hp-dGFEM for Second-Order Elliptic Problems in Plyhedra I: Stability and Quasioptimality on Geometric Meshes

We introduce and analyze hp-version discontinuous Galerkin (dG) finite element methods for the numerical approximation of linear second-order elliptic boundary-value problems in three-dimensional polyhedral domains. To resolve possible corner-, edge- and corner-edge singularities, we consider hexahedral meshes that are geometrically and anisotropically refined toward the corresponding neighborhoods. Similarly, the local polynomial degrees are increased linearly and possibly anisotropically away from singularities. We design interior penalty hp-dG methods and prove that they are well-defined for problems with singular solutions and stable under the proposed hp-refinements. We establish (abstract) error bounds that will allow us to prove exponential rates of convergence in the second part of this work.

hp-dGFEM for Second-Order Elliptic Problems in Plyhedra II: Exponential Convergence

The goal of this paper is to establish exponential convergence of $hp$-version interior penalty (IP) discontinuous Galerkin (dG) finite element methods for the numerical approximation of linear second-order elliptic boundary-value problems with homogeneous Dirichlet boundary conditions and piecewise analytic data in three-dimensional polyhedral domains. More precisely, we shall analyze the convergence of the $hp$-IP dG methods considered in [D. Schötzau, C. Schwab, T. P. Wihler, SIAM J. Numer. Anal., 51 (2013), pp. 1610--1633] based on axiparallel $\sigma$-geometric anisotropic meshes and $\bm{s}$-linear anisotropic polynomial degree distributions.

Expression, purification, and projection structure by single particle electron microscopy of functional human TRPM4 heterologously expressed in Xenopus laevis oocytes

Despite efforts implicating the cationic channel transient receptor potential melastatin member 4 (TRPM4) to cardiac, nervous, and immunological pathologies, little is known about its structure and function. In this study, we optimized the requirements for purification and extraction of functional human TRPM4 protein and investigated its supra-molecular assembly. We selected the Xenopus laevis oocyte expression system because it lacks endogenous TRPM4 expression, it is known to overexpress functional human membrane channels, can be used for structure-function analysis within the same system, and is easily scaled to improve yield and develop moderate throughput capabilities through the use of robotics. Negative-stain electron microscopy (EM) revealed various sized low-resolution particles. Single particle analysis identified the majority of the projections represented the monomeric form with additional oligomeric structures potentially characterized as tetramers. Two-electrode voltage clamp electrophysiology demonstrated that human TRPM4 is functionally expressed at the oocyte plasma membrane. This study opens the door for medium-throughput screening and structure-function determination of this important therapeutically relevant target.

Expression, purification and low-resolution structure of human vitamin C transporter SVCT1 (SLC23A1)

Expression and purification of human membrane proteins for structural studies represent a great challenge. This is because micro- to milligram amounts of pure isolated protein are required. To this aim, we successfully expressed the human vitamin C transporter-1 (hSVCT1; SLC23A1) in Xenopus laevis oocytes and isolated highly pure protein in microgram amounts. Recombinant hSVCT1 was functional when expressed in oocytes and glycosylated. Structural analysis of purified hSVCT1 by transmission electron microscopy and single particle analysis unveiled its shape, dimensions and low-resolution structure as well as the existence of a major monomeric and minor dimeric population. Chemical crosslinking of isolated oocyte membranes containing expressed hSVCT1 indicated similar oligomeric states of hSVCT1 in lipid bilayers. This work reports the first purification and structural analysis of a human SVCT protein and opens the way for future functional and structural studies using purified hSVCT1.

