The nonlinear Schroedinger equation for the delta-comb potential: quasi-classical chaos and bifurcations of periodic stationary solutions

The nonlinear Schroedinger equation is studied for a periodic sequence of delta-potentials (a delta-comb) or narrow Gaussian potentials. For the delta-comb the time-independent nonlinear Schroedinger equation can be solved analytically in terms of Jacobi elliptic functions and thus provides useful insight into the features of nonlinear stationary states of periodic potentials. Phenomena well-known from classical chaos are found, such as a bifurcation of periodic stationary states and a transition to spatial chaos. The relation of new features of nonlinear Bloch bands, such as looped and period doubled bands, are analyzed in detail. An analytic expression for the critical nonlinearity for the emergence of looped bands is derived. The results for the delta-comb are generalized to a more realistic potential consisting of a periodic sequence of narrow Gaussian peaks and the dynamical stability of periodic solutions in a Gaussian comb is discussed.Comment: Enhanced and revised version, to appear in J. Nonlin. Math. Phy

Haplotypes of DNA repair and cell cycle control genes, X-ray exposure, and risk of childhood acute lymphoblastic leukemia

[[abstract]]Background: Acute leukemias of childhood are a heterogeneous group of malignancies characterized by cytogenetic abnormalities, such as translocations and changes in ploidy. These abnormalities may be influenced by altered DNA repair and cell cycle control processes. Methods: We examined the association between childhood acute lymphoblastic leukemia (ALL) and 32 genes in DNA repair and cell cycle pathways using a haplotype-based approach, among 377 childhood ALL cases and 448 controls enrolled during 1995-2002. Results: We found that haplotypes in APEX1, BRCA2, ERCC2, and RAD51 were significantly associated with total ALL, while haplotypes in NBN and XRCC4, and CDKN2A were associated with structural and numerical change subtypes, respectively. In addition, we observed statistically significant interaction between exposure to 3 or more diagnostic X-rays and haplotypes of XRCC4 on risk of structural abnormality-positive childhood ALL. Conclusions: These results support a role of altered DNA repair and cell cycle processes in the risk of childhood ALL, and show that this genetic susceptibility can differ by cytogenetic subtype and may be modified by exposure to ionizing radiation. To our knowledge, our study is the first to broadly examine the DNA repair and cell cycle pathways using a haplotype approach in conjunction with X-ray exposures in childhood ALL risk. If confirmed, future studies are needed to identify specific functional SNPs in the regions of interest identified in this analysis

Congenital dyserythropoietic anemia type III (CDA III) is caused by a mutation in kinesin family member, KIF23

Haplotype analysis and targeted next-generation resequencing allowed us to identify a mutation in the KIF23 gene and to show its association with an autosomal dominant form of congenital dyserythropoietic anemia type III (CDA III). The region at 15q23 where CDA III was mapped in a large Swedish family was targeted by array-based sequence capture in a female diagnosed with CDA III and her healthy sister. Prioritization of all detected sequence changes revealed 10 variants unique for the CDA III patient. Among those variants, a novel mutation c.2747C>G (p.P916R) was found in KIF23, which encodes mitotic kinesin-like protein 1 (MKLP1). This variant segregates with CDA III in the Swedish and American families but was not found in 356 control individuals. RNA expression of the 2 known splice isoforms of KIF23 as well as a novel one lacking the exons 17 and 18 was detected in a broad range of human tissues. RNA interference-based knock-down and rescue experiments demonstrated that the p.P916R mutation causes cytokinesis failure in HeLa cells, consistent with appearance of large multinucleated erythroblasts in CDA III patients. We conclude that CDA III is caused by a mutation in KIF23/MKLP1, a conserved mitotic kinesin crucial for cytokinesis