不连续二阶周期边值问题的可解性

考察了一类非线性项含有一阶导数的二阶周期边值问题的解的存在性,其中非线性项是Carathèodory函数.通过构造非线性项的高度函数并且利用Leray-Schauder不动点定理建立了两个存在定理.第一个定理表明只要高度函数的积分是适当的,这类问题至少有一个解.第二个定理表明当非线性项在无穷远处增长的极限是一个无界函数时在适当条件下这问题仍可能有一个解.     

Polycomb-mediated methylation on Lys27 of histone H3 pre-marks genes for de novo methylation in cancer

Many genes associated with CpG islands undergo de novo methylation in cancer. Studies have suggested that the pattern of this modification may be partially determined by an instructive mechanism that recognizes specifically marked regions of the genome. Using chromatin immunoprecipitation analysis, here we show that genes methylated in cancer cells are specifically packaged with nucleosomes containing histone H3 trimethylated on Lys27. This chromatin mark is established on these unmethylated CpG island genes early in development and then maintained in differentiated cell types by the presence of an EZH2-containing Polycomb complex. In cancer cells, as opposed to normal cells, the presence of this complex brings about the recruitment of DNA methyl transferases, leading to de novo methylation. These results suggest that tumor-specific targeting of de novo methylation is pre-programmed by an established epigenetic system that normally has a role in marking embryonic genes for repression.     

Finding finer functions for partially characterized proteins by protein-protein interaction networks

Based on high-throughput data, numerous algorithms have been designed to find functions of novel proteins. However, the effectiveness of such algorithms is currently limited by some fundamental factors, including (1) the low a-priori probability of novel proteins participating in a detailed function; (2) the huge false data present in high-throughput datasets; (3) the incomplete data coverage of functional classes; (4) the abundant but heterogeneous negative samples for training the algorithms; and (5) the lack of detailed functional knowledge for training algorithms. Here, for partially characterized proteins, we suggest an approach to finding their finer functions based on protein interaction sub-networks or gene expression patterns, defined in function-specific subspaces. The proposed approach can lessen the above-mentioned problems by properly defining the prediction range and functionally filtering the noisy data, and thus can efficiently find proteins’ novel functions. For thousands of yeast and human proteins partially characterized, it is able to reliably find their finer functions (e.g., the translational functions) with more than 90% precision. The predicted finer functions are highly valuable both for guiding the follow-up wet-lab validation and for providing the necessary data for training algorithms to learn other proteins.     

Alternative exon usage selectively determines both tissue distribution and subcellular localization of the acyl-CoA thioesterase 7 gene products

Acyl-CoA thioesterases (ACOTs) catalyze the hydrolysis of acyl-CoAs to free fatty acids and coenzyme A. Recent studies have demonstrated that one gene named Acot7, reported to be mainly expressed in brain and testis, is transcribed in several different isoforms by alternative usage of first exons. Strongly decreased levels of ACOT7 activity and protein in both mitochondria and cytosol was reported in patients diagnosed with fatty acid oxidation defects, linking ACOT7 function to regulation of fatty acid oxidation in other tissues. In this study, we have identified five possible first exons in mouse Acot7 (Acot7a–e) and show that all five first exons are transcribed in a tissue-specific manner. Taken together, these data show that the Acot7 gene is expressed as multiple isoforms in a tissue-specific manner, and that expression in tissues other than brain and testis is likely to play important roles in fatty acid metabolism. Received 5 February 2007: received after revision 3 April 2007; accepted 19 April 2007