Solution of the pulse width modulation problem using orthogonal polynomials and Korteweg-de Vries equations

The mathematical underpinning of the pulse width modulation (PWM) technique lies in the attempt to represent “accurately” harmonic waveforms using only square forms of a fixed height. The accuracy can be measured using many norms, but the quality of the approximation of the analog signal (a harmonic form) by a digital one (simple pulses of a fixed high voltage level) requires the elimination of high order harmonics in the error term. The most important practical problem is in “accurate” reproduction of sine-wave using the same number of pulses as the number of high harmonics eliminated. We describe in this paper a complete solution of the PWM problem using Padé approximations, orthogonal polynomials, and solitons. The main result of the paper is the characterization of discrete pulses answering the general PWM problem in terms of the manifold of all rational solutions to Korteweg-de Vries equations.

Specific cleavage of chromosomal and plasmid DNA strands in gram-positive and gram-negative bacteria can be detected with nucleotide resolution

A sensitive and precise in vitro technique for detecting DNA strand discontinuities produced in vivo has been developed. The procedure, a form of runoff DNA synthesis on molecules released from lysed bacterial cells, mapped precisely the position of cleavage of the plasmid pMV158 leading strand origin in Streptococcus pneumoniae and the site of strand scission, nic, at the transfer origins of F and the F-like plasmid R1 in Escherichia coli. When high frequency of recombination strains of E. coli were examined, DNA strand discontinuities at the nic positions of the chromosomally integrated fertility factors were also observed. Detection of DNA strand scission at the nic position of F DNA in the high frequency of recombination strains, as well as in the episomal factors, was dependent on sexual expression from the transmissable element, but was independent of mating. These results imply that not only the transfer origins of extrachromosomal F and F-like fertility factors, but also the origins of stably integrated copies of these plasmids, are subject to an equilibrium of cleavage and ligation in vivo in the absence of DNA transfer.

Identification of a structural determinant for resistance to β-lactam antibiotics in Gram-positive bacteria

Streptococcus pneumoniae is the main causal agent of pathologies that are increasingly resistant to antibiotic treatment. Clinical resistance of S. pneumoniae to β-lactam antibiotics is linked to multiple mutations of high molecular mass penicillin-binding proteins (H-PBPs), essential enzymes involved in the final steps of bacterial cell wall synthesis. H-PBPs from resistant bacteria have a reduced affinity for β-lactam and a decreased hydrolytic activity on substrate analogues. In S. pneumoniae, the gene coding for one of these H-PBPs, PBP2x, is located in the cell division cluster (DCW). We present here structural evidence linking multiple β-lactam resistance to amino acid substitutions in PBP2x within a buried cavity near the catalytic site that contains a structural water molecule. Site-directed mutation of amino acids in contact with this water molecule in the “sensitive” form of PBP2x produces mutants similar, in terms of β-lactam affinity and substrate hydrolysis, to altered PBP2x produced in resistant clinical isolates. A reverse mutation in a PBP2x variant from a clinically important resistant clone increases the acylation efficiency for β-lactams and substrate analogues. Furthermore, amino acid residues in contact with the structural water molecule are conserved in the equivalent H-PBPs of pathogenic Gram-positive cocci. We suggest that, probably via a local structural modification, the partial or complete loss of this water molecule reduces the acylation efficiency of PBP2x substrates to a point at which cell wall synthesis still occurs, but the sensitivity to therapeutic concentrations of β-lactam antibiotics is lost.

Solution structure and peptide binding studies of the C-terminal Src homology 3-like domain of the diphtheria toxin repressor protein

The diphtheria toxin repressor (DtxR) is the best-characterized member of a family of homologous proteins that regulate iron uptake and virulence gene expression in the Gram-positive bacteria. DtxR contains two domains that are separated by a short, unstructured linker. The N-terminal domain is structurally well-defined and is responsible for Fe2+ binding, dimerization, and DNA binding. The C-terminal domain adopts a fold similar to eukaryotic Src homology 3 domains, but the functional role of the C-terminal domain in repressor activity is unknown. The solution structure of the C-terminal domain, consisting of residues N130-L226 plus a 13-residue N-terminal extension, has been determined by using NMR spectroscopy. Residues before A147 are highly mobile and adopt a random coil conformation, but residues A147-L226 form a single structured domain consisting of five β-strands and three helices arranged into a partially orthogonal, two-sheet β-barrel, similar to the structure observed in the crystalline Co2+ complex of full-length DtxR. Chemical shift perturbation studies demonstrate that a proline-rich peptide corresponding to residues R125-G139 of intact DtxR binds to the C-terminal domain in a pocket formed by residues in β-strands 2, 3, and 5, and helix 3. Binding of the proline-rich peptide by the C-terminal domain of DtxR presents an example of peptide binding by a prokaryotic Src homology 3-like protein. The results of this study, combined with previous x-ray studies of intact DtxR, provide insights into a possible biological function of the C-terminal domain in regulating repressor activity.

