The Wiener-Hopf solution of a class of mixed boundary value problems arising in surface water wave phenomena

Two mixed boundary value problems associated with two-dimensional Laplace equation, arising in the study of scattering of surface waves in deep water (or interface waves in two superposed fluids) in the linearised set up, by discontinuities in the surface (or interface) boundary conditions, are handled for solution by the aid of the Weiner-Hopf technique applied to a slightly more general differential equation to be solved under general boundary conditions and passing on to the limit in a manner so as to finally give rise to the solutions of the original problems. The first problem involves one discontinuity while the second problem involves two discontinuities. The reflection coefficient is obtained in closed form for the first problem and approximately for the second. The behaviour of the reflection coefficient for both the problems involving deep water against the incident wave number is depicted in a number of figures. It is observed that while the reflection coefficient for the first problem steadily increases with the wave number, that for the second problem exhibits oscillatory behaviour and vanishes at some discrete values of the wave number. Thus, there exist incident wave numbers for which total transmission takes place for the second problem. (C) 1999 Elsevier Science B.V. All rights reserved.

Advantage of the ether linkage between the positive charge and the cholesteryl skeleton in cholesterol-based amphiphiles as vectors for gene delivery

Twelve novel cationic cholesterol derivatives with different linkage types between the cationic headgroup and the cholesteryl backbone have been developed. These have been tested for their efficacies as gene transfer agents as mixtures with dioleoyl phosphatidylethanolamine (DOPE). A pronounced improvement in transfection efficiency was observed when the cationic center was linked to the steroid backbone using an ether type bond. Among these, cholest-5-en-3b-oxyethane-N, N,N-trimethylammonium bromide (2a) and cholest-5-en-3b-oxyethane-N, N-dimethyl-N-2-hydroxyethylammonium bromide (3d) showed transfection efficiencies considerably greater than commercially available reagents such as Lipofectin or Lipofectamine. To achieve transfection, 3d did not require DOPE. Increasing hydration at the headgroup level for both ester- and ether-linked amphiphiles resulted in progressive loss of transfection efficiency. Transfection efficiency was also greatly reduced when a 'disorder'-inducing chain like an oleyl (cis-9-octadecenyl) segment was added to these cholesteryl amphiphiles. Importantly, the transfection ability of 2a with DOPE in the presence of serum was significantly greater than for a commercially available reagent, Lipofectamine. This suggests that these novel cholesterol-based amphiphiles might prove promising in applications involving liposome-mediated gene transfection. This investigation demonstrates the importance of structural features at the molecular level for the design of cholesterol-based gene delivery reagents that would aid the development of newer, more efficient formulations based on this class of molecules.

A fixed-grid finite element based enthalpy formulation for generalized phase change problems: role of superficial mushy region

The enthalpy method is primarily developed for studying phase change in a multicomponent material, characterized by a continuous liquid volume fraction (phi(1)) vs temperature (T) relationship. Using the Galerkin finite element method we obtain solutions to the enthalpy formulation for phase change in 1D slabs of pure material, by assuming a superficial phase change region (linear (phi(1) vs T) around the discontinuity at the melting point. Errors between the computed and analytical solutions are evaluated for the fluxes at, and positions of, the freezing front, for different widths of the superficial phase change region and spatial discretizations with linear and quadratic basis functions. For Stefan number (St) varying between 0.1 and 10 the method is relatively insensitive to spatial discretization and widths of the superficial phase change region. Greater sensitivity is observed at St = 0.01, where the variation in the enthalpy is large. In general the width of the superficial phase change region should span at least 2-3 Gauss quadrature points for the enthalpy to be computed accurately. The method is applied to study conventional melting of slabs of frozen brine and ice. Regardless of the forms for the phi(1) vs T relationships, the thawing times were found to scale as the square of the slab thickness. The ability of the method to efficiently capture multiple thawing fronts which may originate at any spatial location within the sample, is illustrated with the microwave thawing of slabs and 2D cylinders. (C) 2002 Elsevier Science Ltd. All rights reserved.

