Clathrin binding by the adaptor Ent5 promotes late stages of clathrin coat maturation

Clathrin is a ubiquitous protein that mediates membrane traffic at many locations. To function, clathrin requires clathrin adaptors that link it to transmembrane protein cargo. In addition to this cargo selection function, many adaptors also play mechanistic roles in the formation of the transport carrier. However, the full spectrum of these mechanistic roles is poorly understood. Here we report that Ent5, an endosomal clathrin adaptor in Saccharomyces cerevisiae, regulates the behavior of clathrin coats after the recruitment of clathrin. We show that loss of Ent5 disrupts clathrin-dependent traffic and prolongs the lifespan of endosomal structures that contain clathrin and other adaptors, suggesting a defect in coat maturation at a late stage. We find that the direct binding of Ent5 with clathrin is required for its role in coat behavior and cargo traffic. Surprisingly, the interaction of Ent5 with other adaptors is dispensable for coat behavior but not cargo traffic. These findings support a model in which Ent5 clathrin binding performs a mechanistic role in coat maturation, whereas Ent5 adaptor binding promotes cargo incorporation

Kruskal--Katona-Type Problems via Entropy Method

In this paper, we investigate several extremal combinatorics problems that ask for the maximum number of copies of a fixed subgraph given the number of edges. We call this type of problems Kruskal--Katona-type problems. Most of the problems that will be discussed in this paper are related to the joints problem. There are two main results in this paper. First, we prove that, in a $3$-colored graph with $R$ red, $G$ green, $B$ blue edges, the number of rainbow triangles is at most $\sqrt{2RGB}$, which is sharp. Second, we give a generalization of the Kruskal--Katona theorem that implies many other previous generalizations. Both arguments use the entropy method, and the main innovation lies in a more clever argument that improves bounds given by Shearer's inequality.Comment: 18 page

Regulation of Membrane Traffic by Intrinsic and Extrinsic Mechanisms

Vesicular membrane traffic regulates many biological activities, such as cell growth, motility and the maintenance of the cell shape. One of the most important types of traffic is mediated by clathrin coated vesicles. To form a vesicle, clathrin must be recruited to the membranes where cargoes are located by clathrin adaptors. Although it is well established that clathrin adaptors are essential for the recruitment of clathrin and the initiation of traffic, not much is known about the mechanisms by which cells regulate the recruitment and activities of adaptors. Furthermore, the role of clathrin adaptors in traffic beyond simple clathrin recruitment remains largely unexplored. In this dissertation, I explored the regulation of adaptor activities and recruitment by intrinsic regulatory motifs and extrinsic energy dependent mechanisms. I revealed the motifs on adaptors Gga2 and Ent5 that are important for the temporal regulation of adaptor recruitment. I also demonstrated a multi-step, energy dependent mechanism that regulates the recruitment of adaptors in response to the energy availability. Finally, we revealed that in addition to recruiting clathrin and initiating traffic, clathrin adaptors are also involved in the late stage of traffic. These findings suggest the role of adaptors in traffic is more diverse.Doctor of Philosoph

MICROSOFT-NOKIA MERGER CONTROL IN EAST ASIA

MICROSOFT-NOKIA MERGER CONTROL IN EAST ASI

Tight Bound and Structural Theorem for Joints

A joint of a set of lines $\mathcal{L}$ in $\mathbb{F}^d$ is a point that is contained in $d$ lines with linearly independent directions. The joints problem asks for the maximum number of joints that are formed by $L$ lines. Guth and Katz showed that the number of joints is at most $O(L^{3/2})$ in $\mathbb{R}^3$ using polynomial method. This upper bound is met by the construction given by taking the joints and the lines to be all the $d$-wise intersections and all the $(d-1)$-wise intersections of $M$ hyperplanes in general position. Furthermore, this construction is conjectured to be optimal. In this paper, we verify the conjecture and show that this is the only optimal construction by using a more sophisticated polynomial method argument. This is the first tight bound and structural theorem obtained using this method. We also give a new definition of multiplicity that strengthens the main result of a previous work by Tidor, Zhao and the second author. Lastly, we include some discussion on the constants for the joints of varieties problem.Comment: 39 page