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.

Structural characterization of an engineered tandem repeat contrasts the importance of context and sequence in protein folding

To test a different approach to understanding the relationship between the sequence of part of a protein and its conformation in the overall folded structure, the amino acid sequence corresponding to an α-helix of T4 lysozyme was duplicated in tandem. The presence of such a sequence repeat provides the protein with “choices” during folding. The mutant protein folds with almost wild-type stability, is active, and crystallizes in two different space groups, one isomorphous with wild type and the other with two molecules in the asymmetric unit. The fold of the mutant is essentially the same in all cases, showing that the inserted segment has a well-defined structure. More than half of the inserted residues are themselves helical and extend the helix present in the wild-type protein. Participation of additional duplicated residues in this helix would have required major disruption of the parent structure. The results clearly show that the residues within the duplicated sequence tend to maintain a helical conformation even though the packing interactions with the remainder of the protein are different from those of the original helix. It supports the hypothesis that the structures of individual α-helices are determined predominantly by the nature of the amino acids within the helix, rather than the structural environment provided by the rest of the protein.

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.

Nucleotide excision repair in rat male germ cells: low level of repair in intact cells contrasts with high dual incision activity in vitro

The acquisition of genotoxin-induced mutations in the mammalian germline is detrimental to the stable transfer of genomic information. In somatic cells, nucleotide excision repair (NER) is a major pathway to counteract the mutagenic effects of DNA damage. Two NER subpathways have been identified, global genome repair (GGR) and transcription-coupled repair (TCR). In contrast to somatic cells, little is known regarding the expression of these pathways in germ cells. To address this basic question, we have studied NER in rat spermatogenic cells in crude cell suspension, in enriched cell stages and within seminiferous tubules after exposure to UV or N-acetoxy-2-acetylaminofluorene. Surprisingly, repair in spermatogenic cells was inefficient in the genome overall and in transcriptionally active genes indicating non-functional GGR and TCR. In contrast, extracts from early/mid pachytene cells displayed dual incision activity in vitro as high as extracts from somatic cells, demonstrating that the proteins involved in incision are present and functional in premeiotic cells. However, incision activities of extracts from diplotene cells and round spermatids were low, indicating a stage-dependent expression of incision activity. We hypothesize that sequestering of NER proteins by mispaired regions in DNA involved in synapsis and recombination may underlie the lack of NER activity in premeiotic cells.

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.