Gene Expression Profiling of Preovulatory Follicle in the Buffalo Cow: Effects of Increased IGF-I Concentration on Periovulatory Events

The preovulatory follicle in response to gonadotropin surge undergoes dramatic biochemical, and morphological changes orchestrated by expression changes in hundreds of genes. Employing well characterized bovine preovulatory follicle model, granulosa cells (GCs) and follicle wall were collected from the preovulatory follicle before, 1, 10 and 22 h post peak LH surge. Microarray analysis performed on GCs revealed that 450 and 111 genes were differentially expressed at 1 and 22 h post peak LH surge, respectively. For validation, qPCR and immunocytochemistry analyses were carried out for some of the differentially expressed genes. Expression analysis of many of these genes showed distinct expression patterns in GCs and the follicle wall. To study molecular functions and genetic networks, microarray data was analyzed using Ingenuity Pathway Analysis which revealed majority of the differentially expressed genes to cluster within processes like steroidogenesis, cell survival and cell differentiation. In the ovarian follicle, IGF-I is established to be an important regulator of the above mentioned molecular functions. Thus, further experiments were conducted to verify the effects of increased intrafollicular IGF-I levels on the expression of genes associated with the above mentioned processes. For this purpose, buffalo cows were administered with exogenous bGH to transiently increase circulating and intrafollicular concentrations of IGF-I. The results indicated that increased intrafollicular concentrations of IGF-I caused changes in expression of genes associated with steroidogenesis (StAR, SRF) and apoptosis (BCL-2, FKHR, PAWR). These results taken together suggest that onset of gonadotropin surge triggers activation of various biological pathways and that the effects of growth factors and peptides on gonadotropin actions could be examined during preovulatory follicle development.

Phenobarbitone-mediated translocation of the cytosolic proteins interacting with the 5 '-proximal region of rat liver CYP2B1/B2 gene into the nucleus

The positive element (PE) (-69 to -98 bp) within the 5'-proximal region of the CYP2B1B2 gene (+1 to -179 bp) of rat liver is essential for phenobarbitone (PB) response and gives a single major complex with the rat liver cytosol in gel shift analysis. This complex corresponds to complex I (top) of the three complexes given by the nuclear extracts. PB treatment of rats leads to a decrease in complex I formation with the cytosol and PE and an increase in the same with the nuclear extract in gel shift analysis. Both the changes are counteracted by simultaneous okadaic acid administration. The nuclear protein giving rise to complex I has been isolated and has an M-r of 26 kDa. The cytosolic counterpart consists of two species, 26 and 28 kDa, as revealed by Southwestern blot analysis using labeled PE. It is concluded that PB treatment leads to the translocation accompanied by processing of the cytosolic protein species into the nucleus that requires protein dephosphorylation. It is suggested that PB may exert a global regulation on the transcription of many genes by modulating the phosphorylation status of different protein factors involved in transcriptional regulation. (C) 2002 Elsevier Science (USA).

Scaling analysis of momentum, heat, and mass transfer in binary alloy solidification problems

A systematic approach is developed for scaling analysis of momentum, heat and species conservation equations pertaining to the case of solidification of a binary mixture. The problem formulation and description of boundary conditions are kept fairly general, so that a large class of problems can be addressed. Analysis of the momentum equations coupled with phase change considerations leads to the establishment of an advection velocity scale. Analysis of the energy equation leads to an estimation of the solid layer thickness. Different regimes corresponding to different dominant modes of transport are simultaneously identified. A comparative study involving several cases of possible thermal boundary conditions is also performed. Finally, a scaling analysis of the species conservation equation is carried out, revealing the effect of a non-equilibrium solidification model on solute segregation and species distribution. It is shown that non-equilibrium effects result in an enhanced macrosegregation compared with the case of an equilibrium model. For the sake of assessment of the scaling analysis, the predictions are validated against corresponding computational results.

