Maximum Covering Subtrees for Phylogenetic Networks

Tree-based phylogenetic networks, which may be roughly defined as leaf-labeled networks built by adding arcs only between the original tree edges, have elegant properties for modeling evolutionary histories. We answer an open question of Francis, Semple, and Steel about the complexity of determining how far a phylogenetic network is from being tree-based, including non-binary phylogenetic networks. We show that finding a phylogenetic tree covering the maximum number of nodes in a phylogenetic network can be be computed in polynomial time via an encoding into a minimum-cost maximum flow problem

Fragile-X Carrier Screening and the Prevalence of Premutation and Full-Mutation Carriers in Israel

Fragile-X syndrome is caused by an unstable CGG trinucleotide repeat in the FMR1 gene at Xq27. Intermediate alleles (51–200 repeats) can undergo expansion to the full mutation on transmission from mother to offspring. To evaluate the effectiveness of a fragile-X carrier–screening program, we tested 14,334 Israeli women of child-bearing age for fragile-X carrier status between 1992 and 2000. These women were either preconceptional or pregnant and had no family history of mental retardation. All those found to be carriers of premutation or full-mutation alleles were offered genetic counseling and also prenatal diagnosis, if applicable. We identified 207 carriers of an allele with >50 repeats, representing a prevalence of 1:69. There were 127 carriers with >54 repeats, representing a prevalence of 1:113. Three asymptomatic women carried the fully mutated allele. Among the premutation and full-mutation carriers, 177 prenatal diagnoses were performed. Expansion occurred in 30 fetuses, 5 of which had an expansion to the full mutation. On the basis of these results, the expected number of avoided patients born to women identified as carriers, the cost of the test in this study (U.S. $100), and the cost of lifetime care for a mentally retarded person (>$350,000), screening was calculated to be cost-effective. Because of the high prevalence of fragile-X premutation or full-mutation alleles, even in the general population, and because of the cost-effectiveness of the program, we recommend that screening to identify female carriers should be carried out on a wide scale

Two-Dimensional Packing of Short DNA with Nonpairing Overhangs in Cationic Liposome–DNA Complexes: From Onsager Nematics to Columnar Nematics with Finite-Length Columns

We report the formation of liquid crystalline (LC) phases of short double-stranded DNA with non-pairing (non-sticky) overhangs, confined between two-dimensional (2D) lipid bilayers of cationic liposome–DNA complexes. In a landmark study (Science 2007, 318, 1276), Nakata et al. reported on the discovery of strong end-to-end stacking interactions between short DNAs (sDNAs) with blunt ends leading to the formation of 3D nematic (N) and columnar LC phases. Employing synchrotron small-angle X-ray scattering, we have studied the interplay between shape anisotropy-induced and DNA end-to-end interaction-induced N ordering for 11 bp, 24 bp, and 48 bp sDNA rods with single-stranded oligo-thymine (T) overhangs modulating the end-to-end interactions. For suppressed stacking interactions with 10-T overhangs, the volume fraction of sDNA at which the 2D isotropic (I) to N transition occurs for 24 bp and 48 bp sDNA rods depended on their length to width (L/D) shape anisotropy, qualitatively consistent with Onsager's theory for the entropic alignment of rigid rods. As the overhang length is reduced from 10 T to 5 T and 2 T for 24 bp and 48 bp sDNA, the N to I transition occurs at lower volume fractions, indicating the onset of some degree of end-to-end stacking interactions. The 11 bp sDNA rods with 5-T and 10-T overhangs remain in the I phase, consistent with their small shape anisotropy (L/D ≈ 1.9) below the limit for Onsager LC ordering. Unexpectedly, in contrast to the behavior of 24 bp and 48 bp sDNA, the end-to-end interactions between 11 bp sDNA rods with 2-T overhangs set in dramatically and a novel 2D columnar N phase (N(C)) with finite-length columns formed. The building blocks of this phase are comprised of 1D stacks of (on average) four 11bp DNA-2T rods with an effective L(STACKED)/D ≈ 8.2. Our findings have implications for the DNA-directed assembly of nanoparticles on 2D platforms via end-to-end interactions and in designing optimally packed LC phases of short anisotropic biomolecules (such as peptides and short-interfering RNAs) on nanoparticle membranes, which are used in gene silencing and chemical delivery