Genetic and physical analysis of the bacteriophage P22 tail protein

A plasmid based genetic system was developed for the tail protein of the Salmonella typhimurium bacteriophage P22 and used to isolate and characterize tail protein mutants. The tail protein is a trimeric structural protein of the phage and an endorhamnosidase whose activity is essential for infection. The gene for the tail protein has previously been cloned into a plasmid expression vector and sequenced. A plate complementation assay for tail protein produced from the cloned gene was developed and used to isolate 27 tail protein mutants following mutagenesis of the cloned gene. These mutations were mapped into 12 deletion intervals using deletions which were made on plasmids in vitro and crossed onto P22. The base substitutions were determined by DNA sequencing. The majority of mutants had missense or nonsense mutations in the protein coding portion of the gene; however four of the mutants were in the putative transcription terminator. The oligomeric state of tail protein from the 15 missense mutants was investigated using SDS and nondenaturing polyacrylamide gel electrophoresis of cell lysates. Wild-type tail protein retains its trimeric structure in SDS gels at room temperature. Two of the mutant proteins also migrated as trimers in SDS gels, yet one of these had a considerably faster mobility than wild-type trimer. Its migration was the same as wild-type in a nondenaturing gel, so it is thought to be a trimer which is partially denatured by SDS. Four of the mutants produced proteins which migrate at the position of a monomer in an SDS gel but cannot be seen on a nondenaturing gel. These proteins are thought to be either monomers or soluble aggregates which cannot enter the nondenaturing gel. The remainder of mutants produce protein which is degraded. The mutant tail protein which had normal trimeric mobility on SDS and nondenaturing gels was purified. This protein has essentially wild-type ability to attach to phage capsids, but its endorhamnosidase activity is only 4% of wild-type. ^

Protein quaternary structure determination using matrix-assisted laser desorption/ionization time-of-flight mass spectrometry and chemical crosslinking

A means of analyzing protein quaternary structure using matrix-assisted laser desorption ionization time-of-flight mass spectrometry (MALDI MS) and chemical crosslinking was evaluated. Proteins of known oligomeric structure, as well as monomeric proteins, were analyzed to evaluate the method. The quaternary structure of proteins of unknown or uncertain structure was investigated using this technique. The stoichiometry of recombinant E. coli carbamoyl phosphate synthetase and recombinant human farnesyl protein transferase were determined to be heterodimers using glutaraldehyde crosslinking, agreeing with the stoichiometry found for the wild type proteins. The stoichiometry of the gamma subunit of E. coli DNA polymerase III holoenzyme was determined in solution without the presence of other subunits to be a homotetramer using glutaraldehyde crosslinking and MALDI MS analysis. Chi and psi subunits of E. coli DNA polymerase III subunits appeared to form a heterodimer when crosslinked with heterobifunctional photoreactive crosslinkers.^ Comparison of relative % peak areas obtained from MALDI MS analysis of crosslinked proteins and densitometric scanning of silver stained sodium dodecyl sulfate polyacrylamide gel electrophoresis (SDS-PAGE) gels showed excellent qualitative agreement for the two techniques, but the quantitative analyses differed, sometimes significantly. This difference in quantitation could be due to SDS-PAGE conditions (differential staining, loss of sample) or to MALDI MS conditions (differences in ionization and/or detection). Investigation of pre-purified crosslinked monomers and dimers recombined in a specific ratio revealed the presence of mass discrimination in the MALDI MS process. The calculation of mass discrimination for two different MALDI time-of-flight instruments showed the loss of a factor of approximately 2.6 in relative peak area as the m/z value doubles over the m/z range from 30,000 to 145,000 daltons.^ Indirect symmetry was determined for tetramers using glutaraldehyde crosslinking with MALDI MS analysis. Mathematical modelling and simple graphing allowed the determination of the symmetry for several tetramers known to possess isologous D2 symmetry. These methods also distinguished tetramers that did not fit D2 symmetry such as apo-avidin. The gamma tetramer of E. coli DNA polymerase III appears to have isologous D2 symmetry. ^

Phototaxis signaling by the membrane complex of archaeal sensory rhodopsins and their transducers