Characterization of the gene encoding the envelope fusion glycoprotein GP64 from Bombyx mori nucleopolyhedrovirus

We describe here the characterization of the gene gp64 encoding the envelope fusion protein GP64 (open reading frame) ORF 105 from Bombyx mori nucleopolyhedrovirus (BmNPV). gp64 was transcribed from the early to late stages of infection and the transcripts were seen from 6 to 72 h post infection (hpi). The early transcripts initiated from a consensus CAGT motif while the late transcripts arose from three conserved TAAG motifs, all of which were located in the near upstream region of the coding sequence. Both early and late transcripts terminated at a run of T residues following the second polyadenylation signal located 31 nt downstream of the translation termination codon. BmGP64 protein was detectable from 6 hpi and was present in larger quantities throughout the infection process from 12 hpi, in BmNPV-infected BmN cells. The persistent presence of GP64 in BmN cells differed from the protein expression pattern of GP64 in Autographa californica multinucleocapsid nucleopolyhedrovirus infection, where the protein levels decreased significantly by late times (48 hpi). BmGP64 was located in the membrane and cytoplasm of the infected host cells and as a component of the budded virions. The production of infectious budded virus and the fusion activity were reduced when glycosylation of GP64 was inhibited. (C) 2003 Elsevier Science B.V. All rights reserved.

Two-Parameter Uniformly Elliptic Sturm–Liouville Problems With Eigenparameter-Dependent Boundary Conditions

We consider the two-parameter Sturm–Liouville system $$ -y_1''+q_1y_1=(\lambda r_{11}+\mu r_{12})y_1\quad\text{on }[0,1], $$ with the boundary conditions $$ \frac{y_1'(0)}{y_1(0)}=\cot\alpha_1\quad\text{and}\quad\frac{y_1'(1)}{y_1(1)}=\frac{a_1\lambda+b_1}{c_1\lambda+d_1}, $$ and $$ -y_2''+q_2y_2=(\lambda r_{21}+\mu r_{22})y_2\quad\text{on }[0,1], $$ with the boundary conditions $$ \frac{y_2'(0)}{y_2(0)} =\cot\alpha_2\quad\text{and}\quad\frac{y_2'(1)}{y_2(1)}=\frac{a_2\mu+b_2}{c_2\mu+d_2}, $$ subject to the uniform-left-definite and uniform-ellipticity conditions; where $q_{i}$ and $r_{ij}$ are continuous real valued functions on $[0,1]$, the angle $\alpha_{i}$ is in $[0,\pi)$ and $a_{i}$, $b_{i}$, $c_{i}$, $d_{i}$ are real numbers with $\delta_{i}=a_{i}d_{i}-b_{i}c_{i}>0$ and $c_{i}\neq0$ for $i,j=1,2$. Results are given on asymptotics, oscillation of eigenfunctions and location of eigenvalues.

Identification of a core promoter and a novel isoform of the human TSCI gene transcript and structural comparison with mouse homolog

Tuberous sclerosis complex (TSC) is an autosomal dominant disorder with loci on chromosome 9q34.12 (TSC1) and chromosome 16p13.3 (TSC2). Genes for both loci have been isolated and characterized. The promoters of both genes have not been characterized so far and little is known about the regulation of these genes. This study reports the characterization of the human TSC1 promoter region for the first time. We have identified a novel alternative isoform in the 5' untranslated region (UTR) of the TSC1 gene transcript involving exon 1. Alternative isoforms in the 5' UTR of the mouse Tsc1 gene transcript involving exon I and exon 2 have also been identified. We have identified three upstream open reading frames (uORFs) in the 5' UTR of the TSC1/Tsc1 gene. A comparative study of the 5' UTR of TSC1/Tsc1 gene has revealed that there is a high degree of similarity not only in the sequence but also in the splicing pattern of both human and mouse TSC1 genes. We have used PCR methodology to isolate approximately 1.6 kb genomic DNA 5' to the TSC1 cDNA. This sequence has directed a high level of expression of luciferase activity in both HeLa and HepG2 cells. Successive 5' and 3' deletion analysis has suggested that a -587 bp region, from position +77 to -510 from the transcription start site (TSS), contains the promoter activity. Interestingly, this region contains no consensus TATA box or CAAT box. However, a 521-bp fragment surrounding the TSS exhibits the characteristics of a CpG island which overlaps with the promoter region. The identification of the TSC1 promoter region will help in designing a suitable strategy to identify mutations in this region in patients who do not show any mutations in the coding regions. It will also help to study the regulation of the TSC1 gene and its role in tumorigenesis. (C) 2003 Elsevier B.V. All rights reserved.

