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 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

Inhibition of granulocytic differentiation by mNotch1

Effective hematopoiesis requires the commitment of pluripotent and multipotent stem cells to distinct differentiation pathways, proliferation and maturation of cells in the various lineages, and preservation of pluripotent progenitors to provide continuous renewal of mature blood cells. While the importance of positive and negative cytokines in regulating proliferation and maturation of hematopoietic cells has been well documented, the factors and molecular processes involved in lineage commitment and self-renewal of multipotent progenitors have not yet been defined. In other developmental systems, cellular interactions mediated by members of the Notch gene family have been shown to influence cell fate determination by multipotent progenitors. We previously described the expression of the human Notch1 homolog, TAN-1, in immature hematopoietic precursors. We now demonstrate that constitutive expression of the activated intracellular domain of mouse Notch1 in 32D myeloid progenitors inhibits granulocytic differentiation and permits expansion of undifferentiated cells, findings consistent with the known function of Notch in other systems.

On the classification of binary shifts of finite commutant index

We provide a complete classification up to conjugacy of the binary shifts of finite commutant index on the hyperfinite II1, factor. There is a natural correspondence between the conjugacy classes of these shifts and polynomials over GF(2) satisfying a certain duality condition.

Oncogenic mutation in the Kit receptor tyrosine kinase alters substrate specificity and induces degradation of the protein tyrosine phosphatase SHP-1

Activating mutations in the Kit receptor tyrosine kinase have been identified in both rodent and human mast cell leukemia. One activating Kit mutation substitutes a valine for aspartic acid at codon 816 (D816V) and is frequently observed in human mastocytosis. Mutation at the equivalent position in the murine c-kit gene, involving a substitution of tyrosine for aspartic acid (D814Y), has been described in the mouse mastocytoma cell line P815. We have investigated the mechanism of oncogenic activation by this mutation. Expression of this mutant Kit receptor tyrosine kinase in a mast cell line led to the selective tyrosine phosphorylation of a 130-kDa protein and the degradation, through the ubiquitin-dependent proteolytic pathway, of a 65-kDa phosphoprotein. The 65-kDa protein was identified as the src homology domain 2 (SH2)-containing protein tyrosine phosphatase SHP-1, a negative regulator of signaling by Kit and other hematopoietic receptors, and the protein product of the murine motheaten locus. This mutation also altered the sites of receptor autophosphorylation and peptide substrate selectivity. Thus, this mutation activates the oncogenic potential of Kit by a novel mechanism involving an alteration in Kit substrate recognition and the degradation of SHP-1, an attenuator of the Kit signaling pathway.

The targeting pathway of Escherichia coli presecretory and integral membrane proteins is specified by the hydrophobicity of the targeting signal

Previous studies have demonstrated that presecretory proteins such as maltose binding protein (MBP) and outer membrane protein A (OmpA) are targeted to the Escherichia coli inner membrane by the molecular chaperone SecB, but that integral membrane proteins are targeted by the signal recognition particle (SRP). In vitro studies have suggested that trigger factor binds to a sequence near the N terminus of the mature region of OmpA and shunts the protein into the SecB pathway by blocking an interaction between SRP and the signal peptide. By contrast, we have found that the targeting pathway of a protein under physiological conditions is dictated by the composition of its targeting signal. Replacement of the MBP or OmpA signal peptide with the first transmembrane segment of AcrB abolished the dependence on SecB for transport and rerouted both proteins into the SRP targeting pathway. More modest alterations of the MBP signal peptide that simply increase its hydrophobicity also promoted SRP binding. Furthermore, we obtained evidence that SRP has a low affinity for typical signal peptides in vivo. These results imply that different classes of E. coli proteins are targeted by distinct pathways because bacterial SRP binds to a more restricted range of targeting signals than its eukaryotic counterpart.

