It is shown that the two-component Camassa-Holm and Hunter-Saxton systems are geometrically integrable, namely they describe pseudo-spherical surfaces. As a consequence, their infinite number of conservation laws are ...It is shown that the two-component Camassa-Holm and Hunter-Saxton systems are geometrically integrable, namely they describe pseudo-spherical surfaces. As a consequence, their infinite number of conservation laws are directly constructed. In addition, a class of nonlocal symmetries depending on the pseudo-potentials are obtained.展开更多
Revolutionary in scope and application, the CRISPR Cas9 endonuclease system can be guided by 20-nt single guide RNA （sgRNA） to any complementary loci on the double- stranded DNA. Once the target site is located, Cas...Revolutionary in scope and application, the CRISPR Cas9 endonuclease system can be guided by 20-nt single guide RNA （sgRNA） to any complementary loci on the double- stranded DNA. Once the target site is located, Cas9 can then cleave the DNA and introduce mutations. Despite the power of this system, sgRNA is highly susceptible to off-target homologous attachment and can consequently cause Cas9 to cleave DNA at off- target sites. In order to better understand this flaw in the system, the human genome and Streptococcus pyogenes Cas9 （SpCas9） were used in a mathematical and computational study to analyze the probabilities of potential sgRNA off-target homologies. It has been concluded that off-target sites are nearly unavoidable for large-size genomes, such as the human genome. Backed by mathematical analysis, a viable solution is the double-nicking method which has the promise for genome editing specificity. Also applied in this study was a computational algorithm for off-target homology search that was implemented in Java to confirm the mathematical analysis.展开更多
基金Supported by the China NSF for Distinguished Young Scholars under Grant No.10925104
文摘It is shown that the two-component Camassa-Holm and Hunter-Saxton systems are geometrically integrable, namely they describe pseudo-spherical surfaces. As a consequence, their infinite number of conservation laws are directly constructed. In addition, a class of nonlocal symmetries depending on the pseudo-potentials are obtained.
文摘Revolutionary in scope and application, the CRISPR Cas9 endonuclease system can be guided by 20-nt single guide RNA （sgRNA） to any complementary loci on the double- stranded DNA. Once the target site is located, Cas9 can then cleave the DNA and introduce mutations. Despite the power of this system, sgRNA is highly susceptible to off-target homologous attachment and can consequently cause Cas9 to cleave DNA at off- target sites. In order to better understand this flaw in the system, the human genome and Streptococcus pyogenes Cas9 （SpCas9） were used in a mathematical and computational study to analyze the probabilities of potential sgRNA off-target homologies. It has been concluded that off-target sites are nearly unavoidable for large-size genomes, such as the human genome. Backed by mathematical analysis, a viable solution is the double-nicking method which has the promise for genome editing specificity. Also applied in this study was a computational algorithm for off-target homology search that was implemented in Java to confirm the mathematical analysis.