Right-Definite Multiparameter Sturm–Liouville Problems With Eigenparameter-Dependent Boundary Conditions

We study a system of ordinary differential equations linked by parameters and subject to boundary conditions depending on parameters. We assume certain definiteness conditions on the coefficient functions and on the boundary conditions that yield, in the corresponding abstract setting, a right-definite case. We give results on location of the eigenvalues and oscillation of the eigenfunctions.

Doubly spectral stochastic finite element method (DSSFEM) for random field problems

Uncertainties in complex dynamic systems play an important role in the prediction of a dynamic response in the mid- and high-frequency ranges. For distributed parameter systems, parametric uncertainties can be represented by random fields leading to stochastic partial differential equations. Over the past two decades, the spectral stochastic finite-element method has been developed to discretize the random fields and solve such problems. On the other hand, for deterministic distributed parameter linear dynamic systems, the spectral finite-element method has been developed to efficiently solve the problem in the frequency domain. In spite of the fact that both approaches use spectral decomposition (one for the random fields and the other for the dynamic displacement fields), very little overlap between them has been reported in literature. In this paper, these two spectral techniques are unified with the aim that the unified approach would outperform any of the spectral methods considered on their own. An exponential autocorrelation function for the random fields, a frequency-dependent stochastic element stiffness, and mass matrices are derived for the axial and bending vibration of rods. Closed-form exact expressions are derived by using the Karhunen-Loève expansion. Numerical examples are given to illustrate the unified spectral approach.

NETGEM: Network Embedded Temporal GEnerative Model for gene expression data

Background: Temporal analysis of gene expression data has been limited to identifying genes whose expression varies with time and/or correlation between genes that have similar temporal profiles. Often, the methods do not consider the underlying network constraints that connect the genes. It is becoming increasingly evident that interactions change substantially with time. Thus far, there is no systematic method to relate the temporal changes in gene expression to the dynamics of interactions between them. Information on interaction dynamics would open up possibilities for discovering new mechanisms of regulation by providing valuable insight into identifying time-sensitive interactions as well as permit studies on the effect of a genetic perturbation. Results: We present NETGEM, a tractable model rooted in Markov dynamics, for analyzing the dynamics of the interactions between proteins based on the dynamics of the expression changes of the genes that encode them. The model treats the interaction strengths as random variables which are modulated by suitable priors. This approach is necessitated by the extremely small sample size of the datasets, relative to the number of interactions. The model is amenable to a linear time algorithm for efficient inference. Using temporal gene expression data, NETGEM was successful in identifying (i) temporal interactions and determining their strength, (ii) functional categories of the actively interacting partners and (iii) dynamics of interactions in perturbed networks. Conclusions: NETGEM represents an optimal trade-off between model complexity and data requirement. It was able to deduce actively interacting genes and functional categories from temporal gene expression data. It permits inference by incorporating the information available in perturbed networks. Given that the inputs to NETGEM are only the network and the temporal variation of the nodes, this algorithm promises to have widespread applications, beyond biological systems. The source code for NETGEM is available from https://github.com/vjethava/NETGEM