Novel type of coagulation equation and its application to DNA repeat expansion process.

DNA molecules containing repetitive motifs are prone to expand in their lengths. Once there appear a head to tail tandem of two identical DNA sequences in the system, they can propagate indefinitely by the mechanism involving cycles of staggered annealing of complementary DNA strands of variable lengths and polymerase mediated filling-in of the generated overhangs. Microgene Polymerization Reaction (MPR) is an experimental model for expansion of short repetitive DNA to longer lengths. The testable kinetic model of (MPR) was formulated and solved numerically by Itsko et al. in Kinetics of Repeat Propagation in the Microgene Polymerization Reaction (2009). Here, the simple cases of MPR were solved analytically using modified Smoluchowski coagulation equation. It was found that the repeats propagate according to Gumbel probability density function when the distribution of lengths of obtained polymers follows inverted Gumbel probability density function.

The draft genome of Tibetan hulless barley reveals adaptive patterns to the high stressful Tibetan Plateau.

The Tibetan hulless barley (Hordeum vulgare L. var. nudum), also called "Qingke" in Chinese and "Ne" in Tibetan, is the staple food for Tibetans and an important livestock feed in the Tibetan Plateau. The diploid nature and adaptation to diverse environments of the highland give it unique resources for genetic research and crop improvement. Here we produced a 3.89-Gb draft assembly of Tibetan hulless barley with 36,151 predicted protein-coding genes. Comparative analyses revealed the divergence times and synteny between barley and other representative Poaceae genomes. The expansion of the gene family related to stress responses was found in Tibetan hulless barley. Resequencing of 10 barley accessions uncovered high levels of genetic variation in Tibetan wild barley and genetic divergence between Tibetan and non-Tibetan barley genomes. Selective sweep analyses demonstrate adaptive correlations of genes under selection with extensive environmental variables. Our results not only construct a genomic framework for crop improvement but also provide evolutionary insights of highland adaptation of Tibetan hulless barley.