agglutinin showed segmental labeling of cone domains in the interphotoreceptor matrix, and interphotoreceptor retinoid binding protein immunoreactivity was found. Glial fibrillary acidic protein and vimentin immunoreactivity revealed normal Müller cell morphology. In 3 transplants the AB5-antibody-labeled ganglion cells in the ganglion cell layer and all transplants contained nerve fibers in the nerve fiber layer labeled by an antibody against neurofilament of 160 kD. The latter also labeled fibers connecting the transplant with the host. Conclusions: Full-thickness embryonic retinal transplants develop the normal retinal appearance and display several of the retinal components necessary for normal function which are not found in transplants produced by previous methods.

Symmetric duality for multiplicatively separable fractional mixed integer programming problem

A pair of symmetric dual fractional mixed integer programming problems is formulated and an appropriate duality theorem is established under suitable convexity and multiplicative separability assumptions on the kernel function. A self duality theorem and the extension of the formulation to convex cone domains are also discussed

In vitro acrylamide exposure alters growth cone morphology.

Acrylamide intoxication leads to degeneration of the longest axons of the central and peripheral nervous systems in humans and laboratory animals. Axonal derangements resulting from in vivo acrylamide exposure are first noted within synapses of the longest axons before involving more proximally located axonal segments or shorter axons, thus illustrating the specificity of acrylamide for the terminal axonal regions. As a possible model system for investigating the mechanism of toxicity of acrylamide on the distal axon, we exposed neurite-extending chick dorsal root ganglion (DRG) cells to acrylamide in vitro and then examined growth cones for alterations in morphology and function. Exposing DRG explants to media containing from 0.125 to 1.0 mM acrylamide for 16 hr leads to specific and dose-responsive alterations of growth cone morphology including: a nearly total loss of filopodial elements, the preservation of highly active but two-dimensional lamellar structures, an inappropriate extension of the axonal cytoskeleton into the forward region of most growth cones, and a frequent breakdown of the central and peripheral growth cone domains. The sulfhydryl alkylating agents ethacrynic acid, iodoacetamide, and iodoacetic acid were tested and none produced acrylamide-like morphological alterations at any dose. DRG cultures were also exposed to the neurotoxic acrylamide analogs glycidamide, N-hydroxy-methacrylamide (HM-ACR), and methacrylamide (M-ACR). At concentrations of 0.25 to 1.0 mM, glycidamide exposure resulted in acrylamide-like growth cone alterations. HM-ACR exposure also resulted in growth cones that were acrylamide-like but only at concentrations > 1.5 mM. M-ACR did not produce acrylamide-like growth cones at doses of up to 16.6 mM. Thus, in vitro exposure of DRG explants to acrylamide and two neurotoxic acrylamide analogs leads to reproducible and specific morphological alterations that are dose-dependent and separable from the effects of sulfhydryl alkylation.

Development and Fate of Interphotoreceptor Matrix Components During Dysplastic Photoreceptor Differentiation: A Lectin Cytochemical Study of Rod-Cone Dysplasia 1

The autosomal recessive retinal degeneration rod-cone dysplasia 1 ( rcd1) affects Irish setter dogs during early postnatal development. The disease is the result of a cyclic guanosine monophosphate metabolic abnormality and morphological evidence of disease onset correlates with initiation of photoreceptor outer segment formation. Rod photoreceptors are affected earlier and more severely than cones. Postnatal development of specific interphotoreceptor matrix (IPM) constituents was examined in tissue sections and extracted matrix preparations from control and affected dogs using peanut agglutinin (PNA) and wheat germ agglutinin (WGA) lectin cytochemistry. These lectins bind two photoreceptor-specific domains through their affinity for specific terminal carbohydrate sequences present on proteoglycans and glycoproteins in the IPM. Development of rod and cone matrix domains in the normal dog occurs in parallel to the development and differentiation of outer segments (between postnatal days 10 and 60 in the dog); during this period the lectin specificity or distribution in the rcd1 retina did not differ from the normal control. Structural changes of the matrix domains were present and reflected the morphological alterations of the diseased and degenerating photoreceptor cells. Cone domains were present around severely degenerated cone cells as long as these cells were found within the interphotoreceptor space. The matrix domain investing surviving cones did not differ significantly from the normal to indicate an altered binding specificity or structure. The rod domain was still present around rod inner segments in late degeneration. The matrix domains are present in the IPM as long as the photoreceptor cell body remains in the interphotoreceptor space; photoreceptor loss results in disappearance of the matrix. We detected no change in matrix composition or distribution with the lectins used, either during development or degeneration, despite the serious biochemical and structural abnormalities of the photoreceptor cell that are characteristic of the disease.

A note on Gordan′s theorem over cone domains

This note presents a proof of Gordan′s Theorem over general closed, convex cone domains which follows in a natural way appealing to the standard definitions of closed convex cones and their respective polar cones.

An Existence Theorem for Quadratic Programs Over Cone Domains

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und MechanikVolume 62, Issue 3 p. 207-208 Kleine Mitteilungen An Existence Theorem for Quadratic Programs Over Cone Domains Dr. J. Parida, Dr. J. Parida Department of Mathematics, Regional Engineering College, Rourkela 769008 (Orissa), IndiaSearch for more papers by this authorMrs. K. L. Roy, Mrs. K. L. Roy Department of Mathematics, Regional Engineering College, Rourkela 769008 (Orissa), IndiaSearch for more papers by this author Dr. J. Parida, Dr. J. Parida Department of Mathematics, Regional Engineering College, Rourkela 769008 (Orissa), IndiaSearch for more papers by this authorMrs. K. L. Roy, Mrs. K. L. Roy Department of Mathematics, Regional Engineering College, Rourkela 769008 (Orissa), IndiaSearch for more papers by this author First published: 1982 https://doi.org/10.1002/zamm.19820620307Citations: 1AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat No abstract is available for this article.Citing Literature Volume62, Issue31982Pages 207-208 RelatedInformation

A note on “real and complex Fritz John theorems”

In a recent paper by Craven and Mond a unified proof is given of the Fritz John necessary theorem for nonlinear programming problems over cone domains. This note will underscore some necessary assumptions that are needed to establish this generalization which are not stated, but assumed in the proofs given by Craven and Mond.

Necessary optimality conditions for programming problems over cone domains

In earlier results by Sposito and David, Kuhn-Tucker type duality associated with a certain saddlepoint problem was established convex cone domains (not necessarily polyhedral) without differentiability. Recent variants have established necessary optimality conditions of the Fritz John and Kuhn-Tucker type for programming problems over convex polyhedral cone domains which require differentiability assumptions. This paper extends the present results in the literature to programming problems arbitrary convex cone domains (not necessarily polyhedral).

On a sufficient optimality condition over convex feasible regions

In this note a sufficient optimality condition is established for nonlinear programming problems over arbitrary cone domains. A Kuhn-Tucker type sufficient condition is established if the programming problem has a pseudoconvex objective function and a convex feasible region.