Sensory rhodopsins I and II (SRI and SRII) are visual pigment-like phototaxis receptors in the archaeon Halobacterium salinarum. The receptor proteins each consist of a single polypeptide that folds into 7 $\alpha$-helical membrane-spanning segments forming an internal pocket where the chromophore retinal is bound. They transmit signals to their tightly bound transducer proteins, HtrI and HtrII, respectively, which in turn control a phosphotransfer pathway modulating the flagellar motors. SRI-HtrI mediates attractant responses to orange-light and repellent responses to UV light, while SRII-HtrII mediates repellent response to blue light. Experiments were designed to analyze the molecular processes in the SR-Htr complexes responsible for receptor activation, which previously had been shown by our laboratory to involve proton transfer reactions of the retinylidene Schiff base in the photoactive site, transfer of signals from receptor to transducer, and signaling specificity by the receptor-transducer complex.^ Site-directed mutagenesis and laser-flash kinetic spectroscopy revealed that His-166 in SRI (i) plays a role in the proton transfers both to and from the Schiffbase, either as a structurally critical residue or possibly as a direct participant, (ii) is involved in the modulation of SIU photoreaction kinetics by HtrI, and (iii) modulates the pKa of Asp-76, an important residue in the photoactive site, through a long-distance electrostatic interaction. Computerized cell tracking and motion analysis demonstrated that (iv) His-166 is crucial in phototaxis signaling: a spectrum of substitutions either eliminate signaling or greatly perturb the activation process that produces attractant and repellent signaling states of the receptor.^ The signaling states of SRI are communicated to HtrI, whose oligomeric structure and conformational changes were investigated by engineered sulfhydryl probes. It was found that signaling by the SRI-HtrI complex involves reversible conformational changes within a preexisting HtrI dimer, which is likely accomplished through a slight winding or unwinding of the two HtrT monomers via their loose coiled coil association. To elucidate which domains of the Htr dimers confer specificity for interaction with SRI or SRII, chimeras of HtrI and HtrII were constructed. The only determinant needed for functional and specific interaction with SRI or SRII was found to be the four transmembrane segments of the HtrI or HtrII dimers, respectively. The entire cytoplasmic parts of HtrI and HtrII, which include the functionally important signaling and adaptation domains, were interchangeable.^ These observations support a model in which SRI and SRII undergo conformational changes coupled to light-induced proton transfers in their photoactive sites, and that lateral helix-helix interactions with their cognate transducers' 4-helix bundle in the membrane relay these conformational changes into different states of the Htr proteins which regulate the down-stream phosphotransfer pathway. ^

Studies of subcellular localization and complex formation of the Agrobacterium tumefaciens transport ATPase VirB11

The VirB11 ATPase is an essential component of an Agrobacterium tumefaciens type IV bacterial secretion system that transfers oncogenic nucleoprotein complexes to susceptible plant cells. This dissertation investigates the subcellular localization and homo-oligomeric state of the VirB11 ATPase in order to provide insights about the assembly of the protein as a subunit of this membrane-associated transfer system. Subcellular fractionation studies and quantitative immunoblot analysis demonstrated that $\sim$30% of VirB11 partitioned as soluble protein and $\sim$70% was tightly associated with the bacterial cytoplasmic membrane. No differences were detected in VirB11 subcellular localization and membrane association in the presence or absence of other transport system components. Mutations in virB11 affecting protein function were mapped near the amino terminus, just upstream of a region encoding a Walker 'A' nucleotide-binding site, and within the Walker 'A' motif partitioned almost exclusively with the cytoplasmic membrane, suggesting that an activity associated with nucleotide binding could modulate the affinity of VirB11 for the cytoplasmic membrane. Merodiploid analysis of VirB11 mutant and truncation derivatives provided strong evidence that VirB11 functions as a homo- or heteromultimer and that the C-terminal half of VirB11 contains a protein interaction domain. A combination of biochemical and molecular genetic approaches suggested that VirB11 and the green fluorescence protein (GFP) formed a mixed multimer as demonstrated by immunoprecipitation experiments with anti-GFP antibodies. Second, a hybrid protein composed of VirB11 fused to the N-terminal DNA-binding domain of bacteriophage $\lambda$ cI repressor conferred immunity to $\lambda$ superinfection, demonstrating that VirB11 self-association promotes dimerization of the chimeric repressor. A conserved Walker 'A' motif, though required for VirB11 function in T-complex export, was not necessary for VirB11 self-association. Sequences in both the N- and the C-terminal halves of the protein were found to contribute to self-association of the full length protein. Chemical cross-linking experiments with His$\sb6$ tagged VirB11 suggested that VirB11 probably assembles into a higher order homo-oligomeric complex. ^

Variation of the detergent-binding capacity and phospholipid content of membrane proteins when purified in different detergents.

