Shuichi Kawashima

The KEGG resource for deciphering the genome

A grand challenge in the post-genomic era is a complete computer representation of the cell and the organism, which will enable computational prediction of higher-level complexity of cellular processes and organism behavior from genomic information. Toward this end we have been developing a knowledge-based approach for network prediction, which is to predict, given a complete set of genes in the genome, the protein interaction networks that are responsible for various cellular processes. KEGG at http://www.genome.ad.jp/kegg/ is the reference knowledge base that integrates current knowledge on molecular interaction networks such as pathways and complexes (PATHWAY database), information about genes and proteins generated by genome projects (GENES/SSDB/KO databases) and information about biochemical compounds and reactions (COMPOUND/GLYCAN/REACTION databases). These three types of database actually represent three graph objects, called the protein network, the gene universe and the chemical universe. New efforts are being made to abstract knowledge, both computationally and manually, about ortholog clusters in the KO (KEGG Orthology) database, and to collect and analyze carbohydrate structures in the GLYCAN database.

The KEGG databases at GenomeNet

The Kyoto Encyclopedia of Genes and Genomes (KEGG) is the primary database resource of the Japanese GenomeNet service (http://www.genome.ad.jp/) for understanding higher order functional meanings and utilities of the cell or the organism from its genome information. KEGG consists of the PATHWAY database for the computerized knowledge on molecular interaction networks such as pathways and complexes, the GENES database for the information about genes and proteins generated by genome sequencing projects, and the LIGAND database for the information about chemical compounds and chemical reactions that are relevant to cellular processes. In addition to these three main databases, limited amounts of experimental data for microarray gene expression profiles and yeast two-hybrid systems are stored in the EXPRESSION and BRITE databases, respectively. Furthermore, a new database, named SSDB, is available for exploring the universe of all protein coding genes in the complete genomes and for identifying functional links and ortholog groups. The data objects in the KEGG databases are all represented as graphs and various computational methods are developed to detect graph features that can be related to biological functions. For example, the correlated clusters are graph similarities which can be used to predict a set of genes coding for a pathway or a complex, as summarized in the ortholog group tables, and the cliques in the SSDB graph are used to annotate genes. The KEGG databases are updated daily and made freely available (http://www.genome.ad.jp/kegg/).

AAindex: Amino Acid Index Database

AAindex is a database of numerical indices representing various physicochemical and biochemical properties of amino acids and pairs of amino acids. It consists of two sections: AAindex1 for the amino acid index of 20 numerical values and AAindex2 for the amino acid mutation matrix of 210 numerical values. Each entry of either AAindex1 or AAindex2 consists of the definition, the reference information, a list of related entries in terms of the correlation coefficient, and the actual data. The database may be accessed through the DBGET/LinkDB system at GenomeNet (http://www.genome.ad. jp/dbget/) or may be downloaded by anonymous FTP (ftp://ftp.genome. ad.jp/db/genomenet/aaindex/).

Asymptotic stability of traveling wave solutions of systems for one-dimensional gas motion

The asymptotic stability of traveling wave solutions with shock profile is investigated for several systems in gas dynamics. 1) The solution of a scalar conservation law with viscosity approaches the traveling wave solution at the ratet−γ (for someγ>0) ast→∞, provided that the initial disturbance is small and of integral zero, and in addition decays at an algebraic rate for |x|→∞. 2) The traveling wave solution with Nishida and Smollers condition of the system of a viscous heat-conductive ideal gas is asymptotically stable, provided the initial disturbance is small and of integral zero. 3) The traveling wave solution with weak shock profile of the Broadwell model system of the Boltzmann equation is asymptotically stable, provided the initial disturbance is small and its hydrodynamical moments are of integral zero. Each proof is given by applying an elementary energy method to the integrated system of the conservation form of the original one. The property of integral zero of the initial disturbance plays a crucial role in this procedure.

