Recent trends and future directions in vertex-transitive graphs

A graph is said to be vertex-transitive if its automorphism group acts transitively on the vertex set. Some recent developments and possible future directions regarding two famous open problems, asking about existence of Hamilton paths and existence of semiregular automorphisms in vertex-transitive graphs, are discussed, together with some recent results on arc-transitive graphs and half-arc-transitive graphs, two special classes of vertex-transitive graphs that have received particular attention over the last decade

Inferring phylogenetic networks with maximum pseudolikelihood under incomplete lineage sorting

Phylogenetic networks are necessary to represent the tree of life expanded by edges to represent events such as horizontal gene transfers, hybridizations or gene flow. Not all species follow the paradigm of vertical inheritance of their genetic material. While a great deal of research has flourished into the inference of phylogenetic trees, statistical methods to infer phylogenetic networks are still limited and under development. The main disadvantage of existing methods is a lack of scalability. Here, we present a statistical method to infer phylogenetic networks from multi-locus genetic data in a pseudolikelihood framework. Our model accounts for incomplete lineage sorting through the coalescent model, and for horizontal inheritance of genes through reticulation nodes in the network. Computation of the pseudolikelihood is fast and simple, and it avoids the burdensome calculation of the full likelihood which can be intractable with many species. Moreover, estimation at the quartet-level has the added computational benefit that it is easily parallelizable. Simulation studies comparing our method to a full likelihood approach show that our pseudolikelihood approach is much faster without compromising accuracy. We applied our method to reconstruct the evolutionary relationships among swordtails and platyfishes ($Xiphophorus$: Poeciliidae), which is characterized by widespread hybridizations

The Impact of Cross-Species Gene Flow on Species Tree Estimation

Recent analyses of genomic sequence data suggest cross-species gene flow is common in both plants and animals, posing challenges to species tree estimation. We examine the levels of gene flow needed to mislead species tree estimation with three species and either episodic introgressive hybridization or continuous migration between an outgroup and one ingroup species. Several species tree estimation methods are examined, including the majority-vote method based on the most common gene tree topology (with either the true or reconstructed gene trees used), the UPGMA method based on the average sequence distances (or average coalescent times) between species, and the full-likelihood method based on multilocus sequence data. Our results suggest that the majority-vote method based on gene tree topologies is more robust to gene flow than the UPGMA method based on coalescent times and both are more robust than likelihood assuming a multispecies coalescent (MSC) model with no cross-species gene flow. Comparison of the continuous migration model with the episodic introgression model suggests that a small amount of gene flow per generation can cause drastic changes to the genetic history of the species and mislead species tree methods, especially if the species diverged through radiative speciation events. Estimates of parameters under the MSC with gene flow suggest that African mosquito species in the Anopheles gambiae species complex constitute such an example of extreme impact of gene flow on species phylogeny. [IM; introgression; migration; MSci; multispecies coalescent; species tree.

Structural and biophysical investigation of +TIPs in yeast and -TIPs in higher eukaryotes