Structural aspects of activation pathways of aspartic protease zymogens and viral 3C protease precursors

The three-dimensional structures of the inactive protein precursors (zymogens) of the serine, cysteine, aspartic, and metalloprotease classes of proteolytic enzymes are known. Comparisons of these structures with those of the mature, active proteases reveal that, in general, the preformed, active conformations of the residues involved in catalysis are rendered sterically inaccessible to substrates by the residues of the zymogens’ N-terminal extensions or prosegments. The prosegments interact in nonsubstrate-like fashions with the residues of the active sites in most of the cases. The gastric aspartic proteases have a well-characterized zymogen conversion pathway. Structures of human progastricsin, the inactive intermediate 2, and active human pepsin are known and have been used to define the conversion pathway. The structure of the zymogen precursor of plasmepsin II, the malarial aspartic protease, shows a new twist on the mode of inactivation used by the gastric zymogens. The prosegment of proplasmepsin disrupts the active conformation of the two catalytic aspartic acid residues by inducing a major reorientation of the two domains of the mature protease. The picornaviral 2A and 3C proteases have a chymotrypsin-like tertiary structure but with a cysteine nucleophile. These enzymes cleave themselves from the viral polyprotein in cis (intramolecular cleavage) and carry out trans cleavages of other scissile peptides important for the virus life cycle. Although the structure of the precursor viral polyprotein is unknown, it probably resembles the organization of the proenzymes of the bacterial serine proteases, subtilisin, and α-lytic protease. Cleavage of the prosegment is known to occur in cis for these precursor molecules.

cAMP-response element modulator tau is a positive regulator of testis angiotensin converting enzyme transcription.

Testis angiotensin-converting enzyme (ACE) is a unique form of ACE, only produced by male germ cells, and results from a testis-specific promoter found within the ACE gene. We have investigated the role of cAMP-response element modulator (CREM)tau in testis ACE transcription. In gel shift experiments, testes nuclear proteins retard an oligonucleotide containing the cAMP-response element (CRE) found at position -55 in the testis ACE promoter. Anti-CREM antibody supershifts this complex. Competitive gel shift shows that recombinant CREM tau protein and testis nuclear proteins have a similar specificity of binding to the tests ACE CRE. Functional analysis using in vitro transcription and transfection studies also demonstrate that CREM tau protein is a transcriptional activator of the testis ACE promoter. Western blot analysis identifies CREM tau protein in the protein-DNA complex formed between nuclear proteins and the testis ACE CRE motif. This analysis also identified other CREM isoforms in the gel-shifted complex, which are thought to be CREM tau 1/2, CREM alpha/beta, and S-CREM. These data indicate that CREM tau isoforms play an important role as a positive regulator in the tissue-specific expression of testis ACE.

Primordial emergence of the recombination activating gene 1 (RAG1): sequence of the complete shark gene indicates homology to microbial integrases.

The rearrangement of antibody and T-cell receptor gene segments is indispensable to the vertebrate immune response. All extant jawed vertebrates can rearrange these gene segments. This ability is conferred by the recombination activating genes I and II (RAG I and RAG II). To elucidate their origin and function, the cDNA encoding RAG I from a member of the most ancient class of extant gnathostomes, the Carcharhine sharks, was characterized. Homology domains identified within shark RAG I prompted sequence comparison analyses that suggested similarity of the RAG I and II genes, respectively, to the integrase family genes and integration host factor genes of the bacterial site-specific recombination system. Thus, the apparent explosive evolution (or "big bang") of the ancestral immune system may have been initiated by a transfer of microbial site-specific recombinases.

Do cyanobacteria swim using traveling surface waves?

Bacteria that swim without the benefit of flagella might do so by generating longitudinal or transverse surface waves. For example, swimming speeds of order 25 microns/s are expected for a spherical cell propagating longitudinal waves of 0.2 micron length, 0.02 micron amplitude, and 160 microns/s speed. This problem was solved earlier by mathematicians who were interested in the locomotion of ciliates and who considered the undulations of the envelope swept out by ciliary tips. A new solution is given for spheres propagating sinusoidal waveforms rather than Legendre polynomials. The earlier work is reviewed and possible experimental tests are suggested.

Targeted disruption of the mouse beta1-adrenergic receptor gene: developmental and cardiovascular effects.