Purified membrane proteins are ternary complexes consisting of protein, lipid, and detergent. Information about the amounts of detergent and endogenous phospholipid molecules bound to purified membrane proteins is largely lacking. In this systematic study, three model membrane proteins of different oligomeric states were purified in nine different detergents at commonly used concentrations and characterized biochemically and biophysically. Detergent-binding capacities and phospholipid contents of the model proteins were determined and compared. The insights on ternary complexes obtained from the experimental results, when put into a general context, are summarized as follows. 1), The amount of detergent and 2) the amount of endogenous phospholipids bound to purified membrane proteins are dependent on the size of the hydrophobic lipid-accessible protein surface areas and the physicochemical properties of the detergents used. 3), The size of the detergent and lipid belt surrounding the hydrophobic lipid-accessible surface of purified membrane proteins can be tuned by the appropriate choice of detergent. 4), The detergents n-nonyl-β-D-glucopyranoside and Cymal-5 have exceptional delipidating effects on ternary complexes. 5), The types of endogenous phospholipids bound to membrane proteins can vary depending on the detergent used for solubilization and purification. 6), Furthermore, we demonstrate that size-exclusion chromatography can be a suitable method for estimating the molecular mass of ternary complexes. The findings presented suggest a strategy to control and tune the numbers of detergent and endogenous phospholipid molecules bound to membrane proteins. These two parameters are potentially important for the successul crystallization of membrane proteins for structure determination by crystallographic approaches.

Mitochondrial protein import receptors in Kinetoplastids reveal convergent evolution over large phylogenetic distances

Mitochondrial protein import is essential for all eukaryotes and mediated by hetero-oligomeric protein translocases thought to be conserved within all eukaryotes. We have identified and analysed the function and architecture of the non-conventional outer membrane (OM) protein translocase in the early diverging eukaryote Trypanosoma brucei. It consists of six subunits that show no obvious homology to translocase components of other species. Two subunits are import receptors that have a unique topology and unique protein domains and thus evolved independently of the prototype receptors ​Tom20 and ​Tom70. Our study suggests that protein import receptors were recruited to the core of the OM translocase after the divergence of the major eukaryotic supergroups. Moreover, it links the evolutionary history of mitochondrial protein import receptors to the origin of the eukaryotic supergroups.

Peptide-based interactions with calnexin target misassembled membrane proteins into endoplasmic reticulum-derived multilamellar bodies.

Oligomeric assembly of neurotransmitter transporters is a prerequisite for their export from the endoplasmic reticulum (ER) and their subsequent delivery to the neuronal synapse. We previously identified mutations, e.g., in the gamma-aminobutyric acid (GABA) transporter-1 (GAT1), which disrupted assembly and caused retention of the transporter in the ER. Using one representative mutant, GAT1-E101D, we showed here that ER retention was due to association of the transporter with the ER chaperone calnexin: interaction with calnexin led to accumulation of GAT1 in concentric bodies corresponding to previously described multilamellar ER-derived structures. The transmembrane domain of calnexin was necessary and sufficient to direct the protein into these concentric bodies. Both yellow fluorescent protein-tagged versions of wild-type GAT1 and of the GAT1-E101D mutant remained in disperse (i.e., non-aggregated) form in these concentric bodies, because fluorescence recovered rapidly (t(1/2) approximately 500 ms) upon photobleaching. Fluorescence energy resonance transfer microscopy was employed to visualize a tight interaction of GAT1-E101D with calnexin. Recognition by calnexin occurred largely in a glycan-independent manner and, at least in part, at the level of the transmembrane domain. Our findings are consistent with a model in which the transmembrane segment of calnexin participates in chaperoning the inter- and intramolecular arrangement of hydrophobic segment in oligomeric proteins.

