Calculating effective resistances on underlying networks of association schemes

Recently, in Refs. \cite{jsj} and \cite{res2}, calculation of effective resistances on distance-regular networks was investigated, where in the first paper, the calculation was based on stratification and Stieltjes function associated with the network, whereas in the latter one a recursive formula for effective resistances was given based on the Christoffel-Darboux identity. In this paper, evaluation of effective resistances on more general networks which are underlying networks of association schemes is considered, where by using the algebraic combinatoric structures of association schemes such as stratification and Bose-Mesner algebras, an explicit formula for effective resistances on these networks is given in terms of the parameters of corresponding association schemes. Moreover, we show that for particular underlying networks of association schemes with diameter $d$ such that the adjacency matrix $A$ possesses $d+1$ distinct eigenvalues, all of the other adjacency matrices $A_i$, $i\neq 0,1$ can be written as polynomials of $A$, i.e., $A_i=P_i(A)$, where $P_i$ is not necessarily of degree $i$. Then, we use this property for these particular networks and assume that all of the conductances except for one of them, say $c\equiv c_1=1$, are zero to give a procedure for evaluating effective resistances on these networks. The preference of this procedure is that one can evaluate effective resistances by using the structure of their Bose-Mesner algebra without any need to know the spectrum of the adjacency matrices.Comment: 41 page

Absence of \u3ci\u3esodA\u3c/i\u3e Increases the Levels of Oxidation of Key Metabolic Determinants of \u3ci\u3eBorrelia burgdorferi\u3c/i\u3e

Borrelia burgdorferi, the causative agent of Lyme disease, alters its gene expression in response to environmental signals unique to its tick vector or vertebrate hosts. B. burgdorferi carries one superoxide dismutase gene (sodA) capable of controlling intracellular superoxide levels. Previously, sodA was shown to be essential for infection of B. burgdorferi in the C3H/HeN model of Lyme disease. We employed two-dimensional electrophoresis (2-DE) and immunoblot analysis with antibodies specific to carbonylated proteins to identify targets that were differentially oxidized in the soluble fractions of the sodA mutant compared to its isogenic parental control strain following treatment with an endogenous superoxide generator, methyl viologen (MV, paraquat). HPLC-ESI-MS/MS analysis of oxidized proteins revealed that several proteins of the glycolytic pathway (BB0057, BB0020, BB0348) exhibited increased carbonylation in the sodA mutant treated with MV. Levels of ATP and NAD/NADH were reduced in the sodA mutant compared with the parental strain following treatment with MV and could be attributed to increased levels of oxidation of proteins of the glycolytic pathway. In addition, a chaperone, HtpG (BB0560), and outer surface protein A (OspA, BBA15) were also observed to be oxidized in the sodA mutant. Immunoblot analysis revealed reduced levels of Outer surface protein C (OspC), Decorin binding protein A (DbpA), fibronectin binding protein (BBK32), RpoS and BosR in the sodA mutant compared to the control strains. Viable sodA mutant spirochetes could not be recovered from both gp91/phox−⁄− and iNOS deficient mice while borrelial DNA was detected in multiple tissues samples from infected mice at significantly lower levels compared to the parental strain. Taken together, these observations indicate that the increased oxidation of select borrelial determinants and reduced levels of critical pathogenesis-associated lipoproteins contribute to the in vivo deficit of the sodA mutant in the mouse model of Lyme disease. This study, utilizing the sodA mutant, has provided insights into adaptive capabilities critical for survival of B. burgdorferi in its hosts

Disruption of Myelin Leads to Ectopic Expression of K(V)1.1 Channels with Abnormal Conductivity of Optic Nerve Axons in a Cuprizone-Induced Model of Demyelination

The molecular determinants of abnormal propagation of action potentials along axons and ectopic conductance in demyelinating diseases of the central nervous system, like multiple sclerosis (MS),are poorly defined. Widespread interruption of myelin occurs in several mouse models of demyelination, rendering them useful for research. Herein, considerable myelin loss is shown in the optic nerves of cuprizone-treated demyelinating mice. Immuno-fluorescence confocal analysis of the expression and distribution of voltage-activated K+ channels (K(V)1.1 and 1.2 alpha subunits) revealed their spread from typical juxta-paranodal (JXP) sites to nodes in demyelinated axons, albeit with a disproportionate increase in the level of K(V)1.1 subunit. Functionally, in contrast to monophasic compound action potentials (CAPs) recorded in controls, responses derived from optic nerves of cuprizone-treated mice displayed initial synchronous waveform followed by a dispersed component. Partial restoration of CAPs by broad spectrum (4-aminopyridine) or K(V)1.1-subunit selective (dendrotoxin K) blockers of K+ currents suggest enhanced K(V)1.1-mediated conductance in the demyelinated optic nerve. Biophysical profiling of K+ currents mediated by recombinant channels comprised of different K(V)1.1 and 1.2 stoichiometries revealed that the enrichment of K(V)1 channels K(V)1.1 subunit endows a decrease in the voltage threshold and accelerates the activation kinetics. Together with the morphometric data, these findings provide important clues to a molecular basis for temporal dispersion of CAPs and reduced excitability of demyelinated optic nerves, which could be of potential relevance to the patho-physiology of MS and related disorders