At least three distinct beta-adrenergic receptor (beta-AR) subtypes exist in mammals. These receptors modulate a wide variety of processes, from development and behavior, to cardiac function, metabolism, and smooth muscle tone. To understand the roles that individual beta-AR subtypes play in these processes, we have used the technique of gene targeting to create homozygous beta 1-AR null mutants (beta 1-AR -/-) in mice. The majority of beta 1-AR -/- mice die prenatally, and the penetrance of lethality shows strain dependence. Beta l-AR -/- mice that do survive to adulthood appear normal, but lack the chronotropic and inotropic responses seen in wild-type mice when beta-AR agonists such as isoproterenol are administered. Moreover, this lack of responsiveness is accompanied by markedly reduced stimulation of adenylate cyclase in cardiac membranes from beta 1-AR -/- mice. These findings occur despite persistent cardiac beta 2-AR expression, demonstrating the importance of beta 1-ARs for proper mouse development and cardiac function, while highlighting functional differences between beta-AR subtypes.

Steel mutant mice are deficient in hippocampal learning but not long-term potentiation.

Mice carrying mutations in either the dominant white-spotting (W) or Steel (Sl) loci exhibit deficits in melanogenesis, gametogenesis, and hematopoiesis. W encodes the Kit receptor tyrosine kinase, while Sl encodes the Kit ligand, Steel factor, and the receptor-ligand pair are contiguously expressed at anatomical sites expected from the phenotypes of W and Sl mice. The c-kit and Steel genes are also both highly expressed in the adult murine hippocampus: Steel is expressed in dentate gyrus neurons whose mossy fiber axons synapse with the c-kit expressing CA3 pyramidal neurons. We report here that Sl/Sld mutant mice have a specific deficit in spatial learning. These mutant mice are also deficient in baseline synaptic transmission between the dentate gyrus and CA3 but show normal long-term potentiation in this pathway. These observations demonstrate a role for Steel factor/Kit signaling in the adult nervous system and suggest that a severe deficit in hippocampal-dependent learning need not be associated with reduced hippocampal long-term potentiation.

Expression of the human acute myeloid leukemia gene AML1 is regulated by two promoter regions.

The human chromosome 21 AML1 gene is expressed predominantly in the hematopoietic system. In several leukemia-associated translocations AML1 is fused to other genes and transcription of the fused regions is mediated by upstream sequences that normally regulate the expression of AML1. The 5' genomic region of AML1 was cloned and sequenced. The two 5' untranslated regions (UTRs) previously identified in AML1 cDNAs were located in this region and the distance between them was established. The distal 5' UTR maps over 7 kb upstream of the proximal one. Using primer extension with mRNA, transcription start sites were identified at two distinct sites above these 5' uTRs. Sequence analysis revealed the absence of a TATA motif and the presence of Sp1, PU.1, Oct, CRE, Myb, Ets, and Ets-like binding sites in both upstream regions. Several initiator elements (Inr) that overlap the transcription start sites were also identified. These proximal and distal upstream regions and their deletion mutants were cloned in front of a luciferase reporter gene and used in transfection assays. We demonstrate that both upstream regions function as promoters in hematopoietic (Jurkat) and nonhematopoietic (HEK) cell lines. The activity of both promoters was orientation dependent and was enhanced, in a cell-type specific manner, by a heterologous enhancer sequence. These results indicate that additional control elements, either negative or positive, regulate the tissue-specific expression of AML1.

An induction gene trap screen in embryonic stem cells: Identification of genes that respond to retinoic acid in vitro.

We have developed a novel induction gene trap approach that preselects in vitro for integrations into genes that lie downstream of receptor/ligand-mediated signaling pathways. Using this approach, we have identified 20 gene trap integrations in embryonic stem cells, 9 of which were induced and 11 of which were repressed after exposure to exogenous retinoic acid (RA). All but one of these integrations showed unique spatially restricted or tissue-specific patterns of expression between 8.5 and 11.5 days of embryogenesis. Interestingly, expression was observed in tissues that are affected by alterations in RA levels during embryogenesis. Sequence analysis of fusion transcripts from six integrations revealed five novel gene sequences and the previously identified protooncogene c-fyn. To date, germ-line transmission and breeding has uncovered one homozygous embryonic lethal and three homozygous viable insertions. These studies demonstrate the potential of this induction gene trap approach for identifying and mutating genes downstream of signal transduction pathways.