On the asymptotic behaviour of semigroups for flows in infinite networks

We study transport processes on infinite networks. The solution of these processes can be modeled by an operator semigroup on a suitable Banach space. Classically, such semigroups are strongly continuous and therefore their asymptotic behaviour is quite well understood. However, recently new examples of transport processes emerged where the corresponding semigroup is not strongly continuous. Due to this lack of strong continuity, there are currently only few results on the long-term behaviour of these semigroups. In this paper, we discuss the asymptotic behaviour for a certain class of these transport processes. In particular, it is proved that the solution semigroups behave asymptotically periodic with respect to the operator norm as a consequence of a more general result on the long-term behaviour by positive semigroups containing a multiplication operator. Furthermore, we revisit known results on the asymptotic behaviour of transport processes on infinite networks and prove the asymptotic periodicity of their extensions to the space of bounded measures.Comment: Correction of typos, rewritten introduction, some further simplifications of arguments, strengthened main result -- final versio

RPA and Rad51 constitute a cell intrinsic mechanism to protect the cytosol from self DNA.

Immune recognition of cytosolic DNA represents a central antiviral defence mechanism. Within the host, short single-stranded DNA (ssDNA) continuously arises during the repair of DNA damage induced by endogenous and environmental genotoxic stress. Here we show that short ssDNA traverses the nuclear membrane, but is drawn into the nucleus by binding to the DNA replication and repair factors RPA and Rad51. Knockdown of RPA and Rad51 enhances cytosolic leakage of ssDNA resulting in cGAS-dependent type I IFN activation. Mutations in the exonuclease TREX1 cause type I IFN-dependent autoinflammation and autoimmunity. We demonstrate that TREX1 is anchored within the outer nuclear membrane to ensure immediate degradation of ssDNA leaking into the cytosol. In TREX1-deficient fibroblasts, accumulating ssDNA causes exhaustion of RPA and Rad51 resulting in replication stress and activation of p53 and type I IFN. Thus, the ssDNA-binding capacity of RPA and Rad51 constitutes a cell intrinsic mechanism to protect the cytosol from self DNA