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.

A very limited number of keywords (main patterns) describes all sequences of the human variable heavy (VH) and κ (Vκ) domains

Sequences of the variable heavy (VH) and κ (Vκ) domains of Ig structures were divided into 21 fragments that correspond to strands, loops, or parts of these structural units of the variable domains. Amino acid sequences of fragments (termed “words”) were collected from the 1,172 human heavy and 668 human κ chains available in the Kabat database. Statistical analysis of words of 17 fragments was performed (fragments that comprise the complementary determining regions′ fragments will not be discussed in this paper). The number of different words (those with different residues in at least one position) ranged, for various fragments, from 11 to 75 in the κ chains, and from 23 to 189 in the heavy chains. The main result of this study is that very few keywords, or main patterns of words, were necessary to describe over 90% of the sequences (no more than two keywords per fragment in the κ and no more than five per fragment in the heavy chains). No identical keywords were found for different fragments of the variable domains. Keywords of aligned fragments of the VH and Vκ domains were different in all but two instances. Thus, knowing the keywords, one can determine whether any given small part of a sequence belongs to a heavy or κ chain and predict its precise localization in the sequence. In addition, by using all of the keywords obtained through analysis of the Kabat database, it was possible to describe completely the sequences of the human VH and Vκ germ-line segments.

The importance of being discrete: Life always wins on the surface

Many systems in chemistry, biology, finance, and social sciences present emerging features that are not easy to guess from the elementary interactions of their microscopic individual components. In the past, the macroscopic behavior of such systems was modeled by assuming that the collective dynamics of microscopic components can be effectively described collectively by equations acting on spatially continuous density distributions. It turns out that, to the contrary, taking into account the actual individual/discrete character of the microscopic components of these systems is crucial for explaining their macroscopic behavior. In fact, we find that in conditions in which the continuum approach would predict the extinction of all of the population (respectively the vanishing of the invested capital or the concentration of a chemical substance, etc.), the microscopic granularity insures the emergence of macroscopic localized subpopulations with collective adaptive properties that allow their survival and development. In particular it is found that in two dimensions “life” (the localized proliferating phase) always prevails.

Molecular determinants of tissue selectivity in estrogen receptor modulators

Interaction of the estrogen receptor/ligand complex with a DNA estrogen response element is known to regulate gene transcription. In turn, specific conformations of the receptor-ligand complex have been postulated to influence unique subsets of estrogen-responsive genes resulting in differential modulation and, ultimately, tissue-selective outcomes. The estrogen receptor ligands raloxifene and tamoxifen have demonstrated such tissue-specific estrogen agonist/antagonist effects. Both agents antagonize the effects of estrogen on mammary tissue while mimicking the actions of estrogen on bone. However, tamoxifen induces significant stimulation of uterine tissue whereas raloxifene does not. We postulate that structural differences between raloxifene and tamoxifen may influence the conformations of their respective receptor/ligand complexes, thereby affecting which estrogen-responsive genes are modulated in various tissues. These structural differences are 4-fold: (A) the presence of phenolic hydroxyls, (B) different substituents on the basic amine, (C) incorporation of the stilbene moiety into a cyclic benzothiophene framework, and (D) the imposition of a carbonyl “hinge” between the basic amine-containing side chain and the olefin. A series of raloxifene analogs that separately exemplify each of these differences have been prepared and evaluated in a series of in vitro and in vivo assays. This strategy has resulted in the development of a pharmacophore model that attributes the differences in effects on the uterus between raloxifene and tamoxifen to a low-energy conformational preference imparting an orthogonal orientation of the basic side chain with respect to the stilbene plane. This three-dimensional array is dictated by a single carbon atom in the hinge region of raloxifene. These data indicate that differences in tissue selective actions among benzothiophene and triarylethylene estrogen receptor modulators can be ascribed to discrete ligand conformations.