In eukaryotic cells, microtubules represent a highly dynamic protein filament system that is involved in cellular processes as cell division or transport of cargo. Microtubules oscillate between growth and shrinking, and the switch between these states is caused by catastrophe and rescue events. The building block of microtubules is the heterodimer tubulin, which polymerizes into tubular structures and switches from a curved state in the soluble form to a straight state in microtubules. Due to the polarity of tubulin, microtubules feature a plus-end and a minus-end. The highly dynamic plus-end is regulated by the plus-end tracking proteins (+TIPs). Certain +TIPs can function as a microtubule polymerase or rescue shrinking microtubules. Since budding yeast contains only a small number of microtubules, this organism is predestinated to study +TIPs and microtubule dynamics by microscopy on the system level. The exact function and mechanism of yeast +TIPs such as Bik1 remain unresolved. In addition, it is unexplained how kinesins such as Kip2 or Kip3 can act as a microtubule polymerase or rescue factor. In my thesis, the budding yeast +TIPs Bik1, Kip2 and Kip3 were investigated to understand the role of these proteins in the formation of the +TIP network and how these proteins are capable of influencing microtubule dynamics. Recently, it has been discovered that minus-end tracking proteins (-TIPs) recognize the minus-end in cells such as neuronal cells. However, it is enigmatic how -TIPs target the microtubule minus-end. In order to elucidate the mechanism how -TIPs track the minus-end, my work focused on the discovered first -TIP class of CAMSAPs. In all projects, biophysical methods were applied, and besides for Kip2 crystal structures were determined to unravel mechanistic details of the proteins. In budding yeast, Bik1 plays an important role especially in the dynein pathway, which is one of two major pathways for spindle positioning. Bim1 localizes Bik1 to the microtubule plus-end because Bik1 cannot autonomously track the plus-end. Here, we biophysically and structurally describe the interaction of the Bik1 CAP-Gly domain with the C-terminal tail of the +TIP Bim1. The crystal structure of the complex showed that Bik1 CAP-Gly binds specifically to C-terminal phenylalanine residues with a different binding mode compared to CAP-Gly domains of higher eukaryotes. Based on the structure, two different mutants were conceived to perturb the Bik1-Bim1 interaction. Then, the effect of this perturbation on Bik1 localization, microtubule length and Kar9 function was analyzed in yeast cells. Besides, we proved that the coiled-coil of Bik1 interacts with the C-terminal tail of microtubule polymerase Stu2, establishing Bik1 as an adaptor protein between Bim1 and Stu2. Apart from Bim1, the budding yeast kinesin Kip2 also has the ability to transport Bik1 to the plusend. We biophysically characterized the interaction of the Bik1 coiled-coil with the Kip2 coiledcoil. The C-terminal unstructured part of Kip2 turned out to be essential for the Bik1-Kip2 interaction, allowing an elegant way to disrupt this interaction without removing the Kip2 coiledcoil. In addition, Kip2 functions as a microtubule polymerase. By studying the interaction of the Kip2 motor domain with soluble tubulin, we were able to postulate a mechanism how Kip2 can polymerize microtubules. Furthermore, we identified the importance of the Bik1-Kip2 interaction for the polymerase activity. The budding yeast kinesin Kip3 can depolymerize microtubules but exhibits the ability to rescue them as well. The N-terminal motor domain of Kip3 is responsible for the depolymerization activity. We discovered that Kip3 possesses a C-terminal tubulin-binding domain (TBD), followed by a weak microtubule-binding domain. The crystal structure of the Kip3 TBD was solved, and a sophisticated assembly of alpha-helices was revealed. Furthermore, the combination of the Kip3 motor domain together with the Kip3 TBD was identified as the minimal construct that can rescue microtubules. Therefore, we proposed that the Kip3 motor domain can also act as an anchor at the microtubule plus-end so that the Kip3 TBD can fulfill its rescue function by either increasing the tubulin concentration or facilitating the exchange of tubulin. Most microtubules minus-ends are attached to the centrosome. However, some microtubules can occur with free minus-ends because not all microtubules are attached to the centrosome or cells such as neuronal cells entirely lack the centrosome. Thus, -TIPs like CAMSAPs can stabilize these free minus-ends. CAMSAP proteins have a CKK domain that can autonomously track the microtubule minus-end. In this study, we determined the crystal structure of this CKK domain. Our collaborator used this structure for fitting into a cryo-EM map of microtubules decorated by the CKK domain. Combined with other experimental results, we found that the CKK domain recognizes a unique curved state of tubulin that only occurs at the microtubule minus-end. Overall, important insights into the mechanisms of Bik1 Kip2, Kip3 and CAMSAP were obtained. In the +TIP network, the understanding of Bik1 as a critical adaptor protein was considerably increased. Furthermore, we revealed new insights into the function of Kip2 as a microtubule polymerase. For Kip3, a mechanism for its microtubule rescue function was postulated. In the case of CAMSAP, it was discovered how this protein can recognize the microtubule minus-end. This represents the first described mechanism of a -TIP

The Jewel of Annual Astrology

The Jewel of Annual Astrology is an encyclopaedic treatise on Tājika or Sanskritized Perso-Arabic astrology, dealing particularly with the casting an interpretation of anniversary horoscopes. Authored in 1649 CE by Balabhadra Daivajña, court astrologer to Shāh Shujāʿ – Governor of Bengal and second son of the Mughal emperor Shāh Jahān – it casts light on the historical development of the Tājika school by extensive quotations from earlier works spanning five centuries. Readership: Anyone interested in the history of Indian astrology, the transmission of horoscopic astrology generally, the Indian reception of Perso-Arabic astral sciences, or intellectual history in early modern South Asia

Graphlet Correlations for Network Comparison and Modelling: World Trade Network Example

We propose methods on two fundamental graph theoretic problems: (1) network comparison, and (2) network modelling. Our methods are applied to five real-world network types, with an emphasis on world trade networks (WTNs), which we choose due to the world's current economic crisis. Finding topological similarities of complex networks is computationally intractable due to NP-Completeness of the subgraph isomorphism problem. Hence, simple heuristics have been used for this purpose. The most sophisticated heuristics are based on graph spectra and small subnetworks including graphlets. Among these, graphlets are preferred since spectra do not provide a direct real-world interpretation of network structure. However, current graphlet-based techniques can be improved. We improve graphlet-based heuristics by defining a new network topology descriptor, Graphlet Correlation Matrix (GCM), which eliminates all redundancies and quantifies the dependencies in graphlet properties. Then, we introduce a new network distance measure, Graphlet Correlation Distance (GCD), that compares GCMs of two networks. We show that GCD has the best network classification performance, is highly noise-tolerant, and is computationally efficient. Using this methodology, we highlight a three-layer organization in the WTNs: core, broker, and periphery. Furthermore, we uncover the link between the dynamic changes in oil price and trade network topology. Network models should shed light on the rules governing the formation of real networks. Using GCD, we identify models that fit five real-world network types. However, none of these standard network models fit WTNs. Hence, we introduce two new network models: one that mimics the Gravity Model of Trade, and the other that mimics brokerage / peripheral positioning of a country in WTN. Also, we show that economic wealth indicators of a country are predictive of its future brokerage position. Finally, we use exponential-family random graph modelling approach to build a generic framework that enables modelling based on any graphlet property.Open Acces

多様なポストゲノムデータのためのアラインメントフリーなアルゴリズムの構造

学位の種別: 課程博士審査委員会委員 : （主査）東京大学教授 今井 浩, 東京大学教授 小林 直樹, 東京大学教授 五十嵐 健夫, 東京大学教授 杉山 将, 東京大学講師 笠原 雅弘University of Tokyo(東京大学

Studying Multicellular Dynamics with Single-cell Micropattern Clusters

Ph.DDOCTOR OF PHILOSOPH