Lagging strand replication of rolling-circle plasmids: Specific recognition of the ssoA-type origins in different gram-positive bacteria

Many bacterial plasmids replicate by a rolling-circle mechanism that involves the generation of single-stranded DNA (ssDNA) intermediates. Replication of the lagging strand of such plasmids initiates from their single strand origin (sso). Many different types of ssos have been identified. One group of ssos, termed ssoA, which have conserved sequence and structural features, function efficiently only in their natural hosts in vivo. To study the host specificity of sso sequences, we have analyzed the functions of two closely related ssoAs belonging to the staphylococcal plasmid pE194 and the streptococcal plasmid pLS1 in Staphylococcus aureus. The pLS1 ssoA functioned poorly in vivo in S. aureus as evidenced by accumulation of high levels of ssDNA but supported efficient replication in vitro in staphylococcal extracts. These results suggest that one or more host factors that are present in sufficient quantities in S. aureus cell-free extracts may be limiting in vivo. Mapping of the initiation points of lagging strand synthesis in vivo and in vitro showed that DNA synthesis initiates from specific sites within the pLS1 ssoA. These results demonstrate that specific initiation of replication can occur from the pLS1 ssoA in S. aureus although it plays a minimal role in lagging strand synthesis in vivo. Therefore, the poor functionality of the pLS1 in vivo in a nonnative host is caused by the low efficiency rather than a lack of specificity of the initiation process. We also have identified ssDNA promoters and mapped the primer RNAs synthesized by the S. aureus and Bacillus subtilis RNA polymerases from the pE194 and pLS1 ssoAs. The S. aureus RNA polymerase bound more efficiently to the native pE194 ssoA as compared with the pLS1 ssoA, suggesting that the strength of RNA polymerase–ssoA interaction may play a major role in the functionality of the ssoA sequences in Gram-positive bacteria.

Double-level “orthogonal” dynamic combinatorial libraries on transition metal template

Dynamic combinatorial libraries are mixtures of compounds that exist in a dynamic equilibrium and can be driven to compositional self adaptation via selective binding of a specific assembly of certain components to a molecular target. We present here an extension of this initial concept to dynamic libraries that consists of two levels, the first formed by the coordination of terpyridine-based ligands to the transition metal template, and the second, by the imine formation with the aldehyde substituents on the terpyridine moieties. Dialdehyde 7 has been synthesized, converted into a variety of ligands, oxime ethers L11–L33 and acyl hydrazones L44–L77, and subsequently into corresponding cobalt complexes. A typical complex, Co(L22)22+ is shown to engage in rapid exchange with a competing ligand L11 and with another complex, Co(L22)22+ in 30% acetonitrile/water at pH 7.0 and 25°C. The exchange in the corresponding Co(III) complexes is shown to be much slower. Imine exchange in the acyl hydrazone complexes (L44–L77) is strongly controlled by pH and temperature. The two types of exchange, ligand and imine, can thus be used as independent equilibrium processes controlled by different types of external intervention, i.e., via oxidation/reduction of the metal template and/or change in the pH/temperature of the medium. The resulting double-level dynamic libraries are therefore named orthogonal, in similarity with the orthogonal protecting groups in organic synthesis. Sample libraries of this type have been synthesized and showed the complete expected set of components in electrospray ionization MS.

Orthogonal combinatorial mutagenesis: a codon-level combinatorial mutagenesis method useful for low multiplicity and amino acid-scanning protocols

We describe here a method to generate combinatorial libraries of oligonucleotides mutated at the codon-level, with control of the mutagenesis rate so as to create predictable binomial distributions of mutants. The method allows enrichment of the libraries with single, double or larger multiplicity of amino acid replacements by appropriate choice of the mutagenesis rate, depending on the concentration of synthetic precursors. The method makes use of two sets of deoxynucleoside-phosphoramidites bearing orthogonal protecting groups [4,4′-dimethoxytrityl (DMT) and 9-fluorenylmethoxycarbonyl (Fmoc)] in the 5′ hydroxyl. These phosphoramidites are divergently combined during automated synthesis in such a way that wild-type codons are assembled with commercial DMT-deoxynucleoside-methyl-phosphoramidites while mutant codons are assembled with Fmoc-deoxynucleoside-methyl-phosphoramidites in an NNG/C fashion in a single synthesis column. This method is easily automated and suitable for low mutagenesis rates and large windows, such as those required for directed evolution and alanine scanning. Through the assembly of three oligonucleotide libraries at different mutagenesis rates, followed by cloning at the polylinker region of plasmid pUC18 and sequencing of 129 clones, we concluded that the method performs essentially as intended.

