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.

Carbohydrate-deficient glycoprotein syndrome type V: Deficiency of dolichyl-P-Glc:Man9GlcNAc2-PP-dolichyl glucosyltransferase

Deficiency of dolichyl-P-Glc:Man9GlcNAc2-PP-dolichyl glucosyltransferase is the cause of an additional type of carbohydrate-deficient glycoprotein syndrome (CDGS type V). Clinically this type resembles the classical type Ia of CDGS caused by the deficiency of phosphomannomutase. As a result of the glucosyltransferase deficiency in CDGS type V nonglucosylated lipid-linked oligosaccharides accumulate. The defect is leaky and glucosylated oligosaccharides are found on nascent glycoproteins. The limited availability of glucosylated lipid-linked oligosaccharides explains the incomplete usage of N-glycosylation sites in glycoproteins. This finding is reflected in the presence of transferrin forms in serum that lack one or both of the two N-linked oligosaccharides and the reduction of mannose incorporation to about one-third of control in glycoproteins of fibroblasts.

A new mechanism of sound generation in songbirds

Our current understanding of the sound-generating mechanism in the songbird vocal organ, the syrinx, is based on indirect evidence and theoretical treatments. The classical avian model of sound production postulates that the medial tympaniform membranes (MTM) are the principal sound generators. We tested the role of the MTM in sound generation and studied the songbird syrinx more directly by filming it endoscopically. After we surgically incapacitated the MTM as a vibratory source, zebra finches and cardinals were not only able to vocalize, but sang nearly normal song. This result shows clearly that the MTM are not the principal sound source. The endoscopic images of the intact songbird syrinx during spontaneous and brain stimulation-induced vocalizations illustrate the dynamics of syringeal reconfiguration before phonation and suggest a different model for sound production. Phonation is initiated by rostrad movement and stretching of the syrinx. At the same time, the syrinx is closed through movement of two soft tissue masses, the medial and lateral labia, into the bronchial lumen. Sound production always is accompanied by vibratory motions of both labia, indicating that these vibrations may be the sound source. However, because of the low temporal resolution of the imaging system, the frequency and phase of labial vibrations could not be assessed in relation to that of the generated sound. Nevertheless, in contrast to the previous model, these observations show that both labia contribute to aperture control and strongly suggest that they play an important role as principal sound generators.

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.

Naturally variant autosomal and sex-linked loci determine the severity of iron overload in β2-microglobulin-deficient mice

Hereditary hemochromatosis (HH) is a common chronic human genetic disorder whose hallmark is systemic iron overload. Homozygosity for a mutation in the MHC class I heavy chain paralogue gene HFE has been found to be a primary cause of HH. However, many individuals homozygous for the defective allele of HFE do not develop iron overload, raising the possibility that genetic variation in modifier loci contributes to the HH phenotype. Mice deficient in the product of the β2-microglobulin (β2M) class I light chain fail to express HFE and other MHC class I family proteins, and they have been found to manifest many characteristics of the HH phenotype. To determine whether natural genetic variation plays a role in controlling iron overload, we performed classical genetic analysis of the iron-loading phenotype in β2M-deficient mice in the context of different genetic backgrounds. Strain background was found to be a major determinant in iron loading. Sex played a role that was less than that of strain background but still significant. Resistance and susceptibility to iron overload segregated as complex genetic traits in F1 and back-cross progeny. These results suggest the existence of naturally variant autosomal and Y chromosome-linked modifier loci that, in the context of mice genetically predisposed by virtue of a β2M deficiency, can profoundly influence the severity of iron loading. These results thus provide a genetic explanation for some of the variability of the HH phenotype.

Cerebral organization for language in deaf and hearing subjects: Biological constraints and effects of experience

Cerebral organization during sentence processing in English and in American Sign Language (ASL) was characterized by employing functional magnetic resonance imaging (fMRI) at 4 T. Effects of deafness, age of language acquisition, and bilingualism were assessed by comparing results from (i) normally hearing, monolingual, native speakers of English, (ii) congenitally, genetically deaf, native signers of ASL who learned English late and through the visual modality, and (iii) normally hearing bilinguals who were native signers of ASL and speakers of English. All groups, hearing and deaf, processing their native language, English or ASL, displayed strong and repeated activation within classical language areas of the left hemisphere. Deaf subjects reading English did not display activation in these regions. These results suggest that the early acquisition of a natural language is important in the expression of the strong bias for these areas to mediate language, independently of the form of the language. In addition, native signers, hearing and deaf, displayed extensive activation of homologous areas within the right hemisphere, indicating that the specific processing requirements of the language also in part determine the organization of the language systems of the brain.

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.