Iterated Monodromy Groups of Rational Mappings

We give the wreath recursion presentations of iterated monodromy groups of post-critically finite quadratic rational mappings fc whose ramification portrait are of the form 0 ↦ av2 ↦ … ↦ avm ↦1 ↦ ∞ ⇌ 1 To find a pattern of these wreath recursions, we compute the wreath recursions of iterated monodromy groups of capture maps composed with the Basilica polynomial. This computation gives rise to the notion of addresses, which is used to represent wreath recursions. Then we conjecture that each capture map composed with the Basilica polynomial is topologically equivalent to a post-critically finite quadratic rational mapping, and thus we conclude that the iterated monodromy groups of fc can be represented by addresses

DYNAMIC HISTONE MODIFICATIONS COORDINATE TRANSCRIPTION, DNA REPAIR AND RECOMBINATION ACROSS DISTINCT METABOLIC STATES

Eukaryotic genomes are packed in the form of chromatin, a complex of DNA and protein. The basic unit is called a nucleosome and consists of 147 bp of DNA wrapped around a histone octamer consisting of two molecules each of core histones H2A, H2B, H3 and H4. Histone proteins are subject to diverse types of post-translational modifications (PTMs), which exert dramatic influence on almost all DNA-associated processes, such as transcription, DNA replication and repair. The pervasiveness of biological dynamics suggests that temporal interrogation of chromatin function is warranted. By using the yeast metabolic cycle (YMC) as the system model, we examined the genome-wide transcription and chromatin states at unprecedented temporal resolution by RNA-seq and ChIP-seq. We revealed a “just in time supply chain” by which specific cellular processes such as ribosome biogenesis are coordinated in time with remarkable precision. We identified distinct chromatin and splicing patterns associated with different gene categories and determine the relative timing of chromatin modifications to maximal transcription. We examined the dynamic occupancy of chromatin modifiers and revealed subtly distinct spatial and temporal patterns compared to the modifications themselves. Genetic analyses support a potentially cooperative role of histone modifications in the YMC. Additionally, We identified ~1000 H3K56ac peaks in the YMC of a haploid prototrophic yeast strain which spatially correlate with meiotic DSB hotspots. Spo11 and other meiotic DSB proteins are actively regulated and contribute to the formation of H3K56ac peaks under stress conditions. Spo11 is required for mitotic DNA recombination at meiotic DSB hotspots and facilitates yeast evolution under stress conditions. Furthermore, we developed a computational pipeline to predict the dynamic activity of transcription factors via integrating transcription factor motif sites with time-course ChIP-seq data of histone modification. We screened 177 transcription factors in the YMC and found that 55 of them are enriched at specific stages. We further validated the binding and function of eight transcription factors in this process. This method is a valuable tool to study the functions of transcription factors during dynamic processes

Iterated Monodromy Groups of Rational Mappings

We give the wreath recursion presentations of iterated monodromy groups of post-critically finite quadratic rational mappings fc whose ramification portrait are of the form 0 ↦ av2 ↦ … ↦ avm ↦1 ↦ ∞ ⇌ 1 To find a pattern of these wreath recursions, we compute the wreath recursions of iterated monodromy groups of capture maps composed with the Basilica polynomial. This computation gives rise to the notion of addresses, which is used to represent wreath recursions. Then we conjecture that each capture map composed with the Basilica polynomial is topologically equivalent to a post-critically finite quadratic rational mapping, and thus we conclude that the iterated monodromy groups of fc can be represented by addresses