Systematic Design and Implementation of a Novel Synthetic Fold-Change Detector Biocircuit In Vivo

Biological signaling systems not only detect the absolute levels of the signals, but are also able to sense the fold-changes of the signals. The ability to detect fold-changes provides a powerful tool for biological organisms to adapt to the changes in environment. Here we present the first novel synthetic fold-change detector (FCD) circuit built from ground up in vivo. We systematically designed the FCD circuit in silico, prototyped it in cell-free transcription-translation platform (TX-TL), and eventually implemented it in E. coli cells. We were able to show that the FCD circuit can not only generate pulse-like behavior in response to input, but also produce the same pulse response with inputs of the same fold-change, despite of different absolute signal levels

Representations of a class of lattice type vertex algebras

In this paper we study the representation theory for certain ``half lattice vertex algebras.'' In particular we construct a large class of irreducible modules for these vertex algebras. We also discuss how the representation theory of these vertex algebras are related to the representation theory of some associative algebras.Comment: latex 24 page

Toroidal vertex algebras and their modules

We develop a theory of toroidal vertex algebras and their modules, and we give a conceptual construction of toroidal vertex algebras and their modules. As an application, we associate toroidal vertex algebras and their modules to toroidal Lie algebras.Comment: 36 page