High-resolution atomic force microscopy imaging of rhodopsin in rod outer segment disk membranes.

Atomic force microscopy (AFM) is a powerful imaging technique that allows recording topographical information of membrane proteins under near-physiological conditions. Remarkable results have been obtained on membrane proteins that were reconstituted into lipid bilayers. High-resolution AFM imaging of native disk membranes from vertebrate rod outer segments has unveiled the higher-order oligomeric state of the G protein-coupled receptor rhodopsin, which is highly expressed in disk membranes. Based on AFM imaging, it has been demonstrated that rhodopsin assembles in rows of dimers and paracrystals and that the rhodopsin dimer is the fundamental building block of higher-order structures.

Deletion of exon 8 from the EXT1 gene causes multiple osteochondromas (MO) in a family with three affected members.

Multiple osteochondromas (also called hereditary multiple exostoses) is an autosomal dominant disorder characterized by multiple cartilaginous tumors, which are caused by mutations in the genes for exostosin-1 (EXT1) and exostosin-2 (EXT2). The goal of this study was to elucidate the genetic alterations in a family with three affected members. Isolation of RNA from the patients' blood followed by reverse transcription and PCR amplification of selected fragments showed that the three patients lack a specific region of 90 bp from their EXT1 mRNA. This region corresponds to the sequence of exon 8 from the EXT1 gene. No splice site mutation was found around exon 8. However, long-range PCR amplification of the region from intron 7 to intron 8 indicated that the three patients contain a deletion of 4318 bp, which includes exon 8 and part of the flanking introns. There is evidence that the deletion was caused by non-homologous end joining because the breakpoints are not located within a repetitive element, but contain multiple copies of the deletion hotspot sequence TGRRKM. Exon 8 encodes part of the active site of the EXT1 enzyme, including the DXD signature of all UDP-sugar glycosyltransferases. It is conceivable that the mutant protein exerts a dominant negative effect on the activity of the EXT glycosyltransferase since it might interact with normal copies of the enzyme to form an inactive hetero-oligomeric complex. We suggest that sequencing of RNA might be superior to exome sequencing to detect short deletions of a single exon.

Functional Characterization of AtxA, the Bacillus anthracis Virulence Regulator

Coordinated expression of virulence genes in Bacillus anthracis occurs via a multi-faceted signal transduction pathway that is dependent upon the AtxA protein. Intricate control of atxA gene transcription and AtxA protein function have become apparent from studies of AtxA-induced synthesis of the anthrax toxin proteins and the poly-D-glutamic acid capsule, two factors with important roles in B. anthracis pathogenesis. The amino-terminal region of the AtxA protein contains winged-helix (WH) and helix-turn-helix (HTH) motifs, structural features associated with DNA-binding. Using filter binding assays, I determined that AtxA interacted non-specifically at a low nanomolar affinity with a target promoter (Plef) and AtxA-independent promoters. AtxA also contains motifs associated with phosphoenolpyruvate: sugar phosphotransferase system (PTS) regulation. These PTS-regulated domains, PRD1 and PRD2, are within the central amino acid sequence. Specific histidines in the PRDs serve as sites of phosphorylation (H199 and H379). Phosphorylation of H199 increases AtxA activity; whereas, H379 phosphorylation decreases AtxA function. For my dissertation, I hypothesized that AtxA binds target promoters to activate transcription and that DNA-binding activity is regulated via structural changes within the PRDs and a carboxy-terminal EIIB-like motif that are induced by phosphorylation and ligand binding. I determined that AtxA has one large protease-inaccessible domain containing the PRDs and the carboxy-terminal end of the protein. These results suggest that AtxA has a domain that is distinct from the putative DNA-binding region of the protein. My data indicate that AtxA activity is associated with AtxA multimerization. Oligomeric AtxA was detected when co-affinity purification, non-denaturing gel electrophoresis, and bis(maleimido)hexane (BMH) cross-linking techniques were employed. I exploited the specificity of BMH for cysteine residues to show that AtxA was cross-linked at C402, implicating the carboxy-terminal EIIB-like region in protein-protein interactions. In addition, higher amounts of the cross-linked dimeric form of AtxA were observed when cells were cultured in conditions that promote toxin gene expression. Based on the results, I propose that AtxA multimerization requires the EIIB-like motif and multimerization of AtxA positively impacts function. I investigated the role of the PTS in the function of AtxA and the impact of phosphomimetic residues on AtxA multimerization. B. anthracis Enzyme I (EI) and HPr did not facilitate phosphorylation of AtxA in vitro. Moreover, markerless deletion of ptsHI in B. anthracis did not perturb AtxA function. Taken together, these results suggest that proteins other than the PTS phosphorylate AtxA. Point mutations mimicking phosphohistidine (H to D) and non-phosphorylated histidine (H to A) were tested for an impact on AtxA activity and multimerization. AtxA H199D, AtxA H199A, and AtxA H379A displayed multimerization phenotypes similar to that of the native protein, whereas AtxA H379D was not susceptible to BMH cross-linking or co-affinity purification with AtxA-His. These data suggest that phosphorylation of H379 may decrease AtxA activity by preventing AtxA multimerization. Overall, my data support the following model of AtxA function. AtxA binds to target gene promoters in an oligomeric state. AtxA activity is increased in response to the host-related signal bicarbonate/CO2 because this signal enhances AtxA multimerization. In contrast, AtxA activity is decreased by phosphorylation at H379 because multimerization is inhibited. Future studies will address the interplay between bicarbonate/CO2 signaling and phosphorylation on AtxA function.