A positivity result in the theory of Macdonald polynomials

We outline here a proof that a certain rational function Cn(q, t), which has come to be known as the “q, t-Catalan,” is in fact a polynomial with positive integer coefficients. This has been an open problem since 1994. Because Cn(q, t) evaluates to the Catalan number at t = q = 1, it has also been an open problem to find a pair of statistics a, b on the collection

Similarities between the DNA replication initiators of Gram-negative bacteria plasmids (RepA) and eukaryotes (Orc4p)/archaea (Cdc6p)

The proteins responsible for the initiation of DNA replication are thought to be essentially unrelated in bacteria and archaea/eukaryotes. Here we show that RepA, the initiator from the Pseudomonas plasmid pPS10, and the C-terminal domain of ScOrc4p, a subunit of Saccharomyces cerevisiae (Sc) origin recognition complex (ORC), share sequence similarities. Based on biochemical and spectroscopic evidence, these similarities include common structural elements, such as a winged-helix domain and a leucine-zipper dimerization motif. We have also found that ScOrc4p, as previously described for RepA-type initiators, interacts with chaperones of the Hsp70 family both in vitro and in vivo, most probably to regulate the assembly of active ORC. In evolutionary terms, our results are compatible with the recruitment of the same protein module for initiation of DNA replication by the ancestors of present-day Gram-negative bacteria plasmids, archaea, and eukaryotes.

Acyl-homoserine lactone quorum sensing in Gram-negative bacteria: A signaling mechanism involved in associations with higher organisms

Recent advances in studies of bacterial gene expression have brought the realization that cell-to-cell communication and community behavior are critical for successful interactions with higher organisms. Species-specific cell-to-cell communication is involved in successful pathogenic or symbiotic interactions of a variety of bacteria with plant and animal hosts. One type of cell–cell signaling is acyl-homoserine lactone quorum sensing in Gram-negative bacteria. This type of quorum sensing represents a dedicated communication system that enables a given species to sense when it has reached a critical population density in a host, and to respond by activating expression of genes necessary for continued success in the host. Acyl-homoserine lactone signaling in the opportunistic animal and plant pathogen Pseudomonas aeruginosa is a model for the relationships among quorum sensing, pathogenesis, and community behavior. In the P. aeruginosa model, quorum sensing is required for normal biofilm maturation and for virulence. There are multiple quorum-sensing circuits that control the expression of dozens of specific genes that represent potential virulence loci.

Purification and molecular cloning of an inducible gram-negative bacteria-binding protein from the silkworm, Bombyx mori.

A 50-kDa hemolymph protein, having strong affinity to the cell wall of Gram(-) bacteria, was purified from the hemolymph of the silkworm, Bombyx mori. The cDNA encoding this Gram(-) bacteria-binding protein (GNBP) was isolated from an immunized silkworm fat body cDNA library and sequenced. Comparison of the deduced amino acid sequence with known sequences revealed that GNBP contained a region displaying significant homology to the putative catalytic region of a group of bacterial beta-1,3 glucanases and beta-1,3-1,4 glucanases. Silkworm GNBP was also shown to have amino acid sequence similarity to the vertebrate lipopolysaccharide receptor CD14 and was recognized specifically by a polygonal anti-CD14 antibody. Northern blot analysis showed that GNBP was constitutively expressed in fat body, as well as in cuticular epithelial cells of naive silkworms. Intense transcription was, however, rapidly induced following a cuticular or hemoceolien bacterial challenge. An mRNA that hybridized with GNBP cDNA was also found in the l(2)mbn immunocompetent Drosophila cell line. These observations suggest that GNBP is an inducible acute phase protein implicated in the immune response of the silkworm and perhaps other insects.

Local densities orthogonal to beta-sheet amide planes: patterns of packing in globular proteins.

We have investigated the efficiency of packing by calculating intramolecular packing density above and below peptide planes of internal beta-pleated sheet residues in five globular proteins. The orientation of interest was chosen to allow study of regions that are approximately perpendicular to the faces of beta-pleated sheets. In these locations, nonbonded van der Waals packing interactions predominate over hydrogen bonding and solvent interactions. We observed considerable variability in packing densities within these regions, confirming that the interior packing of a protein does not result in uniform occupation of the available space. Patterns of fluctuation in packing density suggest that the regular backbone-to-backbone network of hydrogen bonds is not likely to be interrupted to maximize van der Waals interactions. However, high-density packing tends to occur toward the ends of beta-structure strands where hydrogen bonds are more likely to involve nonpolar side-chain groups or solvent molecules. These features result in internal protein folding with a central low-density core surrounded by a higher-density subsurface shell, consistent with our previous calculations regarding overall protein packing density.

Peptide synthesis using unprotected peptides through orthogonal coupling methods.

We describe an approach to the synthesis of peptides from segments bearing no protecting groups through an orthogonal coupling method to capture the acyl segment as a thioester that then undergoes an intramolecular acyl transfer to the amine component with formation of a peptide bond. Two orthogonal coupling methods to give the covalent ester intermediate were achieved by either a thiol-thioester exchange mediated by a trialkylphosphine and an alkylthiol or a thioesterification by C alpha-thiocarboxylic acid reacting with a beta-bromo amino acid. With this approach, unprotected segments ranging from 4 to 37 residues were coupled to aqueous solution to give free peptides up to 54 residues long with high efficiency.