Development of a Selective Inhibitor for Kv1.1 Channels Prevalent in Demyelinated Nerves

Members of the voltage-gated K+ channel subfamily (Kv1), involved in regulating transmission between neurons or to muscles, are associated with human diseases and, thus, putative targets for neurotherapeutics. This applies especially to those containing Kv1.1 α subunits which become prevalent in murine demyelinated axons and appear abnormally at inter-nodes, underlying the perturbed propagation of nerve signals. To overcome this dysfunction, akin to the consequential debilitation in multiple sclerosis (MS), small inhibitors were sought that are selective for the culpable hyper-polarising K+ currents. Herein, we report a new semi-podand – compound 3 – that was designed based on the modelling of its interactions with the extracellular pore region in a deduced Kv1.1 channel structure. After synthesis, purification, and structural characterisation, compound 3 was found to potently (IC50 = 8 µM) and selectively block Kv1.1 and 1.6 channels. The tested compound showed no apparent effect on native Nav and Cav channels expressed in F-11 cells. Compound 3 also extensively and selectively inhibited MS-related Kv1.1 homomer but not the brain native Kv1.1- or 1.6-containing channels. These collective findings highlight the therapeutic potential of compound 3 to block currents mediated by Kv1.1 channels enriched in demyelinated central neurons

A manganese-rich environment supports superoxide dismutase activity in a lyme disease pathogen, Borrelia burgdorferi

Author Posting. © The Author(s), 2013. This is the author's version of the work. It is posted here by permission of American Society for Biochemistry and Molecular Biology for personal use, not for redistribution. The definitive version was published in Journal of Biological Chemistry 288 (2013): 8468-8478, doi:10.1074/jbc.M112.433540.The Lyme disease pathogen Borrelia burgdorferi represents a novel organism in which to study metalloprotein biology in that this spirochete has uniquely evolved with no requirement for iron. Not only is iron low, but we show here that B. burgdorferi has the capacity to accumulate remarkably high levels of manganese. This high manganese is necessary to activate the SodA superoxide dismutase (SOD) essential for virulence. Using a metalloproteomic approach, we demonstrate that a bulk of B. burgdorferi SodA directly associates with manganese and a smaller pool of inactive enzyme accumulates as apoprotein. Other metalloproteins may have similarly adapted to using manganese as co-factor including the BB0366 amino-peptidase. While B. burgdorferi SodA has evolved in a manganese-rich, iron-poor environment, the opposite is true for Mn-SODs of organisms such as E. coli and bakers’ yeast. These Mn-SODs still capture manganese in an iron-rich cell, and we tested whether the same is true for Borrelia SodA. When expressed in the iron-rich mitochondria of S. cerevisiae, B. burgdorferi SodA was inactive. Activity was only possible when cells accumulated extremely high levels of manganese that exceeded cellular iron. Moreover, there was no evidence for iron inactivation of the SOD. B. burgdorferi SodA shows strong overall homology with other members of the Mn-SOD family, but computer assisted modeling revealed some unusual features of the hydrogen bonding network near the enzyme’s active site. The unique properties of B. burgdorferi SodA may represent adaptation to expression in the manganese-rich and iron-poor environment of the spirochete

Immunization with Dendritic Cells Pulsed ex vivo with Recombinant Chlamydial Protease-Like Activity Factor Induces Protective Immunity Against Genital Chlamydia muridarum Challenge

We have shown that immunization with soluble recombinant chlamydial protease-like activity factor (rCPAF) and a T helper 1 type adjuvant can induce significantly enhanced bacterial clearance and protection against Chlamydia-induced pathological sequelae in the genital tract. In this study, we investigated the use of bone marrow derived dendritic cells (BMDCs) pulsed ex vivo with rCPAF + CpG in an adoptive subcutaneous immunization for the ability to induce protective immunity against genital chlamydial infection. We found that BMDCs pulsed with rCPAF + CpG efficiently up-regulated the expression of activation markers CD86, CD80, CD40, and major histocompatibility complex class II (MHC II), and secreted interleukin-12, but not IL-10 and IL-4. Mice adoptively immunized with rCPAF + CpG-pulsed BMDCs or UV-EB + CpG-pulsed BMDCs produced elevated levels of antigen-specific IFN-γ and enhanced IgG1 and IgG2a antibodies. Moreover, mice immunized with rCPAF + CpG-pulsed BMDCs or UV-EB + CpG-pulsed BMDCs exhibited significantly reduced genital Chlamydia shedding, accelerated resolution of infection, and reduced oviduct pathology when compared to infected mock-immunized animals. These results suggest that adoptive subcutaneous immunization with ex vivo rCPAF-pulsed BMDCs is an effective approach, comparable to that induced by UV-EB–BMDCs, for inducing robust anti-Chlamydia immunity

