Geometric aspects of the moduli space of Riemann surfaces

We describe some recent progress in the study of moduli space of Riemann surfaces in this survey paper. New complete Kahler metrics were introduced on the moduli space and Teichmuller space. Their curvature properties and asymptotic behavior were studied in details. These natural metrics served as bridges to connect all the known canonical metrics, especially the Kahler-Einstein metric. We showed that all the known complete metrics on the moduli space are equivalent and have Poincare type growth. Furthermore, the Kahler-Einstein metric has strongly bounded geometry. This also implied that the logarithm cotangent bundle of the moduli space is stable in the sense of Mumford.     

Hydrogen‐Bonding Induced Cooperative Effect on the Energy Transfer in Helical Polynorbornenes Appended with Porphyrin‐Containing Amidic Alanine Linkers

Polynorbornenes appended with porphyrins containing a range of different linkers are synthesized. The use of bisamidic chiral alanine linkers between the pending porphyrins and the polymeric backbone has been shown to bring the adjacent porphyrin chromophores to more suitable orientation for exciton coupling owing to hydrogen bonding between the adjacent linkers. The hydrogen bonding between the adjacent pendants in these polymers may induce a cooperative effect and therefore render single‐handed helical structures for these polymers. Such a cooperative effect is reflected in the enhancement of FRET efficiencies between zinc–porphyrin and free base porphyrin in random copolymers.     

Selection of aptamers for signal transduction proteins by capillary electrophoresis

High‐affinity aptamers for important signal transduction proteins, i.e. Cdc42‐GTP, p21‐activated kinase1 (PAK1) and MRCK (myotonic dystrophy kinase‐related Cdc42‐binding kinase) α were successfully selected in the low micro‐ to nanomolar range using non‐systematic evolution of ligands by exponential enrichment (SELEX) with at least three orders of magnitude enhancement from their respective bulk affinity of naïve DNA library. In the non‐SELEX procedure, CE was used as a highly efficient affinity method to select aptamers for the desired molecular target through a process that involved repetitive steps of partitioning, known as non‐equilibrium CE of equilibrium mixtures with no PCR amplification between successive steps. Various non‐SELEX conditions including the type, concentration and pH of the run buffer were optimized. Other considerations such as salt composition of selection buffer, protein concentration and sample injection size were also studied for high stringency during selection. After identifying the best enriched aptamer pool, randomly selected clones from the aptamer pool were sequenced to obtain the individual DNA sequences. The dissociation constants (K_d) of these sequences were in the low micromolar to nanomolar range, indicating high affinity to the respective proteins. The best binders were also subjected to sequence alignment to generate a phylogenetic tree. No significant consensus region based on approximately 50 sequences for each protein was observed, suggesting the high efficiency of non‐SELEX for the selection of numerous unique sequences with high selectivity.     

Evaluating Quasilocal Energy and Solving Optimal Embedding Equation at Null Infinity

We study the limit of quasilocal energy defined in Wang and Yau (Phys Rev Lett 102(2):021101, 2009; Commun Math Phys 288(3):919–942, 2009) for a family of spacelike 2-surfaces approaching null infinity of an asymptotically flat spacetime. It is shown that Lorentzian symmetry is recovered and an energy-momentum 4-vector is obtained. In particular, the result is consistent with the Bondi–Sachs energy-momentum at a retarded time. The quasilocal mass in Wang and Yau (Phys Rev Lett 102(2):021101, 2009; Commun Math Phys 288(3):919–942, 2009) is defined by minimizing quasilocal energy among admissible isometric embeddings and observers. The solvability of the Euler-Lagrange equation for this variational problem is also discussed in both the asymptotically flat and asymptotically null cases. Assuming analyticity, the equation can be solved and the solution is locally minimizing in all orders. In particular, this produces an optimal reference hypersurface in the Minkowski space for the spatial or null exterior region of an asymptotically flat spacetime.     

Harnack inequalities for graphs with non-negative Ricci curvature

We establish a Harnack inequality for finite connected graphs with non-negative Ricci curvature. As a consequence, we derive an eigenvalue lower bound, extending previous results for Ricci flat graphs.     

Rhodamine‐Ethylenediol,A Novel Vital Fluorescent Probe for Labelling Alkaline Phosphatase‐Rich Organelles

Zebrafish have received considerable attention as an organism‐based model in the development of pharmacological agents.^1,2 Many small molecules applied to zebrafish show important behaviours and may constitute new kinds of markers for clinical purposes.³ Analysis of these molecules can facilitate the development of useful tools for monitoring environmental changes.⁴ Many chemicals that are toxic to the environment are known to influence the sensory systems of humans⁵ and fish.⁶ One important sensory system in all fish is the lateral line organ,⁷ which is readily accessible for the assessment of environmental changes.⁸ Neuromasts, which are located on the surface of the fish body, are one of the major components of the lateral lines of the zebrafish.⁹ Copper‐enriched water is known to affect the olfactory system in fish. Therefore, small molecules that induce specific patterns in the neuromasts of zebrafish should provide an important animal model with which to explore the effects of environmental changes on the sensory system.^10,11 Recently, chemical sensors based on the rhodamine skeleton¹² have been designed to specifically detect metal ions, such as Cu(II)¹³ and Fe(III)/Hg(II),¹⁴ in zebrafish. However, there has been no report of these rhodamine derivatives used in the specific recognition of the sensory system of zebrafish. Commonly, the sensory system is studied with antibody staining assays of scarified fish. Here, we report that a new rhodamine derivative can be used as a fluorescent chemical probe to visualize the neuromasts and intestinal villi of living zebrafish. Based on the specific recognition of this area in zebrafish, we narrowed the possible enzymes targeted by this rhodamine probe to alkaline phosphatase and confirmed this with a binding assay. It is a well‐recognized challenge to develop a fluorescent chemical probe that specifically recognizes a particular enzyme. Furthermore, the transfer of phosphate groups to certain enzymes can activate their catalytic reactivity, triggering a cascade reaction in a signal transduction pathway. The alkaline‐phosphatase‐specific recognition by this rhodamine derivative may be applicable to clinical purposes.