Comparative and evolutionary studies of mammalian arylsulfatase and sterylsulfatase genes and proteins encoded on the X-chromosome

At least 19 sulfatase genes have been reported on the human genome, including four arylsulfatase (ARS) genes (ARSD; ARSE; ARSF; ARSH) and a sterylsulfatase (STS) gene located together on the X-chromosome. Bioinformatic analyses of mammalian genomes were undertaken using known human STS and ARS amino acid sequences to study the evolution of these genes and proteins encoded on eutherian and marsupial genomes. Several domain regions and key residues were conserved including signal peptides, active site residues, metal (Ca²⁺) and substrate binding sequences, transmembranes and N-glycosylation sites. Phylogenetic analyses describe the relationships and potential origins of these genes during mammalian evolution. Primate ARSH enzymes lacked signal peptide sequences which may influence their biological functions. CpG117 and CpG92 were detected within the 5′ region of the human STS and ARSD genes, respectively, and miR-205 within the 3′-UTR for the human STS gene, using bioinformatic methods A proposal is described for a primordial invertebrate STS-like gene serving as an ancestor for unequal cross over events generating the gene complex on the eutherian mammalian X-chromosome.     

Evolutionary Boussinesq model with nonmonotone friction and heat flux boundary conditions

In this paper we prove the existence and regularity of a solution to a two-dimensional system of evolutionary hemivariational inequalities which describes the Boussinesq model with nonmonotone friction and heat flux. We use the time retardation and regularization technique, combined with a regularized Galerkin method, and recent results from the theory of hemivariational inequalities.     

High-order evolution equation for nonlinear wave-packet propagation with surface tension accountingÉquation d'évolution d'ordre élevé de groupes d'ondes non linéaires en présence de tension superficielle

The nonlinear problem for propagation of wave-packets along the interface of two semi-infinite fluids is solved on the basis of multiple scale asymptotic expansions. Unlike all previous investigations dealing only with third-order approximations, here fourth-order approximation is developed. The corresponding solvability condition is obtained and the evolution equation in the case away from the cut-off wave number is derived. As a result, the nonlinear higher-order Schrödinger equation is obtained which contains the nonlinear part in a compact form. This equation is valid for a wide range of wave numbers. The stability diagram shows regions of stability and instability of capillary-gravity wave-packets. To cite this article: I. Selezov et al., C. R. Mecanique 331 (2003).     

Evolution of fabric tensors in damage mechanics of solids with micro-cracks: Part I – Theory and fundamental concepts

The evolution of fabric tensors based on micro-crack distributions is formulated based on sound thermodynamic principles. In Part I of this work, the exact definition of fabric tensors based on micro-crack distributions is presented. This definition is seen to incorporate both the orientation and length of a micro-crack. In this regard, the micro-crack distribution is assumed to be radially symmetric, i.e. symmetric about a line through the origin.The equations of thermodynamics are employed in order to derive the exact evolution equations of the fabric tensors defined in the first part. In this regard, a thermodynamic force that is associated with the fabric tensor is defined and utilized in the derivation of the evolution equations. The application of the theory to the case of uniaxial tension is derived in Part II (companion paper) of this work.     

Evolution of fabric tensors in damage mechanics of solids with micro-cracks: Part II – Evolution of length and orientation of micro-cracks with an application to uniaxial tension

In Part II of this work, the equations of thermodynamics are employed in order to derive the exact evolution equations of the fabric tensors defined in Part I (companion paper). In this regard, a thermodynamic force that is associated with the fabric tensor is defined and utilized in the derivation of the evolution equations. A special case of uniaxial tension is solved in order to illustrate the theory.We also derive specific uncoupled equations for the evolution of the length and orientation of micro-cracks. In this regard, some interesting results are obtained. It is concluded that the micro-crack length and orientation cannot evolve simultaneously for the same set of micro-cracks. However, two different sets of micro-cracks may be considered in the same RVE where in one set the micro-crack length evolves, while in the second set the micro-crack orientation evolves.     

Bacterial protein structures reveal phylum dependent divergence

Protein sequence space is vast compared to protein fold space. This raises important questions about how structures adapt to evolutionary changes in protein sequences. A growing trend is to regard protein fold space as a continuum rather than a series of discrete structures. From this perspective, homologous protein structures within the same functional classification should reveal a constant rate of structural drift relative to sequence changes. The clusters of orthologous groups (COG) classification system was used to annotate homologous bacterial protein structures in the Protein Data Bank (PDB). The structures and sequences of proteins within each COG were compared against each other to establish their relatedness. As expected, the analysis demonstrates a sharp structural divergence between the bacterial phyla Firmicutes and Proteobacteria. Additionally, each COG had a distinct sequence/structure relationship, indicating that different evolutionary pressures affect the degree of structural divergence. However, our analysis also shows the relative drift rate between sequence identity and structure divergence remains constant.     

Global decaying solution to dissipative nonlinear evolution equations with ellipticity

We establish the global existence and decaying results for the Cauchy problem of nonlinear evolution equations:

(E)     

A posteriori error estimates for optimal distributed control governed by the evolution equations

We describe a technique for a posteriori error estimates suitable to the optimal control problem governed by the evolution equations solved by the method of lines. It is applied to the control problem governed by the parabolic equation, convection-diffusion equation and hyperbolic equation. The error is measured with the aid of the L²-norm in the space-time cylinder combined with a special time weighted energy norm.