Analysis of VirB4, a membrane-associated ATPase subunit essential for T -complex transport in Agrobacterium tumefaciens

Agrobacterium tumefaciens is a plant pathogen with the unique ability to export oncogenic DNA-protein complexes (T-complexes) to susceptible plant cells and cause crown gall tumors. Delivery of the T-complexes across the bacterial membranes requires eleven VirB proteins and VirD4, which are postulated to form a transmembrane transporter. This thesis examines the subcellular localization and oligomeric structure of the 87-kDa VirB4 protein, which is one of three essential ATPases proposed to energize T-complex transport and/or assembly. Results of subcellular localization studies showed that VirB4 is tightly associated with the cytoplasmic membrane, suggesting that it is a membrane-spanning protein. The membrane topology of VirB4 was determined by using a nested deletion strategy to generate random fusions between virB4 and the periplasmically-active alkaline phosphatase, $\sp\prime phoA$. Analysis of PhoA and complementary $\beta$-galactosidase reporter fusions identified two putative periplasmically-exposed regions in VirB4. A periplasmic exposure of one of these regions was further confirmed by protease susceptibility assays using A. tumefaciens spheroplasts. To gain insight into the structure of the transporter, the topological configurations of other VirB proteins were also examined. Results from hydropathy analyses, subcellular localization, protease susceptibility, and PhoA reporter fusion studies support a model that all of the VirB proteins localize at one or both of the bacterial membranes. Immunoprecipitation and Co$\sp{2+}$ affinity chromatography studies demonstrated that native VirB4 (87-kDa) and a functional N-terminally tagged HIS-VirB4 derivative (89-kDa) interact and that the interaction is independent of other VirB proteins. A $\lambda$ cI repressor fusion assay supplied further evidence for VirB4 dimer formation. A VirB4 dimerization domain was localized to the N-terminal third of the protein, as judged by: (i) transdominance of an allele that codes for this region of VirB4; (ii) co-retention of a His-tagged N-terminal truncation derivative and native VirB4 on Co$\sp{2+}$ affinity columns; and (iii) dimer formation of the N-terminal third of VirB4 fused to the cI repressor protein. Taken together, these findings are consistent with a model that VirB4 is topologically configured as an integral cytoplasmic membrane protein with two periplasmic domains and that VirB4 assembles as homodimers via an N-terminal dimerization domain. Dimer formation is postulated to be essential for stabilization of VirB4 monomers during T-complex transporter assembly. ^