A neuromodulatory role of interleukin-1β in the hippocampus

It is widely accepted that interleukin-1β (IL-1β), a cytokine produced not only by immune cells but also by glial cells and certain neurons influences brain functions during infectious and inflammatory processes. It is still unclear, however, whether IL-1 production is triggered under nonpathological conditions during activation of a discrete neuronal population and whether this production has functional implications. Here, we show in vivo and in vitro that IL-1β gene expression is substantially increased during long-term potentiation of synaptic transmission, a process considered to underlie certain forms of learning and memory. The increase in gene expression was long lasting, specific to potentiation, and could be prevented by blockade of potentiation with the N-methyl-d-aspartate (NMDA) receptor antagonist, (±)-2-amino-5-phosphonopentanoic acid (AP-5). Furthermore, blockade of IL-1 receptors by the specific interleukin-1 receptor antagonist (IL-1ra) resulted in a reversible impairment of long-term potentiation maintenance without affecting its induction. These results show for the first time that the production of biologically significant amounts of IL-1β in the brain can be induced by a sustained increase in the activity of a discrete population of neurons and suggest a physiological involvement of this cytokine in synaptic plasticity.

Control of time-dependent biological processes by temporally patterned input

Temporal patterning of biological variables, in the form of oscillations and rhythms on many time scales, is ubiquitous. Altering the temporal pattern of an input variable greatly affects the output of many biological processes. We develop here a conceptual framework for a quantitative understanding of such pattern dependence, focusing particularly on nonlinear, saturable, time-dependent processes that abound in biophysics, biochemistry, and physiology. We show theoretically that pattern dependence is governed by the nonlinearity of the input–output transformation as well as its time constant. As a result, only patterns on certain time scales permit the expression of pattern dependence, and processes with different time constants can respond preferentially to different patterns. This has implications for temporal coding and decoding, and allows differential control of processes through pattern. We show how pattern dependence can be quantitatively predicted using only information from steady, unpatterned input. To apply our ideas, we analyze, in an experimental example, how muscle contraction depends on the pattern of motorneuron firing.

Use of intrinsic modes in biology: Examples of indicial response of pulmonary blood pressure to ± step hypoxia

Recently, a new method to analyze biological nonstationary stochastic variables has been presented. The method is especially suitable to analyze the variation of one biological variable with respect to changes of another variable. Here, it is illustrated by the change of the pulmonary blood pressure in response to a step change of oxygen concentration in the gas that an animal breathes. The pressure signal is resolved into the sum of a set of oscillatory intrinsic mode functions, which have zero “local mean,” and a final nonoscillatory mode. With this device, we obtain a set of “mean trends,” each of which represents a “mean” in a definitive sense, and together they represent the mean trend systematically with different degrees of oscillatory content. Correspondingly, the oscillatory content of the signal about any mean trend can be represented by a set of partial sums of intrinsic mode functions. When the concept of “indicial response function” is used to describe the change of one variable in response to a step change of another variable, we now have a set of indicial response functions of the mean trends and another set of indicial response functions to describe the energy or intensity of oscillations about each mean trend. Each of these can be represented by an analytic function whose coefficients can be determined by a least-squares curve-fitting procedure. In this way, experimental results are stated sharply by analytic functions.

Prevention of hepatitis C virus infection in chimpanzees by hyperimmune serum against the hypervariable region 1 of the envelope 2 protein

The identification of the neutralization domains of hepatitis C virus (HCV) is essential for the development of an effective vaccine. Here, we show that the hypervariable region 1 (HVR1) of the envelope 2 (E2) protein is a critical neutralization domain of HCV. Neutralization of HCV in vitro was attempted with a rabbit hyperimmune serum raised against a homologous synthetic peptide derived from the HVR1 of the E2 protein, and the residual infectivity was evaluated by inoculation of HCV-seronegative chimpanzees. The source of HCV was plasma obtained from a patient (H) during the acute phase of posttransfusion non-A, non-B hepatitis, which had been titered for infectivity in chimpanzees. The anti-HVR1 antiserum induced protection against homologous HCV infection in chimpanzees, but not against the emergence of neutralization escape mutants that were found to be already present in the complex viral quasispecies of the inoculum. The finding that HVR1 can elicit protective immunity opens new perspectives for the development of effective preventive strategies. However, the identification of the most variable region of HCV as a critical neutralization domain poses a major challenge for the development of a broadly reactive vaccine against HCV.

