Refined geometric transition and qqqq-characters

We show the refinement of the prescription for the geometric transition in the refined topological string theory and, as its application, discuss a possibility to describe $qq$-characters from the string theory point of view. Though the suggested way to operate the refined geometric transition has passed through several checks, it is additionally found in this paper that the presence of the preferred direction brings a nontrivial effect. We provide the modified formula involving this point. We then apply our prescription of the refined geometric transition to proposing the stringy description of doubly quantized Seiberg--Witten curves called $qq$-characters in certain cases.Comment: 44 pages, 11 figures; v2: references corrected, text corrected, published in JHE

Supersymmetric Rényi entropy in two dimensions

We compute the exact partition function on the branched two-sphere by the localization technique. It is found that it does not depend on a branching parameter q, which means that supersymmetric R\'enyi entropy defined by utilizing it is equivalent to the usual entanglement entropy. We also provide the interpretation of the conical singularities on the branched sphere as defects sit on the poles of the nonsingular two-sphere.Comment: 27 pages; v2: typos and discussions revised, and reference added; v3: typos corrected and published in JHE

Allosteric Regulation of HIV-1 Reverse Transcriptase by ATP for Nucleotide Selection

Background: Human immunodeficiency virus type 1 reverse transcriptase (HIV-1 RT) is a DNA polymerase that converts viral RNA genomes into proviral DNAs. How HIV-1 RT regulates nucleotide selectivity is a central issue for genetics and the nucleoside analog RT inhibitor (NRTI) resistance of HIV-1. Methodology/Principal Findings: Here we show that an ATP molecule at physiological concentrations acts as an allosteric regulator of HIV-1 RT to decrease the Km value of the substrate, decrease the kcat value, and increase the Ki value of NRTIs for RT. Computer-assisted structural analyses and mutagenesis studies suggested the positions of the ATP molecule and NRTIresistance mutations during a catalytic reaction, which immediately predict possible influences on nucleotide insertion into the catalytic site, the DNA polymerization, and the excision reaction. Conclusions/Significance: These data imply that the ATP molecule and NRTI mutations can modulate nucleotide selectivity by altering the fidelity of the geometric selection of nucleotides and the probability of an excision reaction