Absence of sodA Increases the Levels of Oxidation of Key Metabolic Determinants of Borrelia burgdorferi

Borrelia burgdorferi, the causative agent of Lyme disease, alters its gene expression in response to environmental signals unique to its tick vector or vertebrate hosts. B. burgdorferi carries one superoxide dismutase gene (sodA) capable of controlling intracellular superoxide levels. Previously, sodA was shown to be essential for infection of B. burgdorferi in the C3H/HeN model of Lyme disease. We employed two-dimensional electrophoresis (2-DE) and immunoblot analysis with antibodies specific to carbonylated proteins to identify targets that were differentially oxidized in the soluble fractions of the sodA mutant compared to its isogenic parental control strain following treatment with an endogenous superoxide generator, methyl viologen (MV, paraquat). HPLC-ESI-MS/MS analysis of oxidized proteins revealed that several proteins of the glycolytic pathway (BB0057, BB0020, BB0348) exhibited increased carbonylation in the sodA mutant treated with MV. Levels of ATP and NAD/NADH were reduced in the sodA mutant compared with the parental strain following treatment with MV and could be attributed to increased levels of oxidation of proteins of the glycolytic pathway. In addition, a chaperone, HtpG (BB0560), and outer surface protein A (OspA, BBA15) were also observed to be oxidized in the sodA mutant. Immunoblot analysis revealed reduced levels of Outer surface protein C (OspC), Decorin binding protein A (DbpA), fibronectin binding protein (BBK32), RpoS and BosR in the sodA mutant compared to the control strains. Viable sodA mutant spirochetes could not be recovered from both gp91/phox-⁄- and iNOS deficient mice while borrelial DNA was detected in multiple tissues samples from infected mice at significantly lower levels compared to the parental strain. Taken together, these observations indicate that the increased oxidation of select borrelial determinants and reduced levels of critical pathogenesis-associated lipoproteins contribute to the in vivo deficit of the sodA mutant in the mouse model of Lyme disease. This study, utilizing the sodA mutant, has provided insights into adaptive capabilities critical for survival of B. burgdorferi in its hosts

A Rational Design of a Selective Inhibitor for Kv1.1 Channels Prevalent in Demyelinated Nerves That Improves Their Impaired Axonal Conduction

K+ channels containing Kv1.1 α subunits, which become prevalent at internodes in demyelinated axons, may underlie their dysfunctional conduction akin to muscle weakness in multiple sclerosis. Small inhibitors were sought with selectivity for the culpable hyper-polarizing K+ currents. Modeling of interactions with the extracellular pore in a Kv1.1-deduced structure identified diaryldi(2-pyrrolyl)methane as a suitable scaffold with optimized alkyl ammonium side chains. The resultant synthesized candidate [2,2′-((5,5′(di-p-topyldiaryldi(2-pyrrolyl)methane)bis(2,2′carbonyl)bis(azanediyl)) diethaneamine·2HCl] (8) selectively blocked Kv1.1 channels (IC50 ≈ 15 μM) recombinantly expressed in mammalian cells, induced a positive shift in the voltage dependency of K+ current activation, and slowed its kinetics. It preferentially inhibited channels containing two or more Kv1.1 subunits regardless of their positioning in concatenated tetramers. In slices of corpus callosum from mice subjected to a demyelination protocol, this novel inhibitor improved neuronal conduction, highlighting its potential for alleviating symptoms in multiple sclerosis

Journal of Pharma and Pharmaceutical Sciences Indirect Determination of Process Impurity Cetrimonium Bromide in Neisseria meningitidis A/C/Y/W-135-DT Conjugate Vaccine by HPAEC-PAD Method

Abstract A validated High Performance Anion Exchange-Pulsed Amperometric Detection (HPAEC-PAD) indirect method is described to determine traces of process impurity cetrimonium bromide (CTAB) in Neisseria meningitidis A/C/Y/W-135-DT conjugate vaccine. Method reported here, measures the bromide ion present in CTAB. As part of impurity profiling, samples of crude and purified meningococcal four serogroup (A, C, W-135 and Y) polysaccharides and final vialed conjugate vaccine were analyzed for CTAB content. Vaccine grade pure polysaccharides, the control and the final vaccines both formulated in phosphate buffered saline (PBS) showed sub ppm levels of CTAB impurity. PBS used in this work showed detectable bromide levels presumably due to contamination originated from saline. The proposed method is very sensitive (LOD=0.04 ppm, LOQ =0.11 ppm), accurate, reproducible and compatible with polysaccharide and PBS environments