Stimulation of bacteriophage T4 middle transcription by the T4 proteins MotA and AsiA occurs at two distinct steps in the transcription cycle

The bacteriophage T4 encodes proteins that are responsible for tightly regulating mRNA synthesis throughout phage development in Escherichia coli. The three classes of T4 promoters (early, middle, and late) are utilized sequentially by the host RNA polymerase as a result of phage-induced modifications. One such modification is the tight binding of the T4 AsiA protein to the σ70 subunit of the RNA polymerase. This interaction is pivotal for the transition between T4 early and middle transcription, since it both inhibits recognition of host and T4 early promoters and stimulates T4 middle mode synthesis. The activation of T4 middle transcription also requires the T4 MotA protein, bound specifically to its recognition sequence, the “Mot box,” which is centered at position −30 of these promoters. Accordingly, the two T4 proteins working in concert are sufficient to effectively switch the transcription specificity of the RNA polymerase holoenzyme. Herein, we investigate the mechanism of transcription activation and report that, while the presence of MotA and AsiA increases the initial recruitment of RNA polymerase to a T4 middle promoter, it does not alter the intrinsic stability of the discrete complexes formed. In addition, we have characterized the RNA polymerase-promoter species by UV laser footprinting and followed their evolution from open into initiating complexes. These data, combined with in vitro transcription assays, indicate that AsiA and MotA facilitate promoter escape, thereby stimulating the production of full-length transcripts.

Structural Analysis and Molecular Model of a Self-Incompatibility RNase from Wild Tomato1

Self-incompatibility RNases (S-RNases) are an allelic series of style glycoproteins associated with rejection of self-pollen in solanaceous plants. The nucleotide sequences of S-RNase alleles from several genera have been determined, but the structure of the gene products has only been described for those from Nicotiana alata. We report on the N-glycan structures and the disulfide bonding of the S3-RNase from wild tomato (Lycopersicon peruvianum) and use this and other information to construct a model of this molecule. The S3-RNase has a single N-glycosylation site (Asn-28) to which one of three N-glycans is attached. S3-RNase has seven Cys residues; six are involved in disulfide linkages (Cys-16-Cys-21, Cys-46-Cys-91, and Cys-166-Cys-177), and one has a free thiol group (Cys-150). The disulfide-bonding pattern is consistent with that observed in RNase Rh, a related RNase for which radiographic-crystallographic information is available. A molecular model of the S3-RNase shows that four of the most variable regions of the S-RNases are clustered on one surface of the molecule. This is discussed in the context of recent experiments that set out to determine the regions of the S-RNase important for recognition during the self-incompatibility response.

Antisense ribosomes: rRNA as a vehicle for antisense RNAs.

Although rRNA has a conserved core structure, its size varies by more than 2000 bases between eubacteria and vertebrates, mostly due to the size variation of discrete variable regions. Previous studies have shown that insertion of foreign sequences into some of these variable regions has little effect on rRNA function. These properties make rRNA a potentially very advantageous vehicle to carry other RNA moieties with biological activity, such as "antisense RNAs." We have explored this possibility by inserting antisense RNAs targeted against one essential and two nonessential genes into a site within a variable region in the Tetrahymena thermophila large subunit rRNA gene. Expression of each of the three genes tested can be drastically reduced or eliminated in transformed T. thermophila lines containing these altered rRNAs. In addition, we found that only antisense rRNAs containing RNA sequences complementary to the 5' untranslated region of the targeted mRNA were effective. Lines containing antisense rRNAs targeted against either of the nonessential genes grow well, indicating that the altered rRNAs fulfill their functions within the ribosome. Since functional rRNA is extremely abundant and stable and comes into direct contact with translated mRNAs, it may prove to be an unparalleled vehicle for enhancing the activity of functional RNAs that act on mRNAs.

Mitochondrial diversity and the origins of African and European cattle.

The nature of domestic cattle origins in Africa are unclear as archaeological data are relatively sparse. The earliest domesticates were humpless, or Bos taurus, in morphology and may have shared a common origin with the ancestors of European cattle in the Near East. Alternatively, local strains of the wild ox, the aurochs, may have been adopted by peoples in either continent either before or after cultural influence from the Levant. This study examines mitochondrial DNA displacement loop sequence variation in 90 extant bovines drawn from Africa, Europe, and India. Phylogeny estimation and analysis of molecular variance verify that sequences cluster significantly into continental groups. The Indian Bos indicus samples are most markedly distinct from the others, which is indicative of a B. taurus nature for both European and African ancestors. When a calibration of sequence divergence is performed using comparisons with bison sequences and an estimate of 1 Myr since the Bison/Bos Leptobos common ancestor, estimates of 117-275,000 B.P. and 22-26,000 B.P. are obtained for the separation between Indians and others and between African and European ancestors, respectively. As cattle domestication is thought to have occurred approximately 10,000 B.P., these estimates suggest the domestication of genetically discrete aurochsen strains as the origins of each continental population. Additionally, patterns of variation that are indicative of population expansions (probably associated with the domestication process) are discernible in Africa and Europe. Notably, the genetic signatures of these expansions are clearly younger than the corresponding signature of African/European divergence.