Large-time behaviour of solutions to hyperbolic–parabolic systems of conservation laws and applications

We study the large-time behaviour of solutions to the initial value problem for hyperbolic-parabolic systems of conservation equations in one space dimension. It is proved that under suitable assumptions a unique solution exists for all time t ≧ 0, and converges to a given constant state at the rate t − ¼ as t → ∞. Moreover, it is proved that the solution approaches the superposition of the non-linear and linear diffusion waves constructed in terms of the self-similar solutions to the Burgers equation and the linear heat equation at the rate t − ½ +α, α > 0, as t →∞. The proof is essentially based on the fact that for t → ∞ the solution to the hyperbolic-parabolic system is well approximated by the solution to a semilinear uniformly parabolic system whose viscosity matrix is uniquely determined from the original system. The results obtained are applicable straightforwardly to the equations of viscous (or inviscid) heat-conductive fluids.

EGassembler: online bioinformatics service for large-scale processing, clustering and assembling ESTs and genomic DNA fragments.

Expressed sequence tag (EST) sequencing has proven to be an economically feasible alternative for gene discovery in species lacking a draft genome sequence. Ongoing large-scale EST sequencing projects feel the need for bioinformatics tools to facilitate uniform EST handling. This brings about a renewed importance for a universal tool for processing and functional annotation of large sets of ESTs. EGassembler () is a web server, which provides an automated as well as a user-customized analysis tool for cleaning, repeat masking, vector trimming, organelle masking, clustering and assembling of ESTs and genomic fragments. The web server is publicly available and provides the community a unique all-in-one online application web service for large-scale ESTs and genomic DNA clustering and assembling. Running on a Sun Fire 15K supercomputer, a significantly large volume of data can be processed in a short period of time. The results can be used to functionally annotate genes, to facilitate splice alignment analysis, to link the transcripts to genetic and physical maps, design microarray chips, to perform transcriptome analysis and to map to KEGG metabolic pathways. The service provides an excellent bioinformatics tool to research groups in wet-lab as well as an all-in-one-tool for sequence handling to bioinformatics researchers.

Sur la solution à support compact de l’equation d’Euler compressible

The Cauchy problem for the compressible Euler equation is discussed with compactly supported initials. To establish the localexistence of classical solutions by the aid of the theory of quasilinear symmetric hyperbolic systems, a new symmetrization is introduced which works for initials having compact support or vanishing at infinity. It is further shown that as far as the classical solution is concerned, its support does not change, and that the life span is finite for any solution except for the trivial zero solution.

On the decay of solutions to the linearized equations of electro-magneto-fluid dynamics

The linearized equations of the electrically conducting compressible viscous fluids are studied. It is shown that the decay estimate (1+t)−3/4 inL2(R3) holds for solutions of the above equations, provided that the initial data are inL2(R3)∩L1(R3). Since the systems of equations are not rotationally invariant, the perturbation theory for one parameter family of matrices is not useful enough to derive the above result. Therefore, by exploiting an energy method, we show that the decay estimate holds for the solutions of a general class of equations of symmetric hyperbolic-parabolic type, which contains the linearized equations in both electro-magneto-fluid dynamics and magnetohydrodynamics.

On the fluid-dynamical approximation to the Boltzmann equation at the level of the Navier-Stokes equation

The compressible and heat-conductive Navier-Stokes equation obtained as the second approximation of the formal Chapman-Enskog expansion is investigated on its relations to the original nonlinear Boltzmann equation and also to the incompressible Navier-Stokes equation. The solutions of the Boltzmann equation and the incompressible Navier-Stokes equation for small initial data are proved to be asymptotically equivalent (mod decay ratet−5/4) ast→+∞ to that of the compressible Navier-Stokes equation for the corresponding initial data.

Global existence and exponential stability of small solutions to nonlinear viscoelasticity

The global existence of smooth solutions to the equations of nonlinear hyperbolic system of 2nd order with third order viscosity is shown for small and smooth initial data in a bounded domain ofn-dimensional Euclidean space with smooth boundary. Dirichlet boundary condition is studied and the asymptotic behaviour of exponential decay type of solutions ast tending to ∞ is described. Time periodic solutions are also studied. As an application of our main theorem, nonlinear viscoelasticity, strongly damped nonlinear wave equation and acoustic wave equation in viscous conducting fluid are treated.