Acridones: a chemically new group of protonophores.

Although the interaction of proton-conducting ionophores (protonophores) with photosynthetic electron transport has been extensively studied during the past decade, the mode of action of protonophores remained uncertain. For a better understanding of the molecular mechanism of the action of protonophores, the introduction of chemically new types of molecules will be required. In this work, we demonstrate that acridones (9-azaanthracene-10-ones) completely fulfill this requirement. At low concentrations of acridones, the thermoluminescence bands at +20 degrees C and +10 degrees C were strongly inhibited, while normal electron transport activity was retained. This indicates that the concentrations of S2 and S3 states involved in the generation of these bands are reduced. At higher concentrations, an increased activity of electron transport was observed, which is attributed to the typical uncoupler effect of protonophores. Indeed, acridones accelerate the decay of the electrochromic absorbance change at 515 nm and also inhibit the generation of the transmembrane proton gradient, measured as an absorbance transient of neutral red. Variable fluorescence induction was quenched even at low concentrations of acridones but was restored by either a long-term illumination or high light intensity. Acridones, similarly to other protonophores, promoted the autooxidation of the high-potential form of cytochrome b559 and partially converted it to lower potential forms. These results suggest that acridones, acting as typical protonophores, uncouple electron transport, accelerate the deactivation of the S2 and S3 states on the donor side, and facilitate the oxidation of cytochrome b559 on the acceptor side of photosystem II.

The SNAP45 subunit of the small nuclear RNA (snRNA) activating protein complex is required for RNA polymerase II and III snRNA gene transcription and interacts with the TATA box binding protein.

The RNA polymerase II and III small nuclear RNA (snRNA) promoters contain a common basal promoter element, the proximal sequence element (PSE). The PSE binds a multisubunit complex we refer to as the snRNA activating protein complex (SNAPc). At least four polypeptides are visible in purified SNAPc preparations, which migrate with apparent molecular masses of 43, 45, 50, and 190 kDa on SDS/polyacrylamide gels. In addition, purified preparations of SNAPc contain variable amounts of TATA box binding protein (TBP). An important question is whether the PSEs of RNA polymerase II and III snRNA promoters recruit the exact same SNAP complex or slightly different versions of SNAPc, differing, for example, by the presence or absence of a subunit. To address this question, we are isolating cDNAs encoding different subunits of SNAPc. We have previously isolated the cDNA encoding the 43-kDa subunit SNAP43. We now report the isolation of the cDNA that encodes the p45 polypeptide. Antibodies directed against p45 retard the mobility of the SNAPc-PSE complex in an electrophoretic mobility shift assay, indicating that p45 is indeed part of SNAPc. We therefore refer to this protein as SNAP45. SNAP45 is exceptionally proline-rich, interacts strongly with TBP, and, like SNAP43, is required for both RNA polymerase II and III transcription of snRNA genes.

Analysis of the relation between the sequence and secondary and three-dimensional structures of immunoglobulin molecules.

Methods of structural and statistical analysis of the relation between the sequence and secondary and three-dimensional structures are developed. About 5000 secondary structures of immunoglobulin molecules from the Kabat data base were predicted. Two statistical analyses of amino acids reveal 47 universal positions in strands and loops. Eight universally conservative positions out of the 47 are singled out because they contain the same amino acid in > 90% of all chains. The remaining 39 positions, which we term universally alternative positions, were divided into five groups: hydrophobic, charged and polar, aromatic, hydrophilic, and Gly-Ala, corresponding to the residues that occupied them in almost all chains. The analysis of residue-residue contacts shows that the 47 universal positions can be distinguished by the number and types of contacts. The calculations of contact maps in the 29 antibody structures revealed that residues in 24 of these 47 positions have contacts only with residues of antiparallel beta-strands in the same beta-sheet and residues in the remaining 23 positions always have far-away contacts with residues from other beta-sheets as well. In addition, residues in 6 of the 47 universal positions are also involved in interactions with residues of the other variable or constant domains.